Design Practices: Passenger Car Automatic Transmissions [4 ed.] 0768011256, 9780768011258

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Fourth Edition About the authors

For nearly half a century, Design Practices: Passenger Car Automatic Transmissions has been the “go-to” handbook of design considerations for automatic transmission industry engineers of all levels of experience. This latest 4th edition represents a major overhaul from the prior edition and is arguably the most significant update in its long history. In summary, this team has put together the most definitive handbook for automatic transmission design practices available today.

• Ernest J. DeVincent (Chairman), Getrag Transmissions Corp. and Ford Motor Co. (retired) • Michael T. Berhan, Ford Motor Co. • Susan M. Bothe, Freudenberg-NOK General Partnership • Thomas Brand, BorgWarner Corp. • Gang (George) Chen, Chrysler Group LLC • Louis Crocco, Greening Associates • Mark R. Dobson, Ford Motor Co. • Hussein A. Dourra, Chrysler Group LLC • Charles (Chip) Hartinger, Ford Motor Co. • James D. Hendrickson, General Motors Co. • Harry A. Hildebrandt, Oakland Community College • Andrew F. Joseph, Freudenberg-NOK General Partnership • Ibrahim A. Khalil, SPX Filtran • John M. Kremer, BorgWarner Corp. (retired) • Larry Larkin, Filtertek Corp. (retired) • Maurice B. Leising, Chrysler Corp. (retired) • Glenn Mann, Nichols Portland Corp. • Gregory Mordukhovich, General Motors Co. • Michael D. Myers, Otis Elevator Corp. and Timken Corp. (retired) • Thomas M. O’Brien, Chrysler Group LLC • Lev Pekarsky, Ford Motor Co. • John Titlow, Conxall Corp. and Honeywell Corp. (retired)

Virtually all existing chapters have been updated and improved with the latest state-of-the-art information and many have been significantly expanded with more detail and design consideration updates; most notably for torque converters and start devices, gears/splines/chains, bearings, wet friction, one-way clutch, pumps, seals and gaskets, and controls. In fact, all new chapters have been added, including state-of-the-art information on: lubrication; transmission fluids; filtration, and contamination control. Finally, details about the latest transmission technologies—including dual clutch and continuously variable transmissions—have been added. This edition is made possible in part through sponsorship by The Lubrizol Corporation.

This complete overhaul was an exhaustive effort by many of the industry’s most knowledgeable experts, developed over a significant period of time. This required major commitment from both individual chapter authors and also the members of SAE’s Automatic Transmission & Transaxle Technical Standards Committee, who provided invaluable material development oversight. Those colleagues include:

Sponsored by

Passenger Car Automatic Transmissions

Fourth Edition

Sponsored by

AE-29

Design Practices

Fourth Edition

Since the mid Twentieth Century, automatic transmissions have benefited drivers by automatically changing gear ratios, freeing the driver from having to shift gears manually. The automatic transmission’s primary job is to allow the engine to operate in its speed range while providing a wide range of output (vehicle) speeds automatically. The transmission uses gears to make more effective use of the engine’s torque and to keep the engine operating at an appropriate speed.

Design Practices

Passenger Car Automatic Transmissions

Passenger Car Automatic Transmissions

Design Practices

Sponsored by

Sophisticated transmission lubricants for evolving transmissions Automatic transmissions are the most fascinating, complicated, ever-changing piece of equipment in a moving vehicle. Now more than ever you need the right fluid to support advancements in automatic transmission technology. Lubrizol can help. With you every step of the way.

www.lubrizol.com © 2012 All rights reserved. 120273

Design Practices: Passenger Car Automatic Transmissions

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Other SAE titles of interest: Electric and Hybrid-Electric Vehicles—Engines and Powertrains Ronald K. Jurgen PT-143/3 Continuously Variable Transmission (CVT) Bruce D. Anderson and John R. Maten PT-125 Automotive 2030—North America Bruce Morey T-127

For more information or to order a book, contact SAE International at 400 Commonwealth Drive, Warrendale, PA 15096-0001, USA; phone 877-606-7323 (U.S. and Canada only) or 724-776-4970 (outside U.S. and Canada); fax 724-776-0790; email [email protected]; website http://books.sae.org

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Design Practices: Passenger Car Automatic Transmissions fourth edition AE-29 Prepared under the auspices of SAE Transmission/Axle/Driveline Forum Committee

First edition published 1962 Second edition published 1973 Revised second edition published 1988 Third edition published 1994 Fourth edition published 2012

Warrendale, Pennsylvania USA Sponsored by

Copyright © 2012 SAE International.

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eISBN: 978-0-7680-7531-1

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400 Commonwealth Drive Warrendale, PA 15096-0001 USA E-mail: [email protected] Phone: 877-606-7323 (inside USA and Canada) 724-776-4970 (outside USA) Fax: 724-776-0790 This edition is made possible in part by sponsorship of The Lubrizol Corporation.

Copyright © 2012 SAE International. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, distributed, or transmitted, in any form or by any means without the prior written permission of SAE. For permission and licensing requests, contact SAE Permissions, 400 Commonwealth Drive, Warrendale, PA 15096-0001 USA; email: [email protected]; phone: 724-772-4028; fax: 724-772-9765. ISBN 978-0-7680-1125-8 SAE Order Number AE-29 DOI 10.4271/AE-29 Library of Congress Cataloging-in-Publication Data Design practices—passenger car automatic transmissions. — 4th ed.    p.  cm.   “SAE Order Number AE-29.”   “Prepared under the auspices of SAE Transmission/Axle/Driveline Forum Committee.”   Includes bibliographical references.   ISBN 978-0-7680-1125-8   1. Automobiles—Transmission devices, Automatic—Design and construction.  I. SAE Transmission/Axle/Driveline Forum Committee.  II. Title: Passenger car automatic transmissions.   TL263.D47   2012   629.2′446—dc23 2011044834 Information contained in this work has been obtained by SAE International from sources believed to be reliable. However, neither SAE International nor its authors guarantee the accuracy or completeness of any information published herein and neither SAE International nor its authors shall be responsible for any errors, omissions, or damages arising out of use of this information. This work is published with the understanding that SAE International and its authors are supplying information, but are not attempting to render engineering or other professional services. If such services are required, the assistance of an appropriate professional should be sought. To purchase bulk quantities, please contact: SAE Customer Service Email: [email protected] Phone: 877-606-7323 (inside USA and Canada) 724-776-4970 (outside USA) Fax: 724-776-0790 Visit the SAE International Bookstore at http://books.sae.org

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Contents Foreword Preface to the Fourth Edition

xi xv

Chapter 1 Transmission Cases and Parking Mechanisms

1-1

1.1

Transmission Cases

1-1

C. E. Shellman with updates by Ernest DeVincent

1.2

Parking Mechanisms

1-10

A. Gupta

Chapter 2 Torque Converters and Start Devices 2.1

Fluid Couplings

2-1 2-1

J. W. Qualman and E. L. Egbert

2.2

Multiturbine Torque Converters

2-17

F. H. Walker

2.3

Application of Hydrodynamic Drive Units to Passenger Car Automatic Transmissions

2-31

E. W. Upton

2.4

Design of Single-Stage, Three-Element Torque Converter

2-49

V. J. Jandasek

2.5

Technology Needs for the Automotive Torque Converter— Part 1; Internal Flow, Blade Design, and Performance

2-70

Robert R. By and John E. Mahoney with updates by Thomas G. Brand

2.6

An Experimental Analysis of Fluid Flow in a Torque Converter

2-85

Akio Numazawa, Fumihiro Ushijima, Kagenori Fukumura, and Tomo-o-Ishihara

2.7

A Loss Analysis Design Approach to Improving Torque Converter Performance

2-93

Masaaki Kubo and Eiji Ejiri

2.8

The Chrysler Torque Converter Lock-Up Clutch

2-103

A. P. Bloomquist and S. A. Mikel with updates by Thomas G. Brand

2.9

Control Technology of Minimal Slip-Type Torque Converter Clutch

2-117

Takeo Hiramatsu, Takao Akagi, and Haruaki Yoneda v

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Contents

2.10 Dynamic Behavior of a Torque Converter with Centrifugal Bypass Clutch

2-125

M. C. Tsangarides and W. E. Tobler

Chapter 3 Gears, Splines, and Chains 3.1

3-1

Design of Planetary Gear Trains

3-2

O. K. Kelley, with updates by E. L. Jones and M. T. Berhan

3.2

Transmission Gear Design for Strength and Surface Durability

3-8

E. L. Jones, with updates by E. L. Jones, M. T. Berhan, H. Dourra, and M. B. Leising

3.3

Manufacturing Considerations Affecting Transmission Gear Design 3-17 A. Hardy, with updates by R. J. Garrett

3.4

Gear Design for Noise Reduction

3-25

W. D. Route, with updates by E. L. Jones, D. K. Ducklow, and M. T. Berhan

3.5

The Lever Analogy

3-40

H. L. Benford and M. B. Leising, with updates by M. B. Leising, H. Dourra, and M. T. Berhan

3.6

Design Practice for Automotive Driveline Splines and Serrations

3-50

W. B. McCardell, J. Mahoney, and D. Cameron, with updates by D. Cameron, E. L. Jones, and C. E. Dieterle

3.7

The Effective Fit Concept of Involute Splines and Inspection

3-68

L. DeVos, with updates by C. E. Dieterle and M. T. Berhan

3.8

Chain Drives in the Vehicle Powertrain

3-75

R. H. Mead, T. O. Morrow, and R. G. Young, Jr., with updates by M. Giovannini, R. G. Young, Jr., and M. T. Berhan

3.9

The Gemini Phased Chain System: A New Tool in Automotive Power Transmission

3-86

P. Mott and B. Martin

Chapter 4 Transmission Shaft Fatigue Design

4-1

Jeffrey K. Baran and Keith D. VanMaanen

4.1

Abstract

4-1

4.2

Introduction

4-1

4.3

Nomenclature

4-2

4.4

Stress Calculation

4-2

4.5

Mass Relationship

4-3

4.6

Stress Concentration

4-3

4.7

Fatigue Properties (S-N Curve)

4-4

4.8

S-N Modifying Factors

4-5 vi

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Contents

4.9

Loading Conditions

4-8

4.10 Combined Loading

4-8

4.11 Summary

4-11

4.12 References

4-11

4.13 Bibliography

4-11

4.14 Appendix A—Stress Concentration Factors

4-12

4.15 Appendix B—Example Problems

4-18

Chapter 5 Bearings 5.1

5-1

Design of Sleeve Bearings and Plain Thrust Washers

5-1

L. J. Pesek and W. E. Smith

5.2

Improving the Performance of Sleeve Bushings and Thrust Washers

5-20

Brad L. Blaine and Christopher D. Wiegandt

5.3

The Use of Polymeric Thrust Elements in Powertrain Applications

5-26

R. G. Van Ryper

5.4

Rolling Element Bearings in Light Vehicle Automatic Transmissions

5-30

J. R. Hull, with updates by M. D. Myers

5.5

Design and Selection Factors for Automatic Transaxle Tapered Roller Bearings

5-66

B. Martin and H. E. Hill

Chapter 6 Friction Clutches

6-1

Robert C. Lam, Donn K. Fairbank, Keith Martin, Anthony J. Grzesiak, and Ted D. Snyder

6.1

Evolution of High-Energy Wet Friction Materials

6-2

6.2

Multi-Plate Friction Clutch

6-8

6.3

Bands

6-30

6.4

References

6-44

Chapter 7 One-Way Clutches

7-1

Updated by John M. Kremer

7.1

Roller One-Way Clutches

7-2

7.2

Sprag One-Way Clutches

7-29

7.3

Pawl One-Way Clutches

7-49 vii

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Contents

Chapter 8 Automatic Transmission Controls 8.1

Introduction

8-1 8-2

Maurie Leising

8.2

Basic Shift Processes—The “How of Shifting”

8-2

M. Leising, Hussein Dourra, and Gang Chen

8.3

Shift Torque Analysis and the Continuously Variable Transmission 8-21 John E. Mahoney, Joel M. Maguire, and Shushan Bai

8.4

Shift Scheduling

8-26

Gang Chen and M. Leising

8.5

Transmission Control and Types of Controls

8-40

Ronald Cowan, Charles Marshall, and M. Leising

8.6

Transmission Operational Features

8-44

Ronald Cowan, Charles Marshall, and M. Leising

8.7

Automatically Shifted Manual Transmissions

8-47

M. Leising, G. Chen, and H. Dourra

8.8

Control Components

8-65

John Titlow and Joseph Gierut

8.9

Development Technology

8-112

Hussein Dourra and Ronald Cowan

Chapter 9 Automatic Transmission Pump Design

9-1

T. Roeber, M. Goulet, P. Dion, and Glenn B. Mann

9.1

Introduction

9-2

9.2

Types of Pumps

9-2

9.3

Types of Pumping Systems

9-2

9.4

Pump Design Guidelines

9-2

9.5

Survey of Transmission Pumps Currently in Use

9-11

9.6

What is Coming?

9-12

9.7

References

9-12

Chapter 10 Seals and Gaskets

10-1

10.1 An Overview of Automatic Transmission Gaskets

10-2

Andrew F. Joseph, Jeff Nelson, and Lane Noble

10.2 An Overview of Transmission Radial Shaft Seals

10-13

Susan M. Bothe and Jeff Dieterle

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Contents

Chapter 11 Transmission Temperature Control and Lubrication 11.1 Introduction

11-1 11-1

Maurie Leising and Charles Redinger

11.2 Transmission Cooling Systems: Oil-to-Water Type

11-2

E. F. Farrell and T. M. Wang

11.3 Transmission Cooling Systems: Air Cooling

11-10

M. G. Gabriel

11.4 Temperature Effects on Transmission Operation

11-20

T. J. Griffen

11.5 Temperature Control and Fuel Consumption

11-27

M. Leising and C. Redinger

11.6 Design and Validation of Automatic Transmission Lubrication Circuits

11-30

James T. Gooden

Chapter 12 ATF and Driveline Fluids

12-1

Craig Tipton, Tze-Chi Jao, and Timothy Newcomb

12.1 Introduction

12-2

12.2 History of ATF Development

12-3

12.3 Key Physical Properties

12-5

12.4 Basestocks and Their Impact on Performance

12-8

12.5 Chemical Composition

12-10

12.6 Driveline Fluid Specifications

12-12

12.7 Evaluating the Condition of Used Driveline Oils

12-18

12.8 Future Directions

12-23

12.9 Acknowledgments

12-23

12.10 Glossary of Terms

12-23

12.11 Key References

12-25

Chapter 13 Metal Belt Drive Continuously Variable Ratio (CVT) Automatic Transmissions

13-1

Bruce Anderson

13.1 Introduction

13-1

13.2 Definitions

13-1

13.3 Application Considerations

13-2

13.4 Belt Design

13-5

ix

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Contents

13.5 Sheave Design

13-9

13.6 Variator System Considerations

13-11

13.7 Controls Design

13-18

13.8 Fluid

13-20

13.9 References

13-22

13.10 Applicable Publications

13-25

13.11 Appendix A—CVT Cross Sections

13-26

13.12 Appendix B—Transmission Oil Tests

13-27

Chapter 14 Automatic Transmission and Transaxle Filter Design

14-1

Larry Larkin, Andy Boast, Ibrahim Khalil, and Dan Haggard

14.1 Introduction

14-2

14.2 History

14-2

14.3 Transmission Filter Functions and Requirements

14-2

14.4 Filter Construction

14-5

14.5 Other Design Features That Can Be Built into the Transmission Sump Filter

14-10

14.6 Pressure-Side Filters

14-11

14.7 Transmission Sump Filter Testing

14-13

14.8 References

14-17

Index

I-1

x

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Foreword carbon-containing composites, graphitic materials, and/or woven carbon fiber to handle the higher energy shifts.

One of the greatest innovations in automotive technology was the automatic transmission. Automatic transmissions have allowed both the vehicle driver and builder to optimize the driving experience and efficiency. The automatic transmission permits the driver to have full enjoyment of the vehicle without the worry and effort of shifting gears, with one hand and two feet, for the desired acceleration and deceleration— similar to a manual transmission except with fewer manipulations of the controls. No more worries about missing a gear and losing power! Meanwhile, the automatic transmission gives automotive manufacturers the ability to maximize gearshift timing for better vehicle fuel economy, thus allowing for increased U.S. Corporate Average Fuel Economy miles per gallon, which is crucial for EPA requirements.

One might ask why The Lubrizol Corporation, the world’s number-one lubricant additive company and a subsidiary of Berkshire Hathaway, would be interested in being a primary sponsor for the updating of this book. All of these design changes, which continue to evolve, have influenced the development of new and more-sophisticated transmission lubricants. These new fluids must have better friction durability and anti-shudder protection across many types of friction materials, especially the newer carbon-containing and woven carbon fiber materials. These fluids also must have more thermally stable additive chemistry for longer OEM warranties and higher sump temperatures.

Automatic transmissions are the most fascinating, complicated, and ever-changing piece of equipment used in a transportation vehicle, be it a passenger car or commercial vehicle. Globally, original equipment manufacturers have focused on further enhancing transmission efficiency for better fuel economy performance, while striving to maintain durability for their extended warranties.

Dual-clutch transmission fluids specifically must provide excellent synchronizer friction durability in addition to paper-on-steel friction durability for the startup clutch, as in a stepped (speed) automatic transmission. Continuously variable transmission fluids have a major challenge in providing a frictional balance; these fluids must have a high metal-tometal friction coefficient for good belt-pulley or chain-pulley contact to handle the varying vehicle speeds effectively, as well as have a lower paper-on-steel static friction coefficient to prevent anti-shudder within the CVT startup assembly when the vehicle begins motion.

Since the turn of the new century, there has been a move toward a higher number of gear ratios (six, seven, eight, nine, and ten speeds) in automatic transmissions from the traditional three- and four-speed automatic transmissions, and a move from manual transmissions to dual-clutch transmissions (DCT), another form of automatic transmission. Continuously variable transmissions (CVT) are also being introduced to the global market for smaller passenger vehicles as an alternative to stepped-ratio transmissions.

An additional change in automatic transmission fluids by the OEMs in the past ten years has been the lowering of the kinematic viscosity of their factory fill automatic transmission fluids for improved fuel economy benefits; lower fluid viscosity reduces churning losses within the transmission. This significant lowering of kinematic viscosity places a greater emphasis on having better gear and bearing wear protection.

Along with these changes, significant advances in design specifics have occurred, with a concentration on reduced energy losses (greater efficiency) and lighter equipment. One of these design changes includes the reduction of the number of clutch plates in the clutch pack; reducing the number of clutch plates reduces the spin losses, which, in turn, helps vehicle fuel economy. However, this adjustment requires more thermally stable friction plate materials such as higher

Lubrizol’s latest commercialized automatic transmission, CVT, and DCT fluids accomplish this need of superior wear performance through the balanced use of additives containing phosphorus, boron, and sulfur. Finally, many of xi

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Foreword

these automatic transmission design changes have caused an increased need for improved oxidation and thermal stability in ATFs due to observed higher operating sump temperatures and the introduction of smaller transmission sump sizes.

highly recommend this new, 4th Edition of AE-29 Design Practices: Passenger Car Automatic Transmissions, to be the lead reference of use, especially for those working in and supporting the area of automatic transmissions.

Anyone involved in the passenger car industry, even remotely, should take the time to learn how the automatic transmission operates and, most importantly, become more familiar with the latest advances in automatic transmission technology. We

William D. Abraham, Ph.D. Driveline Technology Manager, Senior Fellow Automatic Transmission & Farm Tractor Fluids The Lubrizol Corp.

xii

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Preface to Fourth Edition Design Practices: Passenger Car Automatic Transmissions has a long history—nearly half a century—as the “go-to” handbook of current and relevant design considerations for automatic transmission industry engineers of all levels of experience.

cal Standards Committee, who provided invaluable material development oversight. Those colleagues include: • Ernest J. DeVincent (Chairman), Getrag Transmissions Corporation, and Ford Motor Company (retired) • Michael T. Berhan, Ford Motor Company • Susan M. Bothe, Freudenberg-NOK General Partnership • Thomas Brand, BorgWarner Corporation • Gang (George) Chen, Chrysler Group LLC • Louis Crocco, Greening Associates • Mark R. Dobson, Ford Motor Company • Hussein A. Dourra, Chrysler Group LLC • Charles (Chip) Hartinger, Ford Motor Company • James D. Hendrickson, General Motors Company • Harry A. Hildebrandt, Oakland Community College • Andrew F. Joseph, Freudenberg-NOK General Partnership • Ibrahim A. Khalil, SPX Filtran • John M. Kremer, BorgWarner Corporation (retired) • Larry Larkin, Filtertek Corporation (retired) • Maurice B. Leising, Chrysler Corporation (retired) • Glenn Mann, Nichols Portland Corporation • Gregory Mordukhovich, General Motors Company • Michael D. Myers, Otis Elevator Corp, and Timken Corporation (retired) • Thomas M. O’Brien, Chrysler Group LLC • Lev Pekarsky, Ford Motor Company • John Titlow, Conxall Corporation, and Honeywell Corporation (retired)

This edition represents a major overhaul from the prior edition and is arguably the most significant update in its long history. Virtually all existing chapters have been updated and improved with the latest state-of-the-art information. Many previously existing chapters have been significantly expanded with more detail and design consideration updates; most notably: • • • • • • • •

Torque Converters and Start Devices Gears/Spline/Chain Bearings Wet Friction One Way Clutch Automatic Transmission Controls Pumps Seals and Gaskets

Additionally, all new chapters have been added, including state-of-the-art information on: • Lubrication • Transmission Fluids • Filtration and Contamination Control Finally, details about the latest transmission technologies have been added, including Dual Clutch Transmissions and Continuously Variable Transmissions. This complete overhaul was an exhaustive effort by many of our industry’s most knowledgeable experts, developed over a significant period of time. This required major commitment from both individual chapter authors (whose credits are shown at the introduction to each chapter) and also the members of the Automatic Transmission & Transaxle Techni-

It should be noted that the manual itself is not intended as a design requirements document, but rather a compilation of the latest design practices in the industry. Therefore, it should

xiii

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Preface to Fourth Edition

importantly—the OEM and supplier companies who allowed their expert employees to contribute their valuable time to this effort.

not be considered a basis for legal regulation or administrative ruling. In summary, this team has put together the most definitive handbook for Automatic Transmission Design Practices available today. There are many to sincerely thank for this: the chapter authors, the members of the Auto Trans Technical Standards Committee, the SAE Staff, and—very

Ernest J. DeVincent, Chairman SAE Automatic Transmission & Transaxle Technical Standards Committee

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Preface to the Third Edition The Automatic Transmission Design Practices Manual has a long and distinguished history of technical contribution to the automotive engineer dating back to the first published manual in 1962. This manual is a compendium of the latest current practices of transmission engineering sponsored and compiled by the SAE Transmission/Axle/Driveline Forum Committee of the SAE Power Train Systems Group. It retains some of the original papers from the previous manual wherein the technical material is still valid. Design calculations are included wherever possible to enhance the usefulness of this document for the design engineer.

• Karl Schneider, Vice President, Advanced Transmission Technology, Automatic Transmission Systems, Borg Warner Automotive • Carl E. Shellman, Chief Design Engineer, F F Developments • Leo G. Steinl, Staff Project Engineer, Advance Engineering Staff, General Motors Corp. • John R. Tanzer, Ford Motor Company (retired) • Kevin L. Wicks, Mgr. Mechanical Components, Power Train Division, General Motors Corp. • Stanley N. Smith, Director of Technical Dev., Chassis Products Operations, Federal Mogul Corp.

Special credit for coordinating the planning of this Herculean work goes to Co-Chairmen Kevin L. Wicks and Carl E. Shellman (detailed credit below). It is evident that many people have contributed toward the preparation, writing and editing of the Automatic Transmission Design Practices Manual. The task was divided into sections, many of them championed by the chairperson of the applicable standards committee of the Forum Committee as credited below in alphabetical order:

There has been no attempt to cite applicable patents covering any section of the art contained in the material presented. Neither SAE nor the authors wish to imply that discussion of a topic indicates there are no patent rights involved. The reader is responsible for his own investigation to establish his right to use any device or principle described herein. No material presented in this manual is to be construed as a design standard or a recommended practice by the Society of Automotive Engineers. It is a compilation of existing design practices as interpreted by the Transmission/Axle/Driveline Forum Committee and individual authors. It is not intended to be a basis for legal regulation litigation or administrative ruling by a regulatory body.

• Martin G. Gabriel (Chairman), Senior Reliability Engineer, Power Train Reliability and Quality Office, Ford Motor Company • John E. Mahoney (Vice-Chairman), General Motors Corp. (retired) • Edward L. Clary, Buick Motor Div., General Motors Corp. (retired)

The many contributors including the members of the committees and the authors of the papers are recognized for their many hours of effort to make this latest reference manual available to the automotive engineer.

• Robert J. Fanella, Vice President, Worldwide Advanced Product Technology, Automatic Transmission Systems, Borg Warner Corp.

Martin G. Gabriel, Chairman SAE Transmission/Axle/Driveline Forum Committee

• Merrill L. Haviland, Sr. Automotive Dev. Specialist, Exxon Chemical

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Preface to the Revised Second Edition The original editions of this handbook were an indispensable tool for both the experienced and the novice transmission design engineer and have become classics. To improve upon these was considered a Herculean task, and so it was decided to split the task in two. This revised edition of the design practices handbook is a corrected version of the second edition. A new version of the handbook will be written in the next few years.

• W.E. McCarthy, Staff Research Engineer, General Motors Corporation • J.H. Tanzer, Supervisor, Transmission & Axle Engineering, Ford Motor Company • K.L. Wicks, Senior Project Engineer, Hydra-Matic Division, General Motors Corporation • L.G. Steinl, Staff Project Engineer, General Motors Corporation • D.L. Otto, Product Development Specialist, Timken Company • S.N. Smith, Manager, Engineering & Research, Federal Mogul Corporation • E.L. Clary, General Motors Corporation (retired) • M.C. Sefcik, Advanced Engineering Staff, General Motors Corporation • J.R. Grady (Sponsor), Vice President, North American Sales, Borg-Warner Automotive, Inc. • A.R. Fisher, Ford Motor Company (retired) • E.W. Upton, Staff Engineer, General Motors Corporation

The corrections are to the obvious errors and omissions, and you will find that most of the typographical errors are corrected. There have been minor changes to update the information along with certain rewriting of phrases to clarify and assist in understanding. Added to this volume is a copy of the SAE metric standards (1916) so that conversion of any of the information contained herein can be done from one reference source rather than needing to look elsewhere for conversion factors. There is also a listing of the SAE papers that were considered relevant to the topics in this volume. There are many areas of design that have become increasingly important since the original publication of this volume, but we have been unable to include them. The application of electronics on what was essentially a mechanical device is not covered; neither are the design alterations driven by the need to improve fuel economy of passenger car vehicles equipped with automatic transmissions. Problems of designing four-wheel-drive automatic transmissions and Continuously Variable Transmissions (CTV) are not included. For the reader interested in the CVT, a separate SAE publication is available (PT-30).

Many others helped to produce this edition including many of the original authors who reviewed and corrected their own work, plus practitioners in the field who had used the previous editions and were able to offer constructive criticism. These efforts to clarify and update this volume were sincerely appreciated. N.F. Avery Chief Engineer Long Manufacturing

The revision required to produce this edition has required much time by many people. Those who volunteered to bring this edition to print include: • M.G. Gabriel (Chairman, Transmission & Drivetrain Technical Committee), Supervisor of Product Reliability, Ford Motor Company

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Preface to the Second Edition expansion of the information contained in the original twovolume edition. Most of the papers included in the original edition are retained, with many of them edited to reflect current practices. Several papers presented since 1962 have been included to add new subject matter. The papers have been grouped in sections identified by subject, material, or component—for example, seals, friction material, lubrication, etc. Each section is subdivided into chapters to cover the various categories of information within that section.

The automatic transmission is one of the most complex components in the automobile. The design reflects knowledge from almost every branch of the field of mechanical engineering. Its more than 600 parts are expected to be so well designed and fabricated that the assembled unit is not only lightweight, compact, and durable, but also easy to service, quiet in operation, and smooth shifting under all driving conditions. The goal of every automatic transmission engineer is to design a unit that has all of these qualities at a low competitive cost.

The task of producing this volume was assigned to a new Editorial & Publication Subcommittee established within the SAE Transmission and Drivetrain Committee. The members of this Subcommittee who participated in the organization of this material are:

The need for a manual of design practices to aid transmission engineers in achieving their goals was recognized as early as 1955, when a Design Standards Subcommittee was established within the SAE Hydrodynamic Drive and Transmission Committee—renamed the Transmission Committee in 1957. In 1959, the Subcommittee under the chairmanship of Charles S. Chapman undertook to fill a void in design information on passenger car automatic transmissions. Recognizing that an invaluable wealth of knowledge was possessed by many transmission experts with widely varying experience and background, the Subcommittee set out to get this information documented, compiled, and published in a form that would be useful to both the experienced and the novice transmission design engineer. To achieve its goal, the Subcommittee sponsored a number of Transmission Workshop Meetings at which papers on the various aspects of automatic transmissions were presented by many authors of considerable experience. These papers were later edited and compiled into two hardbound volumes that sold over 2,000 copies each.

• Harold Fischer (Chairman), Senior Staff Engineer, Buick Motor Div., General Motors Corp. • M.G. Gabriel (Section Chairman), Automatic Transmission Engineering, Transmissions and Chassis Div., Ford Motor Co. • E.L. Jones, Managing Editor, Axle Engineering, Chrysler Corp. • T.F. Ristau, Director of Advanced Engineering, Saginaw Steering Gear Div., General Motors Corp. • G.R. Smith, Engineering Staff, General Motors Corp. • R.W. Wayman, Vice President, Advance Transmission Engineering, Borg-Warner Corp. • E.L. Clary, Research and Development Engineering, Buick Motor Div., General Motors Corp.

The preface appearing in each of those two volumes—now recognized as the first edition of this reference work—is reproduced in this revised edition for two reasons: first, to recognize the members of the group responsible for getting that valuable first edition published, and second, to capture and retain some of that group’s thinking and philosophy with regard to the purpose, scope, and format of the publication.

The members of this Subcommittee, the authors of the papers, and several members of the SAE Transmission and Drivetrain Committee have unselfishly devoted many hours of personal effort to make this a truly useful reference manual. Bert W. Cartwright Engineering & Research Office Chrysler Corp.

The revised edition of Design Practices: Passenger Car Automatic Transmissions represents both an updating and an xix

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Preface to the First Edition The material printed in this volume has been gathered and published as a result of the activities of the Design Standards Subcommittee of the SAE Transmission Committee. The members of this Subcommittee who participated in the organization of this material are:

mittee that the use of a device at a known design level in millions of automatic transmissions in customer service is information of the highest utility. In addition to this information, the methods of design calculation are included as an attempt to consolidate this information in order to make a useful reference for the design engineer.

• Charles S. Chapman (Chairman), Staff Engineer, New Transmission Design, Buick Motor Div., General Motors Corp. • Bert W. Cartwright, Manager, Product Engineering, Axle and Transmission Div., Chrysler Corp. • Jack R. Doidge, Chief Engineer, Detroit Transmission Div., General Motors Corp. • Harold Fischer, Section Engineer, Current Transmission Design, Buick Motor Div., General Motors Corp. • John W. Holdeman, Vice-President, Engineering, Warner Automotive Div., Borg-Warner Corp. • Robert W. Smith, Executive Engineer, Automatic Transmission and Axle Engineering, Transmission and Chassis Div., Ford Motor Co. • Frank J. Winchell, Assistant Chief Engineer, Research and Development Section, Chevrolet Motor Div., General Motors Corp.

There are members of this Subcommittee from every transmission manufacturing organization now producing passenger car automatic transmissions in large volume in the United States. These Subcommittee members and their engineering organizations have made available to the Subcommittee the design and dimensional information on all of the components of the transmission currently in production. Of course, no proprietary information on new designs not yet in production was given nor was it requested. Most of the information on the production units is available to anyone who wishes to purchase a unit and measure and calculate these design stresses or other information. Normally, except in cases of detailed interest, this is too time-consuming and costly a procedure to carry out for all production units by an individual organization, and, for this reason, the data are of considerable interest to most engineers. The material was broken down into sections according to the function of the components for presentation. Members of the Subcommittee were assigned various subjects and were made session chairman for SAE meetings to present the material. Authors who had considerable experience with the subject material were invited to present papers at these Transmission Workshop sessions. The time and arrangements for these sessions were made available by the Passenger Car Activity Committee, which gave our efforts enthusiastic support as part of a general effort to improve constantly the technical content of SAE papers and presentations.

Several years ago, this Subcommittee undertook to fill a void in design information on passenger car automatic transmissions. The means and format for accomplishing this have changed as the effort progressed. The textbook and recommended practice approaches have given way to a form in which the current practices of the industry are tabulated or analyzed for the information of designers without any recommendation telling designers what they should or should not do specifically. This does not exclude comments on what is considered poor design by current standards, but does avoid dogmatic recommendations in a field where the number of design variables is too large and the differences in environment and application have too large a bearing to make any specific recommendations. It is the feeling of the Subcom-

These papers have been edited and revised by the Subcommittee where necessary to make them more compatible with the Subcommittee’s objectives. This is particularly true of the earlier papers that were presented while the objectives were being formulated. The papers presented later benefited from xxi

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Preface to the First Edition

these earlier efforts and needed less revision for incorporation into this volume.

There has been no attempt to cite current or expired patents covering any section of the art contained in the material discussed. Neither SAE nor the authors wish to imply that discussion of an item indicates that there are no patent rights involved, and the reader is responsible for making his own investigation to determine his right to use any device or principle described herein.

The effort put into the papers by the authors and the Subcommittee members can be well appreciated only by those involved in similar undertakings. These men have given a great deal of their personal time and effort very unselfishly and have made a substantial contribution to this profession. The fact that no one involved will ever be completely satisfied with the results is testimony to the high professional standards of those participating in the presentation of this material.

As stated previously, no material presented in this volume is to be construed as a design standard or a recommended practice of the Society of Automotive Engineers. It is a compilation of existing design practices as interpreted by the Transmission Design Standards Subcommittee and individual authors. It is intended in no way to be a basis for legal regulation, litigation, or administrative ruling by a legally constituted regulatory body.

The encouragement and active sponsorship of this activity by other members of the SAE Transmission Committee has greatly aided this program. The cooperation of the Passenger Car Activity Committee and the help of Forest McFarland in presenting the program to the Committee to arrange for the Transmission Workshop sessions has been very much appreciated.

C.S. Chapman Buick Motor Div. General Motors Corp.

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Chapter 1

Transmission Cases and Parking Mechanisms Introduction

certain exterior connections to be made to the case. Some of the important considerations for the actual case design are mentioned. Another increasingly important functional requirement of the case is its contribution to NVH and powertrain bending stiffness.

Transmission Cases and Parking Mechanisms This chapter will give an overview of two areas of an automatic transmission which have been overlooked in the past. In retrospect, one can look back to earlier versions of this book and realize that front-wheel-drive transmissions had not begun to make the inroads on the marketplace which they enjoy today. The tremendous problems which exist in these areas are due to space considerations caused by the design activities related to front-wheel-drive vehicles.

Parking Mechanisms’ importance to transmission design cannot be overemphasized. Parking mechanisms have become a very important safety-critical element of virtually all of today’s automatic transmissions, and are regulated by the U.S. Government via FMVSS. This section will present an overview of parking mechanism design techniques.

The move to mass reduction of the entire vehicle, increased fuel economy to conserve fuel, use of smaller-displacement engines with very little reduction in the performance of the vehicle, and increased passenger comfort are some of the main reasons for the emphasis on front-wheel-drive vehicles.

Original Author: C. E. Shellman, F F Developments, Inc., Livonia, Michigan Updated By: Ernest J. DeVincent, Ford Motor Company, Dearborn, Michigan

Transmission Cases will give an overview of a part of an automatic transmission which is all too often taken for granted; namely, the transmission case. No other single part is as large, as heavy, or as expensive. The shape of the case affects packaging within the confines of the vehicle, more so with front-wheel-drive than rear-wheel-drive installations. For this reason mainly, the design of the case is usually started as part of the initial concept package.

1.1 Transmission Cases Original Author: C. E. Shellman, F F Developments, Inc., Livonia, Michigan Updated Material By: Ernest J. DeVincent, Ford Motor Company, Dearborn, Michigan

1.1.1

After packaging, the purpose of the case is reviewed as it relates to housing the working parts of the transmission, sealing the necessary fluid within the case, and allowing

Introduction

The transmission case is best looked at as the package or container that holds all of the working parts of the transmission. 1-1

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Design Practices: Passenger Car Automatic Transmissions

1.1.1.4

As such, it is important at the initial design concept of a powertrain installation. The case design should occur simultaneously with the advent of a new vehicle design because it will have a lasting space requirement for the life of the vehicle platform.

1.1.2 Transmission Packaging

This discussion of the case will consist of four parts, which in practice are performed by different persons or groups of persons. These are further categorized next and will be briefly mentioned. This format for the case portion was the most logical manner to cover the subject, but allows for the vast number of differences caused by the individual nature of each transmission application. 1.1.1.1

1.1.2.1

1. Front-Wheel Drive—Transverse Positioning (vs. Longi­ tudinal) Attached to, and in line with the engine; usually structurally stronger. Styling aid since more suitable for smaller engines, less space between the wheel wells, and more streamlined modern hood appearance. Differential is more easily designed as an integral part of the overall transmission assembly. 2. Front-Wheel Drive—Longitudinal Positioning (vs. Transverse) Favored for longer and larger-displacement engines. Separate differential is easier to service if needed. Usually requires mounting methods of its own instead of being mounted as a part of the more unified transverse positioned unit. All-wheel drive becomes a natural option since an end of the transmission is already directed toward the rear axle. 3. Front-Wheel Drive (vs. Rear-Wheel Drive) Flat passenger compartment floor; no driveshaft tunnel. More weight over the front driving wheels, thus better traction. Usually part of an overall vehicle mass reduction program. Usually better utilization of the passenger compartment from the standpoint of space available for passengers. Serviceability is more of a problem due to poorer accessibility to the transmission assembly. 4. Rear-Wheel Drive (vs. Front-Wheel Drive) Usually easier to package since space is less of a consideration. More adaptable to larger, higher-powered vehicles, including trucks.

Transmission Packaging

Purpose of the Case

Relationship of the working parts of the case to the case itself. What are the internal components which the case structure must support? What goes inside the case? How does what is inside the case stay inside the case? What goes through the case? What are some of the exterior connections to the case? 1.1.1.3

Where is the case in the vehicle?

The criterion here is that the case must be designed for either a front- or rear-drive vehicle. Usually this location is predetermined by the segment of the market at which the car is targeted after market research.

Where is the case in the vehicle? Front-wheel or rear-wheel drive? Relationship of the case to the vehicle. What areas of the vehicle limit the size and attitude of the case? What is outside the case? Are there any engine compartment components, normally at high temperatures, that will be too close to intended oil lines or electric wiring? 1.1.1.2

Powertrain Structural Analysis: S. C. Jasula, P. R. Perumalswami, and V. J. Borowski; Excerpt from SAE 840742

Case Design Considerations

Prototype or production? Sand casting, permanent mold casting, or die casting? Material considerations. Where do aluminum and magnesium stand? Vendor and Trade Association references. What are some sources for casting and material design information?

1-2

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Transmission Cases and Parking Mechanisms

Weight shift when accelerating uphill aids tractive effort. 1.1.2.2

Compatibility to use existing components, such as propshafts, usually leads to compromise in transmission length. Use of common transmission mounting brackets is another limitation.

Relationship of the case to the vehicle

This usually involves a study of the surrounding area of the vehicle once it has been determined where the transmission and driveline are to be placed. There are many parts of the vehicle which must occupy certain general areas or volumes of space. Studying actual transmission installations readily shows that front-wheel drives are more crowded than rearwheel drives. Some of the problem areas for both locations are mentioned next.

1.1.2.3

What is outside the case?

The surrounding area to the case must be shown due respect in several locations because of potential problem conditions. The exhaust system needs clearance from all oil pipes and electrical wiring. Attachment to the transmission, engine, or vehicle itself will determine the amount of clearance, but allowance must be made for torque reaction of the engine, as well as vehicle jounce and rebound movements.

1. Front-Wheel Drive Cooling fan, radiator shroud, and radiator can be limits to the front. Engine accessories and mounting brackets are restrictions on all sides. Exhaust pipe and manifolds can be limits to both sides and the rear. Engine shape can be a limit to available center distance space. Turning radius of the wheels determines the shape of the wheel wells, which again limit overall length of a transverse position. Brake master cylinder and its lines are limits. Spring and shock absorber assemblies also limit space under the hood. Hood profile is a limitation on going up with the transmission. Ground clearance is a controlling factor when going down. Oil sump capacity must be satisfied between these last two mentioned limits, thus causing unique sump arrangements. Desired vehicle items, such as equal-length axle shafts, are usually one of the first features that are compromised out of the design since precedence has shown that this is not a necessity. 2. Rear-Wheel Drive The underbody floor tunnel is the starting surface for the design. Protrusions from the case are limited by the floor, after it flares away from the tunnel shape. Access to attachments like cooling lines and electrical connectors is also limited by the tunnel and the floor pan shape.

The shift linkage to the instrument selector lever is of particular importance. In front drives, cables are generally used. Sharp bends cannot be used due to high friction, kinking or unduly stressing the cable, and inaccuracy at the selector lever indicator. Pullout effort for the parking pawl can be a critical item, as will be addressed. In rear drives, rods and linkages are traditionally used. These require careful layout studies to match travels at the steering column and clearances for all linkage movement. Both locations require that dipsticks must be freely removable to check fluid levels. Also, access must be allowed to service cooler fluid lines, pressure taps, and electrical connectors. A complete assembly installation and disassembly or removal procedure should be studied to prevent surprises from occurring later during a build.

1.1.3

Purpose of the Case

1.1.3.1

Relationship of the working parts of the case to the case itself

The case may be considered as the container which houses the working parts of an automatic transmission. These working parts are the gears, clutches, band drum, oil pump, and torque converter. Most of these components are mounted on rotating or stationary shafts, through the use of bushings or bearings. These shafts are related back to the case for support, through direct mounting of the bushing or bearing, or through an intermediate housing, center support, end cover, or converter cover.

1-3

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The gears are used to multiply engine torque and provide different speed ratios corresponding to gear ratios. The gears need a torque reaction to properly control them. This reaction is provided by a clutch or a band. The clutch can either connect two elements to rotate at the same speed or it can carry a reaction to ground, which happens to be the case.

Thick, rubberized cork gasket: Case to oil pan Case to valve body cover (if stamped) Case to servo cover (if stamped) Thin, paper-fiber gasket:

The band which goes around the drum has one end anchored to the case and the other end actuated by a servo piston, which is typically housed in the case and reacts against the case through its servo cover. The oil pump assembly is usually a pair of round castings fastened together and mounted in the case. Its inside diameter will support one or more shafts, and the converter is typically mounted on the outer end. The converter gets a second case support through a bushing rotating on another case member.

Case to converter housing Case to extension or end cover Much engineering effort has been expended over the past years to study the materials, surface finishes, and bolt spans for gasketed surfaces. Individuals with this knowledge should always be consulted for gasket applications. 1.1.3.3

It is evident that the case must not only house these components, but it must be rigid and stiff enough to provide proper support for the reactions, but also prevent undue torsional deflections. 1.1.3.2

What goes through the case?

All of the mating surfaces mentioned above represent a leak path. However, there still are a number of others. These will be grouped by their type of seal between the case and outside elements.

What goes inside the case?

Rotating shaft radial lip seals (all highly specialized seals):

The mechanical components inside the case are actuated, operated, and controlled by the transmission fluid within the case. The case provides many of the passageways for the fluid. There are innumerable drilled holes and cored passages for the fluid. These connect from the oil pump assembly to the different units, usually through routes that involve rotating shaft seals which mount in the case or rotate on the inside of a case bore.

• Converter cover—This seal mounts in the case and seals the O.D. of the hub of the converter cover. • Propshaft yoke (rear drive)—This seal mounts in the extension and seals the O.D. of the yoke when it is installed over the transmission output shaft. • Axle shafts (2) (front drive)—These seals mount in the case and converter housing. They seal the yokes which attach to the axle shafts.

The holes and passages in the case must allow these fluids to flow without leaking through to the outside. Thus, the case must be made of a porosity-free casting to prevent leakage. A case assembly consists of several separate parts which are bolted together. Each of these attachments must be sealed to prevent leakage of the fluid.

“O” ring seals (completely described by an SAE “J” standard): • • • • •

The general name for a seal between two mating flat surfaces is a face seal. In the past, these have been thick, rubberized cork gaskets when one surface is a sheet metal part, and somewhat thin paper-fiber gaskets when both surfaces are thick metal parts such as castings. Some examples of typical locations where these seals might be used follow. More recent designs have replaced rubberized cork gaskets with integrated composite gaskets with a stiff steel or plastic carrier, overlaid with elastomeric rubber and compression-limiting inserts (particularly on oil pans). Other sealing solutions at case joints include RTV sealant, encapsulated paper, Teflon bead screened, etc. For more information on gaskets and joint design, refer to Chapter 10.

Transmission fluid level dipstick. Electrical connector which goes through the case. Manual detent lever shaft. Pressure modulator altitude compensator assembly. Oil pump assembly which pilots in the case (usually rear drive).

Pipe thread attachments (metal to metal fit): • Cooler line fittings. • Hydraulic pressure tap connections. • Oil pan drain plug. The transmission cooler lines connect the case to the radiator. The out-flowing oil from the case is normally oil which has

1-4

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Transmission Cases and Parking Mechanisms

1.1.4.2

circulated through the torque converter. This is recognized as the hottest oil that is in the transmission. It flows to the radiator, where it is cooled and returned to the case by the cooler return line, i.e., the other line attached to the case. The integrity of these lines is very critical because transmission fluid, often called Automatic Transmission Fluid (ATF), absolutely cannot be mixed with engine cooling fluid, which is a mix of water and antifreeze.

Die cast aluminum presently dominates as the material of choice for automatic transmissions. Today, the use of magnesium is underway, although it still faces several challenges. The goals are still the same; the predominant one is achieving lighter weight. It will be found from studying the Die Casting Alloys table that the physical properties give an advantage to aluminum, but the need for these properties must first be evaluated. Magnesium generally weighs one-third less than aluminum.

There is one hole which goes through the case that is not sealed. That is the transmission breather vent. To equalize the air pressure inside the case with that outside, a connection must be made. This is made in the least likely place to be subject to oil splash. Labyrinth dams are frequently used to do this, and a top location is preferred to prevent water intrusion.

1.1.4

Case Design Considerations

1.1.4.1

Prototype or production?

Material considerations

The full range of engineering data must be thoroughly evaluated before making a usage decision. Noticeable differences occur in the modulus of elasticity in tension, modulus of rigidity (stiffness) for shear and torsion, fatigue, and creep strength—especially for elevated temperature, thermal expansion rate within the range noted, galvanic corrosion (which requires use of special material fasteners with magnesium), and damping capacity. Structural problems related to magnesium stiffness are usually resolved with the use of ribs or tapered conical sections. However, the material increases that are sometimes used can rapidly diminish magnesium’s weight advantage.

This question is often asked at the start of a case design. It cannot be generalized except to view the type of casting when considering the final use for it. A prototype company will be thinking only of small quantities from the start. As the usage increases, the low-volume sand casting will go from use of wooden patterns to plastic patterns.

The problem of corrosion has been reviewed numerous times. SAE has a number of papers on the use of magnesium, giving specific examples and the methods by which problems encountered were solved. Corrosion has to be thought of as a galvanic action which has the greatest reactive capability with steel and iron. An aluminum gasket between the parts is a normal solution. Coated bolts are another aid.

Next in volume and precision is the permanent mold casting. This uses metal patterns which are reusable for a greater number of parts. The precision will also become greater. Costs will rise also, but piece price will be reduced. The method favored for the automotive transmission industry is precision die casting. The volume requirements are the determining factors. Initial costs and size of the manufacturing equipment are such that there are only a limited number of die casters in any one country who are large enough to do this type of casting. Although precision die casting is the most expensive method, precision, volume per day, and production run for any one die are by far the greatest using this method.

The use of bolted joints follows the common practice of having the bolt as the weakest link in the system. With a certain hardness of bolt, the length of engagement of the thread can be determined. The use of coated bolts has an advantage from a service standpoint. Bolts without special identification features are generally more easily misplaced, or haphazardly replaced, with the wrong grade of bolt used unless the correct bolt specification is identified in some easy manner. Safety considerations that once were often heard when discussing use of magnesium have long since been overcome. Some relatively simple safety precautions must be taken. One manufacturer has processed over 40,000,000 lb (18,000,000 kg) of magnesium die castings per year with a wide size variation and has experienced no great difficulty.

Most of the large companies will do a two-way approach. A wood and plastic sand casting will be pursued parallel to the design of a die casting. This allows the manufacturing engineers to work simultaneously with the product engineers on the new case casting. It also allows the machinery, which will be used to manufacture the case, to be investigated and planned at the same time.

One advantage of fabricating cases from magnesium is that there is direct-conversion sand-cast magnesium available

1-5

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Design Practices: Passenger Car Automatic Transmissions

1.1.4.4

that gives all of the physical properties of a die-cast magnesium case. Recognition of this will allow engineers to do prototype testing of the new case by working around certain types of tests, or performing them with wrought stock or from machined die cast ingots that are available from the larger die casters.

This chart is from Hydro Magnesium (see Table 1.1). 1.1.4.5

Vendor and Trade Association references

Dow Chemical U.S.A. Field representatives and application engineers available worldwide. Chemicals and Metals Department Midland, Michigan, U.S.A.



Norsk Hydro Corporation Field representatives and application engineers available worldwide. Hydro Magnesium Marketing 21644 Melrose Avenue Southfield, Michigan, U.S.A. 48075-7905



The Aluminum Association Design standards for aluminum die cast design practices. 420 Lexington Avenue New York, New York 10017

1.1.5

Structural Analysis—A Case Study (Ref. SAE 840742)

1.1.5.1

Introduction

Finite element analysis is an integral part of the automotive design process. Because the technique can be used to conduct a “paper” analysis of a component’s structural design before fabricating actual prototype hardware, several design alternatives can be explored before selecting the most promising for fabrication. This powerful analytical method provides an opportunity to reduce product development time while improving durability and functional performance.

The material on magnesium was made available by two of the largest companies, Dow Chemical U.S.A. and Norsk Hydro Corporation.

Magnesium Casting Alloys

This chart is from Hydro Magnesium (see Table 1.2 on page 1-8).

One other way to resolve the material problem is that AZ92 T6 may be substituted for die-cast alloy AZ91D. The AZ92 must be heat treated and tempered to a T6 level. At this point, this sand-cast alloy will give a very close approximation of the final product AZ91D die-cast alloy. Also, new alloys such as AE42 have improved castability and mechanical properties. This last selection comes as a recommendation from the industry sources mentioned in the next section. 1.1.4.3

Die Casting Alloys

1.1.5.2

Background

The following discussion presents the results for a popular front-wheel-drive (FWD) vehicle analyzed with the finite element technique. The engine block and the transmission were modeled using mostly plate/shell elements, and normal mode dynamic analysis was performed with MSC/NASTRAN. Natural frequencies and mode shapes were computed and correlated well with actual laboratory test data. (The first three calculated frequencies for flexural modes were found to correlate within 7% of test data). This study established validity of the finite element analysis technique and modeling procedures for the simulation of powertrain bending. Several design updates were evaluated to provide directions for improvement, including the elimination of local modes. More recently, it was desired to determine the feasibility and effectiveness of a cast aluminum oil pan for increasing rigidity of a new powerplant. The study results are presented here.

There are many excellent vendors in the various countries of the world where automatic transmissions are made. They should be contacted at the start of any new case design project for suggestions.

1.1.5.3

Finite Element Model

The powertrain assembly consisted of three components— engine block, transmission case, and cast oil pan. Finite ele-

1-6

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Transmission Cases and Parking Mechanisms

Table 1.1  Die Casting Alloys, Typical Properties Comparison Property Density Ultimate Tensile Strength Tensile Yield Strength Elongation, % Hardness Brinell Modulus of Elasticity (Tension) Modulus of Rigidity (Shear & Torsion) Shear Strength Fatigue Strength R.R. Moore 5 ¥ 108 Cycles Creep Strength Stress to produce 0.5% strain in 100 hours 100 HR @ 70°F

Magnesium AZ91D

Aluminum A380

Zinc† AG40A

0.065 lb/in.3 34,000 psi 23,000 psi 3 63 6.5 ¥ 106 psi

0097 lb/in.3 48,000 psi 24,000 psi 3 80 10.3 ¥ 106 psi

0.24 lb/in.3 41,000 psi * 10 82 *

2.4 ¥ 106 psi

3.85 ¥ 106 psi

*

20,000 psi 14,000 psi

27,000 psi 21,000 psi

31,000 psi   6,900 psi

20,000 psi

24,000 psi

11,000 psi

100 HR @ 200°F

13,000 psi

23,000 psi

  3,500 psi

100 HR @ 250°F

  7,000 psi

21,000 psi

†

100 HR @ 300°F

  5,000 psi

20,000 psi

†

100 DAYS @ 70°F Thermal Conductivity (cal/cm2/cm/°C/sec) (w/m ¥ k) Thermal Expansion (in./in./°C @ 20–100°C) Specific Damping Capacity at 5,000 psi at 15,000 psi Impact Strength (Charpy Unnotched)

20,000 psi 0.17

24,000 psi 0.23

  7,000 psi 0.27

72 26

93 22

113 27.4

25% 53% 5 ft. lb.

1% 4%

18% 40% 43 ft. lb.

* Not normally defined. †

This zinc alloy is not intended for high temperature use as it will creep significantly above 165°F.

Property sources ASTM, ASM Handbook and Hydro Magnesium data.

ments (Fig. 1.1). The transmission case finite element model consisted mainly of plate and shell elements and it contained 1540 grid points and 1472 elements (Fig. 1.2). The oil pan finite element model consisted of 2065 grid points and 2372 plate and shell elements (Fig. 1.3). Bolt connections between the three components were simulated by coupling degrees of freedom at interfaces between solid element descriptions of the bolt areas. The finite element model of the assembled powertrain is shown in Fig. 1.4.

ment models were constructed for each of these components. It should be noted that these models were created early in the design phase. A finite element stress analysis was carried out on the engine block to determine the effect of impact forces in rail car shipment. Stresses in the transmission case and oil pan were evaluated under manufacturing stack-up tolerances, and the pan also was evaluated for thermal stresses. The finite element model of the engine block consisted of 17,387 grid points and 11,349 three-dimensional solid ele-

1-7

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Design Practices: Passenger Car Automatic Transmissions

Table 1.2  Magnesium Casting Alloys, Mechanical Properties

Alloy

Usage

AZ92A

Sand Casting

Temper1

Tensile Yield Strength Strength SI 0.2% KSI

Elongation %

Brinell Hardness HB-5/250

Fatigue Strength KSI2

NS

65

NS

Specific Damping Capacity3

–F

(23)

(11)

–T4

(34)

(11)

(6)

63

NS

–T5

(23)

(12)

NS

69

NS

–T6 –F

(34) (23)

(18) (11)

(1) NS

81 60

NS 10–13*

–T4

(34)

(11)

(7)

55

12–15*

–T5

(23)

(12)

(2)

62

–T6 –F

(34) (23)

(16) (11)

(3) NS

70 55–70*

12–15* 10–13*

–T4

(34)

(11)

(7)

55–70*

12–15*

–T5

(23)

(12)

(2)

–T6 –F

(34) 34

(16) 23

(3) 3

60–90* 63

12–15* 144

25%

AZ91B

–F

34

23

3

63

14

25%

AZ91D AZ81A

–F –F –T4 –F –T4

34 23–32(19)* (34) 23–32(19)* (34)

23 13–16(12)* (11) 13–16(12)* 11

3 2–6(1)* (7) 2–6(1)* 7

63 50–65* 55 50–65* 50–65*

14 10–13* 12–15* 10–13* 12–15*

25%

AZ91C & AZ91E

AZ91C & AZ91E

AZ91A

Sand Casting

Permanent Mold Casting

Die Casting

Sand Casting Permanent Mold Casting

4 4

AM60A* & AM60B*

Sand Casting

–F –T4

26–35(20)* 28–36(22)*

12–16(12)* 13–16(13)*

8–12(4)* 8–15(6)*

50–65(50)* 50–65(50)*

10–13* 10–13*

AM60A & AM60B AS41A AS21*

Die Casting

–F

32

19

8

55–70*

7–104*

45%

Die Casting Die Casting

–F –F

31 25*

20 16*

6 4*

60–90* 63*

7–104* NS

40% 60%

Numbers in parentheses are minimum values which can be used in calculating stresses in castings with wall thickness up to 0.600 in. Temper: F = As Cast. T4 = Solution Treated. T5 = Artificially Aged. T6 = Solution Treated & Artificially Aged. Rotating beam fatigue test unless otherwise noted. Stress corresponding to a lifetime of 50 ¥ 106 cycles. 3 Measured at 5000 psi. Bureau of Mines Data. 4 Reverse bending fatigue test (RR Moore). Stress corresponding to a lifetime of 50 ¥ 106 cycles. All data were obtained directly from ASTM Specs unless otherwise noted. *Hydro Magnesium Data NS Not specified. 1 2

Fig. 1.1  Finite element model of the engine block (17,387 grid points and 11,349 solid elements, HEXAS and PENTAS).

AE-29_Ch01.indd 8

Fig. 1.2  Finite element model of the transmission (1540 grid points and 1472 elements, mainly plate/shell type). 1-8

4/12/12 8:22:40 AM

Transmission Cases and Parking Mechanisms

1.1.5.5

Discussion of Results

Natural frequencies and mode shapes were computed without and with the cast oil pan to determine contributions of the oil pan as a structural member. A comparison of the natural frequencies is shown in Table 1.3. The addition of the oil pan results in a natural frequency increase of about 103 Hz in the first mode, 116 Hz in the second mode, and 99 Hz in the third mode. The mode shapes for the first two modes are shown in Figs. 1.5 through 1.8, using simplified display models. The undeformed shape is shown by solid lines and the deformed shape is represented by dotted lines. Figures 1.5 and 1.6 show the first and second mode shapes of the powertrain without the oil pan. The first mode is torsional and the second mode is vertical bending in nature. Corresponding mode shapes with the oil pan are shown in Figs. 1.7 and 1.8. Since the oil pan provides significant stiffness, it is not surprising that the mode shapes are changed. The first mode is lateral bending and the second mode is vertical bending.

Fig. 1.3  Finite element model of the aluminum-cast oil pan (2065 grid points and 2372 elements, mainly shell type).

Table 1.3  Computed Natural Frequencies of the Powertrain. Without Oil Pan Hz 259.25 286.24 354.16 495.99 564.47 572.38 680.26

Fig. 1.4  Finite element model of the powertrain assembly. 1.1.5.4

Analysis Details

Normal mode analysis was performed with the MSC/ NASTRAN finite element computer program using the substructuring (super-element) approach. A single-step Eigen-solution approach is not practical to obtain vibration modes and frequencies in models of this size, but the super-element method with Guyan reduction is a feasible solution technique. Although it requires a selection of ASET (analysis points) in the structure, it yields reasonably good results. In the previous Escort/Lynx powertrain analysis study, component mode synthesis was used along with the Guyan reduction approach. The two methods yielded nearly identical results. Because it was slightly easier to implement, the Guyan reduction solution technique was selected for further powertrain analysis work.

With Oil Pan Hz 361.87 402.40 452.96 608.70 633.22 695.93 726.85

Fig. 1.5  Dynamic display, powertrain assembly without oil pan, 1st mode (torsion).

1-9

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Design Practices: Passenger Car Automatic Transmissions

complex geometry. Alternatively, such components could be analyzed individually and the system response obtained by assembling component modal data through the component mode synthesis technique.

1.2 Parking Mechanisms A. Gupta F F Developments, Inc.

1.2.1 Introduction Parking mechanisms in automatic transmissions are designed to put the car into park position at a certain inhibiting speed varying from 1 to 5 mph. A typical parking mechanism is composed of the following main parts (see Fig. 1.9) : parking gear, detent lever with a detent lever spring, parking pawl with a torsion spring for pawl return, actuator rod with an actuator to move the pawl into engagement with the parking gear and a compression spring to load the actuator for engagement in a tooth butt condition, and a lockout spring and lockout plunger if the parking pawl is located above the parking gear, such as is a typical design for front-wheel-drive transmissions.

Fig. 1.6  Dynamic display, powertrain assembly without oil pan, 2nd mode (vertical bending).

The parking pawl normally pivots about a shaft which is held in the case. The torsion spring holds the parking pawl from going into engagement with the parking gear when the car is not in park (P) position.

Fig. 1.7  Dynamic display, powertrain assembly with oil pan, 1st mode (lateral bending).

The helical compression spring, also called an actuator spring, is designed under tooth butt condition (this is a condition when the pawl lines up with a gear tooth instead of a tooth space when the shift selector is moved to park (P) position). The actuator spring should be designed for a load which is enough to put the car in park (P) position at the required inhibiting speed. The lockout spring and lockout plunger locate the actuator rod when moving out of park (P) position. The spring load just needs to be enough to overcome friction of the plunger in its bore.

Fig. 1.8  Dynamic display, powertrain assembly with oil pan, 2nd mode (vertical bending). 1.1.5.6

The purpose of the detent lever spring is to allow the detent lever to remain in each notch position so that the manual valve in the valve body and the range selector lever on the steering wheel maintain their correct alignment.

Observations

The oil pan raised the natural frequencies of the assembly substantially and reduced relative amplitudes of vibration.

Parking mechanisms are normally designed to withstand transient loads imposed while putting the vehicle into park (P) when it is still in motion, or when bumped by another vehicle while in park (P).

The finite element models for these components were generated by different groups for different applications, and the powertrain assembly finite element model was a combination of the existing models. The engine block could have been modeled with coarse solid elements to obtain overall dynamic behavior with plate/shell elements and proper attention to its

The contact face angles on the parking pawl should be designed so that a spit out tendency exists on the parking 1-10

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Transmission Cases and Parking Mechanisms

1.2.2

pawl when the shift selector is taken out of park, even when the vehicle is parked uphill or downhill on a 30% grade.

Detent Lever Spring

The purpose of this spring is to allow the detent lever to remain in each notch position so that the manual valve in the valve body and the range selector lever on the steering wheel maintain their correct alignment. The load of the detent spring allows 50% safety factor in the design compared to the load of the actuator spring.

The mechanism should be designed to allow for over travel when the shift selector is put into park. In the event that a pawl tooth meets a gear tooth instead of a space, there should be a positive force on the pawl to allow for engagement as soon as the gear has rotated enough to expose a tooth space, and vehicle speed is less than the inhibiting speed stated above.

Calculations: Taking moments about the point where the detent lever is attached:

Parking mechanisms for front- and rear-wheel drives are essentially identical. In most front-wheel drives, the parking pawl is mounted on top of the transmission. This is mainly due to the fact that it is easier to have access to the linkage in front-wheel drives if the pawls are on top of the transmission. In this case, care must be taken to include the effect of gravity while designing the mechanism. In rear-wheel drives, the parking pawl is generally mounted at the bottom of the transmission, in which case the effect of gravity of the pawl may be ignored.

Fh ¥ R 2 = Pact. spring ¥ R 1



(1.1)

where: Fh = horizontal force on the spring. R2 = distance from the point where the horizontal spring force acts to the point where the lever is attached. Pact. spring = load on the actuator spring. R1 = distance from the point of application of the load to the point where the lever is attached. With 50% safety factor: ⎛ R ⎞ Fh = ⎜Pact.spring × 1 ⎟ × 1.5 R 2 ⎠ ⎝





(1.2)

The installation stress and installation deflection can be calculated from the formulas depending on the type of spring used. Total Deflection = Deflection at the installed position + Rise of the spring At the full deflection, the maximum stress should be below the minimum yield stress for the spring material. Spring design: the spring should be designed in the space available. Existing designs use flat cantilever springs or a combination of small lever and compression spring.

1.2.3

Parking Pawl Return Spring

Parking pawl return spring should be designed to withstand the torque required by it to prevent pawl butting on tooth tip under 2 g acceleration. For torque calculations, the weight of the parking pawl and the reaction of the parking sprag rod assembly on the pawl should be considered.

Fig. 1.9  Parking lock pawl and actuator assembly.

Methodology: Pawl weight:  Weight of the pawl, W1 = Pawl Area ¥ Width ¥ Density of pawl material 1-11

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Design Practices: Passenger Car Automatic Transmissions

Actuator rod weight: 

for the pawl to engage with the parking gear is calculated. Consequently the load on the actuator spring is determined, and the spring is designed for that load.

 e weight of the actuator rod is calculated Th by multiplying the volume of each part of the rod with the density. The total weight of the rod is known. Let the total weight of the actuator rod be represented by WR.

Calculations: Load on the spring:

Calculation of the reaction at the pawl Rp:

Let Vt be the maximum velocity of the car at the time of engagement. Let rt be the radius of the tires. Angular Velocity of  the tires, Wt =

Assume that the tooth form is involute.

Then,

Let T1 be the thickness at the pitch diameter D1 be the pitch diameter Φ1 be the pressure angle

(1.3)

Taking moments about RA,

Pitch radius r1 =

Weight of each part of the actuator rod × Distance from point A = Rp × Distance from point A (rp).

Major radius =

Due to sudden bumps or shock loads on the vehicle, take the effect of acceleration due to gravity as 2 g.

cos Φ 2 =

(1.4)

where:  k = Radius of gyration of the parking pawl. Therefore, torque can be calculated.

r1 cos Φ1 r2

⎛ r cos Φ1 ⎞ Φ 2 = arc cos ⎜ 1 ⎟ ⎝ r2 ⎠



(1.6)

⎛ T ⎞ T2 = 2r2 ⎜ 1 + Inv Φ1 − Inv Φ 2 ⎟ ⎝ 2r1 ⎠

Spring design: Knowing the torque required by the spring, the spring could be designed by referring to the Associated Spring Design Handbook, or any comparable reference source such as the SAE Spring Design Manual, AE-21, and following the design procedure.

Now Space, I=

1.2.4

D2 2

Therefore:

Therefore: T = 2 [Wp ¥ k + Rp ¥ rp]

D1 2

If the Major diameter is D2:

Therefore, Rp is known.



(1.5)

Angular velocity of the parking gear, wp = wt ¥ d

Let RA be the reaction of the actuator rod at a point where it is linked to the detent lever.

Rp + R A = WR



Depending on the final drive ratio between the wheel axis and the parking gear axis, the angular velocity of the parking gear is calculated. If d is the final drive ratio:

Fig. 1.10  Reaction at the pawl.



Vt rt

Actuator Spring

Major dia. × π − Tooth thickness N

Angular displacement, θ =

The actuator spring is mounted on a park actuator rod and is designed under a tooth butt condition. The load on the actuator spring is calculated assuming that the pawl engages with the parking gear at a speed not more than the inhibiting speed. At the inhibiting speed, the acceleration required



Time, t1 =

θ w

I r2

(1.7)

1-12

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Transmission Cases and Parking Mechanisms

If t is the time taken by the gear to travel distance l:

Spring design: knowing the load required by the compression spring, the spring could be designed by following the design procedures given in the references mentioned.

Length of the parking pawl tooth = s Linear velocity of the parking gear, vp = r2 ¥ w

t2 =

s vp

1.2.5

(1.8)



The lockout spring and the lockout plunger position the actuator rod when the detent lever is moved out of the park position (see Fig. 1.11). This mechanism prevents the actuator rod from falling down and inadvertently trying to apply the parking pawl when in some other manual detent position. It is used when the parking pawl is located above the parking gear, which is a typical design for front-wheel-drive transmissions.

Difference in time, t = t1 − t2 For the parking pawl to engage with the parking gear, the radius of the pawl should fall below the chamfer on the gear. Under tooth butt condition, the parking pawl should travel a distance s2 equal to the sum of radius on the pawl and the chamfer on the gear in time t, so that the engagement is made effective.

Spring design: The spring can be designed by following standard spring design formulas.

2s Acceleration required by the pawl, a = 22 t

Angular Acceleration required by the pawl, α =

Lockout Spring

a r

where r = distance from the center of rotation of the parking pawl.

Torque T = Jα = Fr

(1.9)

where J = mass moment of inertia of the parking pawl. Therefore, normal force on the pawl can be calculated. Depending on the ramp angle on the actuator spring, the vertical and horizontal component of the force on the actuator spring can be calculated.

Fig. 1.11  Lockout spring and parking rod interaction.

Let the horizontal component of force be given by Fh. Therefore, the actuator spring should be allowed to withstand a load of Fh.

1-13

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Chapter 2

Torque Converters and Start Devices Introduction

to the authors of these white papers. Special recognition is given to the editor of this subject matter in the preceding AE publication: Leo G. Steinl, AE-18 Chapter 2, Torque Converters. Mr. Steinl’s work has helped define the structure and content of this chapter.

The primary purpose of a start device is to accelerate the vehicle from rest. In a manual transmission, this is accomplished by the driver through a controlled slipping of the input clutch. In automatic transmissions this function has traditionally been given to the torque converter.

John M. Kremer

At the core of its functioning, the torque converter is a closedcircuit fluid coupling. Fluid in the impeller is centrifugally accelerated by the vehicle’s engine and is directed toward the turbine. The turbine accepts the fluid and imparts much of its kinetic energy to the transmission input shaft, then directs the fluid back toward the impeller. In simple fluid couplings, the fluid then re-enters the impeller directly, and in doing so the remainder of the fluid’s kinetic energy works against the momentum of the impeller. This undesirable characteristic of a fluid coupling is addressed in torque converter design with the addition of the reactor. The reactor redirects the fluid from the turbine so that its residual kinetic energy adds to that of the impeller, which increases the system torque. This torque multiplication is greatest at stall conditions and decreases to unity at the coupling speed (i.e., when impeller speed equals turbine speed).

The fluid coupling was used later as a shifting clutch in passenger car transmissions starting in 1955. In 1960, a transmission was introduced in which the same hydrodynamic unit was used as both the primary drive unit and as a shifting clutch.

This chapter is a compilation of technical papers that address design and analysis topics of torque converters and fluid couplings. Credit for the content of this chapter goes exclusively

This type of hydrodynamic unit is extremely versatile. The two-member drive coupling and shifting coupling are discussed.

2.1 Fluid Couplings J. W. Qualman and E. L. Egbert Hydra-Matic Div., General Motors Corp. Fluid couplings have been used as the primal hydrodynamic drive unit for passenger car fully automatic step-gear transmissions since 1939, and somewhat earlier as a starting device, between the engine and conventional clutch in a three-speed synchromesh transmission.

2-1

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Design Practices: Passenger Car Automatic Transmissions

2.1.1

Rg = radius (or distance) from axis of rotation to any point on design path rg = radius of design path circle (or instantaneous radius for design path curve) rs = radius of shell circle or instantaneous radius for shell curve S = spin or whirl velocity, tangential component of absolute velocity, ft/s T = torque, lb.-ft. Ti, TT = torque on impeller, torque on turbine Tin, Tout = input, output torque TH, TM = torque in hydraulic, mechanical path Tint, TS = torque on internal, sun gear U = linear or tangential velocity of point on a blade, ft/s w = angular velocity, rad/s XS = horizontal distance from vertical toric section centerline to any point on shell curve

Nomenclature

A = area, normal to axial plane, ft2 Ao = area of outermost fluid flow path AI = area of innermost fluid flow path ā = fluid flow angle relative to reference plane (may differ from blade angle a) ai, ai¢ = impeller exit, impeller entrance blade angles aT, aT¢ = turbine exit, turbine entrance blade angles C = capacity constant or coefficient CF = flow loss coefficient, dimensionless CA = variable area correction factor, dimensionless D = nominal diameter, max. diameter of flow path, ft d = density of fluid, lb/ft3 E = efficiency, % F = fluid velocity in axial plane, ft/s g = gravity constant, 32.2 ft/s/s H = head, ft Hi, HT = head of impeller, turbine HC = circulation head HSh = shock head HL = head loss hpin, hpout = input, output horsepower hpH, hpM = horsepower in hydraulic, mechanical path K = capacity factor (N/ T ) K = unit diameter capacity factor (KD5/2) M = mass flow, lbm/s Mm = moment of momentum, ft2/s N = angular speed, rpm Ni, NT = angular speed of impeller, turbine Nin, Nout = input, output speed NH, NM = speed in hydraulic, mechanical path n = speed ratio (NT ÷ Ni) nint, nS = number of teeth on internal, sun Q = quantity of fluid flow, ft3/s R = radius, ft RS = radius (or distance) from axis of rotation to any point on shell curve RSO = outermost shell radius RSI = innermost shell radius RC = radius (or distance) from axis of rotation to any point on core curve or to core point for coreless coupling RCO = outermost core radius RCI = innermost core radius Ro = outer radius on design path RI = inner radius on design path

2.1.2

Two-Member Drive Coupling

This is the most common type of fluid coupling and consists of an impeller and a turbine contained in a suitable housing (Fig. 2.1.1). It generally is used to replace the conventional friction clutch employed with synchromesh transmissions. It transmits the engine torque to the transmission. It may be connected directly to the engine, thereby transmitting full engine torque, or it may be under-driven or over-driven by functionally placing a gear-set between it and the engine, thereby transmitting more or less than engine torque. Torque is transmitted at a ratio of 1:1 through this drive coupling.

Fig. 2.1.1  Typical two-member fluid coupling.

2-2

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Torque Converters and Start Devices

2.1.2.1

Design Requirements

Rearranging, we get:

1. Stall torque capacity must be chosen such that vehicle creep at engine idle speed is acceptable and full-throttle stall speed is sufficiently near the engine torque peak to provide near-maximum starting torque without objectionable engine noise level. 2. The coupling must be capable of reaching high efficiency at low vehicle speeds to provide good fuel economy. 3. The coupling must be of sufficient size to do the job acceptably and small enough to fit the space provided. 4. The coupling must be designed for ease of manufacture and low cost. 5. The coupling must be of durable design to last the life of the transmission. Meeting all of these requirements usually means some extremely fine compromises and necessitates balancing of the design.

H=



Tw dQ

(2.1.1)

The torque on a hydrodynamic member is equal to the mass flow per unit time, times the differential moment of momentum across the member. This gives: T = M ( ΔM m )



(2.1.2)

Moment of momentum is equal to tangential velocity times radius: M m = SR

Also:

M=



dQ g

(2.1.3)

Therefore, Eq. 2.1.2 may be rewritten as: 2.1.2.2

Basic Theory and Formulas

The theory to be presented here assumes that the mean effective flow follows a curve, called the design path, which is a closed curve connecting all the points representing the radii of gyration of each successive section (frustrum of a cone) around the toric shape. The direction of fluid flow in this plane (plane containing the axis of rotation), then, is always tangent to this path. If this curve (design path) is a circle, then the flow front may be pictured as progressing around the section as the hand of a clock having a center at the center of this circle. Another assumption is that the discharge radius of one member is equal to the entrance radius of the adjacent member (Fig. 2.1.2). The equation relating shaft horsepower to hydraulic horsepower is: Tw HdQ = 550 550

T=

dQ (S R – S R ) g 1 1 2 2

(2.1.4)

Let us assume that the coupling has straight and radial (or 90°) blades. Then the whirl velocity S will be equal to the linear velocity U of a point on the blade, since there is no component of the flow velocity F in the tangential direction: S = U



(2.1.5)

Considering the impeller first, the torque that must be impressed on the impeller (from an external source), or on the fluid by the impeller, is equal to the mass flow per unit time multiplied by the difference in moment of momentum of the oil leaving and entering the impeller. From Eqs. 2.1.4 and 2.1.5, we get:

Ti =

dQ (Ui0R 0 − UT1R I ) g

(2.1.6)

Substitution in Eq. 2.1.1 gives:

Hi =

wi (Ui0R 0 − UT1R I ) g

Expanding this gives: Fig. 2.1.2  Two-member fluid coupling with core ring.



1 Hi = g (Ui0 R 0 w i0 − U TI R I w iI ) w i0 =

Ui0 U and w iI = iI RI R0

2-3

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Design Practices: Passenger Car Automatic Transmissions

Substituting again: Hi =

1 2 1 Ui0 − U TI UiI ) = (2Ui20 − 2U TI UiI ) ( g 2g

In the simple fluid coupling dealt with here, there are two shock losses, the impeller to turbine shock loss HSh(i – T), and the turbine to impeller shock loss HSh(T – i). From Eq. 2.1.12 we get:

(2.1.7)

Similarly, the torque impressed on the turbine by the fluid is equal to the mass flow per unit time multiplied by the difference in moment of momentum of the fluid entering and leaving the turbine. TT =



dQ (Ui0R 0 − UTIR I ) g

HSh(i − T) = =



(2.1.8)

HSh(T − i) =

and: 1 HT = (Ui0 R 0 w T0 − U TI R I w TI ) g



w T0 =





1 (Ui UT − U2T1 ) = 2g1 (2Ui0UT0 − 2U2TI ) g 0 0

(2.1.9)

Since the impeller head Hi represents the total energy put into the system, and the turbine head HT represents the total energy taken out of the system:

HL = Hi − H T

HL = HSh − HC





(2.1.11)

HC =



C FF 2 2g

(2.1.16)

2 1 ⎛ 2Ui0 − 2U TI UiI ⎞ HL = Hi − H T = ⎜ ⎟ 2g ⎜⎝ −2Ui U T + 2U T2 ⎟⎠ 0 0 I

=

(2.1.17)

2 2 2 2 1 ⎛ Uio + U To + U TI + UiI ⎞ C FF 2 ⎜ ⎟+ 2g ⎜⎝ −2Ui U T − 2Ui U T ⎟⎠ 2g o

o

I

I



(2.1.18)

Equating Eqs. 2.1.17 and 2.1.18 and rearranging:

C FF 2 = Ui20 − Ui2I − U 2T0 + U 2TI

(2.1.19)

The value of CF must be determined empirically, or assumed, to permit a solution of all the coupling equations and the resultant determination of the coupling’s torque capacity at various speed ratios. The usual practice is to select some constant-input torque and solve for the impeller (input) speeds at stall and several other speed ratios. Assuming that we have established that

In our case, S = U, so:

(2.1.15)

HL = HSh + HC

(S1 – S2 represents the differential tangential velocity) 1 (U1 − U2 )2 2g

2 2 2 2 1 ⎛ Ui0 + UiI + U T0 + U TI ⎞ HSh(total) = ⎜ ⎟ 2g ⎜⎝ –2Ui U T – 2U T Ui ⎟⎠ 0 0 I I

From Eqs. 2.1.11, 2.1.15, and 2.1.16:

1 2 = (S1 − S2 ) 2g

HSh =

(2.1.14)

From Eqs. 2.1.10, 2.1.9, and 2.1.7:

(2.1.10)

Shock loss may be considered to be an impact loss. It is caused by the change in tangential velocity of the oil as it passes from one member to another, or the loss of kinetic energy due to the change in velocity. The term “shock loss” generally is used in hydraulic texts to describe the loss inherent with a sudden change in velocity. The loss is believed to be due to the generation of a whirlpool or eddy effect caused by the rapid turning of the fluid stream. These eddies constitute a loss, because the fluid has internal friction characteristics. Theoretically, this loss is: HSh

1 (UTI − UiI )2 2g



The loss head HL is broadly divided into two categories—the shock head HSh and the circulation head HC.

(2.1.13)

The circulation loss may be likened to the friction loss of a fluid flowing through a pipe or channel. This loss is proportional to the square of the velocity and is commonly taken as:

This gives: HT =

1 2 (Ui − 2Ui0UT0 + U2T0 ) 2g 0

1 2 (UTI − 2UTIUiI + Ui2I ) 2g

=



U T0 U and w TI = TI R0 RI

2 1 Ui0 − U T0 ) ( 2g

(2.1.12) 2-4

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Torque Converters and Start Devices

T = CN2D5 for each speed ratio, an efficiency curve may then be plotted for any constant or variable-torque curve by using either the log-log plot or K-factor methods described in Section 2.3.

Another method that can be used is to make a trial-anderror head balance until Eq. 2.1.10 is satisfied. This method is used particularly when the blade angles are other than 90°, since the equations become quite burdensome. An assumption of the value of F is made, permitting a value for Ni to be obtained from Eq. 2.1.21. The circulation head is then calculated from Eq. 2.1.16, and the shock head is calculated from Eq. 2.1.15. The impeller and turbine power heads can readily be calculated from Eqs. 2.1.24 and 2.1.25, which will be developed here.

To demonstrate a method of solution for a coupling: Substituting U = 2πRN / 60 and Q = AF in Eq. 2.1.6 gives: Ti =



dAF ⎛ Ni N ⎞ 2 − 2πR I2 T ⎟ ⎜⎝ 2πR 0 g 60 60 ⎠

Substituting Q = AF and w = 2πN / 60 in Eq. 2.1.1 gives:

Since NT = nNi: Ti =

=

⎞⎤ R o2nNi ⎟⎥ 2 R o / R i ⋅ 60 ⎠ ⎥⎦

⎛ dAF ⎡ ⎛ Ni ⎞ ⎢2πR o2 ⎜ ⎟ − 2π ⎜ ⎝ 60 ⎠ g ⎢⎣ ⎝(



)

⎞ dAF ⎛ Ni ⎞ ⎛ n 2 ⎜⎝ 2πR o ⎟⎠ ⎜1 − 2⎟ g 60 ⎝ (R o / R i ) ⎠



Ti g ⎞ ⎛ n 2 ⎟ 2πR 0dAF ⎜1 − 2 ⎜ ⎛ R0 ⎞ ⎟ ⎜ ⎜⎝ R ⎟⎠ ⎟⎠ ⎝ I

(2.1.20)





2.1.2.3



2

⎤ ⎡⎛ ⎞ 1 2 ⎢⎜1 − 2 ⎟ (1 − n )⎥ (R o / R I ) ⎠ ⎥⎦ ⎢⎣⎝

(2.1.24)

HT =

2πN T TT 60dAF

(2.1.25)

Coupling without Core Rings (Coreless Coupling)

The torque capacity for a given set of dimensions for the outer shell will be larger if the void space within the core ring is utilized. In other words, the larger the flow area for a given diameter (design path) and Ro/RI ratio, the higher the capacity (Eq. 2.1.20).

Using Eq. 2.1.21 and NT = nNi, Eq. 2.1.22 may be expanded and rearranged to yield: 1 ⎡ gTi ⎤ ⎥ ⎛ ⎞ CF ⎢ n ⎢ R odA ⎜1 − ⎥ ⎢⎣ (R o / R I )2 ⎟⎠ ⎥⎦ ⎝

2πNi Ti 60dAF

With either method, the validity of the solution will, of course, depend on having chosen the proper flow loss coefficient CF.

2 2 ⎤ ⎡⎛ Ni ⎞ Ni ⎞ ⎛ 2 R 2 R − π π ⎥ ⎜⎝ ⎟⎠ ⎢⎜⎝ ⎟⎠ 0 I 60 60 ⎥ ⎢ 2 C FF = ⎢ 2 2⎥ ⎢− ⎛ 2πR NT ⎞ + ⎛ 2πR NT ⎞ ⎥ (2.1.22) ⎜⎝ ⎟ ⎟ 0 I ⎢⎣ ⎜⎝ 60 ⎠ 60 ⎠ ⎥⎦

F4 =

Hi =

If F is properly chosen, the impeller head Hi will be equal to the sum of turbine head HT, circulation head HC, and shock head HSh. With some experience, the heads can be balanced with a few trials.

(2.1.21)

Eq. 2.1.19 may be expanded to:



2πNT 60dAF

This equation holds for all members of a hydrodynamic drive unit. It follows that:

Rearranging: Ni = 60

H=

Looking at Fig. 2.1.2, let us increase the flow area by shrinking the inner core smaller and smaller until it becomes a single point. Then RCo = PCI = RC. This point RC is also the center for the design path circle. Incidentally, the circular design path is the only one that will permit shrinking the core to a point, since all normal lines drawn from the design path must converge at the core (point).

(2.1.23)

Eq. 2.1.23 may be solved for any given input torque Ti and speed ratio n, because all other terms are constant for a particular coupling. Having thus found the flow velocity F, the impeller speed Ni may be determined from Eq. 2.1.21.

Our coreless coupling is shown in Fig. 2.1.3. For this coupling,

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This torque capacity Eq. 2.1.20 then becomes:

A0 = π (R S20 − R C2 ) (neglecting blade thickness) (2.1.26)

4π 2dF i R 04Ni ⎛ ⎜1 − Ti = 60g ⎜⎝

Since Ro is the radius of gyration for the annular area bounded by RSo and RC:

2.1.2.4

When a core is used, there are infinite numbers of shapes that satisfy the theory presented here. The design path could have any shape, as long as Ro and RI were the proper values; the flow area could be constant or variable (with 90° blades), resulting in an unlimited number of possible shapes for the shell and core. It has been common practice, however, to make the toric section essentially circular. Some designs have been made with the shell a perfect circle, others with the design path a perfect circle. Theoretically, it is possible to make any two of the curves (shell, design path, and core) as circles, with the third curve determined by simultaneous solution of the area and radius of gyration equations.

Substituting in Eq. 2.1.26: A0 = 2π (R 02 − R C2 )

(2.1.28)

Also: R0 –

R – R1 R R C = R1 + 0 = R 00 + 2 RI

( )

=

R0

( ) R0 RI

= R0

+

R0

( )–R 2( ) R0 RI

2

R0

( ) R0 RI

0

R0 RI

For simplicity, we will choose a toric section in which the design path is circular and the flow area is constant (neglecting blade thickness).

R0 RI

( )–1 ( ) 2( ) 1

+

R0 RI

R0 RI

(2.1.29)

To proceed:



1. Divide the design path into angular increments. 2. At each increment, calculate the value for Rg (a simple procedure with a circular design path). 3. At each increment, make a simultaneous solution of the area and radius of gyration equations.

Substituting Eq. 2.1.29 in Eq. 2.1.28: A0 =

⎡

2πR 02 ⎢1 − ⎢ ⎣

{ } { }

2 ⎛ RR0 + 1⎞ ⎤ I ⎜ ⎟ ⎥ R0 2 ⎝ ⎠ ⎥⎦ RI

Determining Shell and Core Curves

Core Contour

R S20 + R C2 or R S20 = 2R 02 − R C2 (2.1.27) 2



{ }

It can be seen from Eq. 2.1.31 that the desired stall torque capacity can be obtained by many combinations of Ro and Ro/RI values, Ro being smaller when Ro/RI is larger. The best choice, however, will be the largest Ro/RI value permitted by the physical limitations of the design. (The inner shell radius RSI must be large enough to permit sufficient hubs and shafting, and total width, which increases with Ro/RI, may be a factor in length required for installation.) This is because of the fact, as can be shown, that for a given stall torque capacity, the capacity at any other speed ratio is higher as the Ro/ RI value is higher.

Fig. 2.1.3  Two-member coreless fluid coupling.

R 02 =

{ } { }

2 R ⎤ ⎡ n ⎞ ⎢ ⎛ R0I + 1⎞ ⎥ ⎟ 1− ⎜ (2.1.31) ⎟ R0 R0 2 ⎟ ⎢ ⎥ ⎠ ⎣ ⎝ 2 RI ⎠ ⎦ RI

(2.1.30)

The outer flow area Ao (and also the inner flow area AI) is now determined when values for Ro and Ro/RI are chosen. The value of Ao from Eq. 2.1.30 may now be substituted in Eqs. 2.1.20 or 2.1.21 and Eq. 2.1.23 for solution of this type of coupling.



R 2g = A=

R 2s + R c2 2

π (R12 − R 22 ) sin α

where:

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α = cone angle measured from axis of rotation R1 = outer cone radius (may be either RS or RC) R2 = inner core radius (may be either RS or RC)

represent the angle between the vertical torus centerline and any position of the generating line or ray. Also, let Rg equal the radius from the axis of rotation to the intersection of the design path and the ray. Let rg equal the radius of the design path circle and RS equal the radius from the axis of rotation to the intersection of the shell curve and the ray.

4. Plot the calculated points on an oversize layout and determine, by trial and error, a series of arcs passing through the points. Shell Contour



For a coupling such as shown in Fig. 2.1.3, the selection of the Ro/RI value will automatically determine the shell contour. The various geometric relations for such a coupling will first be developed, followed by the procedure for determining the shell contour.



rg =

R0 − RI 2

R g = R c + rg cos θ Rs =

2R 2g − R c2

For convenience and better accuracy as θ approaches zero and 180°, a horizontal distance XS from the toric centerline also is calculated.

By definition, the design path is a closed curve representing the loci of the radii of gyration of all sections of the toric section. In this coreless coupling, this curve is a perfect circle whose center is also the core point for the torus. The entire toric section may be generated by sweeping a line, one end of which is fixed at the core point RC, through 360° while varying the length of the line to trace the shell curve in such a manner that a fixed intermediate point on the line will trace the curve of the radii of gyration. Referring to Fig. 2.1.4, let θ

X S = (R S − R C ) tan θ The shell curve is determined by calculating and plotting enough points to establish a smooth curve. An oversize layout is made, the points plotted, and a series of arcs is determined by a trial-and-error process to pass through the points. Of course, only 180° of the toric section need be calculated since

Fig. 2.1.4  Shell curve calculations. 2-7

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Design Practices: Passenger Car Automatic Transmissions

the section is symmetrical. Fig. 2.1.4 shows an example set of calculations. 2.1.2.5

Substituting Eq. 2.1.36 in Eq. 2.1.35, and Eq. 2.1.35 in Eq. 2.1.34:

Flow or Circulation Loss Coefficient CF

The flow velocity F is usually calculated at the outer flow area of the toric section. When the flow area is constant around the toric section, the flow velocity is constant, and Eq. 2.1.16 satisfactorily represents the circulation loss. However, if the flow area is variable, as in the case of the coreless couplings described in this chapter, the circulation loss should be expressed in terms of the average flow velocity Favg. The coefficient CF determined on this basis will be more consistent, regardless of whether the flow area is constant or variable.



⎡ 2 CA = ⎢ 2 ⎛ R 0 / R I + 1⎞ 1 ⎢ ⎢ ⎜⎝ 2{R / R } ⎟⎠ − (R / R )2 0 I 0 I ⎢1 + 2 ⎢ ⎛ {R 0 / R I} + 1⎞ 1−⎜ ⎢ ⎝ 2{R 0 / R I} ⎟⎠ ⎢⎣

⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦

2

(2.1.37)



See Figs. 2.1.5 and 2.1.6 for flow loss coefficients as determined from analysis of test data on various coupling designs.

Eq. 2.1.16 may be rewritten as: HC =



2 C FFavg 2g

(2.1.32)

It will be more convenient, however, if we use the flow velocity Fo at the outer flow area Ao and introduce a variable area correction factor CA. Eq. 2.1.16 may also then be written in a more general form as: HC =



C AC FF02 2g

(2.1.33)

Equating Eqs. 2.1.32 and 2.1.33:

Fig. 2.1.5  Flow loss coefficients for core ring type of fluid coupling.

2

⎛ Favg ⎞ CA = ⎜ ⎝ F0 ⎟⎠



(2.1.34)

The coefficients CF presented in this paper are determined from the general flow loss (Eq. 2.1.33). When the flow area is constant, the coefficient CA has a value of unity, as can be seen from Eq. 2.1.34. For coreless couplings with variable areas as described here, the coefficient CA may be determined as follows: Q = A0F0 = AavgFavg

Favg =

A0F0 A0F0 2A0F0 = = A A + Aavg ⎛ 0 A0 + AI I⎞ ⎟ ⎜⎝ 2 ⎠

(2.1.35)

Fig. 2.1.6  Flow loss coefficients for coreless type of fluid coupling.

The inner flow area AI may be expressed in terms of Ao and Ro/RI as:



{ } { } ( ) { } { }

⎡ ⎛ R 0 + 1⎞ 2 1 ⎢⎜ RI ⎟ − R 0 ⎢ ⎝ 2 RR0I ⎠ RI AI = ⎢ 2 ⎢ ⎛ RR0 + 1⎞ I ⎢ 1− ⎜ ⎟ R0 ⎢ ⎝ 2 RI ⎠ ⎣

⎤ ⎥ 2 ⎥ ⎥ A0 ⎥ ⎥ ⎥ ⎦

2.1.2.6

Unit Diameter Capacity Factors

A common method of expressing the torque versus speed relationship for fluid couplings and torque converters consists of plotting the capacity factor K = N/ T versus speed ratio. This is a very useful term for finding the speed for given speed

(2.1.36)

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ratios and input torque values or for comparing units of the same nominal diameter. This information, to be of value, must be accompanied with information as to the size of the unit, since the value of the capacity factor is a function of the diameter of the unit. If we wish to compare various hydrodynamic units of various sizes, it is much more informative to compare them on the basis of equal nominal diameters. This can be done by computing a capacity factor K = KD5/2 which eliminates the effect of the diameter. The factor K is equal to the capacity factor of a hydrodynamic unit of 1 ft. (or unit) diameter. We may thus refer to the factor K as the unit diameter capacity factor. It also has the characteristic shape of the input speed curve and is equal to 1/ C in the equation T = CN2D5.

Fig. 2.1.9  Unit diameter capacity factors for coreless couplings.

For this discussion, it will be more informative to compare various units on this basis. Figs 2.1.7 through 2.1.9 show the unit diameter capacity factors for various coupling designs.

2.1.2.7

Rate of Fluid Circulation

Some idea of the rate of fluid circulation in a fluid coupling may be interesting and useful. As an example, the 11.50-in.diameter unit, for which flow coefficients and unit diameter capacity factors are given in Figs. 2.1.5 and 2.1.7, has a flow velocity of 38.7 ft/s, or approximately 2350 gpm at stall, with an input torque of 150 lb.-ft. (and input speed of 825 rpm). The flow velocity varies directly with the speed, which in turn varies with the square root of the torque so that, at 300 lb.-ft., the circulation rate is 3320 gpm. 2.1.2.8

Fig. 2.1.7  Unit diameter capacity factors for core ring type of single coupling.

Effects of Angular Blades (other than 90°)

If the blades are inclined with respect to the axis of rotation, there is a component of the flow velocity F in the plane of rotation. This component must be taken into account in determining the whirl velocity S. With 90° blades, the whirl velocity S is equal to the tangential velocity of the blade U. But the tangential component of F must be added algebraically to U.

S = U + F cot ā

(2.1.38)

Eq. 2.1.4 then becomes: T=

dQ ⎡(U1 + F1 cot a1 )R 1 − (U 2 + F2 cot a2 )R 2 ⎤⎦ (2.1.39) g ⎣

Of course, the tangential component (F cot ā) must also be added to U in all other equations. By properly choosing the blade angles, these components can be canceled out in the shock loss expression, leaving only the U terms as in Eqs. 2.1.13 and 2.1.14. This can be done by making the exit blade angle of one member and the entrance blade angle of the next member equal.

Fig. 2.1.8  Unit diameter capacity factors for core ring type of double coupling.

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It can be seen from Eq. 2.1.39 that the torque capacity for a given Q, U, and R will be greater if ā1 is less than 90° and ā2 is greater than 90°. The flow Q may not necessarily remain the same as with 90° blades, but the net result of inclining the blades so as to induce tangential components of the flow velocity F, which are in the direction of impeller rotation at the impeller exit and opposite to impeller rotation at the turbine exit, is an increase in torque capacity for a given input speed and speed ratio. This can readily be accomplished by using flat (or plane surface) blades inclined to the axis of rotation and with the entrance and exit blade edges in radial planes containing the axis of rotation. For instance, if a flat (radial-edge) blade is used in the impeller so as to make the exit angle, say 60°, then the entrance angle will be 120°. If the turbine member is constructed identically (shell and blade relationship), the entrance angle will be 60° and the exit angle will be 120° (Fig. 2.1.10). A representative blade diagram for this coupling is shown in Fig. 2.1.11.

Fig. 2.1.11  Blade diagram for fluid coupling with flat angular blades.

If the members are to be die-cast, helical surface blades are used instead of the flat blades. The torque capacity can be duplicated by properly choosing the lead for the helix (Fig. 2.1.12). Figs. 2.1.13 through 2.1.15 illustrate the effect of angular blades on the torque capacity.

Fig. 2.1.12  Fluid coupling with helical blades.

Fig. 2.1.10  Fluid coupling with flat angular blades.

Fig. 2.1.13  Unit diameter capacity factors for flat angular blades.

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Fig. 2.1.16  Fluid coupling designed for automatic assembly.

Fig. 2.1.14  Unit diameter capacity factors for flat angular blades.

Fig. 2.1.17  Fluid coupling designed for hand assembly. 2.1.2.10 Charge Pressure—to Prevent Cavitation A positive-charge pressure usually is required in the coupling to prevent cavitation, which occurs whenever the vapor pressure of the fluid becomes greater than the static pressure. This phenomenon is most likely to occur during stall conditions where all of the input horsepower is being converted to heat.

Fig. 2.1.15  Unit diameter capacity factors for flat angular blades.

2.1.2.9

The presence of cavitation is evidenced by the occurrence of noise and by a drop in torque capacity, which, under normal operating conditions, would be proportional to the square of the input speed. Cavitation can be prevented if sufficient pressure is applied from an external source. The pressure required varies with the size of the coupling and the power being applied.

Methods of Fabrication

Fluid couplings commonly are made from aluminum diecastings or fabricated steel stampings. The steel stamping method is most commonly used because of low cost and flexibility of design. Blades with tabs are stamped from strip steel and inserted in punched slots in stamped shells and cores. The assembly is secured by rolling down the tabs. Copper brazing of the assembly is used where additional strength is required. Hubs are attached by welding, brazing, or riveting. For high-volume production, it is desirable to locate blade tabs and shell slots to permit use of simple automatic blade loading machines (Figs. 2.1.16 and 2.1.17).

Charging pressures used in current automotive applications vary from 30 to 180 psi. Figure 2.1.18 illustrates the effect of various values of charging pressure on torque capacity at stall. It shows the increase in torque capacity with increase in charging pressure of an 8.00-in.-diameter unit.

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2.1.2.13 Split-Torque Application The efficiency of a given fluid coupling varies inversely with the torque being transmitted at any given speed. Thus, if the torque input to the coupling can be reduced, efficiency can be increased, or a smaller coupling will give the same efficiency. This can be accomplished by splitting the torque; that is, transmitting part of the torque through the fluid coupling and the remainder mechanically through planetary gearing. The split-torque principle has been used widely in step-gear automatic transmissions with fluid couplings for many years and is now coming into use with torque converter transmissions.

Fig. 2.1.18  Effect of charging pressure on stall torque capacity.

To illustrate the principle, a simple form of split-torque arrangement is shown in Fig. 2.1.19. This illustrates the parallel paths of mechanical and fluid torque which are combined at the gear-set. If we assume that the number of teeth on the internal gear is twice the number of teeth on the sun gear, the hydrodynamic torque will be reduced to one-third of input torque, and the mechanical torque will be the remaining two-thirds of input torque. There are many other possible arrangements.

2.1.2.11 Oil Circulation for Cooling Fluid is circulated continuously through the coupling and cooled to keep the maximum oil temperature as low as practicable. This prevents rapid oxidation of the transmission fluid and reduces cavitation in the coupling, because cavitation is a function of vapor pressure, which increases with oil temperature. The rate of circulation depends on the application and varies from 0.5 to 3.0 gpm.

For a split-torque system as shown in Figs. 2.1.19 and 2.1.20, the following analysis is presented. There are two power and torque paths in this system—one hydrodynamic and one mechanical. Power and torque in the two paths are added together at the output shaft. Assuming no mechanical loss in the system:

2.1.2.12 Blade Spacing to Reduce Noise If both members of the fluid coupling have the same number of equally spaced radial blades, pulsations of the flow will occur due to the alternate registry of all blades, and then blades and spaces. This results in torsional fluctuations and noise. The simultaneous registry of all blades can be presented in several ways. One method that has been very successful is to use unequally spaced blades. Usually, the blade spaces are increased in equal increments in a quadrant system. The advantage of this method is that it permits manufacture and assembly of both members on the same tooling, because both members are identical until the hubs are attached.



Tin = Tout = TM + TH = Tint + TS



TM Tint nint = = TH Ts ns



⎛n ⎞ ⎛n ⎞ Tin = ⎜ int ⎟ TH + TH = TH ⎜ int + 1⎟ ⎝ ns ⎠ ⎝ ns ⎠ TH =



Another successful method consists of using different numbers of equally spaced blades in the two members. A difference of one or two blades has been very successful. This method is used where the two members differ considerably in design or method of construction, and particularly when one member is a casting.

Tin nint +1 ns

nint =2 ns

If

If

then

TH = 0.333 Tin

(2.1.40)

and

TM = 0.667 Tin

(2.1.41)

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Or, since all the power loss is in the coupling: hploss = E= Fig. 2.1.19  Simple split-torque system. =

2π (0.333Tin )(Nin − nNin ) 33,000

hpin − hploss × 100% hpin TinNin − 0.333TinNin (1 − n) × 100% TinNin

= (1 − 0.333 + 0.333n) × 100% = (0.667 + 0.333n) × 100%

It can readily be seen that the gain in efficiency over the straight coupling drive is twofold. The coupling efficiency is higher due to the reduced torque load, and the loss is a smaller percentage of the total input, since a portion is transmitted mechanically.

Fig. 2.1.20  Power flow in split-torque system. Since there is no slip in the mechanical path: NM = Nin



Again assuming no mechanical loss:

Fig. 2.1.21 shows the increase in efficiency for the split-torque arrangement, previously described, compared with the fluid coupling alone. The same fluid coupling and input torque are used in both cases. Fig. 2.1.22 shows the speed ratio of the coupling versus output speed in this same split-torque arrangement.

2πTM N M (0.667 ⋅ TinNin ) ⋅ 2π (2.1.42) = 33,000 33,000

hpM =

In the hydrodynamic path, this is a slip. The speed of the hydrodynamic path is equal to engine speed times the speed ratio of the coupling:

It is of interest to note here that when the output speed is zero, the turbine member is running backwards at twice the input speed because of the gear ratio. As the output speed increases, the negative speed ratio decreases to zero, and then the speed ratio increases in the positive direction. Thus, the stall condition of the coupling occurs at some output speed, depending on the capacity of the coupling and the input torque. This stall point of the coupling is known as the point of coupling reversal and, if encountered in the vehicle, is evidenced by some rather severe gyrations. It is therefore necessary to make all up-shifts into, and downshifts out of, this range at output speeds above this reversal point. If the vehicle were started from a standstill in this range, it would also have to pass through the point of –1 speed ratio. At this point, the centrifugal heads of the two halves of the coupling are equal, there is no flow of oil, no energy transfer, and thus a momentary loss of drive occurs.

NM = nNin

and



hpH =

2πTHNH (0.333 ⋅ TinNin ) ⋅ 2π (2.1.43) = 33,000 33,000

     hpout = hpM + hpH



hpout = 2πTinNin E= =



(Eq. 2.1.42 plus Eq. 2.1.43)

(0.667 + 0.333n) 33,000

(2.1.44)



hpout × 100% hpin TinNin (0.667 + 0.333n) × 100% TinNin

= (0.667 + 0.333n) × 100%



(same as Eq. 2.1.45)

(2.1.45)

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2.1.2.15 Tip Bending of Blades It is shown in section 2.1.2.8 that considerable difference in torque capacity can be obtained in the same size coupling by using blade angles other than 90°. This effect can be obtained to some degree by simply bending the tip ends of the blades on sheet-metal fabricated units (Fig. 2.1.23). By this means, the same basic coupling design may be modified readily to suit several applications. This method is especially adaptable to mass production. Figures 2.1.24 and 2.1.25 illustrate the effect of tip bending in increasing both the stall capacity and efficiency of the fluid coupling.

Fig. 2.1.21  Efficiency comparison, split-torque versus straight coupling drive.

These curves compare the characteristics of an 11.5-in.diameter coupling with 90° blades and those of the same coupling with the outer tip ends of the blades bent to 65° in the impeller and turbine. Of course, the opposite effect would be obtained if the blades were bent in the opposite direction, or if the direction of rotation was reversed.

Fig. 2.1.22  Coupling speed ratios in split-torque system. 2.1.2.14 Hydraulic Forces in Coupling Fig. 2.1.23  Tip bending of blades.

One of the major forces to be concerned with is the piston force tending to separate the two halves of the coupling housing. This force is the result of the static, or charging pressure, plus the centrifugal pressure due to rotation of the housing, acting on the piston area of the housing. In large-diameter couplings, or couplings with high charging pressures, this force can be quite large, necessitating substantial design of the joint to prevent separation and oil leakage. This force also causes ballooning of the housing, which must be kept within reasonable limits. Axial thrust forces are the result of differential areas, centrifugal pressure gradients, and turning or redirecting the oil within the coupling in the longitudinal plane. These forces can be substantially self-contained within the coupling, and provision of adequate thrust washer area usually is not a great problem. There are conditions, however, when some of these forces can be transmitted to members outside the coupling, and they must be taken into account in the design of other thrust bearings. The major problem here has been with engine crankshaft thrust bearings.

Fig. 2.1.24  Stall torque capacity comparison, showing effect of tip bending.

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filled with fluid, and creep torque is reduced. An anti-drag baffle also is used in this coupling to reduce further the idling drag or creep torque. The baffle effectively impedes the fluid circulation at stall when the flow velocity is high but does not materially impede the circulation at high rotative speeds when the flow velocity is low.

Fig. 2.1.25  Efficiency comparison. 2.1.2.16 Number of Blades and Thickness The optimum number of blades has been determined to be approximately three blades per inch of nominal diameter. The thickness of the blade is, of course, dependent mostly upon the strength requirements, or methods of manufacture. Steel stamped blades generally range 0.040 to 0.050 in. in thickness. In cast members, the thickness usually is determined by the caster’s ability to fill the mold or die cavity. Die-cast blades usually need to be about 0.060 in. at the blade edge with 1° to 2° draft on each blade surface.

Fig. 2.1.26  Reservoir type of fluid coupling.

2.1.3

Shifting Coupling

Fluid couplings also are used for shifting, and a typical current-production unit of this type is shown in Fig. 2.1.27. As the name implies, the shifting coupling is a fluid coupling used to accomplish a shift from one ratio to another in step gear automatic transmissions. As such, it is comparable to and replaces a friction clutch within the transmission. Engaging and disengaging is accomplished by filling and emptying the working fluid. It has the ability to absorb more energy than a friction clutch and thus permit a smoother transition from one ratio to another (Fig. 2.1.28).

2.1.2.17 Reservoir Fluid Coupling An early passenger car application of the reservoir type of fluid coupling is shown in Fig. 2.1.26. The principal difference between this coupling and other couplings described here is that the former has a reservoir space within the coupling housing and outside the toric section. There were two principal reasons for this design. 1. It permitted the use of a sealed and partially filled unit; the reservoir permitting space for expansion of the fluid as the temperature increased, and avoiding the development of excessive hydraulic pressures. 2. It permitted the use of a relatively large-diameter unit to give good cruising efficiency without excessive idling drag or creep torque. At high speeds, centrifugal force causes the fluid to be forced toward the outer periphery of the unit, completely filling the toric section and, therefore, permitting transmission of the maximum possible torque. At idling speeds, a larger portion of the fluid is contained in the reservoir space outside of the toric section. Thus the coupling is effectively only partially

Fig. 2.1.27  Typical shifting coupling. 2-15

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Design Practices: Passenger Car Automatic Transmissions

these valves. When the coupling shift valve moves to the fill position, as shown in Fig. 2.1.30, signal oil is directed to close the coupling exhaust valve. At the same time, the coupling feed oil is directed through the limit valve and through the coupling shift valve to fill the coupling. The limit valve ensures that the line pressure remains high enough to keep the coupling exhaust valves closed during the filling of the coupling. In order to make the shifting coupling satisfactory as a speed changing or shifting device, the filling and exhausting must be accomplished rather quickly. The fill rate necessary may be as high as 20 gpm. This requires a pump of very high capacity at fairly low speed. Common constant-displacement pumps of such capacity would be greatly over capacity at any time other than when the coupling is being filled and would cause unacceptably high transmission loss. For this reason, variable-displacement pumps generally have been used. In addition, generous and unrestricted fill passages must be provided. To ensure fast and complete exhausting of the coupling, the exhaust valves must be placed at or very near the periphery of the coupling members. If the exhaust valves are below the periphery of the coupling, some pumping means must be provided to exhaust this outer flywheel rim of oil. This has been accomplished with small blades on the outer surface of the turbine shell. The exhaust valve ports must be fairly generous in size. Angular ramps ending at an abrupt wall adjacent to the exhaust ports also have been used to aid the exhausting of the oil.

Fig. 2.1.28  Shifting characteristics, coupling versus band and clutch. 2.1.3.1

Design Requirements

Since this unit is used primarily to replace a friction clutch, it must have high capacity to provide good efficiency. It must be as small as possible due to the ever-present space problem and to require the minimum quantity of oil. The quantity of oil required is important, not only to ensure sufficiently fast filling with as small a transmission oil pump as possible, but because a breather and oil-level problem is created when the coupling is emptied. The capacity must be such that reasonably high efficiency is obtained at the minimum full-throttle speed at which the coupling is filled. Fortunately, the transmitted torque is usually a small fraction of engine torque, and the coast capacity requirement is small. This permits use of low blade angles to obtain high efficiency with small diameter. Adequate valving must be provided to obtain sufficiently fast exhausts for downshifts. The basic theory and formulas for designing shifting fluid couplings are the same as previously discussed for drive coupling. 2.1.3.2

Filling and Exhausting

Filling and exhausting of the coupling requires special controls. Figure 2.1.29 shows the environment of the controlling valves and the shifting coupling. Signal for fill or exhaust of this coupling is received from the coupling shift valve. This figure shows the coupling shift valve and coupling exhaust valve in the exhausted position, which closes off the flow to the coupling and exhausts the oil from the top of the coupling exhaust valve. This allows the coupling exhaust valves to move radially outward, exhausting the coupling directly through

Fig. 2.1.29  Shifting coupling and controlling valves.

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Torque Converters and Start Devices

H = head, ft

I = moment of inertia, slug ft2 Il = impeller

N = angular speed, rpm P = pressure, psf

R = radius of gyration, ft R1 = first reactor, etc.

r = gear ratio s = seconds

T = torque, lb.-ft.

Tl = first turbine, etc. t¢ = time, s

t = number of gear teeth V = velocity, ft/s

ω = angular velocity, rad/s

Fig. 2.1.30  Shifting coupling filled.

2.1.4

The multiturbine units to be discussed here are actually more than hydrodynamic torque converters. They are a combination of hydraulic members and mechanical gear trains, linked coaxially in such a way as to give the smooth torque characteristics of the pure hydraulic converter and also provide a combination of broad ratio coverage and high efficiency that has not been possible in a pure hydrodynamic converter.

Conclusions

The information presented here describes the basic types of units now in use and points out the considerations involved in their design. Every effort has been made to be as specific as possible, rather than to deal in general terms. In addition, we have tried to show the effects of varying the critical factors involved. This was done to serve as a guide where departure from the basic design may be necessary to accomplish the desired objectives, which vary for each installation. It is hoped that this information will enable the engineer to understand more fully the function and design of fluid couplings.

Black and Dundore [1] have shown that torque ratios as high as 7.0:1 are possible with three-element converters, but the peculiar speed characteristics and relatively low capacity of this type of converter limits it to commercial applications. Figure 2.2.1 shows a comparison of a high-torque-ratio, threeelement converter with a five-element, two-turbine geared converter. It can be seen that in this example the torque ratios at stall are very nearly equal, but the efficiency of the five-element geared converter rises more rapidly and peaks at a higher value than the three-element converter. Also, the geared five-element converter has a rising input speed with rising output speed, while the three-element converter has a falling input speed characteristic with rising output speed at the lower speed ratios. This latter gives an unusual feeling in an accelerating automobile, as though the engine were stalling or being loaded excessively.

2.2 Multiturbine Torque Converters F. H. Walker, Buick Motor Div., General Motors Corp.

2.2.1 Nomenclature A = net area, normal to converter axis, ft2 a = vane exit angle, degree

a1 = vane entrance angle, degree

b1 = relative entrance angle, degree

As a result of this characteristic of the high-ratio, three-element converter, all American transmissions known to the author with three-element torque converters use converters with ratios of 2.70 or less, and the majority use converters having stall ratios between 2.2 and 2.1. This requires that the three-element converter be combined in the transmission with a shifting gearset, resulting in either a two-speed or three-speed transmission.

C = constant

Cf = flow coefficient

Cs = shock coefficient

d = specific weight, lb.-ft.3

g = acceleration due to gravity, ft/s2

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Design Practices: Passenger Car Automatic Transmissions

Figures 2.2.3 through 2.2.7 show schematically four multiturbine torque converters which have been, or are currently in production in United States passenger cars. Figure 2.2.3 is a two-stage, two-phase, four-element torque converter having an impeller, two turbines connected together as one member, and one reactor. This was the first torque converter to appear in an American passenger car that incorporated more than one turbine, and the only one to have turbines connected as one member with a reactor between them. The converter was used in a nonshifting transmission; however, a governor-actuated direct-drive clutch, ahead of the converter, bypassed the fluid members soon after the coupling point was reached. Performance characteristics for this converter are shown in Fig. 2.2.4 [2]. Fig. 2.2.1  Comparison of performance characteristics of high-torque-ratio, three-element converter versus five-element, two-turbine geared converter.

Figure 2.2.5 shows a single-stage, three-phase, four-element torque converter having an impeller, two turbines, and one reactor. A planetary gearset links the first turbine to output while the second turbine drives to output directly.

Figure 2.2.2 shows the characteristics of a two-speed transmission having a three-element torque converter, versus a nonshifting transmission incorporating a five-element converter comprised of an impeller, two turbines, and two reactors.

Figure 2.2.6 is a single-stage, four-phase, five-element torque converter similar to the one shown in Fig. 2.2.5, except that a reactor has been added between the first and second turbines. Figure 2.2.7 is a single-stage, four-phase, five-element torque converter having one impeller, three turbines, and one reactor. The first and second turbines are geared at different ratios to the output shaft, while the third turbine is directly connected. Each of the hydromechanical units, or geared converters, shown schematically in Figs. 2.2.5 through 2.2.7 is used in a nonshifting transmission, and each has a smooth output torque characteristic as output speed is increased. Even though the geared turbines are connected to the output shaft by fixed-gear ratios, the hydraulic torques of the individual turbines increase and decrease smoothly due to their series or coaxial arrangement, adding together to give an output torque curve, unbroken and free from sharp bumps, and a smooth input speed characteristic.

Fig. 2.2.2  Comparison of performance characteristics of two-speed transmission, three-element converter versus nonshifting transmission, five-element geared converter. The main objective of the multiturbine converter is to provide a transmission requiring no shifts in a normal acceleration from a stop.

Fig. 2.2.3  Two-stage, two-phase, four-element converter with two turbines connected as one member.

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2.2.2

Operation of Converters

Figure 2.2.8 shows pictorially the four-element converter having one geared turbine and one direct turbine (schematic Fig. 2.2.5). In this converter, the oil travels outward through the impeller into the first turbine, inward through the second turbine, through the reactor, and back to the impeller. At stall, the oil leaving the impeller has a high tangential velocity component, thus entering the stationary first turbine as a revolving hollow cylindrical extrusion of oil. Since the tangential or rotating component of the velocity changes direction as it passes through the stationary first turbine, the rate of change of angular momentum is high, thus imparting to the first turbine a high mechanical torque. Fig. 2.2.4  Performance characteristics of two-stage converter referred to in Fig. 2.2.3.

Fig. 2.2.5­  Single-stage, three-phase, four-element converter with one geared turbine and one direct turbine.

Fig. 2.2.8  Cutaway drawing of four-element converter having one geared turbine and one direct turbine as shown schematically in Fig. 2.2.5.

Fig. 2.2.6  Single-stage, four-phase, five-element converter with one geared turbine and one direct turbine.

The oil enters the second turbine as it left the first turbine, with its tangential, or rotational, component opposite in direction to that of the pump or impeller. The oil leaves the second turbine as an extrusion of much smaller mean diameter, still having a tangential component rearward, but with less total momentum than the entering oil. The net effect is that the mechanical torque imposed upon the second turbine at stall is slightly negative, again being equal to the rate of change of angular momentum of the oil as it passes through this element.

Fig. 2.2.7  Single-stage, four-phase, five-element converter with two geared turbines and one direct turbine. 2-19

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Design Practices: Passenger Car Automatic Transmissions

From the second turbine, the oil enters the reactors, a stationary element of the converter grounded through a one-way clutch. As the oil passes through the reactor, it is again given a forward component tangential velocity, from which it passes on to the impeller. Mechanical torque transmitted from the reactor through its grounding shaft is negative, being opposite in direction to the rotation of the impeller.

first turbine, its torque is zero. At this point, the sun gear, which had been reacting through a one-way clutch, begins to free-wheel. This allows the first turbine to continue to turn at a speed at which it will not deflect the oil from the impeller. An interesting observation concerning this free-wheel point is that the first turbine actually overruns the impeller by about 35%.

The first turbine is mechanically connected to the ring gear of the planetary set. With the planet carrier acting as the output member, and the sun gear as reaction, the first turbine torque is multiplied by the planetary gear ratio to the output shaft. In this case, the gear ratio is found by the equation: r=

where:

t1 + t 2 t1

(2.2.1)

r = planetary gear ratio t2 = number of teeth on sun gear t1 = number of teeth on ring gear For our example, the ratio is:

r=

79 + 47 = 1.595 79

The second turbine is directly connected to the output shaft. Therefore, the total output torque of the converter at all speed ratios is represented by the equation:

T = r ⋅ TT1 + TT2

(2.2.2)

With the torque of the second turbine negative at stall, the algebraic summation at stall would be slightly less than the output torque contributed by the first turbine alone driving through the gearset. As the converter output speed increases, the speed of the first turbine driving through the planetary gearset increases at a higher rate than the second turbine by a factor of the geared ratio. Additionally, due to the relationship of the exit angles of the impeller and first turbine, the first turbine actually increases to a speed greater than that of the impeller. As the speed of the first turbine increases, the negative tangential component of the oil leaving it decreases, eventually passing through zero and then increasing in the positive direction. This means a decrease in the rate of change of angular momentum, thus a decreasing output torque of the first turbine. Figures 2.2.9A through 2.2.9C show pictorially what happens at various stages as the speed ratio increases. Eventually, the angular momentum of the oil leaving the first turbine is exactly equal to that leaving the impeller, as shown in Fig. 2.2.9C. With no change in angular momentum across the

Fig. 2.2.9  Vector diagrams of flow conditions at first turbine. 2-20

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Torque Converters and Start Devices

As the first turbine deflects the oil less and less, the tangential component of the oil entering the second turbine increases so that the rate of change of momentum across the second turbine is increasing. Thus, while the torque of the geared first turbine is decreasing, the torque of the second turbine is increasing. As the speed of the second turbine increases, the rearward component of the oil leaving the second turbine decreases, thus decreasing the change in momentum across the reactor and decreasing its torque. Figure 2.2.10 shows a plot of the output torques of the individual elements versus output speed for constant-input torque. Moving to the five-element converter shown schematically in Fig. 2.2.6, the significant change is the positive torque of the second turbine at stall, caused by the deflection of the oil through the first reactor. The gains caused by the addition of the first reactor wash out at approximately 0.35 speed ratio, after which the performance of the converter is nearly identical to the four-element converter. Figure 2.2.11 shows a plot of the individual torques of the elements of this converter. The losses at higher speed ratios due to the one additional free-wheeling element and the slight increase in flow path length are well compensated. The higher ratio coverage and improved efficiency at lower speed ratios contribute to improved feel in the passenger car installation.

Fig. 2.2.11  Torques of individual elements; five-element, two-turbine converter. Stall torque ratio can be increased further by the converter shown schematically in Fig. 2.2.7. In this arrangement, the first turbine driving through the planetary sun gear is geared to the output shaft at a ratio of 2.83:1. The second turbine is geared to the output shaft with a ratio of 1.55:1, using a gearset very similar to the two-turbine arrangement mentioned previously, except that the gears are located physically outside the converter housing. At stall, the oil passes outward through the impeller, entering the first turbine similarly to the other two converters previously explained. However, the torque transmitted to the output shaft will be higher because it is the product of the first turbine torque and the higher mechanical gear ratio. The torques of the second and third turbines are negative at stall but increase rapidly as the speed ratio increases. Figure 2.2.12 is a plot of individual torques of the five elements in this arrangement. It can be seen that output torque is derived mainly from the first turbine at stall and at lower speed ratios. At midrange speed ratios, the second turbine torque is most important, gradually fading out to the third turbine as coupling is approached. It should be noted that the total output torque progresses smoothly from one turbine to the next, somewhat approaching the ideal parabolic output curve of a 100% efficient torque converter, but still far enough below to challenge the torque converter engineer for several decades to come.

Fig. 2.2.10  Torques of individual elements; four-element, two-turbine converter.

Each of the three geared converters described has a torus diameter of 11.28 in. with a flow area of approximately 21 in.2 at the outside and 18 in.2 at the inside of the torus. 2-21

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Design Practices: Passenger Car Automatic Transmissions

the converter. A torque converter with the variable basic capacity has these main advantages: 1. In the high-capacity range, the tighter converter allows starts with a minimum of engine speed and fuss. 2. The high-capacity converter gives a very efficient coupling. 3. In the low-capacity range, engine speed is allowed to increase for high-performance starts, thus allowing more power input to the converter. 4. Extension of the torque multiplication range is increased to higher values of output speed in the low-capacity range. Production cars with high-performance engines and low axle ratios have had coupling points as high as 90 mph in this range. 5. A transition from the high-capacity converter to lowcapacity converter and vice versa can be very easily and smoothly accomplished. One recent production design incorporated a reactor in which the vane angle could be maintained at any position between the two extremes as a function of throttle angle. 6. Converter capacity can easily be tailored to the peculiar torque and speed characteristics of a particular engine or to the requirements of a particular vehicle.

Fig. 2.2.12  Torques of individual elements; five-element, three-turbine converter.

2.2.3

Varying Converter Capacity

Now that a very brief description has been made, we will look further at some of the more interesting details. In an effort to maintain the nonshift feature in the transmission and still compete with the high performance and efficiency of some of the shifting transmissions, it was necessary to find a method of varying torque converter capacity within an individual unit.

2.2.4

Performance Characteristics

Overall performance characteristics for each of the three geared turbine converters in their two extreme reactor positions are shown in Figs. 2.2.13 through 2.2.15.

When the converter capacity was high enough to give pleasing light-throttle starts and good highway cruising efficiency, the full-throttle performance was sadly lacking due to low engine speed and poor extension of the torque multiplication range. When performance was improved by decreasing the basic converter capacity, light-throttle feel and coupling tightness suffered. The controlled change in the exit angle of any element in the circuit could eliminate this dilemma. Needless to say, it would be very difficult to try to provide a control mechanism to change the exit angle of an element such as the impeller while it is in motion and loaded to full capacity. From both the hydrodynamic and the mechanical control standpoint, the reactor immediately preceding the impeller works very well in this role of varying the basic capacity of

Fig. 2.2.13  Performance characteristics of four-element, two-turbine converter (schematic Fig. 2.2.5).

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Torque Converters and Start Devices

input speed, which is, by definition, lowering the capacity of the converter. The second factor that works in favor of decreasing the converter capacity is that, as the reactor vanes are moved to the lower-angle position, they cause an increase in the restriction to converter flow. This higher restriction is shown by comparing Fig. 2.2.16A with Fig. 2.2.16B.

Fig. 2.2.14  Performance characteristics of five-element, two-turbine converter (schematic Fig. 2.2.6).

Fig. 2.2.16  Comparison of flow area in two extreme reactor vane positions. The impeller acts as a converter from mechanical power to hydrokinetic power; thus a quantity of mechanical energy will add a given amount of kinetic energy to a given quantity of fluid. If the quantity of fluid is decreased by external means, such as increasing the restriction to flow, more energy is added per unit to the fluid which does pass through the impeller. In this case, the only way in which the energy, or head, can be increased as the fluid passes through the centrifugal impeller is to increase its terminal velocity. Therefore, as restriction to flow increases, impeller speed must increase. Both the angular change of the reactor vanes and the increased restriction have combined to give increased impeller speed, or decreased converter capacity.

Fig. 2.2.15  Performance characteristics of five-element, three-turbine converter (schematic Fig. 2.2.7).

In terms of converter capacity, the two extreme reactor vane angles usually bracket what would otherwise be considered an optimum position. The actual vane profile cannot be optimized for both vane positions, so a balance must be reached. Past practice has usually favored the flat design preferred by the higher-capacity, higher-angle position.

In a typical installation, the reactor blade exit angles are 52°, as measured by SAE standard system B in the high-capacity, low-deviation position and 15° in the low-capacity, highdeviation position. This is illustrated in Fig. 2.2.16. As the vanes are shifted to the lowest-angle, high-deviation position, there are two basic reasons why the capacity of the converter decreases. First, the oil passing through the reactor is redirected to have a high tangential component in the direction of pump impeller rotation. Since the torque of the impeller is equal to the rate of change of angular momentum of the oil, then increasing the angular momentum at the impeller entrance for a constant-torque input merely increases the angular momentum at the impeller exit by the same amount. Thus, the impeller is applying its torque to the fluid at a higher

Looking now at the mechanical or control aspects of the twoposition reactor, Fig. 2.2.17 shows a schematic of the control mechanism. Each vane is mounted on a serrated crank, with the throws of the cranks retained by a groove in the reactor piston to maintain all of the vanes in the same angular position. For the higher-angle position, oil is fed through the control passage to the cylinder behind the reactor piston. The reactor pressure, being greater than the converter pressure on the opposite side of the piston, forces the piston rearward until it contacts the piston stop. To change the vane angle to

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Design Practices: Passenger Car Automatic Transmissions

the lower-angle position, the oil in the control cylinder is exhausted so that the converter pressure behind the reactor piston moves the piston forward until it contacts the lowerangle piston stop.

in any mechanical device, the algebraic summation of input energy, output energy, and losses is zero. The equation relating shaft power to hydraulic power is: (2.2.3)

Tω = HdQ

where:

T = torque, lb.-ft. ω = angular speed, rad/s H = head, ft d = fluid density, lb/ft3 Q = circulation flow, ft3/s Rearranging, we have: H=

Tω dQ

Since the impeller provides the only means of energy input to the converter, and the turbines provide the only means of energy output from the converter, then the equation follows:

Fig. 2.2.17  Control mechanism, two-position reactor. By orificing the feed and exhaust lines to the control cylinder, the speed with which the angle change takes place can be controlled so the final result is a pleasing one. The valve that controls the reactor pressures is mechanically connected to the accelerator pedal through linkage so that the angle change to the lower-capacity converter is accomplished when the driver requires high performance.

HI + H t1 + H t2 + Σ HL = 0

where:

(2.2.4)

HI = head of impeller; Ht1 = head of first turbine; Ht2 = head of second turbine; HL = total head loss.

Since the efficiency of a torque converter changes from 0% to a peak of approximately 90% in the torque multiplication range, and then higher in coupling, it is of interest to see exactly where the energy goes throughout the various speed ranges of the converter. The five-element, two-turbine converter will be used in this analysis. Table 2.2.1 shows a summary of the physical data of this converter. As is the rule

Losses are of two types: flow loss and shock loss. Flow loss can be compared to the piping loss or the friction of a fluid flowing through a channel. Shock loss is associated with the

Table 2.2.1  Dimensional Data—Two-Turbine, Five-Element Converter. Approximate Coefficients

Component Impeller First Turbine First Reactor Second Turbine Second Reactor (high-capacity) Second Reactor (low-capacity)

Entrance Angle (degree)

Exit Angle (degree)

Entrance Area (ft²)

Exit Area (ft²)

Entrance Radius (ft)

Exit Radius (ft)

Shock CS

Flow Cf

132 101   90   90   96

  45 146   55 123   52

0.1108 0.0728 0.0922 0.1148 0.0992

0.1325 0.1325 0.1124 0.1051 0.1074

0.2269 0.4476 0.4460 0.4460 0.2220

0.4476 0.4476 0.4460 0.2269 0.2220

0.60 0.42 0.42 0.60 0.42

1.83 1.08 0.40 1.73 0.45

  44

  19

0.0782

0.0994

0.2220

0.2220

0.42

3.95

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Torque Converters and Start Devices

loss in kinetic energy due to rapid change in velocity. The equation for flow loss in a channel is: H = CV 2



The velocity head of a fluid in motion is defined as:

(2.2.5)



where:

Many volumes have been written concerning the turbulent flow of fluids in closed channels. It will suffice here to say that the flow coefficient is directly proportional to the friction factor, which is dependent upon the Reynolds number and the channel roughness. It is also approximately directly proportional to the length of the channel and to the ratio of perimeter of the channel, or wetted surface, to channel flow area. Since:

V2 =

Q2 A 2s 2a



(2.2.7)



HS =

(V1 − V2 )2 2g

(2.2.8)



However, with round nose blades as used in axial flow elements in torque converters, such as the first turbine and first and second reactors of the two-turbine unit, the values of shock losses derived from the equations are high. Therefore, a constant, the value of which must be determined experimentally, is placed in the equation, making it:

(2.2.6)



then the A2s2a can be incorporated in the C for a given element and the equation can be rewritten to be:

HS =

CS (V1 − V2 )2 2g

(2.2.9)

Substituting for the tangential and axial velocities of the leaving and entering elements, in terms of the converter geometry, we get:

H = Cf Q2



V2 2g

Since the shock loss is dependent on the instantaneous change in velocity, it seems reasonable that the velocity head corresponding to the shock loss is:

C = flow coefficient V = flow, ft/s



H=

2 ⎡⎛ Qcota1 ⎞ ⎤ Qcota 2 R R + ω − − ω ⎢⎜ 1 1 2 2⎟ ⎥ ⎠ ⎥ A2 C S ⎢⎝ A1 HS = ⎥ ⎢ 2 2g ⎢ ⎥ ⎛Q Q⎞ − ⎥ ⎢+ ⎜ ⎟ ⎥⎦ ⎢⎣ ⎝ A1 A 2 ⎠

Figure 2.2.18 shows a plot of the coefficient versus position along the channel, so that the area under the curve is approximately proportional to the total flow coefficient for the converter, assuming that the friction factor remains nearly constant. Two values are shown for the second reactor, indicating that the flow coefficient is considerably higher for the lower reactor angle than for the higher reactor angle.

(2.2.10)

The value of CS, or shock coefficient, is left to be determined through analysis of experimental test data. Since torque is the time rate of change of angular momentum, a form of Newton’s second law, the equation can be written:

T=

d (Iω) dt′

(2.2.11)

The moment of inertia for a cylinder is:

I = MR2

(2.2.12)

For a flowing cylinder of fluid having a finite length, the equation becomes:

d I = Qt¢ g R 2



(2.2.13)

The angular velocity of a fluid leaving a member has two components: the angular velocity of the member and the

Fig. 2.2.18  Representation of relative flow coefficients. 2-25

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Design Practices: Passenger Car Automatic Transmissions

velocity of the fluid relative to the member. The former can be expressed as:

+

2 2 ⎞ ⎛Q C sT1 ⎡⎛ Q Q Q⎞ ⎤ ⎢⎜ cota I + ω IR I − 1 cota1T1 − ω T1R 1T1 ⎟ + ⎜ − 1 ⎟ ⎥ 2g ⎢⎝ A1 A T1 ⎠ ⎝ AI A T1 ⎠ ⎥⎦ ⎣

+

2 2 ⎞ ⎛ Q C sR1 ⎡⎛ Q Q Q ⎞ ⎤ ⎢⎜ cota T1 + ω T1R T1 − 1 cota1R1 − ω R1R 1R1 ⎟ + ⎜ − 1 ⎟ ⎥ 2g ⎢⎝ A T1 A R1 ⎠ ⎝ A T1 AR1 ⎠ ⎥⎦ ⎣

(2.2.15)

+

⎞ ⎛ Q C sT2 ⎡⎛ Q Q Q⎞ ⎢⎜ – 1 ⎟ cota R1 +ω R1R R1 – 1 cota1T2 – ω T2 R 1T2 ⎟ + ⎜ 2g ⎢⎝ AR1 A T2 ⎠ ⎝ AR1 A T2 ⎠ ⎣

Thus, the total expression for Iω at the exit of a given element becomes:

+

⎞ ⎛ Q C sR 2 ⎡⎛ Q Q Q ⎞ ⎢⎜ cota T2 + ω T2 R T2 − 1 cota R 2 − ω R 2 R 1R 2 ⎟ + ⎜ − 1 ⎟ 2g ⎢⎝ A T2 AR 2 ⎠ ⎝ A T2 AR 2 ⎠ ⎣

+

⎞ ⎛ Q C sI ⎡⎛ Q Q Q⎞ ⎢⎜ cota R 2 + ω R 2 R R 2 − 1 cota1I − ω IR 1I ⎟ + ⎜ − 1⎟ 2g ⎢⎝ AR 2 AI ⎠ ⎝ AR 2 AI ⎠ ⎣

ω=



2π N 60

(2.2.14)

The latter is: ⎛ Qcota ⎞ ⎟ ⎜⎝ A ⎠ ω= R



2

d ⎛ Qcota 2π ⎞ NR ⎟ Iω = Qt¢ g R ⎜ + ⎝ A ⎠ 60



(2.2.16)

2





Tω dQ

⎤ ⎥ ⎥⎦

⎤ ⎥=0 ⎥⎦

Figures 2.2.19 and 2.2.20 show, in terms of constant input head, the values of the heads of each of the turbines and each of the losses involved within the converter. Since the converters under discussion have been described as hydromechanical units, it is of academic interest, at least, that we investigate the effects of mechanical gear ratios.

(2.2.17)

and when substituted into the equation for power head: H=

2

2

This then becomes the basic energy equation for the fiveelement, two-turbine converter. Having the proper values of shock and flow coefficients, plus the basic geometric data of the converter, as shown in Table 2.2.1, it is possible to calculate the energy transmitted and the energy lost by each element in the converter.

d ⎛ R cota1 R 2 cota 2 ⎞ T2 = Q 2 g ⎜ 1 − A 2 ⎟⎠ ⎝ A1



⎤ ⎥ ⎥⎦

2

Since torque is the rate of change of momentum across a given element, it is related to the algebraic difference between the momentum of the oil as it enters that element and the momentum of the oil as it leaves the element. It can be assumed that oil enters the element with exactly the angular momentum which it had when it left the immediate upstream element. Therefore, the torque equation becomes:

d + Q g (R 12ω1 − R 22ω 2 )

2

(2.2.18)

we arrive at the equation: H1 =

⎤ ω1 ⎡ ⎛ R 1 cota1 R 2 cota 2 ⎞ − + (R 12ω1 − R 22ω 2 )⎥ ⎢Q ⎜ ⎟ g ⎣ ⎝ A1 A2 ⎠ ⎦



(2.2.19)

for each of the power input and power output elements. Thus, substituting into the basic head equation, we arrive at the equation: H1 =

⎤ ω1 ⎡ ⎛ R 1 cota1 R 2 cota 2 ⎞ − + (R 12ω1 − R 22ω 2 )⎥ ⎢Q ⎜ ⎟ ⎝ ⎠ g ⎣ A1 A2 ⎦

+

⎤ ω T1 ⎡ ⎛R I cota I R TI cota T1 ⎞ ⎢Q – + (R I2ω I – R T21ω T1 )⎥ A T1 ⎠ g ⎣ ⎝ AI ⎦

+

⎤ ω T2 ⎡ ⎛ R R1cota R1 R T2 cota T2 ⎞ – +(R R1ω R1 -R T22 ω T2 )⎥ +∑ C FQ 2 ⎢Q ⎜ ⎟ g ⎢⎣ ⎝ AR1 A T2 ⎠ ⎥⎦

Fig. 2.2.19  Energy output and losses as percent of input energy; two-turbine converter, 52° reactor.

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Torque Converters and Start Devices

Fig. 2.2.22  Effect of first turbine gear ratio; three-turbine converter.

Fig. 2.2.20  Energy output and losses as percent of input energy; two-turbine converter, 19° reactor. Figure 2.2.21 shows a plot of various gear ratios for the twoturbine converter. However, physical limitations of simple planetary gearsets limit the range of ratios between approximately 1.3 to 1.6 with the sun gear as a reaction member, and between 2.6 to 4.3 with the internal gear as a reaction member. Therefore, those curves outside the shaded area in Fig. 2.2.21 are not physically possible with a simple planetary gearset. Figures 2.2.22 and 2.2.23 show, respectively, the effect of varying the first turbine gear ratio and second turbine gear ratio in the three-turbine design. Again, those shown outside the shaded area are not possible with simple planetary gearsets. Vane angle changes can be coupled with these gear ratio changes to multiply greatly the number of combinations of overall performance available.

Fig. 2.2.23  Effect of second turbine gear ratio; three-turbine converter. Since the three-turbine converter is used in a transmission that has no gear trains other than those used in conjunction with the two geared turbines, it is of interest to observe the methods used in obtaining the reverse and grade-retarding ranges. Shown in Fig. 2.2.24 is the schematic for reverse range. The reverse clutch is applied, grounding the front ring gear and the second turbine. The two planetary units are compounded, with the rear ring gear being connected through a one-way clutch to the front sun gear. The first turbine drives the rear sun gear forward. With the rear planetary pinion acting as a fulcrum, the rear ring gear and front sun gear are driven backward. The front ring gear is grounded, and with sun gear driving backward, the carrier is driven backward at a high

Fig. 2.2.21  Effect of first turbine gear ratio; two-turbine converter. 2-27

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Design Practices: Passenger Car Automatic Transmissions

Table 2.2.2  Reverse Gear Ratio Calculations.

reduction. The third turbine, with its slightly negative torque, adds to the reverse from the first turbine.

Front Ring Gear

Table 2.2.2 shows the calculation of the reverse gear ratio from the compound planetary set. Multiplying the mechanical ratio from the table by the first turbine hydraulic ratio and adding the third turbine ratio gives an overall reverse ratio at stall of 4.50:1.

Gearsets locked Carrier stationary Front ring gear held

The grade-retarding range is necessary in this three-turbine design since there is no conventional “low gear” behind the converter. Fig. 2.2.25 shows schematically the arrangement used. For this case, the output shaft and planet carrier are considered the input members, while the impeller, connected to the engine, is considered the output member. By application of the grade range clutch, the rear ring gear is grounded, causing the rear sun gear and first turbine to overdrive by the ratio of 2.86:1. This causes the first turbine to act as an axial impeller, as shown at the top of Fig. 2.2.25. All other members except the converter impeller are allowed to rotate freely. It is interesting to note that the direction of oil circulation in grade-retarding range is the same as normal driving in drive range.

2.2.5

Carrier

Front Sun Gear

Rear Ring Gear

Rear Sun Gear

–1

–1

–1

–1

–1

+1

 0

–1.86

–1.86

+1.86²

 0

–1

+2.46

Construction

Some of the methods of construction used in the multi­ turbine converters are both unique and interesting. The two-position reactor has previously been mentioned. The individual vanes are sections of extrusion cut off and pressed onto serrated cranks made from steel wire. The reactor carrier, which retains the vanes and houses the control piston, is made from cast-iron, machined all over with the blade crank holes located on the split line between the front and rear half, thus allowing assembly of the cranks into the holes. The reactor one-way clutch is a simple cam and roller design, being rather light duty because of the low torque involved. The vane control pistons are sintered iron and cast-iron in the various transmission applications. In addition to the two-position reactor in each of the fiveelement converters discussed, there are also two other elements that have short axial-flow streamline blade designs. In the two-turbine transmission, these are the first turbine and first reactor. In the three-turbine design, they are the first turbine and second turbine. In the current-production models, all of these elements are die-cast aluminum and all are made in a simple two-piece axial draw die.

Fig. 2.2.24  Three-turbine converter, reverse range.

Figure 2.2.26 reveals a section through a number of these adjacent vanes, showing the minimum space between two adjacent vanes required by the axial-draw, die-cast process. In most cases, this requirement can be met with little or no sacrifice in the hydrodynamic performance characteristics of the converter. Figure 2.2.27 shows a typical comparison in the two-turbine converter of a first turbine having optimum blade design with one which has been modified to meet the axial-draw, die-cast specifications. Some alternatives to the axial-draw, die-cast process that could be used in parts of this nature are:

Fig. 2.2.25  Three-turbine converter, grade-retarding range.

1. 2. 3. 4.

Fabrication from extrusion Radial-draw die-cast Sand-cast Plaster-cast

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Torque Converters and Start Devices

values of speed ratios. One of the solutions has been to use streamlined vanes in the axial-flow elements. The streamlined nose of the vane makes it less sensitive to the direction of the incoming oil, thus being efficient over a wide range of speed ratios.

Fig. 2.2.26  Spacing requirements for axial-draw, die-cast requirements.

Fig. 2.2.28  Fluid approach angle versus speed ratio, twoturbine converter, 52° reactor. Fig. 2.2.27  Comparison of performance characteristics, two-turbine converter with die-cast design versus optimum blade design first turbine. While none of these alternatives have the spacing limitations shown in Fig. 2.2.26, each has other liabilities of cost, draft, surface smoothness, casting seams, minimum vane thickness, or parting lines which could make it undesirable in the overall compromise. The present state-of-the-art in torque converter design requires considerable design balance between optimum torque ratio, efficiency, and speed characteristics. Broadly speaking, it could be stated that the exit angle of each element in the torque converter primarily determines its overall speed and performance characteristics; the entrance angle of the element is set at the value that will most efficiently receive the oil from the preceding element in the flow path over the operating range of speed ratios. Since the relative speeds of adjacent elements in the converter change considerably from stall through midrange to coupling, the determination of the design entrance angle is one place where definite compromise is necessary.

Fig. 2.2.29  Fluid approach angle versus speed ratio, twoturbine converter, 19° reactor. The short axial-flow elements have one unique characteristic. Since the ratio of length to width of the flow channel between these blades is low, the exit angle of the oil leaving the element is not independent of the angle of incidence at the nose or entrance of the blade. This phenomenon has been proved in some tests and it has been a very convenient tool for making calculated data agree with test data. It is also felt that by careful design, the characteristic can be more of an advantage than disadvantage since higher exit angles may be desirable at one range of speed ratios, and lower exit angles

Looking again at the two-turbine converter, Fig. 2.2.28 shows a plot of the fluid approach angle for each of the five elements with the reactor in its higher-angle, high-capacity position. Figure 2.2.29 shows the same relationship for the reactor in the lower angle. It can be seen that it is not possible to have one best angle which fits the entrance conditions for all 2-29

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desirable in another range. In the three-turbine converter design, the exit angle of the first turbine is 124° while the exit angle of the second turbine is 155°. Therefore, it would be expected that at stall, with both turbines stationary, the oil would be deflected rearward by the first turbine and then further deflected as it passes through the second turbine. However, this is not the case. Test fixtures, which measure individually the torques of the three turbines by measuring the value of the torque on the reaction members of the two geared turbines, have shown that the torque on the second turbine is actually negative at stall, while the torque on the first turbine is greater than would be predicted by the torque equations. Therefore, the oil must be traveling through the turbines, as shown by the arrows in Fig. 2.2.30.

Axial thrusts are very complex and will only be dealt with briefly in this section. Some of the factors affecting thrust are: 1. Accelerations of the fluid in the axial direction, particularly in the impeller and the final turbine 2. Centrifugal pressures caused by a rotating mass of oil, defined by the equation: P = (d/g)ω2R2 3. Hydrodynamic lift caused by streamlined vane sections 4. Differential areas of effective pistons 5. Frictional drag of the fluid in the axial direction 6. Gear thrusts of helical gears that exist within the converter 7. Expansion and contraction of the converter housing 8. External thrusts from input, output, or reaction shafts

Figure 2.2.31 shows a plot of the probable exit angle versus approach angle for the first turbine of the three-turbine design, the data being determined through correlation between test data and calculated performance of a complete converter.

Since analysis is difficult, a test fixture has been built, and the results for the three-turbine converter are shown in Fig. 2.2.32. Forces may appear to be extremely high, but when one considers the large projected areas involved and the large volume of fluid circulated, the forces become more understandable. Thrusts can be modified to a certain extent by adding balance holes, paddles, labyrinths, or by diverting the converter charging oil or outlet oil.

Fig. 2.2.30  Path of fluid through first and second turbines showing bounces of fluid at low-speed ratios.

Fig. 2.2.32  Thrusts of individual members, three-turbine converter with 13° reactor.

2.2.6

Conclusions

It is the opinion of the author that the multi-element geared converters are slightly less subject to performance degeneration due to manufacturing tolerances than are the threeelement converters. This is due to the fact that flow velocities

Fig. 2.2.31  Fluid exit angle versus approach angle, first turbine element in three-turbine converter. 2-30

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Torque Converters and Start Devices

for a five-element converter are less than those for a corresponding three-element converter, making it less sensitive to surface finish and small imperfections such as burrs, slots, and flash lines. Also, with less hydrodynamic torque multiplication and more mechanical multiplication through planetary gearsets, there is a very good chance that production converters can be made that will closely resemble in performance the hand-polished prototypes which are the delight of the converter development engineer.

2.2.7

equations, terminology, general characteristics, and methods for evaluating an application are included here to provide a general background for further study.

2.3.1

Terminology

The field of fluid mechanics, which is the heart of hydrodynamic drive design, was as confused as any technical field in regard to terminology. The immediate usefulness of a good technical publication is reduced when the terminology is not familiar to the user. SAE has contributed greatly to a solution of this problem. Representatives of the various interested groups have met under SAE auspices and agreed upon recommended symbols, terminology, and a test code for hydrodynamic drives. Where differences exist that affect design practices, as in the case of blade angle terminology, the most used systems are shown, and one system has been agreed upon as preferred for technical publications. A study of the SAE Handbook sections on Automotive Transmission Terminology and Test Codes will also be helpful to the transmission engineer.

References

1. Black, J. B. and M. W. Dundore, “Torque Converters Can Be Different,” SAE Transactions, Vol. 66, SAE International, Warrendale, PA, 1958. 2. Vincent, J. G. and Forest McFarland, “Packard Automatic Transmission,” Paper No. 343 presented at SAE Summer Meeting, French Lick, Ind., June 1949.

2.3 Application of Hydrodynamic Drive Units to Passenger Car Automatic Transmissions

2.3.2

E. W. Upton Engineering Staff, General Motors Corp.

Definitions

The following definitions are necessary to an understanding of the discussions of the operation, application, characteristics, and design.

Hydrodynamic drive devices have proved themselves to millions of American motorists. After the introduction of the fluid coupling in a 1938 model passenger car, the volume increased, and by 1961, nearly 40 million [1] transmissions employing hydrodynamic units had been sold, resulting in increasing numbers of satisfied customers. Today, all current American production passenger car automatic transmissions use at least one hydrodynamic unit.

Hydrodynamic Drive—As contrasted with electrical, mechanical, etc., a hydrodynamic drive is one that transmits power solely by dynamic fluid action in a closed recirculating path. Element—An element consists of a single row of flowdirecting blades. Figure 2.3.1 shows a typical axial flow type of element. Figure 2.3.2 shows a typical mixed flow type of element. Blade—Within an element, the blade is the means of directing fluid flow. Member—A member is an independent component of a hydrodynamic unit such as an impeller, reactor, or turbine. It may be comprised of one or more elements. Multiple Member—Nomenclature of multiple members of basically the same function in both polyphase and multistage torque converters should be named in the order of fluid circulation in normal operation—first impeller, second impeller, etc.; first turbine, second turbine, etc.; first reactor, second reactor, etc.

The customer driving miles represent some of the most severe test conditions. Much effort is expended to devise engineering test procedures that will accurately evaluate transmission performance in the customer’s hands in order to design a product that will satisfactorily meet customer requirements without overdesign, which leads to excessive cost. The increasingly high percentage of new cars sold equipped with automatic transmissions (73.0% in 1960, 91.3% in 1970) [2] attests to the success of current engineering practices. Several top line cars are equipped 100% with automatics. Today’s designers of automatic transmissions know that hydrodynamic units will perform satisfactorily if properly applied. Their problem is how best to design and use them in their applications. This paper is intended to serve as a design reference on this subject. The fundamental concepts,

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Design Practices: Passenger Car Automatic Transmissions

Fluid Coupling—The fluid coupling is a hydrodynamic drive that transmits power without the ability to change torque. (Torque ratio is unity for all speed ratios.) All previous definitions apply to this device and torque converters as well. The typical simple fluid coupling configuration is shown in Fig. 2.3.3.

Fig. 2.3.1  Typical axial flow type reactor element.

Fig. 2.3.2  Typical mixed flow type of turbine element.

Fig. 2.3.3  Fluid coupling.

Impeller—The impeller is the power input member. An impeller is also commonly called a pump—this is accurate technically. Impeller is recommended to avoid confusion with the transmission pressure pumps (Figs. 2.3.3 to 2.3.5, and 2.3.14). Turbine—The turbine is the output member (Figs. 2.3.2 to 2.3.5, and 2.3.14). Torus Section—The torus section is within the confines of a flow circuit in a radial plane of a torque converter or fluid coupling (Figs. 2.3.3 to 2.3.5, and 2.3.14). Shell—The shell is the outside wall of the torus section in any member (Figs. 2.3.3 to 2.3.5, and 2.3.14). Core—The core is the inside wall of the torus section in any member (Figs. 2.3.3 to 2.3.5, and 2.3.14). Design Path—The design path is the path of the assumed mean effective flow and is used for definition of blade angles, entrance and exit radii, etc. (Figs. 2.3.3 and 2.3.4).

Fig. 2.3.4  Three-element torque converter (two-phase, single-stage).

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Reactor—The reactor is the reaction member (Figs. 2.3.1, 2.3.4, 2.3.5, and 2.3.14). A reactor is also commonly called a stator. The term reactor is preferred for uniformity in SAE papers. It also clearly describes the function of this member. One-Way Clutch—The one-way clutch is a device that transmits torque in only one direction. The term clutch is applied here because of common usage, although this device may be used as a clutch or brake (Figs. 2.3.4, 2.3.5, and 2.3.14). Torque Converter—The torque converter is a hydrodynamic drive that transmits power with the ability to change torque. All previous definitions apply to this device. A typical arrangement of a three-member converter is shown in Fig. 2.3.4. The reaction member is the unique feature of this drive. It performs the same basic function in the fluid circuit as the fulcrum point in a simple lever system. The use of a one-way clutch permits the torque converter to function as a fluid coupling at speed ratio conditions greater than that at which torque increase ends. Without the one-way clutch, turbine torque becomes less than the impeller torque at the higher speed ratios as a result of torque reversal on the reactor. With the one-way clutch, the reactor torque cannot reverse, but remains zero. The reactor begins to rotate (free-wheel) in the direction of the impeller when the speed ratio becomes greater than that at the one-to-one torque condition. This operational condition will be clarified below. Phase (Single-, Two-, Three-, etc.)—The term phase applied to a torque converter refers to the number of functional arrangements of the working elements when the functional change is produced by a one-way clutch or other mechanical means such as a clutch or brake. The free-wheeling reactor operation described above represents the coupling phase for a two-phase converter (Figs. 2.3.4 and 2.3.5). Stage (Single-, Two-, Three-, etc.)—A stage is a turbine element interposed between elements of other members. The number of stages is the number of such elements of the turbine member.

Size—In general terms, the size is designated by the maximum diameter of the flow path. Fluid coupling sizes have ranged 7.2 to 15.0 in. in diameter. The first coupling used in an American passenger car was 15.0 in. in diameter. Torque converters in use range 10.0 to 12.2 in.

Fig. 2.3.5  Two-stage torque converter (four-element, two-phase).

2.3.3

Advantages of Hydrodynamic Drives

The hydrodynamic drive, in performing the combination of functions for which it is suitable, offers the advantages of complete smoothness during its speed ratio changes and torque ratio changes in the case of the torque converter. Considering the complex nature of these changes, the unit is relatively simple, completely automatic, and reliable. It can be designed to be sufficiently rugged and durable to last the life of the vehicle without requiring service. When the hydrodynamic device is driven directly by the engine, the other driveline components are substantially free of effects of the normal engine torsional disturbances, in most cases eliminating the need for torsional dampers or isolators. Shock effects on the driveline components, resulting from abrupt changes in the resistance to vehicle motion, wheel rotation, and transmission gear ratio changes, are greatly reduced. The combination of reduced torsional and shock loads results in longer life for nearly all functional components of the vehicle and reduced repair costs.

Figure 2.3.5 shows one arrangement of a two-stage converter that was used in the production transmission first introduced in a 1949 model. The second turbine element is directly connected to the first turbine element. This arrangement is defined as a three-member, fourelement, two-stage, two-phase converter. Two elements, separated by the reactor, are combined to form the two stages of the turbine.

The ability of one member of a hydrodynamic drive unit to perform a function normally provided by another member permits the designer to exercise more ingenuity in the selection of the type and arrangement of components to meet the required performance specifications. 2-33

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Design Practices: Passenger Car Automatic Transmissions

2.3.4

Description of Operation of Hydrodynamic Units

is transmitted unless there is circulation of fluid through the torus system.

In the simplest configuration, the fluid coupling shown in Fig. 2.3.3, the impeller driven by the engine functions as a centrifugal pump. Oil, which substantially fills the space within which the bladed elements are located, flows into the impeller inlet (the part of the torus nearest the axis of rotation), as shown by the arrow. It passes outwardly through the impeller passages and leaves at the outer part of the torus, where it enters the turbine member and flows inwardly through the passages to be again discharged at the inner part of the torus into the impeller inlet. Because the flow is subject to changes in the axial direction as well as the radial direction, bladed cascades of this type are termed mixed-flow elements.

2.3.5 1. 2. 3. 4. 5. 6. 7. 8.

The fluid flow is established in the direction described because of the difference in centrifugal pressure caused by the difference in the speed of the two members. The impeller turning at the higher speed produces a greater centrifugal pressure difference between the inlet and outlet at zero-flow condition than is produced by the turbine. The resulting net pressure gradient from the impeller circuit to the turbine circuit causes flow, which stabilizes at the value where the sum of the flow loss heads and the turbine work head exactly equals the impeller total head. As the turbine speed increases, its potential centrifugal pressure difference increases, resulting in a smaller net pressure differential between the impeller circuit and the turbine circuit and, therefore, a lower circulation rate. Since the torque transmitted is directly related to the rate of flow around the torus, the impeller speed must increase as turbine speed increases in order to transmit a constant torque. The action of the fluid produces torque loading on the blades of the turbine equal in magnitude but opposite in direction to that on the impeller. Couplings using identical blading in the two members operate equally well when the turbine is used as the impeller. In some units, the blading is not identical, but is designed to favor one direction of rotation and one direction of power flow.

Functional Uses of Hydrodynamic Drives

Starting device—automatic Speed changer—automatic Engine speed—control device Retarding device—automatic Shifting mechanism Torque ratio change—automatic Reversing device—multiple function Capacity changer

Fluid couplings and torque converters perform alike in regard to the first five functions. The first application of a hydrodynamic unit in the American motor car was a fluid coupling used primarily as a starting device. It was used in a 1938 passenger car between the engine and the conventional clutch along with a three-speed synchromesh transmission. In all current American passenger car production automatic transmissions, these units serve as an automatic starting device, eliminating the need for automatically engaging a friction element simultaneously with opening the engine throttle. As used, the hydrodynamic unit at normal engine idle speeds does not absorb, and therefore does not transmit enough torque to cause objectionable creep. The unit is, however, fully operational and ready to respond immediately to an increase in throttle opening, resulting in an increase in engine speed and torque capacity of the unit, and therefore increased drive forces. It is this immediate readiness of the unit to respond to the slightest throttle change that makes it advisable for the driver to learn to maintain brake pressure at all times when the car is standing at idle in a driving range. It is desirable to form this habit when driving any automobile, and particularly those equipped with an automatic transmission—whether it uses a hydrodynamic unit or not.

In order to obtain a change in torque between the impeller and turbine, a third member, the reactor, must be added to the circuit. Figure 2.3.4 shows this member in a typical three-element converter arrangement. The reactor may be of mixed-flow design. Frequently, however, the primary cause of the torque reaction of this member is the change in the spin velocity of the fluid mass around the shaft centerline without any change in radius, in which case the blade cascade is an axial type of flow element (Fig. 2.3.1). The reactor performs the same function in the hydraulic circuit that the fulcrum serves in a lever system.

As the vehicle accelerates, the coupling or converter automatically accommodates the speed of the engine and the vehicle with complete smoothness. It also controls the engine speed automatically, depending only on engine torque and vehicle speed conditions without any other control means. When vehicle and throttle conditions establish a coasting or overrun condition, the fluid unit automatically accommodates the reversal of power flow. In the case of the simplest (radial-blade) fluid coupling, the overrun power flow operation has the same efficiency as the forward operation for the

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same load conditions. Some couplings and all torque converters are designed to be more efficient for forward power flow. Torque converters employing free-wheeling reactors operate as couplings under coast conditions.

Another dual-function system obtains reverse by using a second turbine as the reactor and the first turbine as the primary reverse-drive member. Again, the speed range and efficiency are not as great as forward drive, but the arrangement produces a satisfactory passenger car reverse when used with an appropriate gear train and results in a better overall design balance or transmission arrangement than would be possible if the more conventional reversing gear system was used.

Special applications in the heavy-duty fields use fluid couplings as retarders for downhill runs. One member is locked to ground; the other member is connected to the driveshaft. The retarding force is a function of the vehicle speed and is further controlled by the amount of fluid in the torus. Some passenger car transmissions use a special range and functional arrangement to obtain increased braking for downgrade operation.

The capacity characteristic of the fixed-blade coupling or converter of a given design is fixed. However, considerable range in capacity can be obtained by use of variable-blade elements. The choice of the particular member selected for this effect depends on the type of unit and transmission arrangement used. Any one of the three basic types of members—impeller, turbine, or reactor—can be used if properly designed. The reactor is usually the most convenient for this purpose. Two production automatic transmissions employed this latter scheme, which also produces a change in maximum torque ratio and maximum efficiency.

Fluid couplings and torque converters can both be used as shifting mechanisms to accomplish transmission gear ratio changes with maximum smoothness. In this application, they are used with a planetary gearset to connect two of the three elements of the gearset. The fluid unit is emptied to permit the gearset to function in ratio range. The individual members of the hydrodynamic unit rotate with complete freedom relative to each other because of the absence of the fluid—transmission oil—which is the medium of force transfer within these units. The coupling is filled to accomplish the lockup or direct-drive condition of the gearset usually obtained by engaging a friction clutch. Use of the fluid device achieves the one-to-one torque transfer, but the speed transfer is slightly less than one-to-one, the hydrodynamic drive requiring a difference of speed between input and output members in order to establish fluid circulation within the passages and thereby establishing torque transfer. Because the fluid unit has a higher heat capacity, these shifts can be stretched over a longer time period than can be tolerated in a friction clutch without special attention to the cooling problem.

2.3.6

Location in Passenger Car

The primary factors that determine the location of the hydrodynamic unit in the vehicle are size, functional use, and transmission schematic arrangement. Because of the first two factors, all current-production passenger car front-end transmission installations using a hydrodynamic unit for fullpower transmission locate the coupling or converter close to the rear of the engine. Minimum interference with the floorboard in the passenger compartment dictates that this relatively large diameter component be located as far forward as possible. This is also the most convenient location in which to obtain the direct drive from the engine crank flange.

The function of torque ratio change is peculiar to the torque converter by definition. This change is performed automatically and simultaneously with changes in speed ratio, a given design providing a specific torque ratio for each speed ratio. An infinite number of torque ratios are available between the maximum occurring at vehicle standstill (stall conditions) and the one-to-one point (coupling point).

Two transaxle systems locate the torque converter behind the rear axle. In both cases, space is a factor, since the diameter is large enough to interfere with the rear seat if the unit were located ahead of the axle. In one instance, the extreme rearend location is again adjacent to the engine, thus facilitating the direct drive from the crankshaft. Figure 2.3.6 shows the other transaxle design in which the engine is in the conventional location at the front of the car. It is clear in this figure that moving the converter ahead of the axle would cause space problems in the vicinity of the rear seat. It is also clear why front-end installations locate the hydrodynamic unit as close to the engine as possible. The two transaxle installations are a good example of the third factor affecting location—transmission schematic arrangement. By using a similar arrangement, a very real cost advantage is obtained through a large number of common parts.

To utilize the torque converter as a reverse-drive device, it is necessary only to exchange the functions of at least two members—as, for example, the simple three-member unit. The turbine is used as the reactor, and the reactor as the turbine. The speed range and the efficiency of this arrangement are less than for normal drive. Combined with a suitable gear arrangement, this principle was used in one production automatic [3].

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A hydrodynamic unit used as a shifting device may be small enough to permit its use in a location that is most compatible with the gearset it controls.

2.3.7

limited in the practical sense when using the equation. Further study of the derivation will show that a particular speed-ratio condition represents a particular set of vector flow relationships in the torus circulation system. It can also be shown that the equation can be applied, using some values for an input member and some for an output member. In all cases, the important point is that the solutions for new conditions represent values corresponding to those that established C in the first case. In general, C is determined from test data, and the transitions are generally used for input or output conditions.

Equation Governing Application

The performance characteristics of a hydrodynamic unit are established by the particular geometric shapes of its components and the fluid used. Performance under different conditions of speed, torque, and size are predictable by use of the following equation, as long as the original proportionality between physical dimensions is maintained when size changes are made.

T = CN2D5

2.3.8

The following items describe completely the operation characteristics of a given design:

(2.3.1)

where:

1. 2. 3. 4.

T = torque, lb.-ft. C = capacity constant N = speed, rpm D = size of flow path, ft

Input speed Output speed Input torque Output torque

To describe the performance in the most usable form, these terms are combined into the following characteristics:

The maximum diameter of the design path or the torus (depending on the designer) is usually selected for D. The value of the capacity coefficient C is particular for each speed ratio condition and is dependent on: 1. 2. 3. 4.

Typical Characteristic Plots

1. 2. 3. 4.

Specific geometric design Dimensional system used for T, N, and D Fluid density Fluid viscosity

Speed ratio, n = output speed ∏ input speed Torque ratio, t = output torque ∏ input torque Efficiency (%), E = (n ¥ t) ¥ 100% Capacity factor, K = N T

From the torque capacity, Eq. 2.3.1, it is obvious that:

The relationship shown holds equally well for input or output elements. In fact, it is technically correct to substitute the flow velocity at a particular point in the flow path for the speed term and apply the equation for reactor elements. Elements that free-wheel during some part of the operational range are

K=

1 = CD5

1 CD5

(2.3.2)

Two forms of plot are commonly used to display the corresponding values of these characteristics. Figure 2.3.7 shows the speed-ratio plot in which torque ratio, efficiency, capacity factor, and input speed are plotted as ordinates against

Fig. 2.3.6  Location of hydrodynamic unit in vehicle. 2-36

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Torque Converters and Start Devices

speed ratio as the abscissa. This plot is frequently used by the designer to compare the hydrodynamic excellence of two or more designs. The advantage of using the capacity factor is evident from this plot. It has the characteristic shape of the input speed curve and eliminates the necessity of noting the torque level at which the data apply. The impeller torque must always be noted when input speed is used. Such a plot must also be accompanied by information about the size of — the unit. From Eq. 2.3.1, a characteristic constant (K) can be used which incorporates the diameter D and thus eliminates the need for specifying the size.

N D5 1 K= = T C

Fig. 2.3.8  Typical output speed plot of converter characteristics (150 lb.-ft. input torque test).

(2.3.3)

—

Since D is constant for a given unit, the K curve also has the characteristic shape of the input speed curve.

2.3.9

Figure 2.3.8 shows the output speed plot in which the same characteristics are plotted as ordinates against output speed as the abscissa. This plot relates the characteristics more nearly to vehicle speed and load conditions. Some designers add speed rate to this plot. A convenient method of obtaining speed ratio data as required, without confusing the plot with an extra curve, consists of constructing a speed ratio line for the desired value. This is done by selecting a convenient value for impeller speed and calculating the corresponding turbine speed for the desired speed ratio. A straight line is drawn from the common zero points on the speed scales through the calculated impeller-turbine speed point. The point at which this line intersects the impeller speed curve provides data for the speed ratio condition chosen.

Engine and Hydrodynamic Unit— Combined Operation

The torque capacity equation becomes the means for obtaining the actual values at which the engine and fluid unit will operate together. Two methods are listed—the log-log plot and the capacity factor. The log-log plot method recognizes the torque capacity equation as linear when transformed into a logarithmic form as follows:

logT = logC + 2 logN + 5 logD

(2.3.4)

At a particular speed ratio condition for a specific unit, C and D are constant. The equation therefore can be written:

logT = constant + 2 log N

(2.3.4a)

y = a + 2x

(2.3.4b)

or:

If the logarithm of the torque is plotted as the ordinate and the logarithm of the speed as the abscissa, the curve of this equation becomes a straight line extending upward at a twoto-one slope (Fig. 2.3.9). When graph paper having the ordinate and abscissa scales divided logarithmically is used, the values of T and N are plotted directly. It is necessary then to have data at only one input torque level for each selected speed ratio condition. The points are plotted at the known torque level at the various corresponding speed values and straight-line curves drawn through the points at the slope of two-to-one. A typical family of curves is shown in Fig. 2.3.10. To determine the combined operating points of engine and fluid unit at these speed ratio values, the engine torque versus speed curve is plotted on the same log-log graph. The intercepts of the engine curve with the fluid unit capacity lines are the particular common values of torque and speed for the combination (Fig. 2.3.10). The values of engine speed and torque can be tabulated at the specific speed ratio con-

Fig. 2.3.7  Typical speed-ratio plot of converter characteristics. 2-37

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Table 2.3.1  Operating Conditions of Engine and Hydrodynamic Unit from Fig. 2.3.10.

ditions (Table 2.3.1). If the fluid unit is a torque converter, corresponding torque ratio conditions are tabulated from either the speed ratio or output speed plot of the fluid unit, as previously discussed. Corresponding output torque and speed values can then be calculated.

Speed Ratio n

Engine Speed Ne

Engine Torque Te

0 0.2 0.4 0.6 0.8 0.9 0.92 0.94

1880 1965 2096 2296 2630 3100 3365 3750

168.4 167.8 166.8 164.4 159.0 144.7 134.8 120.0

Capacity Factor K 144.8 151.8 163.2 179.0 208.4 257.6 290.0 342.2

The capacity factor method involves calculating an engine Ne Te characteristic using the selected engine torque versus speed curve. The values are plotted on the same linear coordinate graph paper on which the engine torque versus speed and engine horsepower versus speed are plotted (Fig. 2.3.11). The fluid unit capacity factor value corresponding to a speed ratio for which a solution is needed is located on the engine Ne Te curve, and the corresponding engine speed is noted. The engine torque is read from the torque versus speed curve. Output speed and torque values are found in the same manner as before. An example of this type of solution is shown in Fig. 2.3.11. From Table 2.3.1, the capacity factor K at 0.8 speed ratio is 208.4. In Fig. 2.3.11, engine speed corresponding to this K value is 2630 rpm, and the engine torque at this speed is 159 lb.-ft.. These values are the same as recorded in Table 2.3.1 from Fig. 2.3.10.

Fig. 2.3.9  Impeller torque versus impeller speed.

Fig. 2.3.10  Typical input capacity plot used to determine operating conditions of engine and hydrodynamic unit combined. All engine driving situations can be explored by this process as long as the engine torque versus speed curve is known— as, for example, curves at fixed-throttle settings, constant manifold depression, or specified altitude conditions.

Fig. 2.3.11  Typical engine plot showing capacity factor used to determine operating conditions with hydrodynamic unit.

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Table 2.3.2  Operating Conditions of Automobile and Hydrodynamic Unit on 10% Grade from Fig. 2.3.12. Speed Ratio n

Torque Ratio t

0.6 0.7 0.8 0.85 0.9 0.92

1.315 1.190 1.055 1.0 1.0 1.0

Turbine Speed NT 1035 1374 1850 2176 2800 3340

Turbine Torque TT 122 124.5 130 134 145 158

Engine Speed Ne

Engine Torque Te

1727 1963 2315 2560 3115 3630

  92.9 104.6 123.2 134 145 158

2.3.11 Effect of Gearing Several current-production transmissions include gear ratio changes to supplement the hydrodynamic drive unit. The functional arrangements of the fluid units with the gearsets fall into three general classes: 1. Input gears in series 2. Output gears in series 3. Split torque

Fig. 2.3.12  Typical output capacity plot used to determine operating conditions of automobile and hydrodynamic unit.

These arrangements are discussed here to demonstrate the effect of gears on the combined operation of the engine or vehicle with the fluid unit when gearsets are used in the system. In no instance does the use of the gearset, as discussed here, affect the operational characteristics of the hydrodynamic drive device. Changes in these characteristics can only be accomplished by changing the function of one or more of the components, as, for example, the special use of a reactor as a reverse-drive turbine or the reactor as a rotating reactor.

2.3.10 Vehicle and Hydrodynamic Unit— Combined Operation It is frequently desirable to know the operating conditions of the fluid unit and the transmission at specified vehicle speed and road-grade conditions. This problem is not easily solved by the above methods, which assume input conditions. However, a similar set of fluid unit speed-ratio capacity characteristics can be calculated using output values of torque and speed. Figure 2.3.12 shows the log-log plot of the output for the same unit as the input capacity line shown in Fig. 2.3.10. Using a suitable vehicle rolling-resistance equation or actual test data, the curve of output speed and load referred to the output of hydrodynamic unit is plotted on the same graph sheet. Figure 2.3.12 shows curves for 0 and 10% grades. Again, the intersection points are the common conditions of operation. Applying the corresponding speed ratio and torque ratio values, the engine speed and torque required to maintain the chosen vehicle conditions can be calculated. Table 2.3.2 records the values from Fig. 2.3.12 for the 10% grade. Obviously, the capacity factor method can be used for this solution by using output values to calculate the factors.

2.3.11.1  Input Gearing When a gearset is interposed between the engine and the fluid unit, the input torque versus speed characteristic is changed in a manner directly related to the gear ratio. Figure 2.3.13 shows examples of a 1.5 underdrive ratio and a 1.5 overdrive ratio. The engine curve is shown as the dashed line. Point 1 is the intercept of the 0.4 speed ratio line with this engine curve. Point 2 is the point on the 1.5 underdrive input to the hydrodynamic corresponding to conditions at point 1. Point 3 represents the input to the hydrodynamic unit for 1.5 overdrive, again at the engine condition of point 1. The mathematical relationships for underdrive follow:

Ti = 1.5 Te

(2.3.5)

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Design Practices: Passenger Car Automatic Transmissions



Ni =

Ne 1.5

The procedures previously outlined are followed, using the new input capacity factors instead of the engine values.

(2.3.6)

Writing these in logarithmic form:

log Ti = log1.5 + log Te

(2.3.5a)



log Ni = log Ne − log1.5

(2.3.6a)

2.3.11.2  Output Gearing What has been outlined for input gear relationships applies as well to output gearing when considering vehicle speed and grade load conditions.

The effect of the gear ratio is, therefore, to raise each of the points of the engine curve vertically the same distance and to move each point horizontally to the left the same distance. Because logarithmic scales usually complete one cycle in the same distance vertically and horizontally, the shift in these directions is equal, which results in each point of the original curve moving diagonally upward to the left at a 45° angle. The new input curve is then exactly the same shape as the original engine curve, but is displaced along the 45° line. Overdrive ratios shift the curve downward to the right on the graph, as shown by the curve representing the input when a 1 to 1.5 overdrive ratio is used. By adding the capacity factor speed ratio lines to the plot, the corresponding operating points for direct drive, 1.5 to 1 underdrive, and 1 to 1.5 overdrive are clearly shown (Fig. 2.3.13).

2.3.11.3  Split-Torque Gearing The term “split torque” describes an operational condition in which the power flow through the transmission is divided between two or more parallel paths—a mechanical path and a hydrodynamic path. Split-torque systems can be divided into two basic arrangements—input splits and output splits. Each of these arrangements can be further divided into two types—pure splits and regenerative or recirculation splits. Pure splits are those in which torque flow through the hydrodynamic unit is normal and is not augmented by feedback torque from the mechanical path. Reference 4 presents an extensive discussion and equations for two-path systems. Five current-production passenger car automatic transmissions incorporate a two-path pure split arrangement. These arrangements combine the advantages of the flexibility and smoothness of hydrodynamic drives and the higher efficiency of the mechanical path. They also permit the use of smaller hydrodynamic units, resulting in less creep and better utilization of engine horsepower in the nonsplit range. The splittorque range provides lower engine speeds and, therefore, a tight feel for normal cruising. Satisfactory application of split torque requires correct analysis of the system in terms of its effect on:

Further study of the log-log plot will show that the 45° line is a constant horsepower line. Such lines provide a quick observation of the maximum horsepower speed and torque for any given engine curve. If the designer prefers the capacity factor curve method, the engine Ne Te values are converted to input values as follows:

Ni Ne G N = = e ÷ G1.5 Ti Te × G Te

(2.3.7)

1. Transmission component design 2. Vehicle performance 3. Vehicle vibration characteristics Once the characteristics of the split-torque system have been determined, the arrangement can be treated like a hydrodynamic drive when studying the combined performance of the engine-transmission-vehicle system. Speed ratio capacity factor curves are used in the same manner as outlined for the pure hydrodynamic unit. Figure 2.3.14 shows a schematic diagram of one production split-torque system. Some split-torque arrangements require a torsion vibration damper to minimize the effect of engine torsionals which are transmitted by the mechanical branch of power flow in the split-torque ranges.

Fig. 2.3.13  Effect of input gear ratio on combined operating conditions.

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Torque Converters and Start Devices

The input conditions corresponding to the common output conditions are shown in Table 2.3.2 for 10% grade. These input conditions are now shown on the input log-log plot and represent the minimum torque and speed requirements for the engine. A particular engine wide open throttle (WOT) curve is shown added to this graph (Fig. 2.3.15). A simple calculation will show the percentage of maximum engine power required for each previous vehicle performance requirement. The plot also shows the stall speed (engine rpm at 0 mph) as well as the other WOT characteristics.

Fig. 2.3.14  Schematic diagram of current-production output split-torque arrangement.

The effect of altitude on the engine torque versus speed curve is an important consideration in selecting the size of hydrodynamic units. Figure 2.3.15 also shows the estimated curve for 12,000 ft for the same engine. This plot demonstrates the compound effect engine torque loss has on performance. Because the engine speed is determined by the torque capacity characteristic (Eq. 2.3.1), engine speed is reduced, resulting in a greater reduction in horsepower than is the case with a mechanical gear train. This phenomenon prevails for all speed-ratio conditions and limits utilization of the available engine horsepower. It is, therefore, particularly important to consider the grade performance and cooling requirements at altitude conditions.

2.3.12 Sizing Hydrodynamic Units Important considerations in the determination of the size are: 1. 2. 3. 4. 5. 6. 7.

Vehicle weight Vehicle performance requirements Transmission arrangement Type of hydrodynamic unit Inertia effects on shifting Engine torque versus speed characteristics Altitude effect on engine

Fundamentally, the hydrodynamic unit must be matched to the vehicle. The basic concept of the vehicle size, weight, and performance requirements must precede the selection of the powerplant and drivetrain. The discussion outlining the methods used to obtain the combined operating characteristics of the engine-transmission-vehicle system provides the technique for selecting the size of the hydrodynamic unit. The output load conditions can be established based on performance requirements such as:

Fig. 2.3.15  Engine requirements for 10% grade compared with engine at sea level and 12,000 ft altitude.

1. Maximum speed 2. Cruising economy 3. Gradeability

Stall speeds, in general, have been increasing since the first introduction of hydrodynamic units for several reasons:

Using the log-log plot as previously discussed (Fig. 2.3.12), the output capacity speed-ratio characteristics of the hydrodynamic unit are matched to these requirements. This is best accomplished by shifting the speed-ratio lines horizontally until the best balance of performance conditions is found. Reviewing the previous discussion of the log-log plots, it can be shown that shifting these lines is, in effect, changing the size of the hydrodynamic unit.

1. 2. 3. 4. 5. 6.

Engine power-to-weight ratio increases Altitude performance considerations Idle creep reduction Use of split-torque arrangements Increased stall-torque ratios Variable-capacity units

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Design Practices: Passenger Car Automatic Transmissions

2.3.13 Designing Hydrodynamic Units

Some of these factors will be discussed further in the following sections.

The design of successful hydrodynamic units depends on relatively simple, but vitally important fundamentals:

The transmission engineer will be concerned particularly with the type and size of the fluid unit to be used when evaluating the gear ratio changes. Larger hydrodynamic units have larger inertia values, which affect shift quality and stress loads on drivetrain components.

1. 2. 3. 4. 5. 6. 7.

Referring again to Eq. 2.3.1, the capacity constant C is dependent on the fluid density and viscosity, which are characteristics of specific fluids. These characteristics vary with the temperature of the fluid, but are not influenced by the normal pressure variations used in the passenger car applications under discussion, except for cavitation conditions discussed under Special Problems. Figure 2.3.16 shows the effect of density change on converter performance for oils with Type A transmission oil viscosity characteristics. Figure 2.3.17 shows the effect of temperature on converter performance for a Type A oil.

Steady-state equilibrium Newton’s second law of motion Newton’s third law of motion Continuity concept Momentum law Conservation of energy A consistent system for description of angles and vectors

Steady-state equilibrium is assumed for all bladed elements comprising the hydrodynamic unit. Since the motion of the elements is rotary about a common axis, equilibrium requires that the sum of all torques is zero. Equation 2.3.8 is written for a three-element system as: where:

∑ T = 0 = Ti + TT + TR

(2.3.8)

Ti = impeller torque TT = turbine torque TR = reactor torque In the following pages, all element torques will be defined as the torque imposed on the blades by the action of the fluid flowing through the passages. Further, torque that tends to produce rotation in the direction of engine rotation will be considered positive. Torques opposite to this will be negative. Under this definition, turbine torques acting directly on the propeller shaft to produce forward motion of the car are positive, and impeller torques, which in effect oppose engine rotation, are negative. This concept of negative impeller torque is an application of Newton’s third law, which states that for each force there must be an equal and opposite reaction.

Fig. 2.3.16  Effect of fluid density on converter performance (150 lb.-ft. input torque test).

Element torques are expressed in equation form as follows (similar to the equation given in the SAE Handbook): where:

T = M(S¢R ¢ − SR)



(2.3.9)

M = mass flow rate S¢ = tangential component of absolute velocity of fluid entering element S = tangential component of absolute velocity of fluid leaving element R¢ = radius at which fluid mass is considered effective at entrance to element

Fig. 2.3.17  Effect of fluid temperature on converter performance (170 lb.-ft. input torque test).

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Torque Converters and Start Devices

R = radius at which fluid mass is considered effective at exit of element

dV d(MV) = dt dt

V = final velocity in x direction V¢ = initial velocity in x direction Torque can now be expressed by incorporating radius corresponding to the particular velocity component:

(2.3.10)

f = force in direction of V M = mass of particle V = velocity in direction of force MV = momentum

U = 2πRN

S = F cot a

Equation 2.3.10 applies to a solid mass M . In order to apply — the principle to fluid flow, a definite mass corresponding to M must be identified. This is accomplished by defining a control surface enclosing a constant mass of fluid. The change in the momentum of the mass contained within the control surface between time t and t + dt represents the force exerted on the mass. The principle applies to real fluids, compressible and noncompressible. For application to automotive hydrodynamic units, the fluid is considered noncompressible and the density essentially constant, in which case the control surface enclosing the constant mass becomes a constant-volume system for which the continuity equations apply as follows:



(2.3.14)

F=Q÷A —

Q = A¢ V¢ = AV

T = fx ⋅ R = M(VR − V¢R¢)

The last two equations developed from Newton’s second law represent the external force and torque acting on the fluid, respectively. To obtain Eq. 2.3.9 for a blade element representing the torque on the element produced by the fluid action, the sign of Eq. 2.3.14 is reversed and the symbol S is substituted for V. A more thorough theoretical derivation of Eqs. 2.3.13 and 2.3.14 will be found in Ref. 5. Equation 2.3.9 is written in a more convenient form for design use by expanding the individual terms. The following relationships are clarified by the vector diagram (Fig. 2.3.18):

where:



(2.3.13)

fx = force in direction x

For application to fluid-mechanics problems, the equation is written expressing acceleration as the time rate of change of velocity. This results in an equation evaluating force in terms of a time rate of change of momentum. f=M



where:

Equation 2.3.9 is a mathematical statement of the rate of outflow of moment of momentum from the fluid stream as it passes through the element. This moment of momentum change has the dimensions of force and distance and represents the torque exerted on the blade surfaces. The development of the moment of momentum concept is based upon the momentum law, which in turn is derived from Newton’s second law of motion: force = mass ¥ acceleration.



fx = M(V − V¢)





d ⋅ Q = d ⋅ A¢V¢ = d ⋅ AV = M

s = U + S = 2πRN + F cot a S = tangential component of relative velocity W F = fluid velocity in axial plane, torus flow A = net flow area normal to axial plane V = absolute flow velocity W = flow velocity relative to blade a = flow angle relative to reference plane (may differ from blade angle a) U = physical velocity, linear velocity of blade tip at radius R

(2.3.11)

Substituting in Eq. 2.3.9 and adding the prime to entrance values,

(2.3.12)

where:



Q = volume flow rate A¢ = area normal to flow at inlet A = area normal to flow at outlet d = density of fluid

T = d ◊ AF[(2πR ¢N¢ + F¢ cot –a¢) R ¢ – (2πRN + F cot –a) R]

(2.3.15)

Adding the appropriate subscript, this equation applies to the particular member so designated. Since the fluid in the general case does not approach the element at the minimum loss condition, corresponding to values obtained at the blade entrance tip, values for the approach condition must be based on the exit conditions of the preceding element. In practice, preliminary performance computations frequently assume

Integrating Eq. 2.3.10 results in the following force equation:

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Design Practices: Passenger Car Automatic Transmissions

the radius of the entrance equal to the radius of the preceding exit, resulting in the commonly used form shown here for the impeller of a fluid coupling: Ti = d ¥ AF[(2πNTRT + FT cot aT) RT – (2πNpRp + Fpcot ap) Rp]



increment are treated like the entrance and exit, respectively, of the element in the previous discussions. The load on the blade, and therefore the curvature, is distributed along the length of the blade.

(2.3.16)

By inspection, it is clear that the corresponding turbine torque equation for the fluid coupling would contain the same quantities, except that the terms within the brackets would be reversed in sign; hence, the proof that the fluid coupling always operates hydraulically at 1:1 torque ratio. Furthermore, it becomes evident why the exit values of the elements are the primary factors affecting the performance characteristics. 2.3.13.1 Blade Angle and Vector Systems A consistent system of vector and angle definitions is vital to the successful prediction and analysis of hydrodynamic performance. The system shown in Figs. 2.3.18 and 2.3.19 is known as system B and is the preferred system in SAE hydrodynamic terminology. The blade angle is always measured from the tangential line in the direction of rotation and in the direction of fluid flow. The sign of the angle is determined by the sign of the geometric cotangent in the first or second quadrant as it applies to the particular angle value. Rotation is positive when in the direction of impeller rotation. System A is also widely used and differs only in that the angles are measured from the radial plane (plane containing the axis of rotation). The advantage of system A is that angle values are always less than 90°. The sign of the angle is positive if in the direction of rotation of the impeller, and negative if opposite. Either of these systems will yield correct results if consistently applied.

Fig. 2.3.18  Vector diagram of fluid velocities at impeller exit.

The general torque equation applies equally to free-wheeling elements. By definition, the net torque on the element is zero when it is free-wheeling. The free-wheeling point is the point at which torque is zero and speed zero. The free-wheeling speed is determined by rearranging the equation with torque equal to zero. A typical reactor speed equation follows:



Fig. 2.3.19  Vector diagram of fluid velocities at turbine inlet.

⎛ R 2 ⎞ F cot a TR T FR cot a R NR = N t ⎜ T ⎟ + T − (2.3.17) ⎝ RR ⎠ 2πR R2 2πR R

The torque equations in themselves are not sufficient to determine the actual operating characteristic curves. The flow velocity for each condition must be determined. To accomplish this, an energy balance is determined using the following relationships, which express the energy in terms of the head.

if RT = RR

NR = N t +

FT cot a T − FR cot a R 2πR R



(2.3.17a)

The general torque equation is also used for blade design. In this application, the blade length is divided into many incremental lengths. The upstream and downstream edges of each



H input = H output + H losses

(2.3.18)

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For rotating components, the work energy is: H=

where:

T ⋅ w 2πNT = d ⋅Q d ⋅Q

where: Hi–T = shock loss at impeller and turbine junction HT–R = shock loss at turbine and reactor junction HR–i = shock loss at reactor and impeller junction

(2.3.19)



w = angular velocity, rad/s

Referring to the vector diagram (Fig. 2.3.19), S represents the vector difference between the absolute Vg in the gap, and the absolute velocity V¢ at the entrance tip of the downstream element. I I ΔS = Vg − V′ = Sg − S¢ (2.3.25)

Loss heads are evaluated by the familiar general equation:



HL = C L

V2 F2 ΔS 2 = CF ⋅ + ∑ CS 2g 2g 2g



(2.3.20)

where:

Vg and Sg are determined from conditions at the upstream exit assuming no torque change across the gap. By substitution, (3.2.24a) becomes:

g = gravitation constant, 32.17 ft/s2 The losses are considered to consist of two types—friction losses and shock losses. Each element contributes to the losses, and therefore the system loss is the sum of several losses of the form of Eq. 2.3.20. Two basic types of loss are considered to occur within the individual members as a result of the internal fluid friction and the rubbing action of the fluid on the passage walls. Shock losses are considered to occur across the junctions of members resulting from sudden velocity changes (direction and magnitude) as the fluid enters passages at other than the minimum loss direction. Because the passage configuration is fixed for a given design, the friction losses are expressed in terms of an effective relative velocity for each element. For a typical three-element system, Wi2 ⎞

WT2 ⎞

WR2 ⎞

⎛ ⎛ ⎛ HF = ⎜ C F ⋅ + ⎜ CF ⋅ + ⎜ CF ⋅ ⎟ ⎟ 2g ⎠ i ⎝ 2g ⎠ T ⎝ 2g ⎟⎠ R ⎝

HS =



W = F ÷ sin a

∴ HF = C F

—

F 2g

(2.3.21)

HS = Hi–T + HT–R + HR–i

Select a desired input torque. Select an output speed value. Estimate flow velocity F. Calculate impeller speed using impeller torque, Eq. 2.3.15. 5. Calculate turbine torque, Eq. 2.3.15. 6. Calculate impeller and turbine workheads, Eq. 2.3.19. 7. Calculate loss head as difference of workheads, Eq. 2.3.18. 8. Calculate friction loss head, Eq. 2.3.23. 9. Calculate shock loss heads, Eq. 2.3.26. 10. Sum friction and shock loss heads, Eq. 2.3.20. 11. Difference of workheads must equal the sum of the loss heads. 12. If the two values of loss heads are not equal, assume new value for flow F. 13. Repeat procedure until balance is obtained. 14. Calculate n, t, and E.

(2.3.24)

⎛ ⎛ ΔS 2 ⎞ ΔS 2 ⎞ HS = ⎜ C S ⋅ + C ⋅ S 2g ⎟⎠ i − T ⎜⎝ 2g ⎟⎠ T − R ⎝



⎛ ΔS 2 ⎞ + ⎜ CS ⋅ 2g ⎟⎠ R − i ⎝



(2.3.26)

1. 2. 3. 4.

CF is characteristic of the particular system. It is not necessarily constant for all velocities. Values are determined empirically. Because the vector relationships across the junctions between members change with speed ratio, the junction (shock) losses must be individually evaluated. This is done by considering the loss a function of the change in tangential velocity S across the gap:



All of the equations necessary for estimating flow velocity and performance data are available. One sequence used in actual practice proceeds as follows:

(2.3.23)



CR −i (SR − S¢i ) 2g

The values of Ci–T, CT–R, and CR–i depend on the shape and size of the blade on which the flow is impinging. First approximations frequently assume these values to be unity. Effective values for actual designs including hydrofoil shapes are obtained empirically.

(2.3.22)

2

+



At any point in a passage:

Ci− T C (Si − S¢T )2 + T − R (S T − S¢R ) 2g 2g

(2.3.24a) 2-45

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Design Practices: Passenger Car Automatic Transmissions

Performance of all hydrodynamic units can be estimated by applying the equations and procedures outlined.

Torque and speed data are recorded using specified fluids under controlled conditions of temperature and pressure. Frequently, the input torque is kept constant (at approximately one-half of maximum engine torque) while output speed is varied from zero (stall) to the maximum required by the vehicle or permitted by the test equipment. These data are plotted in the form of speed ratio or output speed plots, as previously discussed. It is also common practice to make runs at very low input torque levels for zero-grade road-load evaluations and at high torque levels for WOT evaluations. The value of the exponent for speed in the torque capacity (Eq. 2.3.1), previously shown as 2, can be verified by making log-log plots of corresponding input torque and speed data at common speed-ratio values. The slope of the capacity lines is then measured. Slopes less than 2 have been observed and can be expected from a more detailed study of fluid mechanics. All of the previously discussed methods of obtaining combined performance can be used by substituting the new exponent obtained from careful and accurate laboratory tests. Capacity lines are easy to obtain for zero speed-ratio conditions (stall) from one run in which both torque and speed vary with the output locked. Performance runs of this type can provide data at actual installation conditions of pressure and temperature, which may differ from ideal conditions because of overall transmission design requirements and limitations. The overall influence of design variations—both hydraulic and mechanical—such as blade angles, blade shapes, torus shape, bearings, thrust balancing methods, and running seals, can be evaluated best by the general performance tests.

2.3.14 Laboratory Experiments Laboratory experiments have been an important factor in the development of the hydrodynamic units in use today. All phases of the design problem have been studied in order to verify the theoretical fluid mechanics equations, the mechanical design of the major components and related parts, and the materials and processes used for the production units. The types of tests include the following: 1. Hydraulic performance—complete unit 2. Mechanical performance—complete unit 3. Cooling tests—complete unit 4. Thrust measurements—components 5. Torque measurements—components 6. Speed measurements—components 7. Deflection measurements—components 8. Component mechanical tests—fatigue 9. Component hydraulic tests—qualitative data 10. Component hydraulic tests—quantitative data Hydraulic performance of the complete unit for all drive arrangements (drive and coast) is usually obtained by means of a typical dynamometer arrangement, using one driving machine and one absorbing machine. The hydrodynamic unit is housed in a suitable fixture. Relatively simple fixtures are used for basic performance data (Fig. 2.3.20). More complex fixtures are required to obtain thrust, speed, torque, and deflection data for all elements under actual load conditions.

Durability of the unit is evaluated by use of cycling tests made under specified conditions of load, speed, temperature, and pressure. This is done using the complete unit and is supplemented in many cases by mechanical tests of individual components. Blade form testing is done in specialized facilities where the performance of individual cascades can be measured and observed. These tests are used to verify and augment the theoretical design work and provide a means of comparing the performance of individual components and correlating these results with the performance of the complete system. Test facilities for this purpose have been constructed employing oil, water, and air as the fluid media. Careful study, testing, and analysis can yield helpful design information with either facility. One facility uses a large flow table (Fig. 2.3.21) to observe flow patterns. Other equipment is used for measuring pressures and forces (direction and magnitude). This laboratory uses water as the working medium.

Fig. 2.3.20  Typical fixture used to performance test hydrodynamic units. 2-46

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Torque Converters and Start Devices

on each blade tip as it passes tips of the adjacent member. The frequency of the pulse on each blade and the higher system frequency resulting for all such pulses depend on the number of blades in the various elements and the relative arrangement and rotational speed of the elements. If several tip pulses occur simultaneously, the intensity effect of the pulse is increased. Noise is heard when the pulses cause mechanical parts of the converter or transmission to vibrate and produce sound. This type of noise is controlled by selecting prime numbers for the blades of elements, providing a difference of one or two blades for the adjacent elements, avoiding common factors for blade numbers of adjacent blade systems, and varying blade spacing. Cavitation refers to the phenomenon of alternate formation and collapse of gas bubbles on the surface of the passages at points where the pressure is lower than the vapor pressure of the fluid. The gas bubble is formed by vaporization of the fluid at the low-pressure point. The bubble collapses as it moves downstream into a region where the pressure is again greater than the vapor pressure. The collapse of the bubble is accompanied by a localized impact of the fluid on the surface. The net result is a noise band including extremely high frequencies and many frequencies or harmonics in the audible range. This type of noise is controlled by maintaining necessary temperature and pressure.

Fig. 2.3.21  Large flow table used to cascade flow information.

2.3.15 Special Problems The engineer with any imagination at all will, by now, be aware of many potential problems that may need to be solved before a transmission can be released for use by the driving public. The following is a list of items that must be considered and require special attention. 1. Noise 2. Construction materials and methods 3. Thrust 4. Deflections 5. Cooling 6. Pulsations 7. Instability 8. Transients 9. Special control devices 10. Dimensioning and tolerances 11. Fatigue

Mechanical interference results from rubbing contact of the elements caused by incorrect dimensions or deflections of elements at junctions with inadequate running clearance. Construction materials and methods selected depend on: function of the part, accuracy required, production volume, material cost, process cost, assembly cost, and replacement or repair cost. Three production methods for completing the assembly of the hydrodynamic unit are excellent examples of different answers to these problems. These assemblies must be oiltight under stress caused by centrifugal and static pressures. Some designs complete the assembly by bolting at a flange diameter. Sealing is accomplished by an O-ring, either square or round section. A second design type uses a seam weld at the overlap of the housing and cover. The third method employs a double O-ring type of seal arrangement between the cover and the housing and a large retainer ring to hold the cover in the housing.

Noise is produced by hydrodynamic units because of the following conditions: a. Hydraulic interference—blade tips passing b. Cavitation—dependent on fluid temperature and pressure c. Mechanical interference

Thrust loads result from pressure differences existing on the surfaces of the elements and the housings. The pressures are a combination of static charge, centrifugal, and passage flow pressures. Because of the differences in physical shape, speed, and flow characteristics of the various elements, ­complex systems of pressure distribution exist. High axial

Hydraulic interference refers to the peripherally nonuniform flow of the fluid from the finite number of blades and passages of a given member. It is not practical to space elements far enough apart to obtain homogeneity in the gap between members. There is, therefore, a uniform pulse type of force 2-47

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thrust forces can result because of relatively large effective piston areas (of the order of 100 in.2). A knowledge of the static and dynamic pressures within the hydrodynamic unit is a help to determine means of controlling these forces that cause deflections (noted above) and bearing thrust loads. Running seals (labyrinths), pressure balance holes, and fins are some of the means available to limit the loads by altering the pressures within the unit.

Special control devices include means to produce changes in the performance and pressure characteristics; these include special attachments and special modifications of the torus or blading, such as baffles, variable blades, fins, and auxiliary blades. Dimensioning and tolerance systems need careful study by the designer to ensure maximum results with minimum cost.

Cooling is obtained by circulating oil from the transmission sump, circulating cooling air around the unit, and radiation.

Fatigue problems may occur, usually as the result of the hydraulic tip interference pulsations. Experience has shown the discharge end of pump blades to be particularly vulnerable. Sheet-metal assemblies require strong, tight attachment. Castings require fillets at the intersections of the blade surfaces with the core and shell surfaces. The strains imposed on the impeller housing at and near the outer diameter contribute to the fatigue problem.

Depending on the application, special provision is usually made to circulate some oil from the transmission sump through the hydrodynamic unit, through an oil-to-water cooler, and back to the sump. The water side of the cooler is connected to the engine cooling system. Frequently, the cooler is incorporated at the bottom of the engine radiator. In some instances, the cooler is not required. In other cases, cooling fins are provided on the outside surface of the impeller housing. The fins are designed to function as an air blower to circulate cooling air over the hot housing and also to increase the cooling surface area. They are particularly effective in adding cooling surface when forming part of an integral casting.

2.3.16 Acknowledgments The field of design and application of hydrodynamic drive units is an intriguing one, particularly for the engineer who likes to cope with problems requiring solutions not found in textbooks and handbooks. Problems remain to be solved, and better solutions are needed for others. The author is grateful for the associations with and the cooperation of many persons through the years, especially those of the Engineering Staff of the General Motors Corp., during the working out of solutions to problems in this field. These experiences have provided the background material for the paper. To those who helped directly with the preparation of the manuscript, sincere thanks.

Pulsations are usually encountered during steady-state dynamometer tests occurring when system conditions permit unstable flow in the normal operating range. Flow surges may occur, resulting in large cyclic changes in speed and torque. Examples of conditions that may cause pulsation are zero torus (circulation) flow, element rotation reversal, and two or more possible speeds for an element at one speed ratio. The transmission engineer usually avoids using the units under the first and second conditions. The third condition is seldom experienced in the vehicle, but provides an interesting fluid dynamics problem.

2.3.17 References 1. Ward Automotive Year Book. 2. Wards Automotive Reports, Vol. 36, No. 10 (March 6, 1961) and 1970 Summary. 3. Chapman, C. S. and R. Gorsky, “The New Buick Special Automatic Transmission-The Dual-Path Turbine Drive,” Paper 290B presented at SAE Automotive Engineering Congress, Detroit, January, 1961. 4. Block, P. and R. C. Schneider, “Hydrodynamic Split Torque Transmissions,” SAE Transactions, Vol. 68, (1960). 5. Hunsaker, J. C. and B. G. Rightmire, “Engineering Applications of Fluid Mechanics,” New York: McGraw Hill Book Co., Inc., 1947.

Instability, like pulsations, may be evidenced by large cyclic changes in speeds and torques but is caused by a different phenomenon. The condition considered here is one of a change in the basic performance characteristics, such as that accomplished with a variable-blade element. As the direction of the flow approaching the blades changes, the center of pressure (load center) shifts and changes in magnitude. The resulting change in the force moment about the blade pivot causes the blade to change position. The new position establishes new flow vector relationships and again shifts the load center, causing the blade to return to or near its original position. This problem is solved by proper blade mounting and control design.

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2.4 Design of Single-Stage, Three-Element Torque Converter*

growing competition from other forms of infinitely variable mechanisms.

V. J. Jandasek Transmission and Chassis Div., Ford Motor Co.

In the past, the hydrodynamic torque converter has been discussed in a number of papers that gave the theory and equations for the various details of function. However, these have omitted the important coefficients and constants required to complete a usable design. Rather than basic theory, this paper will be concerned with specific coefficients and practical guidance to enable the designer to compute and build a competitively acceptable unit. Since the number of variables involved in the design of a converter is sizable, the approach has been confined to a specific type.

Interest in the hydrodynamic torque converter became serious in the United States in the early 1930s, and by 1938 its use had been initiated in city bus installations. During World War II, considerable effort was applied to the development, and a number of applications to heavier military vehicles resulted. Following the war, development of the torque converter was undertaken extensively by several organizations for application to passenger cars and trucks. A prime objective was to obtain a simple unit susceptible to fabrication by methods that would result in low cost.

Our discussion will be concerned solely with a three-element converter; that is, three members, each with only one element or row of flow-directing blades. It will, therefore, be a single-stage unit. It will be two-phase in operation, with the first phase encompassing operation as a torque converter and the second involving a fluid coupling range. It will have a rotating housing and torus with a disposition of impeller, turbine, and reactor as given in Figs. 2.4.1 and 2.4.2.

Evidence of the success of this work is shown by the millions of converter units built since 1950, with applications ranging from passenger cars to heavy commercial and military vehicles. Included are a wide variety of units for off-road usage such as wheel and track-laying tractors, loaders, highway rollers, graders, lift trucks, and cranes. This has been accomplished almost wholly in the United States, although, as is well known, the torque converter was originally developed in Europe for ship propulsion by Foettinger in the first decade of the twentieth century, and subsequently by others for additional uses. Recent indications from Europe show an increasing interest in the converter for application to various types of vehicles, and it can be expected that its usage there will expand accordingly. The primary function of the torque converter is torque multiplication. This is a maximum at stall and decreases without step to a value of unity at the coupling point. Thus, a converter provides an infinitely variable transmission within the limits of these ratios.

Fig. 2.4.1  Three-element torque converter.

Aside from this, the converter has several other important features. It is a rugged, durable device, simple in construction if not function, that can readily be made to outlast other components of a transmission system. It provides a fluid smooth startup that is predictable, consistent, and has unlimited durability. This permits a gradual assumption of the load and is controllable to the degree that makes it possible to hold a load as, for example, a vehicle on a grade. It can give an acceptably efficient fluid coupling for normal cruising or operating conditions. Lastly, it provides excellent torsional damping at all speeds and provides a cushion in the driveline, protecting it from shock. The increasing application of converters, both in number and variety, substantiates the desirability of these advantages and features in spite of *This was the seventh L. Ray Buckendale Lecture. It was presented in January 1961.

Fig. 2.4.2  Torus section. 2-49

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In its simplest form, the torque converter consists of three elements working in a closed circuit: an impeller rotated by the prime mover, a turbine attached to the output shaft, and a reactor fixed to the case through a one-way clutch. The impeller centrifugally pumps fluid into the turbine. In turn, the turbine absorbs the energy of the fluid by deflecting and discharging it in a backward direction. The reactor provides the necessary torque reaction by redirecting the backward flow from the turbine to a forward direction to discharge it into the impeller. This completes the cycle and, since we have a closed circuit, it is repeated continuously. As the speed of the turbine increases, it builds up a centrifugal head that is counter to the head of the impeller. This gradually reduces the flow and consequently reduces the force on the reactor. As this process continues with the turbine further increasing in speed, the flow is eventually reduced to a value where the force on the reactor becomes zero. This is the point at which the converter ceases to multiply torque and starts to function as fluid coupling. It defines the coupling point. Beyond this, the reactor rotates in a forward direction with a gradually increased speed as the turbine increases its speed.

this calculation. Stall speed is determined from its effect on a number of performance characteristics. The engine torque curve is a prime factor. If the maximum torque output at stall is desired, the converter stall should coincide with the speed at peak engine torque. Another factor is the carryout of torque ratio into the vehicle speed range. As will be seen subsequently, selection of stall speed for a given converter also selects the speed characteristic quite definitely and thus determines the speed to which torque conversion will extend. For example, a converter may be selected to have an engine stall speed of 1600 rpm with torque conversion extending to 2400 rpm. By reducing the size appropriately, a converter with characteristics otherwise unchanged may have a stall of 2500 rpm and torque conversion extending to 3750 rpm. Obviously, this is a drastic change, but it serves to illustrate possible adjustment of range of torque conversion. Factors contrary to high stall speeds include high fuel consumption and excessive powerplant noise level. Most vehicle installations today using engines with peak horsepower occurring at 3600 to 4400 rpm have stall speeds ranging 1500 to 2000 rpm which place them at or sufficiently near the torque peak to give near-maximum starting torque. With the stall ratio figure established, it is possible to arrive at an impeller exit angle from the curve on Fig. 2.4.3. It represents the relation of

This explains the function of the converter in elementary terms. As we proceed through the details involved in design, a more complete explanation of function will be apparent.

2.4.1

Circuit Size

The fundamental relationships of torque and power to speed and diameter have been well established for torque converters. These can be expressed for the impeller by equations:

Ti = CNi2D5i

(2.4.1)



hpi = cN3i D5i

(2.4.2)

where: Ni = impeller speed Di = impeller diameter C, c = coefficient for given design Although both torque and power equations are given, size computations will be on the basis of torque, as is common in transmission design, since this is more nearly related to engine size. In the calculation of converter size, the desired stall torque ratio and speed must first be determined from the performance requirements projected for the vehicle under consideration. Tractive effort requirements for startup will determine the stall torque ratio and, if a gearbox is used for supplementing this ratio, its efficiency, which may be 85% to 90% at stall or near-stall conditions, must be included in

Fig. 2.4.3  Relationship of stall-torque ratio and impeller exit. 2-50

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of coefficient based on design path diameter and circuit is obtained as follows:

impeller exit angle and stall torque ratio for a 12-in.-diameter converter, which had been derived from the experimental development of a number of converter sizes over a period of about 15 years. Blade angles of the other elements have been established at optimum for stall ratios between 2 to 2.5 with peak efficiencies occurring at high-speed ratios and having good coupling characteristics. This will be our reference unit with circuit, blading, and other pertinent dimensions specified in the Appendices.

5

⎛D ⎞ C = ⎜ 1i⎟ C = 1.357C ⎝Di⎠ 1

where:

(2.4.3)

D1i = diameter at design path

Di = outside diameter of circuit at impeller C = capacity coefficient shown in Fig. 2.4.4 and used in computation of outside diameter of circuit

From Fig. 2.4.4, a value for the coefficient C at stall (0 speed ratio) may be taken. This coefficient is then used in Eq. 2.4.1, and, with the torque and speed as given for a particular installation, the diameter of the converter may be calculated. It may be well to note at this point that both larger and smaller converters can be projected accurately from the procedure just outlined, providing that strict similarity is maintained in circuit configuration and blading.

The use of coefficient C1 in place of C in Eq. 2.4.1 will then give a correct solution for the diameter D1 at the design path.

2.4.2

Performance Analysis

A more complete evaluation of the suitability of the converter tentatively selected may be made from Fig. 2.4.5, which illustrates the torque ratio curves related to speed ratio, with the latter defined as the ratio of the output to the input speed. For a particular stall torque ratio, the relationship of torque ratio and speed ratio is given by a characteristic curve of this figure. Having thus obtained values of torque ratio and speed ratio, efficiency is readily computed from the equation E = t ¥ n. Characteristic curves of efficiency for the full range of impeller exit angles are shown in Fig. 2.4.6.

Fig. 2.4.4  Variation of converter torque capacity at stall with impeller exit angle. The computation of the converter on the basis of the O.D. is used as a simplified method that gives the circuit size directly. For greater accuracy, and particularly for the computation of units differing greatly in size from the reference unit, the design path diameter should be used. Since by definition the design path is the path of assumed mean effective flow, the design path diameter of the circuit more correctly applies to the torque and power relationships than does O.D.; however, a corrected coefficient must be used. For the 12-in.-diameter converter used here as a reference unit, the design path diameter is 11.289 in. From these diameters, a relationship

Fig. 2.4.5  Relationship of torque ratio to speed ratio for various impeller exit angles. 2-51

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From these figures illustrating torque ratio and efficiency characteristics, it is apparent that an increased torque ratio results in a decreased peak efficiency and coupling point. This is a surprisingly rigid relationship, almost as fixed as in gearing, when not disturbed by major dissimilarities apart from blade angles. Although this observation is predicated on the effect of impeller exit angle, changes in other blade angles, particularly at the entrance, generally show the same characteristic. Some of the reasons for this will be apparent from the vector studies discussed later in conjunction with blade angles.

provide specific conditions for this example. This shows that an impeller with an exit of 145° or backward bend has a dropping input speed from stall to 0.5 speed ratio and thereafter increased to the coupling point (0.82 speed ratio), but does not regain a level equal to stall. As the impeller exit angle is decreased, this changes, and, with radial and forward bend exit, the input speed has a rising characteristic of a substantial amount. This is advantageous for most road vehicle applications, because it extends torque conversion to higher speeds and thus improves vehicle performance. Much of the early work on torque converters was based on the use of impeller blades of considerable backward bend, about 135° exit, similar to those common in centrifugal pumps. While this design gave high stall ratios, the torque capacity was low requiring large-diameter units, and coupling point and fluid coupling characteristics left much to be desired. With the use of radial and forward-bend impellers, the stall torque ratios were reduced but the favorable effect on the capacity, speed rise characteristic, coupling point, and converter and coupling efficiency at high-speed ratios was of such magnitude that it made possible the application of the converter to automotive transmission applications. Today, this impeller blading is generally used in applications where both converter and fluid coupling efficiency is desired.

Fig. 2.4.6  Efficiency characteristics at various impeller exit angles. When plotted against speed ratio, the characteristics of torque ratio and efficiency are extremely useful in readily appraising converter performance. This is more apparent when one realizes that the torque ratio and efficiency characteristics remain substantially constant for similar converters regardless of size or torque applied. Similarity here must include both flow circuit configuration and blade details. The factor of size or torque does affect the absolute speed at which given values of torque ratio and efficiency occur. In the foregoing determination of converter size, we have seen that the impeller exit angle is the major factor affecting stall torque ratio. In addition to this, it is also of major significance in its effect on the speed characteristic. In order to illustrate the point, this characteristic is shown in Fig. 2.4.7 for the various impeller exit angles with the impeller speeds computed for a 12-in.-diameter unit and a 200 lb.-ft. torque to

Fig. 2.4.7  Effect of impeller exit on speed characteristics.

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An accurate projection of performance can be made using values of torque ratio and efficiency from the previous information in conjunction with the speed characteristic obtained by solving Eq. 2.4.1 for N at constant input torque and various speed ratios using applicable values for coefficient C from Fig. 2.4.8. For a 12-in.-diameter converter with a 75° impeller exit, the result will give curves as illustrated in Fig. 2.4.9 when plotted against speed ratio and Fig. 2.4.10 when related to output speed. In addition to the characteristics of ratio, efficiency, and input speed, a value of factor K has been included in these figures. The K factor is a parameter representing the relationship of torque and speed for a converter of a particular size and blading and is expressed by the equation: K=



N T

(2.4.4)

where: N, T = speed and torque, respectively.

Fig. 2.4.9  Converter performance as typically plotted against speed ratio.

Fig. 2.4.10  Converter performance as typically related to output rpm. It is useful for the expeditious computation of converter performance for different torque and speed conditions and can be used for either input or output conditions. Speed and torque must be consistent for either input or output. Another form of the capacity as defined in Eq. 2.4.1 is derived by introducing the factor K: 1 (2.4.5) 2 5 K Di Using this, K may be calculated from coefficients given in Fig. 2.4.8 and the diameter Di obtained previously. The impeller speed corresponding to any torque curve can then be computed. C=

Fig. 2.4.8  Torque capacity coefficient as affected by various impeller exits.

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Another example of the use of the K factor is the calculation of converter slip at road-load conditions for a truck installation, resulting in a typical slip curve as shown in Fig. 2.4.11. This is indicative of the low value of slip attainable with a properly sized and designed unit.

reached a point of diminishing returns, and peak efficiency is less than optimum. Torque ratio is adversely affected only when the area is drastically reduced. Table 2.4.1  Flow Area from a Range of Production Converters. Converter Diameter (in) 10.25 11.75 12 12.31 13

Circuit Flow Area (in²) 20.0 23.9 26.0 25.1 30.0

Area* (%) 24 22 23 21 23

*Area, %, relates circuit flow area to the area of a circle represented by the converter diameter.

Fig. 2.4.11  Converter slip at road load. In the foregoing, the performance has been appraised with the assumption of converter ratio and stall speed which appeared to be best for a given installation. In order to obtain a broader analysis, it is advisable to assume other plausible ratio and speed values and compute the performance characteristics. Since the converter is normally supplemented by gearing, this should be included. It is thus possible to readily simulate and thoroughly evaluate several converters having different stall ratios and speeds within the range of ratios provided prior to embarking on the detailed design of the unit.

2.4.3

Flow Circuit

Assuming that our selection of a converter acceptably meets the performance requirements and will fit in the space available, we are ready to continue with the circuit design. The practical limit for the maximum flow area for a given converter diameter is determined by several factors, including effectiveness of increments of flow area at the core, reactor blade height and efficiency due to large pitch-to-chord variation from shell to core sides, and provision for an overrunning clutch assembly between the reactor blading and shaft axis. Taking all such factors into account, a range of production converters gives the flow areas shown in Table 2.4.1. It may be observed that values for flow area vary from 21 to 24%. A more graphic illustration of a determination of optimum flow area results from an experimental development on an 11.75-in.-diameter former production converter in which the flow circuit was altered to several values of larger and smaller areas by changing the core. All blading and other conditions were unchanged. A comparison of performance of this unit at the various flow areas in Fig. 2.4.12 shows that at the maximum circuit of 28 in.2, the capacity (size factor) has

Fig. 2.4.12  Effects of circuit flow area on converter performance characteristics. The most efficient torus configurations of three-element converters have been shown to be circular sections or minor modifications of such sections. Severe modifications of the circular section were tried in order to obtain a more compact circuit but the results were discouraging in that capacity and

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efficiency was decreased. Current practice indicates that the minor diameter of the circuit is about one-third the O.D. From this it can be determined that the torus diameter (Fig. 2.4.2) is also equal to one-third the O.D. if a circular section is assumed. Having established the outlining dimensions and flow area of our converter circuit, it is now possible to compute the dimensions of the core and the complete design path. The circuit design is predicated on a uniform flow area throughout the design path, which has been shown to be good practice. A detailed procedure for the calculation of the circuit, including the design path and core, is given in Appendix A.

2.4.4

Blading

Since the blading of the torque converter transmits all of the torque, its design is of utmost importance. Ideally, each of the blade systems would receive fluid without shock, deflect the flow smoothly throughout the length of blade passage, and discharge the fluid at the optimum angle at all conditions of speed and torque. Unfortunately, it is not possible to meet these ideal requirements, particularly with respect to shock losses. The problems involved will be discussed later in conjunction with inlet angles.

Fig. 2.4.13  Effect of reactor exit angle on performance.

The function of the impeller blades is to impart energy to the fluid. As we have already seen in the determination of the converter circuit, the impeller blade discharge angle directly affects stall torque ratio. Thus, the selection of stall ratio effectively determines the discharge angle.

Next we will consider the inlet conditions. Flow direction at each blade entrance is obtained from vector analyses involving blade exit angle, peripheral velocity, and torus flow. Examples of vector diagrams at various speed ratios are illustrated in Fig. 2.4.14. The detailed computations are given in Appendix B.

The turbine receives fluid from the impeller and absorbs the energy by deflecting the fluid and discharging it in a backward direction as determined from practice. The optimum discharge angle for maximum rearward deflection without flow resistance is approximately 150°.

A complete vector study for the reference converter gives relative entrance angles to each blade system at several speed ratios from stall to coupling point, as shown in Fig. 2.4.15. This provides an extremely useful means for readily appraising flow shock. From these diagrams, it is quickly apparent that both the impeller and reactor blade receive flow through a wide range of angles, whereas flow into the turbine occurs through a much more limited range of angles and thus presents relatively little difficulty in matching blade entrance angle and inlet flow. The blade entrance angles of the impeller, turbine, and reactor were selected as optimum for overall minimum shock losses at 0.7 speed ratio. This gave the desired stall torque ratio with best peak efficiency, high coupling point, and good coupling characteristics.

Finally, the reactor receives the backward discharge from the turbine and deflects it to a forward direction, thereby increasing the momentum of the fluid entering the impeller. This provides the reaction necessary for torque multiplication. Curves (Fig. 2.4.13) show the effect of reactor exit angle on the performance of a converter of 11.75 in. diameter. Torque capacity, as represented by the size factor, increases in a reasonably consistent manner with increasing exit angles. For maximum torque ratio and peak efficiency, it is obvious that the 19°, 22°, and 25° exit angles are best. From this experience and other like determinations, the optimum reactor exit angle ranges from 20° to 25° for highest efficiency and a high coupling point. In our reference converter, the particular exit angle used is 22°.

Having now selected entrance and exit angles, the design of the portion of the blade between these extremities may proceed. This is the real working part of the blade, and generally it can accomplish this best by the most uniform deflection

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of fluid possible, whether this be the impeller blade which imparts energy to the fluid or the turbine blade which absorbs energy from the fluid.

One proven method of obtaining such uniform fluid deflection involves dividing the blade into a number of segments and making each segment assume an equal part of the total torque transmitted. This may be derived as follows from the equation for the torque of the impeller:

Ti = M(R iSi − Ri¢Si¢ )

(2.4.6)

where: Ti = torque M = mass flow Ri = radius of impeller exit Ri¢ = radius of impeller entrance Si = tangential component of absolute velocity at impeller exit Si¢ = tangential component of absolute velocity at impeller entrance The term (RiSi – Ri¢ Si¢) represents in part blade geometry at entrance and exit and as a quantity is a factor in the computation of torque T in Eq. 2.4.6. Dividing this quantity into a given number of equal parts will give a like number of increments of blade, each loaded equally. From this the blade angles are calculated. The complete method showing the stepby-step procedure for calculating blade angles, dimensions, and detailing blades is included in Appendix C.

Fig. 2.4.14  Blade geometry and vectors for reference 12-in. converter.

The elements of the family of converters described herein utilize sheet-metal fabrication for the impeller and turbine and a die-cast aluminum reactor. As a practical measure, in the interest of cost, this dictates the use of single-thickness sheet-metal blades in the impeller and turbine. In the reactor, however, the cast-aluminum construction allows the use of hydrofoil-shaped blades. A comparison of the characteristics of the hydrofoil profile and the sheet-metal blades of identical curvature and length obtained from flow tunnel is shown in Fig. 2.4.16. This indicates the advantage of the hydrofoil profile, particularly at angles of cascade representative of stall and low-speed ratio conditions. Tests of these profiles in an actual converter installation (Fig. 2.4.17) substantiate the advantage of the hydrofoil profile by an improvement in ratio, especially at lower speed ratios. There is, however, some loss in capacity due to the decrease in flow area resulting from the thick blades. Profile proportions and dimensions are given in Appendix C. Although this provides specific guidance in the design of reactor blading for this type of converter, much additional information must be developed to provide a broader background of profile characteristics suitable for use in converters. Some advantages have been experienced in the use of hydrofoil blades in impeller and turbine members; however, even more development is required for this application to establish an adequate design basis.

22°

Fig. 2.4.15  Variation in entrance vectors.

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performance as converter and coupling. A rough guide for the impeller and turbine gives spacing with a pitch-to-chord ratio of 0.46 where the pitch is taken at the O.D. of the design path and chord taken as the radial distance between the blade and inlet and exit on the design path. In conventional practice in converter design, the blades are spaced equally in each member. With a like number of blades in the impeller and turbine, the simultaneous registry of all blade spaces gives an above-average flow, whereas coincidence of blade and blade space gives a below-average flow, thus creating pulsations in flow. This, in turn, causes torsional fluctuations with a frequency equal to the product of the number of blades and the rotational speed. Occurrences of this nature—by design or accident—have resulted in torsional vibrations that are most undesirable even though they may not be detrimental mechanically. A simple but effective means to prevent such conditions consists of giving the impeller and turbine different numbers of blades and selecting these preferably to be prime numbers.

Fig. 2.4.16  Comparison of lift drag characteristics of hydrofoil and sheet-metal blades.

A guide for the selection of the number of reactor blades may be taken from the relationship of pitch-to-chord where, with optimal blade spacing, pitch-to-chord ratio is 0.54. Pitch is taken at the design path at the blade entrance, and the chordal distance is taken from blade entrance to the exit at the design path. Generally, odd numbers of blades are used, although the problem of fluctuations in flow and resultant torsional disturbances attributable to coincidence of blade passages are minimized because of the substantial difference in bias of the blading at both the turbine-reactor and reactor-impeller junctions. Fortunately, the selection of blade spacing need be only approximate at the initiation of a new design. In members fabricated from sheet-metal, the number of blades is readily changed during the experimental stage by increasing or decreasing the number of blade slots as desired. In cast members such as the reactor, provision can be easily made in the pattern equipment for adjusting the core box to permit use of different numbers of blades of the same profile. Optimum blade spacing is then obtained by tests of individual members in all possible combinations and selecting those that most nearly give the characteristics of performance desired for the particular application being considered.

Fig. 2.4.17  Comparison of converter performance using hydrofoil and sheet-metal blades. In a converter of the type we are concerned with here, it is necessary not only to provide the proper blading for the converter function, but also to obtain an efficient fluid coupling function. Reflecting these requirements in terms of blade spacing, we have conflicting conditions. With the impeller and turbine members, maximum efficiency for fluid coupling operation may require 2.0 to 2.5 times the number of blades necessary for best performance as a torque converter. Obviously, it is necessary to select optimal blade spacing if both of these conditions are to be met with acceptable overall

In the foregoing discussions of blading, the assumption has been made that the blades have been fixed. This is typical of all three-element converters being produced today. Pivoted or movable blades and blades that are split to form a separate element are used in more complex converters to obtain more compatible blade angle and flow conditions. Experience with these has shown that extreme care is necessary in their design to preclude the introduction of more resistance to flow in the 2-57

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form of pivots or added blades than is gained by the more compatible blade angles.

2.4.5

Fabrication Techniques

Early methods of fabricating converter members were crude and often involved compromised blade design in order to expedite fabrication. As designers and fabricators became familiar with the problems of making blades and assemblies, methods were developed that permitted complete freedom in design in spite of the complex three-dimensional blade shapes necessary. Additionally, the development of such methods as the making of soft-metal blade dies and blade molds directly from wood models expedited experimental fabrication, both in time and cost sufficient to make extensive converter development possible. Current production techniques were derived from these experiences and exceeded the expectations of the most optimistic proponents of torque converters with respect to accuracy, consistency of performance, and ease of manufacture resulting in low cost. Both cast and sheet-metal construction are used in making the bladed components. Castings are normally made of aluminum, using sand or plaster core molds or die-casting methods. Construction in sheet-metal uses stamped sheet-metal blades formed to the required contour and assembled into shell and core stampings. Several variations of making the assembly are used.

Fig. 2.4.18  Representative cast-aluminum impeller and turbine members.

For low-volume production, the sand and plaster casting methods are most advantageous because of the low tooling cost, although the piece cost is higher than obtained with other methods. The casting of the blades in one piece with the shell and core sections gives adequate strength and durability. It is readily adaptable to hydrofoil-shaped blades and thus allows complete freedom of design in this respect. This method of fabrication is used predominately for the heavyduty units manufactured in sizes ranging from 9 to over 24 in. in diameter. Representative cast impeller and turbine members are illustrated in Fig. 2.4.18.

Fig. 2.4.19  Die-cast aluminum reactor showing detail of blading.

Die-casting of converter members has the advantages of low piece cost with high accuracy and excellent surface finish, but involves high tooling cost. As with sand-castings, die-casting affords adequate strength and durability of the one-piece blade and shell structure. It likewise provides freedom in the design of blade profiles of the hydrofoil type, although care must be taken to provide for core withdrawal and practical die construction. This type of fabrication, shown in Figs. 2.4.19 and 2.4.20, is used principally in high-volume production of reactors. Both radial (die) pull and axial pull reactor designs are used.

Fig. 2.4.20  Die-cast aluminum reactor assembly.

surface finish, but involve a high tooling cost. Since the blades are stamped from a single thickness of metal, this method is not readily adaptable to hydrofoil blades. Several variations of the method of assembly currently in use include:

Converter members fabricated from sheet-metal stampings have the advantages of low piece cost and excellent accuracy and 2-58

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1. Blades with tabs inserted into slots in the shell and core pieces and rolled to make the assembly permanent. Impeller and turbine constructions of this type are shown in Figs. 2.4.21 to 2.4.24. 2. Blades with tabs inserted into an embossed slot in the shell and tabs inserted into the core. The assembly is completed by rolling the tabs at the core side. 3. Copper-brazed units using blades positioned by tabs and slots or blades with flanges spot-welded in position prior to brazing. Sheet-metal fabrication is used in most passenger car applications and in the truck adaptations obtained from such units. Although the durability of the sheet-metal converter members is adequate, care must be exercised to provide proper support for the blade. This requires a sufficient number and strategic location of tabs. In addition, experience has shown that fillets in the corner between the tab and the body of the blade are necessary to prevent cracks from developing with the normally used metal thicknesses of 0.030 to 0.045 in.

Fig. 2.4.23  Fabricated steel turbine components.

Fig. 2.4.24  Steel turbine assembly.

2.4.6

Fig. 2.4.21  Fabricated steel impeller components.

Other Performance Considerations

The combination of the characteristics of the converter and the engine to which they apply may give unexpected results unless carefully analyzed. One such circumstance that may occur is operation at high altitudes where engine output is reduced considerably. Figure 2.4.25 compares converter stall and turbine or output torque conditions of a converter at a 12,000 ft altitude with the same converter at sea level. From this, it will be noted that at 12,000 ft. the output torque at stall is 44% of that at sea level, whereas peak engine torque is reduced to only 52%. This difference results from the engine torque characteristic as it affects the speed at which the converter stalls. At high altitude, the converter stall occurs at a lower point in relation to the torque peak than it does at sea level. In terms of input torque, we find that the converter stalls at 99 lb.-ft. at 12,000 ft, and at 225 lb.-ft. at sea level, and accounts for the reduction of 56%, which is reflected directly into output torque difference as quoted above. A further effect of altitude as shown by these curves

Fig. 2.4.22  Steel impeller assembly.

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is in the speed at which the coupling point occurs. This further reduces the availability of torque multiplication and emphasizes the need for selecting the size of the converter to stall sufficiently near the torque peak of the engine to be acceptable at all conditions of operation expected. As a corollary, an engine with a characteristic that would maintain a more constant value of torque at low speeds could accomplish the same result.

Fig. 2.4.25  Relationship of converter and engine performance at altitude.

Fig. 2.4.26  Tractive resistance of truck with converter type transmission.

In many applications, the converter is required to provide an effective drive when overrunning or coasting. This involves a reversal of the direction of fluid flow in the circuit and the use of the back side of the blades in the impeller and turbine as these members interchange function. When coasting, the turbine becomes the impeller and the impeller becomes the turbine. Since the blade profiles are designed to function most efficiently when driving, the use of the back side during overrunning entails some loss in ability to transmit torque. Furthermore, the unit can function only as a coupling under these conditions and will not multiply torque. Fortunately, when overrunning, the engine is being driven and the torque that must be transmitted is limited to engine friction. This is a small part of the torque normally transmitted when the engine is driving and accounts for the acceptability of the drive. Curves in Fig. 2.4.26 give the tractive resistance available in a truck of 15,000 lb gross vehicle weight (gvw) with a converter type of transmission when coasting in intermediate and low gears. Curves have also been included to show the tractive resistance obtainable with the converter locked out, thus eliminating slip. Except at very low speeds, the loss attributable to slip is a matter of 1 to 3%.

2.4.7

Cooling

Some of the initial installations of converter transmissions indicated the need for cooling beyond that normally accomplished by radiation and flow of air over the housings. As a result, forced air circulation was provided by putting blades on the outside of the impeller and adequate air inlet and outlet passages in the converter housing. In one construction with an impeller made of die-cast aluminum (Fig. 2.4.27), the outside had fins cast integrally, which acted as blades for centrifugally blowing air and simultaneously increased the cooling surface of the impeller quite substantially. The heat dissipation and airflow of this arrangement with an 11.75-in.diameter impeller (Fig. 2.4.28) was adequate for passenger car and light-duty truck installation up to 160 hp. Acceptability was determined by test under a variety of conditions including operation on grades at Pike’s Peak and Death Valley, hill routes in Pittsburgh and San Francisco, and traffic routes representative of the maximum congestion occurring in large cities. In the operation on grades, temperature equilibrium was not usually attained. On the hill and traffic test routes under severe conditions, temperatures stabilized at acceptably lower temperatures of 250° to 275°F. Since operation at

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the temperatures indicated is normally encountered infrequently and for brief periods of time, the durability of items such as oils and seals is satisfactory. Protracted operation at high temperatures requires additional care in the selection of materials to assure adequate life.

from the converter to a heat exchanger where it is cooled by the engine cooling system. It is then returned to oil sump and completes its circuit back to the converter. The capacity of the cooling system must be estimated by careful appraisal of the conditions of operation of the particular application being considered. This, in combination with the converter efficiency curve, permits calculation of heat rejection throughout the speed range and determination of critical conditions. Subsequently, verification of acceptable cooling performance is obtained by test at the most severe conditions. An important consideration for obtaining maximum flow is the location of the inlet and outlet in the converter circuit. This has been found best with inlet into the converter at the impeller entrance and the outlet at the turbine exit. With this relative location, the pressure head generated by the impeller assists the flow through the cooling circuit. Interchanging inlet and outlet locations will drastically reduce flow and, at some speed ratios, may even stop it completely. Areas should be determined for both inlet and outlet to give flow velocities not exceeding 15 ft/s. Charging of the converter is necessary under some conditions to prevent cavitation, which is most likely to occur at stall where flow velocities are highest. Cavitation is usually discernible by the occurrence of noise and by a falling off of impeller torque from values that in normal operation are proportional to the square of the speed of the impeller. Noise also occurs in some units without a perceptible drop in impeller torque. Where most-quiet operation is desired or necessary, an increased charge pressure will usually accomplish this purpose. Charging pressures of 25 to 75 psi are common in units today and are supplied by an oil pump in conjunction with the circulation of oil through the converter. Such circulation is provided in both air-cooled and liquid-cooled converters; however, the rate is designed to meet the cooling requirements.

Fig. 2.4.27  Air-cooled converter arrangement.

2.4.8

Converter Fluids

Light mineral oils of various kinds have been used in torque converter and automotive service since their introduction. Included in some of the early fluids used experimentally and in the field were diesel fuel oil and combinations of kerosene and light engine lubricating oil. Over a period of many years, light lubricating oil has become the predominant converter fluid. A considerable influence in the selection of this oil has resulted from the requirements of other components included in many transmissions, of which the converter and its function are only a part. Some of the other components included are bearings of both plain and antifriction types, highly loaded gears, disc friction clutches, bands, free-wheel units, and hydraulic control valves. Thus, the converter fluid must, in many instances, not only be the power-transmitting

Fig. 2.4.28  Air-cooled converter heat dissipation curves. Air-cooling continues in use today with both the aluminum impeller construction described and impellers fabricated of steel with cooling blades welded on. It is limited to relatively low-power installations involving light-duty operation. For applications of higher power and heavy-duty operation, liquid cooling is used predominantly. In these, oil is pumped

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medium, but must be a lubricant having good film strength, be resistant to oxidation and foaming, and have a high viscosity index in order to maintain acceptable viscosities through the range of temperatures encountered. Two fluids that are available for such service are Type A and Type F automatic transmission oil. Usual practice is to approve oils for specific transmission use and service conditions by engineering test. At various times, synthetic fluids of higher density have been suggested for use in converters as a means of increasing the torque capacity. Figure 2.4.29 shows a comparison of performance of a fluid of 1.10 sp gr with that of a Type A oil, which has a specific gravity of 0.821.

speed, and flow is reduced to zero since the impeller head creating flow is exactly balanced by the head of the turbine. Under this condition, all pressures causing thrust have been eliminated because all the oil in the converter rotates as one mass, and the only pressure remaining is that due to centrifugal force. This acts equally and oppositely on each member of the converter and thus does not cause thrust. Axial thrust can be formidable in converters, but in the type of unit discussed here, it has not been a serious problem. This is due, to some extent, to the fact that the majority of operation occurs at high speed ratios where the thrust is reduced considerably. Typical thrust load characteristics of the members of a 12.31-in.-diameter converter as determined experimentally with the use of strain-gage instrumentation are given in Fig. 2.4.30. Provision of adequate thrust washer area to support such loads and acceptable rubbing factor of pressure velocity (PV) values can usually be accomplished without difficulty. These curves further indicate that the thrust loads are self-contained within the converter. The impeller thrust is substantially equal and opposite in direction to the sum of the thrusts of the turbine and reactor. This is normally the condition; however, there are circumstances when the turbine or reactor may be locked on its connecting splines, and the thrust may be transmitted to members outside the converter. An example of this has been the imposition by the converter of additional load on the thrust bearing of the engine crankshaft. This necessitated improvement in the bearing to provide adequate life.

The viscosity of the two is the same. The torque capacity shows the expected increase with the higher-density fluid, while torque ratio and efficiency remain the same. While increased capacity is definitely advantageous in many applications, costs projected to date for such synthetic fluids have not been sufficiently attractive to justify their use.

2.4.9

Axial Thrust

No attempt will be made here to present the theory and computations involved in the solution of thrust loads, since considerable treatment of the subject is available in most literature on centrifugal pumps. However, some observations peculiar to the converter may be of interest. As in the centrifugal pump, thrust encountered within the converter is the result of pressure head and flow generated by the impeller. Apart from this, circumstances differ in the converter in that thrust is affected by speed ratio. For example, at stall we have the greatest difference in speed between the impeller and turbine. At this point, the pressure head and flow created by the impeller are greatest. In addition to its effect within the torus, this pressure head also acts on the forward side or outside of the turbine shell. Since the area on which this pressure acts is large, this is probably the single most significant item of axial thrust and it is of such magnitude that it overcomes the axial forces within the torus, tending to separate impeller and turbine. The net result is that at stall the thrust loads are highest. As the speed ratio increases, the turbine speed increases, which creates a pressure head that is counter to the pressure created by the impeller, with the result that flow is decreased. The rotation of the turbine also causes the body of oil in the axial space between the outside of the turbine shell and the impeller housing to rotate and thereby to build up a pressure head opposing the head of the impeller. While the decreased flow and opposing head both reduce thrust forces, the latter is again most significant because of the large area involved. To explore thrust further, let us assume an increase of speed ratio to unity. Impeller, turbine, and reactor rotate at the same

Fig. 2.4.29  Effect of high-density fluid on performance. 2-62

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defined by a 2-in. radius with a radial flat equal to 0.125 in. (Fig. 2.4.A1) for the purpose of a slight reduction in axial length. After the shell contour is determined, development of the core contour is the next step in the design of the circuit. Based on experience with various converter sizes, the optimum flow area is equal to approximately 23% of the total area defined by the torus outside diameter. For the example 12-in.-diameter converter, a flow area equal to 26 in.2 is the result. Neglecting blade thickness, the flow area is constant in order to maintain a near uniform flow velocity F. Referring to Fig. 2.4.A1, the circuit flow area at an arbitrary element line is given by the formula for the surface of revolution of the frustum of a right circular cone:

Fig. 2.4.30  Axial thrust of impeller, turbine, and reactor.

2.4.10 Conclusions where:

In the foregoing, information has been presented outlining the considerations involved in the design of a torque converter. It has been directed at providing adequate and detailed information to enable young engineers to understand more fully the function and details of the torque converter and, further, to enable them to design a practical unit. While a specific unit has been used for guidance, and many factors have been held constant—including blade angles, except impeller exit—it will be recognized with experience in this field that departure from this design may be necessary to accomplish objectives other than those given here and can result in an equally acceptable unit. Beyond this it is hoped that these first steps may lead to the development of further knowledge in this field, with the ultimate goal of improvements in the capabilities and even broader application of the torque converter.

area =

π (R 2s − R c2 ) cosp

(2.4.A1)

p = angle of element line with respect to vertical. Element lines are perpendicular to design path. Rs = radius at intersection point of arbitrary element line with shell contour. Rc = radius at intersection point of same element line with core contour. R = radius at intersection point of same element line with design path.

2.4.11 Acknowledgments The efforts represented by this paper are the result of the work of many individuals in the field of torque converter development over a period of a considerable number of years. In addition, I wish to acknowledge particularly the efforts of Martin Gabriel and others of the engineering staff of the Transmission and Chassis Division, Ford Motor Co., for their valuable assistance in the preparation of this paper.

Appendix A 2.4.12 Converter Circuit Design Computation of converter diameter in accordance with the procedure and performance charts outlined in the paper is the first step in the circuit design. Basic circuit dimensions can then be established and the core profile developed. The reference 12-in.-diameter converter will be used as an example in the discussions to follow. It is comprised of a shell 2-63

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Fig. 2.4.A1  Development of torus for 12-in.-diameter converter.

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The actual development of the core contour may be accomplished by means of a design layout procedure. First, it is comprised of the selection of arbitrary element lines and calculation of an initial core and design path contour. The Rs points and angle p are measured from the layout and the corresponding Rc and R calculated.

1/2 ⎛ Acosp⎞ ⎟ R c = ⎜R s2 − π ⎠ ⎝

⎛ Acosp⎞ R = ⎜R 2s − ⎟ 2π ⎠ ⎝

1/2



To establish the final element line locations, the entrance and exit edge of the reactor must now be defined. Experience has indicated that the projected axial length of the reactor blade is about optimum at one-half of the torus diameter d, illustrated in Fig. 2.4.A2. In the reference converter, the reactor is approximately 2 in. long, measured on the chord of the design path in a plane passing through the axis of the reactor. To obtain the maximum utilization of the flow circuit, a minimum gap between blades of adjacent members is used. Furthermore, the blade design based on forced vortex theory also necessitates a minimum gap to reduce vortex effects. Finally, dimensional tolerances have dictated a nominal gap of 0.093 in. as practical.

(2.4.A2) (2.4.A3)

The resulting core contour is the focus of the intersection points of the above-calculated radii with the corresponding element lines. Following somewhat of a reiteration process, new element lines are selected more closely perpendicular to the design path and the above calculations repeated until the core is a smooth curve defined by the shell contour and the design flow area.

With the blade entrance and exit edges positioned, the design path lengths can be divided into ten equal distances and the corresponding element lines constructed, each closely perpendicular to the design path. Element line location dimensions for the reference converter are given in Figs. 2.4.A2 to 2.4.A4.

Fig. 2.4.A2  Detail of impeller blade for 12-in.-diameter converter.

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Fig. 2.4.A3  Detail of turbine blade for 12-in.-diameter converter.

Fig. 2.4.A4  Detail of reactor blade for 12-in.-diameter converter. 2-65

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Appendix B 2.4.13 Vector Diagram Development

Solving for F,

To calculate the flow velocities necessary to construct a vector triangle, the entrance and exit blade angles and radii, the rotational speeds of the bladed elements, and the circuit flow area must be given.

F=

−ω iR i2 ±

4 R cota − R cota T (ω iR i2 )2 + ( i i R R ) i 1.59A 2(R i cota i − R R cota R )



(2.4.B3)

Eq. 2.4.B3 will yield an approximate value for the torus flow F based on impeller speed ωi and torque Ti taken from the converter projected performance curves and the pertinent blade exit radii and angles. However, after an initial determination of blade profile, it is usually necessary to recalculate F from Eq. 2.4.B3, inserting exit fluid angles. A method developed from water tunnel tests of determining the approximate fluid exit angle is illustrated in Fig. 2.4.B1. This technique averages the blade exit angle and the blade angle measured at the point of tangency of a circle drawn to the adjacent blade, as determined by the pitch at the exit. For the reference converter, the angles thus obtained are 77° 50¢ for the impeller exit and 26° 41¢ for the reactor exit.

The calculation of the normal flow velocity F is the first step in this procedure. To compute this torus flow velocity accurately is a difficult step in itself because of the complexity of the total velocity distribution within the bladed members and because the various flow losses can only be estimated. Euler’s equation may be utilized, which, for steady flow, states that the torque transmitted by a rotating blade member is equal to the moment of momentum of the fluid leaving the member minus the moment of momentum of the fluid entering the member. It is based on the assumption of incompressible flow and neglects the effects due to flow shear stresses at the entrance and exit regions. For the impeller, Ti = M (R iSi − R R SR )

where:

(2.4.B1)

Ti = impeller torque M = mass flow Ri, RR = exit radius of impeller blade and reactor blade, respectively, at design path ai, aR = exit angle of flow at impeller and reactor Si, SR = tangential component of absolute flow velocity at impeller exit and reactor exit, respectively. By substitution, where:

Ti =

dAF (ω iR i2 + R iFcot a i – R RFcot a R ) (2.4.B2) g

Fig. 2.4.B1  Determination of fluid exit angle. Accordingly, a sample calculation for F at 0.5 speed ratio based on a projected K = 117.5, which corresponds to 1620 rpm at 190 lb.-ft. input torque, is in Eq. 2.4.B4.

d = fluid density, lb/ft A = torus flow area (assumed constant) ft2 F = torus flow velocity, ft/s g = gravitational constant ωi = impeller angular velocity, rad/s d/g = 1.59 for transmission oil 3

With experience in this work, it will be recognized that determination of true values of torus flow are difficult because of the many factors involved such as the various flow losses, corrections for blade thickness, and deviation of actual exit flow angle from blade angle. As knowledge of these factors increases, improvements in the calculation of torus flow will be possible.

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F=

4(0.4704 ¥ cot77°50¢ – 0.253cot26°41¢)190 1.59 ¥ 0.181 = 23.7ft/s (2.4.B4) 2(0.4704 ¥ cot77°50¢ – 0.253cot26°41¢)

–169.6 ¥ 0.4704 2 ± (169.6 ¥ 0.4704 2)2 +



From the graphic solution (Fig. 2.4.B3), angle L¢ = 27°.

To complete the vector diagram, it is necessary to compute the linear velocity U on the design path. At the impeller exit for the reference converter: Ui = 0.1048 R i Ni



= 80 ft/s at 1620 impeller rpm

(2.4.B5)

Continuing with this example, the vector solution for the absolute fluid velocity and angle leaving the impeller may now be completed by graphical or trigonometric methods, as illustrated in Fig. 2.4.B2. Fig. 2.4.B3  Vector diagram at entrance of turbine at 05. speed ratio. The above procedure of determining inlet flow vectors is also applicable to the reactor and impeller. A completed study for all three members at various speed ratios is given in Fig. 2.4.15.

Appendix C 2.4.14 Blade Design

Fig. 2.4.B2  Vector diagram at exit of impeller at 0.5 speed ratio.

As outlined in the foregoing, the impeller exit angle is established by stall ratio requirements. For the reference converter with a stall ratio selected at 2.1:1, the impeller exit (Fig. 2.4.3) is 75°. With the other blade angles, as determined for optimum performance as both torque converter and fluid coupling, we then have the blade specifications shown in Table 2.4.C1 for the complete unit as designated in terms of SAE blade angle system B. These, along with the circuit dimensions, are prerequisites to the initiation of blade design.

The vector diagram is often used to determine the blade entrance angle required for shockless fluid entrance. To determine this angle for the turbine blade, it is first necessary to calculate the linear velocity at the entrance of the turbine. The turbine entrance linear velocity at 0.5 speed ratio for the reference converter:

Table 2.4.C1  Blade Specifications for Complete Unit as Designed by SAE Blade Angle System B, Degree.

U ¢T = 0.1048 × R ¢T N T = 0.1048 × 0.4704 × 810

= 40 ft / s at design path at 810 rpm (2.4.B6)

2-67

Impeller  Entrance  Exit

105°  75°

Turbine  Entrance  Exit

 32° 150°

Reactor  Entrance  Exit

 90°  22°

Design Practices: Passenger Car Automatic Transmissions

A 0.5 speed ratio was assumed in the initial design of the blade contours. Although subsequent development resulted in a design point for entrance angles with minimum shock loss at 0.7 speed ratio, these contours were adhered to as expedient, since the difference between contours designed to these different speed ratios was not significant.

losses at the blade exit. Next, the corresponding blade angle at each point along the design path is computed by rearranging Eq. 2.4.C1 or 2.4.C2 to give:

From the equation for impeller torque (Eq. 2.4.6):

Once the angles at each element along the design path have been calculated, we are in position to obtain the corresponding angles for the core and shell using the method given next.

⎛ RS ⎞1 cota = ⎜ − U⎟ ⎝R ⎠F



Ti = M (R iSi – R ¢i S¢i) the term (RiSi – R¢i S¢i) is a factor that defines the change in the moment of momentum occurring in the impeller. At the assumed speed ratio of 0.5 and an input torque of 190 lb.-ft. at 1620 rpm, the value of torus flow F from Eq. 2.4.B3 is 23.7 ft/s. Substituting numerical values, we have the following for the impeller:

To determine the blade angle at the point of intersection of the element line with the core:

R¢i S¢i (at inlet) = R¢i (U¢i + Fcota 'i ) = R¢i (R¢i × ω i + Fcota¢i )

cota c cota = Rc R

(2.4.C4)

cota s cota = Rs R

(2.4.C5)

Similarly at the shell:

= 0.2577[0.2577 × 169.6 + 23.7(−0.2679)]

(2.4.C1)

= 9.629

(2.4.C3)



At entrance element 0 for the reference converter:

Similarly: R iSi (at exit) = R i (U + F cot a) = 40.524





(2.4.C2)



The net change in RS is 40.524 – 9.629 = 30.895.



Dividing this change in RS factor into nine equal parts of about 10.5% each and one part of 5% gives RS values at each element line, as listed in Table 2.4.C2. The use of the 5% increment between element lines 9 and 10 is for the purpose of reducing the energization of the fluid and consequent eddy

cota c =

Rc 3.589 cota = (−0.2679) = −0.3109 R 3.092

cota s =

Rs 2.490 cota = (−0.2679) = −0.2157 R 3.092

and: angle ac = 107° 16¢ at the blade entrance angle as = 102° 10¢ at the blade entrance

Table 2.4.C2  Pertinent Blade Data for Reference Converter Impeller.

Entrance

Exit

Angle a (on Design Path)

Element Line

RS (Design Path)

R, ft (Design Path)

cot a

°

min

°

min

°

min

 0  1  2  3  4  5  6  7  8  9 10

  9.629 12.873 16.117 19.361 22.605 25.849 29.093 32.337 35.581 38.825 40.524

0.2577 0.2789 0.3048 0.3335 0.3630 0.3910 0.4170 0.4388 0.4553 0.4662 0.4704

–0.2678 –0.0485 0.0486 0.0627 0.0332 –0.0101 –0.0407 –0.0312 0.0383 0.1768 0.2681

105   92   87   86   88   90   92   91   87   79   75

– 47 13 25  6 35 20 47 48 58 —

102   92   87   86   88   90   92   91   87   79   74

10 28 22 28  4 36 26 53 40 22  6

107   93   87   86   88   90   92   91   87   80   75

16  4  5 22  8 33 13 41 56 38 58

Shell as

Core Ac

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Table 2.4.C2 shows the pertinent blade data for the reference converter impeller.

this example, the exit edge (element 10) is also in a radial plane, as shown in Fig. 2.4.A2.

It is now necessary to transform the calculated angles into a three-dimensional blade profile that can be dimensioned and built. We have found that a combination of radius and offset dimension on the shell and core are accurate and easily used to define a blade profile.

2.4.14.1 Turbine Blade Following the same procedure, the turbine blade may be similarly calculated. The completed blade for a 12-in. reference converter is shown in Fig. 2.4.A3. Blade angles are tabulated in Table 2.4.C4.

Although they are straightforward, the actual calculations are quite lengthy and therefore have been programmed on a digital computer.

Table 2.4.C4  Turbine Blade Angles.

To determine any blade element offset Xk: k

X k = R k sin y = R K ∑



0

Jk Rk



(2.4.C6) Entrance

where: J k = e cota



J = distance along arc from one point to next, in. y = angle defined by J and pertinent radius from center of converter, rad e = distance between adjacent element lines Rk = radius at point of intersection of element line with design path, core, or shell, as the case applies k = element line 0, 1, 2, º 10

Exit

Entrance

Exit

 0  1  2  3  4  5  6  7  8  9 10

Offset

Core Radius

Offset

2.490 2.962 3.458 3.948 4.420 4.850 5.233 5.550 5.790 5.941 6.000

0.020 0.105 0.120 0.106 0.093 0.097 0.118 0.144 0.150 0.106 0

3.589 3.689 3.844 4.055 4.286 4.533 4.764 4.963 5.118 5.221 5.265

0.043 0.071 0.073 0.064 0.056 0.056 0.065 0.077 0.078 0.053 0

10  9  8  7  6  5  4  3  2  1  0

0.4704 0.4662 0.4553 0.4388 0.4170 0.3910 0.3630 0.3335 0.3048 0.2789 0.2577

Angle a deg     32   38   46   55   65   78   94 113 130 144 150

min  0 40 20 21 58 53 52 4 33 28 —

The design calculations for the reactor follow the same procedure as for the impeller blade. Since the reactor does not rotate during torque conversion at the design point of 0.5 speed ratio, the RS calculations are somewhat simplified with the elimination of the tangential velocity U.

Table 2.4.C3  Final Impeller Blade Dimensions, in. Shell Radius

Radius, ft (Design Path)

2.4.14.2 Reactor Blade

Final impeller blade dimensions are shown in Table 2.4.C3. The impeller blade profile is constructed by joining the corresponding shell and core points with straight lines.

Element

Element Line

For the reference converter with reactor entrance and exit blade angles equal to 90° and 22°, respectively: Entrance Exit

RS = RF cot a R R ′S ′ = 0.253 × 23.7 cot 90° = 0

RS = 0.253 × 23.7cot 22° = 14.83

(2.4.C7)

When based on linear RS distribution, as used in the impeller and turbine blade, the reactor blade length presents diecasting problems. Therefore, a modified RS distribution that shortens the blade is incorporated, as given in Table 2.4.C5. This results in draft angles in the critical area near the blade exit, which are practical for die-casting. Experience indicates that the shortening of the blade does not detract from performance.

The core profile is located relative to the shell profile so that the blade surface is generally perpendicular to the shell. In

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Table 2.4.C5  Reactor Blade Mean Camberline. Blade Angle a (on Design Path) Entrance

Exit

Element

R, ft (Design Path)

 0  1  2  3  4  5  6  7  8  9 10

0.2530 0.2450 0.2383 0.2339 0.2314 0.2305 0.2314 0.2339 0.2383 0.2450 0.2530

RS 0 0.79 1.72 2.79 4.02 5.58 7.43 9.28 11.13 12.98 14.83

When the profile corresponding to the mean camberline has been calculated, the hydrofoil surfaces can be applied to it. Blade thickness, expressed as percent of blade length, that has been proved satisfactory in reactor blade designs is given in Table 2.4.C6. The radius of the entrance edge is equivalent to approximately 4% of the blade length. Figure 2.4.A4 gives the reactor blade dimensions as used in the reference converter.

   0    5   10   20   30   40   50   60   70   80   90 100

deg

min

  5.3   6.3   7.2   8.3 10.5 12.5 12.5 12.5 12.5 12.5

90 82 73 63 53 44 36 30 26 24 22

— 16 5 17 44 24 26 51 54 3 —

2.5 Technology Needs for the Automotive Torque Converter—Part 1: Internal Flow, Blade Design, and Performance Robert R. By and John E. Mahoney Advanced Engineering Staff General Motors Corp. Based on SAE Paper No. 880482 Additions by:

Table 2.4.C6  Satisfactorily Proved Blade Thickness For Reactor Blade Designs. Distance Along Blade, %

RS Increment %

Thomas G. Brand BorgWarner Inc.

Blade Thickness % of Blade Length

2.5.1

 0  9 11 10  8  7  5  4  3 2.5  2 1.5

Abstract

The torque converter is a very complex turbomachine. Its geometry is highly three-dimensional, the working fluid is viscous oil, and it operates under a wide range of flow conditions. However, its hydrodynamic design technology had advanced very little over the past few decades. The design procedure has been based greatly on the use of the cut-andtry approach. The use of such an approach may satisfy the design requirements in terms of diameter, axial length, and K factor, but it may never lead to an optimized design for any given application. In addition, it has been proven to be too costly and time consuming. Recent developments in Computational Fluid Dynamics modeling and various measuring techniques have led to advances in torque converter design.

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A review of the technology need in the area of internal flow, blade design, and performance is presented as well as current advances in the areas of modeling and flow field measurements. First, the three-dimensional internal flow field and the physical mechanism of the internal flow losses are described. Secondly, two analyses of the stator blade passage, using potential flow and viscous flow finite element computer codes, are shown. Thirdly, experimental techniques used to obtain internal flow data are discussed. Finally, new advances in developing accurate performance models are presented.

2.5.2

section with axial length to diameter ratio as low as 0.23. Analytical and experimental investigations on the internal blade flow will be presented later in the chapter.

Introduction

The torque converter is a hydrodynamic device used to transfer power smoothly from an engine to a transmission. It has been used in automatic transmissions for numerous applications, including passenger cars, trucks, buses, tractors, and tanks. A typical torque converter cross section is shown in Fig. 2.5.1. It consists of three elements working in a fluid circuit. The three elements are a mixed-flow pump connected to the engine crankshaft, an output mixed-flow turbine attached directly to the transmission shaft, and an axial or mixed-flow stator attached to a grounded member through a one-way clutch.

Fig. 2.5.1  Three-element torque converter.

The hydrodynamic design of this complex product has been based almost entirely on the technology developed during the period of the 1940s to 1960s [1, 2]. This technology involves the use of one-dimensional performance analysis, the overall performance of the previously built torque converters, and the formulation for scaling. The scaling formulation works extremely well as long as the torque converter, as shown in Fig. 2.5.2, tends to have circular cross section with torus axial length to diameter ratio of about 0.30. The most informative design procedure was given by Jandasek [1]. It may be the single most useful reference for the design of the torque converter. The effects of the pump exit angle, stator exit angle, circuit flow area, hydrofoil blade shape, and fluid density on the converter performance were systematically presented. In Ref. 2, Upton presented the application of hydrodynamic drive units to passenger car automatic transmissions. The necessity of reducing the overall axial length of the transmission dictates that the axial length of the torque converter must be shortened. Since the previous performance data were based on a large axial length to diameter ratio, there is no known analytical method to predict just how short axial length must be before there is a penalty on the converter efficiency and capacity. The reduced-axial-length torque converter, as shown in Fig. 2.5.3, tends to have elliptical cross

Fig. 2.5.2  Conventional axial length torque converter. Over the last several years, new methods of analyzing the fluid flow in complex geometries, such as the torque ­converter components, have become available. These new methods

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offer the potential for significantly improving the overall design process. The application of the new analytical and experimental tools to the overall torque converter design is the subject of this chapter.

Performance analysis is used to determine the overall steadystate performance in terms of input speed, output speed, input torque, and output torque. Internal flow analysis is used to analyze the flow inside blade passage rows. The following information may be obtained from the internal flow analysis: pressure distribution, velocity distribution, flow exit angle distribution, viscous and incidence flow losses.

Fig. 2.5.3  Reduced-axial-length torque converter.

2.5.3

Physical Description of the Internal Flow Field

2.5.3.1

Internal Flow Description

Fig. 2.5.4  Flow circulating in a torque converter.

The flow through the torque converter is one of the most difficult to analyze. The flow, as shown in Figs. 2.5.4 and 2.5.5, is highly three-dimensional due to complex three-­dimensional geometries, with three elements rotating at different speeds. In addition, it is seen from the velocity diagram in Fig. 2.5.6 that the torque converter elements operate under an extremely wide range of inlet flow conditions. Furthermore, the working fluid is viscous oil. Therefore, in order to analyze the flow accurately so that an optimum hydrodynamic design can be obtained, a powerful three-dimensional, viscous, turbulent, transient, and incompressible flow computer code is required to model the internal blade passages of the entire machine. This technology is now becoming available to the engineer for use in torque converters and will be discussed later. In the past a simplified approach was used successfully to model the performance and the internal flow of turbomachinery such as the torque converter. From the standpoint of computational fluid dynamics, there are two types of flow analysis associated with the design of the torque converter.

Fig. 2.5.5  Flow in a typical turbine blade passage.

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Torque Converters and Start Devices 2.5.3.2.1 Leakage Flow Losses

The leakage flow losses are caused by the leakage flow areas throughout the flow circuit. There are essentially three main sources of leakage flow areas: the clearance between the blade tabs and the slots, the clearance between the blades and the shell/core caused by pressure ballooning, and the stator radial tip clearance. The effect of leakage flow can cause a reduction of 0.1 in stall torque ratio, and two points in converter peak efficiency. The effect of leakage flow may be predicted by subtracting the leakage flow rate from the total inlet flow rate. Empirical correlations may be made and verified from the overall performance data. 2.5.3.2.2 Viscous Flow Losses

The viscous flow losses are mainly caused by the development of a boundary layer on the blade, inner wall (core), and outer wall (shell) surfaces. They may be divided into two groups: the profile losses and the end-wall loss. These losses are shown qualitatively in Fig. 2.5.7.

Fig. 2.5.6  Velocity diagram for a typical torque converter. 2.5.3.2

Internal Flow Losses

There are mainly three types of flow losses associated with the internal flow of the torque converter. They are the leakage flow losses, the viscous flow losses for each of the three elements, and the losses due to the interaction effects between the elements. In the discussion of the viscous flow losses, the flow is assumed to enter the blade row at the same angle as the physical blade inlet angle. That is, the viscous flow losses do not include the effect of the incidence angle. The incidence angle is defined as the difference between the inlet flow angle and the physical blade inlet angle. The incidence loss is assumed to be part of the losses due to the interaction effects between the elements. In order to significantly advance the hydrodynamic design technology of the torque converter, the physical mechanism of the internal flow losses must be understood.

Fig. 2.5.7  Distribution of viscous flow losses. The profile loss may be interpreted from the cascade data as that portion of the overall viscous loss on the blade profile, in the absence of any disturbance effects, due to the presence of

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walls at the blade ends. A full explanation of the blade profile loss is given by McNally and Prust [3, 4]. It consists of the following: the friction loss or surface shear stress resulting from the flow of the viscous fluid over the blade surfaces, the trailing edge, and the mixing loss downstream of the blades resulting from the mixing of the low-velocity boundary layer fluid with the high-velocity free stream fluid. Figure 2.5.8 shows the regions where the three components of the profile loss occur. Station 0 is the inlet to the blade row. Station 1a is just within the trailing edge of the blade. Station 1 is just beyond the blade trailing edge, where the boundary layer fluid has filled the void but where little mixing with the free stream has occurred. Station 2 is located at a distance sufficiently downstream of the blade row such that complete mixing, with the associated mixing loss, has taken place. The profile loss depends heavily on the upstream flow condition, the blade geometry, and the fluid properties. The upstream flow condition is characterized by the following parameters: inlet flow distribution; inlet flow pressure; inlet flow temperature; inlet flow angle; and nature of flow in terms of laminar or turbulent, transient or steady. The blade geometry is described in terms of blade camber, blade thickness, blade chord length, blade spacing, blade throat, and blade angles. Density, viscosity, and specific heat are the three main fluid properties that affect the profile loss.

ratio of blade height to chord length, is the main geometrical parameter that affects the end-wall loss. For high aspect ratio blades such as those in the torque converters, the end-wall loss is the dominant viscous loss. Over the past few decades, an extensive amount of theoretical and experimental work has been made to understand and predict the profile and end-wall losses in axial turbomachine cascades. A number of profile and end-wall loss correlations are available in turbomachinery literature [6, 7]. Profile loss correlations are expressed in terms of pitch to chord ratio, trailing edge thickness to pitch ratio, blade maximum thickness to chord ratio, flow inlet angle, blade exit angle, and Reynolds number. End-wall loss correlations are formulated in terms of blade aspect ratio, pitch to chord ratio, boundary layer thickness to chord ratio, inlet flow angle, and blade exit angle. These correlations, however, may not be suitable to the torque converter elements since they were developed mainly from the cascade data of axial flow turbines and compressors. Over the years, a number of computer codes [8, 9, 10, 11] have been developed which have the potential to predict accurately the viscous losses in turbomachinery. Hah [8] developed a viscous flow computer code for the three-dimensional turbulent steady flows inside turbine blade rows. It was found that the complex three-dimensional viscous flow phenomena, such as the three-dimensional flow separation near the leading edge, and the formation of the horseshoe vortex near the end-walls, were well predicted. Rhie et al. [9] developed a viscous flow computer code for the three-dimensional turbulent steady flows inside centrifugal impeller rows. The code was found to be accurate in predicting the three-dimensional secondary and jet/wake flows. Schipke and Rice [10] developed a viscous flow computer code for the two-dimensional turbulent steady flows inside vaned diffusers. The code was able to predict accurately the two-dimensional viscous flow phenomena, such as the flow separation point and the counter-vortices in the recirculation region. The use of viscous flow computer codes may be the best approach to analyze the viscous flow losses in the torque converter elements. The geometry of a blade passage may be generated and analyzed at different flow conditions. An analysis of a stator blade passage will be shown to demonstrate the application of the viscous flow technology to the torque converter.

Fig. 2.5.8  Schematic diagram used to describe the blade profile loss. The end-wall loss is the viscous loss due to the presence of walls at the blade ends. It occurs because of the threedimensional boundary layer at the walls and its interaction with the blades in the blade row passage. It is an extremely complex phenomenon. A comprehensive study of the endwall loss was made by Langston et al. [5]. The end-wall also depends heavily on the upstream flow conditions, the blade geometry, and the fluid properties. The blade aspect ratio, the

2.5.3.2.3 Losses Due to the Interaction Effects

They are mainly caused by the discontinuity of the flow as it leaves one element and enters another. The two main sources of the interaction effects are: the flow incidence loss due to the mismatch between the flow exit angle of one element and the physical blade inlet angle of the adjacent element; and the loss due to the mismatch in torus flow path. 2-74

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The incidence loss occurs when the oil enters a blade flow at some angle other than the physical blade inlet angle. From the velocity diagram of Fig. 2.5.6, it is seen that the inlet flow angles change with the speed ratio conditions. Since the physical blade inlet angles are always at fixed values, the torque converter elements operate under a wide range of incidence angles. Therefore, the incidence loss is an important parameter to be considered in the design of the torque converter. In some speed ratio conditions, the incidence loss can be the dominant loss in the torque converter. For example, the inlet flow angle to the stator blade row may vary from –60° at stall to +48° at the coupling point. But, the physical blade inlet angle is a constant value of 20°. Thus, the incidence angle is –80° at stall and +28° at the coupling point. The incidence loss may be the major loss of the stator blade row at the stall condition. Most of the incidence loss correlations are based on the assumption that the difference in the absolute tangential velocity is lost. The nomenclature used to describe the incidence loss phenomenon is shown in Fig. 2.5.9, where:

to 0.75, and 0.3 to 0.65 for the pump, turbine, and stator, respectively.

W = relative velocity Wt = tangential component of the relative velocity U = blade rotational velocity V = absolute velocity Vt = tangential component of the absolute velocity β = flow angle α = physical blade angle first subscript = element number second subscript = inlet or exit location i = incidence angle = inlet flow angle – physical blade inlet angle

In Ref.14, Roelke showed that the variation of loss with incidence angle is different for the positive and negative angles. The incidence loss is not symmetrical about the zero incidence angle. It is larger for positive incidence than for negative. Roelke also indicated that the minimum loss does not occur at zero incidence, but at some small amount of negative incidence. He formulated the incidence loss as follows:

The most widely used incidence loss correlation for the torque converter applications was developed by Nagornaya [12] as:



where:

Hinc = C inc

(Vt1,ex Vt2,in )2 2g

Fig. 2.5.9  Schematic diagram used to describe the incidence loss.

where:

(2.5.1)

⎛ V2 ⎞ Hinc = ⎜ 1 ⎟ ⎡⎣1 − cos n i − i opt ⎤⎦ ⎝ 2g ⎠

(

)

(2.5.2)

V1 = absolute inner velocity iopt = optimum or minimum-loss incidence angle n = 2 for negative incidence angle, and n = 3 for positive incidence angle

Hinc = specific power loss Cinc = incidence loss coefficient Vt1,ex − Vt2,in = difference in the tangential components of the absolute velocity g = gravitational acceleration

Viscous flow computer code may be used to predict the incidence loss as well as the viscous flow losses. In the example of the stator blade analysis, the effects of the incidence and the profile losses were predicted by TURBO2D.

In Ref. 13, the incidence loss coefficients were correlated as a function of the incidence angles for all the three elements. These coefficients were determined from the experimental pressure data. They are in the range of 0.75 to 0.85, 0.35

The loss due to the mismatch in torus flow path is influenced by the following parameters: the upstream flow characteristics, the gaps between the elements, and the mismatch in 2-75

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torus curvatures. The latter two are schematically shown in Fig. 2.5.10. The upstream flow characteristics may be predicted from a viscous flow analysis. There are no known published data to explain the effect of blade gaps on the overall performance. The mismatch in torus curvatures may be included by incorporating different radii into the incidence loss calculations.

simultaneously yield the required flow turning with a satisfactory velocity distribution around the blade. Torus shape is chosen based on the following factors: the available working space, the torus curvatures, and the flow area distribution. The design of a proper blade profile requires calculation of the blade row and flow field. However, the actual velocity distribution in the torque converter flow field cannot be predicted at this time because of the extreme complexity of nonsteady, viscous flow through geometrically complex passages. Therefore, a number of simplifying assumptions must be made. First, the flow is assumed to be steady. Secondly, the flow is assumed to be axisymmetric. That is, only one representative of the blade passage with appropriate periodic boundary conditions needs to be analyzed. Thirdly, the interaction effect due to the mismatch in torus flow path is assumed to be small. That is, each of the three elements may be analyzed separately. In the potential flow solution, it is further assumed that the flow is inviscid and irrotational. The potential flow and viscous flow solutions are discussed in this chapter.

Fig. 2.5.10  Schematic diagram used to describe the mismatch in flow path. The best approach to determine the overall interaction effects may be to model the entire torque converter. That is, the three elements are modeled three-dimensionally together. Miner [15] used a three-dimensional potential flow finite element computer code to analyze an entire centrifugal pump. Both the rotating impeller and the stationary pump casing were analyzed in the same model. Laser velocimeter measurements were also taken in this centrifugal pump. A fair correlation was found between computational and laser velocimeter results. It was concluded that the potential flow theory was useful in determining the overall interaction phenomena in tubomachinery. This type of computational approach may also be applied to the torque converter.

2.5.4

2.5.4.1

Potential Flow Analysis

The potential flow solution is an ideal flow solution based on the principal of conservation of mass. All the phenomena associated with the boundary layer flow such as the wall shear stress, flow separation, and reverse flow cannot be directly obtained from this solution. However, it often has been used to solve the flow problems in turbomachinery for two reasons. First, it is simple and economical. Secondly, it is felt that the potential flow solution can provide a better understanding about the overall three-dimensional flow field. The equation to be solved is the conservation of mass equation expressed for the relative system in the following form: LI LLI (2.5.3) ∇ ⋅ ( ρW ) = 0 I where ∇ is the LLI vector differential operator, ρ is the mass density, and W is the relative velocity vector. A potential function formulation forLIEq. 2.5.3 is possible by defining the absolute velocity vector V such that:

Internal Flow Analysis and Blade Design Considerations

Blade spacing, blade profile, and torus shape are the key geometrical parameters to be considered in the converter blade design. Blades are needed to guide the oil to flow smoothly within the converter blade passages. When the blades are spaced too far apart, the loading per blade becomes so great that the blade effectiveness is decreased due to separated flow. On the other hand, when the blades are spaced very close together, the flow becomes smooth but the additional number of blades also reduces the overall working flow area. The optimum blade spacing can be determined by considering these two conflicting effects. Blade thickness and profile are chosen such that they can provide structural integrity and



LI LLI I V=W+i0ΩR



   ∇ × W = –2Ω



(2.5.4)

LI where Ω is the angular velocity, R is the radius, and V is the absolute flow velocity that is irrotational when the relative flow satisfies the condition.

(2.5.5)

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For such flows it is possible to find a potential function such that:   V = —φ (2.5.6)

within the actual blade passage and 5 elements within each of the inlet and outlet extensions. Figures 2.5.11 and 2.5.12 show finite elements grids of one representative blade passage with and without extensions. The meridional distribution of relative velocities and pressure differences at the two flow conditions are shown in Figs. 2.5.13 to 2.5.16. The following observations can be made from these figures:

The substitution of Eqs. 2.5.4 and 2.5.6 into 2.5.3 yields:     — ⋅ ( ρ—φ ) – — ⋅ ( i 0ρΩR ) = 0 (2.5.7)

1. Since the prerotation, RVt is assumed to be constant, the velocities at the shell are higher than those at the core location. 2. The velocity and pressure distributions are very similar between shell and core locations; i.e., the flow is nearly two-dimensional. Since the stator geometry is almost two-dimensional, two-dimensional flow results are expected. 3. At the stall condition, the stagnation point occurs on the pressure surface at about 17% of the chord length. In reference to the velocity diagram of Fig. 2.5.6, the stagnation point is expected to occur on the pressure surface. 4. At the 0.81 SR condition, the stagnation point occurs on the suction surface at about 3% of the chord length. Again, this result is expected. 5. At the stall condition, the minimum pressure difference on the blade suction surface is about –1100 KPa. Since the torque converter charging pressures are normally less than this value, the stator blade should be redesigned to avoid cavitation.

On the boundaries, the following must hold:   ρW ¥ n=f (2.5.8)  where n is the outward normal vector to the boundary and f denotes the known mass fluxes. The values for f are specified as f=fin, at the inlet, f=fex at the exit, and f=0 on the solid boundaries. The exit flux fex can be computed either from the given exit flow angles or from the kutta condition at the trailing edges of the blades. In addition, the velocity potential φ must be set to a constant at an arbitrary point in the flow field to assure a unique solution. For a turbomachine blade row, only a representative channel between two blades is analyzed. The absolute mass flow at the inlet and the outlet of the channel is specified as uniform. On the blade surfaces, the zero-normal flux condition is provided automatically by setting f to zero. Also, in order to maintain the axisymmetry and the uniformity of the flow ahead and far aft of the blade row, the passage is extended in both directions. Imaginary walls are placed as continuation of the blades among the pressure and suction surfaces to define the extension of the passage. Periodically boundary conditions are then imposed along the boundaries of these imaginary channels. The kutta condition at the trailing edges of the blade is also imposed by controlling the total circulation around the blades such that the pressures on either side of the sharp trailing edges are equalized.

Table 2.5.1  Flow Conditions for the Potential Flow Analysis. SR 0 0.81

In Ref. 6, Mecure used potential flow computer programs to model a torque converter. A stator was analyzed and redesigned by using a two-dimensional finite difference potential flow program. A quasi three-dimensional finite difference potential flow program was used to redesign a turbine and pump. Diffusion factor, the ratio of the maximum surface velocity to the exit velocity, was used as the parameter for flow separation. An example of stationary stator blade passage is presented. The potential flow computer code used in this analysis was developed by Ecer and Akay [17]. Two flow conditions were considered, as shown in Table 2.5.1. The finite element grids employed are NR ¥ NT ¥ NZ = 9 ¥ 9 ¥ 35 where NR, NT, and NZ are the numbers of elements in the core-to-shell, bladeto-blade, and meridional direction, respectively. Out of 35 elements in the meridional direction, 25 elements are located

R Vt (m²/s) –0.0090 +0.0039

m (kg/s) 97.2 60.3

Density (kg/m³) 826 826

Fig. 2.5.11  Stator blade passage showing the boundaries with no extension. 2-77

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Fig. 2.5.14  Pressure distribution at stall. Fig. 2.5.12  Stator blade passage showing the boundaries with extensions.

Fig. 2.5.15  Velocity distribution at 0.81 SR.

Fig. 2.5.13  Velocity distribution at stall.

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Conservation of Mass: ∂u ∂v ∂w + + =0 ∂x ∂y ∂z



(2.5.12)

where u, v, and w are the velocity components in the x, y, and z directions, respectively. The three-dimensional viscous flow technology is very complicated and challenging. Although significant developments of computational fluid mechanics have been accomplished along with increasing computer capabilities, there are not many viscous flow computer codes which have the capability to predict accurately the viscous flow phenomena in turbomachinery.

The Navier-Stokes equations are used to describe the notion of all viscous, Newtonian fluids. The basic conversation equations governing the three-dimensional steady flow of an incompressible fluid in a Cartesian coordinate system rotating with constant angular velocity Ω is given by:

The flow in the stator passage was previously treated using a three-dimensional potential flow computer code. Although the potential flow solution provided much insight into the performance of the stator, results indicated that the flow most likely exhibited substantial regions of flow separation. A potential flow analysis cannot predict such regions of separation. Thus, to more realistically treat the flow in the stator passage, a fully viscous analysis method is required. Since the three-dimensional potential flow analysis showed that the flow in the stator passage was essentially two-dimensional, a two-dimensional viscous flow approach was chosen to analyze the stator blade passage at the core location. TURBO2D [10] was used for this analysis. The same two flow conditions are considered as shown in Table 2.5.2.

Conservation of Momentum: X-Momentum

Table 2.5.2  Flow Conditions for the Viscous Flow Analysis.

Fig. 2.5.16  Pressure distribution at 0.81 SR. 2.5.4.2

u

Viscous Flow Analysis

∂u ∂u ∂u 1 ∂p + ν— 2 u + 2Ωv + Ω2 x + f x +v +w =– ∂x ∂y ∂z r ∂x

↑ Convection Terms

↑ Coriolis Term

SR 0 0.81

(2.5.9)

Y-Momentum ∂v ∂v ∂v 1 ∂p u +v +w = + ν— 2 v – 2Ωu + Ω 2 y + f y ∂x ∂y ∂z r ∂ x ↑ ↑ Centrifugal Term Body Force Term

(2.5.10)

Z-Momentum u

1 ∂p ∂w ∂w ∂w +v +w =– + ν— 2 w + f z ∂x ∂y ∂z r ∂z ↑ Pressure Gradient Term

↑ (2.5.11) Viscous Terms

Inlet FlowAngle (degrees) –39.52 +30.15

R Vt (m²/s) –0.0090 +0.0039

Radius (m) 0.072 0.072

The finite-element mesh is shown in Fig. 2.5.17. Each mesh was designed with several criteria in mind. First of all, it was desired to obtain elements with a minimum of skew and an aspect ratio as close as practical to unity in all regions of the solution domain. Ideally, all elements would be perfect squares. A reasonable mesh is difficult to obtain, particularly in the vicinity of the trailing edge of the blade, unless an unstructured mesh is employed. Hence, the unstructured form of grid was used. As illustrated in Fig. 2.5.18, this type of grid allows the mesh to be wrapped around the blade in the blunt leading edge region and allows reasonably shaped elements to be obtained in the trailing edge region. A second criteria in the design of the mesh is the location of periodic boundaries. Nodes lying along these boundaries must form periodic pairs with the nodes lying on the corresponding

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velocity components are specified. The tangential velocity component was calculated from the value of RVt given in Table 2.5.2 for each of the two cases. The axial component of velocity was then calculated from the tangential component to provide the specified inlet flow angle shown in Table 2.5.2. The pressure value is not specified along the inlet, but is calculated as part of the solution procedure. There are two pairs of periodic boundaries—lines BC and IA form one pair of periodic boundaries while lines EF and HG form a second pair of periodic boundaries. The input data for periodic boundaries involves specifying each node along one of the boundaries and the corresponding node lying on the other boundary. In the actual calculations, the periodic boundary conditions merely involve a modification to the assembly procedure whereby the elements lying on one boundary are assembled with the contributions for the node lying on the other boundary. The resulting nodal equations are computationally the same as an interior node; i.e., a periodic node is computationally or topologically an interior node, not a boundary node. For the stator passage model, there are two no-slip boundaries; natural boundary conditions are used for the pressure equations (i.e., no special treatment is required). The exit boundary, line FG, is treated as a constant pressure boundary. The pressure is specified along this boundary as a constant, i.e., zero. Note that in an incompressible analysis, the value for pressure at the exit boundary may be any constant value. Natural boundary conditions are used for both velocity components. Again this means that no special treatment is required. Neither the velocity magnitude nor angle is specified. The boundary condition for pressure is chosen such that it will have a minimum of impact on the predicted results upstream in the solution domain. The flow conditions at the exit of the solution domain are of course unknown in advance. However, since this is an elliptic problem, sufficient information must be specified at this boundary to form a well-posed problem. In essence, the minimum possible constraint required to form a well-posed problem is the specification of the pressure. In addition, this constraint is consistent with the problem at hand; i.e., the pressure in this region of the flow will be nearly constant.

periodic boundary. This means that these nodes must be translated in the circumferential direction. These periodic pairs of nodes must have the same value for the z-coordinate. This constraint is met most effectively by the use of the unstructured mesh that was chosen. Finally, to minimize the effect of the downstream boundary conditions on the results obtained in the vicinity of the blades, the inlet and exit regions of the mesh are arbitrarily extended ahead of the leading edge and downstream of the trailing edge. As will be demonstrated in the results section, the extensions used appear adequate.

Fig. 2.5.17  Finite element mesh for the stator blade passage.

The results of the flow analysis are presented in the form of overall graphical displays of the streamlines, pressure contours, and contours of the axial-velocity components for each of the two cases. These plots were chosen since they best illustrate the flow phenomena occurring in the passage. The streamlines for each of the two cases are shown in Figs. 2.5.19 and 2.5.20. As illustrated, each of these two cases shows significant regions of separated flow on the suction side of the blade. The separation occurs at approximately 30% of the mean chord length in all of the cases. Somewhat surprisingly, the suction side separation region is not significantly different for the two different speed ratios. There is more of a difference

Fig. 2.5.18  Boundary conditions for the viscous flow analysis. Four types of boundaries are represented in the stator passage analysis. These types are: inlet boundaries, no-slip solid wall boundaries, periodic boundaries, and flow exit boundaries. Each of the two cases includes these same boundary conditions with only the inlet boundary conditions varying from case to case. As shown in Fig. 2.5.18, the line AB forms the inlet boundary. Along the inlet boundary, the values of both

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between the pressure side flow in the two different SR cases. For the case with a SR of 0.81, there is no separated region on the pressure surface. For the SR of zero, however, the flow shows a small separated region near the leading edge at the stagnation point. The pressure contours for the two cases are shown in Figs. 2.5.21 and 2.5.22. Although the pressure contours are similar, there are several key differences that should be noted. First of all, the highest pressure occurs at the stagnation point near the leading edge, as expected. This pressure point moves consistent with the shift of the stagnation point. Second, the validity of the exit plane boundary condition used in each of the cases is enforced by the results shown in these plots. As illustrated in the plots, most of the pressure variation occurs at the leading edge of the blade and within the first 50% of the mean chord length. At the trailingedge region of the blade, there is very little pressure variation relative to the changes occurring at the leading-edge region. The plots of the axial-velocity contours are most informative in identifying separated regions and the wake region downstream of the separation point. As shown in Figs. 2.5.23 and 2.5.24, these plots clearly highlight the wake region and low velocity regions near the blade surfaces and at the stagnation points. These plots also show the highest velocity. The highest velocity occurs, as expected, at approximately 10 to 20% of the mean chord length and just outside the boundary layer on the suction surface. In addition, the flow exit angle can also be obtained. The flow exit angle is found to be about 53° and 51° for the stall and 0.81 SR conditions, respectively. The physical blade exit angle is 62°. It is interesting to note that there is a surprisingly small variation in these velocity contours, even though these cases feature a large variation in the inlet flow angle. It should be noted, however, that these plots are of the axial velocity magnitude only and do not therefore show any effect due to the difference in the inlet velocity angle from case to case.

Fig. 2.5.20  Streamlines for the .81 SR condition.

Fig. 2.5.21  Pressure contours for the stall condition.

Fig. 2.5.22  Pressure contours for the 0.81 SR condition.

Fig. 2.5.19  Streamlines for the stall condition. 2-81

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[2] used a large flow table to observe the flow patterns of blade cascades. Numazawa et al. [18] developed a flow visualization technique to trace flow patterns on the blade and end-wall surfaces. This technique was successfully used to design a torque converter with elliptical cross section. The most extensive published research in the area of internal flow measurements was made by Fister and Adrian [13]. The researchers used a spark tracer method in a torque converter with air and a Laser Two Focus (L2F) method for water in a torque converter. The flow in the blade passages was found to be highly three dimensional throughout the whole range of operation. It was concluded that the one-dimensional performance concept is not sufficient to accurately model the flow in a torque converter. Multi-holed probes were also used to measure pressure inside a torque converter. The measured data were used to determine incidence loss coefficients as a function of incidence angles for all the three elements.

Fig. 2.5.23  Axial velocity contours for the stall condition.

Fig. 2.5.24  Axial velocity contours for the .81 SR condition.

Over the past decades, significant progress has been made in the area of internal flow measurements to the development of highly experimental instrumentation. Manufacturers of instrumentation have experimentally studied flow fields in a number of turbomachines: axial flow pumps, centrifugal pumps, axial flow compressors, axial flow turbines, and centrifugal compressors [19, 20, 21]. Brownwell et al. [19] developed a streak photography method to visually study the flow in the tongue region of a pump volute. Many important flow phenomena such as flow recirculation, flow separation, and stagnation point were detected. Hamkins and Flack [20] measured the flow in shrouded and unshrouded radial flow pump impellers using a two-component frequency-shifted laser velocimeter. The data were used to analyze tip clearance leakage, angular momentum through the impellers, and slip factors. Erwin [21] presented several experimental techniques used in the internal flow measurements of gas turbine components.

2.5.5

2.5.6

Internal Flow Measurements

Performance Analysis

Most widely used performance models for torque converters are based on the simple concept of a one-dimensional mean design flow path with constant circulating flow rate. As discussed previously, it was found in Ref. 13 that the flow in the torque converter is highly three-dimensional in the whole range of operation. Furthermore, the loss correlations used in the one-dimensional model do not account for all geometric factors that affect the overall performance. Therefore, the current cone-dimensional performance model needs to be upgraded to accurately represent the flow in the torque converter.

The theoretical analysis of turbomachinery has not developed to the position permitting complete design from results obtained solely by calculations. Experimental data on the three-dimensional flow field, in terms of velocity distribution, pressure distribution, flow exit angle, and overall flow visualization, are required to verify computational results. Furthermore, experimental data can also provide a deeper understanding about the overall flow characteristics. Although the torque converter is one of the most complicated turbomachines, it has received very little attention in the area of internal flow measurements in the past. Upton

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• Meet the packaging constraints with squashed torus design. • Ensure modeling repeatability and archive design parameters.

Analytical investigations have been initiated to improve performance predictions of torque converters. Whitfield et al. [22] developed a modified one-dimensional performance model for the torque converter. The circulating flow motion was assumed to be similar to a forced vortex where the flow velocity is zero at the center and increasing linearly to the outer wall of the torus. A detailed integration method was used in the model to integrate the losses, and the change in momentum from core to shell was also included in the mathematical model. The results showed better agreement with the experimental data than those given by the one-dimensional model. Anderson [23] developed a two-dimensional, inviscid model for the performance and internal flow calculations of torque converters. The flow was assumed to have no variation in the tangential direction. The results from this theory were also found to be more accurate than those given by the one-dimensional model.

Further information relative to CFD and torque converter analysis will be presented as an additional section in this chapter.

2.5.7

Conclusions

A review of the technology needs in the area of internal flow, blade design, and performance has been presented. The important conclusions drawn from this investigation are as follows: 1. Internal flow analyses can be used to effectively determine the physical phenomena associated with the flow losses in the torque converter. 2. Internal flow data on the three-dimensional flow field are needed to verify predicted results and to provide a deeper understanding about the actual flow characteristics in the torque converter. 3. The one-dimensional performance model is not sufficient to accurately represent the flow in the torque converter. The performance model should be improved to include the effects of both the geometry on the flow distribution and the flow distribution on losses. Note: three-dimensional performance models have been developed and are widely used in current torque converter design and analysis.

Boyle et al. [7] developed a quasi three-dimensional performance calculation system for axial flow turbines. The method used a quasi three-dimensional potential flow analysis interactively coupled to calculate losses. That is, the effects of both the geometry on the flow distribution and the flow distribution on losses were accounted for in the overall performance calculation. The calculation system was used to predict the performance of several turbines. Good agreement was found between the predicted and measured efficiencies. This type of computational approach may also be applied to the torque converter. Viscous flow computer codes may be used to predict the flow distribution, viscous flow losses, exit flow angles, and incidence loss. The leakage flow loss may be obtained from experimental data. Potential flow codes may be used to determine the overall interaction effects between the elements. In this manner, most of the physical flow phenomena are included in the overall performance model.

2.5.8

Acknowledgments

The authors wish to express their gratitude to the following:

In the years since the initial publication of this paper, extensive work has been accomplished in the area of computational fluid dynamics (CFD) with respect to torque converters. Various design tools have been developed and implemented for the analysis and design of the torque converter [27, 28]. All of these tools have the following goals:

1. Mr. Goetz Schaefer of the Allison Transmission Division, GMC, who persuaded the authors to undertake this study. 2. Mr. Ernest Upton and other colleagues at the Advanced Engineering Staff, GMC, who have provided valuable guidance and assistance. 3. The management of the Advanced Engineering Staff for the permission to publish this paper.

• Perform parametric blade design to reduce development time and cost. • Obtain the desired K-curve to meet the system requirements. • Automate air-foil reactor design to achieve the required performance curves.

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2.5.9

References

15. Miner, S. M., PhD dissertation, University of Virginia, October 1987. 16. Mecure, R. A., “Review of the Automotive Torque Converter,” SAE Paper No. 700046, SAE International, Warrendale, PA, 1970. 17. Ecer, A., H. U. Akay, and S. Mattai, “Finite element Analysis of Three-dimensional Flow Through a Turbocharger Compressor Wheel,” ASME #83-GT-92. 18. Numazawa, A., F. Ushijima, F. Kagenori, and T. Ishihara, “An Experimental Analysis of Fluid Flow in a Torque Converter,” SAE Paper No. 830571, SAE International, Warrendale, PA, 1983. 19. Brownwell, R. B., R. D. Flack, and G. J. Kostrzewsky, “Flow Visualization in the Tongue Region of Centrifugal Pump,” The Journal of Thermal Engineering, Vol. 2, No. 2, 1985, pp. 35–45. 20. Hamkins, C. P. and R. D. Flack, “Laser Velocimetry Measurements in Shrouded and Unshrouded Radial flow Pump Impellers,” ASME #86-GT-129. 21. Erwin, J. R., “Aerodynamics of Turbines and Compressors,” Vol. X, 1964. High Speed Aerodynamic and Jet Propulsion, Edited by W. R. Hawthorne, Princeton University Press, Princeton, New Jersey, Chapter 3, Section D, pp. 167–266. 22. Whitfield, A., F. J. Wallace, and R. Sivalingham, “A Performance Prediction Procedure for Three-Element Torque Converters,” Int. J. Mech. Sci., Vol. 20, 1978, pp. 801–814. 23. Anderson, S., “On Hydrodynamic Torque Converters,” Transactions of Machine Elements Division, Lund Technical University, Lund, Sweden, 1982. 24. Schlichting, H., Boundary-Layer Theory, 7th edition, McGraw-Hill, New York, 1979. 25. White, F. M., Viscous Fluid Flow, McGraw-Hill, New York, 1974. 26. Wilson, D. G., The Design of High-Efficiency Turbomachinery and Gas Turbines, MIT Press, Cambridge, Massachusetts, 1984. 27. Shieh, T., C. Perng, D. Chu, and S. Makim. “Torque Converter Analytical Program for Blade Design Process,” SAE Paper No. 2000-01-1145, SAE International, Warrendale, PA, 2000. 28. Kubo, Masaaki and Eiji Ejiri, “A Loss Analysis Design Approach to Improving Torque Converter Performance,” SAE Paper No, 981100, SAE International, Warrendale, PA, 1998.

1. Jandasek, V. J., The Design of a Single-Stage Three-Element Torque Converter, SAE Design Practices—Passenger Car Automatic Transmission, Volume 1, 1962. 2. Upton, E. W., Application of Hydrodynamic Drive Units to Passenger Car Automatic Transmissions, SAE Design Practices—Passenger Car Automatic Transmission, Volume 1, 1962. 3. McNally, W. D., “Introduction to Boundary-Layer Theory, Turbine Design and Application,” Vol. 2, 1973, Edited by A. J. Glassman, NASA SP-290. 4. Prust, H. W., Boundary-Layer Losses, Turbine Design and Application, Vol. 2, 1973, Edited by A. J. Glassman, NASA SP-290. 5. Langston, L. S., M. L. Nice, and R. M. Hopper, “Three Dimensional Flow Within A Turbine Cascade Passage,” Journal of Engineering for Power, Transactions of the ASME, January 1977, pp. 21–28. 6. Kacker, S. C., and U. A. Okapuu, “A Mean Line Prediction Method for Axial Flow Turbine Efficiency,” ASME #81-GT-58. 7. Boyle, R. J., J. E. Haas, and T. Katsanis, Comparison Between Measured Stage Performance and the Predicted Performance Using Quasi-Flow and Boundary Layer Analysis, #AIAA-84-1299. 8. Hah, C., “A Navier-Stokes Analysis of Three-Dimensional Turbine Flow Inside Turbine Blade Rows at Desing and Off-Design Conditions,” Journal of Engineering for Gas Turbines and Power, Transactions of the ASME, April 1984, Vol. 106, pp. 421–428. 9. Rhie, C. M., R. A. Delaney, and T. F. McKain, “ThreeDimensional Viscous Flow Analysis for Centrifugal Impellers,” #AIAA-84-1296. 10. Schipke, R. J. and J. G. Rice, “A Streamline Upwind Finite Element Method for Laminar and Turbulent Flow,” University of Virginia, Report No. UVA/643092/ MAE86/342, June 1986. 11. Ecer, A. and H. U. Akay, Passage Presentation, November 19, 1987, Southfield, Michigan. 12. Nagornaya, N.K., “Impact Losses and Coefficients in Hydraulic Torque Converter Blade Systems,” Russian Engineering Journal, Vol. 6 1961, pp. 21–24. 13. Fister, W. and F. W. Adrian, “Experimental Researches of Flow in Hydrodynamic Torque Converters, Proc. 7th conference on Fluid Machinery, Budapest, Hungary, 1983, Vol. 1. 14. Roelke, R. J., Miscellaneous Losses, Turbine Design and Application, Vol. 2, 1973, Edited by A.J. Glassman, NASA SP-290. 2-84

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2.6 An Experimental Analysis of Fluid Flow in a Torque Converter

number at the same level as under actual operating conditions in the experiments.

Akio Numazawa, Fumihiro Ushijima, and Kagenori Fukumura Toyota Motor Corp. (Japan)

In this study, instead of the oil film method we developed a liquid-resin film method which enabled a flow visualization in a torque converter without changing the working fluid from oil to water. Through observations of the flow in a torque converter by this method, it was clarified that the cross, swirl, reverse, and separated flow-types caused by inadequate geometrical configurations result in a decrease in torque converter efficiency.

Tomo-o-Ishihara Univ. of Tokyo (Japan) Based on SAE Paper No. 830571

2.6.1

Abstract

Theoretical analysis of the fluid in a torque converter is not easy because it is a three-dimensional and very complicated problem.

Based on the results, torque converter efficiency was improved by modifying the torus and the blade profiles, and by making the fluid flow smoother. This modified torque converter has been used practically in the Toyota two-way overdrive automatic transmission.

The new flow visualization applicable to oil flow, namely a liquid-resin film method, was developed to observe the fluid flow in a torque converter.

2.6.2

Flow Visualization of Working Fluid

2.6.2.1

Proposed Wall Tracing Method (Liquid-Resin Film Method)

The existence of cross, swirl, reverse, and separated flow in torque converters was made clear by this method, and it was clarified that the existence of these kinds of flow resulted in depressing torque converter efficiency.

The visible flow pattern in the torque converter could not be generated on the surface by the generally used wall tracing methods, such as the oil film method or the oil spot method, because the oil film and the oil spot resolve in the working fluid. On the other hand, the tuft or tracer method was inadequate for observing the fluid flow in a torque converter because of its closed and complicated configuration. For this reason, the development of a new method enabling oil flow observation was required.

Additionally, the flow pattern in a torque converter was predicted theoretically by eliminating the pressure distribution in it. An elliptical torque converter with high efficiency was developed by flow visualization and theoretical considerations. It is important to increase torque converter efficiency for the improvement of the fuel economy of vehicles with automatic transmissions. As torque converter efficiency depends on the flow condition in the converter circuit, it is required to clarify the relationship between the flow condition and the torus and blade profiles. A theoretical analysis of the fluid flow in a torque converter is not easy because it is three dimensional and very complicated. Therefore, an experimental study of the fluid flow in a torque converter is required using the flow visualization technique.

Since observations of the fluid flow in a torque converter are made under various operating conditions, both the preparation time for experiments and the flow pattern generation time must be shortened. Moreover, the flow pattern on the surface must be generated clearly and precisely. The following characteristics are required of the flow visualization material: 1. Insolubility in the working oil 2. Adequate specific gravity comparable to that of the working oil 3. Strong adhesion to the wall surface 4. Good affinity with the pigment 5. Controllable viscosity

Several papers have been written on the flow visualization of a torque converter using the oil film method, where the surfaces were coated with an oil film and water was used as the working fluid instead of the oil to hold the film [1, 2]. In this method, however, modifications are needed on bearing mechanisms to compensate for the poor lubricating properties of water. Additionally, it is difficult to keep the Reynolds

To satisfy these requirements, flow visualization materials such as grease, liquid resin, etc., were selected, and many tests

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were conducted by the spot method to determine the best material. It was found that none of the tested materials generated any clear flow pattern, because they were separated from the surface and mixed into the working oil. This is probably caused by a strong adhesion force of the working oil to the surface, which prevents the flow visualization method from adhering to the surface.

in the stream through a transparent cylinder. Another series of experiments was also made by using a different apparatus to determine the effect of centrifugal force on pattern deformation and the effect of flow velocity on pattern generation time.

To solve these problems, a new wall tracing method was considered, where a thin coat of surface coating material was applied to the surface to prevent the working oil from adhering to the surface, and then the surface coating material was covered properly with dots of a spot material colored by red pigment. Table 2.6.1 shows the surface coating and spot materials suitable to this method. In Table 2.6.1, the mixing ratio of the spot material is defined as m2/m1, where m1 and m2 are the weights of the base material and the pigment, respectfully.

Fig. 2.6.2  Experimental apparatus. 2.6.2.2.1 Effect of Coating Material Thickness

Thick surface coatings (50 to 100 μm) generate long flow patterns which enable us to estimate the stream lines (Fig. 2.6.3a). On the other hand, thin surface coatings (less than 10 μm) generate short flow patterns which enable us to estimate the local flow direction (Fig. 2.6.3b).

Table 2.6.1  Flow Visualization Material. Base material Surface coating material Spot material

Pigment

Mixing ratio

Liquid epoxide resin

—

—

≠

Ferric oxide

0.5~2

2.6.2.2.2 Effect of the Spot Material Mixing Ratio

A high base material content generates a long pattern in a short time compared with that in the case of a low base material content (Fig. 2.6.4). Thus, it is possible to obtain a desirable flow pattern by changing the coating material thickness and the spot material mixing ratio. The transient effect from the standstill to the predetermined speed can be minimized by increasing the mixing ratio because it delays the flow pattern generation time.

Because the base material of the spot material and of the surface coating material are the same, the former resolves and penetrates into the latter gradually and adheres to the surface (Figs. 2.6.1a and 2.6.1b). The spot material is deformed and moves in the flow direction as a result of oil flow shearing stresses together with the surface coating material (Figs. 2.6.1c and 2.6.1d). As the working oil is prevented from adhering to the surface by the coating material, the spot material generates the flow pattern on the surface (Fig. 2.6.1e). 2.6.2.2

2.6.2.2.3 Effect of Centrifugal Force

Low-viscosity spot material generates an undesirable flow pattern due to the centrifugal force acting on the material. The effect of the centrifugal force on pattern generation can be minimized by increasing the viscosity of the spot material, which can be controlled by changing the mixing ratio (Fig. 2.6.5).

Characteristics of Liquid Resin Film Method

Experiments were made to determine the effects of the coating material thickness and the mixing ratio on flow pattern generation. Figure 2.6.2 shows the experimental apparatus. The liquid-resin film method was applied to a specimen plate

Fig. 2.6.1  Mechanism of flow pattern generation. 2-86

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Fig. 2.6.6  Type 1 torque converter.

Fig. 2.6.3  Effect of coating material thickness (V = 10 m/ sec, t = 5 min).

Fig. 2.6.7  Type 2 torque converter.

Fig. 2.6.4  Effect of mixing ratio (V = 10 m/sec, t = 5 min).

Table 2.6.2  Torque Converter Specifications. Diameter (A) Torus (B) Torus (C) Torus (B/C)

Type 1

Type 2

248.0   82.0   84.4 0.972

254.0   58.5   79.0 0.741

Fig. 2.6.5  Effect of centrifugal force (N = 1000 rpm, r = 150 mm, t = 5 min).

2.6.3

Observation of Fluid Flow in Torque Converters

2.6.3.1

Specifications of Tested Torque Converters and Flow Observations

Figures 2.6.6 and 2.6.7 show the cross-sectional views of the tested Type 1 and Type 2 torque converters. Table 2.6.2 shows their specifications. A part of the pump blade, turbine blade, and core ring were disassembled to make observation of the flow pattern on the surface easy (Fig. 2.6.8).

Fig. 2.6.8  Tested torque converter.

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In Figs. 2.6.9 and 2.6.10, the flow patterns on the blade surfaces of the Type 1 torque converter are shown using the liquid-resin film method. The observed blade surface was colored white to make the flow pattern clear. The coating material thickness was 10 to 50 μm; the mixing ratio was 1.0. In these figures, the speed ratio is defined as e = n1/n1 where n1 and n2 are the input and output speed, respectfully. P.S. and S.S. mean the pressure and suction surfaces, respectfully. The temperature of the working oil ranged between 30°C and 100°C, and the operating time necessary to generate the steady state pattern was about 5 minutes.

2.6.4

Flow Pattern

2.6.4.1

Type 1 Torque Converter

Figure 2.6.11 shows the sketched flow patterns on the pressure and suction surfaces of each blade of the Type 1 torque converter, reproduced from the flow pattern photographs in the previous figures.

Fig. 2.6.9  Visualized flow pattern at e = 0.

Fig. 2.6.11  Sketched flow pattern of Type 1 torque converter.

Fig. 2.6.10  Visualized flow pattern at e = 0.8.

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At e = 0, smooth flow (desirable flow) was observed, especially on the pressure surface. At e = 0.8, flow from the shell surface to the core surface was observed on the pressure surface. Disturbed flow was observed on the suction surface, and reverse flow was observed on the suction surface in the vicinity of the blade inlet. 2.6.4.1.2 Flow in the turbine

At e = 0, flow from the shell surface to the core surface was observed on the pressure surface, and disturbed flow was observed on the suction surface. Reverse flow was observed at a part of the suction surface in the vicinity of the blade inlet. At e = 0.8, flow from the shell surface to the blade inlet was observed on the suction surface, and disturbed flow was observed on the pressure surface. Reverse flow was observed on the pressure surface in the vicinity of the blade inlet. 2.6.4.1.3 Flow in the stator

At e = 0, smooth flow was observed on the pressure surface, accompanied by an entirely convergent flow from the shell and core surfaces to the blade inlet. Disturbed flow was observed on the suction surface. At e = 0.8, entirely convergent flow from the shell and core surfaces to the blade inlet was observed on the suction surface, and disturbed flow was observed on the pressure surface. 2.6.4.2

Type 2 Torque Converter

Figure 2.6.12 shows the sketched flow pattern on the pressure and suction surface of each blade of the Type 2 torque converter, reproduced from the flow pattern photographs. 2.6.4.2.1 Flow in the pump

At e = 0, entirely smooth flow was observed on the pressure and suction surfaces, with the exception of a small eddy on the pressure surface at the blade outlet. At e = 0.8, smooth flow was observed on the pressure and suction surfaces at the blade inlet. At the blade outlet, smooth flow and stagnated flow were observed on the pressure and suction surfaces, respectfully.

Fig. 2.6.12  Sketched flow pattern of Type 2 torque converter.

2.6.4.2.2 Flow in the turbine

At e = 0, entirely smooth flow was observed on the pressure surface, accompanied by flow from the shell surface to the core surface at the blade inlet, and reverse flow and stagnated flow were observed on the suction surface. At e = 0.8, smooth flow was observed on the pressure surface at the blade outlet and on the suction surface at the blade inlet. Disturbed flow was observed on the pressure surface at the blade inlet and on the suction surface at the blade outlet.

2.6.4.2.3 Flow in the stator

At e = 0, smooth flow was observed on the pressure and suction surfaces with the exception of reverse flow on the suction surface at the blade inlet. At e = 0.8, smooth flow was observed on the pressure and suction surfaces, with the exception of reverse flow on the pressure surface at the blade inlet. 2-89

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2.6.4.3

2.6.5

Comparison of Type 1 and Type 2 Torque Converters

Figures 2.6.13 and 2.6.14 show the sketched flow patterns projected to the meridian plane for both Type 1 and Type 2 torque converters, which were derived from previous figures. The flow evaluations of each blade from these experiments are summarized in Table 2.6.3.

Relationship between Efficiency and Flow Pattern

Figure 2.6.15 shows a comparison of the efficiency curves for the Type 1 and Type 2 torque converters. The efficiency of Type 2 is higher than that of the Type 1 from the stall point to the coupling point. The difference in the maximum efficiency of Type 1 and Type 2 reaches 4 to 5%. From the above, it can be seen that the effect of the flow improvement is very remarkable. The energy losses from the flow in a torque converter are comprised of the shock loss at the blade inlet; the friction loss on the blade, core, and shell surfaces; and the additional loss caused by secondary flow in the flow passage. It will be assumed that the shock loss is proportional to the square of the shock velocity, and the friction loss is also proportional to the mean relative flow velocity in each member of the torque converter. Although the additional loss may not be strictly expressed by an equation, it will be assumed that it is treated as a kind of friction loss [3].

Fig. 2.6.13  Sketched flow pattern of Type 1 torque converter.

Fig. 2.6.14  Sketched flow pattern of Type 2 torque converter. Table 2.6.3  Comparison of Flow Conditions. Pump e Type 1

Type 2

0.0 0.4 0.8 0.0 0.4 0.8

En. -

× -

Turbine

Ex.

En.

∆ ∆ × ∆ ∆

× ∆ × ∆ -

-

-

Stator

Ex.

En.

Ex.

-

-

∆

-

-

-

-

-

∆

-

∆

-

-

-

-

-

-

-

Fig. 2.6.15  Comparison of torque converter characteristics. The shock loss head hs, and the sum of friction loss head hf and additional loss head ha are expressed by the following Eqs. 2.6.1 and 2.6.2: ⎧(ri⋅1ω i − cκ i⋅1 ) − ⎫ ⎪⎪ ⎧ 1 ⎫ 3 ⎪⎪ hs = ⎨ ⎬ ∑ ϕ i ⎨ ⎬ ⎛ ⎞ r − i 1.2 ⎩ 2g ⎭ i =1 ⎪(ri −1.2ω i −1 − cκ i −1.2 ) ⎜ ⎪ ⎝ ri −1 ⎟⎠ ⎪⎭ ⎪⎩

En: Entrance; Ex: Exit; -: Good; ∆: Poor; ×: Bad

In the table, it can be seen that the Type 1 torque converter tended to have undesirable flow patterns in the range of the high speed ratios, and that the best flow pattern appears at e = 0.4. The Type 2 torque converter had a considerably better flow pattern over a wider range of speed ratios than the Type 1 torque converter. Its geometrical configurations were modified based on the flow pattern observations of the Type 1 torque converter. Significant improvements can be seen in the table.

where:

2

(2.6.1)

⎧ c 2 ⎫ 3 ⎧ (κ 2 + κ i2⋅2 ) ⎫ hf + ha = ⎨ ⎬ ∑ li ⎨1 + i⋅1 ⎬ 2 ⎭ ⎩ 2g ⎭ i =1 ⎩

(2.6.2)

hs = shock loss of head hf = friction loss of head ha = additional loss of head 2-90

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g = gravitational acceleration j = coefficient of shock loss r = radius from the axis of rotation ω = angular velocity of rotation κ = blade angle coefficient = tan α α = blade angle λ = coefficient of friction loss and additional loss c = meridional velocity

ρi∙1 = radius ratio at entrance = ri∙1/r1∙2 ρi∙2 = radius ratio at exit = ri∙1/r1∙2 ei = speed ratio = ωi/ω1 The relationship between the efficiency and the meridional velocity coefficient is expressed by Eq. 2.6.5 from the equation of torque converter efficiency η = (τ2/τ1)e.

β=

front subscripts: i (1, 2, 3) = No. of members, 1: pump, 2: turbine, 3: stator



Using these equations and measured efficiency, energy losses can be calculated at each speed ratio.

rear subscripts: 1 = entrance number 2 = exit number

Assuming the coefficient of shock loss j = 1, the coefficient of friction and additional loss λ can be obtained. As λ means the sum of the non-dimensional friction and additional losses, it may be considered that small flow results in a minimized value for λ.

From angular momentum theory, each torque of the pump, turbine, and stator is expressed by Eq. 2.6.3, and from energy balance, the meridional velocity coefficients are expressed by Eq. 2.6.4. τi = β {(ρi⋅2ε ι − βκ i⋅2 )ρi⋅2 − (ρi −1⋅2ε i −1 − βκ i −1⋅2 )ρi −1⋅2}

3 ⎡ ⎧ ( κ 2 + κ i2⋅2 ) ⎫ ⎛ ( κ i⋅1 - κ i -1⋅2 ρi -1⋅2 ) ⎞ β 2 ∑ λ i ⎢ ⎨1 + i⋅1 ⎬ + ϕi ⎜ ⎟⎠ 2 ρi⋅1 ⎝ ⎢⎣ ⎩ i =1 ⎭

⎧ ⎨κ 1⋅2 ⎩

⎧ ⎛η⎞⎫ ⎨1 − ρ22⋅2e − ⎜⎝ ⎟⎠ ⎬ e ⎭ ⎩ (2.6.5) ⎫ ⎛η⎞ − ρ2⋅2κ 2⋅2 − ⎜ ⎟ (κ 1⋅2 − ρ3⋅2κ 3⋅2 ) ⎬ ⎝ e⎠ ⎭

Figure 2.6.16 shows λ curves calculated for Type 1 and Type 2 torque converters. As speed ratio increases, the λ of Type 1 decreases in the range of the low speed ratio, and sharply increases in the range of the high speed ratio. On the other hand, the λ of Type 2 decreases continuously with increasing speed ratio. The λ of Type 2 is lower than that of Type 1, which causes high efficiency of Type 2 in the range of the high speed ratio.

(2.6.3)

2

⎤ ⎥ ⎥⎦

2 ⎤ ⎡⎧⎪ ⎫⎪ ⎛ρ ⎞ ⎢⎨ϕ iei −1 ⎜ i −1⋅2 ⎟ + (1 − ϕi )ei ⎬ ρi −1⋅2κ i −1⋅2 + ⎥ ⎝ ρi⋅1 ⎠ 3 ⎢⎪ ⎥ ⎪⎭ ⎩ ⎥ −2β∑ ⎢ ⎥ i =1 ⎢ 2 ⎥ ⎢ϕi ⎛ ρi⋅1ei − ρi −1⋅2ei⋅1 ⎞ κ i⋅1 − ρi⋅2eiκ i⋅2 ⎟⎠ ⎥⎦ ⎢⎣ ⎜⎝ ρi⋅1 2 ⎧ ⎛ ρi −1⋅2 ⎞ ⎫ 2 2 2 2 2 3 ⎪(2ρi ⋅2 − ϕ iρi ⋅1) e i − ϕ iρi-1⋅2e i −1 ⎜⎝ ρ ⎟⎠ ⎪⎪ ⎪ i ⋅1 −∑ ⎨ ⎬=0 i =1 ⎪ ⎪ ⎪⎭ ⎪⎩−2(1 − ϕ i )ρi −1⋅2eiei −1

(2.6.4) where:

τ = torque coefficient = T / {(γ /g)ar15⋅2ω12} T = torque A = area coefficient = A/r12⋅2 a = cross-sectional area of flow g = weight of working fluid per unit volume β = meridional velocity coefficient = C/(r1∙2ω1)

Fig. 2.6.16  Comparison of coefficients of friction and additional losses. The relationships between λ and e for both Type 1 and Type 2 torque converters are well related to their characteristics and to the previously described flow patterns (Table 2.6.3). 2-91

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It is understood that improvement of the flow pattern leads to reductions in friction and additional losses and results in a higher-efficiency torque converter.

x = coordinate along the mean flow path from the blade entrance s = length of the mean flow path between the entrance and exit

2.6.6

The pressure difference in the vicinity of the blade inlet is expressed by Eq. 2.6.7, which is derived from the shock loss equation.

Theoretical Considerations of Flow Pattern

It is desirable that the torus and blade profiles are designed so that the working fluid flows along the ideal stream surface in the converter circuit, as shown in Fig. 2.6.17. For a torque converter with these ideal stream surfaces, its characteristics can be estimated by the sum of characteristics of partial torque converters, which are divided by the ideal stream surfaces. To these partial torque converters, the previously described equations may be applied. The pressure distribution along the mean flow path of a partial torque converter is expressed by Eq. 2.6.6, which is derived from the energy equation in consideration of the friction loss [4].

⎧γ ⎫ Pi⋅1 − Pi −1⋅2 = ⎨ ⎬ (ri −1⋅2ω i −1 − cκ i −1⋅2 ) ⎩ 2g ⎭ (ri −1⋅2ω i −1 − cκ i −1⋅2 − 2ω iri −1⋅2 )

[

− (ri⋅1ω i − cκ i⋅1 )(ri⋅1ω i − cκ i⋅1 − 2ω iri⋅1 ) − ⎧ r ⎫ ϕi ⎨ri⋅1ω i − cκ i⋅1 − (ri −1⋅2ω i −1 − cκ i −1⋅2 ) i −1⋅2 ⎬ ri⋅1 ⎭ ⎩

2

]

(2.6.7)

The pressure distribution normal to the ideal stream surface is expressed by Eqs. 2.6.8 and 2.6.9, which are derived from Euler’s equations of motion by assuming the indefinite number of blades and inviscid fluid, ⎧ ⎫ cos δ) ⎪ ∂Pi⋅x ⎛ γ ⎞ ⎪⎛ Wm 2 ⎞ ( 2 = ⎜ ⎟ ⎨⎜ ⎟ + (Wθ + rω) r − rFθ ∂Θ ⎬ ∂n ⎝ g ⎠ ⎪⎝ R ⎠ ⎪ ∂n ⎩ ⎭

Fθ =



Wm {r (Wθ + rω)} r∂ ∂m

(2.6.8) (2.6.9)

where: n = coordinate normal to the stream surface R = radius of curvature of the stream surface in the meridional plane θ = angle between Wm and Wz Wm = meridian plane component of relative flow velocity Wz = z component of relative flow velocity Wθ = θ component of relative flow velocity Θ = θ coordinate of blade surface r, θ, z = cylindrical coordinates m = curvilinear coordinate along mean flow path of partial torque converter in meridian plane Fθ = θ component of body force

Fig. 2.6.17  Ideal flow pattern of torque converter. ⎡(ri2⋅xω12 − ri2⋅1ω i2 ) − c 2 (κ i2⋅x − κ i2⋅1) − ⎤ ⎥ ⎧ γ ⎫⎢ Pi⋅x − Pi⋅1 = ⎨ ⎬ ⎢ 2 2 ⎥ ⎛ 2 + κ i⋅x + κ i⋅1 ⎞ ⎩ 2g ⎭ ⎢λ i⋅xc 2 ⎜ ⎥ ⎟ ⎝ ⎠ 2 ⎥⎦ ⎣⎢ (2.6.6) where: P = pressure λi.x = λi (x/s)

To actualize a smooth flow, the torus and blade profiles are decided as the pressure gradient defined by Eqs. 2.6.6 and 2.6.7 in n-direction (Fig. 2.6.17) becomes the same as the

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2.7 A Loss Analysis Design Approach to Improving Torque Converter Performance

pressure gradient in Eq. 2.6.8. Because pressure distribution in Eqs. 2.6.6 and 2.6.7 is along the mean flow path, the pressure relationship between each partial torque converter must be determined by some method. In other words, the n-direction pressure distribution at a specified section must be determined at the beginning. It is proposed here that the boundary condition to Eqs. 2.6.6 and 2.6.7 is given by Eq. 2.6.8 at the very front of each blade entrance.

Masaaki Kubo and Eiji Ejiri Nissan Motor Co. Ltd. Based on SAE Paper 981100

2.7.1

The result of these calculations enables us to explain qualitatively the observed flow patterns, and provides valuable data for torque converter design.

2.6.7

This section describes the relationship between the design parameters used to define the geometry of an automotive torque converter and the resultant efficiency in relation to the internal flow characteristics. Taking the turbine bias angle and the contraction ratio of the pump flow passage as specific examples, the effects of each of the occurrences of loss was analyzed. A three-dimensional viscous flow analysis code was used in the numerical computation procedure, and a method developed independently by the authors was used in the loss analysis. The flow near the wall was visualized experimentally using a technique resembling the so-called oil film method. The visualized results showed good qualitative agreement with the numerical analysis results.

Conclusions

A liquid-resin film method applicable to the oil flow was developed. Applying this method to the fluid flow in a torque converter, the flow on the blade surface was easily observed. The existence of cross, swirl, reverse, and separated flow in a torque converter was made clear by the flow observations. The relationship between the efficiency and the fluid flow in a torque converter was clarified. Torque converter efficiency was improved by making the flow smoother.

2.7.2

Nomenclature

E: specific energy e: speed ratio I: rothalpy N: revolution speed P: static pressure PT: total pressure s: distance along the design path of the meridian plane T: torque t: torque ratio U: blade circumferential velocity V: absolute velocity W: relative velocity A: cross-section area of flow passage αB: turbine bias angle αC: contraction ratio [=1 – (Amin/A0)] η: efficiency ρ: density ω: angular velocity

A theoretical analysis for prediction of the flow pattern in a torque converter was proposed. This analysis provided valuable data for torque converter design.

2.6.8

Abstract

References

1. Uchiyama, K., “Observation of Fluid Flow in Torque Converter Using Oil Film Method,” Turbo Machine, 3–3:1975. 2. Ishihara, T., S. Furuya, and K. Mori, “Flow Condition in Fluid Couplings,” Reprints of the Japan Society of Mechanical Engineers, No. 781, Aug 8, 1968. 3. Ishihara, T. “A Study of Hydraulic Torque Converters,” Report of the Institute of Industrial Science, University of Tokyo, Vol. 5, No. 7, Serial No. 42, November 1955. 4. Ishihara, T., T. Ida, and T. Kasai, “On Characteristics of Hydraulic Torque Converter and Special Operating Conditions,” Transactions of the Japan Society of Mechanical Engineers, Vol. 22, No. 113, 1956.

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Subscripts 0: position of design path radius at pump exit, or standard used for comparison 1: pump 2: turbine 3: stator c: circulatory θ: circumferential (i,j): i=1: pump j=1: inlet 2: turbine 2: exit 3: stator x: arbitrary position

and efficiency, as well as the mechanism involved, based on the use of numerical computation codes to calculate the internal flow characteristics. An independently developed loss analysis technique was used in the flow analysis. Experiments were also conducted with actual torque converters to verify the validity of the numerical analysis results.

Analysis of the Torque Converter Performance and Internal Flow

2.7.4.1

Element Performance

As shown in Fig. 2.7.1, an automotive torque converter is typically constructed of three major elements—a pump, a turbine and a stator. Efficiency and rothalpy will be evaluated here as typical performance parameters of the three elements.

Superscript *: nondimensionalized

2.7.3

2.7.4

Introduction

Various attempts have been made over the years to investigate the internal flow characteristics of the automotive torque converter because its hydrodynamic performance has a significant effect on vehicle performance. One experimental approach taken in these flow investigations has been the use of five-hole Pitot probes installed between the three torque converter elements [1]. Another experimental approach has involved the use of a laser Doppler velocimeter (LDV) to measure the flow velocities of the stator and pump [2]. However, it is no easy task to measure the flow fields inside a torque converter because it is constructed as a hermetically sealed structure, and the closely positioned blades of its several parts rotate at different speeds. Meanwhile, as a result of the advances achieved in computers and computational schemes in recent years, computational fluid dynamics (CFD) approaches in which Navier-Stokes equations are solved by numerical computations have also come to be widely used. In addition to calculations made separately for each torque converter element on the basis of suitably given boundary conditions [3, 4], attempts have been made to analyze the flow of all three elements together [5–7]. Among the results reported to date, there are some that amply explain the tendencies as secondary flow and boundary layer separation. Valuable data on flow characteristics are also beginning to be obtained. Yet the literature still does not contain any reports of attempts to utilize numerical computation methods to analyze the relationship between the key design parameters of an actual torque converter and the resultant hydrodynamic performance in the context of the internal flow characteristics.

Fig. 2.7.1  Cross-sectional view and computational grid. Efficiency—Overall torque converter efficiency η is the ratio of the output power to the input power and can be expressed as

η=

T2ω 2 T2N 2 = = t ⋅e T1ω1 T1N1

(2.7.1)

Considering efficiency as a one-dimensional representative stream line of a fluid element, it can be expressed in terms of the inlet and exit pressures and velocities as indicated in the following equation:

η=

−U 2,2Vθ2,2 + U 2,1Vθ2,1 U1,2Vθ1,2 − U1,1Vθ1,1

(2.7.2)

Likewise, the individual efficiencies of the pump and turbine can also be expressed as one-dimensional representative stream lines given by Eqs. 2.7.3 and 2.7.4.

This study focuses on torque converter efficiency that has a large effect on vehicle fuel economy. An attempt was made to analyze the relationship between design parameter values 2-94

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η1 =

η2 =

(PT1,2 − PT1,1)

ρ(U1,2Vθ1,2 − U1,1Vθ1,1 )



ρ(−U 2,1Vθ2,1 + U 2,2Vθ2,2 ) (PT2,1 − PT2,2 )

nondimensional rothalpy (i.e., the value of the right term of Eqs. 2.7.8 and 2.7.9) along the flow direction from the inlet to the exit of each element.

(2.7.3)



It should be noted that the pressure and specific energy at the cross-section are flow rate integrated and averaged, and the resulting values are used to find the individual efficiency and rothalpy of each element based on the results of a threedimensional numerical analysis.

(2.7.4)

Stator efficiency η3 can be defined as η3 = 1 −

(PT3,1 − PT3,2 ) (PT1,2 − PT1,1)



(2.7.5) 2.7.4.2

and assuming that PT1,1 = PT2,2, PT2,2 = PT3,1 and PT3,2 = PT1,1, then the overall torque converter efficiency η of Eq. 2.7.2 can be given by Eq. 2.7.6.

The internal flow computations were performed with STARCD [8], a finite volume method. Turbulent flow was modeled with the standard k-ε model, and a wall function was used for the velocity distribution near the wall. The convection term was discretized with a first-order upwind differencing scheme. Fig. 2.7.2 shows the interface boundary conditions that were used in obtaining numerical solutions for the three torque converter elements in turn. The velocity or the pressure was given as the boundary condition at the interface between the inlet and the exit of the adjacent elements. The pressure was calculated via iteration when the velocity was given as the boundary condition and vice versa. The results obtained were averaged circumferentially and given as the boundary condition at the interface with the adjacent element in the next iteration. This procedure was repeated until the circulatory flow rate converged.

(2.7.6)

η = η1 ⋅ η2 ⋅ η3



Rothalpy—Rothalpy, I, is given by Eq. 2.7.7.

I=

P 1 2 1 2 + w − U ρ 2 2

(2.7.7)

This equation is used to calculate the value of nondimensional rothalpy at any arbitrarily chosen position x, and the loss occurring there is estimated. Let ∆I1,X and ∆I2,X represent the amount of change in rothalpy at any arbitrarily chosen cross-section X of the pump and turbine, respectively, using the inlet of each element as the reference plane of each section. Nondimensionalizing ∆I1,X and ∆I2,X by the change in the theoretical specific energy of each element from its inlet to its exit, ∆E1 and ∆E2, we obtain Eqs. 2.7.8 and 2.7.9.

(ΔI1,x )* =

ΔI1,x ΔE 1

(2.7.8)

(ΔI2,x )* =

ΔI2,x ΔE 2

(2.7.9)

Using the amount of change in rothalpy at the respective exit (i.e., x = 2), (∆I1,2)* and (∆I2,2)*, the individual efficiency of the pump and turbine, η1 and η2 can be expressed as Eqs. 2.7.10 and 2.7.11.

η1 = 1 − (ΔI1,2 )

*

η2 =



1

1 + (ΔI2,2 )

Fig. 2.7.2  Interface boundary conditions. A program developed by the authors was used to generate the computational grid. By simply entering the design parameters and designing a blade geometry, this program will quickly generate a computational grid. The grid used in this study had approximately 170,000 computational cells, which were divided into three directions—the circumference, span and main flow. The cell division for the pump and turbine was 26 ¥ 30 ¥ 80 and that for the stator was 28 ¥ 30 ¥ 50. An

(2.7.10)



*



Numerical Analysis Method

(2.7.11)

The magnitude and location of the loss occurring in the flow passage can be analyzed by investigating the distribution of

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example of the computational grid is shown in Fig 2.7.1. The computations were performed on an Indigo2—Impact engineering workstation (made by SGI) and the CPU time for executing one case was approximately 12 hours. Note: recent advances in computing power should significantly reduce this time. 2.7.4.3

Experimental Method

Measurement of Overall Performance—Overall torque converter efficiency can be found with Eq. 2.7.1 by measuring the input and output torque and speed ratio. Measurements were made under a constant input torque of 98 N-m. The fluid pressure at the inlet and exit was 0.392 MPa and 0.196 MPa, respectfully, and the fluid temperature was 80°C. Fig. 2.7.3  Test turbine blades.

Flow Visualization—Because the three torque converter elements are housed in a tightly sealed structure, it is not easy to observe the flow passage directly. Different methods have been devised over the years to visualize the flow near the flow passage wall. In this study, a technique resembling the socalled oil film method was used. With this method, a material made principally of a thermoplastic epoxy resin is heated to a liquid state and coated on the walls. The torque converter is then operated for a certain length of time during which a stream line pattern forms on the coating. The coating is then hardened by returning it to room temperature, and a thin film of silicon rubber is spread over the surface. After the rubber has hardened, it is peeled off and the stream line pattern is transferred to it. As the last step, the surface of the rubber is painted to bring out the pattern clearly. The portions of the blade surface where the flow velocity is fast leave a stream line pattern. In areas where the flow velocity is slow or the flow stagnates, the epoxy resins collects without flowing.

2.7.5

Relationship between Turbine Bias Angle and Efficiency

2.7.5.1

Test Blade Geometries

2.7.5.3

Calculated Results and Discussions

Figure 2.7.4 shows the calculated distribution of the nondimensional rothalpy from the turbine inlet to the exit for the three turbines A-C. The value of the nondimensional rothalpy near the exit indicates the efficiency of the turbine as a single element. Turbine B displayed the highest efficiency, followed in order by turbines A and C. Although turbine B showed larger loss at the blade inlet than turbine A, it suffered less loss in the first half of the flow passage, resulting in a lower loss level overall. Compared with turbine B, turbine C showed larger loss not only at the blade inlet but also in the latter half of the flow passage.

Three turbine blade geometries were prepared by varying only one design parameter, the bias angle. The effect of the different bias angles on internal flow and hydrodynamic performance was examined. Figure 2.7.3 shows the turbine blade geometries that were used. The same pump and stator specifications were used with each test turbine in the calculations and experiments. 2.7.5.2

Fig. 2.7.4  Nondimensional rothalpy.

Calculation Condition

Figure 2.7.5 shows the static pressure distribution, averaged circumferentially from the shell to the core, for the three turbines A-C at the inlet, middle, and exit sections. The static pressure was nondimensionalized by the circumferential

A speed ratio of 0.8 was selected for use in the calculations, which was considered to be representative of the practical efficiency of a torque converter (N1= 2000 rpm; N2 = 1600 rpm). 2-96

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velocity on the design path at the pump exit after subtracting the average static pressure of the pump inlet, P11. Figure 2.7.6 a-c show the circulatory velocity distribution, averaged circumferentially from the core to the shell, at the inlet, middle, and exit sections of the turbine for the three test turbines A-C.

velocities. Accordingly, the flow velocity on the core side of turbine A should be slower than that of turbine C, whereas the opposite should be true on the shell side. On the other hand, provided that the stator conditions downstream of the turbine exit were the same for all three test turbines, turbine A, with higher pressure on the core side, should show a higher flow velocity on that side than turbine C while the flow velocity on the core side should be slower. These tendencies were quantitatively confirmed by the calculated results, which are given in Figs. 2.7.7 and 2.7.8 for the turbine inlet and exit, respectively. At the inlet, the circulatory velocity distribution of turbine A was skewed toward the shell and reverse flow occurred on the core side, compared with the results for turbine B. However, the flow increased in velocity along the core in the downstream direction. It is thought that the reverse flow was suppressed relatively easily in high-velocity areas and that pressure loss was less likely to occur upstream despite the thick boundary layer; rather, loss due to wall friction was dominant on the shell side.

Fig. 2.7.5  Static pressure distribution. In reference to Fig. 2.7.3, we will consider the effect of the change in the blade geometry according to the magnitude of the turbine blade angle. The turbine A blade had a progressively larger bias angle from the shell toward the core in the direction of rotation, whereas the turbine C blade had an increasingly larger bias angle in the opposite direction. Consequently, considering the radial pressure equilibrium, the pressure near the core of turbine A should clearly be higher than that of turbine C. Conversely, the pressure near the shell should be higher for turbine C than for turbine A. Also, turbine B should show pressure value in-between that of turbines A and C. These tendencies are confirmed in the inlet, middle, and exit sections in Fig 2.7.6.

At the exit, turbine C shows a slower flow velocity on the core side than turbine B, and reverse flow occurred. This reverse flow, however, occurred as a result of a decline in flow velocity; the boundary layer became thicker, and loss due to the decreasing velocity was exceptionally large. In summary, these results indicate that turbine B showed the smallest loss. 2.7.5.4

Comparison with Experimental Data

Comparison of Overall Performance—The overall efficiency η of three torque converters incorporating turbines A, B, and C, respectively, was found experimentally and by calculation at a speed ratio of 0.8. The experimental and calculated results were then nondimensionalized and compared by using the overall efficiency η of the torque converter incorporating turbine A as the standard. The results are plotted in Fig 2.7.9. The calculated and experimental results show the same qualitative tendencies, indicating that the macro characteristics of the flow inside the torque converter were accurately obtained by numerical analysis. Visualized Flow near Blade Surface—Figures 2.7.10 and 2.7.11 show the calculated velocity vectors and visualized flow near the core surface of turbines A and B. In the visualized flow results, a low energy region is observed near the inlet of turbine A. The calculated results indicate that reverse flow was calculated in the same region.

Fig. 2.7.6  Circumferentially averaged circulatory velocity distribution. The circulatory velocity distribution is not determined by a single section, but rather is influenced by the pressure gradient with the upstream or the downstream flow. Assuming that the discharge conditions from the pump exit were virtually the same for all three test turbines, places of low pressure on the blade span at the turbine inlet would tend to have higher

Figures 2.7.12 and 2.7.13 present the calculated velocity vectors and visualized flow near the suction and shell surfaces of turbines B and C. A low energy region is observed in the

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Fig. 2.7.7  Circulatory velocity distribution at turbine inlet.

Fig. 2.7.8  Circulatory velocity distribution at turbine exit.

(a) Turbine A

Fig. 2.7.9  Overall efficiencies. (b) Turbine B

Fig. 2.7.10  Calculated velocity vectors near core structure. 2-98

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(a) Turbine A

(b) Turbine B

Fig. 2.7.11  Visualized flow near core structure.

(a) Turbine B

Effect of Pump Flow Passage Contraction Ratio on Efficiency

2.7.6.1

Test Blade Geometries

The geometries of the test pump blades used in the experiments and calculations are shown in Fig. 2.7.14. The flow passage is the portion sandwiched between two blades. In relation to pump A, the flow passage of pumps B and C was progressively narrowed from the core side so that the crosssectional area at the middle of the passage became smaller in the flow direction relative to that at the inlet or exit. The flow passage geometry and cross-sectional area at the inlet and exit were not changed. The contraction ratio αC, defined as the ratio of the smallest area at the middle of the flow passage to the area at the inlet (Amin/A0), was the parameter that was varied to create pumps A–C. Similar to the condition in the previous section, the turbine and stator used with all three pumps were identical elements.

(b) Turbine C

Fig. 2.7.12  Calculated velocity vectors near suction and shell surfaces.

(a) Turbine B

2.7.6

(b) Turbine C

Fig. 2.7.13  Visualized flow near suction and shell surfaces. visualized results near the core surface at the exit of turbine C. It is seen in the calculated results that reverse flow was calculated in the same region. As indicated here, the reverse flow calculated at the inlet of turbine A and the exit of turbine C was clearly visualized experimentally, thereby confirming the validity of the calculated results.

Fig. 2.7.14  Test Pump Blades. 2-99

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2.7.6.2

Calculation Condition

As in the previous section, a speed ratio of 0.8, closely related to efficiency, was selected for use in the calculations (N1 = 2000 rpm; N2 = 1600 rpm). 2.7.6.3

Calculated Results and Discussion

The nondimensional rothalpy distribution calculated for pumps A–C from the pump inlet to the exit is shown in Fig. 2.7.15. Since the nondimensional rothalpy at the pump exit corresponds to the efficiency of the element, it is observed that pump B had the highest efficiency, followed in order by pumps A and C. The loss distribution from the inlet to the exit shows that pump A suffered large loss in the first half of the flow passage to the middle section, whereas pump C suffered large loss in the latter half of the passage from the middle section on.

Fig. 2.7.15  Nondimensional rothalpy distribution.

Figure 2.1.16 shows the circulatory velocity distribution from the pressure side to the suction side. The circulatory velocities were averaged from the core side to the shell side and nondimensionalized by the circumferential velocity. Values were presented for three sections of the flow passage, the first half (s* = 0.25), the middle (s* = 0.50) and the latter half (s* = 0.84). Pump A shows a declining velocity in the first half on the suction side, and reverse flow occurred in the middle. It is thought that the large loss observed for pump A was caused by this decreasing velocity and reverse flow. In contrast, pump C shows a higher average flow velocity in the middle because the cross-sectional area of its flow passage was smaller. It is presumed that large friction loss occurred there. Subsequently, the velocity declined sharply toward the suction side, and reverse flow eventually occurred. Accordingly, it is thought that pump C suffered extremely large friction loss in the middle of the passage and very large loss in the latter half as a result of separation. Figures 2.7.17 to 2.7.19 show the circulatory velocity distribution at three typical sections, represented by the first half (s* = 0.25), the middle (s* = 0.50), and the latter half (s* = 0.84) of the flow passage. In the results for the first half in Fig. 2.7.17, the reverse flow region seen for pump A becomes smaller in size with increasing contraction ratio of pumps B and C. The results in Fig. 2.7.18 for the middle section show that the reverse flow region seen for pump A on the suction side has already disappeared for pump B. These results for the first half through the middle section indicate that the flow of pump B was improved over that of pump A. In the results for the latter half in Fig 2.7.19 there are localized regions near the wall on the pressure side of the core where pumps B and C show higher flow velocities than pump A. It is presumed that large friction loss occurred in those areas. Moreover, the slope of the velocity contours from the pressure side to the suction side increases with the increasing contraction ratio of pumps B and C compared with that for pump A, and reverse flow occurred on the suction side of pump B. The size of the

Fig. 2.7.16  Circulatory velocity distribution. 2-100

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Fig. 2.7.17  Circulatory velocity distribution (s* = 0.25).

Fig. 2.7.18  Circulatory velocity distribution (s* = 0.50).

Fig. 2.7.19  Circulatory velocity distribution (s* = 0.84).

reverse flow area increased further in the case of pump C. This result suggests that pump C suffered large loss due to reverse flow. Based on the foregoing results, it is clear that pump B showed the smallest loss of the three test pumps. 2.7.6.4

Comparison with Experimental Data

Comparison of Overall Performance—The overall efficiency η of the three types of torque converters incorporating pumps

A, B, and C, respectively, and that of a unit with flow passage contraction ratio of αC = 20%, was found experimentally and by calculation at a speed ratio of 0.8. (The latter type was not discussed in detail in the analysis.) The experimental and calculated results were nondimensionalized and compared in relation to the overall efficiency η of the torque converter incorporating pump A. The results are plotted in Fig. 2.7.20. Similar to the results seen for the turbine bias angle, both sets of results show the same quantitative tendencies. This indicates that the macro characteristics of the flow inside the torque converter were accurately obtained by numerical analysis.

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Fig. 2.7.21, the reverse flow region seen in the first half of the passage of pump A decreases in size from the inlet side to the suction side with the increasing contraction ratio of pumps B and C. Additionally, the reverse flow region on the suction side near the exit becomes increasingly larger for pumps B and C. Although it is not clearly indicated in the visualized flow results in Fig. 2.7.22, the low energy region corresponding to the reverse flow region of pump A appears to become increasingly smaller for pumps B and C.

Fig. 2.7.20  Overall efficiencies. Visualized Flow near the Wall—Figures 2.7.21 and 2.7.22 show the calculated velocity vectors and visualized flow near the core surface of pumps A – C. In the calculated results in

Additionally, the low energy region near the exit appears to become larger in size with the increasing contraction ratios of pumps B and C, albeit it does not correspond entirely to the reverse flow region in the calculated result. As indicated here, the tendencies of the calculated and visualized results show good qualitative agreement, confirming that the calculated results obtained with the contraction ratio of the pump flow passage as the design parameter were also valid in general.

Fig. 2.7.21  Calculated vectors near core surface.

Fig. 2.7.22  Visualized flow near core surface. 2-102

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2.7.7 Conclusion The three-dimensional viscous flow analyses were conducted for the turbine bias angle and the contraction ratio of the pump flow passage, which are two design parameters of an automotive torque converter. The results made clear the following points. 1. Both the turbine bias angle and the contraction ratio of the pump flow passage have optimum values that maximize overall torque converter efficiency. The mechanism at work here can be understood as follows. 2. Depending on turbine bias angle, the pressure distribution from the shell to the core varies, causing the flow rate distribution to vary. An excessively small bias angle results in larger wall friction in the first half of the flow passage, while an excessively large bias angle results in larger loss due to the decreasing flow velocity near the core in the latter half. 3. When the contraction ratio of the pump flow passage is too large, the flow velocity decreases on the suction side of the core from the inlet to the middle section, giving rise to reverse flow. Conversely, when the contraction ratio is excessively large, the flow velocity in the middle increases, resulting in larger friction loss. Additionally, it also leads to a sharp decline in the flow velocity on the suction side in the latter half, resulting in reverse flow that gives rise to greater loss. The following points were made clear by the experimental results obtained with actual torque converters. 4. The experimental data also showed that optimum values exist for maximizing overall torque converter efficiency. The tendencies of the experimental data correlated relatively well with the calculated results. 5. The qualitative tendencies of the visualized flow showed relatively good agreement with the numerical analysis results. The results obtained in this study confirmed that the proposed loss analysis design approach is effective in analyzing the hydrodynamic performance of an automotive torque converter. It is believed that the application of this method will make it possible to improve the hydrodynamic performance of torque converters dramatically through the use of theoretical approaches in line with the mechanism presented here.

2.7.8 Acknowledgments The authors are grateful to Dr. Yasutoshi Senoo, Professor Emeritus of Kyushu University, who has continuously offered instructive advice to us during this study. The authors would

like to thank Nissan Motor Co., Ltd. for permission to publish this paper, as well as Yoshihiko Ishii for his help in conducting the experiments and Ikuo Aoki for his assistance in performing the computations.

2.7.9 References 1. Ejiri, E. and M. Kubo, “Performance Analysis of Torque Converter Elements,” Proceedings of ASME FEDSM’97, FEDSM97-3219 (CD-ROM). 2. Brun, K. and R. D. Flack, “The Flow Field Inside an Automotive Torque Converter: Laser Velocimeter Measurement,” SAE Paper No. 960721, 1996. 3. Kubo, M., E. Ejiri, H. Kumada, and Y. Ishii, “Improvement of Prediction Accuracy for Torque Converter Performance: One-dimensional Flow Theory Reflecting the Stator Blade Geometry,” JSAE Review, 15(1994), pp. 309–314. 4. By, R. R., R. Kunz, and B. Lakshminarayana, “NavierStokes Analysis of the Pump Flow of an Automotive Torque Converter,” Trans. Of ASME, J. Fluids Eng., Vol. 117 (1995), pp. 115–122. 5. Fujitani, K., R. Himeno, and M. Takagi, “Computational Study on Flow through a Torque Converter,” SAE Paper No. 881746, 1988. 6. Abe, K. and T. Kondoh, “Three-dimensional Simulation of the Flow in a Torque Converter,” SAE Paper No. 910800, 1991. 7. Cigarini, M. and S. Jonnavithula, “Fluid Flow in an Automotive Torque Converter: Comparison of Numerical Results with Measurements,” SAE Paper No. 950673, 1995. 8. Computational Dynamics Ltd., STAR-CD Version 2.3 Manual, 1995.

2.8 The Chrysler Torque Converter Lock-Up Clutch A. P. Bloomquist and S. A. Mikel Chrysler Corporation Based on SAE Paper Number 780100 Attachments by Thomas G. Brand BorgWarner Inc. Federal fuel economy (CAFÉ) rules have stimulated manufacturers to reach out and investigate all potential means of fuel savings. Since torque converter slip in the coupling range has long been recognized as a source of power loss, a lock-up torque converter was investigated. It was determined that

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significant gains in both urban and highway fuel economy could be achieved with a torque converter lock-up clutch. As improved automobile fuel economy has become essential, there has been an increasing need for lower final drive ratios. As these ratios were lowered, the higher loading imposed on the torque converter caused more slip in the coupling range and, to a significant extent, offset the advantage of lower ratios. The lock-up clutch achieves most of the potential fuel economy benefit of reducing overall driveline ratios. The lower ratio is permissible because the lock-up system still provides the torque converter for breakaway and low-speed acceleration, and automatic “kick-down” shifts when the driver calls for increased acceleration. The lock-up torque converter also achieves lower highway engine speeds due to the elimination of slip. This lower engine speed should improve accessory life and reduces noise levels. Elimination of heat-producing torque converter slip also improves transmission cooling during lock-up operation and thereby enhances transmission oil life.

2.

3. 4. 5.

transfer lines. In addition, components in the immediate area of the transmission would not be disrupted. The lock-up clutch would be engaged only in top gear, so as to provide normal lower gear performance with full torque converter ratio available. Lock-up shifts were to be nearly imperceptible. Present upshift and kickdown shift quality was to be preserved or improved. Top gear lock-up was to be provided at the lowest car speed possible, consistent with good driveability, to maximize the fuel economy gain.

The power flow during lock-up is shown in Fig. 2.8.2, and the cutaway of the system is shown in Fig. 2.8.3.

The lock-up torque converter and transmission assembly weighs only 2.5 lb more than previous models without lockup. (See Fig 2.8.1 for added parts.) It fits within the previous transmission envelope and shifts smoothly into and out of the lock-up mode automatically. A torsional isolator was also incorporated in the lock-up clutch to prevent torsional vibration from passing through the driveline. Some applications have not used the isolator due to the availability of partial lock-up clutch engagement controls which utilize clutch slip to avoid passing torsional vibrations into the body. Fig. 2.8.1  Cutaway of a typical RWD (rear wheel drive) lock-up converter and individual components.

A torque converter lock-up clutch was introduced in a majority of its passenger cars in the 1978 model year. The lock-up clutch improves fuel economy by eliminating torque converter slip in direct gear or overdrive on three-speed and four-speed automatic transmissions, respectively. Lock-up is also available in second and direct gears under some conditions with the Ultradrive 4EATX. The clutch and its controls were designed to fit within the confines of the existing transmission. The development of the clutch was primarily concerned with achieving adequate endurance life, good shift quality, and isolation of torsional vibrations.

2.8.1

Description of the Chrysler Lock-Up Clutch (see Fig. 2.8.1)

Several design criteria were established in the early phases of this program: 1. The general outline of the existing transmission cases would not change. This preserves expensive case dies and

Fig. 2.8.2  Cross section of a typical RWD lock-up torque converter and transmission showing power flow during lock-up.

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In order to provide a lock-up clutch in the available space, it was decided to locate the clutch inside the torque converter between the front cover and the turbine assembly. By using the largest available diameter inside the torque converter, it was possible to install a single surface clutch with a friction wafer between the piston and the torque converter front cover. In this lock-up torque converter, a movable piston is positioned between the front cover and the turbine (Figs. 2.8.2 to 2.8.5). The inner diameter of the piston pilots on the turbine hub and is sealed at this point with a fluoroelastomer “O” ring. The outer face of the piston bears against the friction material that acts to form an oil-tight seal. No piston return springs or energizing spring is used or needed since fluid pressure from the control system keeps the piston “off ” in the unlocked condition, and fluid forces within the torque converter initiate application of the piston when the “off ” side of the piston is vented for lock-up engagement. The piston is connected torsionally to the torque converter turbine

Fig. 2.8.5  A RWD torque converter lock-up clutch piston and turbine assembly showing the vibration isolator springs, spring retainer, and turbine drive ring.

through ten isolator springs, which are intended to prevent torsional vibration from being passed from the engine to the driveline. The springs are restrained in a curved, stamped channel which has tabs formed to provide spring seats. The channel is welded to the piston and is selectively induction hardened for wear resistance. A drive ring having ten fingers is electron-beam welded to the turbine shell. Each finger can contact one of two springs depending on whether the vehicle is coasting or driving. An additional fluoroelastomer lip seal was required between the turbine hub and the front of the input shaft to prevent “apply” pressure from leaking to vent through the input shaft and turbine hub splines and to insure that a nominal “off ” pressure is developed to release the clutch. The original hydraulic controls for the lock-up clutch were located in the transmission valve body assembly. Three new valves and a blow-off relief cap were added (Figs. 2.8.6 to 2.8.10).

Fig. 2.8.3  Cutaway of a typical RWD torque converter lock-up clutch and torsional vibration isolator.

2.8.1.1

Lock-Up Valve

The lock-up valve supplied main system line pressure to the fail-safe valve at the predetermined governor pressure or car speed. The purpose of the valve was to establish the lowest car speed at which lock-up could be engaged and disengaged in direct gear. 2.8.1.2

Fig. 2.8.4  RWD torque converter lock-up clutch piston with inner “O” ring seal and shim.

Fail-Safe Valve

The fail-safe valve got its name from the fact that it maintained main system pressure at a level above 2–3 shift control or balance pressure at the expense of reducing “apply” pressure to the lock-up clutch. This ensured that the car could

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Fig. 2.8.6  Original hydraulic circuit schematic for a torque-flight transmission with lock-up.

Fig. 2.8.8  Original lock-up valve body and components.

Fig. 2.8.7  Original hydraulic circuit schematic of lock-up clutch controls. 2-106

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be driven, even if a system leak developed which caused the lock-up clutch to slip. The valve is influenced by throttle pressure and direct gear clutch apply pressure. It was designed to allow line pressure to pass to the switch valve after direct gear clutch “apply” pressure rose above the 2–3 shift balance pressure established by the kickdown band servo. The valve also insured fast release of venting of the lock-up clutch during a kickdown, since it returns to its venting position at a pressure level at which the direct gear clutch cannot slip, and therefore prior to the initiation of the kickdown speed change. Both the lock-up valve and fail-safe valve were located in a separate body attached to the main body assembly.

2.8.1.3

Switch Valve

The switch valve determines the direction of oil flow to the torque converter. In non lock-up conditions it directs lube oil from the regulator valve to the “off ” side of the lock-up clutch piston via a hole in the center of the input shaft. The oil then passes through the torque converter and out between the reaction shaft and the input shaft. From this point, the oil passes through the switch valve again before going to the oil cooler. In the lock-up mode, main system line pressure is fed from the lock-up valve body through a tube to the end of the switch valve and then to the “apply” side of the piston via the space between the reaction shaft and the input shaft. The “off ” side of the piston is vented through the input shaft hole to the switch valve and then to a vent. Oil from the regulator valve is also directed through this valve in the lock-up mode and fed directly to the cooler without passing through the torque converter. 2.8.1.4

Torque Converter Pressure Relief Valve

A spring loaded blow-off cap or pressure relief valve was incorporated into the valve body transfer plate in order to limit torque converter charging pressure to a maximum of 150 psi in reverse gear. 2.8.1.5 Fig. 2.8.9  The original lock-up torque flight valve body and transfer plate assembly showing lock-up valve body and new switch valve.

The original control system, while being independent of other vehicle systems had considerable lock-up shift speed tolerance and the lock-up shift could only be modified by changing the valve spring load or the valve diameters. Later control systems now use a solenoid to cause the lock-up shift by forcing a valve motion which switches the torque converter feed circuits. And, in the fully electronic transmissions, the lockup pressure is modulated by a duty-cycle-controlled solenoid to control engagement quality and to dampen torsional vibrations at lower engine speeds by allowing some lock-up clutch slippage. This slippage is controlled by comparing engine speed to input shaft speed and adjusting the solenoid duty cycle to limit slip. These solenoids are controlled by the engine (ECU) or in the fully electronic transmission by the transmission control unit.

2.8.2 Fig. 2.8.10  Torque flight valve body and transfer plate assembly showing new torque converter pressure relief valve.

Revised Control System

Development Considerations

Several factors were given consideration during the design and development phases of the lock-up clutch. A brief discussion of some of these factors follows.

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2.8.2.1

Torsional Vibrations

Vibrations generated by the firing impulses of the engine must either be absorbed or isolated in order to provide a smooth and quiet car at low to medium speeds. The torque converter has done an excellent job in this respect for many years. Manual transmission clutch spring damper systems have not done as well. The lock-up clutch is closely related in function to the manual clutch and, as expected, responded similarly. The need for a torsional isolator became apparent early in the development program. In units tested without isolation, a pronounced in-car vibration was noted which peaked at low car speeds. The incorporation of the spring isolator reduced the amplitude of the vibrations at these speeds and provided an improvement in noise and feel within the car. Actually, the isolator produced three new resonant frequencies: one below the operating speed range and two in a range where there are no driveline/body resonances. Therefore, these three peaks add no sound disturbances at their associated car speeds. However, even though the isolator provided a valley in the critical vibration range, a large percentage of cars experienced objectionable noise levels. The problem was most severe in the rear seat of the two-door cars. It was determined that the primary path transmitting the vibrations to the body was the rear spring front mount. Rather than attempt to redesign the car and its suspension system, work was concentrated on the torsional isolator. Spring travel was increased in order to provide low torsional rates. These rates range from 9 to 30 lb.-ft. per degree depending on the engine application. Low isolator hysteresis was achieved by reducing friction points which could short circuit the isolator. In order to further reduce torsional vibrations, it was necessary to raise the minimum speed at which lock-up could be engaged from 850 RPM to 1140 RPM on certain models before the original introduction. Currently, full lockup is at 1300 to 1500 engine RPM and partial lock-up starts at 1100 RPM on models with the feature. 2.8.2.2

Shift Quality

Lock-up clutch shift quality was not a serious development problem with the controls as they were conceived. The failsafe valve provided the required timing sequence and the built-in accumulator action of the system provided smooth lock-up engagements. Extensive recalibration for shift quality was performed for the 1978 models in order to more closely match the transmission to engine output changes and the added inertia of the lock-up clutch. This included revisions to shuttle valve pressure modulation during kickdowns.

2.8.3

Durability

2.8.3.1

Clutch Facing

The clutch facing is a conventional paper-based material, which also acts as an oil seal and therefore must not fail in the interior of the welded torque converter. In order to ensure satisfactory bonding of the friction material, it was necessary to control surface finish of the front cover between 130 and 300 micro inches (RMS). Currently, all lock-up friction material used by Chrysler is of the “floating wafer” non-bonded type. Flatness of both the cover and piston mating faces was held to 0.006 inch radially and 0.010 inch circumferentially to ensure adequate sealing and clutch life. Clutch facing life is enhanced by the fact that it is submerged in oil. Test bogeys were established which assure adequate life. 2.8.3.2

Isolator Parts

Space limitations required that the springs be curved in their retaining channels. Spring seat angles were selected to induce this curvature and to minimize spring rubbing within the channel. It was necessary to harden the outer and inner surfaces of the channel in areas where spring contact is made. 2.8.3.3

Thrust Bearing

With the lock-up clutch in a pre-loaded torque converter, the thrust washer located between the input and output shaft receives more load in low and second gears due to the reversed direction of oil flow through the torque converter. Crankshaft thrust measurements made during wide-openthrottle shift cycles on a dynamometer showed an increase of approximately 3% in peak low gear thrust. For this reason, it was necessary to provide an improved thrust surface for the steel-backed bronze washer by the addition of a hardened steel race. In floating torque converters as in front-wheel drive, this thrust is taken inside the torque converter at the impeller thrust washer. It was also discovered that both the engine crankshaft and the transmission input shaft can be subjected to high thrust loading during and immediately after lock-up or unlock shifts. This is caused by hydraulic loading of the turbine hub in conjunction with spline friction between the turbine hub and the mating input shaft. During lock-up shifts, the lock-up apply pressure pushes the turbine hub toward the engine, which in turn pulls on both the input shaft and the engine crankshaft with approximately 1200 lb load until the spline friction is reduced, letting the turbine hub slide against the front cover thrust washer. A similar loading happens when, after the turbine hub has moved against the front cover thrust washer, an unlock shift then causes the turbine assembly to thrust rearward toward the stator which in turn pushes on the input 2-108

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shaft and crankshaft until spline slippage allows the turbine thrust to be taken by the stator and impeller thrust washers. In some applications, thrust washer/bearing improvements were required because of this increased loading. 2.8.3.4  Cooling Cooling under lock-up conditions is appreciably improved since torque converter slip, the major source of heat generation, is eliminated. The oil flow through the torque converter under non-lock-up conditions is between the front cover end and the lock-up piston. It enters the torus at its major diameter in a direction opposite to normal torus flow. A loss of oil flow was observed under non-lock-up conditions. Slight losses in torque converter performance characteristics were also incurred (Fig. 2.8.11). Reduced valve body restriction and lower pump side clearances contributed to improved cooling; however, larger coolers were required in some models. The net effect of these factors is a cooler operating transmission.

2.8.3.6  Permanent Magnet A magnet was placed in the transmission oil pan in order to collect ferrous particles and thereby reduce the possibility of valve sticking. 2.8.3.7  Improved Pump Efficiency The lock-up clutch transmission pump efficiency was increased by reducing pump side clearance and improving reaction shaft support pump face flatness. This was done by select-fitting pump rotors and lapping the reaction shaft support pump face in order to reduce leakage into the torque converter torus section. This area communicates directly with the apply side of the lock-up clutch piston. In addition to reducing leakage to the apply side of the lock-up piston, these improvements produced additional pump output which provided increased lock-up clutch piston release pressure. The net effect prevented the possibility of lock-up clutch drag in reverse when hot. 2.8.3.8  Performance A typical shift pattern showing the available operating range of the lock-up clutch for a vehicle with a 360 CID engine locking-up at 850 RPM is shown in Fig. 2.8.12. The gains in urban, highway, and composite fuel economy for this shift pattern are approximately 4%, 6%, and 4.7%, respectively. The urban economy gain drops to approximately 2% in units that have the 1140 RPM lock-up speed. The lock-up clutch was made available as standard in most models equipped with 225, 318, 360 engines and some 400 CID engines when first introduced in 1978 MY. Lock-up is now available on almost all automatics transmissions and transaxles.

Fig. 2.8.11  Torque converter performance losses with lock-up. 2.8.3.5  Reverse Line Pressure Modulation Modulation of reverse line pressure as a function of throttle pressure was introduced to provide more oil flow from the regulator valve to the “off ” side of the lock-up clutch piston during light throttle reverse operation on all except electronic transaxles. In addition, a positive lock-up piston off side flow orifice was added to prevent lock-up piston drag in reverse.

Fig. 2.8.12  Typical shift pattern for 360 CID RWD lock-up transmission.

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The economy gains are varied depending upon the schedule used. The lock-up schedule is modified for each engine and vehicle combination to provide optimum economy gains without sacrificing driveability. As was mentioned earlier, part throttle unlock and coast unlock features have been added since the original introduction for enhanced driveability.

2.8.4

Conclusion

Although the lock-up clutch is a relatively simple feature employing components common to many transmissions, the design of the lock-up clutch presented a major challenge due to the space and weight limitations dictated for the design. These objectives were met in the projected time frame with acceptable performance, adequate endurance life, and most of the predicted fuel economy gains.

2.8.5

Appendix

In the ensuing years since the introduction of the torque converter lock-up clutch, as described above, there has been continued pressure to increase the fuel economy of the automatic transmission. One method is to increase the range in which the torque converter lock-up is functional without contributing to an increase in transmissible noise. Modelbased slip control systems have been developed by various manufacturers [1, 2] to extend the range in which the torque converter lock-up clutch controls the amount of slip between the pump (engine) and turbine (transmission input), thus increasing overall automatic transmission efficiency. From Ref. 2, a typical hydraulic circuit, electronic control circuit, block diagram of clutch control system, and implementation region of slip control would be represented by the following (Figs. 2.8.13 to 2.8.16).

Fig. 2.8.13  Hydraulic control circuit.

Fig. 2.8.14  Electronic control circuit. 2-110

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Fig. 2.8.15  Block diagram of clutch control system. Friction material design considerations include surface structure – absorption, compressibility of friction materials, damping effects, fiber effects, effects of temperature, surface structure stability of friction, and interface temperature. The following information is from Ref. 3. 2.8.5.1  Surface Structure – Absorption Fig. 2.8.16  Implementation region of slip control. It is the advancement of the electronic control systems in the vehicle that allow these types of controls to be implemented. With all the advancements in the electronic control of the newer transmissions, a robust lock-up clutch must provide full service life without the onset of transmissible torque fluctuations (shudder). It is generally acknowledged that this phenomenon is a result of slip/stick between the friction material and the mating surface [3, 4, 5, 6, 7, 8, 9]. In addition, a negative friction μ–v curve will aggravate this condition. In investigating this condition numerous studies have looked at the friction material [3], friction material and ATF and ATF additives [5, 6, 7, 8], friction material, fluid and converter geometry [4], and friction material and interface temperatures [9]. In every case the conclusion is almost the same, the μ–v slope must remain positive to have a satisfactory result.

Sheering of the oil film between the friction materials and metal mating surface occurs at low slipping velocities. The low-speed (0 –0.3 m/s) slipping condition of the friction modifiers of the ATF and friction material was discussed in “Squeezing Contact Phase” theory [10]. It is very important that the anti-shudder friction modifiers in the ATF can easily be absorbed into the friction material surface. This will result in anti-shudder performance. Thus it is necessary to design friction materials with highabsorption-capacity surfaces. In order to verify the absorption effect, friction materials with different surface absorption capabilities shown in Fig. 2.8.17 were tested in the same ATF at low-speed slipping conditions, according to Procedure 101 (Table 2.8.1).

The friction material is at the center of most investigations and with the mating surface geometry, the apply geometry of the lock-up clutch, the control strategy, fluid properties, and vehicle properties all determine how well the system will perform. The following discussions will focus on each of the above elements.

Fig. 2.8.17  Absorption capability of different materials. 2-111

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Table 2.8.1  Procedure 101: Continuous-Slip Test. LEVEL Oil Tempera­ture, °C Lining Pressure, MPa Sliding Speed, (m/s) 0.006 0.030 0.060 0.150 0.300 0.600 0.900 1.200 1.800 2.400 3.000 2.400 1.800 1.200 0.900 0.600 0.300 0.150 0.060 0.030 0.006

A

B

C

D

I

G

F

40 0.980

100 0.980

100 0.980

40 0.490

100 1.470

100 0.490

40 1.470

B R E A K I N

Note: Slipping time at each speed = 5 sec.

For illustration purposes only, representative results are depicted in Figs. 2.8.18 to 2.8.21. Figure 2.8.18 shows that friction material MA with the highest surface absorption capability had the highest positive slope (largest positive dμ/dv) from 0 to 3 m/s. On the other hand, material NC with the lowest surface absorption showed a negative slope from 0 – 3 m/s in most of the test conditions. Thus, it can be

concluded that the higher the surface absorption capacity of the friction materials, the better the shudder resistance. It should be noted that for a given material, the 0 – 3 m/s μ–v relationship represents the recovery of the friction material behavior. The 3–0 m/s behavior is affected by the thickness

Fig. 2.8.19  Effect of high surface adsorption (material MA).

Fig. 2.8.18  Effect of surface adsorption on μ-v relationship.

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and nature of material film formation on the friction material surface.

Table 2.8.2  Compression Modulus of Friction Material. Material

Compression Modulus (MPa)

MD ME MG

33.84*, 64.02** 25.84, 57.82 20.51, 41.48

* Modulus at pressure = 0 to 2 MPa ** Modulus at pressure = 2 MPa to 10 MPa

Fig. 2.8.20  Effect of intermediate surface adsorption structure (material MB).

Fig. 2.8.22  Compression-relaxation behavior of typical friction materials.

Fig. 2.8.21  Effect of low surface adsorption structure (material MC). 2.8.5.2  Compressibility of Friction Materials The friction characteristics of friction materials are influenced by the elasticity of the materials. The compression-relaxation behavior of typical friction materials is shown in Fig. 2.8.22.

Fig. 2.8.23  μ–v relationship for high modulus material MD.

The compression-relaxation behavior represents the stressstrain behavior of friction materials. The elastic modulus of the materials can be determined from the slope of the compression-relaxation curves at various pressures. The elastic modulus of materials indicates the compressibility of the materials. Materials with different elastic moduli of compressibility have been tested with Continuous Slip Test Procedure 101. Table 2.8.2 shows the elastic modulus of the three different materials. Material MD has the highest modulus (least compressible) while material MG has the lowest modulus (most compressible). The results for the continuous slip tests for

Fig. 2.8.24  μ–v relationship for medium modulus material ME.

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the three different materials are summarized in Figs. 2.8.23 to 2.8.25.

Fig. 2.8.27  μ–v relationship for material MH (high concentration of damping).

Fig. 2.8.25  μ–v relationship for low modulus material MG. Material MG with the lowest modulus showed a positive slope of the coefficient-speed relationship (Fig. 2.8.25). On the other hand, material MD with the highest modulus showed a highly negative slope of the coefficient speed relationship (Fig. 2.8.23). These results indicate that the compressibility of the material affects the initial shudder of the friction material. High compressibility (low elastic modulus) usually leads to good anti-shudder performance. This is due to the mechanism of material film formation as well as the damping effect. 2.8.5.3  Damping Effects The damping effects provided by the surface of the friction materials are important in eliminating the shudder or lowfrequency vibration in continuously slipping clutches. Damping from the friction materials can be achieved either by

Fig. 2.8.26  μ–v relationship for material MJ (no damping effect).

increasing the compressibility of the surface or increasing the surface area of the damping agents in the friction material. Figures 2.8.26 and 2.8.27 show the coefficient-speed curve for a non-damping friction material surface. Material MH has the highest concentration of damping effects while material MJ has no damping effects. The results showed that material MJ has a high negative slope at level A (40°C, before brake-in) of the μ–v curve (shudder) 2.8.5.4  Fiber Effects In order to understand the effects of fibers on the shudder resistance of friction materials for continuous slip clutch applications, a series of fibers was studied. These fibers vary in shape and composition, and have different surface characteristics and structures. Each fiber was incorporated into a given formula to make nine different friction materials (M1 to M9). Table 2.8.3 summarizes the results of the initial shudder behavior by Continuous Slip Test Procedure 101. The results indicate that only friction materials containing fibers F1 and F6 have fair results (slope =0 of the μ–v curve) at the low temperatures of 40° C before the friction material was broken in. Figures 2.8.28 to 2.8.31 show the μ–v relationship of “fair” and “poor” fibers. Materials with fair fibers refer to materials with a zero slope of μ–v curve, while materials with poor fibers showed a negative slope of the μ–v curve, indicating a tendency to shudder. The continuous slip test results agreed with the above arguments; i.e., surface absorption, compressibility, and damping effects will affect anti-shudder performance. Fibers F1 and F6 have unique surface structure and chemistry so as to increase the absorption capability of the ATF friction modifiers. Also, fibers F1 and F6 are elastic fibers with low elastic modulus, providing damping effects as well as minimizing the material film formation at the interface, as discussed in previous sections. 2-114

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Table 2.8.3  Curve of μ vs. Speed for Fiber Studies. Material

Fiber

MF1 MF2 MF3 MF4 MF5 MF6 MF7 MF8 MF9

F1 F2 F3 F4 F5 F6 F7 F8 F9

Notes:

μ Curve Before

μ Curve After

5 Minutes Continuous Slipping

5 Minutes Continuous Slipping

40°C Fair (0) Poor (–) Poor (–) Poor (–) Very Poor (––) Fair (0) Poor (–) Very Poor (––) Very Poor (––)

100°C Good (+) Good (+) Good (+) Good (+) Poor (–) Good (+) Very Poor (––) Good (+) Fair (0)

100°C Good (+) Good (+) Good (+) Good (+) Good (+) Good (+) Good (+) Good (+) Good (+)

40°C Good (+) Fair (0) Poor (–) Poor (–) Poor (–) Good (+) Poor (–) Poor (–) Poor (–)

– = Negative slope of μ–v curve –– = Highly negative slope of μ–v curve + = Positive slope of μ–v curve 0 = 0 Slope of μ–v curve

Fig. 2.8.30  μ–v relationship for material MF5 containing “Poor” fibers F5.

Fig. 2.8.28  μ–v relationship for material MF1 containing “Fair” fibers F1.

Fig. 2.8.29  μ–v relationship for material MF6 containing “Fair” fibers F6.

Fig. 2.8.31  μ–v relationship for material MF3 containing “Poor” fibers F3.

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2.8.5.5  Effects of Temperature Figures 2.8.32 to 2.8.35 show the effects of temperature on the coefficient-speed curve for various friction materials under the same lining pressure of 0.98 MPa. The results indicate that friction materials have more tendencies to shudder at a low oil temperature of 40°C than at a high oil temperature of 100°C. This phenomenon is related to the material film formation. At low temperatures, it is relatively easy for the higher viscosity ATF and the friction material to form a film of material at the interface (Figs 2.8.32 and 2.8.33). However, if a material has the proper surface structure and treatment, the effects of material film can be minimized. The surface treatment may consist of coating surface modifications so as to modify the contact areas between ATF and friction materials. Figures 2.8.34 and 2.8.35 show that the μ–v relationship of the surface-treated material is relatively independent of temperature.

Fig. 2.8.34  Temperature effect on μ–v shape with treated surface material MM.

Fig. 2.8.35  Temperature effect on shape with treated surface material MN.

Fig. 2.8.32  Temperature effect on μ–v shape with untreated surface material MK.

2.8.5.6  Effects of Speed In order to evaluate the effects of speed on the shudder behavior of continuous slip clutches, it is very important to design a proper test procedure. The general speed range in the literature for continuous slip clutch evaluation is from 0 to 1.5 m/s. However, this speed range may not necessarily be sufficient for the evaluation of the friction behavior of continuous slip clutch material.

Fig. 2.8.33  Temperature effect on μ–v shape with untreated surface material ML.

The initial shudder can exist either at high speeds (0.5 – 3.0 m/s) as shown in Fig. 2.8.36, or at low speeds (0 – 0.5 m/s) as shown in Fig. 2.8.37. Note that negative slopes were observed in the high-speed region in Fig. 2.8.36 and the low-speed region in Fig. 2.8.37. These negative slopes of the μ–v curve will result in shudder.

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6. Tohyama, Mamoru, Toshihide Ohmori and Fumio Ueda, “Anti-Shudder Mechanism of ATF Additives at Slip Controlled Lock-Up Clutch. 7. Chen, Yih-Fang, Timothy Newcomb, and Robert C. Lam, “Friction Material/Oil Interface for Slipping Clutch Applications,” SAE Paper 2001-01-1153. 8. Guan, Jay J., Pierre A. Willermet, Roscoe O. Carter, and Don J. Melotik, “Interaction Between ATFs and Friction Material for Modulated Torque Converter Clutches.” 9. Throop, M. J. and D. G. McWatt, “Slipping Torque Converter Clutch Interface Temperature, Pressure and Torque Measurements Using Inductively Powered Radiotelemetry,” SAE Paper 970679. 10. Ting, L. L., “Engagement Behavior of Lubricated Porous Annular Disk. Part 1: Squeeze Film Phase-Surface Roughness and Elastic Deformation Effects,” Wear. 34, 159 (1975).

Fig. 2.8.36  μ–v relationship with high-speed shudder phenomenon (material MO).

2.9 Control Technology of Minimal Slip-Type Torque Converter Clutch Takeo Hiramatsu and Takao Akagi Mitsubishi Motors Corp. Haruaki Yoneda Japan Automotive Engineering Corp. Based on SAE Paper No. 850460

2.9.1 Abstract Fig. 2.8.37  μ–v relationship with low-speed shudder phenomenon (material MP). 2.8.5.7 References 1. Jauch, Friedemann, “Model-Based Application of a SlopControlled Converter Lock-Up Clutch in Automatic Car Transmissions,” SAE Paper 1999-01-1057. 2. Kono, Katsumi, Hiroshi Itoh, Shinya Nakamura, and Kenichi Yoshizawa, “Torque Converter Clutch Slip Control System.” SAE Paper 950672. 3. Lam, Robert and Yih-Fang Chen, “Friction Material for Continuous Slip Torque Converter Applications: AntiShudder Considerations, SAE Paper 941031. 4. Chen, Yih-Fang, “Friction Materials for Slip Clutch Applications,” SAE Paper 981101. 5. Willermet, P. A., G. K. Gupta, D. Honkanen, J. W. Sprys, and D. G. McWatt, “ATF Bulk Oxidative Degradation and Its Effects on LVFA and the Performance of a Modulated Torque Converter Clutch,” SAE Paper 982668.

If a torque converter clutch is allowed to slip to a minimal amount, engine torque can be transmitted through a transmission without torque variation problems, and also low fuel consumption is realized by operating the clutch even at low engine revolutions. Oil pressure applied to the clutch is electronically feed-back-controlled to keep clutch slip to a minimal amount. However, this feedback system tends to become unstable by impairment of various factors of the system. This section relates to stability analysis of the feedback system, and especially to the control method by which the feedback system can be made stable even when the μ-v characteristic of the clutch facing material is impaired. In order to reduce fuel consumption of a vehicle with automatic transmission, Mitsubishi Motors Corporation has developed a four-speed automatic transaxle that utilizes electronic control extensively [1, 2]. It also has developed and put into production an electronically controlled damper clutch system by which slip loss of the torque converter is greatly reduced. Damper clutch for direct drive is provided

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between input and output shafts of the torque converter, and oil pressure applied to the clutch is feedback-controlled to constantly keep clutch slip closer to a target value. By allowing a slight amount of clutch slip, engine torque variation is intercepted and clutch can be put into operation at low engine revolutions. As a result, actual fuel consumption has been reduced by 10% compared with a vehicle with conventional automatic transmission. In order to secure stability of this system, an analysis according to automatic control theory has been done to comprehend effects on stability which are affected by various elements of the feedback system. Particularly, the μ–v characteristic of the clutch facing material significantly affects system stability. At an early stage of development, after the μ–v characteristic is impaired due to degrading of oil or mixing of different oil, hunting was experienced at a slip of approximately 1 Hz, even on a unit which had been in stabilized operation by improving a control method. It is also reported that shock caused at an early stage of clutch engagement has been sharply reduced.

2.9.2

Outline of System

The torque converter absorbs engine torque variation and increases driving force at a start and in an acceleration of a vehicle, thus ensuring smooth operation; however, it has the

deficiency of a big energy loss due to slip. Slip loss is particularly large in the range of low vehicle speed and heavy load, and it deteriorates actual fuel consumption of a vehicle with an automatic transmission. If slip loss at a time of low speed and heavy load operation is reduced, it will greatly contribute to an improvement of fuel consumption. A damper clutch control system is shown in Fig. 2.9.1. Damper clutch is provided between input and output shafts of the torque converter, and oil pressure applied to the clutch is feedback-controlled to keep clutch slip to a target value. The amount of slip is obtained from a revolution speed difference between the engine and torque converter output shaft. Engine speed is obtained from the primary voltage wave pattern of the ignition coil, and torque converter output shaft speed is obtained by calculations from revolution speeds of the transmission output shaft and one element of planetary gears, each detected from a pulse generator simultaneously. A command sent by control unit actuates the duty control solenoid valve and, thereby, the oil pressure control valve increases oil pressure applied to the clutch when a slip is bigger than a target value and decreases it when a slip is smaller. In this manner, the system is feedback-controlled so that a slip is constantly maintained at a target value. While the damper clutch is released, oil pressure is applied as indicated by a

Fig. 2.9.1  Damper clutch control system. 2-118

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broken line, and inherent advantages of torque converter operation are obtained. A target value of a slip is set at a minimum value plus some margin required for intercepting engine torque variation according to engine revolution and load. Besides engine torque variation, slip loss of torque converter has been greatly reduced by putting damper clutch in operation at low engine revolution; actual fuel consumption has been reduced by about 10%. Since a damper clutch can be installed by shortening part of a blade of the torque converter, it has an excellent adaptability to a transversely mounted FWD vehicle in which a restraint by an overall length is significant.

2.9.3

Fig. 2.9.3  Distribution of revolution variation ratio (%) of crankshaft.

Principle of Engine Torque Variation Interception by Adding a Minimal Slip

If a damper clutch is put into a complete direct drive, engine torque variation is directly transmitted to the drive line system. As shown in Fig. 2.9.2, however, when minimal slip in excess of revolution variation is added to the damper clutch, engine revolution variation is intercepted and engine torque variation is not transmitted to the drive line system. The reason why engine torque variation is intercepted is based upon a principle that a direction of friction force, which is a multiple product of presented force and coefficient of friction, is in line with a direction of slip. If presented force, coefficient of friction, and direction of slip are constant, transmitted torque becomes constant and does not vary.

Figure 2.9.4 shows that as slip ratio at damper clutch is increased, torque variation is gradually absorbed. By adding 2% slip ratio, torque variation is absorbed to an extent similar to an operational condition achieved by the torque converter, even in a range of low revolution and heavy load.

The ratio of crankshaft revolution variation ∆ωe to its mean _ revolution speed ωe is defined as revolution variation ratio. Distribution of crankshaft revolution variation ratio of MMC’s four-cylinder and four-cycle engine is calculated and shown in Fig. 2.9.3. It is noted that revolution variation ratio at low revolution and heavy load is about 5%, but in almost all ranges, it is less than 1%, a slight value.

Fig. 2.9.2  Principle of engine torque variation interception by adding minimal slip.

Fig. 2.9.4  Example of reduction of torque variation transmission by adding slight slip. As mean torque of the crankshaft is totally transmitted to the output shaft by the damper clutch, energy loss is in proportion to mean torque and an amount of slip and, therefore, it is preferable that slip ratio shall be fixed at the minimum. Fundamentally, the damper clutch can be put in operation with an engine at above idling speed because engine torque variation can be intercepted. However, because torque increase effect of the torque converter is not available at low vehicle speeds, and because vibration of an engine block is propagated to the body of a vehicle by way of engine mounts, in practice it is necessary to determine operation range for the damper clutch by considering power characteristic of a vehicle and vibration propagation characteristic to a body. An example of damper clutch slip ratio and operation is shown in Fig. 2.9.5.

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d d d u (t) = −Kω d (t) − L ω d (t) dt dt



tp



d p(t) + p(t) = Ad u (t) dt Tc (t) = a μ R P(t)



−Tc (t) = Ie



(2.9.3) (2.9.4) (2.9.5)

d ω ad (t) dt

∂c ⎞ ⎡ ⎤ ⎛ + ⎢αPaR + ⎜ 2C − e⎟ ω e − β⎥ ⋅ ω ad (t) ⎠ ⎝ ∂ e ⎣ ⎦

(2.9.6)

where:

Fig. 2.9.5  Example of setting of damper clutch operation range and minimal slip ratio.

2.9.4

Stability of Feedback Control System

2.9.4.1  Assumptions The main theme of the damper clutch control system is whether the slip ratio of the damper clutch is constantly maintained at a target value and, therefore, stability of the feedback control system plays a major role to achieve it. Therefore, an analysis according to automatic control theory was done to ensure stability of the feedback system and to determine the degree of effects that various elements would have on stability. The following items were assumed in this analysis. 1. Performance of an engine and a torque converter are represented by static characteristics. 2. The entire system is linearized and continuous, even though an actual system is nonlinear and discontinuous. 3. A vehicle speed is constant. 4. Delays on slip detection and electric-oil pressure conversions are approximated with first-order lag models. 2.9.4.2  Equation of Motion Differential equations of the feedback control system are:

td

d ω c (t) + ω c (t) = ω ad (t) + ω set dt ω d (t) = ω set − ω c (t)

(2.9.1) (2.9.2)

ωset = Target value of slip (rad/s) ωad(t) = Slip difference of an actual value from a target value (rad/s) ωc(t) = Detected and calculated slip (rad/s) ωd(t) = Difference of ωc from ωset (rad/s) td = Time constant of slip detection time lag (s) du(t) = Duty ratio deviation from the value to be converged K = Duty ratio correction rate per unit time in proportion to slip deviation from a target value L = Duty ratio correction rate per unit time in proportion to slip variation speed (s) p(t) = Oil pressure deviation from the value to be converged (kg/cm2) A = Ratio of oil pressure increase to duty ratio increase (kg/cm2) tp = Time constant of electric-oil pressure conversion lag time (s) Tc(t) = Clutch transmission torque deviation from the value to be converged (kg◊cm) a = Oil pressure applying area of a damper clutch piston (cm2) μ = Friction coefficient of damper clutch R = Friction radius of damper clutch (cm) Ie = Rotational inertia of engine and torque converter (kg◊cm◊s2) P = Oil pressure to be converged (kg/cm2) α = Rate of friction coefficient increase to slip increase (s) C = Torque capacity coefficient of torque converter (kg◊cm◊s2) e = Speed ratio of torque converter ω = Engine revolution speed (rad/s) β = Rate of engine torque increase to engine revolution speed increase (kg◊cm◊s) 2-120

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2.9.4.3  Stability Analysis Block diagram (Fig. 2.9.6) has been derived from Laplace transformed equations. The circulating transfer function of this feedback control system is: G(S) =



δ k + δ1S S(tdS + 1)(tpS + 1)(IeS + γ )

(2.9.7)

where:

δ k = Aa µ R K



δ l = Aa µ R L



∂c ⎞ ⎛ γ = αPaR + ⎜ 2C − e⎟ ω e − β ⎝ ∂e ⎠

Figure 2.9.7 shows an example of loci of a vector which were obtained by using the circulating transfer function to study effects on stability to be brought about by various elements of the feedback system.

Fig. 2.9.7   6. Engine torque increase is big compared with engine revolution speed increase. (b is big, especially at low revolutions and heavy load) 7. Big time lag of slip detection. (big td) 8. Big time lag of electric-oil pressure conversion. (big tp)

As a result, it was found that the following eight items were stability impediment elements in feedback systems. 1. Big decrease of friction coefficient μ corresponding to an increase of slip revolution speed v. (small α) 2. Big torque transmission of clutch. (big PaR) 3. Excessive ratio of oil pressure correction to slip deviation. (big K) 4. Too small or too big ratio of oil pressure correction to slip variation speed. (big or small L) 5. In a low-capacity torque converter, torque increase shared by torque converter is small despite increase of slip. (2C – (∂c/∂e)e)ωe is small)

Particularly, item (1) is affected by materials of facing and ATF (Automatic Transmission Fluid) and their deterioration during operation, and attention is required to maintain stability of a control system. In practice, at an early stage of development, μ–v characteristic was impaired as shown in Fig. 2.9.8 (1.0 T(breakaway) then “slip” is true. Otherwise, “stick” is true.

where cg and c¢g are gear train structural and viscous loss coefficients, AR is the differential gear ratio, and the axle shaft torque, Ta, is given by:

If “slip” is true and ωslip (previous) × ωslip (now) ≤ 0, then “stick” is true. Otherwise “slip” is true. A similar procedure may be followed in determining when and how clutches and bands in the gear train are engaged

(

)

Igω g = k gδθg + c g ω t – ω g – c¢gω g –



2Ta AR

θ⎞ ⎛ Ta = k a ⎜ δθa ± 1 ⎟ ⎝ 2⎠



(2.10.13)

(2.10.14)

For dθa outside the backlash region, and

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−θ1 θ ≤ δθa ≤ 1 (2.10.15) 2 2 The axles usually represent the largest compliance in the drivetrain (besides the torsional damper), because of the effect of the differential gear ratio. The equivalent spring rate of the axle system on the driveshaft side of the differential is: Ta = 0,



k ′a =

2k a (AR 2 )

(2.10.16)



The remaining compliance in the system as modeled is provided by the tire torsional wrap-up created as the tire carcass and tread deform in the direction of wheel rotation. The associated torque is related to tire slip and tractive effort using a semi-empirical model [15, 16]. In this model, the tractive effort is given as a function of tire slip. For small values of slip, the two quantities are related as follows:

−C TFz s (1 − s)



TT = kT dθT

(2.10.19)

where dθT is the tire torsional wrap-up and kT is the corresponding spring rate. The forward (longitudinal) vehicle speed, v, and the wheel angular speed ωw, are related by the definition of tire slip: 1 − ωw (2.10.20) ⎛ v ⎞ ⎜⎝ R ⎟⎠ E where RE is the effective rolling radius of the tire. Using the above equations, the state equations for the tire dynamics are expressed as follows: ωw − ν (2.10.21) δθ T = ⎡ ⎛ FT ⎞ ⎤ R 1 − ⎢ E ⎜⎝ C T ⎟⎠ ⎥⎦ ⎣ s≡

2.10.4.6  Tire Model

FT =

where RL is the loaded radius of the tire and the torque, T T, is given by:



(2.10.17)

where Fz is the normal load between the tire and the road, and CT is a constant, known as “tractive stiffness.” The tire slip, s, is negative for traction and positive for braking. The typical tire model behavior for tractive effort and tire slip is plotted in Fig. 2.10.7.

and

Iw ω w = Ta − k TδθT

(2.10.22)

The vehicle-road interaction dynamics (forward motion) are evaluated from the vehicle acceleration produced by the force imbalance created between the applied tractive effort at the tires and the resisting road load term RLD. The latter is derived from quadratic fits to actual steady-state measurements of road load as a function of vehicle speed. Explicitly:

M v v = 2FT − RLD(ν)

(2.10.23)

2.10.4.7  Engine Model

Fig. 2.10.7 Tire tractive effort as a function of tire slip for typical values of CT and vehicle weight on one tire (Fz). The parameter μ is related to tire spin (see [15] for more details).

Throttle angle (defined by the user as a function of time) together with engine speed (a state variable) are used to evaluate the average engine brake torque from mapping data. Typical data are shown in Fig. 2.10.8. The average engine brake torque is then used to calculate instantaneous engine brake torque in the following manner. Prior to the simulation, an engine or a detailed engine combustion model is run at specific speed-load points, and in-cylinder gas pressure is tabulated on a crank angle basis for these points. During the simulation, these data points are used to calculate the instantaneous indicated torque Tp of the engine from:

The tractive effort is given by:

T FT = T RL

⎡ ⎢ r sin2θe Tp = rA pP(θe ) ⎢sin θe + r 2 sin 2 θe ⎢ 2L 1 − ⎢⎣ L2

(2.10.18)

⎤ ⎥ ⎥ ⎥ ⎥⎦

(2.10.24)

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where r is the crankshaft to crankpin length, L is the connecting rod length, P(θe) is the in-cylinder gas pressure at crank angle θe, and Ap is the piston area. This torque is added to the inertia torque, TI, resulting from the reciprocating piston mass, mp:

⎡ (r sin θe − 2Lsin2θe − 3r sin3θe ) ⎤ TI ≅ m pr 2ω e ⎢ ⎥ (2.10.25) 4L ⎣ ⎦



Itω t + G tq = Td − k gδθg − t t (ω t , ω i ,q ) (2.10.29) Isω s + G sq = Towc − t s (ω s , ω t ,q )

Giω i + G tω t + G sω s + Gqq = H (ω i , ω t , ω s ,q )



Both torques are summed with proper phasing in crank angle for four, six, and eight multi-cylinder configurations. Accessory loads are considered in the calculations of the net torque at the flywheel. The engine torque is, therefore, calculated with sufficient details for the simulation of the enginegenerated, torsional excitations of the drivetrain. However, not all drivetrain vibrations are caused by engine forces. As shown later, self-excited oscillations of the bypass clutch are possible, which depend on the frictional characteristics of the clutch and are, therefore, independent of the firing pulsations of the engine.



δθ d =ω c – ω t

(2.10.33)



(2.10.34)

Td = Td (δθ d , δθd ) , hysteresis curve Simplified Gear Train with Axles:



)

Igω g = k gδθg + c g ω t − ω g − c′gω g −

2Ta AR

δθ g = ω t − ω g



(2.10.31) (2.10.32)

µFc (ω c ) , clutch breakaway torque Tc =   Tc (ω e ,ω c ) , slip torque capacity 

(

(2.10.30)

Icω c = Tc − Td







(2.10.35)

(2.10.36)



(2.10.37)



ωg δθ a = − ωw AR

(2.10.38)

(2.10.39)



within backlash ⎫ ⎧ 0, ⎪ ⎪ Ta = ⎨ ⎛ ⎬ θ1 ⎞ ⎪k a ⎜⎝ δθa ± ⎟⎠ , outside backlash⎪ 2 ⎩ ⎭

Tires and Vehicle-Road Interactions: Fig. 2.10.8  Mapping data of engine brake torque as a function of engine speed for different throttle angles in the model.



δθ Τ = ω ω −



2.10.4.8  Summary of System Equations The system equations describing the dynamics of the drivetrain are given below. The corresponding model is shown in Fig. 2.10.6. Engine Torque:   Te = Te (ωe , θe, throttle, #cylinders & type)

(2.10.26)

· θε = ωε

(2.10.27)

Torque Converter with Bypass Clutch:

Ieω e + Giq = Te –Tc – t i (ω i ,ω s ,q )

Iw ω w = Ta − k TδθT



(2.10.28)



v =

ν  F  R E 1 − T   CT 

(2.10.40) (2.10.41)



[2FT − RLD(ν)] Mv



FT =

k TδθT RL

(2.10.42)

(2.10.43)

Engine Block and Transmission Housing:

Ibω b = –Te – Towc – k mθβ – c mω b

(2.10.44)



θ b = ω b

(2.10.45)

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2.10.5 Results 2.10.5.1  Self-Excited Behavior Simulations of the torque converter with centrifugal bypass clutch demonstrate that self-excited vibrations may result from the frictional behavior of the clutch during clutch slip. The model results illustrate the cause of the instability and demonstrate how the associated oscillations propagate through the drivetrain. These self-excited oscillations called “shudder” in this paper are present only when the bypass clutch is slipping and the clutch torque capacity versus clutch slip has sufficiently negative slopes, as shown in Fig. 2.10.9. The results lead to the conclusion that the damping provided by the drivetrain and the torsional damper is insufficient for the elimination of shudder vibrations. Elimination of the negative slope characteristics is the most expedient way to avoid shudder.

Simulation results, shown in Fig. 2.10.10, demonstrate how shudder amplitude increases with increasing magnitude of the negative slope. It is also seen that positive or small negative slopes do not lead to sustainable vibrations. This is found to be in agreement with empirical observations [20].

Fig. 2.10.9  Typical bypass clutch torque capacity vs. clutch slip with negative damping. A good fit to the data is given by the exponential shown in the figure, where C is the centrifugal capacity of the clutch, which increases as the turbine speed increases from Wct to Wc4. The parameter B is used as an indicator of the negative slope magnitude (see Fig. 2.10.17).

Fig. 2.10.10  The effect of the slope of the torque converter capacity (Tc) vs. clutch slip (Wslip) on shudder (drive shaft torque oscillations). With curve A, there is sustainable shudder. Curve B has a marginal sustainable shudder. Note that curve C, with small negative slope, does not lead to sustainable shudder.

Sustained shudder oscillations are possible because they are “self-energized” in the sense that there is net energy gain per cycle to offset any energy losses. As shown in Appendix B, the negative slope of the bypass clutch slip capacity is equivalent to a “negative damping” or “energy source” term [17 to 19], which promotes further oscillations of the lock-up shoes (turbine side) with respect to the converter cover. Furthermore, velocity-dependent, self-excited systems act as their own forcing functions [13]. In other words, they “self-resonate.” For this reason, it is difficult to damp out such vibrations once they are excited.

Additional results, shown in Fig. 2.10.11, demonstrate how a tip-in initiates clutch slip with ensuing shudder vibrations. It is also shown that components of the drivetrain from the turbine (damper) to the axles oscillate in phase with a frequency of the lowest torsional mode of oscillator of the system (excluding the engine-impeller side of the torque converter). A comparison between experimental measurements of drive shaft torque from an instrumented vehicle [20] and model results is shown in Fig. 2.10.12.

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torque Te balances the combined impeller and clutch torques (Ti + Tc). At point A, the clutch slips for a sustained period of time in its negative slope region, which leads to shudder. In contrast, for throttle angles following a large tip-in, the engine equilibrates at point B where the clutch characteristics have nearly zero slope. The simulation results in Fig. 2.10.14 clearly demonstrate sustained and attenuated vibrations following small and large tip-ins, respectfully. Furthermore, it is seen that prolonged operation under destabilizing slip conditions is possible with centrifugal clutch designs in contrast to conventional clutch control (such as during gear shifting). In the latter case, self-excited oscillations may be present (known as “chatter”), but they only last for the brief period of clutch engagement or disengagement [17 to 19].

Fig. 2.10.11  Model simulation of the shudder vibrational mode of a powertrain with 3.5 axle ratio and 4.9-L engine. Note that axle and damper wrap-ups (TH) are nearly in phase. The simulated frequency of 11 Hz agrees well with the measured values of 11 ± 0.5 Hz. Torques are in ft-lb, wrapups in degrees, with speed in rad/sec.

Fig. 2.10.12  Experimental measurements of drive-shaft torques and simulated results during shudder. Note that the second tip-in increases the clutch slip outside the negative slope region. The predicted frequency is within 10% of measured values. Both experimental and theoretical results show that an initial tip-in unlocks the bypass clutch and initiates shudder. Subsequently, a larger tip-in causes the vibrations to dissipate. The dependence of shudder on throttle excitations is examined next. The characteristic torque of the engine, the bypass clutch, and the impeller are plotted in Fig. 2.10.13 as a function of the clutch slip speed, assuming constant lock-up shoe speed (turbine). For throttle angles following small tip-in, it is seen that the engine speed equilibrates at a point A where the engine

Fig. 2.10.13  Example of two possible equilibrium points of the torque converter for small (A) and large (B) throttle angles. Note the bypass clutch operates in the unstable region of A but not B.

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The centrifugal bypass clutch has two major characteristics with regard to self-excited vibrations. First, prolonged slip operation is possible, as explained earlier, which may enhance shudder if the slope allows it. Second, the centrifugally actuated engagement has its own negative slope characteristics that are independent of the friction behavior of the sliding surfaces. This is due to the fact that as centrifugal speed (lock-up shoe speed) increases at constant engine speed, the clutch slip decreases with increasing torque capacity, as shown in Fig. 2.10.16.

Fig. 2.10.14  Shudder excitation following two tip-ins of different magnitude. Torques are in ft-lb and speed in rad/ sec. The model also demonstrates that differences in the static and dynamic friction coefficients of the clutch-sliding surface may cause abrupt stick-slip conditions, but this is not necessarily responsible for shudder. As shown in Fig. 2.10.15, the oscillations of the shoe (turbine) side of the clutch may increase to the point where slip-to-stick transition takes place. In this case, the frequency is slightly lower than before because the locked portion of the cycle includes the engine-impeller inertia. Thus, the model investigation shows that bypass clutch stick-slip is not the cause but a consequence of shudder and that quite often shudder exists without slip-stick if the slope behavior permits it.

Fig. 2.10.16  Typical centrifugal torque capacity vs. lock-up shoe speed shown in (a). A magnified portion of (a) is shown in (b) as a function of slip speed (decreasing shoe speed) at constant engine speed (1600 rpm). Note that in (b) the slope is negative.

Fig. 2.10.15  Shudder with and without locking of the bypass clutch. The simulated powertrain represents a 4.9-L engine with a 3.5-L axle ratio. Torques are in ft-lb and speeds in rad/sec.

The role of the torsional vibration damper in the control of shudder was found to be very limited after extensive parametric studies with the model. The simulation results are summarized in Fig. 2.10.17 where shudder torque amplitude at the drive shaft is plotted against lag for the three different spring rates.

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• • • •

Choice of lubricant and additive Contamination of lubricant and friction surfaces Finish of metal friction surfaces Choice of friction materials

2.10.5.2  Tip-in and Tip-out Response Model simulations of the response of the centrifugally locking drivetrain to large tip-in and tip-out excitations (~ 150 ft-lb) are shown in Figs. 2.10.18 and 2.10.19. The abruptness with which the vehicle accelerates (which may be accompanied by an audible sound) is referred to as “tip-in jerk” in this report. It is closely related to the sudden changes in slope of the drive shaft torques. Following the original impact, a for-and-aft, surge-like motion of the vehicle may be present. It is related to the transient excitation of the lowest torsional mode of the drivetrain. If the torque converter is locked, the frequency is usually 4 to 8 Hz. Otherwise, the frequency is equivalent to shudder values (10 to 18 Hz). The amount of “overshoot” in the driveshaft torque is related to both the original impact and the subsequent drivetrain oscillations. Fig. 2.10.17  Model calibration study of the Coulomb damper with regard to shudder for a powertrain with 3.5 axle ratio and 4.9-L engine. Plots (a), (b), and (c) correspond to damper spring rates (KD) of 5, 10, and 10 ft-lb/deg, respectfully. The parameter B refers to the magnitude of the negative slope as defined in Fig. 2.10.9. The combined actions of the spring and friction (lag) elements of the Coulomb damper dissipate drivetrain vibrations through the hysteretic energy losses. In the case of shudder, however, the effectiveness of the damper is greatly diminished by the conflicting actions of lag and spring rate. Although the dissipated energy is proportional to the lag and travel, increasing the lag to large values renders the device inactive for all disturbances smaller than the lag. Furthermore, a compliant (soft) damper enhances the centrifugal clutch travel, thereby contributing to increased action of the selfenergizing slip behavior. As mentioned earlier, self-excited vibrations are only present with sufficiently large negative slopes of the bypass clutch slip capacity. Model and empirical results show that for small negative or positive slopes the clutch-converter system is stable. For the successful design of such a system, one or more of the following factors are usually considered [9, 18–23]:

The open converter case (Fig. 2.10.18a) is shown to be free of any undesirable tip-in/tip-out response. Similar results are obtained for the centrifugal lock-up case (Figs. 2.10.18b and 2.10.18c) for large tip-ins, because the centrifugal clutch slips. Consequently, the impact is “softened” as the engine inertia breaks and accelerates away from the rest of the drivetrain. The tip-out response is equally good because of the coastdown-one-way-clutch included in the model. As the results show, the torsional damper calibration does not affect the tip-in/tip-out characteristics. Thus, the dynamic response of the drivetrain with centrifugal lock-up clutch to sudden changes in throttle is well behaved. In the case of a hydraulically controlled bypass clutch, the tip-in response may not be as well behaved as in the centrifugal lock-up case if the clutch remains locked. In this case, the simulation results of Fig. 2.10.19 demonstrate that the dynamic response depends strongly on the damper calibration. An extremely stiff damper exhibits the best tip-in response. However, stiff damper calibration can result in other undesirable powertrain NVH conditions, as shown next.

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at low load conditions when the torque converter is locked. At larger engine torques, the clutch is slipping and the transmissibility is again small. At higher speeds and loads (not shown in the results), the converter may be locked but the transmissibility is still small because the excitation frequency is large. On the other hand, the simulation of a hydraulically controlled bypass clutch that is forced to remain locked (Fig. 2.10.20 b and 2.10.20c) shows that the firing signal is very evident, especially at low-speed and high-load conditions. In this case, the soft damper exhibits the least transmissibility (Fig. 2.10.20a). Unfortunately, the soft damper calibration also exhibits the worst tip-in response.

Fig. 2.10.18  Simulated tip-in/tip-out response with lock-up shoes slipping for a powertrain with 3.5 axle ratio and 4.9-L engine. Driveshaft torques are in ft-lb and clutch slip in rad/ sec.

Fig. 2.10.19  Simulated tip-in/tip-out response of the same powertrain as in Fig. 2.10.18 with the bypass clutch forced to remain locked at all times. Note that the “surge” is less evident in the case of a stiff damper. 2.10.5.3  Engine Torque Transmissibility Engine combustion excitations are transmitted to the vehicle body via the engine mounts and via the drivetrain (through the suspension system). The transmissibility of firing disturbances along the drivetrain is summarized in the results of Fig. 2.10.20. As in the case of tip-in response, the open converter (Fig. 2.10.20e) shows almost no transmissibility of the firing signals on the driveline torque. With a centrifugal lock-up (Fig. 2.10.20d), there is some trace of firing pulses

Fig. 2.10.20  Simulations of drive shaft torque (ft.-lb.) at low and high load concentrations, showing the transmissibility of engine firing events through the drivetrain with the bypass clutch disengaged (e), slipping (d), and locked (a to c). The simulated powertrain includes a 3.8-L engine with a 2.73 axle ratio.

2.10.6 Conclusions The simulation results indicate that a torque converter with a centrifugal lock-up may be susceptible to unstable, selfexcited oscillations when the bypass clutch is slipping and the slip capacity has negative damping characteristics. Furthermore, the model demonstrates that the whole drivetrain from the tires to the turbine vibrates in phase at the lowest torsional mode of the system to recreate the observed frequencies. The torsional (Coulomb) damper, in series with the lock-up shoes, is shown to be ineffective in the control of self-excited vibrations. Elimination of the negative slope in the sliding capacity of the clutch, however, results in a stable system. Additional results show that the centrifugally locking 2-136

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drivetrain has a well-behaved tip-in response because the lock-up clutch tends to slip under large increases in torque. Similarly, the transmissibility of firing events under lugging engine conditions is minimal, because the bypass clutch is either not engaged (for turbine speeds below 900 rpm) or it is slipping (at high torques). Most aspects of the dynamic behavior of the torque converter with a centrifugal lock-up are equally applicable to a hydraulically or electro-hydraulically controlled bypass system. In particular, such a system may be susceptible to self-excited vibrations if it is allowed a prolonged slip (“incipient slip”). The simulations also demonstrate that a completely engaged bypass clutch results in larger tip-in jerks than a slipping system. An additional quantity that affects tip-in/tip-out response of the drivetrain is the amount of backlash in the gear train and the final drive. Such a study is not included in this report, but will be part of a future publication [24]. Finally, the model results show that the torsional damper compliance is a readily accessible design parameter that affects the tip-in/tip-out response and the transmissibility of engine firing excitations. However, it is also shown that calibrations beneficial to tip-in jerk improvements (stiff damper) are detrimental to the reduction of engine firinginduced NVH. Consequently, the control and design of a bypass clutch for an automatic transmission must be carefully considered because of potentially conflicting aspects of its dynamic response. In all cases studied, the open converter system (no bypass clutch) is found to have the most desirable behavior with regard to the control of drivetrain vibrations.

2.10.7 Acknowledgments The authors express their appreciations to S. P. Maxwell and the personnel of Torque Converter Engineering, Transmission and Axle Engineering, Ford Motor Co., for their support of this modeling effort and the data they have provided.

2.10.8 References 1. Horvat, D. and W. E. Tobler, “Bond Graph Modeling and Computer Simulation of Automotive Torque Converters,” to appear in the Journal of the Franklin Institute. 2. Ishihara, T. and R. I. Emeri, “Torque Converters as a Vibration Damper and its Transient Characteristics,” SAE Paper No. 660368, Society of Automotive Engineers, Warrendale PA, 1966. 3. Jandasek, J. K., “Design of Single-Stage, Three Element Torque Converter,” SAE Special Publication SP-186, Society of Automotive Engineers, Warrendale, PA, 1961.

4. Lucas, G. G. and A. Rayner, “Torque Converter Design Calculations,” Automotive Engineer, p. 56, Feb. 1970. 5. Walker, F. H., “Multiturbine Torque Converters,” Design Practices-Passenger Care Automatic Transmissions, SAE publication, 1962. 6. Tobler, W. E., personal communication, 1980. 7. Karamochi, K., R. Shindo, S. Kubo, and M. Miura, “Toyota New Four-Speed Automatic Transmission for Front Wheel Drive Vehicles,” SAE Paper No. 840049, Society of Automotive Engineers, Warrendale, PA, 1984. 8. Schwab, M., “Electronic Control of a 4-Speed Automatic Transmission with a Lock-up Clutch,” SAE Paper No. 840448, Society of Automotive Engineers, Warrendale, PA, 1984. 9. Silbershlag, R., “Centrifugal Torque Converter Clutch,” SAE Paper No. 840051, Society of Automotive Engineers, Warrendale, PA, 1984. 10. Shindo, Y., H. Ito, and T. Ishihara, “A Fundamental Consideration of Shift Mechanism of Automatic Transmissions,” SAE Paper No. 790043, Society of Automotive Engineers, Warrendale, PA, 1979. 11. Chkarori, N. and N. Yoshikawa, “Analysis of Drive Train Noise and Vibration,” Int. J. of Vehicle Design, v.2, no. 4, 1982. 12. Delosh, R. G., K. J. Brewer, L. H. Bush, T. F. W. Ferguson, and E. Tobler, “Dynamic Computer Simulation of a Vehicle with Electronic Engine Control,” SAE Paper No. 810447, Society of Automotive Engineers, Warrendale, PA, 1981. 13. Thompson, W. T., “Theory of Vibration with Applications,” Prentice-Hall, New Jersey, 1981. 14. Girard, D. D., “Fixed Step Friction Model,” Proceedings of the 1983 Summer Conference, Vancouver, Canada 1983. 15. Mencik, Z., W. E. Tobler, and P. N. Blumberg, “Simulation of Wide-Open Throttle Vehicle Performance,” SAE Paper No. 780289, Society of Automotive Engineers, Warrendale, PA, 1978. 16. Tobler, W. E. “General Rigid Body Dynamics and Application to Vehicle Behavior,” PhD. Thesis, Cornell University, 1974. 17. Yoshimori, K., H. Morimura, Y. Yoshimura, and M. Tsuchiga, “Dynamic Shock Absorber Effect of Engine Mounting System on the Power-Train Vibration,” SAE Paper No. 840255, Society of Automotive Engineers, Warrendale, PA, 1984. 18. Haviland, M. L., M. C. Goodwin, and J. J. Rodgers, “Friction Characteristics of Controlled Slip Differential Lubricants,” SAE Paper No. 660778, Society of Automotive Engineers, Warrendale, PA, 1966.

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19. Friesen, T. V., “Chatter in Wet Brakes,” SAE Paper No. 831318, Society of Automotive Engineers, Warrendale, PA, 1983. 20. Experimental Results Provided by Torque Converter Engineering, Transmission and Axle Engineering, Ford Motor Co. 21. Fox, J. R. “Design Considerations for Wet Wheel Brakes,” SAE Paper No. 810696, Society of Automotive Engineers, Warrendale PA, 1981. 22. Haviland, M. L. and J. J. Rodgers, “Automatic Transmission Fluids,” Lubrication Engineering, p. 110, March 1961. 23. Bunda, T., A. Tujikawa, and K. Yokoi, “Friction Behavior of Clutch-Facing Materials; Friction Characteristics in Low-Velocity Slippage,” SAE Paper No. 720522, Society of Automotive Engineers, Warrendale PA, 1972. 24. Tsangarides, M. C., W. E. Tobler, and D. R. Heermann, “Interactive Computer Simulation of Drivetrain Dynamics,” presented at the Noise and Vibration Conference, Traverse City, May, 1985.

2.10.9 Appendix A The purpose of this appendix is to give explanations and explicit expressions for the terms of Eqs. 2.10.1 to 2.10.4, describing the hydraulic torque converter model used in this section. A detailed derivation of these equations is beyond the scope of this work. The interested reader may consult [1 to 5] for additional information. The following simplifying assumptions apply:

forces, B, are assumed to be negligible, and vc is defined as the volume spanned by the rotating member about its axis of rotation (zˆ), the integrals of Eq. 2.10.A1 reduce to the following expressions in the case of the impeller (zˆ direction only). The external torque applied on the impeller fluid at the control surface is given by:

∫Sc r × dF = Ti,f zˆ





(2.10.A2)

The steady-state impeller torque is given by:

ρ ∫ ( r × V )(V × ds ) = ρq[ω i Ri2 − ω s Rs2 Sc

+

]

q ( Ri tan α i − Rs tan α s ) zˆ A



(2.10.A3)

The transient term:

ρ

∂ ∂t

∫Vc r ¥ V dv=(Ii,f ω i + Giq )zˆ



(2.10.A4)

is the torque required for the angular accelerations of the impeller fluid inertia, Ii,f, and the torus flow. The parameters used in the previous expressions are defined in the Nomenclature (see also Fig. 2.10.1). The terms Gj (j = i, t, s, q) are line integral constants, which represent the inertial resistance to the torus flow acceleration. Explicit expressions are given in [1]. If the mechanical inertia of the impeller, Ii,m, and the torus flow is included, the desired expression is obtained, namely:

• ωi ≥ ωt (for this discussion only). • Spacing between the converter members (impeller, turbine, and stator) is negligible. • Blade thickness is ignored. • The torus flow cross-sectional area, A, is constant. • The torus flow velocity is uniform over the crosssectional area. The first three equations are derived from the angular momentum conservation expression for flow in the control volume vc with surface sc:

In a similar fashion, Eqs. 2.10.2 and 2.10.3 for the turbine and stator control volumes are obtained.

∫Sc r ¥ dF + ∫Vc r ¥ Bdv =

Equation 2.10.4 is derived from the energy law:

∂ ∂t

∫Vc

ρr ¥ V dv +

∫Sc

ρ(r ¥ V)(V ¥ ds)



(2.10.A1)

where the fluid element absolute velocity, position vector, and external force are V, r, and F, respectively. If the body

Ti = Iiω i + Giq + ρq ω iR i2 − ω sR 2s +

q (R i tan α i − R s tan α s ) A (2.10.A5)

where Ti is the total external torque applied on the impeller, and Ii = Ii,f + Ii,m



(2.10.A6)

dE = Pin − Ploss (2.10.A7) dt

The total kinetic energy term of the converter system is given by:

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where:

 ρ E = E mechanical + ∑ ∫   V 2dv Vcj  2  j =



R i2ω i (ω i – ω t ) +R 2t ω t (ω t – ω s )  H (ω i ,ω t ,ω s ,q ) ≡ ρ  +R 2s ω s (ω s – ω i )   

(Iiω i2 + Itω 2t + Isω 2s ) + Gqq 2 2

2

+q (Giω i + G tω t + G sω s )

ω i (R i tanα i – R s tanα s )    q +ρ + ω t (R t tanα t – R i tanα i )  ×  A  + ω (R tanα – R tanα ) s s s t t  

(2.10.A8)

The total input power is:

Pin = Tiωi + Ttωt + Tsωs

(2.10.A9)

−

and the total power loss is:

(2.10.A17)

The expressions for the viscous and shock loss terms, summarized below, follow closely Refs. [4, 5]. The viscous loss equation is:



ρ

∑ c v,jVv,j2  q 2 ,

j=i,t,s

(2.10.A11)

j



where cv,j are empirically determined coefficients, and Vv,j are the relative velocities between the fluid and the blades. The shock loss expression is given by: Pshock =



ρ

∑ c s,jVs,j2  q 2 ,

j=i,t,s

j



(2.10.A12)

q A

(2.10.A13)

for the stator-to-impeller entrance shock, where α¢1 is the blade entrance angle with respect to the flow cross-sectional area A. Similarly, the impeller-to-turbine and turbine-tostator shock velocities are:

q Vs,t = R i (ω i − ω t ) + (tan α i − tan α′t ) A

(2.10.A14)

q A

(2.10.A15)

Vs,s = R t (ω t − ω s ) + (tan α t − tan α′s )

In this appendix, self-excited oscillations arising from the negative slope of the clutch sliding friction are examined in a simplified form for the purpose of demonstrating analytically the source of the instability. Given the slipping clutch of Fig. 2.10.B1 with the slip capacity depicted in Fig 2.10.B2, the equation of motion for the driven side of the clutch is: · (2.10.B1) T = Iθ¨ + kθ + cθ where c is a positive coefficient of viscous damping. For small oscillations, the clutch capacity, Tc, can be approximated by the linear equation: · Tc = – a(W – θ) + T0 (2.10.B2) where a and T0 are positive constants. The parameter represents the “constant” speed on the driving (engine) side of the clutch. With this simplification, the equation of motion becomes: · I θ¨ + kθ + (c – a)θ = T – aW (2.10.B3) 0

It is seen that Eq. 2.10.B3 has negative overall damping for a > c. The resulting diverging solution is either oscillatory or strictly exponential. In the former case, the frequency is given by:

 1   k  (c – a) f=     –  2π   I  (4I2 )

2

Finally, combining Eqs. 2.10.1 to 2.10.3 with Eqs. 2.10.A7 to 2.10.A12 the following expression is obtained:

Giω i + G tω t + G sω s + Gqq = H (ω i , ω t , ω s ,q ) (2.10.A16)

2.10.10 Appendix B

c

where cs,j are empirically determined coefficients, and Vs,j are the “shock” velocities which result from the mismatch between entering fluid and blade velocities in the boundaries of any two adjacent members of the converter. More explicitly:

Vs,i = R s (ω s − ω i ) + (tan α s − tan α′i )

q

(2.10.A10)

Ploss = Pviscous + Pshock

Pviscous =

[Pviscous+Pshock ]



(2.10.B4)

which is the natural frequency of the damped system. Thus, the negative damping system “self-resonates.”

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Fig. 2.10.B1  Slipping clutch system with constant input speed (W). Fig. 2.10.B2  Clutch slip capacity vs. slip speed.

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Chapter 3

Gears, Splines, and Chains

Introduction

• Evan L. Jones, Engineering Consultant • William Margolin, Engineering Consultant • Roger G. Young, Jr., Product Engineering Supervisor, Morse TEC, BorgWarner Inc. • Michael Tekletsion Berhan, Product Engineer, Transmission/Driveline Research and Advanced Engineering, Ford Motor Company • Maurice B. Leising, Core Transmission Controls, DaimlerChrysler AG • Hussein Dourra, Ph.D., Specialist, Transmission Logic Development, DaimlerChrysler AG • James Hendrickson, Senior Staff Engineer, New Transmission Products, General Motors Corporation • Joe Chen, Staff Engineer, Advanced Gear Systems, General Motors Corporation • John M. Kremer, Ph.D., Manager, Analysis Support, Transmission Systems, BorgWarner Inc.

Since 1962, the SAE Design Practices: Passenger Car Automatic Transmissions book has been a resource for both new and experienced transmission engineers. The gear section was expanded in the third edition, AE-18, to include splines and chain drives. It has been revised where possible in this fourth edition, AE-29, for clarity and to better include metric standards and parameters. An increased focus is also provided on the dynamics and interactions of the systems that these drive components are found in. The individual subsections published herein are still generally based on the material presented in AE-18, as evidenced by the expanded listing of the revision authors for each subsection. In support of the SAE Automatic Transmission/Transaxle Technical Standards Committee’s efforts to update AE-18 to AE-29, the following people in and along with the ATTTSC contributed their time and technical expertise to complete the overall Gears, Splines, and Chains Chapter:

We would also like to thank Jeffrey Worsinger and Tracy Fedkoe of SAE International for their diligent assistance in getting this revised Gears, Splines, and Chains Chapter done.

• Ernest J. DeVincent, Jr. (ATTTSC Chairman), Manager, Transmission/Driveline Research and Advanced Engineering, Ford Motor Company • Charles E. Dieterle, Consultant, C-DOT Engineering

Michael Tekletsion Berhan Ford Motor Company

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3.1 Design of Planetary Gear Trains

transmission gear trains with multiple discrete gear ratios employ multiple simple planetaries, compound planetaries with multiple suns, rings, and/or arrays of pinions, or combinations thereof.

Original Author: O. K. Kelley General Motors Corp.

Designers of planetary gear trains can spend a great deal of time studying and analyzing all of the various combinations of the above configurations available to get the desired ratios, particularly if regenerative torque multiplication and other less obvious phenomena are employed in the gear train.

Revised in 1991 by: E. L. Jones Engineering Consultant Revised in 2005 by:

There are several methods for analyzing gear train configurations and calculating the resulting ratios from the combinations of multiple simple and compound planetaries. Two are covered in this text. The first of these two methods, sometimes referred to as the tabular or relative motion method, computes the ratios by adding up the relative motions of the gearset components in the train. The second, more recent, method converts the gearsets into analogous levers whose dimensions are a function of the number of teeth in each element.

E. L. Jones M. T. Berhan Ford Motor Co.

3.1.1

Calculation of Gear Ratios

A simple planetary, or epicyclic, gearset consists of one sun gear, one ring gear, and a number of planet gears, or pinions, mounted in a carrier and engaged in mesh with both the sun and ring gears. This arrangement provides three locations for the input or output of mechanical power or reaction torque: the sun, the ring, and the carrier. With the input of torque and speed at one of these three elements, reaction torque can be applied at one of the other two elements, and output torque and speed taken at the remaining element. This kinematically allows for six different combinations of input and output torques and speeds, or gear ratios, from a simple planetary set.

The tabular method works as follows: 1. Hold any member of a gear train and turn another member one turn. Record the resulting rotational displacement of each member of the gear train. (Note: the calculation is easier if the initial member is common to each gearset in the train.) The resulting numbers are proportional to the speeds of all the members of the gear train. 2. Choose any of the rotating members for the next possible stationary member and add an equal quantity of opposite sign to its speed value. This makes its speed value zero. Then add this same quantity to the speed values of all the other members. This gives a definite speed value to the previously held zero speed member and changes the speed values of the other members. 3. Repeat this procedure until the speed of every member has been equated to zero, while the other members have changed speeds to corresponding new values. 4. Now examine the potential speed relationships of the compound gear train for usable forward and reverse ratios. The full potential of the gear train is revealed quickly by this simple algebraic addition method.

The term underdrive gear ratio refers to a gear train operating with an input-to-output torque-multiplying and speeddividing ratio. Conversely, an overdrive ratio refers to a gear train operating with an input-to-output torque-reduction and speed-increasing ratio. A forward gear ratio is where the input and output elements rotate in the same direction, and a reverse ratio is where the input and output elements rotate in opposite directions. The six gear ratios available from the simple planetary are two forward overdrive ratios, two forward underdrive ratios, one reverse underdrive ratio, and one reverse overdrive ratio. The higher forward overdrive and the reverse overdrive ratios are typically too high to be of much utility. The two forward underdrive ratios, where, in one, the ring gear is the input, the sun is the reaction member, and the carrier is the output, and, in the other, the sun is the input, the ring is the reaction member, and the carrier the output, require complicated switching between the elements. Therefore, most planetary

Two examples will illustrate the tabular method. Figure 3.1.1 shows the complete analysis of a load-dividing compound planetary gearset. Figure 3.1.2 shows a similar analysis of a “Ravigneaux” train.

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Fig. 3.1.1  Analysis of load-dividing compound planetary gearset.

Fig. 3.1.2  Analysis of Ravigneaux gear train.

3.1.2

The tabular method, though it can become somewhat visually unwieldly with larger combinations and numbers of ratios, has a long history in practice and lends itself to computer applications better than most other methods.

Number of Pinions

After gear ratios are selected, the next thing the designer must determine is the number of planet pinions to use. Fewer than three pinions are seldom worthwhile unless extreme reduction ratios are needed. (The two-pinion design provides the most space for large pinions and sometimes makes possible designs that would be impossible with more pinions.) More pinions than three can be used. The number of pinions is limited only by the space available for pinions and for carrier structure. Four-, five-, and six-pinion planetary gear trains are used in many transmissions. It should be noted that load sharing is particularly important with such planetary sets, for gear life, bearing life, and gear noise. Even if all the pinions

The second method referred to is the lever analogy method, detailed in SAE 810102, “The Lever Analogy: A New Tool in Transmission Analysis” by Howard L. Benford and Maurice B. Leising. The lever analogy method is very visually comprehensible and can greatly simplify the analysis of any gear train as compared to the tabular and other methods. (See Section 3.5 of this book. It is also referenced and used in Section 3.2, “Transmission Gear Design for Strength and Surface Durability.”)

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RULE 2: Number of positions = R – S or S2 – S1

are loaded, the load distribution may not be equal between them all. The challenge goes up with the number of pinions, as well as with compound gearsets such as the Ravigneaux gearset. The level of ideality of the gear teeth involute profiles are a major factor in the load sharing. Pinion shaft restraints impact the load sharing as well. Shaft staking, press fits, or radial set screw use, as well as material wear between the pinion shaft and the locating holes, all can have an impact.

Figure 3.1.3 illustrates the “least-mesh angle” of a simple planetary set. The pinions must mesh in position increments equal to the least-mesh angle in order to assemble with both the sun and ring gears. The least-mesh angle for a simple planetary gearset (of the type covered by Rule 1) is: 360° R+S



First of all, if standard or near-standard gear tooth proportions are used, the sun gear and ring gear of a simple planetary gearset must both have either odd or even numbers of teeth, or they will not fit. This follows from the following simple relationship:

(3.1.1)

R = S + 2P



where the letters stand for the numbers of teeth in the ring gear (R), sun gear (S), and planet pinion (P). Since R, S, and P must be integers, it follows from the above relationship that R – S must be an even number. When it is realized that the pitch diameters of the gears are proportional to the numbers of teeth, the relationship must hold if the gears are to mesh with their pitch diameters in tangent contact. However, using non-standard tooth proportions, it is possible, and in some cases desirable, to violate this particular relationship by one or more teeth. (Since the ring gear has more teeth than the sun gear, it is often able to accommodate more of the nonstandard condition than the sun gear.) Now, R – S can be either an even or an odd integer, and not all the pitch circles will be in tangent contact. Planetary gearsets have definite numbers of positions where pinions can fit in mesh simultaneously with the mating gears. Formulas for these numbers are given here for convenience of reference. Their derivations will be presented later. Four configurations can be handled with two rules:

Fig. 3.1.3  Least-mesh angle of simple planetary gear. If evenly spaced pinions are a requirement, the angle between their axes must be:

Rule 1 covers gear trains in which the driving and driven members rotate in opposite directions when the carrier is stationary. This includes:

360° n



(3.1.2)

where n is the number of pinions to be used. Then, for evenly spaced pinions, this angle must be an integral multiple of the least-mesh angle. Thus:

• the simple planetary (sun gear and ring gear) with individual (not double) pinions • two sun gears linked by double pinions



RULE 1: Number of positions = S + R or S1 + S2 Rule 2 covers gear trains in which the driving and driven members rotate in the same direction when the carrier is stationary. This includes:



360° n = an integer 360° (R + S) so

(R + S) = an integer n

(3.1.3) (3.1.4)

For a double pinion gearset (Fig. 3.1.4),

• sun gear and ring gear with double pinions • two sun gears with individual (they can be stepped) pinions



least-mesh angle =

360° (R − S)

(3.1.5)

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and for evenly spaced pinions,

and for evenly spaced pinions,

(R − S) = an integer n

(3.1.6)



S1 + S2 = an integer n

(3.1.8)

The preceding formulas are developed in the following section. The Ravigneaux planetary gearset must meet all the requirements of the above formulas.

3.1.3

Spacing Planets

In order to begin the design of the planet carrier, it is necessary to determine the number of planets and their spacing. The number of planets is determined from stress and life duty cycle evaluations on the gears, as well as the pinion bearings. The spacing is a function of the number of pinions and the numbers of teeth in the gears mating with the pinions. The spacing analysis and formulas are shown for the three most common gearsets. The method can be used to derive the spacing for any arrangement of planetary gears. Figure 3.1.6 shows a simple planetary gearset. In considering the gearset, we assume that a single pinion is meshed with the sun gear and ring gear. It is desired to find the smallest angle between the meshing positions of the pinion as we lift it out of mesh with the gears and move it around the sun gear. It can be seen by inspection that the smallest angle is found by pulling the pinion out of mesh with the ring gear and rotating it while still in mesh with the sun gear teeth until it can be meshed again with the ring gear. Since the pinion teeth

Fig. 3.1.4  Double pinion gearset. For a long and short pinion meshing with two sun gears (Fig. 3.1.5),

least-mesh angle =

360° S1 + S2

(3.1.7)

Fig. 3.1.5  Long and short pinions meshing with two sun gears.

Fig. 3.1.6  Simple planetary gearset. 3-5

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turn about the axis of the pinion, the size of this “least-mesh angle” is affected by the direction of rotation of the pinion as we turn the carrier around the sun. The fact that the pinion turns in the same direction as the carrier as we turn the carrier around the sun gear makes the least-mesh angle of the simple planetary gearset quite small. This analysis assumes for the convenience of calculation that the ring gear turns one tooth or one circular pitch, and the angle the carrier moves through is the angle required to move from one tooth to another on the ring gear (Fig. 3.1.7).

Having found the least-mesh angle (angle AOB), the pinions must be meshed in position increments of this angle in order to assemble both ring and sun gears. Failure to space the pinions accordingly will result in gears that will not assemble. In order to have evenly spaced pinions, the angle between them must equal 360°/n, where n is the number of pinions to be used. If the pinions are to be evenly spaced, then Equations 3.1.2, 3.1.3, and 3.1.4 apply. For a double pinion gearset (Fig. 3.1.8),

360° angle POA′ = R

angle AOB = angle POB¢ ⎛ 360° ⎞ angle POA¢ = ⎜ ⎝ R ⎟⎠

angle AOB + angle A¢ OB¢ = angle POA¢ but:

angle POA¢ = angle POB¢ – angle A¢ OB¢

⎛ S⎞ angle A¢ OB¢ = angle AOB ⎜⎝ ⎟⎠ since arc A¢ B¢ = arc AB R

⎛ S⎞ angle A¢ OB¢ = angle AOB ⎜ ⎟ ⎝ R⎠

⎛ S⎞ ⎛ 360° ⎞ angle AOB + angle AOB ⎜⎝ ⎟⎠ = angle POA¢ = ⎜⎝ ⎟ R R ⎠

⎛ S ⎞ ⎛ 360° ⎞ angle AOB – angle AOB ⎜⎝ ⎟⎠ = ⎜⎝ ⎟ R ⎠ R

S ⎞ ⎛ 360° ⎞ ⎛ angle AOB ⎜1 + ⎟ = ⎜ ⎟ ⎝ R⎠ ⎝ R ⎠

⎛ R − S ⎞ ⎛ 360° ⎞ angle AOB ⎜⎝ ⎟ =⎜ ⎟ R ⎠ ⎝ R ⎠

⎛ R + S ⎞ ⎛ 360° ⎞ = angle AOB ⎜ ⎝ R ⎟⎠ ⎜⎝ R ⎟⎠

⎛ 360° ⎞ angle AOB = ⎜⎝ ⎟ = least-mesh angle R − S⎠

⎛ 360° ⎞ angle AOB = ⎜ = least-mesh angle ⎝ R + S ⎟⎠ where: R = number of teeth in ring gear S = number of teeth in sun gear

Fig. 3.1.8  Analysis of a double pinion gearset. Evenly spaced pinions: ⎛ R − S⎞ ⎜⎝ ⎟ n ⎠ = an integer

Fig. 3.1.7  Analysis of simple planetary gearset.

The next example will derive the spacing for a long and short pinion meshing with two sun gears (Fig. 3.1.9): 3-6

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Sun gear teeth Number of pinions

⎛ 360° ⎞ angle POA¢ = ⎜⎝ S1 ⎟⎠ = angle POB¢ + angle A¢ OB¢ but angle POB¢ = angle AOB



and, since

⎛ R + S ⎞ ⎛ 79 + 47 ⎞ ⎛ 126 ⎞ ⎜⎝ ⎟ =⎜ ⎟ =⎜ ⎟ = 31.5 n ⎠ ⎝ 4 ⎠ ⎝ 4 ⎠

The resulting quotient is not an integer, so the pinions cannot be equally spaced.

arc A¢ B¢ = arc AB,

⎛ S2 ⎞ angle A¢ OB¢ = angle AOB ⎜⎝ S1 ⎟⎠



where S1 and S2 are the numbers of teeth in the sun gears,

⎛ 360° ⎞ ⎛ 360° ⎞ least-mesh angle = ⎜⎝ R + S ⎟⎠ = ⎜⎝ 126 ⎟⎠ = 2.857143°

Note that two pinions can be placed opposite one another, since 126/2 = 63, an integer. Since four pinions cannot be equally spaced, the number of “least-mesh angles” between the two opposite pinions is an odd number. Therefore, we can determine the spacing angle by subtracting one-half the least-mesh angle from 90° or by multiplying the least-mesh angle by whatever integer makes the product nearly 90°. In the example shown, these angles are 1.42857° and 88.57143° (which equals 31 times 2.857143°), respectively.

⎛ 360° ⎞ ⎛ S2 ⎞ ⎜⎝ ⎟ S1 ⎠ = angle AOB + angle AOB ⎜⎝ S1 ⎟⎠ ⎛ S1 + S2 ⎞ ⎟ = angle AOB ⎜⎝ S1 ⎠

Fig. 3.1.10  Spacing of pinions on torque converter gearset.

Fig. 3.1.9  Analysis of long- and short-pinion meshing with two sun gears.

2. The Ravigneaux gearset (Fig. 3.1.11).

Therefore,

S1 = 23 P1 = 28 n = 3 pinions

⎛ 360° ⎞ angle AOB = ⎜⎝ S1 + S2 ⎟⎠ = least-mesh angle



S = 47 n=4

S2 = 28 P2 = 23 n = 3 pinions

Ring gear R = 79

For equal spacing of planets, ⎛ S1 + S2 ⎞ ⎜⎝ ⎟ n ⎠ = an integer



Let us examine some commercial examples to illustrate the use of these relationships. 1. A production torque converter gearset (Fig. 3.1.10). Ring gear teeth R = 79

Fig. 3.1.11  Ravigneaux gearset. 3-7

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The front gears form a simple planetary gearset.

design goals of durability and quietness in a smaller package than with the use of handbook-proportioned gears.

⎛ R + S1⎞ ⎛ 79 + 23⎞ ⎜⎝ ⎟ =⎜ ⎟ = 34 n ⎠ ⎝ 3 ⎠



Geartrain kinematic architecture arrangements offer further opportunity to the transmission designer. The designer can select the input, output, and reaction members, and the way in which the planetary gears are coupled. Depending on these selections, tooth loads can differ significantly between geartrains of similar size and ratio in a given application.

The simple planetary gearset will permit equal spacing of the three pinions. The rear sun gear S2, the pinions P1 and P2, and the ring gear form a double pinion gearset: ⎛ R − S2 ⎞ ⎛ 79 − 28 ⎞ ⎜⎝ ⎟ =⎜ ⎟ = 17 n ⎠ ⎝ 3 ⎠



3.2.1

This again permits equal spacing.

An example to illustrate the effect of geartrain selection is presented in Fig. 3.2.1. Planetary geartrain arrangements #1 and #2 were chosen to illustrate the potential for major differences in tooth loading due to the kinematics of the geartrains. In this example, no attempt was made to study other factors important to transmission design, such as tooth meshing frequency, gear rotational speeds, and how to use the gears to obtain the other speed ratios needed for a practical transmission. Both geartrains give reduction ratios of 2.452, even with slightly differing tooth counts. However, geartrain #1 operates with much higher tooth loads, as will be shown.

The two sun gears and the pinions form another gearset that must satisfy the relationships. ⎛ S1 + S2 ⎞ ⎛ 23 + 28 ⎞ ⎜⎝ ⎟ =⎜ ⎟ = 17 n ⎠ ⎝ 3 ⎠



Geartrain Selection

This also meets the requirements. This gearset illustrates how the tooth numbers in a geartrain may require checking for planet spacing in several different arrangements before assembly without interface can be assured.

3.2 Transmission Gear Design for Strength and Surface Durability Original Author: E. L. Jones Chrysler Corp. (Ret.) Revised in 1991 by: E. L. Jones Engineering Consultant

Revised in 2005 by: E. L. Jones M. T. Berhan Ford Motor Co.

Fig. 3.2.1  Comparison of planetary geartrain arrangements.

H. Dourra DaimlerChrysler AG

If the internal gears of both geartrains have equal pitch diameters, thereby making the gearsets equal in size, the input gear teeth of geartrain #1 will be loaded 2.13 times as much as those in geartrain #2 for equal input and output torques. This results from the input torque being applied at the pitch diameter of the sun gear in the first case and at the pitch diameter of the annulus, or ring, gear in the second case. Under input torque that would produce 100 units of force at each of the mesh points of geartrain #2, the tooth loads in the front and rear gearsets of geartrain #1 would be 213 and 145, respectively. See Table 3.2.1 for a comparison of the element torques, and consequently, the tooth loads.

M. B. Leising DaimlerChrysler AG

Transmissions for passenger cars and light trucks can be relatively compact and light in weight, when considering the engine powers to be accommodated. One main reason for this is that the heaviest loaded gears in such transmissions are often either lightly loaded or idling during most of the life of the vehicle. This permits the higher-stressed gears to be designed with finite but acceptable fatigue life using the proper selection of dimensions and materials. Economies of mass production make it feasible to use special tooth proportions in such gears because cutter life is distributed over many identical gears. This specialization of cutters makes it possible for the automotive transmission engineer to meet

The reason for the difference can be understood with the aid of lever diagrams of the geartrains (Fig. 3.2.2). Lever diagrams like these are useful for calculating the magnitudes and directions of geartrain element torques and speeds. The

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Fig. 3.2.2  Lever diagrams of planetary geartrains. Using lever analogy equations, the overall ratio for each geartrain is calculated as follows:

paper that popularized the use of lever diagrams was SAE 810102, “The Lever Analogy: A New Tool in Transmission Analysis” [1]. (See Section 3.5 of this book.) Geartrains in the lever analogy method are represented as free-body diagrams of simple vertical levers. The horizontal normal forces on the levers represent actual element torques. The horizontal motions relative to the reaction points represent actual element rotational velocities. The lever dimensions are proportional to the number of teeth on the sun and the ring. With the simple planetaries represented by individual levers as shown here, and the geartrains transformed from left to right for direct comparison, the center points on each lever on the right are the carrier, the upper points shown are the suns, and the lower points are the rings. The sun to carrier dimension on each lever is proportional to the number of ring teeth in that planetary, and the ring to carrier dimension is proportional to the number of teeth on that sun. When planetaries are connected, the lever dimension between the connected elements must be identical. Therefore, all of the dimensions of one of the levers must be multiplied by a scaling factor that will give that equality. Figure 3.2.2 shows the result of applying those rules to geartrains #1 and #2.



Geartrain #1 ratio =

64 + 30 + 14.06 = 2.452 30 + 14.06

Geartrain #2 ratio =

28 + 19.29 = 2.452 19.29

For an input torque of 100 units, the output torque for both geartrains = 100 ¥ 2.452 = 245.2. For geartrain #1, the following lever forces are illustrated:

A comparison of these levers indicates that the forces representing the actual torques in geartrain #1 will be higher than in geartrain #2. With these diagrams, these torque values can be calculated.

Fig. 3.2.3  Geartrain #1 lever forces.

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Table 3.2.1  Torque Magnitude Comparisons Between Geartrains #1 and #2

An overall force balance of the levers yields the following: The force at point A, the ground connection, is:

 

245.2 – 100 = 145.2 In order to find the inter-planetary forces, X and Y, one of the planetary levers needs to be analyzed. A moment balance on planetary 2 around point A gives: X ¥ (30 + 14.06) + Y ¥ 14.06 – 245.2 ¥ (30 + 14.06) = 0

Geartrain #1

Geartrain #2

Planetary 1

Sun Ring

100 213.2

  45.2 100

Connections

X Y

313.2 213.2

145.2   45.2

Planetary 2

Sun Ring

68.1 145.2

  45.2 100

A force balance equation on planetary 2 yields:

These results confirm the earlier assertion that tooth loads can differ significantly between geartrains of similar size and ratio in a given application. The magnitude of these load differences can be large enough that the impact of geartrain kinematic architecture selection can go far beyond the effects obtainable in proportioning the teeth. Consequently, geartrain configuration and gear loading merit strong consideration in the early stages of a transmission design.

X + Y + 145.16 – 245.2 = 0

Solving the above equations for X and Y gives:

X = +313.2



Y = –213.2

The minus sign in the result of Y indicates that the lever force, or actual element torque, is in the opposite direction to what is indicated in Fig. 3.2.3.

3.2.2

If we apply the same analysis on geartrain #2:

In designing transmission gears, the designer seeks to avoid three principal modes of failure: bending fatigue, compressive fatigue, and scuffing. Another form of failure is splitting of gears, particularly planet pinions, under high load. This is not a tooth failure, but it is related secondarily to the bending stress in the teeth. Failure is caused by insufficient stock between the inner or outer diameter and the tooth root circle. In planetary pinions and sun gears, this is between the inner bore and the minor diameter. In ring gears, this is between the outer diameter and the major diameter. The wall section under the teeth must react to the tangential tooth load, while outer fibers are subjected on the bore side to compressive stresses from needle bearings or other reacting bodies and on the tooth side to tensile and compressive stresses imposed by tooth bending. Because of the strong impact of these stresses, there is no fixed rule to determine the amount of stock to provide under the teeth. A commonly accepted design rule is to have a wall thickness equal to or greater than the height, or whole depth, of the teeth. For example, there have been successful applications where the thickness under the root is slightly less than the whole depth of the teeth when the maximum tooth bending stress does not exceed 480 MPa (70 ksi).

Fig. 3.2.4  Geartrain #2 lever forces. Again, the moment equation around point A of planetary 2 gives:

X ¥ 19.29 – 245.2 ¥ 19.29 – Y ¥ 42.71 = 0

The force balance equation yields:

X + Y + 145.2 – 245.2 = 0

Solving for X and Y:

Modes of Gear Failure

X = +145.2 Y = –45.2

Tooth wear can be a problem in many fields of gear application. Automotive transmission gears are enclosed and lubricated with oil by design. Transmission gears usually have very hard, wear-resistant surfaces, so gear tooth wear is generally not significant. A gear tooth wear problem usually suggests the existence of low surface hardness, entry or generation of abrasive particulates, or a lubrication problem.

This shows that the inter-planetary torques are substantially higher for geartrain #1. Thus, at equal pitch diameters, tooth loads will be higher for the elements in geartrain #1 than for the corresponding elements in geartrain #2. The following shows a comparison of the magnitudes of the different element torques: 3-10

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Gear mounting deficiencies often manifest as noise and durability problems. Gear teeth can be thought of as cams designed to transmit uniform velocity. As such, they need to have the load distributed properly over the face for durability. To realize its designed load-carrying capacity, a gear must be positioned and supported with respect to its mate so that the heaviest-pressure portion of the tooth contact pattern lies within the intended boundaries under all load conditions. Proper conjugate action should be maintained throughout the entire mesh cycle. As a good practice, the full-load pattern should be distributed over at least two-thirds of the face. The contact must not bear heavily on an edge. Consequently, efforts should be made during the transmission design to provide a supporting structure with adequate resistance to displacement and angular deflections. Excessive deflections often cause noise problems before durability is impaired.

Almost all passenger vehicle transmissions use helical gears for quietness of action. In designing helical gear teeth, there can be a conflict between requirements for durability and for quietness in selecting such parameters as pitch, pressure angle, and helix angle. When a change is made in one of these to help quietness, it can effect durability, and vice versa. Changes that tend to smooth the transfer of load from one tooth to the next tend to influence durability and quietness together. Examples include involute contact ratio, also called transverse or profile contact ratio, helical contact ratio, also called axial or face contact ratio, and modifications of involute and lead to keep heavy contact off the tooth boundaries. (See Section 3.4 of this book, “Gear Design for Noise Reduction,” for how to calculate contact ratios.) Design parameters for transmission gears can generally be selected in accordance with the following:

A significant increase in capacity can also be made by increasing the number of planet pinions in the gearset to divide the torque among more tooth contacts. Although multiple pinions may not share the load equally, the benefit is almost always directionally positive. 3.2.2.1

3.2.2.1.1 Module, or Pitch

Use as fine a module, or pitch, as possible, consistent with tooth bending strength and manufacturing considerations. Select center distance and gear diameters to meet durability requirements. Metric normal modules (or normal diametral pitches) used in most current transmissions lie in the following approximate ranges, from courser to finer:

Gear Tooth Bending Strength

Tooth bending fatigue is an important type of failure to consider in the design of automotive transmission gears for durability. Figures 3.2.5a and 3.2.5b show a gear failure that was caused by bending fatigue.

• For planetaries, 2.25 to 1.0 (12 to 25) • For passenger car manual shift, 4.0 to 1.5 (6 to 17) • For light truck manual shift, 5.0 to 2.8 (5 to 9) 3.2.2.1.2 Pressure Angle

Normal pressure angles in use lie in the ranges of about 16 to 25° in manual transmissions and 15 to 25° in planetaries. For design for manufacturing, especially when building prototypes with existing tooling, it is important to match the cutting tools, such as hobs and shaper cutters, to the gear, because the pressure angle is generally fixed by the tool used. Lower pressure angles are often favored for quietness resulting from increased involute contact ratio and tooth compliance. The lower limits of the pressure angle, however, can be impacted by the beginning of undercutting on the gear tooth flank, such as seen with short lead hob design considerations. Excessive undercutting will weaken the tooth.

Fig. 3.2.5a  Bending fatigue failure, top view of failure surface.

3.2.2.1.3 Helix Angle

Helix angles are usually made as high as sun and ring thrust loads, subsequent pinion tipping moments and bearing loads, and tooth bending stresses permit (see the ISO and ANSI/ AGMA standards noted in Section 3.2.2.2). Higher helix angles increase helical contact ratios, thereby increasing

Fig. 3.2.5b  Bending fatigue failure, side view of failure through root areas. 3-11

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tooth load sharing and lowering noise generation and gear mesh transmission error. Helix angles in planetaries generally lie in the range of 15 to 25°. The higher limits on the helix angle impact the ease of manufacture, especially with external tooth roll finishing and ring gear internal tooth broaching. In manual transmissions, helix angles used for low-speed and reverse gears generally range from 19 to 31°. Helix angles for other gears in these transmissions may be selected to balance thrust on the countershaft. Helix angles as high as 45° have been used.

where:

3.2.2.1.4 Tooth Depth Proportions

Figure 3.2.6 shows a gear tooth layout in the normal section, with the equivalent spur gear construction required for determination of the form factor X, as set forth in [2]. (Although this is often shown as a graphical procedure for both visual and historical reasons, determining the X-factor and the profile in the root with respect to the tooling and how the gear is cut is now nearly exclusively performed by computer algorithms.) It should be noted that elastic deflection and multiple tooth load sharing aren’t factored into the Lewis and similar basic equations. These and other reasons frequently lead to detailed gear stress analyses being performed using finite element analyses for increased accuracy and insight into the true loading conditions and stresses. For detailed analytical equations, see the International Organization for Standardization (ISO) standard ISO 6336, in particular ISO 6336-3:1996 [3], and the American National Standards Institute (ANSI)/American Gear Manufacturers Association (AGMA) standards [4] for metric gearing and [5] for U.S. Customary unit gearing contain calculations which go beyond the Lewis formula as shown above.

Sb = bending stress at weakest section of tooth, Pa (psi) T = torque transmitted through gear being studied, N-m (lbf-in) N = number of teeth in the gear Z = length of path of contact in transverse section, m (in) F = face width, m (in) X = gear tooth form factor in normal section for tip loading, m (in)

Adjust addenda to balance bending fatigue life between meshing gears and to provide an involute contact ratio of more than 1.4, where possible. In multi-pinion planetaries as used in automobiles, the sun gear often accumulates stress cycles faster than the planet pinions. In such cases, the sun gear needs longer cumulative fatigue cycle life than the pinions, although as discussed later, reversed bending can mean the pinions require higher bending fatigue strength. 3.2.2.1.5 Root Clearance

Provide clearance adequate to permit use of full-radius root fillets where possible. This practice usually will not penalize bending strength because it can reduce the stress concentration considerably. The result is often a substantial net gain in bending fatigue life, accompanied by longer cutter life. When additional torque capacity must be obtained within a given space, and the existing cutters, profiles, and materials must be used, shot peening of the finished gears may add significantly to the capacity of the gears. Care must be taken to ensure that the shot peening properly reaches the root fillets to achieve the full benefits. 3.2.2.2

Gear Tooth Bending Stress

Highly refined methods have been developed for calculating gear tooth bending stresses. In automotive transmissions the relatively simple Almen-Straub modification [2] of the Wilfred Lewis formula has often been used for the initial calculation of bending stresses in helical gears. This formula, which Almen and Straub selected based on correlations to fatigue test results, takes the following form:

Sb =

3π T NZF X

Fig. 3.2.6  X-factor determination for gear tooth bending stress. Table 3.2.2 lists suggested maximum gear tooth bending stresses for passenger car transmissions of various types. These may be regarded as limiting values for gear stresses calculated by the foregoing method. Maximum net torque of the engine is often used as the limiting input value for manual transmissions, and converter stall torque is often used

(3.2.1)

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as the limiting input for torque converter-based automatic transmissions. In either type of transmission, if the input torque multiplied by the overall driveline ratio can produce wheel slippage for a target on- or off-road application, that tire breakaway torque is sometimes used as a less conservative limiting criteria. Conversely, if dynamic shock and/or driveline inertial loads are considered a risk to the gears and other components, the maximum input torque multiplied by some safety factor is sometimes used as a more conservative limiting criteria.

should be determined to properly design for the population of gears subject to such loads and cycles.

Table 3.2.2  Typical Maximum Gear Tooth Bending Stresses—Passenger Car Transmissions, Hardened Steel Gears Type of Transmission Manual shift Torque converter, automatic trans­ mission

Forward Gear Mode Pa (psi)

Reverse Gear Mode Pa (psi)

Fig. 3.2.7  S-N fatigue curves for gear tooth bending stress.

620¥ 106 (90 ¥ 103) 830 ¥ 106 (120 ¥ 103) 900 ¥ 106 (130 ¥ 103) 1030 ¥ 106 (150 ¥ 103)

It should be noted that the sun gear will accumulate cycles in proportion to the number of revolutions it makes with respect to the carrier. This number will increase linearly with the number of pinions in contact with the sun gear. The pinion will accumulate cycles at a rate dependent on the speed of the pinion with respect to the carrier. An additional factor in determining the fatigue life of the pinion is the fact that it contacts the ring gear as well as the sun gear. This produces stress reversals on the pinion teeth, whereas stresses in the sun and ring gears are applied mainly in the forward drive direction. The effect of this fully reversed bending on the pinions may require higher bending strength in the pinion gears than in the sun gears.

The table is a composite of stress criteria used by various passenger car transmission designers. Since some of these values are based on laboratory tests and others on vehicle tests, there is some uncertainty as to the level of gear lives in vehicles associated with the values. The table should be considered a rough guide, and no more. Calculated stresses in some transmissions have exceeded the typical maximums listed in Table 3.2.2 under certain conditions. Such applications probably were occasioned by increasing the engine torque to be applied to an existing transmission. In such applications, thorough analysis and testing is required to establish the acceptability of the highly stressed gearsets, especially if the above-mentioned dynamic loads are an additional concern.

3.2.2.3

Compressive Failure of Tooth Surfaces

Prolonged operation of gears at high contact stress can produce different types of compressive fatigue failure. Failure can begin with individual pits forming in the vicinity of the pitch line from high surface contact stresses. Pitting on the surface is often forced when the elastohydrodynamic lubricating film between the meshing teeth is lost and sliding shear is imposed on top of the compressive loading. Figure 3.2.8 shows pitting along the pitch line of a planetary pinion where some amount of water entered the transmission fluid, causing the film in the mesh to break down.

Stresses in non-shot peened gears in heavy-duty truck transmissions should be limited to about 550 ¥ 106 Pa (80 ¥ 103 psi) in forward speeds, and 620 ¥ 106 Pa (90 ¥ 103 psi) in reverse, for design purposes. This is because high torques are sustained for longer periods in a loaded truck, resulting in more rapid accumulation of high-intensity stress cycles. Figure 3.2.7 shows an example of S-N, or Wöhler, fatigue curves for gear tooth bending stress plotted against numbers of cycles to failure at those stresses [6]. Such curves can be applied to gears for all the speed ratios in a transmission. Using these curves, the allowable stress in each gear can be tailored to its predicted life requirement in cycles. The specific percentage of failure designated by the points along the curve, such as 10th percentile or median 50th percentile,

Fig. 3.2.8  Pitting. 3-13

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Design Practices: Passenger Car Automatic Transmissions

Φt = transverse pressure angle at pitch diameter ν = Poisson’s ratio

Spalling is a more extensive type of fatigue failure associated with high compressive loading. It is also referred to as flaking because the propagation of failure produces flakes of material that can break off from the surface. Unlike pitting, spalling generally originates below the surface, where the stresses can actually be higher than at the surface itself and where a case hardened gear’s strength drops going off toward the case-core interface. Figure 3.2.9 shows a spalled gear tooth with some additional damage from particulates.

The dimensionless 0.59 coefficient as derived applies in cases where mating gears are made of materials with equivalent moduli of elasticity and Poisson’s ratios of 0.3. The formula can be adapted to internal gears by changing the addition sign to a subtraction sign. As mentioned earlier, for added accuracy and insight into the true loading and stress conditions in the gear mesh, finite element analysis is often the next step taken beyond single-equation solutions such as this. Some tests have indicated that the surface fatigue life of hardened steel gears running under conditions of proper lubrication and cooling will be practically infinite for the purposes of the design if the calculated contact stress is 1400 ¥ 106 Pa (200 ¥ 103 psi) or less. Applying the principle of designing for finite life according to the duty cycles of the various gears, contact stresses as high as 3400 ¥ 106 Pa (500 ¥ 103 psi), for example, have been applied to low-speed gears of manual transmissions. Second-speed gears have been stressed as high as 2400 ¥ 106 Pa (350 ¥ 103 psi).

Fig. 3.2.9  Spalling. The actual mechanics of the contact stresses and failures are complex and can sometimes be hard to delineate. The terms pitting and spalling are often used loosely and interchangeably out of habit. In these instances, they are only further specified by noting whether the failure origin is surface initiated or subsurface initiated. The classical definition of pitting as surface initiated and spalling as subsurface initiated may be best to hold to in order to minimize any confusion.

Since truck operations under load involve greater usage of the lower speed ranges, levels of compressive stress in these gear applications and ranges generally must be lower than in passenger cars. As with bending, an S-N curve for compressive fatigue is helpful in designing such gears. One such curve for hardened steel gears was presented by Huffaker [7], and is reproduced here in Fig. 3.2.10.

In general, the comparative tendency toward compressive failures and away from bending failure increases with coarsening pitch and larger teeth. The reason for this is that the bending strength of gear teeth increases faster than their compressive strength as the teeth are made larger. For example, compressive failure is relatively less of a problem in the finer-pitch gears used in passenger car planetary automatic transmissions than it is in the coarser-pitch gears used in manual transmissions. Pitch line Hertzian surface contact compressive stress in external helical transmission gears may be calculated as follows: Sc =

⎛1 1⎞ Wt Ecos (ψ b ) ⎜ + ⎟ π (1 - ν2 ) F m p cos (Φt ) sin (Φt ) ⎝ d D⎠

1 1 = 0.59 Wt Ecos (ψ b ) ⎛⎜ + ⎞⎟ F m p cos (Φ t ) sin (Φ t ) ⎝ d D⎠ (3.2.2)

Sc = maximum compressive stress, Pa (psi) Wt = tangential tooth load at pitch diameter, N (lbf) E = Young’s modulus of elasticity, Pa (psi) ψb = helix angle at base diameter d = pitch diameter of pinion, m (in) D = pitch diameter of gear, m (in) F = active face width (axial), m (in) mp = involute contact ratio

Fig. 3.2.10  Compressive stress fatigue curve. Again, the values given are simply examples of stress criteria used by various transmission designers under varying circumstances and should be considered no more than rough guides. 3-14

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3.2.2.4

Gear Tooth Scuffing

Np ⎞ 2 ⎛ π np ⎞ ⎛ PVTp = ⎜ 1+ ρp − r sin Φ t ⋅ S p ⎟ ⎜ ⎟ ⎝ 360 ⎠ ⎝ NG ⎠

(

Scuffing of gear teeth, when the elastohydrodynamic lubricating film between meshing teeth is lost from high pressure, sliding velocities, and potentially lubricant flashing, and the sliding teeth wear heavily against one another, is not a very common failure in passenger car transmissions. The combination of modest levels of compressive stresses and lower tooth sliding velocities accounts for this. The potential for scuffing is often evaluated using a rating factor known as PVT. Planetary gears with relatively fine-pitch teeth tend to give automatic transmission applications a comfortable margin of safety against scuffing. Some larger manual transmissions run with calculated values of PVT scuffing factor approaching the historically accepted borderline scuffing criterion of 8.0 ¥ 107 N/sec (1.5 ¥ 106 lbf-ft per in-sec). (These generalizations hold for mineral oil based lubricants. Synthetic based lubes or mineral oil-synthetic blends may result in different scuffing behavior.) Heavier-duty units, with larger diameter gears and larger teeth, can encounter PVT factors exceeding this limit, with consequent danger of scuffing failures. It is recommended that such gears be checked for scuffing tendency by calculating the PVT factors at the tips of the gears. If a potential scuffing problem is found, relief may be obtained by changing the outside diameters of the gears, by modifying the tooth profiles for smoother tooth action, or by resorting to a lubricant carrying anti-weld additive.

and at the gear tip: SG = 4.77 ¥ 105

SG = 5740

S p = 5740

)

(3.2.8)

(3.2.11)



ρp = r02 − (rcos Φ t )



ρG = R 02 − (R cos Φ t )

(3.2.12)



Z = ρp + ρG − C sin Φ t

(3.2.13)

2

2



PVTp = scuffing factor at tip of pinion tooth, N/sec (lbf-ft per in-sec) PVTG = scuffing factor at tip of gear tooth, N/sec (lbf-ft per in-sec) Sp = contact stress, tip of pinion, Pa (psi) SG = contact stress, tip of gear, Pa (psi) np = speed of rotation of pinion, rpm Np = number of teeth on pinion NG = number of teeth on gear r = pitch radius of pinion, m (in) R = pitch radius of gear, m (in) Φt = transverse pressure angle Φn = normal pressure angle C = center distance, m (in) Tp = pinion torque, N-m (lbf-in)

(3.2.3)

)

Np ⎞ 2 ⎛ π np ⎞ ⎛ PVTp = ⎜ 1+ ρp − r sin Φ t ⋅ S p (SI units) ⎟ ⎝ 30 ⎟⎠ ⎜⎝ NG ⎠ (3.2.5)

(

(3.2.7)

and:

Tp C sinΦn (U.S. Customary F Z N p ρp C sinΦt - ρp units) (3.2.4)

(

(U.S. Tp C sin Φ n Customary F Z N p ρG (C sin Φ t − ρG ) units)

where:

For steel external gears, at the pinion tip:

(

(SI units)

Np ⎞ ⎛ π np ⎞ ⎛ PVTG = ⎜ 1+ (ρG − R sin Φ t )2 ⋅ SG (U.S. ⎟ Customary ⎝ 360 ⎟⎠ ⎜⎝ NG ⎠ units) (3.2.10)

The following scuffing factor formulas for external gears are derived in and expanded from [6]. The reader is further referred to [6] for internal gears.

Tp C sinΦ n (SI units) F Z N p ρp C sinΦ t – ρp

Tp C sin Φ n F Z N p ρG (C sin Φ t − ρG )

Np ⎞ ⎛ π np ⎞ ⎛ PVTG = ⎜ 1+ (ρG − R sin Φ t )2 ⋅ SG (SI units) ⎝ 30 ⎟⎠ ⎜⎝ NG ⎟⎠ (3.2.9)

Please note that while the terms scuffing and scoring, as used in earlier versions of this work and elsewhere, have often been used interchangeably, scoring is considered a more severe occurrence of scratches and caused by the loss of film or by abrasion.

S p = 4.77 × 105

)

(U.S. Customary units) (3.2.6)

)

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Design Practices: Passenger Car Automatic Transmissions

F = active face width, m (in) Z = length of path of contact, m (in) ρp = involute radius of curvature at pinion tip, m (in) ρG = involute radius of curvature at gear tip, m (in) r0 = pinion outside radius, m (in) R0 = gear outside radius, m (in) (letter symbols conforming to [8])

One most common group consists of carburizing grades of alloy steel such as American Iron and Steel Institute (AISI)SAE 8620 chromium-nickel-molybdenum steels, AISI-SAE 5115 to 5130 chromium steels, and AISI-SAE 4023 to 4027 molybdenum steels. Typical examples of carburized case depths are 0.40 to 0.65 mm (0.015 to 0.025 in) for planetary gears and 0.75 to 1 mm (0.030 to 0.040 in) for manual transmission gears. Hardness in the finished gears is typically specified to 58 HRC minimum at the surface, and 25 to 40 HRC in the core. These gears are desired for their good fatigue strength and ease of processing. The control of maximum core hardness to about that 40 HRC value or less is essential to maintaining high fatigue properties. Too high a core hardness can lead to cracks rapidly propagating through the low ductility material.

The U.S. Customary unit Sp and SG contact stress equations are based on Hertz contact stresses for steel with a modulus of elasticity of 30 ¥ 106 psi and the dimensionless Poisson’s ratio of 0.3. The 5740 coefficients in front of the square roots are in dimensions of pounds1/2 per inch, as the coefficients themselves are the square roots of stress as force per area. These subsequently result in the contact stress equations giving values in pounds per square inch. These coefficient-based formulas are the form found in most references, where PVT calculations were generally based on using psi for contact stresses, inches for gear dimensions, and feet per second for sliding velocities.

Another group has employed what were considered throughhardening grades of alloy steels with higher carbon such as AISI-SAE 5132, 5140, or 5145 chromium steels, carbonitrided to produce hard cases with depths of around 0.13 to 0.30 mm (0.005 to 0.012 in). The gears are tempered at 175 to 220°C (340 to 425°F) for stress relief. This typically yields surface hardnesses of 58 to 60 HRC and core hardnesses of 45 to 60 HRC. Advantages claimed for this group are lower material cost due to reduced alloy content, good static strength, and relatively low distortion. AISI-SAE 4140 chromium-molybdenum steels and 4340 nickel-chromiummolybdenum steels can also be carbonitrided for even higher static and fatigue strength, but are not as common for passenger vehicle automatic transmission gears as they are for highly loaded shafts, for instance. Please note that while these different grades themselves are used, there are few, if any, production automotive transmission gears that are literally through-hardened today due to the crack propagation risk noted above.

When using SI units with lengths in meters, torque in Newton-meters, and an equivalent steel modulus of elasticity of 207 ¥ 109 Pa, the coefficients in front of the square roots in the contact stress equations become 4.77 ¥ 105 Newtons1/2 per meter, resulting in contact stress values in Newtons per square meter (Pa). As shown previously, the borderline PVT scuffing criterion in SI units then becomes 8.0 ¥ 107 Newtons per second as compared to the U.S. Customary unit value of 1.5 ¥ 106 lbf-ft per in-sec. When starting with gear dimensions in the more common millimeters, the conversion to meters for use with the above equations should not be forgotten.

3.2.3

There are other steel alloy grades and heat treat processes used for transmission gears. For instance, AISI-SAE 4615 and 4620 grade nickel-molybdenum steels are also used, and nitrating, nitrocarburizing, and induction heating are other heat treatments beyond just those listed above. The carbon contents used may vary from what is shown here. In addition, some modifications are often made with respect to the alloys included in each grade.

Materials for Transmission Gears

The selection of steels for transmission gears has historically tended to follow certain general groupings, with their surfaces given hardened cases by specific methods to specific depths. Effective case depth is typically defined as the distance from the hardened surface to the point where the material reaches a Rockwell C scale (HRC) hardness of 50 HRC [9, 10] or a similar value on an analogous scale such as 85.5 on the Rockwell HR15N scale. In automotive transmission gears, the effective case depth is generally limited to a maximum of about 25% of the tooth thickness at the mid-height or pitch line of the tooth. Total case depth, sometimes used as a specification instead of effective case depth and generally deeper than that point, is often defined as the depth from the surface to where the case properties and those of the underlying core material are essentially equivalent [11].

Please note the existence and continued growth in use of the Unified Numbering System (UNS) to designate metals and alloys that are in regular commercial standing and production. The nomenclature of AISI-SAE carbon and alloy steels has generally been carried over into the UNS system, with the addition of a prefix of “G” and a suffix of “0.” Thus, an AISISAE 8620 steel is designated G86200 in the UNS system, and an AISI-SAE designation of 5132 is designated UNS G51320.

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SAE and the American Society for Testing and Materials (ASTM) jointly publish SAE HS-1086/2004-ASTM DS-561 [12], which delineates the UNS system, the metals and alloys therein, and gives cross references of the different numbering systems in use. It also reprints SAE Recommended Practice J1086 JUL95-ASTM E 527 [12, 13], which covers the procedure by which UNS numbers are assigned. The carbon and alloy steel designations may also be found in SAE Standards J403 NOV2001 [14] and J404 JUN2000 [15].

8. AGMA Standard Gear Nomenclature—Letter Symbols, No. 112.04, American Gear Manufacturers Association, August 1965. 9. Rakhit, A. K., Heat Treatment of Gears: A Practical Guide for Engineers, ASM International, Materials Park, OH, 2000, p.52. 10. ASM Handbook Volume 04: Heat Treating, ASM International, Materials Park, OH, 1991, p. 454. 11. ibid., p. 454. 12. SAE HS-1086/2004-ASTM DS-561, Metals and Alloys in the Unified Numbering System, Tenth Edition, SAE International, Warrendale, PA, 2004. 13. 2005 SAE Handbook, Vol. 1, SAE International, Warrendale, PA, 2005, J1086 JUL95-ASTM E 527, “Numbering Metals and Alloys,” pp. 1.01–1.05. 14. ibid., J403 NOV2001, “Chemical Compositions of SAE Carbon Steels,” pp. 1.13–1.17. 15. ibid., J404 JUN2000, “Chemical Compositions of SAE Alloy Steels,” pp. 1.18–1.19.

In addition to using steels, some manufacturers have capitalized on the fact that internal gears often operate at considerably lower stresses than their mating external gears by making the internal gears out of pearlitic malleable iron of medium hardness such as Brinell hardness number (BHN, or HB) scale 163 to 207 HB. The gears are machined at that hardness and used without subsequent heat treatment. The lower hardness gives less wear resistance and more susceptibility to pitting, but such gears have been successful in applications where numbers of cycles at load tend to be low. One such application is for internal ring gears used only in reverse.

3.2.4

3.3 Manufacturing Considerations Affecting Transmission Gear Design

References

1. Benford, Howard L. and Maurice B. Leising, “The Lever Analogy: A New Tool in Transmission Analysis,” SAE Paper 810102, SAE International, Warrendale, PA, 1981. 2. Almen, J. O. and J. C. Straub, “Factors Influencing the Durability of Automobile Transmission Gears,” Part 2, Automotive Industries, pp. 488–493, October 9, 1937. 3. ISO 6336-3:1996, Calculation of load capacity of spur and helical gears—Part 3: Calculation of tooth bending strength, International Organization for Standardization, Genève, Switzerland, 1996. 4. ANSI/AGMA 2101-C95, Fundamental Rating Factors and Calculation Methods for Involute Spur and Helical Gear Teeth, Metric Edition of ANSI/AGMA 2001-C95, American Gear Manufacturers Association, Alexandria, VA, 1994. 5. ANSI/AGMA 2001-C95, Fundamental Rating Factors and Calculation Methods for Involute Spur and Helical Gear Teeth, American Gear Manufacturers Association, Alexandria, VA, 1994. 6. “Progress Report” by AGMA Automotive Gearing Committee, John C. Straub, Chairman, Sec. I—”Bending Stress of Spur and Helical Gears,” Sec. II—”Scoring Factor for Spur and Helical Gears,” No. 101.02, American Gear Manufacturers Association, October 1951. 7. Huffaker, G. E., “Compressive Failures in Transmission Gearing,” SAE Paper 600010, SAE Transactions, Vo1. 68(1960), p. 53, SAE International, Warrendale, PA, 1960.

Original Author: A. Hardy Hydra-Matic Div. General Motors Corp Revised in 1991 by: R. J. Garrett Trans Axle Prod. Mfg. Eng. Ford Motor Company This publication was offered as a guide to acquaint and familiar­ize the engineer with the various methods of gear manufacture. An understanding of these manufacturing methods and their related problems should enable the designer to produce a practi­cal design that will be economical to manufacture within com­mercial dimensional tolerance limits.

3.3.1

Full Topping Hob

To illustrate, consider a flywheel ring gear. This gear—with 176 teeth, 12 diametral pitch, and 12° pressure angle to ensure the proper rate of production—will demand a man-sized hob. Concentricity and accuracy of the major and minor diameter of the gear were prime considerations. This gear, in operation, is subject to a wide tolerance in center distance. There is danger of tip to root interference on the one end of 3-17

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Design Practices: Passenger Car Automatic Transmissions

excessive tolerances, and a lack of involute contact ratio on the other end. A full topping hob was selected to produce this gear because it has the ability to qualify the major diameter along with the profile and root. This hob has six threads for economy at the required production rate. Because six is not a multiple of the 176 teeth in the gear, the desirable feature of hunting teeth tends to average out errors. This process of blending out errors is actually the same one that adds tolerances.

Fig. 3.3.1  Effective tolerances of full-topping hob.

The actual dimensional tolerance of the hob tooth thickness at a specified depth is held to 0.0015 in (0.04 mm). The gear, in being cut, is forced to accept this tolerance plus errors in hub and spindle runout, hob O.D. runout, variation in depth of form, flute spacing, lead error, and thread spacing. These errors are interwoven with each other so that they are difficult to treat individually.

These wide tolerances were the price paid to confine the outer and root diameters to 0.010 in (0.25 mm). The blanks before hobbing are mounted ten on an arbor. Their outer diameters were 0.030 in (0.76 mm) in oversize to permit a nominal 0.015 in (0.38 mm) in stock removal on the radius.

The hob runout and depth of form will affect the major and minor diameters directly, and will indirectly add to the lead error of each thread on the hob. Lead errors, of course, will add tolerances to the tooth thickness on the pitch diameter of the part.

The gears, made of hot-rolled steel, SAE 1050, are heat-treated by flame hardening, and the varied degrees of hardness are appropriately controlled. In instances where the ring gear is shrunk on the flywheel, the temperature can be combined with the shrinking operation. This gear does its job well and is produced economically.

A study was made of these tolerances on this 5½ in. (140 mm) O.D., six thread, Class D, accurate unground hob. The possible errors add up to effective dimensions that allow the designer one of two choices shown in Fig. 3.3.1.

3.3.2

If it were possible for production to set each hob so that it would generate an exact outer diameter on the gear, the effective tolerance on this hob would reflect 0.0102 in (0.259 mm) on the tooth thickness along the pitch diameter.

Shaper Cutting and Shaving

Figure 3.3.3 shows an example of a gear in another category. This type carries more torque, requires more life, and is expected to be reasonably quiet. A gear with these requirements deserves the quality demanded of a gear in the power flow circuit of the transmission when the vehicle is in reduction, overdrive, or reverse. This particular gear was chosen because it shows the strong influence cutting tools have in dictating design.

The other theoretical possibility, illustrated on the right in Fig. 3.3.1 is the setting of the hobs to produce the exact tooth thickness on the gear. A 0.048 in (1.22 mm) tolerance would necessarily project itself into the major and minor diameters of the gear. The tolerance on the tooth thickness in this case was considered relatively unimportant; it dictated backlash of a gear that is not in the torque-flow circuit when the vehicle is in motion. The gear designer chose to hold the outer diameter because a closer tolerance on it would ensure proper involute contact ratio. Taking into account the hob’s dimensional tolerances, as well as the effective tolerances mentioned and manufacturing’s working tolerances, the designer was compelled to allow dimensions as shown in Fig. 3.3.2. The tolerances are: 1. Circular tooth thickness, 0.0124 in (0.31 mm) 2. Backlash with mating gear, 0.0164 in (0.42 mm) 3. Overpin size, 0.0684 in (1.74 mm)

Fig. 3.3.2  Flywheel ring gear. 3-18

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Obviously the gear could not be hobbed—there is no hob runout clearance. The undercut behind the gear should be wide enough to allow for overstroke of the shaper cutter and provide space for the chips between cutter and dead end of undercut. The required width of runout groove in shaper cutting can be 5/32 in (4 mm) minimum, and the minor diameter of the undercut should clear the outer diameter of the cutter. A more liberal undercut will help the manufacturing department prevent accidents that result in expensive cutter breakage.

The cutter must have a maximum number of teeth for long life. The maximum number will be limited by the capacity of the machine. An oversized cutter could cause adverse conditions detrimental to the maximum efficiency in the shaving process. For this gear, the Processing Department recommended a cutter with an outer diameter of approximately 8 in (200 mm) to operate on a cross-axis of about 10° to 11°. It is the gear designer’s duty to make an honest effort to satisfy the needs of good production. If for some reason the requirement is impossible, a suitable compromise must be made without sacrificing quality and with reasonable consideration to cost. Figure 3.3.3 shows that the Engineering Department was able to satisfy production by changing the contour, which in no way affected quality. There are many times, unfortunately, when satisfaction to both parties is not attained this easily. Figure 3.3.4 shows an internal gear of dead-end design that prohibits broaching. Here again, we must resort to the shaper cutter for our rough cut and a rotary shaving cutter for finishing. Unlike the external gear, the internal sets a fairly low limit on the size of the cutters. Maximum size is desirable for long life, but the size is restricted by many factors too numerous to mention here. Good literature is made available by the cutter manufactur­ers, and they welcome the opportunity to aid you in making the proper selection.

Fig. 3.3.3  Influence of cutting tool on design of part. In an original cross-sectional layout of the transmission, many problems concerning the manufacturing of gears are hidden. Additional layouts, such as the one shown in Fig. 3.3.3, are necessary. These are made by the gear designer. This layout was made to determine the proper contour required for necessary shaving cutter clearance.

The procedure for determining a suitable shaving cutter for the internal gear and providing necessary cutter clearances is very much the same as in the discussion relating to the external gear. The main differences are limited outer diameter of the cutter and, in this case, because the dead end is so near the teeth, a lower cutting cross-axis of 5° to 6°.

The shaving cutter relies on its cross-axis to the work for its ability to cut. On external gears the angle will normally range between 8° and 12°.

Unlike the action in external gear shaving, the pitch cylinder of the internal gear tends to interfere with the pitch cylinder of the shaving cutter. This mismatch is very comparable to that in a shaft operating off-axis to its bushing. This cylindrical end interference causes crown shaving of the lead in the internal gear, instead of the hollow lead, due to the crossaxis, as in the case of external gear shaving. Here again, the conventional or diagonal traverse shaving will wash out this natural crown in the lead. Where lack of space will prohibit oscillation, or if the radial feed shaving is preferred, modifications in the cutter are necessary to remedy this undesirable effect. The necessary modifications become excessive with a cross-axis over 6° and aggravate the problem of maintaining the cutter for proper life.

In the 8° cross-axis range, the cutting action is just beyond the border of cold-working. As the cross-axis increases, the cutting becomes more free. Beyond the 12° range, the cutter rapidly approaches the tendency to dig into the surface of the gear tooth face. In the case of the gear in Fig. 3.3.3, where the clearance between the end of the gear teeth and shoulder is critically small, there is a danger of inadequate stroke of the shaving cutter. This stroke, whether it be conventional (along the axis of the work) or diagonal (at some angle to it), is very essential. The stroking action of the shaving cutter will wipe out the hollow lead that would result if only the radial feed were employed.

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Design Practices: Passenger Car Automatic Transmissions

3.3.3

Broaching

or welding alone would not serve the purpose in this case. Several more options are now available, such as electron beam welding and laser welding.

The internal gear in Fig. 3.3.4 can be redesigned for broaching. The dead-end design would necessarily be eliminated. This could be done by isolating the flange from the gear portion of this part.

On its outer diameter, this flange is splined to the internal gear through a brake drum, which also serves as a package for a clutch drum, clutch piston, clutch plates, and pressure plate. On the inner diameter, the flange is splined to the sun gear and staked so that it must withstand a 1050-lb (476-kg) end thrust. In actual operation, whether it be drive or coast, the end thrust of the gear is always balanced with the end thrust of the helical spline so that the staking is only to ensure any small off-balance that may exist due to tolerances in variation of lead. Theoretically, there should be no need for staking here, but practically it does not work that way. Frequently, the advice concerning “too many eggs in one basket” could apply to the design of a gear. If a gear with a flange has an induction hardened race on it or a one-way clutch, another ground diameter, and possibly a spline, the odds for rejection of a very expensive part become too high to make a one-piece design practical. This could be good reason to make the flange separate from the gear.

Fig. 3.3.4  Internal gear of closed-end design. Attaching the flange in assembly often presents a problem. The solution usually involves a slight addition of length, an added operation such as staking or welding, added machining such as cutting a spline or snap-ring groove and, of course, there is always the possibility of added parts such as snap rings, dowels, or bolts.

It is also advisable to isolate a component requiring a drastic heat treatment when it is in the critical zone too near the gear teeth.

A part of this added expense may be eliminated, in some cases, by producing the flange of less costly steel, such as SAE 1010 or 1008, possibly stamped and with little or no heat treat.

Gear broaches have their advantage in that they produce more uniform gears as compared with those that are cut by the multiple number of shaper cutters that the broach may replace. An internal gear designed for broaching has ample clearance for the shaving cutter, so that lack of space, as sometimes is the case in a closed-end design, is never the restricting factor on the angle of cross-axis. The broach will produce, at practically no added cost, an undercut, if desired, for shaving. This undercut is difficult and impractical with a shaper cutter.

The type of flange and manner of its assembly to the internal gear is dependent mainly on the function of the flange. Three very successful designs of the open-end internal gear are pictured in Figs. 3.3.5 to 3.3.7. Figure 3.3.5 shows an example of a ring gear which manages to handle all of its own torque through an integral cone of a cone clutch. The flange, in this case, has nothing to do but pilot the gear, holding it concentric about its axis. Absence of torque and end thrust in this flange made it possible to assemble by staking for durability as well as economy.

On the other side of the ledger, the broach has its disadvantages. The cost of the broached internal gear will rise rapidly with any accident involving the broach, which, generally speaking, costs approximately 70 times as much as the shaper cutter. High volume is necessary for the broaching method.

Figure 3.3.6 shows a flange that does a little more work. It must transmit a low torque in second and fourth gear. Note the distance between the active part of the internal gear teeth and that zone in which the teeth might be subject to distortion due to the weld.

The broach is more sensitive to variations in the composition of steel in the blank of the gear. It occasionally has its problems of drifting, tearing, and snow-balling. The shaper cutter design and the techniques in cutting have increased the life of the shaper cutter so that its merits are

In Fig. 3.3.7, we see an internal gear that transmits its full torque through the flange into a sun gear. Obviously, staking

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Gears, Splines, and Chains

nearly enough balanced with those of the broach. Either choice could cause controversy.

Gear-cutting operations raise a long, sharp burr on both ends of the lead of a helical gear. These burrs are always more prominent on the acute angle edge of the gear tooth (Fig. 3.3.8). The elimination of this burr necessitates a chamfer either ground in after heat-treat of the gear or machined after the shaping operation while the part is still soft. Wire brushing after heat treatment, although costly in high production, will serve in a case where a smaller number of parts is involved. Gear honing of hardened parts is another process for eliminating nicks and burrs. This necessary chamfer for the removal of burrs on the ends of the tooth face is always held to a minimum, but with tolerances can significantly decrease the effective width and face contact ratio.

Fig. 3.3.5  Ring gear with flange of no torque load.

Any soft metal part on its way to heat treat is very susceptible to nicks. A chamfer at the tip of a gear tooth serves as protection for the involute. When the outer diameter of a gear is nicked in handling, the resulting protuberance is less likely to affect the active profile. The production department has another reason for requesting this chamfer. In the shaving operation, the chamfer enables the burr to slice off automatically. On the internal gear, the tip chamfer serves to present the gear to a quenching die free of shaving burrs. A shaving burr on the inner tip of the internal gear tooth could certainly obliterate the purpose of the die.

Fig. 3.3.6  Ring gear with flange of low torque load.

3.3.5

Semi-Topping Hob

On external gears, the tooth tip chamfer is very economically included in the hobbing operation, as shown in Fig. 3.3.9. The tool, commonly known as a semi-topping hob, in effect has a double pressure angle. The main body of the hob generates the involute. The ramp actually produces another short involute of a higher pressure angle with wider tolerances in its form, as well as location. This second involute we call a chamfer. Fig. 3.3.7  Ring gear with flange of high torque capacity.

3.3.4

The real cost of this chamfer is not appraised in terms of dollars. The unit of cost is actually thousandths of an inch in the length of the line of action or fraction of a tooth in the involute contact ratio. This chamfer is needed badly by production but is not too popular with gear designers; to them it means a problem of trying to recover the lost involute contact ratio. Figure 3.3.10 shows what this apparently insignificant item can do to the line of action.

Chamfers

The burrs on gear teeth, as small as they may seem, cannot be ignored. They can cause costly damages in the transmission by working free. Their removal will render the part safer in handling.

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Design Practices: Passenger Car Automatic Transmissions

This gearset, with maximum outer diameters, has a 1.534 involute contact ratio. In granting production with a 0.0060 in (0.15 mm) working tolerance on the outer diameters of both gears, we sacrifice 0.052 contact ratio. This loss is small when compared with the cost of the maximum 0.010 in (0.25 mm) tip chamfer, which brings the minimum involute contact ratio down to 1.308.

3.3.6

The increase in stress, if not prohibitive, and the possible decrease in the noise of the gearset should be evaluated from these same chapters. In converting the gear to 20 pitch and retaining the pitch diameters and base circles to prevent any change in the helix and pressure angle, we find that the numbers of teeth are fixed at 21.428 for the pinion and 44.286 for the sun gear. This is not a practical gearset, but for the sake of a true comparison, it should be described.

Finer-Pitch Gears

The addenda, dedenda, and tooth thicknesses will have 14/20 or 0.7 of the value of those of the 14 pitch gears.

Figure 3.3.11 is a 10x size layout of a 14 normal diametral pitch gearset shown in broken line. There are 15 teeth in the pinion, 31 in the sun gear. The helix is 21° and the normal pressure angle is 20°.

It is certain that the 14 pitch gears are balanced for strength and have a good line of action. These qualities and any others will be automatically retained in the 20 pitch gearset. The shaded teeth in Fig. 3.3.11 show the result of this conversion.

The gear designer is considering the possibility of converting these gears to 20 pitch (solid line) to be cut on the same blanks. The weights values explained in this section are on gear strength (by E. L. Jones) and noise reduction (by W. D. Route).

The line of action becomes shorter, but when divided by the fine base pitch, the maximum involute contact ratio shows a sizable increase. The costs of the 0.010 in (0.25 mm) tip chamfer in this case seems excessive. The loss in the line of action is approximately the same as that in the 14 pitch gearset, but this time it has to be divided by a base pitch 30% shorter. It seems that the finer-pitch gears have more involute contact ratio but pay a higher price for the tip chamfer that is necessary for the production of better-quality gears. The loss of contact ratio due to the chamfer is 70% greater in these finer-pitch gears. Since the sizes of transmissions are decreasing, finer pitch gears will become more popular; therefore, more precision machining will be required to maintain comparable results of the currently popular coarser pitches.

Fig. 3.3.8  Gear cutting operation.

Fig. 3.3.9  Hob tooth section of semi-topping hob generating tooth tip chamfer.

Fig. 3.3.10  Effect of tooth tip chamfer on line of section.

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Gears, Splines, and Chains

The maximum line of action in the 20 pitch gearset is dimensionally 0.7 of that in the 14 pitch gear layout. The base pitch is also of that same proportion, so that the maximum involute contact ratio in both cases is 1.534. Although the start of active profile (SAP) measured in degree roll from base circle, is the same in both sets, the tooth action is 30% closer to the base circle in the finer gear. Assuming a tolerance of 0.006 in (0.15 mm), in the outer diameters of the mating gears in both layouts, we find that the 14 pitch gears lose 0.052 contact ratio, the 20 pitch, 0.075. If the effective outer radii of these gears is decreased by 0.010 in (0.25 mm) in maximum chamfer, the final score becomes: 14 pitch gears—1.534:1.308 involute contact ratio; 20 pitch gears—1.534:1.207 involute contact ratio.

Fig. 3.3.11  High cost of tip chamfer on 20 pitch gears. Assume that the 14 pitch gearset in Fig. 3.3.11 is in production and performing very satisfactorily. The chief engineer decided on one just like it for a small compact car. The torque requirements of this car are somewhat less, so that a 20 normal diametral pitch gearset will give stress figures within the recommended limits. The proposed gearset will necessarily occupy a smaller space.

This more rapid loss in contact ratio on the finer gear will continue with the tolerances in center distance and eccentricities. There is one consolation for the finer-pitch gears. If both sets are of the same width, the coarser gears in this example will have 30% less face contact ratio.

It is interesting to note that in this case, where two gearsets are of the same numbers of teeth, helix, angle, and normal pressure angle, the layout of one gearset can be photographically repro­duced from the other. The proper scale would be inverse to normal diametral pitch. All factors, good or bad, will scale from the 14 pitch gearset into the 20. This photographic layout is perfect in all detail because tooth thicknesses, addenda, dedenda pitch circles, and base circles have a direct relation to normal diametral pitch. Unfortunately, there are elements that do not follow this ratio. The gear cutter manufacturers say that the tolerances are the same on tools in the range of 14 to 20 pitch. The Production Department’s ability to hold working tolerances is not related to pitch; the machinery and its inaccuracies will be the same. In referring to Fig. 3.3.12, it becomes apparent that the finerpitch gear is more sensitive to these tolerances.

Fig. 3.3.13  Height of shaving step can vary with its location along involute.

3.3.7

Shaving Step

Figure 3.3.13 shows the trochoid curve described by the tip of the pinion as it enters and leaves, mesh with the internal gear. The start of the active profile is only one point on this curve. It is suggested that more points are required to limit properly the shaving step. The involute of the internal gear is analogous to a landing strip at the airport. The SAP point is not unlike the spot the plane initially touches on landing. For a safe landing, the plane (in this case the tip of the pinion) must make a gradual glide path (trochoid curve) unobstructed by a high obstacle (shaving step). The permissible height of the shaving step will vary with its distance from the SAP point.

Fig. 3.3.12  Sensitivity of finer-pitch gears. 3-23

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Design Practices: Passenger Car Automatic Transmissions

3.3.8

In production, the height and location of the shaving step will be determined by tolerances in the operations of shaper cutting or broaching and shaving. The tolerances in the two cutting tools will also be involved.

Conclusion

In conclusion, the following points should be emphasized: 1. The production department needs practical tolerances to produce gears economically. These tolerances are a constant source of concern to the gear designer. 2. The gear must conform to the specifications set by the Engineering Department to satisfy the customer ultimately. 3. The successful achievement of the above two requisites depends on the designer’s knowledge and appreciation of production problems.

The gear designer, after setting up the proper equations, will go through the long, monotonous, and time-consuming operation of calculating points for the trochoid. Where possible, it is advisable to program this sort of equation into a computer. The trochoid will complete the involute specifications. This complete specification is shown in Fig. 3.3.14. The added curve will pass judgment on the shaving step and accept or reject it on the basis of its height as well as its location from the base circle. The height of the shaving step is shown in the involute check by vertical fine lines at 0.0002 in (0.005 mm) increments. The bolder lines represent 0.001 in (0.03 mm). The horizontal arcs are at ½° roll increments and designate locations along the involute in degree roll. (Degree roll is a term used in designating points along the involute profile.)

Engineers should employ this knowledge intelligently to bargain for closer tolerances. They should realize that calling for unrealistic accuracy on the detail of the gear does not necessarily make that part better. When tolerances are beyond the capabili­ties of the machine and the individual operating it, the Inspection Department will ask the engineer to make the decision of rejecting possibly good gears or increasing tolerances to pass them.

If the involute is visualized as a curve described by the end of a string unwound from the base circle, and the string is unwound 30° to generate the involute to a given point, that point on the involute is said to be at 30° roll from the base circle. The degree roll at the base circle is always zero.

Compromises are necessary. The Engineering, Production, and Inspection Departments must be capable and honest with each other to form a well-coordinated team.

The heavy line shown in Fig. 3.3.14 is a superimposed involute check. The check tells us that the involute is minus 0.0003 in (0.008 mm) from the SAP point to the effective inner diameter of the internal gear at 19.8° roll. The gear tooth has an acceptable shaving step 0.0012 in (0.030 mm) high and located at 27.3° roll; acceptable because it confines itself within the boundary of the trochoid as the involute checker sees it.

3.3.9

References

For detailed information on finishing gears, see AE-15, Gear Design. Chapter 25—Roll Forming of Gears at Ford Motor Company Leon N. DeVos This article explains how it works, how roll forming was developed by starting with the finished product, and how it eliminates tradi­tional chip generating techniques. Chapter 26—Hard Gear Finishing A. Donald Moncrieff, Consultant Zigmund Grutza, Di-Coat Corporation Background and different machines used in this process are explained in detail. Accuracy comparison to other methods, surface finish vs. durability, comparison, coolants, and filtration are covered in this chapter. Chapter 27—Hard Gear Processing with Azumi Skiving Hobs William E. Loy, Barber Colman Company “Skiving,” as applied to hardened gears, is explained. Also, gear blank preparation, suggested speeds and feeds, equipment required, maintenance of hobs, economics, coolants, and expected results are detailed in this article.

Fig. 3.3.14  Complete involute specification for internal gear. 3-24

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Gears, Splines, and Chains

3.4 Gear Design for Noise Reduction

trained ears should always be included in the final acceptance of a design, this practice does not yield reliable quantitative data to the gear engineer. This becomes apparent when we are reminded that the probable error of the single human observer is assumed to be on the order of ±6 phons (or ±6 dB at 1000 Hz), which is a total variation in sound pressure level of 4:1, and that the probable error of a jury of 10 will be ±2 dB. That is to say that a human jury cannot be expected to discriminate between sounds whose pressure levels are different by a ratio of 1.6:1. This does not consider the masking effect of ambient noise. Therefore, before quantitative data concerning the effects of design features on noise levels can be accumulated in statistically valuable amounts, acoustical equipment in some form must be applied to the measurement of the noise levels. Reliable electronic devices that correlate the subjective noise rating in the vehicle to an objective measurement of the gearset or transmission on the test stand are highly valuable tools for gear design and analysis.

Original Author: W. D. Route Chevrolet Motor Div., General Motors Corp. Revised in 1991 by: E. L. Jones Engineering Consultant D. K. Ducklow BorgWarner Automotive Revised in 2005 by: E. L. Jones M. T. Berhan Ford Motor Co.

3.4.1

The Challenges of Gear Noise

3.4.2

Gear noise is a difficult problem that often challenges engineers who are assigned the task of designing automotive transmission gears. It involves great complexity from the components to the powertrain to the vehicle system levels. There is no single answer as to why some gear designs perform quietly while others seem to defy attempts to eliminate or subdue noise. There are some design rules, however, that are popularly accepted as being generally helpful in gear noise reduction. They will be reviewed in this paper. There will be an attempt to explain how and why the application of these rules can help reduce noise. Most of these rules can be justified by hypothesis and popular usage, but few can be supported in all instances by well-documented data. For any rule proposed as helpful, there is likely a designer who has tried it once without success. While this does not in and of itself invalidate these rules, it points out the difficulty of the problem.

Noise Generation and Transmissibility

Noise and vibration in a transmission, as with any mechanical system, is primarily a function of three things. The first is the generation of the noise and vibration, or the forcing function. The second is the reaction and dynamic transmissibility, or frequency response function (FRF), of the overall vehicle system across the frequency spectrum of excitation, whether attenuating, magnifying, or simply transferring the excitation due to the system’s mass, stiffness, and damping properties. The third is the sensitivity of the receiver or target to the output noises and vibrations at their various magnitudes and frequencies; in this case what the passengers or observers can detect. These three are often referred to collectively as source-pathreceiver. (Noise, vibration, and harshness themselves are often referred to by the acronym NVH.) While in the previous paragraphs we’ve briefly discussed the sensitivity of human observers, we will primarily focus on the first two attributes of noise generation and system transmissibility for the rest of this work, and the things that impact them.

There are several reasons for the lack of highly repeatable test data correlating design parameters to their successful effect on improved noise control. One reason is the complexity of the tooth form itself. This makes it difficult to change one parameter significantly without changing some other feature. This difficulty is compounded by the problem of producing otherwise “identical” gears for comparison. Thus, the evaluation of a change must be made statistically with the ratings of many gears differing from one another only by production tolerances.

Gear noise in automotive transmissions, whether they are planetary or countershaft arrangements, is predominately seen at tooth meshing frequencies. The primary origin of the mesh noise is generally the elastic displacements resulting from the teeth entering and leaving engagement. The excitations can be seen at the frequencies of tooth engagement and their harmonics.

A second reason for the lack of data supporting specific design effects on noise is the widespread practice in the automotive industry of rating gears subjectively, usually by human observers in a vehicle on the road. While it can be argued that

Ideal involute gear meshing is defined by perfectly conjugate rolling of two infinitely stiff gears along their line of action, with a constant ratio of the angular velocities of the two gears. 3-25

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Design Practices: Passenger Car Automatic Transmissions

For parallel axis involute gears, this line of action is the common normal of the transverse profiles of the teeth in mesh, along the line of tangency in the transverse rotational plane between the base circles of the two gears. It passes through a fixed pitch, or rolling, point along the line connecting the gears’ axes of rotation.

also have different input and reaction elements. In the figure, the speed at which these gears produce maximum noise is indicated. It will be noted that both sets are noisiest at the same tooth contact frequency. The explanation for such a phenomenon is the resonant amplification by some part of the vehicle, either inside or outside of the transmission. One of the offending structures in this particular instance was the propeller shaft, which was vibrating in a bending mode, with three antinodes along its length.

As an ideal function, perfect conjugate action would involve no variation of the ratio of the angular velocities, and there would be no transfer of input rotational kinetic energy from a gear mesh to elastic deflection and strain energy. Variation from an ideal function can be seen as an error state. Any deviations from ideal conjugate action due to variation away from perfect tooth profiles, positioning and alignment, and/ or rigidity can be referred to as transmission error. Transmission error (TE) for involute gears is often measured in units of dimensional deviation away from a perfect involute profile, typically on the order of micrometers or microns (or microinches in the U.S. Customary units system). This is similar to the way that profile deviation is shown on an involute chart on a gear inspection print. A sign convention is often used whereby positive transmission error is taken as being in the direction external to, or “in front of,” or “above” the ideal involute surface profile and position of the tooth, and negative TE is taken as being internal to, or “in back of,” or “below” the ideal profile and position.

The gear noise generation we are discussing herein is during constant meshing, under unidirectionally powered load or coasting inertia. This is often referred to as gear whine, particularly when the airborne sounds generated strike the observer as having a generally high pitch. Depending on the observed tonal quality, magnitude, frequency, beat phenomena, etc., it can also be semantically referred to by growl, squeal, chirp, or other subjective phrases. Gear rattle, where torque reversals drive the teeth back and forth through the backlash of the mesh, can happen when there is a given rotational direction and mean drive torque under load that is overcome by the alternating torque, or when there is no given mean drive or coast load, just the torque reversals. Rattle as a noise and vibration source is less a gear design problem, in and of itself, beyond having reasonable values for backlash, than a system load control problem, and is best addressed as such.

Transmission error results in a non-ideal transfer of some of the rotational kinetic energy away from perfect input and output motion. This transferred energy becomes the excitation that generates noise and vibration out of the gear mesh to the rest of the system.

Significant reductions in observed gear noise can sometimes be accomplished by altering the transmissibility of the environment of the observer, particularly through the addition of greater damping to the system in the frequency ranges of greatest concern. For instance, vibration of and between components is often attenuated by including a compliant, energy dampening member in series with, or parallel to, the structural member or path in question. Airborne noise transmitted from one structure to another may be attenuated by adding dampening material, such as asphalt sheeting, to the receiving structure, such as the interior of a body panel.

Real gear teeth with finite rigidity and natural deviations from ideal profiles and positioning can be looked at as springs under the classic Hooke’s Law equation where force equals stiffness times displacement. For the particular system stiffness of a given gear mesh, a given amount of transmission error in the mesh produces a particular set of dynamic loads on, and displacements of, the shafts, other connected components, and the surrounding structures. They vibrate these components and structures as well as the body and passenger compartment, and generate airborne sound waves that are received by the ear as gear noise. They can also be picked up by the passengers’ tactile sense as structural vibrations. As noted, whether the initial excitations are amplified or attenuated before reaching the body depends upon the transmissibility of the entire system between the gearset and the body. This is illustrated in Fig. 3.4.1, which show the tooth contact frequency versus car speed of two different planetary gearsets that operate in a particular vehicle. While the gearsets are identical in data, they are totally different in mounting, gear blank configurations, and numbers of pinions. They

Fig. 3.4.1  Tooth contact frequency vs. car speed. 3-26

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Gears, Splines, and Chains

of the Ravigneaux. If the “S” and “R” members rotate in the same direction when the carrier is held, the addition signs change to subtraction signs, as shown in Eq. 3.4.3.

Nevertheless, the origin of the disturbance is still the gear teeth themselves, and one of the most fruitful areas in which to attempt a noise reduction is in the design of the gears.



Listed below are some of the main design parameters of a gearset that impact its noise generation:

nS = speed of gear element S; for example, sun gear nR = speed of other gear element R; for example, ring gear (in case of Ravigneaux gearset, other sun gear) nC = speed of carrier NS and NR = number of teeth in respective elements S and R, or pitch diameters

Module, or pitch Pressure angle Helix angle Angles of recess and approach Pinion spacing and tooth counts, including phasing and hunting 6. Mounting or supporting structure 7. Gear tooth tolerances and modifications

The derivation of Eq. 3.4.2 is given in Appendix A.

3.4.4

Before proceeding with a discussion of the items above, we will define the important terms, tooth contact frequency and contact ratio, and discuss them.

The greater the contact ratios, the greater the load sharing and generally the smoother the action among the teeth in mesh. Therefore, all other things being equal, the higher the contact ratios typically the lower the gear noise generation will be. Contact ratios are direct functions of the modules or pitches, the pressure angles, and the helix angles of gear meshes, hence the importance of these variables as design parameters for noise reduction.

This is the rate at which the teeth of the train are meshing. For a planetary train, it is the product of the number of teeth in any gear and the speed of the carrier relative to the reference gear, thus:

NR (n R − n C ) 60

(3.4.1)

where:

The mathematical expressions for these ratios are as follows: Z mp = (3.4.4) pb F tan Ψ b mF = (3.4.5) pb where:

f = tooth contact frequency, Hz NR = number of teeth in reference gear (sun or ring) nR = speed of reference gear, rpm nC = speed of carrier, rpm For countershaft arrangements, that is geartrains where parallel shafts carry gears meshing between the shafts’ axes of rotation, the carrier speed nC becomes zero, and Eq. 3.4.1 becomes the product of the speed of the gear and its number of teeth.

mp = involute contact ratio Z = length of line of action in the transverse plane pb = base pitch, transverse plane = p cos φ p = circular pitch, transverse plane φ = transverse pressure angle at pitch diameter mF = helical contact ratio F = active face width Ψb = base helix angle = arctan(tan Ψ ¥ cos φ) Ψ = helix angle at pitch diameter

Two other useful relationships for analyzing speeds and contact frequencies in planetary arrangements, particularly where all three elements have the same meshing speed, is given here:

nR NR + nSNS = nC (NR + NS)

Involute and Helical Contact Ratio

Involute and helical contact ratios are measures of the number of teeth in contact. The involute contact ratio is also called the transverse or profile contact ratio. The helical contact ratio is also called the face or axial contact ratio.

Tooth Contact Frequency

f =

(3.4.3)

where:

1. 2. 3. 4. 5.

3.4.3

nR NR – nSNS = nC (NR – NS)

(3.4.2)

Equation 3.4.2 applies to planetary sets that are reversing when the carrier is held, such as the simple sun-planet-ring configuration or the sun-planet-planet-sun configuration 3-27

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Design Practices: Passenger Car Automatic Transmissions

It can be seen from Eq. 3.4.4 that the involute contact ratio is the length of the line of action per unit base pitch. Similarly, the helical contact ratio is the ratio of the face width to the axial pitch pb cot Ψb (shown above as pb / tan Ψb). These ratios may be regarded as the average numbers of teeth in (a) transverse profile contact and (b) axial face contact. Although these ratios involve different parameters, they are often added to form a sum called “total contact ratio,” and written symbolically as “mT.” The integers bounding this sum represent the numbers of teeth that alternately have some portion of their length in engagement. Figure 3.4.2 illustrates contact lines in the field of action for a pair of external helical gears.

Most production transmission designs have a total contact ratio between 2 and 3 or just over. Involute contact ratio of at least 1.4 is considered desirable. The involute contact ratio, when all tolerances accumulate in the direction for the least ratio, should not be less than 1.2. The formula for calculating Z, the length of the line of action in the transverse plane, and subsequently the involute contact ratio, when the variation due to center distance, runout, tip chamfer, etc., must be considered, is given in Appendix B. There is more variation among designs in helical contact ratios; ratios between approximately 1.4 and 1.7 are most common. Referring again to Fig. 3.4.2, it will be noted that x is the distance the tooth element A travels before the next abrupt change in tooth load occurs; that is, when B leaves engagement.

x = pb [(mp – n) + (mF – K)]

(3.4.6A)

if

(mp – n) + (mF – K) < 1

and

x = pb [(mp – n) + (mF – K – 1)]

(3.4.6B)

if

(mp – n) + (mF – K) > 1

where: n = largest integer less than mp K = largest integer less than mF These relationships are useful when considering modification, as will be shown later.

3.4.5

Design Parameters Which Influence Noise

3.4.5.1

Module, or Pitch

It is generally agreed that fine-pitch gears are typically less noise-sensitive than coarse-pitch gears, with respect to noise generation. It is therefore often desirable to select the finest pitch consistent with the bending strength requirements.

Fig. 3.4.2  Helical gear tooth action. The total length of the contact lines can vary as action progresses through the field of action, depending on the numerical values of the involute contact ratio and the helical contact ratio. When either of those ratios is an integer, the summation of the lengths of contact lines remains constant throughout the field of action. Such a condition is thought to contribute to even smoother and quieter action, especially if both contact ratios are integral.

In automotive passenger car transmission planetary applications, normal modules of 2 to 2.25 (12 normal diametral pitch) may be considered relatively coarse pitch, and a normal module of 1.0 (25 normal diametral pitch) would be about the finest in production.

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Gears, Splines, and Chains

For countershaft transmissions, where the tooth loads are usually higher, the pitches are generally coarser. Modules of 2 to 3 (8 to 11 pitch) are typical for the constant-mesh gears. Modules of 3 to 4 (6 to 8 pitch) are more typical for sliding gears. A reason often proposed for the quieter action of the finepitch gears is that involute and helical contact ratios are both linear functions of diametral pitch or inverse functions of module. Therefore, it is easier to obtain adequate teeth in contact if the pitch is fine. More teeth in contact means lower loads per tooth. However, for equivalent contact ratios, fine-pitch gears seem to be generally quieter. The explanation for this lies, it is thought, in the fact that for the same involute contact ratio, the tooth action remains closer to the pitch circle with a consequent reduction in specific sliding and therefore involute sensitivity. Specific sliding versus diametral pitch for a particular gearset is shown in Fig. 3.4.3. The increasing distance of the start of action from the base circle is shown in Fig. 3.4.4. All the other features of this gearset have remained constant; that is, involute overlap, center distance, and base circle diameter. The addenda, as shown in Fig. 3.4.5, have decreased with increasing pitch to keep the involute contact ratio unchanged.

Fig. 3.4.3  Specific sliding vs. diametral pitch.

There are those who also attach some significance to the fact that, for the same contact ratio, the relative sliding is less with the finer pitch. For our sample gearset, the relative sliding as a function of diametral pitch has the same general character as that shown for specific sliding versus diametral pitch (Fig. 3.4.3). If sliding is a significant consideration, then it must be presumed that the sliding interval at tooth contact frequency is capable of developing forces that generate gear sound. See Appendix C for further discussion of sliding and the forces involved.

Fig. 3.4.4  Distance from base circle to start of action vs. diametral pitch.

It is frequently assumed that the spring rate of finer-pitch gears is lower than that of coarser-pitch gears. In Fig. 3.4.6, the relative tooth stiffness of the same gearset is plotted as a function of diametral pitch. Note that the 15 diametral pitch gear is actually stiffer than the 7 pitch gear. The reason for this is that the tooth whole depth is decreasing (for a constant involute contact ratio) faster than the tooth thickness is decreasing. It is thought that this stiffening effect does not generally help noise control; it is probably more often a negative factor. As mentioned earlier, under Hooke’s Law where force equals stiffness times displacement, for a given dimensional deviation away from a perfect tooth mesh, the noise-generating forces are higher with higher stiffnesses. Therefore, it may be concluded that the quieter action of the finer pitches is a result of increased contact ratio with reduced specific sliding and perhaps relative sliding.

Fig. 3.4.5  Addenda vs. diametral pitch.

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all dimensional tolerances, the lowest point of contact will be a radial distance of 0.25 mm (0.010 in) above the base circle.” After quoting the rule, we must hasten to say that several successful production designs with relatively finepitch pinions extend the contact to within 0.13 mm (0.005 in) of the base circle. Some designers follow a rule that the lowest point of contact should not be closer than 8 to 10° of base circle roll. 3.4.5.3

In about 1930, the helix angle was added to the gears of automotive transmissions to improve quietness of action. The overlap obtained as a consequence of the helix contributes much to the relatively low noise level of automotive gears. As may be seen from Fig. 3.4.2, helical teeth in mesh begin and end contact at a point and spread their contact diagonally across the face of the gears. The effective spring rates of the teeth at the start and end of engagement are therefore reduced and, as with a lower pressure angle, the mesh will probably experience less load fluctuation as a consequence of dynamic transients at the start and end of engagement.

Fig. 3.4.6  Stiffness vs. diametral pitch. 3.4.5.2

Helix Angle

Pressure Angle

Normal pressure angles in planetary gearsets generally range from 15 to 25°. In this range, involute contact ratio decreases rather rapidly with increasing pressure angle. Therefore, from the standpoint of achieving a large or adequate contact ratio, the lower pressure angles are preferred. Although the range found may be similar, pressure angles on countershaft transmissions are on the average slightly lower than on planetaries in spite of the higher tooth loads. A common range is about 16 to 18° on constant-mesh gears and higher on sliding gears. The use of lower pressure angles in countershaft arrangements is probably a design compensation for coarser pitches and the consequent loss of contact ratio. In other instances, the lower pressure angles have been used to avoid pointed teeth resulting from large helix angles.

Helix angles of planetary gearsets generally range from 15 to 25°, while for countershaft gearsets, helix angles as high as 45° have been produced. The upper limitations on helix angle selection are generally the sun and ring thrust loads, pinion tipping moments and subsequent bearing life considerations, tooth bending stresses, and manufacturing limitations such as with roll-finished suns and pinions and broached ring gears. The choice of a planetary arrangement that affords the smallest tooth for a given input can permit the use of higher helix angles, resulting in higher helical contact ratios.

From the standpoint of noise reduction, lower pressure angles are generally considered attractive because they directionally reduce tooth stiffness, effectively stretching out the relative cantilever profile of the tooth. This reduction of the tooth spring rate is usually desirable because it tends to reduce transient loads encountered at the start and end of engagement, reduce the load variations produced by dimensional errors, and reduce the dynamic transmissibility of these loads through the geartrain out to the surrounding systems and structures.

The other quantity in determining helical contact ratio is face width. Here, the designer is limited by space. With too small a helix angle, to get up to a very useful helical contact ratio, say 1.2 to 1.4, the face width has to be that much larger. This can become impractical, or simply not worth the tradeoffs. Helical contact ratios much higher than those currently used in automotive gears could be effective in further reducing noise. To use this increased overlap, however, might well require greater precision than is currently found in mass production gears. This is an area where precise knowledge of the spring rate of the gear teeth and the involute, lead, and spacing accuracy capabilities of the production equipment should be made available to the designer. With this information, a study can be instituted to arrive at the greatest helical contact ratio practical.

The limiting considerations to a low pressure angle are proximity of the start of action to the base circle (high values of specific sliding), and bending (with excessive undercutting) and compressive stresses that increase with decreasing pressure angles. When considering profile undercut and proximity of the start of action to the base circle, a rule might be that, “considering

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3.4.5.4

Angles of Approach and Recess

encountered in automotive gears, the argument may still have some validity.

A design feature considered by some authorities as important in obtaining quiet tooth action is the proportioning of addenda, so that the angle of approach is small and the angle of recess large. In a planetary arrangement, a large recess between the sun and pinion will tend to produce a large approach between the pinion and ring unless the designer resorts to a lower operating pressure angle between the pinion and ring than between the sun and pinion. For countershaft transmissions, this arrangement of a small approach and large recess can be accomplished directly.

However, it is unlikely that gear teeth with the finish of production automotive gears, operating in a well-lubricated hydrodynamic environment, experience friction forces of significant value. For example, if the friction coefficient were as high as 0.1 (which would be a pretty sticky gearset), the normal force variation would be something less than 10%. On the other hand, teeth with poor surface finishes, which can result in asperity peaks traversing the lubricating film and introduce metal shear during the sliding action, might well be noisy for the reasons stated. Such gears, however, may be easier to improve by implementing good surface finish than by redesigning them with addenda modification.

For spur gears, the argument for this kind of modification is fairly clear; for helical gears, a bit less so. The tooth action is quieter during the angle of recess because of the direction of the friction forces during this interval. The force normal to the teeth in the transverse plane is a function of the friction coefficient between the teeth and can be expressed as follows: WN =

T in angle of approach R b (1 − μ tan φ)

(3.4.7A)

WN =

T in angle of recess R b (1 + μ tan φ)

(3.4.7B)

3.4.5.5

Pinion Spacing and Tooth Counts, Phasing, and Hunting

Pinion spacing in simple planetary gearsets is governed by the numbers of teeth in the sun and ring gear, and the number of pinions in the gearset. To be able to assemble between the sun and ring, pinions must be spaced around the carrier in integer increments of the “least mesh angle,” or LMA. This is defined by

where: WN = force normal to the teeth in the transverse plane T= input torque Rb = base circle radius φ = transverse pressure angle at instantaneous radius of contact μ = friction coefficient (See Appendix C for derivation of above equations.)

LMA =



360° 2π = NS + NR NS + NR

(3.4.8)

where:

NS and NR = number of teeth in the sun and ring

When the number of pinions, n, can evenly divide into the sum of the number of sun and ring teeth,

Differential sliding velocity components between the gears during approach and recess cause the friction force reversal. In the angle of approach, this normal tooth load increases with friction; in the angle of recess, this normal load decreases. Thus, during approach the teeth are pressed harder together with increasing friction. If the friction is sufficiently high such that μ ≥ cot φ, it could lock up the gearset in effectively the same manner as self-locking or non-backdriveable worm gears and power screw drives. Under such extreme conditions, it might be expected that the tooth action would be noisy. For helical gears, this argument becomes less striking because the line of contact along the length of the tooth is oblique. Therefore, on the same tooth, sliding can occur on both sides of the pitch diameter simultaneously with differing values. For the relatively moderate helical contact ratios

NS + NR n

(3.4.9)

such that this ratio is an integer, the pinions can be equally spaced around the carrier. They will share an equal number of circumferential mesh angle increments between them all. When this ratio is not an integer, the pinions cannot be equally spaced and must be located at positions with integer LMAs, typically one tooth space “ahead” or “behind” of what the equal spacing case would be. There are two most common spacing arrangements for simple planetary gearsets as found in production automatic transmissions. Equally spaced gearsets are generally the most popular. They help keep the design axisymmetric and help keep the net reaction load on the carrier at zero. When the

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pinions can’t all be evenly spaced, an even number of pairs of pinions can be used, where each pinion in each pair is located diametrically opposite its mate. For example, two pairs of two pinions in an unequally spaced four pinion set, where within each pair the two pinions are spaced opposite each other by π, or 180°, with one pair set either forward or behind the π/2 and 3π/4, or 90° and 270°, position angle to the other by half of one LMA to the next integer LMA increment position. (See Section 3.1 of this book, “Design of Planetary Gear Trains,” and Appendix D of this section for more details on calculating spacing for gearsets.)

better enumerated some of the analytical relationships that govern the multibody system dynamics of planetary gearsets. They have laid out some simple but significant equations which help determine the response of both equally spaced gearsets and not equally spaced but diametrically opposed pair sets at their system natural frequencies and their harmonics. Their equations as they have laid them out are similar to, but a bit more definitive than, the basic classical analyses stated above.

3.4.5.5.1 Phasing



κ = i ¥ Zj, modulo n

(3.4.10)

The choices of tooth counts, number of pinions, and spacing arrangements can greatly affect noise generation. These relationships govern the phasing, or relative timing, of mesh engagement, the subsequent dynamic load excitations, and how they interact. Different arrangements can excite or suppress different frequencies and give different noise generation responses, even for otherwise equivalent component designs, materials, manufacturing, and operating conditions. Therefore, depending on the system transmissibility and receiver sensitivity across the spectrum of excitation, the phasing arrangements chosen, just by themselves, can play a significant role in how noisy a particular gearset is and the subsequent NVH characteristics of the transmission and vehicle.



= n ¥ i ¥ Remainder(Zj/n), modulo n

(3.4.11)

Phasing in a simple planetary gearset is governed at each mesh by the ratio of the number of teeth on the ring or the sun to the number of pinions. Many classical phasing analyses were primarily concerned on a high level with the relative timing of the rotational engagement of all of the sun-topinion meshes and the relative timing of all of the ring-topinion meshes. If the ratio of the number of teeth on a sun or ring to the number of pinions was an integer, that mesh was referred to as phased, or in-phase. Phased meshes were considered undesirable for noise because of the simultaneous mesh engagements where the magnitudes of the engagement forces, and therefore the noises, directly add up. If the ratio of the number of teeth on a sun or ring to the number of pinions was not an integer and had a decimal remainder, the mesh was considered dephased or sequentially phased. The engagements did not all occur at the same time, therefore the force and noise peaks will not directly add up. If the ratio was not an integer and had a remainder of 0.5, the mesh was considered counter-phased, a particular type of dephasing or sequential phasing. Pairs of gears may engage at the same time, yet not all the meshes would peak at once but rather alternate, and some forces may directly cancel.

The modulo function, often written as mod or modulo (X/Y), modulo (X,Y), or X modulo Y denotes the integer remainder of the integer division of the integer X by the integer Y. It is numerically equivalent to Y times the decimal remainder of X/Y. For example, for the second harmonic, i = 2, of an equally spaced gearset with a sun of 33 teeth and n = five pinions, 2 ¥ 33 = 66, and 5 goes into 66 thirteen full times with an integer remainder of 1. The decimal remainder of 33 / 5 = 6.6 is 0.6. The decimal remainder of 2 ¥ 33/5 = 13.2 is 0.2. Therefore,

For equally spaced gearsets, [2] and [3] use the following relationship, referred to as the phasing index:

which also equals

= n ¥ Remainder(i ¥ Zj /n)

(3.4.12)

where: κ = phasing index i = ith harmonic of the excitation Zj = NS or NR = number of teeth in the sun or ring for the mesh in question n = number of pinions

from Eq. 3.4.10,

(2 × 33) modulo 5 = mod ⎛⎜⎝

2 × 33⎞ ⎛ 66 ⎞ ⎟⎠ = mod ⎜⎝ ⎟⎠ = 1 5 5

(3.4.13)

from Eq. 3.4.11, ⎛ ⎛ 33⎞ ⎞ = ⎜ 5 × 2 × remainder ⎜ ⎟ ⎟ modulo 5 = ⎝ 5 ⎠⎠ ⎝ 6 (5 × 2 × 0.6)modulo 5 = mod ⎛⎜⎝ ⎞⎟⎠ = 1 5



(3.4.14)

or from Eq. 3.4.12,

Kahraman [1], Kahraman and Blankenship [2], Parker [3], Lin and Parker [4], and others have gone a step further and

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(3.4.15)

attempting to change other details of the gears or system, can be a very effective and efficient way to control the NVH impact of the planetary.

When the phasing index κ equals zero, the excitation in the ith harmonic is in phase. The torsional rotational vibration on the sun or ring about the gear centerline in that mode is excited. However, the translational mode, whereby the sun or ring sees a net reaction and can be driven to vibrate radially outward from the gearset centerline, is suppressed. It can be seen from Eq. 3.4.11 that when the ratio Zj/n is an integer such that the remainder is zero, all of that mesh’s harmonics are in phase; the use of prime number tooth counts can help avoid this due to their indivisibility. Similarly, from Eq. 3.4.12, for any equally spaced gear mesh when i is equal to n such that the remainder of i ¥ Zj/n is zero, that nth = ith harmonic is in phase.

Another similar area for potential consideration might be the targeting of the simultaneous or alternate tooth engagement of a single pinion at both of the mating elements. In other words, to have a pinion engaging a tooth on the sun and another on the ring simultaneously or alternately. This requires that a particular relationship be held between the gear elements. In Fig. 3.4.7, the base circles and lines of action of the sun, pinion, and ring are shown for the case of the sun driving. Contact between the sun and pinion starts at point 1. For simultaneous engagement, the distance a + b + c must be an integral multiple of the base pitch. This would require a specific selection of target pinion O.D. and ring I.D. once the base circle diameters and base pitch have been chosen.

When κ equals either 1 or n – 1, the excitation in that ith harmonic is sequentially phased. The torsional rotational excitation on the sun or ring in that mode is suppressed, but the translational mode can be excited. When μ does not equal 0, 1, or n – 1, excitation in that ith harmonic is sequentially phased to where the torsional rotational and translational modes are both suppressed. Of these three phasing cases for equally spaced gearsets, this represents the most beneficial phasing arrangements for that particular harmonic in that particular mesh.

The effect of this latter type of tooth engagement phasing may be an untried area in automotive production, if not planetary practice overall. Indeed, the tolerances that might have to be accepted on the diameters may preclude such a precise arrangement from being worth the effort. For random tooth engagement, however, an arrangement embodying this concept might be more readily developed.



⎛ 2 × 33⎞ =1 = 5 × remainder ⎜ ⎝ 5 ⎟⎠



For unequally spaced but diametrically opposed pair sets, [3] and [4] further list the following simple phasing relationships which can still be used to mitigate gear noise. When the product i ¥ Zj is an even number, the pinions in each opposed pair are in phase with one another. The ith torsional rotational mode can be excited, but its translational mode is suppressed. Conversely, when i ¥ Zj is an odd number, the pinions in each opposed pair are counter phased. The translational mode can be excited, but the torsional rotational mode is suppressed. While these relationships for both equally spaced and unequally spaced gearsets are for ideal gears and system models, they are quite useful for their respective design purposes. Not all harmonics for any of these cases can be totally removed, as shown above. Different system transmissibilities can exhibit different sensitivities for different excitation modes and harmonics (although torsional rotational modes may be more generally the most impactful for automatic transmissions with coaxial planetaries under torque load). And real planetaries with real non-linearities can require more detailed dynamic modeling for more accurate noise prediction. But initial selection of the right phasing arrangement, or varying a noisy arrangement where possible before

Fig. 3.4.7  Condition for simultaneous engagement at sun and ring gears. 3.4.5.5.2 Hunting

Prime numbers and their indivisibility are also useful for allowing meshes to exhibit a property known as hunting. Hunting is when given teeth in a mesh contact every other tooth on their mating gear before they return to contact each other. Nicks, pits, or other deformations if present will not continuously contact the same mating point. The damage 3-33

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contact will be shared among various other contacting pairs, slowing the progress of further damage and therefore noise generation. Gear meshes are fully hunting when the two tooth counts are not divisible by any common multiple other than unity, such as with a 70-to-29 tooth mesh. Meshes are semi-hunting when their tooth counts can be divided by a common non-unity multiple, such as with a 70-to-28 tooth mesh commonly divisible by 2 and resulting in a 2.5 ratio. This means that there will be a repeating pattern of contact between certain teeth, but any potential damage contact will alternate pairs. Non-hunting meshes are when tooth counts in a pair are evenly divisible, such as with a 75-to-25 tooth mesh. Damage contact for a given pair of mating teeth will continuously repeat, allowing for more rapid progression of damage and noise generation. 3.4.5.6

the design stiffness. Crowning is used in both countershaft and planetary gear designs. It will be noted that in countershaft arrangements, the deflections between two shafts generally increase the backlash between their meshing gears. Therefore, the backlash specification may only need to be sufficient to avoid tight mesh, or contact on two sides of the gear tooth, resulting from dimensional tolerances such as center distance, tooth thickness, lead, and runout. Excessive backlash is objectionable for such considerations as gear rattle when unloaded, driveline noise and harsh engagement during torque reversals, and simple loss in beam strength. Backlash values are as variant as the number of designs but often fall in the range of 0.10 to 0.28 mm (0.004 to 0.011 in) as measured on nominal centers.

Shaft and Support Design for Countershaft Transmission Arrangements

The objective in shaft and bearing design for countershaft transmission arrangements typically is to obtain the highest degree of stiffness permitted by the size, weight, and dynamic transmissibility limitations of the system. Under load, the gears of the countershaft train are not only deflected radially, which results in reduced involute contact ratio, but they are also tilted due to the slope of the deflected shaft. This tilting produces end loading and loss of helical contact ratio. Loss of total contact ratio can be a major contributor to noise.

3.4.5.7

Shaft and Support Design for Planetary Gear Arrangements

In planetary gearing, the radial loads on the supporting structure due to torque loads are zero if the elements are precisely concentric (and, of course, if the pinions are equally spaced or diametrically opposite). Therefore, the primary objective is to achieve the very best concentricity between elements. Short of absolute concentricity, that which must be achieved is a mounting system that prevents eccentricities between the elements greater than the center distance shift permitted by reasonable backlash in the gears.

It is helpful in the initial design to study shaft deflection and slope analytically by such techniques as the conjugate beam method [5]. Attention is given to adequate case ribbing and cover design for maximum stiffness. Under maximum engine torque, calculated deflections and slopes of 0.13 mm (0.005 in) deflection and 0.002 rad slope in the plane of the axes are representative values. Limiting values of deflection at the gear meshes should be bounded by the minimum contact ratio allowable.

For example, when the eccentricities enforced by the mountings between the sun gear and carrier, or the ring gear and carrier, exceed the center distance shift allowed by the backlash of gears, the mounting system is required to deflect under forces provided by the gear teeth operating in tight mesh. These radial forces are a function of the spring rate of the mounting structure and can be of a magnitude to be destructive and exceedingly noisy. To reduce these forces requires one or more of the following:

In the development period, gear contact pattern studies, static and dynamic deflection studies, finite element analyses, and even stress coat techniques are helpful in measuring the deflections of the assembly and altering for maximum stiffness.

1. Improve the concentricity controls. 2. Increase the backlash. 3. Allow either the carrier to float with respect to the sun and ring gear, or the sun or ring gear to float with respect to the carrier and its pinions.

The practice of using some lead modification in the form of a crown on at least one of the two gears of each mesh to eliminate the end loading that will occur as the consequence of any deflection is almost universal in vehicular transmissions. Here, along the normal face of the tooth, the edges are curved inward somewhat. Since this lead crowning reduces helical overlap, the least possible is the most desirable. The least possible is defined by the amount of deflection permitted in

So-called floating gears are generally driven through loosefitting splines or lugs. While these do offer some constraint to a change in position, the centering force resultant acting on a

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real floating gear is generally relatively small when compared to the drive loads.

gear tooth dimensions. These tolerances are likely to undergo continual revision while the noise sensitivity of the design is being established by the production of statistically significant quantities of gears. Listed below are representative tolerances for this class of gearing that may be used as starting values. It is believed that these tolerances can be achieved with tools and processes conventional to the industry.

For example, consider the free-body diagram of a sun gear that is eccentric to the carrier center (Fig. 3.4.8A). If the tooth loads WNl-N2-N3 are all considered equal and their directions are along the lines of action, the summation of these forces is not zero but indicates the necessity for another force (vector force 0 to 5 in the polygon of forces in Fig. 3.4.8B), which must come from a further shift of the sun gear to run eccentric until it is in tight mesh. However, the tooth loads are not all equal for this eccentric condition. The tooth load at 0 to 1 will be less than at 2 to 3 or 3 to 4 because the “spread center” here has reduced the effective spring rate of the gear teeth and similarly increased it on the “closed center” condition occurring at 2 to 3 and 4 to 5. This unequal loading is in the direction to make the 0 to 5 vector approach zero and indeed reverse its direction so that the system might become stable. A free-body study of the ring indicates that a similar load stability relationship applies there.

1. Lead, external gears: a. ±0.0005 mm/mm (in/in) of face width. b. Lead variation between any two charted teeth not to exceed 0.001 mm/mm (in/in) of face width. 2. Lead, internal gears: a. ±0.001 mm/mm (in/in) of face width. b. Variation between any two teeth not to exceed 0.025 mm (0.001 in). 3. Involute: a. +0.0050, –0.0075 mm (+0.0002, –0.0003 in) b. Variation of involute form between any two teeth not to exceed 0.025 mm (0.001 in). 4. Spacing: a. Maximum tooth-to-tooth index error 0.0127 mm (0.0005 in). b. Maximum indexing error 0.025 mm (0.001 in). 5. Pitch diameter runout, maximum: 0.025 mm (0.001 in).

Whatever direction this unbalance force takes, it is by necessity small so that floating gears can effectively eliminate interference loads.

Similar to lead crowning, it is a common practice in automotive transmission gearing to use a modified involute profile. Often, the pinions and/or the sun have a “profile crowned involute” or “tip modification.” That is, looking at the involute checker trace of the profile, the involute is minus at the tip and/or at the root. Even with an unmodified mating tooth, this will produce a delayed entry and an early exit. Involute modification may be thought of as tapered backlash. At the point of tooth engagement with no modification, there may be interference because of deflection or spacing error (Figs. 3.4.9A and 3.4.9B). The modification provides some clearance at this point of theoretical start of engagement to avoid this interference. As the theoretical point of contact now moves down the line of action, this backlash tapers to zero clearance and the load is applied to the tooth at a rate depending on the modification taper and the spring rate of the gear teeth. It is desirable that this taper or modification wash out before the next abrupt change in tooth load, or before the distance x shown in Fig. 3.4.2 and defined in Eq. 3.4.6 has been traveled.

Fig. 3.4.8A  Schematic of structural forces.

Fig. 3.4.8B  Vector diagram of structural requirements. 3.4.5.8

Tolerances and Modification

The correct amount of involute modification is best achieved as a development project proceeding gradually from an ideal

A most important consideration in the design of quiet, durable transmission gears is the tolerances to be assigned to the

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involute. Such a development project involves noise measurements of a large enough sample of gearsets to ensure that a real change has been accomplished by the modification.

2. Select the finest pitch and lowest pressure angle consistent with the strength and stiffness requirements. 3. Avoid tooth action close to the base circle. 4. Favor a long angle of recess and short approach. 5. Select an even number of pinions and space to have half of them engage halfway in the interval of engagement between others. 6. Provide backlash, dimensional control of mounting, or floating elements to avoid tight meshes. 7. Modify lead and involute to compensate for tooth deflections and dimensional errors.

3.4.7

Fig. 3.4.9A  Gear tooth tip interference due to tooth deflection under load.

1. Kahraman, A., “Planetary Gear Train Dynamics,” Journal of Mechanical Design, Transactions of the ASME, v. 116, n. 3, pp. 713–720, September 1994. 2. Kahraman, A. and G. W. Blankenship, “Planet Mesh Phasing in Epicyclic Gear Sets,” International Gearing Conference, Newcastle upon Tyne, pp. 99–104, 1994. 3. Parker, R. G., “A Physical Explanation for the Effectiveness of Planet Phasing to Suppress Planetary Gear Vibration,” Journal of Sound and Vibration, v. 236, n. 4, pp. 561–573, 2000. 4. Lin, J. and R. G. Parker, “Planetary Gear Parametric Instability Caused by Mesh Stiffness Variation,” Journal of Sound and Vibration, v. 249, n. 1, pp. 129–145, 2002. 5. Timoshenko, S. and G. H. MacCullough, Elements of Strength of Materials, 3rd Ed., D. Van Nostrand, Princeton, New Jersey, 1949, p. 179.

Fig. 3.4.9B  Action of driven gear tooth tip at start of engagement. The set of tolerances to be assigned to the positioning of the gears with respect to each other is another important consideration. Proper positioning and alignment of the meshes is impacted by the control and piloting of the sun, pinions, carrier, and ring centerlines and pitch diameters. Even spacing of the pinions in the carrier through pinion pin hole diametral and true position tolerances and pinion bore-needle-pin shaft bearing clearances is crucial for proper load sharing and stress distribution. Pin hole true position is more sensitive and needs to be controlled tighter in the tangential direction, on the order of 0.0127 mm (0.0005 in), than in the radial direction, where requirements can be more on the order of 0.10 mm (0.004 in), due to mesh clearances, transmission error, and load-sharing concerns among the pinions.

3.4.6

References

3.4.8

Appendix A

3.4.8.1

Speed Relationships for Planetary Geartrains

A useful formula defining the speed of the three elements of a planetary train, the sun, ring, and carrier, is given below.

nR NR + nSNS = nc (NR + NS)

(3.4.A–1A)

where: nS = speed of gear element S; for example, sun gear nR = speed of other gear element R; for example, ring gear (in case of Ravigneaux gearset, other sun gear) nC = speed of carrier NS and NR = number of teeth in respective elements S and R, or pitch diameters, etc.

Summary

Some widely accepted design rules believed to aid in the control of gear noise are as follows: 1. Total contact ratio greater than 2.5, with a minimum involute contact ratio not less than 1.2.

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The velocity of point 1 on the gear S is

This relationship applies to all planetary gearsets, including those with double pinions, provided that the direction of the output rotation is opposite the rotation of the input when the carrier is held.

vS = nS ¥ DS ¥ K



Since this is a point common to both P1 and S, the velocities are identical or

If the rotation of the output is in the same direction as the input when the carrier is held, the signs of the equation change as follows:



vS = v p1 + vC

(3.4.A–1B)



nSDSK = −np1Dp1K + nCDSK

To illustrate, the derivation of Eq. 3.4.A-1A will be derived using a Ravigneaux train, as shown in Fig. 3.4.A-1. To match the signs in the figure with the above equations, we will keep a sign convention of + for clockwise rotation, − for counterclockwise rotation, and assume that the carrier, which is not shown, is rotating in the clockwise direction.



nSDS = −np1Dp1 + nCDS

nR NR – nSNS = nC (NR – NS)



(3.4.A-3)

(3.4.A-4)

And in a similar position at the common point 2, nR DR = −np2Dp2 + nCDR



(3.4.A-5)

At the point common to the two pinions; that is, point 3, np1Dp1 = −np2Dp2



(3.4.A-6)

Substituting Eq. 3.4.A-6 in Eq. 3.4.A-5, then adding Eq. 3.4.A-4 to the resulting equation gives Eq. 3.4.A-7. nR DR + nSDS = nC (DR +DS)



(3.4.A-7)

Since the numbers of teeth are proportional to the pitch diameters, Eq. 3.4.A-7 can be rewritten as nR NR + nSNS = nC (NR + NS)



3.4.9

Appendix B

3.4.9.1

Formulas for Involute Contact Ratio

Below are formulas for calculating involute contact ratios. They allow for the calculation of variation in contact ratios that arise from variations in blank diameters, center distance, runouts, and tip chamfers. mp =

Fig. 3.4.A-1  Speed relationships for Ravigneaux planetary.



Referring to Fig. 3.4.A-1, the velocity of point 1 on the pinion P1 is

For external gears:

v p1 + vC = −np1 ¥ Dp1 ¥ K + nC ¥ Ds ¥ K

Z=

(3.4.A-2)

where:

Z pb



(3.4.4)

1⎡ 2 2 2 d o − d 2b + Do2 − D2b − (2C) − (d b + D b ) ⎤ ⎦ 2⎣ (3.4.B-1)

For internal gears:

v = tangential velocity n = angular velocity Dp1 = pitch diameter of pinion P1 K = a proportionality factor depending upon units chosen for v, n, and D.

Z=

1⎡ 2 2 2 d o − d 2b + (2C) − (D b − d b ) − Di2 − D2b ⎤ ⎣ ⎦ 2 (3.4.B-2)

where:

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Z = length of line of action in the transverse plane pb = base pitch = p cos φ p = circular pitch, transverse plane φ = transverse pressure angle at pitch diameter do = outside diameter of pinion db = base diameter of pinion Do = outside diameter of external gear Db = base diameter of gear Di = internal diameter of internal gear C = center distance

Fig. 3.4.C-2  Velocities during recess.

These equations do not apply when there is profile undercut that reaches above the deepest point of contact.

3.4.10 Appendix C 3.4.10.1 Derivation of Forces Normal to the Teeth During Approach and Recess In Figs. 3.4.C-l and 3.4.C-2, the velocity components of a gear and pinion at the point of contact in the transverse plane are shown. In Fig. 3.4.C-1 the contact is in the angle of approach, while in Fig. 3.4.C-2 it is in the angle of recess. The tangential velocities of the pinion and gear at the point of contact are resolved into a common velocity component along the line of action (Vc = angular velocity ¥ base circle radius) and two sliding velocity components normal to the line of action − Vps for the pinion and Vgs for the gear. When contact is on the approach side of the pitch point (or point of zero sliding velocity, Vgs = Vps), the velocity component Vgs of the gear is greater than the velocity component Vps of the pinion, and the friction force on the pinion is toward the pinion center, as shown in Fig. 3.4.C-3. This friction force tends to increase the normal force, as shown by a summation of moments about the pinion center 0. When contact is on the recess side of the pitch point, the friction force on the pinion is up and away from the pinion, tending to reduce the normal force (Fig. 3.4.C-4).

Fig. 3.4.C-3  Forces on pinion during approach.

Fig. 3.4.C-4  Forces on pinion during recess. This normal force then is a function of the friction coefficient between the teeth: WN =

T R b (1 − μ tan φ)

in angle of approach (3.4.C-1)

Fig. 3.4.C-1  Velocities during approach.

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WN =

T in angle of recess R b (1 + μ tan φ)

The least mesh angle is the angular distance that the carrier is displaced when either of the geared elements of the planetary train is displaced by the angle subtended by one circular pitch. Figures 3.4.D-1 to 3.4.D-3 will illustrate the technique for establishing the least mesh angle.

(3.4.C-2)

where: WN = force normal to the teeth in the transverse plane T = input torque Rb = base circle radius φ = transverse pressure angle at instantaneous radius of contact μ = friction coefficient

3.4.11 Appendix D 3.4.11.1 Pinion Spacing Considerations To have pinion A starting engagement halfway between the engagement interval of pinion B on the sun, the spacing must be



⎛ 2π ⎜ nS + ⎝ NS

1⎞ ⎟ 2⎠

Fig. 3.4.D-1  Spacing with respect to sun and ring.

(3.4.D-1)

where: nS = whole number NS = number of teeth in sun Similarly, on the ring, the spacing must be

where:

⎛ 2π ⎜ nR + ⎝ NR

1⎞ ⎟ 2⎠

(3.4.D-2) Fig. 3.4.D-2  Example I: Simple planetary.

nR = whole number NR = number of teeth in ring where nS and nR are selected integers to satisfy this relationship Therefore, 1 2 = NS 1 NR nR + 2 nS +



(3.4.D-3)

Also, to ensure assembly, the space between the pinions must be an integral multiple of the least mesh angle. See Section 3.1 of this book, “Design of Planetary Gear Trains,” for more details.

Fig. 3.4.D-3  Example II: Ravigneaux.

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3.5 The Lever Analogy

3.5.1.2

Original Author: H. L. Benford Chrysler Corp.

Revised in 2007 by: M. B. Leising DaimlerChrysler AG (Ret.)

M. B. Leising Chrysler Corp.

H. Dourra DaimlerChrysler AG



Simple Gearset

The lever replacement for a simple planetary gearset is shown in Fig. 3.5.1. The points labeled A, PC, and S on the lever are points of application of forces analogous to annulus, planet carrier, and sun torques, respectively.

M. T. Berhan Ford Motor Co.

[The original SAE paper #810102, The Lever Analogy— A New Tool in Transmission Analysis, follows with some updates, in particular the “Planet Pinion Speeds” section which the authors revised to improve the ease of analysis.]



This tool is called the “lever analogy.” It should not be confused with methods that analyze gearsets by replacing individual gears with levers; to our knowledge, those methods replace components with levers for study, but are not analogies since forces still represent gear tooth forces and rotational velocities must be figured relative to the centerline. In the lever analogy, an entire transmission can usually be represented by a single vertical lever. The input, output, and reaction torques are represented by horizontal forces on the lever, and the lever motion, relative to the reaction point, represents rotational velocities.

(a) (b) Fig. 3.5.1  Simple planetary gearset (a) and analogous lever (b).

nS = no. teeth on sun nA = no. teeth on annulus K = any suitable scale constant

It is our intent in this paper to describe the lever analogy method of analysis and to present a miniature “cookbook” of levers for various planetary arrangements. It has been our experience that the use of this tool not only makes torque and speed calculations easy, but also improves an engineer’s ability to visualize the results and understand the effect of gear tooth ratios.

There is an alternative approach to scaling the lever which is used and discussed in the later section on “Planet Pinion Speeds and Other Calculations.” In the alternative approach, the distance from the planet carrier to an element is inversely proportional to the number of teeth on that element, e.g., basic planet carrier-to-sun distance = 1/number-of-teeth on the sun (not = number-of-teeth on the annulus). This approach may seem more intuitive, but it results in much smaller distance values which may be more difficult to visualize during analysis and/or manage in manual calculations. This is not an issue in a computer program, however, and all other aspects of the analogy remain the same.

3.5.1

3.5.1.3

Setting up the Lever System

Similarly, the lever replacement for a compound planetary is shown in Fig. 3.5.2.

The procedure for setting up a lever system analogous to a transmission is: 1) replace each gearset by a vertical lever; 2) rescale, interconnect, and/or combine levers according to the gearsets’ interconnections; and 3) identify the connections to the lever(s), according to the gearsets’ connections. 3.5.1.1

Compound Gearset

Levers

The basic building block of the analogy is the lever which replaces the planetary gearset. The lever proportions are determined by the numbers of teeth on (or the working radii of) the sun and annulus (ring) gears.



(a) (b) Fig. 3.5.2  Compound planetary gearset and analogous lever.

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3.5.2

Justification

The justification for these substitutions may not be obvious, but it can be shown that the horizontal force and velocity relationships of the lever are identical to the torque and rotational velocity relationships of the gearset. For example, when the carrier of a simple gearset is grounded, the annulus and sun rotate in opposite directions at relative speeds inversely proportional to their numbers of teeth, and the corresponding points on the analogous lever behave the same (Figs. 3.5.3 and 3.5.4):

Fig. 3.5.6  Lever analogy. The identical form of the torque relationship of a simple gearset and the force relationship of the analogous lever are as follows (Figs. 3.5.7 and 3.5.8):

Fig. 3.5.3  Carrier grounded.

Fig. 3.5.7  Torque relationship.

Fig. 3.5.4  Lever analogy with carrier grounded.

Fig. 3.5.8  Lever torque relationship.

The compound gearset is similar, except that the sun and annulus rotate in the same direction, and thus the analogous lever has the points corresponding to sun and annulus on the same side of the point corresponding to the planet carrier (Figs. 3.5.5 and 3.5.6):

The user may wish to try a few more examples in order to become comfortable with the analogy. Note, from the examples, the convention that rightward in the lever system corresponds to positive drive, typically clockwise in the transmission.

3.5.3

Interconnections

The interconnections between gearsets are replaced by horizontal links connected to the appropriate places on the levers. Whenever two gearsets have a pair of interconnections, the relative scale constants and placement of their analogous levers must be such that the interconnecting links are horizontal. This is illustrated using a Simpson gearset, shown in Fig. 3.5.9, along with the levers representing the two simple planetary gearsets, shown in Fig. 3.5.10.

Fig. 3.5.5  Compound gearset.

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These are rescaled, connected, and combined as shown in Fig. 3.5.13.

Fig. 3.5.9  Simpson gearset.

Fig. 3.5.13  Levers for reference Simpson gearset rescaled and combined. When gearsets have only one interconnection, they are treated as individual levers having one horizontal connecting link. In this case the scale constants may be chosen independently.

Fig. 3.5.10  Simpson gearset lever equivalent. For the interconnections PC1-A2 and S1-S2 to be horizontal, the second lever is scaled such that its “A-S” dimension equals the “PC-S” dimension of the first lever. The levers are then interconnected, as shown on the left in Fig. 3.5.11

3.5.4

Connections

The final step in the creation of the analogous lever system is identification of the connections to the lever(s). These correspond to the connections to the gearset(s), which may include friction elements, freewheels (one-way clutches), inputs, and/or outputs. They are connected to the lever system by horizontal links. For the reference Simpson gearset transmission, the gearset connections are shown in Fig. 3.5.14, and the corresponding lever connections are shown in Fig. 3.5.15.

Fig. 3.5.11  Horizontal interconnection and combining of levers for Simpson gearset. 3.5.3.1

Combining Levers

Levers connected by a pair of horizontal links remain parallel, and therefore can be replaced functionally by a single lever having the same vertical dimension between points (see Fig. 3.5.11). To illustrate, let us apply the method to a Simpson gearset used by Chrysler. The tooth numbers are:

Fig. 3.5.14  Gearset connections for Simpson transmission.

nA1 = 66   nA2 = 61 nS1 = 36   nS2 = 29 The analogous levers are shown in Fig. 3.5.12:

Fig. 3.5.15  Lever connections for Simpson transmission.

Fig. 3.5.12  Simpson gearset used by Chrysler.

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3.5.5

Transmission Analysis Using the Lever System

freewheel torques, and speeds of elements other than input and output, are easily found as well. Second Gear

The lever system thus created is easily evaluated for horizontal forces and/or velocities at the instant the lever is vertical. The relationships among torques or rotational velocities in the transmission are identical to the relationships among horizontal forces or velocities found by evaluating the lever system. 3.5.5.1

VI F = O = VO FI 36 + 66 = 1.55 66 Fig. 3.5.18  Lever connections and force ratio in second gear.

Simpson Gearset

The inputs and reactions for a Simpson gearset (refer to Figs. 3.5.14 and 3.5.15) are given in Table 3.5.1.

Third Gear

Table 3.5.1 Inputs and Reactions for Simpson Gearset Gear

Input

Reaction

1 2 3 R

C2 C2 C1, C2 C1

FW B1 — B2

VI F = O = 1.00 VO FI Fig. 3.5.19  Lever connections and force ratio in third gear.

The solution for low (first) gear ratio in the reference Simpson transmission, on a speed basis, is shown in Fig. 3.5.16:

Reverse Gear

Low Gear

VI −F = O = VO FI −44.7 = –2.10 21.3



Fig. 3.5.20  Lever connections and force ratio in reverse gear.

N V1 36 + 21.3 = = 2.69 = 1 V0 21.3 N0 Fig. 3.5.16  Lever connections for Simpson transmission in low gear.

3.5.5.2

Alternately, the solution for low gear ratio on a force/torque basis is shown in Fig. 3.5.17:

Ravigneaux Gearset

Another commonly used arrangement is the Ravigneaux gearset, shown schematically on the left side of Fig. 3.5.21. The first step with this is to convert it to a simple gearset plus a compound gearset, as shown on the right side of Fig. 3.5.21.

FO T = 2.69 = O FI TI Fig. 3.5.17  Force and torque equation in low gear. Speed and force diagrams for the other ratios are shown in Figs. 3.5.18, 3.5.19, and 3.5.20. Note that friction element or

Fig. 3.5.21  Ravigneaux gearset and equivalent simple plus compound gearsets. 3-43

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The analogous levers (Fig. 3.5.22) are:

Fig. 3.5.25  Gearset connections for reference Ravigneaux transmission. Fig. 3.5.22 Ravigneaux equivalent simple plus compound gearsets’ levers. In order for the interconnections PC-PC and A-A to be horizontal, one lever is inverted and scaled such that the A-PC dimensions are equal. Once horizontal interconnections have been achieved, the levers can again be combined as shown in Fig. 3.5.23.

Fig. 3.5.26  Lever connections for reference Ravigneaux transmission. Note that Fig. 3.5.26 is identical to Fig. 3.5.15 for the Simpson transmission except for the labeling of the points and slightly different lever proportions. Table 3.5.1 is valid for this Ravigneaux transmission as well, and thus its ratio analysis is virtually identical to that for the Simpson transmission. 3.5.5.3

A criterion of strong interest is planet pinion speed relative to the carrier. This represents pinion bearing speed, which can be a limiting factor in the mechanical design. The lever analogy can help in solving for this parameter.

Fig. 3.5.23  Horizontal interconnections and combining of levers for Ravigneaux gearset. For example, in one transmission which uses a Ravigneaux gearset, the tooth numbers are:

The easiest procedure is to employ the alternative approach to lever scaling, which is stated as follows:

nA = 72, nS1 = 36, nS2 = 30



Planet Pinion Speeds and Other Calculations

“The distance from the planet carrier to an element is inversely proportional to the number of teeth on that element.”

By following the above procedure, a lever is obtained whose proportions are given in Fig. 3.5.24. The gearset and lever connections are shown in Figs. 3.5.25 and 3.5.26, respectively.

Figure 3.5.1 then becomes Fig. 3.5.27:

Fig. 3.5.27  Lever scaling alternative approach. It is apparent that the lever proportions are identical using this definition; the advantage is that a pinion point can also be included on the lever and its speed can be found based on

Fig. 3.5.24  Combined lever for reference Ravigneaux transmission.

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the speeds of the other elements. Planet pinion speed, shown in Fig. 3.5.28 as NP, is of interest relative to the carrier, so the carrier point is used as the base.

Planet pinion torque may also be of interest; for example, the product of pinion torque and speed gives a measure of the power transferred through the gear meshes, and this is used in gearset efficiency calculations. The force in the lever system analogous to pinion torque is the force which would exist in the pinion links if the lever were divided as shown in Fig. 3.5.30 for the first Simpson planetary lever, separating sun and annulus.

Fig. 3.5.28  Lever analogy with planet pinion speed. The directional location of the pinion point from the planet carrier point on the lever is determined by the pinion’s direction of rotation. Fig. 3.5.30  Lever division for torque calculation.

Redrawing Fig. 3.5.12, the levers of the Simpson gearset, to include sixteen-tooth pinions in both gearsets gives the following: P1 → PC1 =

1 ⎛ 66 36 ⎞ * K1⎟ = 148.5K1; ⎜ * ⎠ 16 ⎝ 1 1

P2 → PC2 =

1 ⎛ 61 29 ⎞ * K2⎟ = 110.6K2 ⎜ * ⎠ 16 ⎝ 1 1

The torque of the first planet pinion of the Simpson gearset in second gear (the simplest case – S1 is grounded, NI = NA1) is determined as follows: Write the force balance around the carrier:

for comparable scaling, as shown in Fig. 3.5.29.

⎛ 36 * K1 ⎞ then, Since FI = FA1, and, from above, FTP1P1= FTA1 A1 ⎜ ⎝ 148.5 * K1⎟⎠ FP1 = 0.242FI, thus TP1 = 0.242 TI.

The relative pinion speeds in low gear (i.e., input to A1, PC2 stationary) are: NP1 148.5 = = 2.59; NI 36 + 21.3



NP2 81.1 = = 1.42 NI 36 + 21.3

FS1 * 66 K1 = FP1 * 148.5 K1 and FA1 * 36 K1 = FP1* 148.5 K1

The planet pinion speed, NP1, relative to the carrier is determined, referring to Fig. 3.5.29: N A1 NP1 = With S1 grounded and NI = NA1, then 66 * K1 + 36 * K1 148.5 * K1 N A1 NP1 148.5 * K1 and NP1 = = NA1 = 1.46NI 66 * K1 + 36 * K1 148.5 * K1 66 * K1 + 36 * K1

Fig. 3.5.29  Levers for reference Simpson gearset rescaled and combined with pinion speed.

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Therefore, the fraction of power going through the mesh = NPTP = 0.353 . NITI 3.5.5.4

The force diagram (Fig. 3.5.33) for the lever of the reference Simpson transmission (Fig. 3.5.13) is:

Rotational Inertias

When analyzing complete geartrains, the rotational inertias of elements can be included. This has proved helpful in studying shift quality and other factors. In the analogy, rotational inertia is represented by mass.

Fig. 3.5.33  Simpson transmission force diagram.

The procedure is to attach to the lever masses representing the rotational inertias of elements which connect to the gearset. The mass connected to the output (i.e., the vehicle) is normally considered to be infinite, and angular acceleration of the lever is assumed to be about the point to which the output connects. Force and moment balance equations on the lever are then solved.

Solving the force and moment balance equations gives the acceleration of the input point on the lever (A1) as a function of:

FI, FB1, MI, MD1, and MD2

A similar solution for the output force (FO) yields a different function of the same arguments.

For example, during the 1–2 speed change (low, or first, to second gear) in a Simpson transmission, C2 is engaged; and the input torque and band torque are assumed. Equations for rate of change of input speed and output torque can then be found by use of the lever analogy.

The expressions for input acceleration and output torque for the transmission are the same functions, but with the arguments respectively replaced by:

The inertias of interest are included in the schematic (Fig. 3.5.31):

TI, TB1, JI, JD1, and JD2

In this case, the lever analogy was used to ease the task of generating an equation instead of a value. It also helps in understanding how the individual inertias contribute to the overall effect. 3.5.5.5

Stepped Planet Pinion Gearset

This is another planetary arrangement which can be useful; it is shown in Fig. 3.5.34 along with its analogous lever. Fig. 3.5.31  Simpson transmission with inertias. The analogous lever with its effective connections and masses is shown in Fig. 3.5.32:

Fig. 3.5.34  Stepped planet pinion gearset and lever. As with any of the planetaries, only three attachments are required; therefore, for example, both sun gears may be omitted. With this arrangement, very small dimensions between adjacent points are possible which, of course, permits very high ratios.

. ω L = angular acceleration of lever Fig. 3.5.32  Simpson transmission with inertias lever equivalent.

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3.5.5.6

Split Torque Input

A split torque drive is normally used to reduce the slip losses of a torque converter or fluid coupling. A typical arrangement is shown in Fig. 3.5.35:

Fig. 3.5.37  CV device.

Fig. 3.5.35  Split torque input. Using a force diagram for the analogous lever, it is easy to determine the torque carried by the torque converter, and from the speed diagram the effect on speed can be seen in Fig. 3.5.36:

Fig. 3.5.38  CV lever equivalent. 3.5.6.2

Variable-Sheave Belts

These have a same-direction variable speed between input and output. A movable reaction point does not work well in this case (at a 1:1 ratio it would be infinity). Therefore, a movable input or output point is used, the choice depending on how the CV device is connected to the rest of the transmission. The analogous lever for a variable-sheave belt, using a movable input, is shown in Fig. 3.5.39:

Fig. 3.5.36  Split torque input lever equivalent.

3.5.6

Continuously Variable Transmissions

Many continuously variable transmissions (CVTs) employ both planetary gearing and a continuously variable device. To apply the lever analogy to these requires a lever replacement for the CV device. It is usually not difficult to invent a lever whose speed relationships match those of the CV device. (Force/torque basis solutions are best avoided in such cases because torque losses due to inefficiencies are much more significant than with gears.) 3.5.6.1

Reversing CV Devices

Some CV devices have a reverse-direction variable speed between input and output. The easiest way to represent such a device with a lever is to have the input and output at opposite ends and a movable reaction point in between. For example, a disc-and-torus device (Figs. 3.5.37 and 3.5.38): Fig. 3.5.39  Variable-sheave belt and its analogous lever.

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3.5.6.3

3.5.7

Nutating Drive Transmission

In the nutating drive transmission (Fig. 3.5.40), the traction drive element is part of a stepped planet pinion gearset:

Parallel Axis Gearsets

The simple case of a parallel axis gearset is shown at the bottom of Fig. 3.5.43. Its lever is left for the reader to derive. It can be seen for this and the belt drive example shown that the supporting structure is treated like a grounded carrier in a planetary gearset lever. See the Justification section (3.5.2) for further reference.

3.5.8

Synthesis

Although the lever analogy was conceived as a tool for analysis, it is also possible to use it for synthesis; i.e., one can begin by devising a lever system which accomplishes the objectives, and then create the analogous gearset(s). Unfortunately, the existence of a connection in a lever system does not guarantee that a similar connection can be made (at least not easily) in the planetary system. Nonetheless, promising transmission designs have been accomplished starting with a lever.

Fig. 3.5.40  Nutating drive transmission. This unit has the same speed relationships as the stepped planet pinion gearset (Fig. 3.5.41):

3.5.9

Summary

Fig. 3.5.41  Nutating drive transmission equivalent gearset.

The lever analogy allows easy analysis of mechanical transmissions. The following steps should be followed:

The analogous lever shown in Fig. 3.5.34 is adapted to this gearset as shown in Fig. 3.5.42:

Fig. 3.5.42  Nutating drive transmission equivalent lever.

1. Replace planetary gearsets and/or CV devices with their equivalent levers. 2. Rescale (but do not re-proportion) the levers such that their interconnections are horizontal. Combine levers if possible. 3. Identify input(s), output(s), and reaction for each gear. 4. Solve the lever system for horizontal speeds and forces; these are analogous to rotational speeds and torques, respectively. 5. If desired, use the lever system to investigate inertia effects, friction element or freewheel torques, pinion speeds, etc.

When this is done, it becomes relatively easy to explore other possible arrangement variations as well as to analyze this one.

A summary of all of the levers discussed is shown in Fig. 3.5.43. The user will find that the lever analogy method can be useful in analyzing most aspects of a transmission.

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Fig. 3.5.43  Summary.

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3.6 Design Practice for Automotive Driveline Splines and Serrations

Spline requirements and the manufacturing processes with their associated limitations are also discussed. The selection of the spline parameters is explained with respect to the requirements along with spline testing, drafting standards, inspection, and specified situations. Examples of current automotive industry application and practice are presented.

Original Authors: Willard B. McCardell (deceased) Michigan Tool Co., Div. Ex-Cell-O Corp.

Since the only difference stated here relates to the size of the pressure angle, the remainder of this paper will make reference only to the term spline. Therefore the reader should consider the term spline and serration as being synonymous.

John Mahoney Chevrolet Motor Div. General Motors Corp. Dugald Cameron Engineering Staff Chrysler Corp.

SI (metric) units of measure are shown in parentheses in the tables and in the text. Where equations require a different format or constant use with SI units, a second expression is shown after the first, indented, and with “M” included in the equation number.

Updated in 1991 by: Dugald Cameron Associate of Klarich Associates International Evan L. Jones Consultant

3.6.2

Charles E. Dieterle C-Dot Engineering

Designs of spline tooth forms have progressed through evolution. The motivation for this progress was the constant need for improved function, lower cost, ease of manufacture, clearer specifications, and improved inspection concepts to ensure that the assemblies will function to the design intent.

SAE Paper No. 680009 This section is intended to bridge the gap between the initial decision specifying the use of a spline or serration and the actual design and selection of the tooth proportions. It was prepared to acquaint the engineer and designer with the design analysis, selection, application, development, inspection, and general manufacturing technology of the automotive driveline splines and serrations. (Tooth proportions and standards are adequately covered by published standards of the American National Standards Institute (ANSI B92.1-1970 and ANSI B92.2M-1980).)

Earlier tooth forms began with the types shown in Figs. 3.6.1 to 3.6.3. Subsequent improvements in manufacturing technology led to the development of the involute form (Fig. 3.6.4). Because of its widespread use and unlimited applications, the involute profile is the spline form recommended by SAE and ANSI, as well as many industry standards. Reasons for this widespread acceptance are that it offers a variety of advantages: it is self centralizing, has the strongest possible tooth configuration, has infinitely more fatigue resistance, and offers a rational means for quality control and assurance. Addi­tional manufacturing advantages offered by the involute tooth form include:

This paper covers the general design parameters surrounding a spline and serration selection. The definitions of the term spline and serration are as follows: 1. Spline—A machine element consisting of integral keys (spline teeth) or keyways (spaces) equally spaced around a circle or portion thereof. Splines are generally defined as having pressure angles less than 45° and may be either spur or helical. 2. Serration—The definition is the same as splines, except serrations are generally considered as having pressure angles of 45° or greater, and also may be spur or helical.

3.6.1

Introduction to the Involute Form

1. The tooth profile can be generated by straight-sided tools, such as hobs and forming racks. 2. Increased economy from using the same cutting or forming tools to manufacture different size splines with varying numbers of teeth, as long as the pitch (module) and pressure angle remain unchanged. 3. Internal and external mating splines may be cut using a common cutter.

Abstract

3.6.3

This paper covers the detail design considerations between the decision to specify the use of a spline or serration and the final specified tooth proportions.

Spline Considerations

Prior to the detail analysis of the design parameters, it is important for the designer to have a general knowledge and 3-50

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understanding of the manufacturing methods and considerations surrounding the spline selection that have an effect on the final design. The spline design and specification should be simultaneously engineered with inputs from design, service, manufacturing engineering, tooling, and purchasing.

Fig. 3.6.4  Involute tooth form.

3.6.4

Manufacturing Methods

Broaching—Broaching is a machining method in which a hardened steel tool (broach) is pulled through or pushed over the surface being machined. When broaching an internal spline, the broach must be pulled through that portion which has the smallest internal diameter and vice versa for the external. Because the process is nongenerating, the tool is a single purpose. This gives no latitude for change in tooth thickness, pitch (module), number of teeth, and helix angle (in the case of a helical spline).

Fig. 3.6.1  Straight-sided radial flanks.

Broaching is a fast and economical manufacturing method and is also extremely accurate. The designer should also understand that the manufacturing of the broach is done under ideal toolroom conditions with all the spline dimensions ground into the broach with the least possible spacing variations. In addition, the broach is made to provide the maximum space width; this allows for tool regrinds and maintenance.

Fig. 3.6.2  Straight-sided parallel flanks.

The effect of this is a spline fit that tends toward the maximum allowable backlash. Shaper Cutting—Shaper cutting uses gear-shaped cutting tools which reciprocate as they rotate in mesh with a gear blank generating the tooth form. Because the cutting tool progresses tooth by tooth, this is one of the slower production methods. There are also limitations in the flexibility of the numbers of teeth that can be cut with a single cutter. Advantages of this method are the ability to cut an external spline close to a shoulder and to cut an internal spline in a blind hole, provided there is an undercut for tool relief and chip clearance. An additional economic advantage is that a single cutter can often cut both

Fig. 3.6.3  Straight-sided star serration.

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Design Practices: Passenger Car Automatic Transmissions

the external and internal spline, provided the spline design encompasses a standard tooth thickness and space width and the cutter can be fed to the proper depth with the necessary form clearances.

shoulder without an undercut at the inboard end. Advantages of this process are: surface finishes in the range of 3 to 10 rms; it is a generating process; and a single set of tools can roll splines with different numbers of teeth, provided the pitch (module) and pressure angle remain constant. The disadvantage of the process is that it does not allow the designer the opportunity to vary the tooth thickness to any degree with a given tool design. Should the product designer wish to design a spline for the maximum use of tools, it would be necessary to standardize on the pitch (module), pressure angle, and tooth thickness. It is also advisable to standardize either on an even number of teeth or an odd number of teeth, since the design of the tools varies in this respect.

Helical spline cutters are made with the same helix-angle as the spline and therefore are limited-purpose tools. Production ma­chines that produce helical splines are usually tooled with a helical guide to provide the proper helix angle on the part. There are on the market universal guides which allow for a helix angle adjustment. This may be important during the development of prototype parts when the helix angle distortion from heat treat­ment is being evaluated. During shaper cutting of fine pitch (module) splines, there is little difference in the production rates with respect to the pitch (module). There is, however, considerable change in the produc­tion rates when cutting coarse pitch (module) splines. In the coarse pitch (module) range it is sometimes necessary to have two roughing cuts prior to the finish cut. Some economy is realized in tool life in the finer pitches (modules) because of the lighter chip loads.

Grinding—Grinding, as one would expect, is very expensive, but is also extremely accurate. In general the grinding of spline teeth should only be considered when heat treatment distortions are prohibitive, when the class of fit can only be accomplished by the extremely close tolerances inherent with grinding, or when the surface finish specified can only be accomplished by this method. This process is generally confined to the machine tool, aircraft, and aerospace industries or low-volume prototypes.

Shear Speed—Another form of shaper cutting uses multiple tools shaped to the form of the spaces to be cut. All of the spline teeth are cut simultaneously, which lends this process to high production. There are, however, limitations in the number of teeth that can be cut due to the physical spacing of the cutters around a circle.

3.6.5

Physical Considerations

Shapes—Splines may be formed either internally or externally by the manufacturing methods previously outlined. The shapes of members that can be splined are unlimited and are best described as tests of the imagination. In the more complex shapes of parts to be splined, the only restriction is the manufacturing method necessary to produce the spline.

Hobbing—Hobbing is the most commonly used process for the cutting of external splines. The geometry of a hob to a spline is compared to that of a rack and pinion, because the hob has a straight flank and generates an involute tooth profile. When hobbing parallel-sided splines, the hob must have a corresponding curved profile to generate the straight-sided tooth. The same call-out method should be used to specify the straight-sided tooth on the print as is used to specify the involute tooth with respect to the effective fit concept and form diameters.

Fit and Concentricity Requirements—The fit and concentricity requirements are design considerations which must have tolerances allocated to meet the product requirement. To define the requirements the following questions are suggested: 1. What is the permissible rotational backlash? 2. How much axial play is allowable? 3. How does alignment (tilt by wobble) relate to the assembly and how much is tolerable? 4. What is the permissible runout with respect to the other diameters in the assembly?

When a spline is to be cut close to a shoulder, the hob diameter must be considered to prevent the shoulder from being cut away during the latter stages of machining. Cold Roll Forming—Cold roll forming is applied to external splines and uses a pair of rack-type forming tools or planetary rolls. This process involves the displacement of metal; therefore, the spline blank diameter is used as the operating pitch diameter during the forming cycle.

Environment—The common types of environment encountered by splines are:

The backward extrusion of the metal creates the addendum of the spline. The process is extremely fast and usually has forming times of 2 to 4 s. Splines may be formed close to a

1. In oil or lubricant. 2. Exposed to atmospheric conditions. 3. In air, but enclosed from the atmosphere. 3-52

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N = Number of teeth m = Module P = Diametral pitch Ps = Stub pitch t = Circular tooth thickness T = Torque, Pound-inch (Newton-millimeter) z = Section modulus (torsional shear) inch3 (millimeter3) φ = Pressure angle Ψ = Helix angle

A spline exposed to the atmospheric elements should have a coarse pitch (module), since the oxidation or rusting process will reduce the tooth thickness rapidly (especially when there is oscillation). The rust reduction in tooth thickness by percentage will be less with the coarser pitches (modules).

3.6.6

Selection of Parameters

For the purpose of this paper, the consideration of parameters are restricted to those of general design and selection.

3.6.7

3.6.8

Symbols

Design

For specific guidance and detailed tooth proportions, we will rely on the published standards of ANSI B92.1-1970 (inch) and ANSI B92.2m (metric).

The symbols used to designate the various terms and dimensions are listed here (see also Fig. 3.6.5): D = Pitch diameter Db = Base diameter Do = Major diameter, external Dri = Major diameter, internal Dre = Minor diameter, external Di = Minor diameter, internal de = Measuring pin diameter, external di = Measuring pin diameter, internal F = Tangential tooth load, Pounds (Newtons) L = Length of spline engagement, inches (millimeters)

The spline stress analysis is accomplished by the calculation of the principle stresses involved, by applying the following expres­sions: 1. Torsional shear (Ss) for a basic shaft, the diameter (Dre) is as follows: Solid round shaft:

Ss =

16T πDre3

(3.6.1)

Fig. 3.6.5  Symbols and terms. 3-53

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Design Practices: Passenger Car Automatic Transmissions



Ss =

16,000T πDre3

(3.6.1M)

Hollow round shaft (external teeth), with a bore of (Dx):





Sc =

Ss =

16T Dre π Dre 4 − Dx 4

Ss =

16,000T Dre π Dre 4 − Dx 4

( (

)

(3.6.2)

)

(3.6.2M)

16T Dxo π Dxo4 − Dri 4

Ss =

16,000T Dxo π Dxo4 − Dri 4



(3.6.6M)

The same reservations are applied to the modification of the expression as above. 4. Hoop stress (St )or bursting stress induced in a hub of diameter (De) by the load produced by the surrounding internal spline:

Hollow round hub, (internal teeth) with an outside diameter (Dxo): Ss =

4,000T D(Do − Di) LN



St =

2T (Tan φ) π D(De − Dri)L

(3.6.7)

St =

2,000T (Tan φ) π D(De − Dri) L

(3.6.7M)

)

(3.6.3)

)

(3.6.3M)

The material and heat treatment necessary may now be deter­ mined on the basis of the calculated stress levels.

2. Shear stress (Ss) in spline teeth: Assuming teeth shear at pitch line and 100% teeth in contact, then:

The preceding covered the structural design analysis; now con­sider the parameters for the spline elements, since a spline design must encompass the following: size (diameter), pitch (module), number of teeth, tooth thickness, pressure angle, length of engagement, type of fit, type of root, tolerance class, material, and heat treatment.







( (

Ss =

2T DtLN

(3.6.4)

Ss =

2,000T DtLN

(3.6.4M)



The decision for the selection of many of the above items is dependent upon the function, production volume requirements, and method of manufacture. Frequently there is a practical consideration of using existing production equipment.

Assuming teeth shear at minor diameter of the internal spline (Di) and 100% teeth in contact, then:





Ss =

2T Di (tx) LN

Ss =

2,000T Di (tx) LN

3.6.8.1

(3.6.5)

The greatest single factor in a spline selection is the basic shaft diameter required to transmit the applied torque. The following example will clarify this point:

(3.6.5M)

Consider a splined shaft of diameter (D) having an effective spline engagement (L) equal to the diameter (D) and basic tooth thickness and 30° pressure angle (PA).

where tx = tooth thickness at Di The above expressions may be modified according to the appli­cation and tolerances where there is justification that all teeth will not be in contact.

Note: Basic tooth thickness equals:

3. Compressive stress (Sc) in spline teeth: Assuming 100% teeth in contact, then:



Sc =

4T D(Do − Di) LN

Size (Diameter)

(3.6.6)







0.5π + 0.2 P

(3.6.8)

45° PA = 0.5πmm

(3.6.8M)

45° PA =

37.5° PA =

0.5π + 0.1 P

37.5° PA = 0.5πmm

(3.6.8.5) (3.6.8.5M)

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Gears, Splines, and Chains

30° PA =



0.5π P

(3.6.9M)

30° PA = 0.5πmm



Since the shafts are generally held between centers and are motivated by the forming tools, it is important to choose a pitch which provides sufficient number of teeth to ensure continuity of contact between tools, so that proper rolling control is maintained.

(3.6.9)

then, from Eq.3.6.1 or Eq.3.6.1M: Basic shaft shear strength: Torsional Ss =



5.09T Dre3

Torsional Ss =





5.090T Dre3

Manufacturers of this equipment recommend the minimum number of teeth for the spline to be 17 to 19, dependent upon the pitch (module). This limitation does not apply to helicoids with at least one tooth helical overlap.

(3.6.10) (3.6.10M)

3.6.8.3

The determination of the number of teeth follows from:

and from Eq. 3.6.4: Pitch line shear strength: Ss =



Ss =



1.27T

D3 1,270T

D3





(3.6.11)

N = PD

(3.6.12)

D m

(3.6.12M)

N=



(3.6.11M)

having established a diameter range necessary to transmit the torque and the range of pitch (module) consistent with the manufacturing considerations.

Since Dre < D, it should be quite evident that with a ratio of spline length to shaft diameter of unity (L/D =1.0), the shear stress in the spline teeth are of secondary importance.

A practical advantage of selecting an even number of teeth is that it lends to direct measurement of the major and minor diameters with standard micrometers or other measuring devices.

The external minor diameter (Dre) of the shaft can be calculated by applying an acceptable stress level for the proposed materials to Eq. 3.6.1, bearing in mind heat treatment, stress concentration, and the fatigue life expected. Should a restraint limit the outside diameter of the hub surrounding the internal spline, then start with the restraining diameter and apply a suitable stress level to Eq. 3.6.3 and calculate the (Dri) major diameter for the internal spline. 3.6.8.2

Number of Teeth

When cold rolled forming is to be used (with currently available processes), an advantage in specifying an odd number of teeth is the tendency to reduce machine vibrations, which results in better surface finish and dimensional control. 3.6.8.4

Pitch

Tooth Thickness

The tooth thickness is the circular tooth measurement at the pitch circle diameter, normally inspected by a measurement over pins for an external spline, and a between pin measurement for an internal spline (Table 3.6.1).

Inch spline pitches are designated in the P/Ps proportion, a combination number. The upper or first number is the Diametral pitch (the number of teeth per inch of pitch diameter N/D), the lower or second number is the stub pitch (one inch divided by the stub pitch is the basic addendum 1/Ps).

The diameter for the measuring pin may be established from: 1.728 di = internal splines (3.6.13) P

Metric spline modules are designated in a singular number m with the basic external addendums being: 30.0° 0.5 m, 37.5° 0.45 m, and the 45.0° 0.4 m. In general, for a given blank diameter, the finer the pitch the stronger the spline. Other major considerations are the type of manufacture (including consideration of existing equipment, and the type of service and environmental conditions).



When a cold roll forming process is specified, the pitch is usually in the 16 to 32 Diametral pitch (1.5 to 0.75 module) range, the most popular pitch being 24/48 (1 module).



de =

di = 1.728m internal splines 1.92 external splines and all serrations P

de = 1.928m external splines

(3.6.13M)

(3.6.14) (3.6.14M)

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Design Practices: Passenger Car Automatic Transmissions

The pin diameter is optional within a narrow range of tooth thickness, since it is desirable for the pin to contact close to the pitch circle.

The selection of the tooth thickness is dependent upon the shear strength of the material, backlash requirements, and tolerance range allowable.

The clearance between the pin and the minor and major diameters for external and internal splines, respectively, should be calculated to avoid pin interference.

In addition, consideration must be given to heat-treated splines with no after-finishing. This is necessary because of tooth distortion, and generally tooth growth (thickness).

In the case of non-standard tooth proportions, a pin should be selected to contact the flanks of the teeth close to the pitch diameter and provide root clearance. It is sometimes necessary to flatten the pin to provide root clearance.

The following allowances are offered as guidelines: 1. 0.0005 in/in (0.013 mm/25 mm)—Induction hardened parts. 2. 0.0010 in/in (0.025 mm/25 mm)—Through hardened parts. 3. 0.0015/0.0020 in/in (0.038–0.050 mm/25 mm)—Carburized and hardened parts.

The over and between pin dimensions check only the actual tooth thickness and the actual space width. The effective tooth thick­ness and space widths must be checked by other means, as discussed in the section on inspection.

Table 3.6.1  Summary of Involute Spline Over and Between Pin Formula Inv. φ2 =

Type of Spline External  Straight—Even Teeth

Inv φ1 +

Over/Between Pin

t π de − + D N Db

DB sec φ2 + de

90 Db secφ2 cos ⎡⎢ ⎤⎥ + de ⎣N⎦

 Straight—Odd Teeth  Helical—Even Teeth

Inv φ1 +

t π de − + sec ψb D N Db

 Helical—Odd Teeth Internal  Straight—Even Teeth

Inv φ1 +

s di − D Db

 Straight—Odd Teeth  Helical—Even Teeth

Inv φ1 +

s di − sec ψb D Db

 Helical—Odd Teeth



DB sec φ2 + de 90 Db secφ2 cos ⎡⎢ ⎤⎥ + de ⎣N⎦

DB sec φ2 – di

90 Db secφ2 cos ⎡⎢ ⎤⎥ − di ⎣N⎦ DB sec φ2 – di

90 Db secφ2 cos ⎡⎢ ⎤⎥ − di ⎣N⎦

Where          

φ1 = pressure angle at (D) φ2 = Pressure angle at (pin diameter centerline) ψ1 = Helix angle at (D) ψb = Helix angle at (Db) s = space width at (D)

and   ψb = tan ψ1 cos φ1

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The tooth thickness at times must be further modified to suit considerations of the materials as, for instance, a steel shaft splined to a soft material hub (aluminum). The hub tooth thickness should be modified thicker and the external tooth thinner to balance the shear stress in the teeth due to the unequal strength of materials.

If an assembly requires that the members slide under load, the 30° pressure angle is preferred, because the flank is more normal to the tangential tooth load and the greater area in flank contact provides a lower unit pressure. If one or both of the members have a thin-walled tubular cross-section, the bursting tendencies of the 45° pressure angle may dictate the use of the 30° or 37.5° pressure angle.

Should a designer be using SAE (ANSI) standards for the tooth proportions, it is worthy to note that the internal spline data were designed and proportioned to allow a broach or shaper cutter to be used, and since a broach is made for a single part, any additional design allowances should be made in the external spline data. 3.6.8.5

In the cold roll forming of 45°-pressure-angle external splines, all the stresses on the tools are compressive. This gives high tool life and allows the preform blank hardness to be as high as 365 Bhn and still be economical. When roll forming splines with 30° pressure angle, the deeper proportion of teeth with smaller pressure angle and the method of generation imposes beam loads on the forming tools, resulting in less tool life. Also, the pre-roll blank must be held to a lower hardness limit not to exceed 265 Bhn. This is variable, depending upon the pitch (module) and the rate of tool penetration.

Pressure Angle

The angle between a line tangent to an involute and a radial line through the point of tangency is the pressure angle. Unless otherwise specified, it is the main pressure angle (Fig. 3.6.6). In the case of the straight-sided internal serration which is to assemble with an involute external, the pressure angle call-out should be the same as that of the involute external, but it does not equal the form angle (Fig. 3.6.7). Table 3.6.2 lists the internal form angle with respect to the number of teeth for the internal straight-sided serrations. Consider now the available standard tooth proportions, their intended purpose, and limitations (Fig. 3.6.8). The ANSI Stan­dards cover three pressure angle splines: the 30° is given in both flat and fillet root, the 37.5° and 45° splines are in fillet root only. Cold forming tools with a 37.5° pressure angle can form parts in the 200 Bhn range and will usually produce 100,000– 300,000 splines per tool grind. This is approximately 95% of the volume yield from 45°-pressure-angle tools. Under comparable conditions, 30°-pressure-angle tools should produce 50,000–100,000 splines per regrind.

Fig. 3.6.6  Pressure angle. 3.6.8.6

In many cases companies with limited production have standard­ized on the 37.5° pressure angle to satisfy all of their functional requirements and also minimize their number of tools.

Length of Spline Engagement

The general rule of thumb for the ratio of L/D = 1 should be apparent from Eqs. 3.6.10 and 3.6.11. Structurally, this ratio need never be extended, except for extreme circumstances calling for addi­tional stability of the assembly, or where there is an application using unequal-strength materials such as aluminum and steel. It is then advisable to resort to the formula and calculate the length using an acceptable stress level for the material.

The 37.5°-pressure-angle splines are currently used on automotive rear axle shafts, rear axle drive pinions, transmission shafts, torsion bars, power steering pump shafts, and drive shafts. The 37.5° pressure angle is also applied to sliding splines, side fit splines, and major diameter fit applications.

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3.6.8.7

Types of Fit

To assure proper assembly of splines with a major diameter fit and yet to be sure not to reject functionally acceptable parts, the following note is used:

The ANSI and SAE Standards encompass two types of fits: 1. Side fit—In this fit, the mating members contact on the sides of the teeth only; major and minor diameters are clearance dimensions. The tooth sides act as drivers and centralize the mating splines. 2. Major diameter fit—In this fit, the mating members contact at the major diameter for centralizing. The sides of the teeth act as drivers. The minor diameter is a clearance dimension.

“The effective spline at maximum material condition and the major diameter at maximum material condition must be concen­tric and in alignment for xx.xx length.’’

Press fit applications will not be considered because the design must be tailored to the degree of fit (tightness desired), shape of the blank, wall thickness, material and heat treatment, temperature environment (thermal expansion), and the possibility of parts being selective to limit the range of tightness.

Fig. 3.6.8  General tooth proportions. Any additional allowance for lack of relationship between the effective spline and the major diameter would have to be within the tolerance allowed for space width (or tooth thickness) and/or the major diameter. This is in keeping with the recommendation of the SAE Involute Spline, Serration and Inspection Standard. One of the pitfalls of this type of assembly is that, on those occasions where the shafts have little or no warpage, the provided allowance for warpage reflects itself in excess effective clearance (backlash).

The major diameter fit is by far the more difficult to control and therefore should not be specified unless absolutely necessary. It is usually applied in cases where the shaft spline will have excessive runout (usually from warpage during heat treatment) and the mating part is required to operate with a minimum runout—such as the composite action of a gear. If a slip fit spline assembly is required, then runout full indicator reading (FIR) is allowed between the major circle and effective spline. To assure assembly, the same amount must be given as clearance between the effective limits of the space width and tooth thickness.

The other pitfall is that when warpage does occur and there is run­out between the major circle and the effective spline, the torque loads are borne by only a few teeth whose profiles do not match. Thus, shear stresses and unit pressure are high; the latter results in high axial loads if sliding is required under load. When hobbing or shaping splines for major diameter fits, the designer must specify that the chamfers on the external spline are not so large that the remaining top land is too small to be effective. This is especially true on fine pitch splines and splines with small numbers of teeth. When splines are cold formed by rolling, chamfers cannot be provided on the external spline. Thus, the corner clearance must be provided in the internal spline by a protuberance type broach (Fig. 3.6.9). 3.6.8.8

Type of Root

The ANSI and SAE Standards cover the following type of roots: flat root and fillet root (Fig. 3.6.5). Both of these root types are suitable for all types of manufacturing methods, with the exception that the fillet root is required for the cold forming method. In general, the flat root is specified for the coarser pitch (module) splines.

Fig. 3.6.7  Form angle.

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If a spine is broached, the flat root specification is desired, because this reflects in shorter broach lengths.

Table 3.6.3  Material Specification for Selection of Shear and Compressive Stresses

When the design parameters allow, the root type should be specified as optional.

Tensile Ultimate, psi

Bhn Hardness

20,000 40,000 70,000 80,000

150 200 170 200

10 15 25 25

38,000

  80

10

33,000

  90

10

Material Iron Grey Iron Grey Iron Pearlitic Malleable Nodular High Strength Aluminum Type 356 Solution Heat Treat and Aged Type 319 Solution Heat Treat and Aged

Fig. 3.6.9  Protuberance type broach. 3.6.8.9

Materials

Modulus of Elasticity E ¥ 106

Table 3.6.4  Stress Ratios

The selection of materials for most high-volume applications is greatly influenced by past experience. The best material choice is the one which is the most cost efficient and also satisfies the application.

Material

Stress Ratio, Su

Iron Shear Stress Compressive Stress Aluminum Shear Stress Compressive Stress Steel Shear Stress

The material selection is sometimes a development on its own and is studied by a group including representatives from design, product development, metallurgy, and manufacturing. The material specifications in Table 3.6.3 are offered as design guidelines. In conjunction with the specifications shown in

1.1 3.0 0.8 0.75 0.5*

*See Fig. 3.6.10 for tensile strength of steel.

Table 3.6.2  Internal Form Angle for Internal Straight-Sided Serrations, When Tooth Thickness is Basic N

Degrees

N

Degrees

N

Degrees

N

Degrees

N

Degrees

E

Degrees

 6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21

56.2 61.0 64.6 67.4 69.7 71.5 73.1 74.4 75.5 76.5 77.3 78.1 78.7 79.3 79.8 80.3

22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37

80.8 81.2 81.5 81.9 82.2 82.5 82.8 83.0 83.2 83.5 83.7 83.8 84.0 84.2 84.4 84.5

38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53

84.7 84.8 84.9 85.0 85.2 85.3 85.4 85.5 85.6 85.7 85.8 85.9 85.9 86.0 86.1 86.2

54 55 56 57 58 59 60 61 62 63 64 65 66 61 68 69

86.2 86.3 86.4 86.4 86.5 86.6 86.6 86.7 86.7 86.8 86.8 86.9 86.9 87.0 87.0 87.1

70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85

87.1 87.1 87.2 87.2 87.3 87.3 87.3 87.4 87.4 87.4 87.5 87.5 87.5 87.6 87.6 87.6

  86   87   88   89   90   91   92   93   94   95   96   97   98   99 100

87.6 87.7 87.7 87.7 87.7 87.8 87.8 87.8 87.8 87.9 87.9 87.9 87.9 88.0 88.0

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Design Practices: Passenger Car Automatic Transmissions

Table 3.6.3 for the selection of shear and compressive stresses, the ratios shown in Table 3.6.4 may be used.

Pressure Angle—30°–45°. Type of Fit—Side Fit (some applications use small helix angle to provide zero backlash).

3.6.8.10 Machinability

Type of Root and Manufacture: External—Fillet Root; Rolled. Internal—Flat Root; Broached. Length of Engagement as % of Diameter—96 to 140%. Stress Levels Hoop Stress—27,000 psi (186,165 kPa) Compressive Tooth Stress—34,000 psi (234,430 kPa) Shear Stress on Teeth—24,700 psi (170,307 kPa)

If the splines being designed are to be produced by a cutting method, then the presence of sulfur or lead in the chemistry will improve the machinability by decreasing the ductility, which promotes improved chip breakage. The opposite is the case when a cold roll forming process is considered, because the ultimate ductility is desired. For reference, Fig. 3.6.10 is a hardness conversion chart.

3.6.9.2

Manual Transmissions

3.6.9

Automotive Industry Applications

The general industry applications are:

3.6.9.1

Rear Axles

1. Input Shaft

The general industry applications are:

Materials—SAE 1024, 4027, 8620 steel. Heat Treat—Carburize and harden to RC 59 to 63 with a core hardness of RC 28 to 38. Pitches—10 Tooth parallel sided spline and 24/48 involute. (1 Module) Pressure Angle—Parallel sided and 45° Pressure angle involute. Type of Fit—Side fit. Type of Root and Manufacture: External—Flat Root, Fillet Root; Hobbed, Rolled. Internal—Flat Root; Broached. Length of engagement as % of Diameter—100%

1. Shafts Material—SAE 1040-1050 steel. Heat Treat—Induction harden to RC 50 minimum with a core hardness of 250 to 300 Bhn. Pitches—24/48. (1 Module) Pressure Angle—30°–45°–37.5°. Type of Fits—Side fit (increased backlash provides easier assembly of a long shaft in a blind hole). Type of Root and Manufacture: External—Fillet Root; Rolled, Hobbed. Internal—Flat Root; Broached. Length of engagement as % of diameter—110% to 114%.

Stress Levels: Basic Shaft, Torsional Shear—33,600 psi (231,672 kPa) Compressive Tooth Stress—12,000 psi (82,740 kPa) Shear Stress on Teeth—5,000 psi (34,475 kPa)

Stress levels: Basic Shaft, Torsional Shear—80,000 psi (551,600 kPa) Compressive Tooth Stress—40,000 psi (275,800 kPa) Shear Stress on Teeth—22,000 psi (151,690 kPa)

2. Output Shaft First and Second Gear—Hub to Output Shaft. Material—SAE 1146 Heat Treat and Hardness—207 to 255 Bhn Pitches—12/24, 20/40. (2, 1.25 Module) Pressure Angle—30°. Type of Fit—Major diameter or side fit. Type of Root and Manufacture: External—Flat Root; Hobbed. Internal—Flat Root; Broached.

In conjunction with Table 3.6.3, see Table 3.6.4 for allowable shear and compressive stresses. 2. Pinions Material—SAE 4023, 4027, 8617 steel. Heat Treat—Carburize and harden to RC 58. This high hardness is required for the gear teeth. Pitches—24/48. (1 Module)

Stress Levels:

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Gears, Splines, and Chains

Basic Shaft, Torsional Shear—42,000 psi (289,590 kPa) Compressive Tooth Stress—5,000 psi (34,475 kPa) Shear Stress on Teeth—2,000 psi (13,790 kPa) Third and Direct Gear Hub to Output Shaft. Material—SAE 1146. Heat Treat and Hardness—207–255 Bhn Pitches—24/48, 12/24. (1, 2 Module) Type of Fit—Major Diameter or Side Fit. Type of Root and Manufacture: External—Flat Root; Hobbed. Internal—Flat Root; Broached. Length of Engagement as % of Diameter—73 to 87%

Type of Root and Manufacture: External—Fillet Root; Rolled. Internal—Flat Root; Broached. Length of Engagement as % of Diameter—112%. Stress Levels: Basic Shaft, Torsional Shear—47,000 psi (324,065 kPa) Compressive Tooth Stress—65,000 psi (448,175 kPa) Shear Stress on Teeth—24,000 psi (165,480 kPa) Rear Carrier/Shaft Pitches—20/40, 24/48. (1.25, 1 Module) Pressure Angle—37.5° to 45°. Type of Fit—Side fit. Type of Root and Manufacture: External—Fillet Root; Rolled. Internal—Flat Root; Broached. Length of Engagement as % of Diameter—100%.

Stress Levels: Basic Shaft, Torsional Shear—7,850 psi (54,126 kPa) Compressive Tooth Stress—9,500 psi (65,503 kPa) Shear Stress on Teeth—4,000 psi (27,580 kPa) 3.6.9.3

Stress Levels: Basic shaft, Torsional Shear—48,000 psi (330,960 kPa) Compressive Tooth Stress—50,000 psi (344,750 kPa) Shear Stress on Teeth—15,000 psi (103,425 kPa) Shaft/Slip Yoke Pitches—24 modified, 24/48. (1 Module) Pressure Angle—30°. Type of Fit—Side fit. Type of Root and Manufacture: External—Fillet Root; Rolled. Internal—Flat Root; Broached. Length of Engagement as % of Diameter—to satisfy alignment and balance—240 to 350%

Automatic Transmissions

The general industry applications are: 1. Input Shaft Materials—SAE 1141,1024. Heat Treat—Induction harden to a surface hardness of RC 32 to 37, and carburize and harden to RC 58 minimum with a core of RC 25 to 35. Pitches—32/64, 20/40, 24/48. (0.75, 1.25, 1 Module) Pressure Angle—30°–45°. Type of Fit—Side Fit. Type of Root and Manufacture: External—Fillet Root; Rolled. Internal—Flat Root; Broached. Length of Engagement as % of Diameter—68 to 90%.

Stress Levels: Basic Shaft, Torsional Shear—68,000 psi (468,860 kPa) Compressive Tooth Stress—12,000 psi (82,740 kPa) Shear Stress on Tooth—8,000 psi (55,160 kPa)

Stress Levels: Basic Shaft, Torsional Shear—90,000 psi (620,550 kPa) Compressive Tooth Stress—50,000 psi (344,750 kPa) Shear Stress on Tooth—19,500 psi (134,453 kPa)

3.6.10 Special Situations Parallel-Sided Splines—While the SAE and ANSI Spline Standards encompass only the involute spline, there are still many parallel-sided splines in use and in production—some because of service problems, some to take advantage of existing tooling. In most cases the part drawings specifying the spline designs are incomplete in their specifications. The design, manufacture, and inspection concept of the involute spline should be applied to the parallel-sided spline (including the form diam­eter), and effective space width

2. Output Shaft Front Carrier to Output Shaft Materials—SAE 1038, 1042, 4027. Heat Treat—Induction harden, carburize and harden to surface hardness of RC 45. Pitches—32/64, 24/48. (0.75, 1 Module) Pressure Angle—45°. Type of Fit—Side Fit. 3-61

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and tooth thickness limits should be defined—not just the actual limits.

The formula for establishing the angle of cut with an involute external serration of 45° pressure angle is:

A very serious drawback in this design is that it is not tooloriented. For instance, a hob made for a 10-tooth spline can only cut a spline with ten teeth and only to the diameter and tooth thickness for which it was designed. Care must also be exercised in machine set-up; the hob must be centered over the shaft or the spline teeth will have concave flanks on one side and convex flanks on the other side. Determination of the straightness of the flanks is difficult because there is no equipment specifically made for this inspection.

Taper/inch (sin Form Angle) 2 cos φ



(3.6.15)

The form angle is: S (180) πD



(3.6.16)

Form angle for a basic space is:

When torque is applied to the parallel-sided spline, it rotates into driving position with its driven member, and initial contact is made at the tip of the external spline teeth only. This usually brings about early wear in that area, and by the time the assembly has worn into a full-flank bearing condition, a sloppy fit will result.



FA =

101.4591585 N

(3.6.17)

When the external serration is hobbed with an involute profile, the contact between the involute and the straight-sided internal tooth side is shown in Fig. 3.6.11. It is not on the pitch line. The longitudinal line of contact runs from a point near the major diameter to the external tooth at the small end and extends to a point near the form diameter of the external tooth at the large end.

A further drawback to the parallel-sided spline design is that it is often designed to permit very small root radii. The resulting stress risers often prove to be the starting point of shaft failures.

Internal Straight-Sided Serrations—When there are noncritical applications involving light loads or where critical control of backlash is desired, the combination of internal straight-sided and external involute serrations may be specified. (Refer to Design, Pressure Angle Section 3.6.8.5 for the definition of the form angle for internal serrations.)

Tapered Serrations—Tapered serrations are often used in assemblies where there is no backlash permitted, such as steering linkage. The amount of taper on the diameter is usually from 0.75 to 1.50 in/ft (19.0–38.0 mm/305 mm). The designated taper per foot applies to all diameters of the internal serration and to the major and form diameters of the external serration. This arrange­ment allows the two mating parts to be partially assembled by hand, and final location of the assembly is usually effected by torquing the fastening nut.

Conversions from one scale to another are made at the intercepts with the curve crossing the chart. For example, follow the horizontal line representing 400 Diamond Pyramid Hardness to its intersection with the conversion curve. From this point follow vertically downward for equivalent Rockwell C Hardness (41), horizontally to the right for Brinell Hardness (379) and Tensile Strength (187,000 psi), and vertically upward for the equivalent Shore Hardness (55).

The geometry of both members is predicated on the method of manufacture of the internal serration. In some cases the internal serration is broached straight (cylindrical), then swaged into a taper. In other cases the internal spaces are taper broached one space at a time. In both cases it holds that the top land width of the internal space is constant from end to end. This, then, establishes the guidelines for the design of the external member. If the external member is hobbed, then an angle of cut must be used that will provide a constant top land width at the major diameter. Only under these conditions will the space width and tooth thickness conditions of the mating parts be compatible from end to end.

It should be realized that closer control of backlash is possible, since the profile variation is omitted from consideration. Because this combination of members localizes the tooth contact, the tolerance on the form angle is allowed to deviate farther in the direction of the space to the limit of the involute profile. (See Fig. 3.6.12 for deviation allowable.) Riser Free Transition—It should be remembered that, in the transfer of torque through the splines, the stress concentration effects should be studied.

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Fig. 3.6.10  Hardness Conversion Chart (approximate relationship between hardness and tensile strength). Data from SAE Handbook. (Reprinted by permission of the International Nickel Co.)

The transition (runout) of a splined section to the round section should be as smooth as possible, space permitting.

internal spline with a spur design and by specifying a small helix angle on the external spline. The standard approach is to provide a helix angle that will give 0.004 to 0.006 in (0.10 to 0.15 mm) windup within the effective length of engagement. This will usually result in 0.002 to 0.004 in (0.05 to 0.10 mm) effective interference.

A strength of materials handbook on stress concentrations should be consulted for concentration factors. Zero-Backlash Fit via Helix Angle—A common method of effecting a zero backlash (interference) fit is by broaching the

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Fig. 3.6.11  Tapered serration. The dimensions of the mating splines in the transverse plane are usually the same as the ANSI Class 5 (close fit), which allows the parts to assemble one-third to one-half of the way by hand before interfer­ence is reached.

the shaft and hub will be twisted statically in the engaged portion. The hand of helix should be chosen so that the static windup tooth load that exerts torque on the shaft, in the direction of the dominant torque, is located at the deep end of the spline engagement (viewed from the end where the shaft emerges from the spline). This will cause the active tooth contact areas to grow axially as the dominant torque is applied, thus reducing stress concentration. Example: A right-hand helix would be the correct choice for the input spline of a gearbox when the dominant direction of torque is clockwise, viewed axially toward the gearbox. This approach has several advantages over the tapered serration. It is much easier to broach and control the size of a cylindrical member, and it eliminates the swaging operation from the internal member. The advantages in manufacturing the external member are perhaps even greater, in that the control of size and taper angle does not have the serious shortcoming that exists with the tapered member because the position of the two mating parts when assembled can be readily controlled. With the tapered serration it is not uncommon for the relative position of the two parts in the lock-up condition to have as much as 0.25 in (6.4 mm) variation in axial relationship. There can be problems in assembly, when this much variation has to be considered. It also holds that the external member is simpler to inspect because a measurement over pins can be readily taken and composite gages applied.

Fig. 3.6.12  Internal straight-sided serrations. Known successful applications have employed Helix angles ranging from approximately 0.25° to 0.45°. The choice of hand or helix (right or left hand) can be an important consider­ation in highly stressed shafts, particularly when one direction of torque application is dominant over the reverse direction. Obvi­ously, when the helix in the shaft spline teeth reduces the circumferential clearance in the splined joint to a negative value, one end of the spline will be wound statically against the other end. Opposite sides of the spline teeth will be loaded at opposite ends of the spline engagement, and

The inspection of tapered serrations requires two sets of gages with very short teeth to inspect the tooth thickness at the high and low ends of the taper. A single gage can only 3-64

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check the tooth thickness at one end of the taper, because the taper angle affects the possibility of the other end being outside the print tolerance and still having the gage show it to be acceptable. Pressure Angle Deviations for Special Considerations— When spline teeth are to be subjected to high bending stresses, it is desirable to have the loading on the teeth close to the form diameter of the external spline. To accomplish this, a higher pressure angle should be considered for the external that will contact in that area minimizing the bending moment and hence increasing the endurance limit of the spline teeth. This combina­tion is not a mismatched pressure angle from internal to external, but a controlled deviation in the direction of a minus involute profile variation which lowers the point of tooth contact (Fig. 3.6.13).

Fig. 3.6.13  Pressure angle controlled deviation. 1. Test—Automotive driveline sliding spline. 2. Purpose—To study the axial load necessary to slide the spline elements axially under load. 3. Test conditions—140 lb-ft torque applied to spline elements. Spline system lubricated and sealed. Duration of test 100,000 cycles. Stroke 2 inches. 4. Spline Data—30 teeth, 30° Pressure angle, 12/24 pitch, fillet root, side fit.

Self Cutting Serrations—When two parts are to be assembled and there is need to transmit torque greater than the capacity of a cylindrical press fit, a self cutting serration is recommended. This is usually restricted to very fine pitches. This system is composed of an external serration that is straight-sided and has pointed teeth. This is pressed into a hole smaller than the major diameter of the serration and cuts its way into place as it is assembled. The external serration is usually heat treated with the leading edge specified as square and sharp.

Figure 3.6.14 was prepared from the results. The results show that the coefficient of friction increases with the number of cycles. However, it was observed during the same test with the seal removed and the lubricant allowed to flow freely through the spline, that while the coefficient of friction also increased with the number of cycles it had an overall lower magni­tude.

Because this has a cutting action, it precludes the use of a hardened female member. In addition, an annular groove should be planned in front of the leading edge to provide a pocket for the chips. This type of assembly is not recommended for applications that may require servicing.

The conclusion drawn is that the lubricant flowing through the spline system removes entrained metal particles, keeping the mating surfaces clean and free from abrasive action. A complete and careful analysis of all the operating conditions and effects should be explored.

3.6.11 Spline Testing Spline tests are usually conducted during the general test evalu­ation of the shafts and their associated parts. These members undergo practical application testing whereby they are loaded through the splines and cycled for the duration of the test. Failures, if any, generally show up in the early stages.

3.6.12 Typical Failure Types Since splines are usually designed to be stronger than the shaft, the most common type of failure is fatigue failure in torsional shear of the shaft where the spline contact ends (Figs. 3.6.15 and 3.6.16).

Special or unusual spline designs are tested separately.

The modes of spline failure are:

Because splines are generally over designed (see section on design), there is a void in the test data available. However, the following information is offered from a specific test program:

1. Shear of teeth 2. Crushing or rolling over of spline teeth 3. Bursting of hub or crushing of tube containing splines (Fig. 3.6.17) 4. Wear of splines from sliding or rotary eccentric motion

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The standard approach for listing spline data is, on the external, to list the minimum actual tooth thickness and maximum effec­tive tooth thickness and, on the internal, to list the maximum actual space width and the minimum effective space width. In some cases the individual element tolerances are shown as reference dimensions. In cases where splines do not meet gage acceptance, individual element inspection is made to determine the reason for rejection.

Fig. 3.6.14  Load versus cycles slip spline. 5. Corrosion failure of exposed splines 6. Fretting corrosion of lubricated splines Tooth bending failures are not common in the automotive industry.

3.6.13 Drafting Standards

Fig. 3.6.16  Fatigue failure.

The latest SAE Recommendation for spline data format to be specified on drawings is shown in Table 3.6.5. It is interesting to note that there is a trend toward eliminating the spline section view on the drawing and all dimensions thereon and specifying only the spline data, as indicated in the format.

Fig. 3.6.17  Bursting failure. In the same cases, the effective limit is usually inspected by the use of a composite gage. The actual limit is usually inspected by the sector or paddle gage, or the determination of actual limit can be made by a measurement over or between pins.

Fig. 3.6.15  Fatigue failure.

3.6.14 Inspection

In cases where close control of the fit or backlash is required, both the effective limits should be inspected either by means of the composite gages or by use of adjustable effective gages, which are available.

The ANSI B92.1-1970 and ANSI B92.2M standards include an extremely comprehensive inspection section, which describes the use and selection of various types of inspection gages. Careful specification of spline data should be exercised so that splines are not over-inspected.

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In the event that gage acceptance is not reached, the spline must have analytical inspection to determine the reason for rejection. It must be inspected for actual tooth thickness, profile variations, lead or parallelism variations, and spacing.

There are many known methods of inspection for spacing varia­tions. One of the more common practices is a method of indexing and comparing the spacing of the part to the index plate. However, before this type of inspection is of value, one must be absolutely sure there is no runout in the spline, because the amount of runout (FIR) will be added to the index variation in the final recording. Many people use the inspection method by use of micrometers across quadrants of teeth where the maximum reading of this type of check will approximate the value of the maximum effective base tooth thickness, plus an appropriate number of base pitches. This means of inspection is very critical, and if the check shows the spline to be good, then it is indeed good; however, if it shows it to be bad, it does not show exactly how bad. The final total variation of the micrometer reading will usually be about 150% of the actual spacing variation, because the microme­ter checks both sides of every tooth. If a tooth is out of location when the micrometers are on one side of the tooth, it will show the minus reading from the variation and, when it is on the opposite side, it will show the plus reading of the variation, which actually indicates double the value of “out-of-index.”

When checking profile variations, it should be noted that the profile variation that causes rejection is one that is positive; that is, that amount of the profile which deviates from the theoretical in the plus direction from the point of measuring pin contact. It is only at the contact point that the actual tooth thickness is known, and, therefore, any part of the profile that runs plus from that point is a positive variation and is in the direction of interference. Those variations that run lower from this point should not be construed as a cause for gage rejection, since they are in the direction of tooth clearance. When it is deemed necessary to inspect a spline for lead or parallelism variations, four teeth should be chosen as near as possible to 90° intervals. The average deviations of these four teeth should be used as the criteria, since the deviations will be affected by runout, or bowing of the shafts. Using the average of these will nullify the effects of the distortion. Table 3.6.5  SAE Recommendation for Spline Data (English Units) Internal Involute Spline Data

External Involute Spline Data

The following data is required for the part drawing:

The following data is required for the part drawing:

No. of teeth xx

No. of teeth xx

Pitch xx/xx

Pitch xx/xx

Pressure angle 30°

Pressure angle 30°

Base diameter x.xxxx Ref.

Base diameter x.xxxx Ref.

Pitch diameter x.xxxx Ref.

Pitch diameter x.xxxx Ref.

Major diameter x.xx/x.xxx

Major diameter x.xxx/x.xxx

Form diameter x.xxx

Form diameter x.xxx

Minor diameter x.xxx/x.xxx

Minor diameter x.xxx/x.xxx

Circular Space Width:

Circular Tooth Thickness:

Max actual .xxxx

Max effective .xxxx

Min actual *

Min effective *

Max effective **

Max actual **

Min effective .xxxx

Min actual .xxxx

The following information may be added as required:

The following information may be added as required:

Max meas.

Max meas.

between pins x.xxxx Ref.

over pins x.xxxx Ref.

Pin diameter .xxxx

Pin diameter .xxxx

*The minimum actual space width and the maximum actual tooth thickness are not usually required but may be specified to be used as an aid in machine setup. **The maximum effective space width and the minimum effective tooth thickness are not usually required, but are sometimes shown when the assemblies require ex­tremely close control of backlash.

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3.7 The Effective Fit Concept of Involute Splines and Inspection

of industrial applications. In addition, a great deal of interchangeability has been preserved with parts made back when the original ASA standard was revised under the designation B5.15-1960, which is also no longer in use.

Original Author: Leon DeVos (Deceased) Ford Motor Co.

The great flexibility available to meet a variety of industrial applications is demonstrated by the four side-fit size tolerance classifications in the standards. The standards have constant internal minimum effective space widths and external maximum effective tooth thicknesses across their tolerance classes. This provides significant manufacturing advantages by allowing for interchangeability between mating splines in such a way as to average their tolerance classes. For instance, a Class 4 internal spline mated with a Class 6 external spline results in a splined connection having Class 5 level design tolerances.

Revised in 2006 by: C. E. Dieterle C-Dot Engineering M. T. Berhan Ford Motor Co. Note: The effective fit concept for involute splines is in wide use today. With updates to reflect the numerous revisions to the ANSI inch spline standard B92.1 and the addition of a separate and distinct metric standard B92.2M, this paper, originally published as SAE Paper #720671 by Leon DeVos (deceased), is being reprinted due to its lasting value in explaining this concept.

This flexibility is further enhanced by the large selection of sizes, modules and pitches, pressure angles, and tolerances that should satisfy most conditions of design intent. The standards, although based on zero clearance minimum effective fits, do provide means for setting up any amount of minimum effective clearance as necessary for a specific design. The B92.1-1996 inch spline standard also includes a major diameter fit section for those users requiring it; the metric B92.2M-1980 (R1989) standard only uses side-fit splines.

The effective fit concept for involute splines is described herein. It is presently instituted in the American National Standard Institute’s American National Standard B92.1-1996 [1] and its B92.1b-1996 Addendum for inch-based involute splines. For metric (Système International d’Unités, or SI) involute splines, it is set forth in ANSI B92.2M-1980 (R1989) [2] and the International Organization for Standardization’s related standard ISO-4156:1981 [3]. The B92.1 standard, from where the 1996 revision comes, was developed in the 1940s and first published under the American Standards Association (ASA, ANSI’s precursor) designation B5.15, no longer in use. The B92.2M metric standard, the ANSI version of the ISO-4156 standard, is based directly on metric units. It is not a conversion of an inch-based standard to metric units and cannot be treated as such. B92.1 and B92.2M are sponsored as ANSI standards by both SAE and the American Society of Mechanical Engineers (ASME). They are published by SAE.

The use of these spline and inspection standards is supported by a complete list of definitions, all of the basic formulas used to prepare the tables therein, and comprehensive engineering discussions on the effective fit concept. Inspection sections are included that provide detailed guidelines for gage design as well as analytical inspection. These provide practical means to control the product in a framework consistent with the design guidelines. The effective fit concept for use as a control means for splines was introduced by Albert S. Beam in the middle 1940s. The concept made it possible to provide spline specifications that would assure component assembly to the design intent. The part print specifications that are based on this concept dictate exact gage size and inspection methods that make reliable assembly controls possible.

It is important to describe the basics behind the use of the effective fit concept as a means of spline fit control, as well as to describe the advantages that can accrue through the use of a practice that works equally well with both metric and inch splines.

For detailed definitions and explanatory paragraphs for the effective fit concept, see the afore-mentioned ANSI B92.1-1996 and B92.1b-1996 Addendum for inch splines and ANSI B92.2M-1980 (R1989) and ISO 4156:1981 for metric splines. ANSI B92.1-1996 defines an effective spline in paragraph 2.1.1 of its “Spline Terms and Definitions” section as follows:

The fact that the effective fit concept was conceived and implemented in the middle 1940s can be considered one of its prime advantages. The intervening six decades has produced a refined and practical set of spline standards that use this concept. They are able to accommodate a wide variety

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An imaginary perfect mating spline is fitted to the given spline without looseness or interference considering engagement along the entire length of the spline. The effective spline is the surface bounded by this perfect mating spline. The axis of the effective spline is identical to the axis of the perfect mating spline.

effective spline’s center is established by that functional part of the spline that contacts the mating spline. The effective fit concept as used for splines is in reality a form of the maximum material condition (MMC) concept for fit control. This can be seen by comparing Figs. 3.7.1 and 3.7.2, which illustrate the MMC concept as used in a studded connection, and Figs. 3.7.3 and 3.7.4, whose splined members illustrate the use of the effective fit concept.

The effective spline, therefore, is that functional part of the spline that comes into contact with the mating spline and determines the effective fit with the mating spline. This same

Fig. 3.7.1  A plate with eighteen mounting holes controlled by MMC dimensioning and tolerancing specifications.

Fig. 3.7.3  An internally splined part with data based on the effective fit concept.

Fig. 3.7.2  A mating component to the plate in Fig. 3.7.1 with eighteen studs, also controlled by MMC dimensioning and tolerancing specifications.

Fig. 3.7.4  An externally splined part that mates with the part in Fig. 3.7.3 and is also based on the effective fit concept.

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It should be noted that the spline specifications in Figs. 3.7.3 and 3.7.4 allow a “line to line” fit between the mating components, which would not be desirable for proper free assembly. Real-world manufacturing processes, however, would tend to rarely allow this exact condition to occur. The composite gages shown in Figs. 3.7.5 to 3.7.12 are used so as to make a “line to line” fit impossible. In both the studded and spline cases, the way to assure proper assembly to the design intent is to use the methods of specification illustrated here and to use properly designed gages such as shown to assure the parts being within their specified limits. Examination of the gage sizes shows that if the gages confirm that their respective parts’ dimensions are within their limits, the parts will assemble.

tionship of a series of holes and shafts to similar datums, geometric dimensioning and tolerancing (GD&T) specifications are used in Fig. 3.7.1 for controlling the eighteen-hole pattern’s relationship to its diameter “B,” in Fig. 3.7.2 for the eighteen-stud pattern’s relationship to its diameter “B,” and in Figs. 3.7.3 and 3.7.4 for their eighteen-tooth splines’ relationships to their own diameter “B” datums. These types of GD&T specifications and definitions are detailed in the ASME Y14.5M-1994 Dimensioning and Tolerancing standard [4]. For the purpose of analysis related to assembly, fits, etc., the effective spline center can be treated the same as the established center of any other component.

Another important quick check of the fit conditions between mating parts specified in either of the systems is as follows:

An analysis of the previous information further illustrates that when mating splines are confined in position by bearings, bushings, etc., the design must provide a minimum effective spline clearance that is larger than the combined position allowance for both splines.

The amount of interference between the gages for mating parts will be the amount of minimum clearance between mating parts. The amount of clearance between the gages for mating parts will be the amount of maximum press or interference fit between mating parts.

Careful study of the gages shown in Figs. 3.7.5 to 3.7.12 continues to reveal the advantages of the effective fit concept for splines and its similarity to the MMC concept. The gages shown in Figs. 3.7.5 to 3.7.8 are for parts that illustrate the MMC concept shown in Figs. 3.7.1 and 3.7.2. The gages in Figs. 3.7.9 to 3.7.12 are for splined parts that are designed to the effective fit concept. These spline gages follow the specifications detailed in ANSI B92.2M-1980 (R1989) Part III, Inspection.

The use of composite gages for the control of effective size limits on splined mating parts will assure that the minimum effective clearance is never less than the design intent. Measurement of the effective size of mating splined parts, by gages designed to perform this measurement, will determine the minimum effective clearance between these parts. These conditions hold true when the splines are mated without any location constraints such as bearings, bushings, or other items. The effective clearance may be more than that calculated from the measured effective size of the mating parts when the interference variations are positioned in a canceling manner.

Figures 3.7.13 and 3.7.14 are provided to show the relative sizes of different spline pitches and modules. In summary, ANSI B92.1-1996 and its B92.1b-1996 Addendum for inch involute splines, and ANSI B92.2M-1980 (R1989) and ISO-4156:1981 for metric involute splines have wide selections of tolerances, sizes, and pressure angles. These provide engineers and designers a detailed array of choices best suited to their needs and available manufacturing equipment. The selections, applying the effective fit concept, result from careful consideration and improvements over time to produce the most useful standards to the greatest number of users throughout industry.

For splined assemblies that are constrained by bearings, bushings, etc., it becomes necessary to define the center of the effective spline relative to some other geometric features, or datums. The condition of concentricity or relationship control between the effective spline and some diameter is exactly the same as the condition of control between two diameters. It becomes necessary to establish the axis of a component and relate that axis to the established axis of another component. The axis of an effective spline can be determined by use of special gages designed for this purpose.

The assistance of Mark Raye of TIFCO Gage & Gear and chair of the ANSI B92 Spline Committee, Willie Torbert of Michigan Spline Gage Co., and the staff at Invo Spline, Inc. in reviewing the spline gage designs herein is greatly

To illustrate the similarity of concept between the relationship of an effective spline to selected datums and the rela-

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appreciated. The assistance of James Hendrickson and his CAD staff at GM in preparing these graphics is also greatly appreciated.

3.7.1

References

Fig. 3.7.6  A NO-GO plug gage to confirm that any individual hole in the part in Fig. 3.7.1 is not oversized.

1. ANSI B92.1-1996, Involute Splines and Inspection, SAE International, Warrendale, PA, 1996. 2. ANSI B92.2M-1980 (R1989), Metric Module Involute Splines, SAE International, Warrendale, PA, 1989. 3. ISO-4156:1981, Straight cylindrical involute splines— Metric module, side fit—Generalities, dimensions and inspection, International Organization for Standardization, Genève, Switzerland, 1981. 4. ASME Y14.5M-1994, Dimensioning and Tolerancing, American Society of Mechanical Engineers, New York, NY, 1995.

Fig. 3.7.7  A gage for the part in Fig. 3.7.2 designed to confirm the relationship of the eighteen studs to each other as well as the relationship of the entire stud pattern to diameter “B.”

Fig. 3.7.5  A gage designed to confirm that the part in Fig. 1 meets its design intent as to the relationship of the eighteen holes to each other as well as the relationship of the entire hole pattern to diameter “B.” Fig. 3.7.8  A NO-GO ring gage to confirm that any individual stud in the part in Fig. 3.7.2 is not undersized.

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Fig. 3.7.11  A GO composite spline ring gage for confirmation of the maximum effective tooth thickness of the part in Fig. 3.7.4. Fig. 3.7.9  A GO composite spline plug gage to confirm that the minimum effective space width for the part in Fig. 3.7.3 is within specification. A pilot nose is included to confirm proper relationship between the eighteentooth spline and diameter “B.”

Fig. 3.7.12  A NO-GO sector ring gage for confirmation of the minimum actual tooth thickness of the part in Fig. 3.7.4.

Fig. 3.7.10  A NO-GO sector spline plug gage for confirmation of the maximum actual space width of the part in Fig. 3.7.3. 3-72

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Fig. 3.7.13  Basic dimensions for metric involute splines, from ANSI B92.2M-1980 (R1989).

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Fig. 3.7.14  Basic dimensions for inch involute splines, from ANSI B92.1-1996.

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3.8 Chain Drives in the Vehicle Powertrain

than two-wheel drives, chains allow flexibility of positioning and enable the designer to make effective use of available space.

Original Authors: R. H. Mead, T. O. Morrow, R. G. Young, Jr. Morse TEC, BorgWarner Inc.

Three general approaches are used in all-wheel drive vehicles. Manual, automatic, and permanent type drives may employ a chain for power transmission. Refer to SAE standard J1952 [1] for a description of these types of all-wheel drive systems. SAE publication SP-1063 (952600) [2] by Wesley Dick of Dana Corporation also gives an excellent overview of the four-wheel drive (4WD) system. Chain drives can be designed into each type with excellent results in both performance and reliability.

Revised in 2006 by: M. Giovannini, R. G. Young, Jr. Morse TEC, BorgWarner Inc. M. T. Berhan Ford Motor Co. Although some chain drives may appear on the surface to be relatively simple assemblies of components, modern chains in vehicle powertrains have reached impressive levels for low noise, high strength, and high efficiency.

3.8.1

3.8.3

Chain drives work well in both primary and final drives on motorcycles and all-terrain vehicles where the chain offers simplicity, reliability, and flexibility in positioning the final drive unit of these specialized vehicles. Although horsepower levels are not as high as some automotive designs, speeds can be in excess of 10,000 RPM. Chains offer quiet efficiency at high speeds, while requiring minimal maintenance.

Automotive Transmissions

Packaging a front-wheel drivetrain in a passenger car has continued to be an ongoing engineering exercise. In many instances, the transverse-mounted engine has proved more economical as a space saver. A chain drive inside the transmission offers compact, simple designs, with the performance characteristics to meet design requirements of either transverse or longitudinal mounting of the engine. Chains permit flexibility in positioning the drive to fit available space in the system. The designer can “fold” the power path around other components in the drivetrain. Regardless of the path, chains maintain high efficiency and low noise levels over a wide range of operating speeds. This is true in both automatic and manual transmissions. In automatic transmissions a chain often provides the drive between the output of the torque converter and the geartrain in a front-wheel drive (FWD) passenger car. Chains can also transmit power from the output of the geartrain to the final drive subsystem. In manual transmission drives, the chain provides a drive from the output shaft of a manual gearbox to the propshaft(s), or from the clutch to the geartrain.

3.8.2

Specialized High Speed Drives

3.8.4

Choice of Chain Types

Two basic chain joint designs are currently available: the pin-and-rocker joint and the round pin style. Each design has different operating characteristics, which in turn indicate the applications for which they are best suited. 3.8.4.1

Round Pin Design

The round pin chain joint is formed by a single pin inserted into mating holes at each end of the link plate (Figs. 3.8.1a and 3.8.1b). This simple design produces a sliding action of the pin against the link plate hole surface as the chain flexes around each sprocket. Load is distributed over a large aperture area, allowing high chain tensions and high dynamic loads. The robust joint strength is a trade-off resulting in slightly higher friction. For that reason, round pin chain is somewhat less efficient, and pressure lubrication is required for operation at high continuous speed and load. The impactresistant round pin joint chain is widely used in passenger cars with conventional front-wheel drive automatic transmissions, and in transfer cases installed in part-time four-wheel drive vehicles.

Automotive All-Wheel Drive

In all-wheel drive (AWD) applications, the chain delivers power from the transmission to either two or all four wheels through a transfer case. The use of a chain provides a logical method of employing an additional set of driving wheels to the vehicle. Since all-wheel drives require more components

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Fig. 3.8.1a  Round pin chain, perspective view. Fig. 3.8.2b  Rocker joint chain, schematic side view.

3.8.6

Noise Considerations

Noise and vibration are always influenced by the vehicle and driveline. This fact has become even more important as vehicles have become quieter, with more rigid structures and higher standards of noise and vibration. Much has been done to reduce the operating noise levels of chain drives. As with gears, power transmission chains produce a pure sonic tone that varies with speed and the mesh engagement frequency of the sprocket teeth. Since sonic frequencies and their rhythmic harmonics can excite resonant structural elements in the vehicle, noise is generated and transmitted to both the passenger compartment and the surrounding environment. Where resonant noise levels become unacceptable, design alternatives are available to the engineer.

Fig. 3.8.1b  Round pin chain, schematic side view.

3.8.5

Rocker Joint Design

Pin-and-rocker joint chain is comprised of two convex joints that roll against one another as the chain articulates (Figs. 3.8.2a and 3.8.2b). The low friction of this rolling action permits the chain to operate smoothly at very high surface speeds. The pin-and-rocker design has been proven to be very efficient at continuous high speeds, and can be lubricated by an oil bath without excessive temperature buildup. In the past few years, rocker joint designs have been optimized so that the wear benefits can be obtained in a joint with strengths exceeding those of round pin designs. The higher efficiency of the rocker joint chain suggests use in permanent AWD applications and in any applications in which the chain is always turning. With renewed emphasis being placed on efficiency, the rocker joint is proving to be the better choice in any application where chain efficiency can influence fuel economy.

One approach has been the use of hybrid sprockets to reduce pitch-frequency whine. The hybrid sprocket contains a mix of standard involute profile teeth, as well as teeth that have had material relieved from this standard profile. Intermittently spaced with involute teeth, the modified teeth do not contact the chain, thereby breaking up the rhythmic contact. Another chain drive engineering development has proven to be a more effective and durable way of minimizing tooth mesh whine. This “random profile” design employs two different link profiles to break up the rhythmic contact that normally occurs between the chain and sprocket when only a single type of link is used. One link form is designed so that the outside flanks of the links are exposed as the chain approaches the driving sprocket in a straight line, resulting in “outside engagement” between the sprocket and this row of links. The other link profile is designed such that as the chain approaches the sprocket, the inside flanks of the links are exposed when they occupy adjacent rows, creating “inside engagement” between this row of link and the sprocket teeth. Both link

Fig. 3.8.2a  Rocker joint chain, perspective view.

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types are uniform across the width of the chain, but the type of link varies from one to the other along the length of the chain. A pattern is predetermined and then is used in each chain produced for a given application. The “inside-outside” link arrangement enables each sprocket tooth in the driving sprocket to transmit power to the chain, while modulating the time interval between successive link engagements. This design offers optimum power distribution per tooth while altering the natural mesh sequence of the drive to reduce noise (Fig. 3.8.3).

resistance to vibration. Additionally, this system reduces the chain drive’s efficiency.

By varying the pattern of inside and outside link plate profiles, the chain can be tuned to produce the best subjective noise level for each application. In many cases, this random profile linkage feature is able to reduce drive noise to levels that are inaudible in the passenger compartment.

3.8.7.1

3.8.7

Basic Criteria Affecting Drive Design

Four basic criteria affect chain drive design: driveline characteristics, drive layout, type of service and life, and lubrication of the chain drive. Driveline Characteristics

In developing a new drive involving chains, the following procedure is recommended: 1. Sketch the driveline, from the primary mover to the driven member, showing the exact location of the chain drive in the line. 2. For vehicles and mobile equipment applications, tabulate the vehicle characteristics: • vehicle type • gross vehicle weight • weight over front wheels • weight over rear wheels • tire size and rolling radius • coefficient of tire friction • wheel slip torque

A chain pattern analysis program has been developed to allow the modeling of the random patterns and the corresponding frequency output using analytical techniques. This program can save a great deal of time in trial-and-error testing in the vehicle, because the worst points of vehicle resonance can be tuned out initially, and with some relatively simple test results the pattern can be finalized to achieve the best possible noise characteristics. In production, the pattern can be consistently reproduced during assembly, assuring repeatable sound levels. “Random profile” chain has been in production in both round pin and rocker joint styles for many years.

Wheel slip torque should be used to calculate the corresponding torque at the chain. Compare this torque to the maximum output torque from the prime mover to the drive sprocket, generally using whichever is lower for the chain drive design. Other factors to be taken into account are antilock brakes, traction control, and automatic vehicle stability control systems. If the vehicle wheels can be slowed or stopped by an active control system, the entire driveline, including the chain, must be designed for maximum available torque for at least some period of time. 3. In other drive applications such as accessory drives, if the power absorbed by the driven element is lower than the maximum power output of the prime mover, use absorbed power for the chain drive design. 4. Define the prime mover’s characteristics. For vehicles and mobile equipment applications, this includes: • engine make and type (gas/diesel) • number of cylinders • maximum torque at RPM • maximum power at RPM • power at maximum RPM

Fig. 3.8.3  “Random profile” chain. In general, noise levels are reduced as pitch length of the chains is reduced. A balance between chain durability and noise level can usually be achieved if all factors are taken into account in the initial design. Another development in chain noise mitigation is the use of spring links. Thinner spring shaped links can be used to side load the chain links against each other and help prevent chain resonance. However, care must be used to allow for the natural degradation of this side force which reduces the 3-77

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5. Define the chain characteristics as it is used in the vehicle driveline. Define any of the following ratios between the prime mover and the wheels, and define if the transmission is a manual or an automatic with a torque converter. If a torque converter is present, obtain its torque output curve. • converter torque ratio at stall • transmission output gear ratios (all gears) • auxiliary transmission and transfer case ratios • axle ratios 3.8.7.2

vehicle testing provide the best way to verify the final selection of most driveline components. Factors for use as guides to different categories of applications are available from a chain manufacturer. 3.8.7.4

A chain is an extremely efficient form of power transmission, with modest demands for lubrication. However, due to the nature of its operation and the high linear speeds at which it may operate, it is essential that the chosen lubricant be delivered to the chain effectively. It must penetrate to and flow through the articulating joints of the chain.

Chain Drive Layout

Make a dimensional layout of the proposed chain drive, defining its basic requirements, physical limitations, and lubrication options.

3.8.8

• approximate center distance (contact chain manufacturer to select or approve final values) • approximate ratio required (indicating design limits from nominal) • sprocket drive and rotation direction • inclination of chain drive (drop angle)

While design details, including chain, sprocket, and pitch selection, center distances, and tolerances, should be discussed and reviewed with the chain manufacturer while developing a chain drive system, some important design considerations follow.

Physical limitations:

• An odd number of teeth on both sprockets for better sprocket wear is preferable. Any sprocket with an even number will experience somewhat higher wear than if it had an odd number of teeth. • The number of teeth in either sprocket should not be an exact divisor of the number of pitches in the chain, i.e., 25T or 50T sprockets with 100 pitches in the chain. • Check the ratio’s suitability. • Check that the sprocket diameters fit in the center distance, with no contact between the sprockets. • A clearance of about one-half chain pitch should be allowed between the outside diameters of the sprockets. Also, check space limitations for installation purposes.

sprocket diameters width of chain or transfer case sprocket bore size casing dimensions ground clearance inertia limitations on primary drives case mounting and location of mounting pads

Lubricating options: • shared lubrication with other components • pressure lubrication with oil pump 3.8.7.3

Chain Drive Design Procedure

Drive chains are available commercially in several different pitches, most commonly in inch dimensions, including .375 in (9.525 mm), .4346 in (11.039 mm), and .5033 in (12.784 mm).

Basic requirements:

• • • • • • •

Chain Lubrication

If possible, it is preferred to have a small sprocket with thirty-five teeth (35T) or more. In many cases, this is not possible and the chain manufacturer can develop a suitable solution.

Required Life and Duty Cycle

For most vehicle applications, the objective is to select the smallest and most economical drive to suit a specific application and meet a certain duty cycle and drive life. Having to meet differing duty cycles from composite usage across multiple applications can make the final drive selection more complex. If a vehicle is to operate in first gear for long periods of time, the optimal chain drive is not the same as for a vehicle with light first gear usage. Dynamometer and actual

In selection of chain pitches and number of sprocket teeth, the following formula for chain linear speed may be used:

V = number of sprocket teeth ¥ (pitch / 39.73 in/m) ¥ RPM

(3.8.1a)

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Table 3.8.1  Depth of Case Hardening

when converting to SI units from the inch pitch design standard, or

V = number of sprocket teeth ¥ (pitch / 12 in/ft) ¥ RPM

(3.8.1b)

when staying with the inch-based values and using the historically used U.S. Customary unit system, where

V = chain linear speed, m/min (ft/min)

.375 in

0.25 to 0.38 mm (.010 to .015 in)

.4346 in

0.30 to 0.50 mm (.012 to .020 in)

.5033 in

0.38 to 0.64 mm (.015 to .025 in)

Material Standards: Bar stock—UNS G11410 (AISI-SAE 1141) Plate—UNS G10450 or G10400 (AISI-SAE 1045 or 1040) Castings—per EN 10293:2005 [4]

Sprocket Design

Sprocket design involves both material and dimensional considerations. Material considerations include metals specifications, heat treatment, and hardness requirements. Dimensional considerations beyond the tooth counts and diameters and clearances mentioned above include manufacturing tolerances. 3.8.9.1

Case depth

3.8.9.1.2 Medium Carbon Steel

Linear speed is important for the lubrication concerns discussed below and the centrifugal load concerns noted in the appendix.

3.8.9

Pitch

Heat Treatment: Flame or induction heat to 815 to 870°C (1500 to 1600°F) and spray or immersion quench with a soluble oil/water solution or agitated oil. Heating may be single tooth traverse and index spin. Suitable quench media controls must be in effect to avoid cracking and soft spots. Overheating and melting are prohibited; melt zones are cause for scrapping. Temper to hardness range specified; all water quenched parts must be tempered at 204°C (400°F) minimum.

Sprocket Material Considerations

The following standards for materials, heat treating, and hardness should be followed in chain sprocket design.

Effective Hardness Pattern: This defines the zone in which the hardness of HRC 58 minimum must be maintained. Normally, the visual etch pattern will extend at least 0.75 mm (.030 in) below this zone of minimum hardness (Fig. 3.8.4 and Table 3.8.2).

3.8.9.1.1 Carburizing Steel

Material Standards: Bar stock up to 16 inches—UNS G11170 (AISI-SAE 1117) Plate—UNS G10200 (AISI-SAE 1020)

Table 3.8.2  Range of Minimum Surface Hardness, Approximate Dimensions

UNS stands for the Unified Numbering System, as described in SAE HS-1086/2004-ASTM DS-561 [3], jointly published by SAE International and the American Society for Testing and Materials. AISI-SAE stands for the classical American Iron and Steel Institute-Society of Automotive Engineers system for numbering metals and alloys, from which the UNS arose. Heat Treatment: Gas carburize, carbonitride, or cyanide at 815°C (1500°F) and direct oil quench. No tempering is required. Depth of case hardening should be as listed in Table 3.8.1.

Pitch

A

B

.375 in

2.8 mm (.11 in)

4.1 mm (.16 in)

.4346 in

3.1 mm (.12 in)

4.4 mm (.18 in)

.5033 in

3.6 mm (.14 in)

5.3 mm (.21 in)

Hardness Pattern: All tooth surfaces should be case hardened. Hardness should be checked on the tooth O.D. and the root of the flank. They should be at a Rockwell C scale (HRC) hardness of 58 HRC or above. The hub face may be hard or soft as specified. Fig. 3.8.4  Hardness pattern zone. 3-79

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Alternate methods of sprocket manufacture may be considered. Where the highest production volumes are planned, consideration may be given to either sintering or sinter forging of the sprockets. Substantial economies may be found in using one of these alternatives.

Helix: The allowable helix error (tooth face out of parallel with the bore) for sprockets is 0.050 mm (.002 in) per 25 mm (1 in) face width, with a 0.125 mm (.005 in) maximum. Taper:

Sintered sprockets are available in a wide variety of materials and densities to suit different applications. Sprockets for high-performance applications will require higher densities to improve strength and reduce wear. Normally it is necessary to specify a minimum density, apparent hardness, and a file hardness value for a sintered sprocket. Where a sprocket is case hardened it is necessary to specify both a surface hardness and a case depth.

The variance in over-rolls measurement from the extreme end of a sprocket tooth to the opposite end of the same tooth should not exceed 0.025 mm (.001 in) per 25 mm (1 in) of tooth length, up to a maximum of 0.125 mm (.005 in) regardless of the tolerance permitted on over-rolls dimensions. Surface finish: Tooth surface finish should be equivalent to that obtained by the best hobbing or shaping methods. In general, no subsequent tooth finishing operation such as grinding is necessary.

3.8.9.1.3 Non-Standard Materials

A variety of other material can be used to make satisfactory hardened sprockets. Examples: • • • • •

alloy carburizing grades alloy medium carbon grades Meehanite® GM-60 certain grades of ductile iron certain grades of pearlitic malleable iron

3.8.10 Chain Case Design In order to obtain maximum chain life, proper case design is essential. 3.8.10.1 Case Clearances

The load sharing characteristics of chains allow load to be transmitted to several teeth at any given time. This, along with the absence of relative motion between chain links and sprocket teeth during power transmission, means that individual tooth strength requirements are substantially less than with gears. 3.8.9.2

It is essential that clearances within the chain case conform to those specified by the following formulas: Preferred Formula: R = standard chain clearance radius around sprockets R = (sprocket O.D. / 2) + C (3.8.2) Acceptable Equations: R1 = minimum chain clearance radius around sprockets R1 = (sprocket O.D. / 2) + D (3.8.3)

Sprocket Dimensional Considerations

Although, as noted above, sprocket design details should be discussed and reviewed with the chain manufacturer, some important sprocket manufacturing tolerances should generally be addressed as follows.

Values for C and D can be drawn from Table 3.8.3.

Sprocket eccentricity:

Table 3.8.3  Chain Clearance Values

Unless otherwise specified, the maximum allowable eccentricity of the pitch diameter (over-roll diameter) to the bore should be:

Pitch

C

D

.375 in

19.0 mm (.750 in)

12.7 mm (.500 in)

.4346 in

22.4 mm (.880 in)

14.9 mm (.585 in)

.5033 in

25.4 mm (1.000 in)

17.0 mm (.670 in)

• 0.150 mm (.006 in) TIR on sprockets 150 mm (6 in) or less in diameter. • 0.025 mm (.001 in) TIR per 25 mm (1 in) of pitch diameter on sprockets over 150 mm (6 in) pitch diameter.

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3.8.10.2 Thermal Expansion

Table 3.8.4  Maximum Permissible Sprocket Offset Values

Under normal circumstances, it is not necessary to make any allowance on chain case center distance for eventual expansion at the working temperature of the drive. The expansion rate of the chain will provide the necessary compensation.

Width

3.8.10.3 Case Construction

Over 25.4 mm (1.00 in)

Pitch 25.4 mm (1.00 in) or less

Due to the compressive loads between shaft bearings generated by a chain drive, and the relatively modest rigidity and alignment requirements of the sprockets, a chain drive case can be made light, using economical construction. The case may employ cantilevered or center bearing sprockets. It may also be integral with another part of the drivetrain, using thin-wall aluminum casting. Enclosures should be designed to reduce radiation of noise through a combination of stiffness and material.

.375 in

.4346 in

.5033 in

0.50 mm (.020 in)

0.50 mm (.020 in)

0.50 mm (.020 in)

0.50 mm + [chain width ¥ 0.13 mm] (.020 in + [chain width ¥ .005 in])

3.8.11 Bearing Loads and Selection Bearing load is a function of the power transmitted by the chain. The load transmitted to the bearings is the same as the chain strand load, generated by the transmission of torque (or power), and is applied in a direction parallel to the tight strand of the chain. Since all chain drive loads are carried on non-helical sprocket teeth, no axial loads are generated. The direction of load is such that it tends to pull the shafts together rather than separate them as in a gear drive. The centrifugal tension generated within the chain is not transmitted to the bearings. The centrifugal effect at one sprocket is counteracted by the other sprocket with an equal and opposite effect. Therefore, centrifugal tension will not increase bearing loads, although chain tension does increase due to centrifugal force.

3.8.10.4 Shaft Parallelism Shafts must be parallel in two planes within 0.4 mm/m (.005 in/ft) of bearing mounting distance. Special attention must be given to drives with non-horizontal shafts, due to the tendency of the chain to ride on the guide links. 3.8.10.5 Sprocket Offset

Designers have a large variety of bearing types from which to choose. Although selection may require considerable experience, the following can serve as a general guide for conventional applications.

Measured as illustrated in Fig. 3.8.5, offset from the machined face of the second sprocket should be held to zero, with the maximum permissible offset given in Table 3.8.4. Excessive offset will cause wear on the inside of the guide links, or possible chain failure if the chain guides climb the sprocket teeth.

• Generally, ball bearings are the less expensive choice in small sizes and lighter bearing loads, while roller bearings are less expensive for larger sizes or heavier loads. • Roller bearings are more satisfactory under shock or impact loads than ball bearings. • If there is misalignment between housing and shaft, either a self-aligning ball bearing or spherical roller bearing should be used. These bearings have very low friction coefficients under misalignment, as compared to standard ball or roller bearings. • Ball thrust bearings should be subjected to pure thrust loads only. At high speeds, a deep-groove or angular contact ball bearing will usually be a better choice even for pure thrust loads. • Deep-groove ball bearings are available with seals built into the bearings, so that the bearing can be prelubricated for less frequent maintenance.

Fig. 3.8.5  Measurement of sprocket offset.

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3.8.12.1 Oil Bath Lubrication

• Radial needle bearings are used in applications where there are no thrust loads and cost is a serious consideration. Needle bearings, having smaller radial package requirements, can be used to reduce sprocket size.

For composite, or variable, duty cycle chain drives with chain linear speeds not exceeding 1200 m/min (4000 ft/min), or continuous duty less than 760 m/min (2500 ft/min), an oil bath is generally satisfactory.

3.8.12 Chain Lubrication

3.8.12.2 Pump Lubrication

It is important to determine whether the chain will be lubricated with, or independently of, other components in the engine, transmission, or other powertrain unit. It is also important to determine what that lubricant will or should be. Below are recommendations for lubrication type based on linear speed, duty cycle, and temperature. See Tables 3.8.5 and 3.8.6. The chain manufacturer should be contacted for details and questions. Note that any production or service fill automatic transmission fluid (ATF) such as MERCON® or DEXRON® may generally be used in any chain application, at least with respect to the chains themselves.

Where continuous chain linear speeds exceed 760 m/min (2500 ft/min), pressure lubrication should be used. Oil delivery rate should be one liter/min for each inch width of chain, at a minimum of 1.4 bar (0.14 MPa, or 20 psi). The point of delivery should be such that the oil flows into and through the chain as the slack strand enters the driven sprocket, as illustrated in Fig. 3.8.6. In certain instances, where pump lubrication is not feasible, it is possible to develop deflectors within the chain case to ensure that oil flow is directed into the chain at the correct place and throughout the entire range of operating speeds. Holes drilled through the roots of the sprocket teeth across the total tooth width can also provide a means of supplementing lubrication, as shown in Fig. 3.8.7.

Table 3.8.5  Lubrication System Type vs. Duty Cycles and Linear Speeds Duty cycles and speeds

Lube system type

Continuous < 760 m/min (2500 ft/min)

Bath

Composite < 1200 m/min (4000 ft/min) Continuous > 1200 m/min (4000 ft/min)

Pump *

Composite > 1500 m/min (5000 ft/min) * If development and verification work is possible, deflectors or oil collectors in lieu of a pump are possible in some cases. *Engine, or motor, oils should be American Petroleum Institute (API) service (S) category SJ, SL, or SM for gasoline engine applications, or an applicable API diesel engine commercial (C) category oil [7].

Fig. 3.8.6  Lubrication at entrance of slack strand to driven sprocket.

Table 3.8.6  Viscosity and Target Oil Grade Recommendations Per Type

Surrounding or ambient temp. Under 4.4°C (Under 40°F) 4.4°F to 32.2°C (40°F to 90°F) Over 32.2°C (Over 90°F)

Kinematic viscosity: m2/s (Saybolt Universal Seconds) at 37.8°C (100°F), appx.

Automatic transmission fluid

3.2 ¥ 10–5 m2/s (150 SUS) 4.3 ¥ 10–5 m2/s (200 SUS) 6.5 ¥ 10–5 m2/s (300 SUS)

Any production or service fill ATF

SAE automotive (manual transmission) gear oil viscosity grade (per SAE J306 [5])

SAE engine oil viscosity grade (per SAE J300 [6]) *

70W or 75W

0W or 5W

70W or 75W

10W

80 or 80W

15W, 20 or 20W

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3.8.12.4 Oil Temperature—Guidelines Oil durability degrades rapidly with increasing temperature. It is desirable to limit oil sump temperatures to 82°C (180°F) to prevent rapid deterioration of the oil. This can be accomplished by external cooling fins or an oil cooler, if necessary. ATF sump temperatures should not be allowed to go past 104°C (220°F). Generally, chains operate with a temperature rise of approximately 22°C (40°F) above ambient temperature. If an oil cooler is installed as part of the lubrication system, the SAE grade oil for the next lower ambient temperature range as shown in Table 3.8.6, or one with an equivalent kinematic viscosity (often given in Saybolt Universal Seconds, abbreviated as either SUS or SSU, and often primarily specified at 37.8°C or 100°F) can be used. For example, in an engine oil lubricated application, if the ambient temperature is 35°C (95°F) and an oil cooler is not used, an engine oil SAE 20W-300 SUS @ 37.8°C (100°F) with API service classification SJ, SL, or SM should be used. If an oil cooler is added to the system, an SAE 10W-200 SUS @ 37.8°C (100°F) oil can be used.

Fig. 3.8.7  Lubrication holes through sprocket teeth roots. It is recommended that the oil reservoir have a minimum capacity of three minutes’ oil flow. 3.8.12.3 Oil Levels With oil bath lubrication, static oil level must be high enough to provide adequate oiling during operation. An excessively high oil level may cause churning losses and heat buildup. As a rule, a dynamic oil level at the pitch diameter of the lower sprocket will be effective.

It should be noted that higher-viscosity manual transmission gear oils, where applicable, give better chain wear performance than ATF, although at cost to fuel efficiency. Thus, gear oils ranging from SAE 75W to 90, or engine oils ranging from SAE 10W to SAE 50, are feasible for many applications.

The effect of chain case configuration on oil capacity must also be considered. Thus, for the same oil level illustrated in Fig. 3.8.8, drawings A (horizontal) and B (vertical), greatly different sump capacities will be obtained. It may be necessary to increase the sump capacity seen in B by designing a case as shown in drawing C.

3.8.12.5 Lubrication Changes The oil should be kept clean to ensure long, trouble-free service. If the oil becomes dirty or discolored, or otherwise appears to be contaminated, it should be drained, the case flushed, and the oil replaced. Good practice dictates that periodic oil changes should be made with proper SAE viscosity and API changes every 1000 hours or four months, whichever occurs first. If ATF is used, it should be changed if the red color turns brownish, indicating oxidation of the fluid. When oil is changed, the case should be flushed with a suitable solvent and new lubricant installed. If water is found in the lubricant, more frequent changes may be required. Conversely, longer intervals between changes are possible if operating conditions do not cause the oil to deteriorate or become contaminated. The recommended change interval should be determined by careful analysis of the operating conditions and inspection of the lubricant.

Fig. 3.8.8  Chain case configurations.

When making oil changes, a thorough inspection of the lubricant system piping, pump, and spray pipe orifices should be made. The filter element should be inspected and replaced at this time if it is dirty.

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3.8.15 References

A properly functioning lubricant system, with clean oil of the correct type, is necessary for long, quiet, and trouble-free life of the chain drive and case.

1. SAE J1952 NOV2003, “All-Wheel Drive Systems Classification,” SAE International, Warrendale, PA, 2003. 2. Dick, Wesley M., “All-Wheel and Four-Wheel-Drive Vehicle Systems,” SAE SP-1063/Paper No. 952600, SAE International, Warrendale, PA, 1995. 3. SAE HS-1086/2004-ASTM DS-561: Metals and Alloys in the Unified Numbering System, Tenth Edition, SAE International, Warrendale, PA, 2004. 4. EN 10293:2005, “Steel castings for general engineering uses,” European Committee for Standardization, Brussels, Belgium, 2005. 5. SAE J306 JUN2005, “Automotive Gear Lubricant Viscosity Classification,” SAE International, Warrendale, PA, 2005. 6. SAE J300 MAY2004, “Engine Oil Viscosity Classification,” SAE International, Warrendale, PA, 2004. 7. “American Petroleum Institute Motor Oil Guide,” American Petroleum Institute, Washington, DC, 2004. 8. “Morse Hy-Vo Drive Engineering Guide,” Borg Warner Corporation, Ithaca, NY, 1979. 9. “Hy-Vo Transmission Chain,” Borg Warner Corporation, Ithaca, NY, 1987. 10. Binder, R. C., Mechanics of the Roller Chain Drive, Prentice-Hall Inc., Englewood Cliffs, NJ, 1956.

Avoid use of oils with EP (extreme pressure) additives such as those used in hypoid gear lubricants. Such additives have been shown to greatly accelerate chain wear in some applications. When lubrication of other driveline components prohibits the use of the recommended chain lubricant, the chain manufacturer should be consulted.

3.8.13 Automotive Friction Drive Chains The friction drive chain has been developed embodying the form of a metallic “V” belt. It provides the strength and efficiency of a toothed power chain while driving pulleys, or sheaves, which can themselves provide variable drive diameters. Using these chains and variable-diameter sheaves in a suitably designed transmission, a continuously variable transmission (CVT) can be designed for automotive use. CVTs can provide increases in performance, economy, and smoothness over a conventional stepped-ratio automatic transmission. The CVT chain extends the well-developed technology of power chain strength, efficiency, and durability. The chain belt operates wet in automatic transmission fluid using relatively high hydraulic pressure to generate clamping forces at the belt-sheave interface.

3.8.16 Appendix 3.8.16.1  Chain Drive Wear Life Analysis

Design of belt systems follows the requirements of other chain types but requires more stringent attention to details, as the loads and speeds tend to remain at a higher level throughout the duty cycle. Servo design is critical to maintain safety factors and ratio control without overloading the belt. Properly designed belt and sheave systems attain efficiency levels of 95% and durability capability of 100,000 miles.

Only wear or elongation causing the chain to jump over a sprocket tooth limits the life of a properly designed chain drive. The allowable elongation of the slack chain strand of a fixed center drive, after which it will jump a sprocket tooth, is ½ pitch. At this point, the toes along a row of links will have advanced far enough to contact the top of the next tooth of the driven sprocket (see Fig. 3.8.9).

Consult a chain manufacturer for details on the CVT chain and its application.

If the chain center distance (Fig. 3.8.10) is measured on a measuring machine with moveable centers, the center distance will have increased ¼ pitch.

3.8.14 Further Reading

Thus, the allowable center distance elongation for the three chain pitches discussed herein, .375 in, .4346 in, and .5033 in, would be:

This paper has been developed over more than 30 years, and has been revised and edited several times to keep it up to date with current design practices. It draws from past publications by BorgWarner [8, 9]. For further reading on chain drives, a classic work in the field is by R. C. Binder [10].

(.375 in ¥ 25.4 mm/in) / 4 = 2.38 mm (.094 in) (3.8.A-1a) (.4346 in ¥ 25.4 mm/in) / 4 = 2.76 mm (.109 in) (3.8.A-1b) (.5033 in ¥ 25.4 mm/in) / 4 = 3.20 mm (.126 in) (3.8.A-1c)

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This gives only a guideline for usable wear life, and application of high torques can lower this value substantially, depending on the elastic properties of the chain and other design factors.

Chain wear is dependent on the drive characteristics and number of chain cycles, and is not accurately predictable. The rate of elongation, after the initial break-in period, is a nearly linear function of the number of wear surfaces in the chain, with the ratio of the slopes of the curves the same as the ratio of the chain pitch (.375 in/.5033 in = 0.75). Thus, it would be predicted that the wear rate of a .500-in pitch chain would be 75% of that established for a .375-in pitch chain operating under similar conditions.

3.8.16.2  Items Influencing Allowable Elongation The allowable elongation comprises two parts, that due to the elastic properties of chain and that due to wear. Elongation Due to Elastic Properties of Chain

The allowable center distance elongation due to wear is the difference between the allowable elongation (¼ pitch) and the effective elastic center distance elongation.

The elastic elongation of the chain is due to the centrifugal load and/or the working load. Fc = W ¥ V2 / (60 s/min)2



Figure 3.8.11 illustrates typical wear curves for both .375-in pitch and .5033-in pitch drive chains. Also shown are horizontal lines at the theoretical tooth jump condition or wear limit. The difference between the starting points of the curves reflects the effect of elastic elongation, with the allowable wear for each pitch being approximated by the difference between the wear curve and the horizontal line representing the wear limit.

(3.8.A-2a)

in SI units, or

Fc = W ¥ V2 / ((60 s/min)2 ¥ 32.2 ft/min2) = W ¥ V2 / (116,000 lb-ft/min2/lbf) (3.8.A-2b)

in U. S. Customary units, where

Copyright 2006, BorgWarner Inc., 800 Warren Rd., Ithaca, NY 14850

Fc = centrifugal load, N (lbf) W = chain weight, kg/m (lb/ft) V = chain linear speed, m/min (ft/min)

Fw = T ¥ 1000 ¥ 2 / P.D.

(3.8.A-3a)

Fw = T ¥ 12 ¥ 2 / P.D.

(3.8.A-3b)

in SI units, or

in U. S. Customary units, where Fw = working load, N (lbf) T = torque on sprocket, N-m (ft-lbf) P.D. = pitch diameter of sprocket, mm (in)

Fig. 3.8.9  Chain jumping action.

The elastic elongation in the tight strand is due to the sum of the working load and centrifugal tension. The elastic elongation in the slack strand is due to the centrifugal tension alone. The total elastic elongation in the chain is the sum of that for the tight and slack strands, and the effective center distance elastic elongation is half of the total elastic elongation. Effective elastic elongation = ½ (etight + eslack)

(3.8.A-4)

where:

Fig. 3.8.10  Center distance increase.

etight = elongation due to working load + centrifugal load in tight strand eslack = elongation due to centrifugal load in slack strand 3-85

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reduction efforts described in this paper were achieved with a phase lag of 180°. The new system is readily manufacturable. It is made with current processing technology. Its first production volume application is in the 1995 Chrysler Corporation LH vehicles.

3.9.2

Chains have long been in use in power transmission applications in the automotive field. Chain drives compare favorably to gear drives for noise, cost, and durability. This is particularly true when the designer is faced with spanning large center distances where chains are tolerant of tolerance stack ups and where one or more idler gears, idler shafts, and bearings are required for a gear drive. For these reasons, chains are used in many front-wheel drive transaxles, most four-wheel drive transfer cases, and engine timing drives.

Fig. 3.8.11  Generalized wear curve behavior over time.

3.9 The Gemini Phased Chain System: A New Tool in Automotive Power Transmission

One of the critical factors considered in designing chain drives is minimizing noise. While a low noise level has always been a determinant in selecting a power transmission drive, it is becoming increasingly important. Often the quality of the entire system is judged by its noise performance. As background noise levels in vehicles continue to drop, chain noise has become an important issue. There have been several methods of reducing chain noise, which have proven to be effective in problem applications. However, new expectations of further reductions in noise levels have posed new challenges to chain engineers.

P. Mott BorgWarner Automotive B. Martin Chrysler Corp. Based on SAE Paper No. 950667.

3.9.1

Introduction

Abstract

Extremely low noise levels at high power densities are achieved with a new inverted tooth silent chain system. Two chains of random link design are phased such that the first order and subsequent odd orders of sprocket mesh frequency noise are canceled, while remaining even orders are minimized by link randomization.

3.9.3

Chordal Action

Noise and vibration in chain systems are largely caused by chordal action and impact between the chain and the sprocket. The term chordal action derives from the fact that a chain is composed of relatively rigid pitches which make a polygonal approximation to the circular form [1]. Using shorter chords (pitches) makes the approximation better and the drive smoother, but strength requirements impose a lower limit on pitch size. Chordal action causes fluctuations in speed and torque within the chain system. This in turn causes fluctuating bearing force reactions that add vibrational energy to the drive system and enclosure, finally resulting in chain-associated structure and airborne noise.

Current chain noise reduction practice has applied randomization with a primary emphasis on finer link pitch to control mesh frequency noise. As the link pitch becomes finer, however, the chain loses strength and package size must increase to compensate. The principle of operation of the new phased chain system is not primarily a function of the chain pitch. Therefore, significantly higher power transmission densities can be achieved in the same package without sacrificing noise benefits.

In a simple chain that has perfectly identical pitches, the resulting vibrational energy has a very dominant pitch passing frequency component because the chordal action repeats with each passage of a pitch. In most automotive applications pitch frequency is well within the hearing range of the

To achieve the noise cancellation, motive power is transmitted by two chains mounted in such a manner that a specified phased lag exists between them at all times. The noise

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human ear. The resultant noise is characterized by a high pitch whistle, which can be annoying even at low levels due to the tonal content (single pure tone).

Experimental noise comparisons between roller and silent chain are shown in Table 3.9.1.

Early chain construction did not address noise directly. Roller chains, although having excellent wear and strength capability, are inherently noisy. As a result, inverted tooth chains were developed to reduce the forcing function of the noiseproducing mechanism.

Table 3.9.1  Roller vs. Silent Chain Experimental Noise Test Results

The difference in noise performance between silent and roller chains can be attributed to the manner in which they engage and disengage the sprocket. Silent chains have an inside link flank which engages the sprocket tooth in a sort of cam action. Therefore, after the sprocket tooth initially contacts the chain link and as the engagement proceeds, a combination of rolling and sliding motion occurs between the tooth and link contacting surfaces. Such an engagement mechanism effectively spreads the engagement over a given time interval, thereby minimizing the tooth/link impact and its inherent noise generation. Additionally, this cam action further reduces chain drive noise by significantly reducing the chain chordal action discussed earlier. This is accomplished because the sprocket tooth initiates contact on the link inside flank while the chain freestrand is moving downward in its constant up-and-down chordal action motion. The sprocket tooth then essentially pushes the freestrand back up, thereby preventing it from falling to the minimum position it would otherwise attain and reducing the overall freestrand motion range. Roller chain, by contrast, exhibits no such cam action upon sprocket engagement. Thus, the impact between the sprocket tooth and roller occurs over a much smaller time interval than it does in the case of silent chain. Furthermore, there is no mechanism to reduce the degree of chordal action and resulting freestrand motion as there is with silent chain. These factors make roller chain drives inherently louder than silent chain drives. This important distinction is illustrated in Fig. 3.9.1, which plots the freestrand vertical position as a function of time, as the individual chain pitches engage the sprocket.

Chain Type

Pitch Frequency (dBA)

Second Order (dBA)

Overall Level (dBA)

Roller Chain

68.7

63.0

75.6

Silent Chain

62.6

59.6

73.9

Further reductions in noise required chain manufacturers to reduce the pitch of the chain. Unfortunately, the penalty for smaller pitch is high. Chain strength is strongly related (linearly) with chain pitch length. For similar transmitted torque capacity, smaller-pitch chains are necessarily wider. This increases the cost, package size, and weight of the system.

3.9.4

Randomization

Even with small-pitch inverted tooth chain, noise can still be objectionable. The noise is a single pure tone related directly to “pitch frequency,” the passing frequency of the link over the sprocket teeth. To make this noise less objectionable, randomization was introduced into the chain system sprockets in the mid 1960s (1965 Oldsmobile Tornanado). Later, in 1983, a randomized chain was introduced in the New Process Gear 207 transfer case. Randomization is achieved by using at least two different link’s profiles arranged in a predetermined pattern. Computer models are used to search for and select the best pattern. Randomization is capable of reducing pitch frequency even further (although in some applications pitch frequency could still be noted) at the expense of slightly increasing overall noise. Table 3.9.2 presents a comparison between random and non-random inverted tooth chain. Table 3.9.2  Random vs. Non-Random Inverted Tooth Chain Pitch Frequency (dBA)

Second Order (dBA)

Overall Level (dBA)

Non-Random

65.5

62.3

78.1

Random

61.9

55.3

80.2

Chain Style

Still, the requirement for noise reduction has pushed relentlessly further. Smaller, lighter weight transmission housings, reduced noise of other transmission components, and heightened customer awareness are all contributing factors. There-

Fig. 3.9.1  Chordal action of roller chain and silent chain. 3-87

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fore, a new approach is needed. Smaller pitch chains can no longer be considered due to package size constraints on chain width. Randomization has been optimized by computerselected chain patterns. The chain link and sprocket tooth profiles have been developed over many years to minimize noise.

3.9.5

was determined to be capable of transmitting only one half of the power transmitted by the silent chain drive. Further development of the roller chain system was abandoned.

3.9.6

Analysis of Phasing

Chordal action, like any other cyclic phenomenon, can be represented as the sum of a series of sinusoidal functions of various frequencies. In a chain without any randomization, pitch frequency predominates, but there are overtones at twice pitch frequency, three times pitch frequency, etc. Randomized chain produces a full spectrum of frequencies both above and below pitch frequency. By phasing two chains one half cycle apart, all components of vibration at pitch frequency, 3 times pitch frequency, 5 times pitch frequency, etc. are totally canceled, but the even (2, 4, 6, …) multiples are unaffected. This fact is true regardless of the shape of the chordal action forcing function. If chordal action were perfectly sinusoidal, and perfect phasing were accomplished, cancellation would be total. Since chordal action is not perfectly sinusoidal, phasing does not in practice remove all vibration. Since pitch frequency noise has been the dominant problem, phasing can produce dramatic improvements over conventional single-chain systems.

Phasing

The approach taken was to substitute two narrow chains (each approximately half the width of the original chain) for the single, wide chain (Fig. 3.9.2). The two narrow chains run on sprockets which are displaced circumferentially, or phased, by one half pitch. This construction causes the two chains to mechanically cancel out the first order and all odd higher orders of pitch frequency. Thus, seemingly unattainable levels of pitch frequency noise reduction can be achieved even with large pitch chains. Randomization is introduced in the system to reduce any even-order harmonics which remain.

The analytical basis for phasing two chains involves the mathematics of adding two signal traces or waveforms, which represent a characteristic noise and/or vibration signature. Since this concept is best illustrated graphically, a series of three graphs for each of five different combinations is shown in Fig. 3.9.3. In each case, the first plot is the time history of the individual traces and the second plot is the system time history (i.e., the signals added together). The third plot illustrates the vibration spectrum in the frequency domain by performing an FFT (Fast Fourier Transform) on the system time history [3].

Fig. 3.9.2  Gemini™ system showing offset teeth and chains. Phased systems have been tried in the past with limited success. Saab has used a phased roller chain drive with three chains as the transmission input for a manual transmission in their 99 and 900 series vehicles [2]. Noise levels were improved over a traditional non-phased triple roller chain system. The same vehicle series fitted with an automatic transmission used a conventional inverted tooth silent chain drive measuring half the width of the roller chain system. The torque input to the silent chain was nearly twice that of the roller chain (because of the torque converter multiplication inherent in the automatic transmission). In another instance, an experimental phased roller chain system with two chains was evaluated in a front-wheel drive automatic transmission by a North American transmission manufacturer. It was found to be noisier than the conventional inverted tooth silent chain drive used in production. The roller chain system

Configuration 1 consists of a single simple waveform, specifically the absolute value of the sine function:

f = sin(x)

Note the pronounced peak in the FFT plot at the fundamental vibration frequency of 5.0 cycles/time unit. Configuration 2 contains two such wave forms, each having half the vibrational amplitude of the single wave in configuration 1, with no phase difference between them. Note that the system time history and FFT plots are identical to those for configuration 1 since the two waves add together to reinforce each other. In configuration 3 we again have the two sine waveforms, except that in this case they are phased 180° relative to one another. Thus the two waves tend to cancel rather than reinforce each other, resulting in drastically reduced vibrational amplitudes.

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Fig. 3.9.3  Analytical phasing configurations.

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would be minimized and that the short chain would become the dominant noise producer.

The FFT plot for configuration 3 shows that the fundamental vibrational frequency at 5.0 is effectively eliminated, as are all odd multiples thereof (5, 15, 25, etc.). The even multiples of the fundamental frequency (10, 20, etc.) are essentially unchanged.

This issue is complicated by the effect of specific sprocket construction on apparent CD. A small over-pin dimension translates effectively into a greater chain CD because of relatively large tooth spacing. A large over-pin dimension has the effect of tightening the chain; that is, the chain appears “shorter.” Similar effects can be attributed to involute crowns or hollows. Table 3.9.3 and Figs. 3.9.4a and 3.9.4b show the effects on noise of such production variances.

Configurations 4 and 5 contain waveforms of a more complex and randomized nature and are therefore more representative of realistic signal traces from operating chain systems. Note that in spite of the more complicated waveforms, the above stated principles still hold true. Adding signals without relative phasing reinforces the vibrational amplitudes, whereas adding them with phasing greatly reduces and virtually eliminates the fundamental frequency and its odd orders. The importance of this concept cannot be minimized because it is this fundamental or pitch-passing frequency that is the most objectionable from a noise and vibration standpoint in most chain systems. Even though phasing virtually eliminates the pitch frequency content of the chain-induced noise, often the second order (or twice pitch frequency) can be recognized with a nonrandomized Gemini™ system. This is not due to an increase in second order level, but rather a reduction in pitch frequency and overall noise levels, which then makes the second order noticeable. It has been found that randomization, heretofore used primarily to reduce pitch frequency, is effective in reducing the second order level noise of Gemini™ systems.

3.9.7

Gemini System Robustness

Fig. 3.9.4a  Production variance effect on Gemini™ system noise.

In order to quantify the Gemini™ system noise performance in an actual transmission, several factors were considered early during the development stage. Two chain specific factors include center distance (or “CD”) and the random pattern orientation. Sprocket considerations include the over-pin dimension, involute quality, and phase tolerance, while system considerations include sprocket alignment and noise life. Variations of these factors were tested both subjectively in a production vehicle and objectively in a production transmission. Results show that the Gemini™ system out-performed standard chain systems in all instances. Past experience with chain CD (the assembled chain length measured over a set of master sprockets mounted on a set of movable shafts) has shown that longer chains are generally quieter, while short chains tend to be slightly louder. In a Gemini™ system, there is a possibility of the two chains being at the extremes of the CD specification—one being “short” and the other being “long.” There was concern that given normal production tolerances, the noise cancellation effect

Fig. 3.9.4b  Production variance effect on Gemini™ system noise.

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Table 3.9.3  Production Variance Effects—Chrysler 42LE Pitch Frequency (dBA)

Second Order (dBA)

Overall Level (dBA)

1.75” Wide Standard Chain

61.1

57.4

75.8

Long Chains on Min. Sprockets

48.0

57.3

71.9

Short Chains on Max. Sprockets

47.3

58.2

72.8

Long & Short Chain on Max. Sprockets

55.0

53.9

72.6

Short Chains on Crowned, Out of Spec Sprockets

48.2

56.2

72.4

Nominal Gemini™ System

47.2

55.8

71.6

Chain System

Other subjective testing has included mismatched phasing between the drive and driven sprockets, mismatched pattern orientation between the two chains, and mismatched alignment between the two sprockets. None of these parameters has shown a significant degradation in noise performance of the Gemini™ systems. With the Gemini™ system it is possible to better the noise levels of extremely small pitch chains with chains of much larger pitch. Thus an extremely compact, quiet, and robust system can be made available for nearly every application. Table 3.9.4 illustrates the point. It compares a small-pitch chain system vs. a larger-pitch Gemini™ system on the basis of noise level, package size, and weight for chains of equal torque capacities. Clearly the larger-pitch Gemini™ system compares favorably to a conventional chain system in terms of these parameters.

Table 3.9.3 presents “Speed Range Average” data for pitch frequency, 2nd order, and overall level (a broad band level, encompassing the entire range of human hearing). A speed range average, or SRA, is a logarithmic average of the measured sound pressure level data over the tested speed range, in this case 250–700 RPM axle. The SRA represents a convenient method of comparing several curves using a single number rather than having to use subjectivity in a visual comparison. For example, looking at the curves in Fig. 3.9.3, the standard width chain appears above the curves for the Gemini™ system by about 3 dBA, while the speed range average numbers show that the average difference is really closer to 3.5 dBA. The speed range average also eliminates any confusion over noise comparisons given at a single, and often different, discrete speed.

Table 3.9.4  Transaxle #1 Standard vs. Larger Pitch Gemini™ Pitch Frequency (dBA)

Overall Level (dBA)

Package Size (in)

Weight (lb)

Standard 3/8¢¢ Pitch

51.2

70.3

2.00

9.81

Gemini™ 7/16¢¢ Pitch Reduction

42.1

68.1

1.75

9.91

9.1

2.2

.25

(.1)

Chain System

Even larger reductions in pitch frequency can be obtained by directly substituting a Gemini™ system of the same pitch for a standard system. Reductions shown in Table 3.9.5 are typical when comparing standard and Gemini™ systems.

Examination of Table 3.9.3 shows that the nominal Gemini™ system’s pitch frequency level is nearly 14 dBA lower than the standard chain. A long chain and short chain on maximum over-pin sprockets produces the true “worst case” scenario with pitch frequency nearly 7 dBA above that of the other Gemini™ combinations. Even with this increase in level, the improvement is still 6 dB, or twice as quiet as the standard width chain. Better yet, this worst case system has shown to improve itself over time. The two chains’ CD will converge until they are nearly the same length, and the system’s noise level will approach that of the nominal Gemini™ system. This “self healing” phenomenon will be discussed further in the next section.

Table 3.9.5  Transaxle #2 Standard vs. Equivalent Pitch Gemini™ System Pitch Frequency (dBA)

Overall Level (dBA)

Package Size (in)

Standard 7/16¢¢ Pitch

61.2

75.8

1.75

Gemini™ 7/16¢¢ Pitch

47.2

71.6

1.75

Reduction

13.9

4.2

0

Chain System

Looking at the rest of Table 3.9.3, it can be seen that the Gemini™ system is indeed robust with respect to noise. The production tolerances have very little effect on both objective noise measurements and subjective testing.

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3.9.8

Special Consideration of Gemini™ Systems

Figures 3.9.6 and 3.9.7 show time plots of similar data for both gaged teeth over three sprocket revolutions. Figure 3.9.5 represents data obtained from chains of matched center distances, while Fig. 3.9.6 shows data from chains with a center distance mismatch which exceeded production tolerances. The differences in load carried by each row of teeth in the case of mismatched center distances are readily apparent in the second graph.

A Gemini™ system effectively breaks the chain drive into two chain/sprocket systems. These two systems must share the load equally to ensure that the Gemini™ system is robust with respect to durability. A number of manufacturing issues affect the ability of the chains to equally share the load. These factors include initial chain lengths, sprocket over-pin dimension, sprocket runout, and sprocket phasing (tooth to adjacent tooth). The amount of chain load sharing is for the most part determined by chain stiffness. Fortunately, chains are fairly compliant (much more so than gears). This aids load sharing between the two chains even if the previously listed factors cause mismatches in the total chain system. Experimental tests have been performed to determine the amount of load sharing between the chains at various load and speed conditions. The tests were performed by looking at tooth loading on each sprocket half. One tooth from each row of teeth was strain gaged to determine dynamic tooth loads during operation. The strain gages were placed into pockets that had been EDM’ed into the tooth face below the line of contact with the link toes. The gaged teeth were located adjacent to each other, offset by one half of a pitch. For the purpose of these tests, the manufacturing variations due to the previously listed factors were simulated using different chain center distances only. Tests were run using matched center distances and repeated with chains that had a center distance mismatch which exceeded production tolerances. A polar plot of ten sets of load data generated from one tooth is shown in Fig. 3.9.5. The graph indicates the maximum tooth loads encountered as the chain enters engagement with the sprocket, and the reduction of load as the gaged tooth rotates throughout a chain revolution.

Fig. 3.9.6  Time trace for three revolutions-matched CDs.

Fig. 3.9.7  Time trace for three revolutions-mismatched CDs. As would be expected, load sharing between the chains is worse at conditions of low speeds and torques. At these conditions there is little elastic elongation of the chains, resulting in the shorter chain carrying a larger percentage of the total system loading. In experimental testing at conditions of 2000 rpm input speed and 100 lbf-ft input torque, the shorter

Fig. 3.9.5  Load sharing experimental results.

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chain carried 63% of the system load (with an initial center distance mismatch which exceeded production tolerances). Holding the input speed constant but doubling the input torque (200 lbf-ft) decreased the percentage of load carried by the shorter chain to 55%. Similarly, tests run at 6000 rpm input speed and 168 lbf-ft input torque found the shorter chain carrying 54% of the system load. An analytical model of the chain system has also been developed and compared to the experimental results. Analytical results were found to be within 3% of the experimental data at all tested conditions. A representation of typical output from the analytical model showing percentage of carried load verses input torque can be found in Fig. 3.9.8. An additional concern relating to load sharing is chain wear. Ideally the chains would have the same initial center distances and would exhibit equal wear rates. As has been discussed, production variations result in systems with the chain center distances effectively mismatched. Fortunately, the wear rates of the chains are load sensitive, with the highest loaded chain (the shorter one) exhibiting a wear rate greater than that of the lower loaded chain. When two chains of different center distances (either actual or effective) are run, the elongation of the shorter chain is greater. This decreases the variation in center distances between the two chains. Over the life of the system, this difference in wear rates would cause the center distance difference between the chains to approach zero. This, in turn, causes more even load sharing over the life of the system. Figure 3.9.9 shows the reduction in center distance difference between two chains in a Gemini™ system over a 100-hour wear test. Durability testing of chain systems with purposely mismatched center distances has indicated no degradation of system durability.

Fig. 3.9.9  Reduction in CD difference.

3.9.9

Sprocket Manufacturing Considerations

Sprockets used in the Chrysler 42LE transmission consist of two-piece cast nodular iron assemblies. Special consideration must be given to the manufacture of sprockets to ensure acceptable sprocket over-pin dimensions, run out, and phasing from one set of teeth to the other. To address these issues, sprocket halves are paired prior to hobbing. By hobbing the sprocket halves together, over pin dimensions for each half of the sprocket can be held very consistently. The sprocket halves are subsequently maintained as pairs throughout the manufacturing process.

Just-In-Time (JIT) manufacturing techniques also address the chain center distance aspect of the load sharing issue. Chain center distance variations during production occur over large time periods due to the lot nature of chain component manufacturing. Chains used in a particular Gemini™ system are typically sequentially built and therefore have initial center distances that are very evenly matched.

Sprocket runout and phasing from one row of teeth to the other is addressed in the final assembly operation. The Chrysler sprocket halves are held together using four rivets. Special fixturing is used to ensure that the sprockets are in the correct phase relationship and that the outer diameters of the sprockets are concentric. Pilot fits between the two sprocket halves are kept purposely loose to ensure that the assembly fixturing provides the required concentricity. The riveting operation used was also designed to ensure that the system is robust regarding both dimensional stability and system durability. A common riveting operation relies on the tension in the rivet to maintain the relationship between the riveted members while not necessarily filling the hole containing the rivets. The Chrysler 42LE sprocket applications are somewhat unique in that the rivets are used to maintain a closely toleranced phase relationship as well as assemble the two components. To ensure that the phase between the sprocket halves is maintained, the rivets need to fill the hole at

Fig. 3.9.8  Analytical model results: load sharing. 3-93

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Design Practices: Passenger Car Automatic Transmissions

the interface between the two parts. During system development, a rivet process was devised that would fill the hole at the part interface and subsequently swell the rivet head to a diameter at least 10% larger than its original diameter. Figure 3.9.10 shows a cutaway of a riveted portion of the sprocket indicating the complete fill of the hole as well as the swell of the rivet head caused by the secondary operation.

Other changes in the sprocket design used for the Gemini™ systems create additional manufacturing advantages. In the Chrysler application, variation in sprocket lead was found to greatly affect system noise. Lead error is typically more difficult to contain as sprocket face width increases. The face widths of each of the two sprocket halves used in the Gemini™ system are less than half the width of the original sprocket. This, in turn, creates a system that is more easily manufactured, as well as robust, with respect to noise.

3.9.10 Vehicle Tests Gemini™ systems have consistently been characterized by superior pitch frequency control in vehicle evaluation. Table 3.9.6 compares the Gemini™ chain system to the single-chain system for pitch frequency noise in a number of production vehicles. Two effects were noted. The Gemini™ system consistently eliminated pitch frequency noise detected by evaluators. While the noise level produced by the singlechain system has a substantial variation in level from vehicle to vehicle, the Gemini™ system showed no variation. All of these evaluations were performed with essentially new or low-mileage parts.

Fig. 3.9.10  Gemini sprocket cutaway. Rivets were sized so that they would withstand the shear forces caused by applying full system torque to one half of the sprocket while holding the other half locked in place. This ensures that the sprocket assembly would not be the first mode of failure in a severely overloaded system. During development, sprockets also underwent rotary fatigue testing at the same conditions. These tests simulated a condition where one chain would assume 100% of the system torque. This again would ensure a robust system, because as previously discussed, the maximum load assumed to be carried by a single chain in actual operation would be approximately 63% of full system loads. The test stand used for torsional shear and fatigue testing throughout the development of the sprockets is shown in Fig. 3.9.11.

Table 3.9.6  Vehicle Evaluations, Pitch Frequency Noise of New Parts Rating (see rating key below) Vehicle

Single-Chain System

Gemini System

1

C-M

I

2

C

I

3

C

I

4

C

I

5

C-M-L

I

Key: C = Critical Customer M = Medium L = Light I = Inaudible

Evaluations in other vehicles for high-mileage parts has shown no degradation in pitch frequency noise control. In fact, it may be observed that at the mileages indicated, the chains have worn to practically identical lengths. This condition favors equal amplitudes from each chain, which in turn benefits the noise cancellation process. This is shown in Table 3.9.7.

Fig. 3.9.11  Gemini sprocket rotary fatigue tester.

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Gears, Splines, and Chains

Table 3.9.7  Vehicle Evaluations, Pitch Frequency Noise of High-Mileage Parts Miles Vehicle

Test

Actual

Customer Equivalent

A

Powertrain Endurance Death Valley

52,733

184,565

82,200

  82,200

Powertrain Endurance

  2,000

   7,200

84,200

  89,400

B

Chain CD Length, in (Spec: 6.737–6.752) Outer: 6.773 Inner: 6.773 Outer: 6.773 Inner: 6.770

Rating I I

3.9.11 Summary

3.9.12 Acknowledgments

The Morse Gemini™ system offers a clear advancement in power transmission technology. Gemini™ systems provide extremely low noise levels while providing excellent power density. Powertrain engineers can now transmit more power in less space with lower noise levels than previously envisioned.

The authors gratefully acknowledge John Hummel, Tim Ledvina, John Skurka, Matt Sullivan, Dave White, and Roger Young of Borg-Warner Automotive, and Steve Wojdyla of Chrysler Corporation for their generous help in putting this paper together.

In addition to chains, the concept of phasing is currently under development for metal belts in vehicles equipped with continuously variable transmissions (CVT). Experimental vehicles from a variety of manufacturers fitted with Morse Gemini™ CVT belts have demonstrated equally impressive noise reductions compared to the same vehicles fitted with conventional non-phased belts.

3.9.13 References 1. “Engineering Steel Chains (Applications Handbook) for Conveyors, Elevators, and Drives,” pp. 17–18, American Chain Association, St. Petersburg, Florida, 1971. 2. Davies, D. N. C., K. G. Gustafsson, K. E. Nordkvist, and P. J. Owen, “Roller Chain as a Transfer Drive for the Automobile,” American Society of Mechanical Engineers, New York, NY, 1980. 3. Smith, Jon Michael, Mathematical Modeling and Digital Simulation for Engineers and Scientists, Second Edition, John Wiley & Sons, Washington, DC, 1987.

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Chapter 4

Transmission Shaft Fatigue Design Introduction

Transmission Shaft Fatigue Design

Although automatic transmission design has progressed greatly over the years, the basic functioning of many of its components has remained unchanged. The shaft, among others, is one example. Shafts transmit engine torque from component to component, from the input of the transmission to the output. And the shaft must perform its function flawlessly millions of times over the life of the transmission.

Jeffrey K. Baran Advanced Engineering Staff General Motors Corp. Keith D. Van Maanen Advanced Engineering Staff General Motors Corp.

4.1

Abstract

Shafts are one of the basic elements found in all automatic transmissions. Often the sizes of other components in a transmission are determined by the size of the shafts. Because of the increasing pressure to minimize transmission size and mass, it is obvious that the size of the shafts must be minimized while still maintaining the durability demanded by the customer. For these reasons, it is important to pay close attention to the fatigue design of automotive transmission shafts.

To aid the transmission engineer in developing robust designs, Jeffery K. Baran and Keith D. Van Maanen compiled “Transmission Shaft Fatigue Design” for AE-18, the precursor to this publication. In doing so, they drew upon Chapter 27 of AE-5, “Automatic Transmission Shaft Design,” written by Walter Fisher. For their contributions to this publication, these authors are given special recognition. As with most technical publications, more than a few references were used in the creation of this chapter. These are listed for the reader’s benefit in the References and Bibliography sections.

4.2

Introduction

The most common shaft problems are fatigue failures and spline wear. The purpose of this work is to outline a procedure that can be used as a starting point to design against fatigue failures for any shaft and offer some general design guidelines if no other specifics are known. The basic proce-

The Automatic Transmission and Transaxle Technical Standards Committee

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Design Practices: Passenger Car Automatic Transmissions

dure presented here is based on the approach suggested in Mechanical Engineering Design, by Shigley and Mitchell [1] and Engineering Considerations of Stress, Strain, and Strength, by Juvinall [2]. Many other works have been devoted to the topics of fatigue and shaft design. Several helpful works are referenced in the Bibliography.

Snbend Bending endurance strength S103 Strength at 1000 cycles S¢103 Modified strength at 1000 cycles C Miner’s rule summation constant j Number of load ranges in load history ni Number of cycles in ith load range Ni Number of cycles to failure in ith load range σ1, σ2, σ3 Principal stresses σ Axial or bending stress σnom Nominal stress state σmax Maximum stress due to discontinuity or from applied load σmin Minimum stress value from applied load σmean Mean stress value from applied load σalt Alternating stress value from applied load σeq Equivalent reversed stress from Goodman diagram σealt Equivalent alternating stress from distortion energy theory σeqalt Equivalent alternating stress from σ1 – σ2 diagram τeqrev Equivalent reversed torsional stress from Goodman diagram σx,yaltcorr Corrected alternating plane stress σx,yalt Alternating component of plane stress τxyaltcorr Corrected alternating shear stress τxyalt Alternating shear stress σx Plane stress in x-direction σy Plane stress in y-direction τxy Shear stress in x-y plane (biaxial) σx,ymean Mean component of plane stress σx,ymeancorr Corrected mean plane stress τxymean Mean shear stress τxymeancorr Corrected mean stress

4.3 Nomenclature τ T d do di M Th/s mh/s Th Ts mh ms Kt Kf Ktequiv K¢f KfN ka kb kc ke K¢e kl kr km q N Ne Sut Sus Sn S¢n Sntor

Torsional shear stress Torque applied to a shaft Shaft diameter for stress analysis Outer shaft diameter Inner shaft diameter Moment applied to a shaft Torque ratio of hollow to solid shaft Mass ratio of hollow to solid shaft Torque capacity of a hollow shaft Torque capacity of a solid shaft Mass of a hollow shaft Mass of a solid shaft Theoretical stress concentration factor Fatigue stress concentration factor Equivalent theoretical stress concentration factor Fatigue stress concentration factor at 1000 cycles Fatigue stress concentration factor at any number of cycles N Surface finish modifying factor Size modifying factor Reliability modifying factor Stress concentration modifying factor Stress concentration modifying factor at 1000 cycles Load type modifying factor Residual stress modifying factor Miscellaneous effect modifying factor Notch sensitivity factor Number of cycles Number of cycles at endurance limit Ultimate tensile strength Ultimate shear strength Endurance strength or limit Modified endurance strength Torsional endurance strength

4.4

Stress Calculation

The first step in analyzing a shaft design is calculating the nominal stress in the part. This is accomplished by using these familiar equations:

τ =

σ=

16Td for torsion π (d o4 – d i4 )

32Md π ( d o4 – d i4 )

 

for bending

(4.1) (4.2)

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Transmission Shaft Fatigue Design

σ=



4P 2 π ( d o – d i2 )

 

for axial loads

(4.3)



mh = s

m h d o2 – d i2 = ms d o2

(4.5)

Upon substitution, a mass ratio versus torque ratio relationship can be derived:

Some insights into shaft design can be found by examining these equations. For torsion and bending, a stress gradient exists, and it can be seen that the stress, σ or τ , increases linearly with diameter and reaches a maximum at the outer diameter. As a result, the strength requirement is the greatest at the outermost diameter. Failure, however, may not always occur at the surface because there may be a strength gradient as the result of a process such as case hardening. If this situation exists, the stress levels at all points within the part must be compared to the strength at each location in order to avoid a fatigue failure that may initiate below the surface (Fig. 4.1). For axial loading, the stress gradient is uniform across the section of the shaft.



m h = 1 – 1 – Th s

s

(4.6)



From Fig. 4.2, a hollow shaft with 50% of the mass of a solid shaft can still carry 75% of the torque with equal stress at the outer diameter. This relationship may help explain the wide use of thin-section, hollow shafts in automatic transmissions. As more complex loading cases are examined, such as combined bending and torsion, these relationships need to be redefined.

Fig. 4.1  Bending or torsion stress gradient. Fig. 4.2  Torque capacity and mass relationship.

4.5

Mass Relationship

4.6

Another interesting characteristic for torsion and bending of shafts is the load-carrying capacity and mass relationship. As hollow shafts typically are used in an automatic transmission, an interesting relationship can be generated comparing the load-carrying capacity and mass of a hollow shaft to a solid shaft. Let us define some terms:

Th

s

The critical sections, or sections where a shaft is most likely to fail, usually are located at a discontinuity such as a fillet, transverse oil hole, oil groove, or spline. The nominal stresses at these locations must be modified by a stress concentration factor. The stress concentration factor is the ratio of the maximum stress at the discontinuity to the nominal stress in the section:

= Torque ratio of hollow to solid shaft

m h = Mass ratio of hollow to solid shaft s For equivalent shear or bending stresses, a torque ratio equation can be derived from Eq. 4.1 or Eq. 4.2:

Th

s

T d4 – d4 = h = o 4 i Ts do

Stress Concentration



Kt =

σ max σ nom

(4.7a)

Figure 4.3 illustrates a stress concentration curve for an oil groove in torsional loading. Appendix A contains formulas and corresponding graphs that can be used to determine stress concentration factors for various types of features and loading conditions commonly found in automatic transmissions. These are theoretical stress concentrations based only

(4.4)

Similarly, for shafts of equal length, a mass ratio also can be developed as:

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Design Practices: Passenger Car Automatic Transmissions

cut or blind spline broached, the undercut can be treated the same as an oil groove.

on the geometry of the part. It is important that the nominal stresses used in conjunction with these stress concentrations are calculated in the manner indicated for each particular concentration (e.g., net area, gross area). When two or more discontinuities occur at the same location, such as a hole in an oil groove, an equivalent stress concentration factor can conservatively be estimated by multiplying together the stress concentration factor for each discontinuity.

Ktequiv = Kthole ¥ Ktgroove

4.7

Fatigue Properties (S-N Curve)

To predict the fatigue life of a particular shaft design, the fatigue properties of the shaft material must be known. It is convenient and typical to present these properties in the form of an S-N diagram, which is simply a plot of the fatigue strengths of the material versus the number of stress cycles (Fig. 4.4). Usually, the S-N diagram for a material is determined by cyclically stressing a specially prepared test specimen. If no fatigue test data are available for a material, an S-N diagram can be estimated. For automatic transmission shafts, the area of interest on the S-N diagram is the region beyond 103 cycles, which is defined as high cycle fatigue. Most

(4.7b)

The stress concentration effect of splines may be approximated as a fillet for hobbed or rolled splines with the minor diameter of the splines being used as the small diameter of the shaft and the radius being that at the spline runout. If the spline has an undercut groove as when a spine is shaper

Fig. 4.3  Oil groove stress concentration factor for torsion [3c].

Fig. 4.4  Example of an S-N curve.

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Transmission Shaft Fatigue Design

4.8

common shaft materials have a linear relationship between 103 cycles and the endurance limit when plotted on log– log coordinates. The endurance limit, or fatigue limit, is the limiting value of stress below which an unlimited number of completely reversed cycles can be endured without failure.

S-N Modifying Factors

As mentioned previously, the standard test to determine S-N data is a rotating beam test in which a specially prepared specimen undergoes fully reversed bending stresses. However, an automatic transmission shaft differs from the test specimen in many ways that affect the fatigue life of the shaft. There are several modifying factors that can be applied to the fatigue strengths to account for these differences. An explanation of each of these modifying factors and recommendations for modifying the S-N curve for a transmission shaft are presented in the following subsections.

One generality that can be made for steels is that the endurance limit, or endurance strength, is a constant fraction of the tensile strength. This fraction can vary from about 0.25 to 0.6, depending on the microstructure of the steel [4]. If the exact microstructure is not known, it is commonly recommended that the endurance strength be estimated as 0.5 times the tensile strength for steels with ultimate tensile strengths less than 1400 MPa, and 700 MPa for steels with ultimate strengths greater than 1400 MPa. The endurance limit of cast iron may occur at a greater number of cycles than steel, but it is conservatively placed at 106 cycles. Although aluminum may not have a true endurance limit, the strength at 5*108 cycles is used as the endurance limit.

4.8.1 Surface Finish Factor, ka The roughness of the surface is important because most fatigue failures originate at the surface. The irregularities on the surface act as stress concentrations. Also, certain operations can alter the strength of the surface (e.g., decarburization) or introduce residual stresses (both favorable [compressive] and unfavorable [tensile]). Figure 4.5 can be used to estimate the effects of surface finish on steels processed in various ways. Figure 4.6 can be used (for ground parts only) to determine the surface finish modifying factor for steels when the surface measurement (ra) is known.

Table 4.1 summarizes the recommended factors that can be used to estimate the fatigue strengths for steel, cast iron, and aluminum at the given number of cycles [2a, 4]. Again, note that actual fatigue data are much better to use than estimated fatigue strengths. A good reference for material S-N data has been published by the American Society for Metals (ASM) [5]. Table 4.1 Fatigue Strength Estimation Factors Material Steel (Sut 1400 MPa) Steel – Ferrite Steel – Ferrite and Pearlite Steel – Pearlite Steel – Untempered Martensite Steel – Highly Tempered Martensite Steel – Highly Tempered Martensite and Tempered Bainite Steel – Tempered Bainite Steel – Austenite Cast Iron Wrought Aluminum (Sut 260 MPa) Permanent Mold Cast Aluminum Sand Cast Aluminum

Cycles 6

Strength

10 106 106 106 106 106 106 106

0.5*Sut 700 MPa

106 106 106 5*108 5*108 5*108 5*108

0.5*Sut 0.37*Sut 0.4*Sut 0.4*Sut 130 MPa 80 MPa 55 MPa

0.58*Sut 0.38*Sut 0.38*Sut 0.26*Sut 0.55*Sut 0.5*Sut

Fig. 4.5  Surface factor based on manufacturing process— steel parts [2b]. (Reprinted with permission from Engineering Considerations of Stress, Strain, and Strength, Robert C. Juvinall, copyright 1967, McGraw-Hill, Inc., New York.)

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Design Practices: Passenger Car Automatic Transmissions

Table 4.2 Reliability Factors Reliability

Reliability factor, kc

0.50 0.90 0.95 0.99 0.999 0.9999 0.99999 0.999999

1.000 0.897 0.868 0.814 0.753 0.702 0.659 0.620

4.8.4 Stress Concentration Modifying Factor, ke The stress concentration factors in Appendix A are based only on the geometry of the shaft. Under fatigue loading conditions, some materials are not as sensitive as others to the stress concentrations. This is indicated by the notch sensitivity, q, of the material and is defined as:

Fig. 4.6  Surface factor based on surface roughness, ra [1a]. (Reprinted with permission from Mechanical Engineering Design, 4th Edition, Joseph E. Shigley and Larry D. Mitchell, copyright 1983, McGraw-Hill, Inc., New York.)

4.8.2 Size Factor, kb



Larger parts have lower fatigue strengths because a larger volume of material is stressed at a high level. Therefore, it is more likely that a crack will be loaded and propagate to failure. This is especially the case in bending and torsion where the stress gradient is reduced as the diameter increases. The reduced stress gradient results in a higher volume of material being stressed at the higher levels near the outside of the part. Thus, there is a higher probability that a nucleating point for failure will be encountered in a larger part. The size factor for bending and torsion is as follows [lb]: k b = 0.869d –0.097 0.3 in. 176.6

2 2 2 2 2

** limit of machinery

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Design Practices: Passenger Car Automatic Transmissions

5.4 Rolling Element Bearings in Light Vehicle Automatic Transmissions

consider several combinations of the variables described in this paper.

J. R. Hull The Torrington Co.

5.3.8 Contact

Revised and updated in 2009

Richard G. Van Ryper is a Senior Consultant at E. I. DuPont in Newark, Delaware. He has been involved with the application of anti-friction polymers for the last 20 years. He can be contacted at richard.g.van-ryper @usa.dupont.com.

M. D. Myers Private Bearing Consultant Note: This section updates Section 5.3 of AE-18 Design Practices—Passenger Car Automatic Transmissions Third Edition as well as “Rolling Element Bearings in Passenger Car Automatic Transmissions—1967 Edition,” also by J. R. Hull (SAE Paper 670048). The new section has been changed as necessary to reflect SI units and incorporate changes in bearing theory and application practice in current light vehicle automatic transmissions.

5.3.9 References 1. Pesek, L. J. and W. E. Smith, “Design of Sleeve Bearings and Plain Thrust Washers,” DESIGN PRACTICES: Passenger Car Automatic Transmissions, 3rd ed., SAE AE-18, SAE International, Warrendale, PA, 1994. 2. Blaine, B. L and C. D. Wiegandt, “Improving the Performance of Sleeve Bushings and Thrust Washers,” DESIGN PRACTICES: Passenger Car Automatic Transmissions, 3rd ed., SAE AE-18, SAE International, Warrendale, PA, 1994. 3. Savoie, M. S. and E. N. Willis, “High Performance Thrust Washer Bearings for Drive Train Applications Using Celadyne™ Bearing Grade Plastics,” SAE Technical Paper No. 930916, SAE International, Warrendale, PA, 1993. 4. Griffiths, I., D. Kemmish, M. Morgan, and P. Tweedale, “High-Performance Polymeric Wear Testing for Powertrain Transmissions,” SAE Technical Paper No. 970658, SAE International, Warrendale, PA, 1997. 5. Griffiths, I., D. Kemmish, and M. Morgan, “Wear Performance of High Performance Polymeric Bearing Materials,” SAE Technical Paper No. 980716, SAE International, Warrendale, PA, 1998. 6. Gosstelow, K., I. Griffiths, D. Kemmish, and P. Tweedale, “A Comparative Study of High Performance Materials in Automotive Applications,” JSAE Spring Convention Proceedings No. 55-99, 9934366, Japan Society of Automotive Engineers, Tokyo, Japan, 1999. 7. Hyde, L. J. and R. M. Smith, “Bearing-Grade Thermoplastic Polyimides in Automotive Tribological Applications,” SAE Technical Paper No. 950190, SAE International, Warrendale, PA, 1995. 8. Murakami, K. and R. Van Ryper, “Evaluation of Polymeric Thrust Washers for Powertrain Applications: Methods, Apparatus, and Initial Results,” SAE Technical Paper No. 2000-01-1152, SAE International, Warrendale, PA, 2000. 9. SAE Surface Vehicle Standard J924, Thrust WashersDesign and Application, latest revision.

Light vehicle automatic transmissions have two major construction types. Type one is comprised mainly of a hydraulically activated planetary gearbox. Type two is a countershaft gearbox with fixed ratios of gear pairs that are also hydraulically activated. Both types use a hydraulic torque converter to transmit torque from the engine to the gearbox. This section will discuss both types and the rolling element bearing designs used in each. Specific details related to the design and selection of tapered roller bearings will be discussed in Section 5.5. The first part of this section will be a detailed discussion of bearing application practice for planet pinion gears. The second part will discuss thrust needle bearing application practice, followed by discussion of other bearings related to specific areas of the transmission. These include chain sprocket supports and oil pump shaft supports, which are sometimes used.

5.4.1 Planet Pinions The life in hours of any roller bearing varies inversely as the product of the speed and the 10/3 power of the load; that is:

life ∝

r

1 10 min × (load) 3

(5.4.1)

Since the load on the bearings in the planet pinions is proportional to the gearbox input torque, which is the same as the output torque of the converter, the life in hours of the planet pinion bearings can be written:

life ∝

r

1 10 min × (torque) 3

(5.4.2)

Note that when the product of the r/min and the (torque)10/3 is a maximum, the life of the planet pinion bearings is at a minimum. 5-30

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Bearings

5.4.1.1  Critical Point on Converter Curve

If details of the load and speed cycles for the transmission are available, they can be used to obtain a more accurate estimate of bearing life at each condition and then combine them to determine the overall life. An example is detailed in Section 5.5.

The top curve in Fig. 5.4.1 is a plot of a typical converter output (or gearbox input) torque versus converter output r/min. The lower curve is a plot of the converter output r/ min times (torque)10/3 versus converter output r/min. At the peak of this lower curve, the planet pinion bearing life is at a minimum. It is the combination of torque and speed at this peak, called the critical point, that is often used as a basis for calculations and bearing selection.

5.4.1.2  Speed of Planetary Members The speed of the planetary members can be calculated by any of the conventional methods. Appendix A outlines one method to determine the bearing speed relative to the planet gear and pinion pin in the carrier. 5.4.1.3  Planet Pinion Tooth and Bearing Forces Figures 5.4.2 and 5.4.3, and Tables 5.4.1 and 5.4.2 explain how both simple and compound helical planet pinion tooth forces are calculated, and how these forces are translated into bearing forces. In Figs. 5.4.2 and 5.4.3, each planet pinion tooth load is represented by three vectors acting at the center of the tooth meshing area: 1. The tangential or torque-producing vector (F). 2. The separating force due to the pressure angle of the gear (S). 3. The thrust force due to the helical angle of the gear (T).

Fig. 5.4.1  Converter curve. As indicated in Fig. 5.4.1, the r/min ¥ (torque)10/3 curve may have two peaks. Sometimes, the second peak is slightly higher than the first. Even when this occurs, however, the torque and speed at the first peak are chosen. This is done because at the lower speed, the bearing loads and thus the shaft deflections, which also affect bearing lives, are more severe. Selection of bearings for passenger cars based on “worst conditions” is useful as a means of comparing new bearing applications with older, proven applications. Nevertheless, because planet carrier deflections, lubrication, and many other factors affect bearing life, the bearing application technique described here should only be considered as a starting point. Detailed analyses to optimize roller profiles and design verification testing for the whole range of speed and load conditions are also necessary. This worst-condition technique should not be carried over to other transmissions such as those used in trucks and tractors. Such transmissions operate for so much of their lives in various gear ratios that the total life of their bearings must be based on the sum of the lives required for each geared speed and load condition.

Fig. 5.4.2  Simple planetary gear forces. 5-31

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Fig. 5.4.3  Compound planetary gear forces.

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Bearings

Table 5.4.1  Simple Planetary Gear Calculations Calculation of Planet Gear Forces Explanation

Numerical Example

Q = torque input, N-m rs = pitch radius of input sun rp = pitch radius of planet gear NPA = normal pressure angle HA = helix angle (sun in this figure is left-hand helix) L = distance between centers of roller paths

Q = 508.5 N-m rs = 23.813 mm rp = 19.05 mm NPA = 18.2° HA = 25° L = 44.45 mm

Then: F= 508.5 ¥ 103/(23.813 ¥ 3) = 7117 N

F = Q ¥ 103/( rs ¥ no. of planet gears) S= F ¥ tan NPA/ cos HA

S = 7117 ¥ tan 18.2/cos 25 = 2580 N

T = F ¥ tan HA

T = 7117 ¥ tan 25 = 3318 N

Calculation of Planet Bearing Forces Explanation

Numerical Example

1. Since the two tangential tooth forces (F) are in the same direction, the total force due to them is 2F. Since they are half-way between the bearings:

H1 = H2 = F = 7117 N

H1 = H2 = ½ ¥ 2F = F 2. In this simple planetary, the separating forces (S) are directly opposite and cancel each other, thus contribute nothing to the bearing load.

S – S = 2580 – 2580 = 0

3. Each of the tooth thrust forces creates a couple which contributes to bearing loads.

Taking moments about the right bearing: T ¥ rp + T ¥ rp = V1 ¥ L V1 = 2(T ¥ rp)/L



V1 = 2 ¥ 3318 ¥ 19.05 / 44.45 = 2847 N

Also taking moments about the left bearing: V2 = 2(T ¥ rp)/L

V2 = 2 ¥ 3318 ¥ 19.05 / 44.45 = 2847 N

(Note direction of forces on diagram is shown as loads on the bearing, not reactions to the tooth forces on the gears.) 4. Total load on each bearing is the vector sum of the components.

Total load left bearing = H12 + V12



Total load right bearing = H 22 + V22

(7117)2 + (2847)2 = 7665 N (7117)2 + (2847)2 = 7665 N

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Design Practices: Passenger Car Automatic Transmissions

Table 5.4.2  Compound Planetary Gear Calculations Calculation of Planet Gear Forces Explanation

Numerical Example

Q = torque input, N-m rs = pitch radius of input sun rp = pitch radius of planet gear NPA = normal pressure angle HA = helix angle (input sun in this figure is left-hand helix)

Q = 508.5 N-m rs = 23.813 mm rp = 19.05 mm NPA = 18.2° HA = 25°

As seen in View I of Fig 5.4.3, the two bearings in the planet nearly fill the full length of the gear. Thus, the tooth mesh points are almost directly over the bearing centers. L = 44.45 mm

L = distance between tooth mesh and bearing centers

F = 508.5 ¥ 103/(23.813 ¥ 3) = 7117 N

F1 = F2 = Q ¥ 10 /( rs ¥ no. of long planets) 3

S1 = S2 = F ¥ tan NPA/ cos HA

S1 = S2 = 7117 ¥ tan 18.2/cos 25 = 2580 N

θ = angle between tooth mesh points

θ = 68°

Calculation of Long Planet Bearing Forces Explanation

Numerical Example

T1 = T2 = F ¥ tan HA

T1 = T2 = 7117 ¥ tan 25 = 3318 N

As shown in View II of Fig. 5.4.3, F1 and S1 are not parallel to F2 and S2. F1 and S1 should first be resolved into forces V1 and H1 which are parallel to F2 and S2. V1 = F1 sin θ – S1 cos θ

V1 = 7117 sin 68 – 2580 cos 68 V1 = 6595 – 970 = 5625 N

H1 = F1 cos θ + S1 sin θ

H1 = 7117 cos 68 + 2580 sin 68 H1 = 2667 + 2383 = 5050 N

Since the tooth mesh points are directly over the centerline of the bearings, forces V1 and H1 must be carried entirely by bearing 1, and F2 and S2 carried entirely by bearing 2. This is illustrated in View III of Fig. 5.4.3. In View IV, the only tooth forces shown are the thrust forces T1 and T2. Each thrust force creates a couple whose effect on the radial bearings is load TC. TC = (T1 ¥ rp)/L = (T2 ¥ rp)/L

TC = (3318 ¥ 19.05)/44.45 = 1422 N

Note that the loads TC on bearings 1 and 2 caused by T1 are not parallel to the loads caused by T2. TC due to T1 should thus be resolved into vertical and horizontal components TV and TH. TV = TC cos θ

TV = 1422 cos 68 = 535 N

TH = TC sin θ

TH = 1422 sin 68 = 1320 N

The total vertical and horizontal load components on each bearing (RV and RH) are computed by the algebraic additions of the individual actions. RV and RH are then combined into a resultant (R) by vector addition. In other words, R =

RV + RH

Bearing 1, N

Bearing 2, N

V1

5625 T

—

H1

5050 

—

TV

  535 c

  535 T

TH

1320 

1320 

F2

—

7117 

S2

—

2580 c

TC

1422 T

1422 c

RV

6490 T

3440 c

RH

6390 

8440 

R

9110

9110

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Bearings

investigated before freezing a design. Appendix B illustrates the variation in bearing loads (and planet pin deflections) caused by planet arrangement and helix hand.

The methods used to calculate the tooth forces are quite precise when the gears mesh at their normal pitch circles, and give a good approximation even when the gears operate at spread centers.

From a bearing standpoint, the gear position selected should give the lowest loads and/or the smallest slopes through the bearings. This is not always possible because the gear position may also affect other conditions such as gear tooth life and noise.

Just as gear forces are assumed to act in the center of the teeth, so the forces transmitted to the bearings are assumed to act at the center of the roller path. Theoretically, two bearings should be used in the bore of helical planet pinions. However, many transmissions operate quite satisfactorily with only a single roller path in simple planet pinions, as shown in Fig. 5.4.4. When this latter arrangement is used, the single path of rollers is assumed to be cut into two paths, and the loads are applied at the center of each of the resulting roller paths. Though these assumptions are not entirely accurate, their consistent use permits comparisons of new designs with older proven designs.

5.4.1.4  Bearing Types Caged needle roller assemblies often make good choices as bearings. Caged assemblies are widely used in the planet gears of heavy equipment as well as in constant-mesh gears of many manual transmissions and countershaft automatic transmissions. Although a caged assembly has less theoretical capacity and a greater cost than a full complement of rollers, the caged assembly’s higher speed capability and greater tolerance of poor lubrication or misalignment may outweigh its lower capacity. Since many transmissions use full complements of needle rollers in at least some of their planet gears, the discussion of load rating calculations which follows will consider only that kind of planet bearing. Where recommendations for successful applications differ for caged bearings, they will be noted.

Fig. 5.4.4  Planet gear with single roller path.

5.4.1.5  Bearing Capacity and Life Factors

In the case of compound planetaries, because the location of the tooth mesh points is not symmetrical, the position of the long planet relative to the short planet affects bearing loads. Figure 5.4.5 shows how the long planet may either lead or lag the short planet.

The Basic Dynamic Load Rating (C) for a single row of a full complement of needle rollers is calculated by using the International Organization for Standardization (ISO) Standard 281:2007 formula

C = fc × Z3/4 × leff 7/9 × Dw29/27

(5.4.3)

where: fc = factor depending on ratio of roller diameter to roller complement pitch diameter (listed in ISO 281 standard) leff = effective length of roller contact, mm (for spherical end rollers, leff = maximum overall roller length – Dw/2) (for flat end rollers, leff = maximum overall roller length – 2 ¥ roller corner radius) Z = number of rollers Dw = roller diameter, mm C = load rating, N

Fig. 5.4.5  Alternate planet locations. Helix hand also affects bearing loads in compound planet sets. Each combination of gear position and helix hand should be 5-35

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Design Practices: Passenger Car Automatic Transmissions

If A is set equal to fc ¥ Z3/4, the formula for C becomes C = A × leff 7/9 × Dw29/27



The Basic Static Load Rating (Co) for a single row of a full complement of needle rollers is calculated by using the International Organization for Standardization (ISO) Standard 76:2006 formula:

(5.4.4)



Table 5.4.3 provides values of A for typical roller complements used in automotive planetary gears.

⎡ D ⎤ Co = 44 ⎢1− w ⎥ Zleff Dw ⎢ Dpw ⎥ ⎦ ⎣



Table 5.4.3  Values of “A” for Load Rating Calculations

where:

Values to be used with mm dimensions for needle rollers to calculate load rating in N

leff = effective length of roller contact, mm (for spherical end rollers, leff = maximum overall roller length – Dw/2) (for flat end rollers, leff = maximum overall roller length – 2 ¥ roller corner radius) Z = number of rollers Dw = roller diameter, mm Dpw = bearing pitch diameter, mm Co = static load rating, N

Z

A

15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

493 520 544 569 592 614 636 656 676 693 711 729 747 763 780

The static load rating of the bearing must be, at a minimum, equal to or greater than the maximum calculated load. In addition, the contact stress should be calculated and not exceed the recommended ISO 76:2006 limit of 4000 MPa for roller bearings. Note that this value is not an actual material stress, it is the pressure at the contact between the roller and the raceway for the most heavily loaded contact. The value comes from the load applied to the roller divided by the area created by the deformed region of the bodies in contact. This can then be used as a boundary condition to determine the actual stresses in the material below the point of contact.

The life factor (LF) for a roller assembly is computed by dividing its Basic Dynamic Load Rating (C) by the product of the applied load and the speed factor (SF) for its rotational speed. This is used to estimate the fatigue life for the bearing. where:

LF =

C load × SF

⎤ ⎡ ⎢ r min ⎥ ⎥ SF = ⎢⎢ 1 ⎥ ⎢ 33 ⎥ ⎢⎣ 3 ⎥⎦

5.4.1.6  Slope Calculations

(5.4.5)

Before life factors can be properly evaluated, it is necessary to go one step further and calculate the slope of the shaft through the bearings. Because transmissions are compact, the planet pinion shafts are rather small in diameter compared to their length and therefore deflect under the loads imposed.

3/10

(5.4.6)

To simplify calculations, certain conventions are followed, which may not give exact values of slope. However, they do permit comparison of one transmission with another, and give a basis for predicting bearing success or failure. These conventions are:

Example—A full complement of 20 spherical end rollers, each 3.000 mm in diameter and 14.00 mm long, has an applied load of 9000 N. The bearing speed is 1700 r/min. Determine the basic load rating C and the life factor LF.

1. Civil engineering deflection and slope formulas for long beams are used. 2. Shafts are assumed to be simply supported beams with the supports located at the inside faces of the carrier. 3. The loads applied to the shafts are assumed to be concentrated at the center of the roller paths. If a single roller

leff = 14.00 – 3.000/2 = 12.50 mm A= 614 (for 20 rollers) C = 614 ¥ (12.50)7/9 ¥ (3.000) 29/27 = 14250 N SF = [1700/(33 1/3)]3/10 = 3.25 Load = 9000 N LF = 14250/(9000 ¥ 3.25) = 0.49 5-36

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Bearings

5.4.1.7  Life Factor-Shaft Slope Relationship

path is used in a helical pinion, the roller path is assumed to be cut in half and the loads concentrated at the center of the resulting roller paths.

The slope of the shaft affects the capacity and life of the bearing. A study of past United States production automobile transmissions indicates that the life factors for various shaft slopes should be no less than those given in Table 5.4.5, when the calculations are based on the critical torque input into the transmission.

Figure 5.4.6 and Table 5.4.4 illustrate the method used to calculate slopes.

Fig. 5.4.6  Slope calculations. Table 5.4.4  Slope Calculations θLB =

P1ab(b + c) P2c[(a + b)(L + c) – 3a 2] ± 3LEI 6LEI

P a[(b + c)(L + a) – 3c 2] P2bc[(a + b)] θRB = 1 ± 6LEI 3LEI Where:

θLB–V =

3470 × 12.7[(12.7 + 44.45)(69.85 + 12.7) − 3 × (12.7)2 6 × 69.85 × 207 × 103 × 2485 = 0.00194 – 0.00087 = 0.00107 −



8452 6383 × 0.00194 − × 0.00087 3470 6494 = 0.00191 – 0.00212 = –0.00021

θLB = shaft slope through left bearing

θLB–V =

E = modulus of elasticity of shaft = 207 ¥ 103MPa



θRB = shaft slope through right bearing

I = moment of inertia of shaft, mm4 =

π ⋅ (shaft diameter)4 64

Resultant θLB = (0.00107)2 + (–0.00021)2 = 0.0011 : 1 θRB−V =

P1, P2 = bearing loads (see Fig. 5.4.6)

a = distance from left support to center of left bearing, mm b = distance between bearing centers, mm

c = distance from center of right bearing to right support, mm L = distance between supports, mm For example (see Fig. 5.4.6), Let V = c T plane

Shaft = 15 mm



E = 207 ¥ 103 MPa

H=   plane

I = 2485 mm4

6494 × 12.7 × 44.45(44.45 + 12.7) 3 × 69.85 × 207 × 103 × 2485

–



6494 × 12.7[(44.45 + 12.7)(69.85 + 12.7) – 3 × (12.7)2] 6 × 69.85 × 207 × 103 × 2485 3470 × 44.45 × 12.7(44.45 + 12.7) 3 × 69.85 × 207 × 103 × 2485

= 0.00180 – 0.00104 = 0.00076

θRB−H =

8452 6383 × 0.00180 − × 0.00104 3470 6494

= 0.00177 – 0.00253 = 0.00076

Resultant, θRB = (0.00076)2 + (–0.00076)2 = 0.0011 : 1

NOTE: Principle of Superposition—When a shaft is subjected to the simultaneous action of several loads of similar nature, the slope at any point equals the sum of the slopes at that point produced by each force separately. The slope is calculated by first considering only the vertical forces and then by considering only the horizontal forces. The resultant slope at a given point is then found by the vector sum of these vertical and horizontal components.

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Design Practices: Passenger Car Automatic Transmissions

Table 5.4.5  Life Factor-Shaft Slope Relationship Gear

Up to 0.002:1 Slope

0.002:1 to 0.004:1 Slope

Low Int Rev

LFmin = 0.20 LFmin = 0.30 LFmin = 0.10

LFmin = 0.30 LFmin = 0.45 LFmin = 0.15

HV 350) are allowed to enter a bearing, denting and fatigue damage progresses rather quickly. Even softer contaminants can cause wear and shorten bearing life. The effect of contamination varies, but some manufacturers suggest using a life reduction factor of 0.5 for “normal” conditions where the filtration may only be 30–100 µm particle size [1]. The point here is to make sure that contaminants are not built into the transmission and wear particles are filtered out.

When shaft slopes exceed 0.004:1, the life factors should be considerably higher. In addition, detailed bearing analysis should be done by a bearing expert to optimize the roller profiles and contact stresses for such high slope applications, followed by thorough testing. Transmission designs with higher numbers of gear ratios can have complex planetary gear set combinations which make the simplified slope calculation difficult and require alternate methods of analysis.

5.4.1.10  Limiting Speed All rolling element bearings will have some practical limit to the rotational speed that can be applied to the bearing, under a certain set of loading circumstances, before the onset of failure of the bearing system from overheating. Because many major bearing manufacturers list “limiting speed” in product catalogs along with dimensional data and load ratings, it is often assumed that bearing limiting speed is strictly an attribute of the bearing design (size, type, etc.). Although design details do have a significant impact, the environment in which the bearing is operating can also have a profound effect on the actual limiting speed performance of a bearing system [2].

5.4.1.8  Life and Reliability The life calculation using the bearing industry standard determines what is called the L – 10 life. This is the life (in hours or millions of revolutions) which 90% of a population of bearings should be expected to exceed under the defined operating conditions before experiencing rolling contact fatigue. In effect this defines the point of 90% reliability. If a different reliability estimate is desired, the coefficients from Table 5.4.6 can be used to adjust the basic L – 10 life, where

Tabulated “limiting speeds” from catalogs or drawings are best interpreted as reasonably conservative estimates of the maximum design limit for bearing speed under the environmental conditions (load, lubrication, temperature, cleanliness, etc.) found in basic applications (without highly engineered bearing systems).

L – n = a1 ¥ L – 10. Table 5.4.6  Reliability Coefficients L–n

Reliability %

Rating Life

a1 Life Adjustment Reliability Factor

90 95 96 97 98 99

L – 10 L–5 L–4 L–3 L–2 L–1

1.00 0.64 0.55 0.47 0.37 0.25

5.4.1.11  Bearing Selection Good bearing design must now be considered. The gear bore should be as large as possible, consistent with the necessary gear strength. The diameter of the needle rollers should not be less than 10% of the gear bore. The ratio of the roller length to roller diameter should be between 4:1 and 8:1. The exact dimensions for the raceway diameters based on a given roller diameter and number of rollers are calculated as outlined in Fig. 5.4.7 and Table 5.4.7. The chordal factor K is an adjustment for the fact that the minimum clearance between the rollers is not exactly at the pitch diameter. Note particularly the circumferential clearance (C.C.) between the rollers and the diametrical clearance (D.C.) between the bore of the rollers and the shaft. This C.C. represents a starting point. In some instances, a higher C.C. may be necessary to prevent overheating under high-speed-no-load conditions. The next to last transmission in Table 5.4.8 (see page 5-40) needed extraordinary C.C. (or C.C./π) for this reason.

5.4.1.9  Contamination In addition to slope and deflection which create uneven loading in the rollers, there is another factor which can reduce bearing life considerably. Bearing testing with clean filtered lubrication often provides lives well in excess of those predicted by conventional life calculations. If hard particles (>

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Bearings

Table 5.4.7  Dimensions for Bearing Selection Loose Needle Roller Bearing Calculation Form Step

Data

Variable

Value

1 2 3 4 5 6 7 8 9 10

Given Chordal Factor (1) ¥ (2) Given (3) + (4) Given (5) – (6) Given (7) – (8) (5) + (6)

D K for 20 rollers K¥D C.C./π Pitch Diameter D

3.000 max 6.39245 19.177 0.025 min 19.202 3.000 16.202 0.013 min 16.189 max 22.202 min

D.C. Shaft Dia. (d) OR Bore (B)

Definition of Variables 2.997 min

where: D = roller dia. (max) d = shaft dia. (max)

B = outer race bore (min) K = 1/(sin (180°/Z))

16.180 min 22.215 max

ISO h5 tolerance ISO H6 tolerance

Chordal Factors (K) for typical numbers of rollers (Z) Z 15 16 17

K 4.80973 5.12583 5.44219

Z 18 19 20

K 5.75877 6.07553 6.39245

Z 21 22 23

K 6.70951 7.02667 7.34394

and indicates those that have fixed washers and those that have free washers.

Fig.5.4.7  Needle roller design calculations. Fig. 5.4.8  Planet thrust washer and spacer arrangement.

5.4.1.12  Thrust Washers and Spacers

If the thrust washer is faced with a soft bearing material, a thin hardened steel spacer or washer hardened to Rc 58 minimum must be put between this softer surface and the ends of the rollers. These steel washers are often electroless nickel plated to achieve this hardness. When two rows of needle rollers are used, they must be separated by a hardened steel sleeve or spacer, often called a “wedding band.” These spacers should be file-hard to Rc 40 minimum, and held to a flatness of 0.15 mm (measured between parallel plates). It is important to consider this flatness so that a minimum end

Theoretically, the thrust loads on planet gears caused by the helix angle cancel, and thus there should be no gear thrust problems. However, inaccuracies in manufacture, deflection of the pinion shaft, and skew and microslip in the roller contacts actually create thrust loads. Thrust washers or plates must be provided between the gears and the carrier. As Fig. 5.4.8 shows, some washers are keyed to prevent rotation and some are not. Many transmission builders found it necessary to key the washers. Others found that plain, flat washers sufficed. Table 5.4.8 includes information on each transmission 5-39

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Design Practices: Passenger Car Automatic Transmissions

Table 5.4.8  Design Details for Production Transmissions Input

Pinion Shaft Data

Pinion Data

Case Depth mm

Hardness, Rc

Bore Finish, μm

Face Finish, μm

Case Depth mm

Hardness

Bore Taper mm

Face to Bore, TR mm

Bore Conc. to Gear Pitch Dia, TR mm

Root to Bearing and Tooth Height mm

Bore Chamfer Max mm

Torque, N-m

Speed r/min

Material

Finish, μm

468

1000

1080

0.25

0.635 1.016

60

5130

0.51

0.66

0.305 0.381

RA 80

—

0.076

0.05

4.216 3.734

0.762 ¥ 30°

705

1140

1080

0.25

1.016 1.524

60

5130

0.51

0.19

0.305 0.381

RA 80

—

0.076

0.05

5.156 3.81

0.762 ¥ 30°

583+

2100

1024

0.25

0.762 1.143

81 (RA) 5130 1330

0.25

0.76

0.305 0.381

Rc 58

0.0051

0.076

0.05

5.08 4.064

0.762 ¥ 30°

617

  630

1065

0.13

0.653 1.905

58

4027

0.38

0.38

0.254 0.457

R15N89 0.0102

0.038

0.127 (Bore OD)

4.47 4.115

0.762 ¥ 45°

458+

  833

1065 1085

0.13

0.889 1.27

58–62

8620

0.51

0.38

0.457 0.584

Rc 58

0.0064

0.025

0.05

3.581 3.594

0.635 ¥ 45°

553

  800

1041

0.25

0.254 0.508

58

4024

0.51

0.38

0.381 0.635

Rc 58

0.0025

0.038

0.05

3.404 3.912

0.381 ¥ 45°

715

1140

1041

0.25

0.254 0.508

58

4024

0.51

0.51

0.305 0.381

Rc 58

0.0051

0.038

0.05

3.454 4.216

0.508 ¥ 45°

900

1115

1085

0.13

1.27 3.81

60–64

5140-H

0.51

0.51

0.178 0.305

RA 0.0064 79–82½

0.051

0.03

3.835 4.699

0.762 ¥ 30°

553

  816

1024

0.23

0.508 0.762

58

4027-H

0.41

0.25

0.203 0.406

R15N89 0.0051

0.038

0.127 (Bore OD)

4.089 3.226

0.508 ¥ 45°

857

  895

1024

0.23

0.508 0.889

80 (RA) 4027-H

0.41

0.25

0.305 0.381

R15N89 0.0051

0.038

0.127 (Bore OD)

3.861 3.327

0.508 ¥ 45°

583

  950

1084

0.13

1.27 3.81

0.51

0.51

0.254 0.406

R15N64 0.0076

0.051

0.05

3.759 3.327

0.762 ¥ 30°

60–64

Material

5130

*No longer in production + Transmission input (converter output) taken from critical point on converter curve—see Fig 5.4.1 (L) indicates data for long planet (S) indicates data for short planet

5-40

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Bearings

Roller Data

End Clearance Diameter mm mm

Length mm

Thrust Washers

Length Dia ratio

Material

Wedding Bands

Fixed or Free

Lube Slots

Material

General

Flatness mm

Pilot

cc/p min

dc min

Carrier Pitch Diameter mm

Pinion Shaft Location

0.178 0.737

2.362 2.38

17.12 16.612

7:1

Steel-backed bronze, lead tin overlay

Fixed

Yes

Low-carbon carburized, file hard

0.152

Shaft

0.079

0.010

76.71 (L) 84.14 (S)

Slip fit and keyed

0.178 0.737

2.769 2.774

17.526 17.018

6.3:1

Steel-backed bronze, lead tin overlay

Fixed

Yes

Low-carbon carburized, file hard

0.152

Shaft

0.025

0.008

91.71 (L) 98.99 (S)

Cross tol. And supset

0.203 0.737

2.769 2.774

21.082 20.574

7.6:1

Steel-backed bronze, lead tin overlay

Fixed

Yes

Low-carbon carburized, file hard

0.152

Shaft

0.025

0.008

91.71 (L) 98.99 (S)

Slip fit and keyed

0.127 0.559

2.362 2.377

22.352 21.844 12.7 12.217

9.3:1 (L) 5.4:1 (S)

Steel electroless nickel plated

Free

No

Low-carbon carburized, file hard

0.127

Shaft

0.025

0.008

95.5 (L) 85.85 (S)

Press one end, stake both ends

1.981 1.979

17.526 17.018 20.574 20.091

8.6:1 (L) 7.4:1 (S)

Fiber

Free

No

Low-carbon carburized, file hard

0.127

Shaft

0.061 0.013 (L) 80.06 (L) 0.089 0.013 (S) 73.41 (S)

Press one end, stake both ends

0.203 0.533

2.337 2.352

15.748 15.24

6.5:1

Steel-backed bronze, lead tin overlay

Fixed

Yes

Low-carbon carburized, Rc 58 min

0.102

Shaft

0.018

0.008

71.63

Slip fit and pinned

0.203 0.533

2.362 2.377

17.78 17.272

7.5:1

Steel-backed bronze, lead tin overlay

Fixed

Yes

Low-carbon carburized, Rc 58 min

0.102

Shaftbore

0.028

0.008

81.28

Slip fit and pinned

0.254 0.66

2.286 2.301

18.932 18.415

8.1:1

1 bronze 3 hard steel

Free

No

None used

0.074

0.008

79.25

Pressed and upset

0.178 0.584

2.362 2.377

17.78 17.272

7.5:1

Steel electroless nickel plated

Free

No

None used

0.025

0.008

72.9

Slip fit and pinned

0.178 0.508

2.311 2.311

20.574 20.066

8.8:1

Lead-tin overlay

Fixed

Yes

Low-carbon carburized, file hard

0.330

0.008

81.46

Slip fit and pinned

0.203 0.635

1.956 1.956

18.923 18.415

10.0:1

Steel-backed bronze

Fixed

Yes

0.051

0.008

77.06

Press one end, stake both ends

Must turn free

0.254

None used

Shaft

5-41

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Design Practices: Passenger Car Automatic Transmissions

clearance of 0.2 mm per path of rollers can be maintained. The surface finish of the spacer facing the roller end should be 0.5 μm Ra maximum. Pitted surfaces may prevent smooth roller operation.

A pressure lubrication system would be ideal, but it is not economically feasible. Lubrication slots in the thrust washer or carrier pinion pocket faces, or scallops in the washer bore were often the only concession to lubrication in past designs. Slots are not always necessary, but when used their edges should be well blended. Some transmission designs have used combinations of lube catchers and drilled pinion shafts to direct lubricant to the planetary bearings, as shown in Fig. 5.4.10 [3].

End spacers should be wide enough to maintain the entire needle roller contact lengths inside the chamfer on the bore of the planet gear, to realize maximum bearing performance. When the contact length of the rollers extends beyond the gear chamfer, a stress concentration is formed at the chamfer point, which can cause early spalling of both the rollers and the gear bore. Instead of end spacers, most planet pinions now use rollers that have a modified end shape and profile which not only serves to keep the roller contact length within the cylindrical portion of the pinion bore, but also reduces end stress by the careful blending of the roller corner with the roller OD. Both the center and end spacers should float and be piloted or guided on the shaft. However, if the washer OD is too small, it can shift radially during assembly, enough to interfere with the installation of the planet shaft. Thus, although the spacer pilots from its ID, the clearance between the spacer OD and the gear bore should also be kept as low as possible. Whenever a center spacer is used without end spacers, it can be piloted by the gear bore for ease of assembly. If the roller paths are spaced far enough apart, a formed and hardened spacer similar to a cage for a bearing assembly can be used as shown in Fig. 5.4.9 [3].

Fig. 5.4.10  Planetary set with formed roller spacer. 5.4.1.14  Metallurgy Since the bore of the gear and the shaft OD are integral parts of the bearing system, their metallurgy must be satisfactory for bearing components. The bore of the gear should be at least case hardened. The finished case depth necessary depends on the core hardness. A 0.63 mm minimum case is needed with a relatively soft core. With a harder core, the case depth should not be less than 0.25 mm. The case hardness should be equivalent to Rc 58 minimum. Fortunately, the gear teeth require good quality steels having high surface hardness. Usually, materials and heat treatments satisfactory for gears are also satisfactory for bearing raceways. However, in no instance should leaded steels be used because their rolling contact fatigue properties will lead to early spalling.

Fig. 5.4.9  Planetary set with lubrication features.

The planet pinion shafts must also be of good metallurgical quality and have a high surface hardness. Some of the materials used for pinion shafts are shown in Table 5.4.8. Various other data regarding the planet gears, needle rollers, thrust washers, etc., are also included in the table.

5.4.1.13  Lubrication In addition to lubricating the bearing, the oil supplied to the planet pinion takes away the heat generated by the gear teeth, the friction of the radial bearing, and the friction of the thrust surface. Although comparatively little heat is developed, the ability of the mechanism to dissipate heat is limited by the small parts and the poor path for conduction. With inadequate lubricant flow, the temperature will not stabilize at a reasonable value, and the hardened steel parts will actually temper [4].

5.4.1.15  Tolerances The bearing raceways of the planet pinion gear and shaft must be held to reasonably close tolerances to ensure proper bearing performance. Note the gear bore tolerance of 0.013 mm (ISO 286-2:1988 H6 hole tolerance) and the pinion shaft diameter tolerance of 0.009 mm (ISO h5 shaft tolerance) 5-42

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2.779 mm. The tendency was to use smaller—rather than larger—diameter rollers. The smaller roller diameter allowed an increased shaft diameter and minimized the shaft deflection and slope as an aid in achieving maximum bearing life. In recent years the trend to more forward speeds in automatic transmissions has resulted in more planetary sets with shorter pinion lengths but larger pinion pin and gear bore diameters. Roller diameters up to 3.5–4.0 mm nominal have become more common.

specified in Table 5.4.7. These tolerances have proven to be satisfactory and are within standard manufacturing capabilities. In addition, the diameter of the gear bore should never be smaller at the ends than in the middle. The bore should be from cylindrical to high at the ends (slightly bellmouth) to lessen stress at the roller ends. 5.4.1.16  Surface Finish The gear bore surface finish should not exceed 0.3 μm arithmetical average (Ra). This finish is usually obtained by honing.

5.4.1.19  Cage and Roller Assemblies Caged needle roller assemblies are also widely used as planet pinion bearings. Caged assemblies have historically been, and are still widely used in the planet gears of heavy equipment as well as in constant-mesh gears of manual and automatically shifted manual transmissions. Multiple bearing paths can be utilized without the addition of wedding band spacers, which makes for easier assembly. A significant design advantage is the ability of caged bearings to operate at high speeds and in high centrifugal loading fields, which are commonplace in planetary or epicyclic geartrains.

The planet pinion shaft finish should not exceed 0.2 μm Ra. This finer finish on the shaft is necessary since the contact stress between the shaft and rollers, because of curvatures, is higher than between the rollers and the gear bore. Fortunately, a 0.2 μm finish on the shaft can be attained by centerless grinding and finishing. With newer transmission designs moving toward higher speeds and reduced viscosity lubricants, improving surfaces lower than these limits can lead to improved bearing life by better preventing breakdown of the lubricant film separating the rollers and raceways.

Shaft rotation and axial movement is prevented by crosspinning, press-fitting, staking, or riveting the shaft into the carrier, or by slabbing the shaft and keying it to a holder. Table 5.4.8 tabulates the planet shaft retention methods which have been used in production transmissions.

If a cage and roller assembly is being considered, a thorough analysis should be done to determine the optimum design. Steel and polymer type caged designs are available, and several successful applications of cage and roller assemblies in automatic transmission planetaries exist. They are used in both simple planetary and compound planetary systems. Planetary pinion loading and relative speed conditions are determined by the same methods as discussed in the loose roller complement section. Once the operating conditions are defined for the transmission power flow being evaluated, the designer can start the selection process by comparing the operating requirements to the dynamic load rating of a design which will physically fit into the planetary gear system. In addition, cage loads and stresses from high-speed operation should be considered for both fatigue and cage wear failure modes.

5.4.1.18  Bearing Rollers

5.4.1.20  Summary of Current Practice

The rollers are made of SAE 52100 steel through-hardened to Rc 60 to 64 and finished to 0.2 μ m Ra maximum. Most planet pinion rollers have a diameter tolerance of 0.005 mm. Some manufacturers use rollers produced to a 0.003 mm tolerance. Although these rollers are more costly, they can offer better load distribution and more consistent bearing life.

Tables 5.4.9 and 5.4.10 tabulate pinion bearings, as well as other related data for a selection of United States automatic transmissions. Note that all of these bearings are approximately the same size. However, each bearing presented its own problem which had to be resolved at the time of the transmission design. The tables also show the life factors and slopes at the critical point on the converter torque-speed curve mentioned earlier.

5.4.1.17  Planet Shaft Retention The planet shaft must be positioned in the carrier by some method that will prevent both rotation and axial movement. The rotational moment on the shaft is due to bearing friction. The thrust force on the planet pin is caused by skew of the bearing rollers.

When the outer raceway diameter is limited, as it is in planet gears, the dynamic capacity of a row of rollers in an outer raceway of a fixed diameter varies only slightly with a change in the roller diameter. Historically, most roller diameters used in production planet pinions ranged from 1.958 to

In summary, planet pinion radial bearing loads and speeds can be determined quite well mathematically and the pos5-43

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Table 5.4.9  Bearing Data For Production Compound Planetary Transmissions Input**

Pinion Data

Torque (Nm)

Speed (r/min)

Shaft Dia. (mm)

Gear Bore (mm)

468

1000

12.929

17.704

12.926

17.724

705

583

617

1140

2100

630

14.986

20.549

14.996

20.579

14.986

20.549

14.974

20.579

14.376

19.126

14.369

19.162

Bearing

Gear

Pinion

Life Factor

Slope

Long planets—two paths of 20 rollers (2.385 ¥ 17.12)

Low

Short planets—two paths of 20 rollers (2.385 ¥ 17.12)

Rev

Long planets—two paths of 20 rollers (2.779 ¥ 17.526)

Low

Short planets—one path of 20 rollers (2.779 ¥ 17.526)

Rev

Long (ea.) Short (LB) Short (RB) Long (ea.) Short (LB) Short (RB) Long (ea.) Short Long (ea.) Short

0.73 2.24 3.34 0.50 0.26 1.26 0.70 0.30 0.47 0.10

0.00271 0.00045 0.00040 0.00271 0.00344 0.00320 0.00200 0.00006 0.00200 0.00050

Long planets—two paths of 20 rollers (2.779 ¥ 21.082)

Low

Short planets—one path of 20 rollers (2.779 ¥ 21.082)

Rev

Long planets—two paths of 22 rollers (2.383 ¥ 22.352)

Low

Short planets—two paths of 22 rollers (2.383 ¥ 12.7)

Int

Long (ea.) Short Long (ea.) Short Long (LB) Long (RB) Short (ea.) Long (LB)

0.81 0.44 0.56 0.14 1.79 0.52 0.69 1.27

0.00219 0.00008 0.00219 0.00057 0.00216 0.00220 0.00041 0.00165

Long (RB) Short (ea.) Long (LB) Long (RB) Short (ea.) Long (LB) Long (RB) Short Long (LB) Long (RB) Short Long (LB) Long (RB) Short

0.72 0.00168 0.85 0.00041 0.78 0.00267 0.88 0.00267 Not Loaded 0.98 0.00276 0.35 0.00279 0.35 0.00072 0.79 0.00207 0.51 0.00208 0.42 0.00072 0.53 0.00350 0.53 0.00350 Not Loaded

Rev

458+

833

11.354

15.342 15.367

Long planets—two paths of 21 rollers (1.984 ¥ 17.526)

Low

11.369 14.986 14.994

14.986 14.995

Short planets—one path of 14 rollers (2.779 ¥ 20.574

Int

Rev

* No longer in production + Transmission input (converter output) taken from critical pin on converter curve—see Fig. 5.4.1.

sibility of success predicted. Selection of thrust washers and provisions for lubrication must be determined by test.

will be limited to the application of thrust needle roller bearings, as thrust washers and bushings have been covered in Sections 5.1 through 5.3.

5.4.2 Thrust Bearings

This type of thrust bearing is illustrated in Fig. 5.4.11. It takes about the same amount of space as a washer, but it has superior frictional characteristics and higher capacity than a washer. Another particularly desirable characteristic is its ability to handle momentary overloads that occur in a

Rolling element thrust bearings, as well as thrust washers, are used in various positions in both the converter and planetary gearbox sections of automatic transmissions. This discussion 5-44

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Table 5.4.10  Bearing Data for Production Simple Planetary Transmissions Input**

Pinion Data

Torque (Nm)

Speed (r/min)

Shaft Dia. (mm)

Gear Bore (mm)

553

800

11.963

16.688

11.966

16.708

Bearing

Gear

Pinion

Front and rear planets— one path of 19 rollers (2.357 ¥ 15.748)

Low

Front Rear Front Rear Front Rear Front Rear Front Rear Front Rear Front Rear Front Rear Front Rear Front Rear Front Rear Front Rear Front Rear Front Rear Front Rear Front Rear Front Rear Front Rear

Int Rev

715

1170

15.113

19.888

15.126

19.919

Front and rear planets— one path of 23 rollers (2.357 ¥ 17.78)

Low Int Rev

900

1115

11.024

15.621

11.024

15.657

Front and rear planets— one path of 18 rollers (2.304 ¥ 18.923)

Low Int Rev

553

816

11.328

16.104

11.336

16.124

Front and rear planets— one path of 23 rollers (2.38 ¥ 17.78)

Low Int Rev

857

895

14.986

19.634

14.994

19.649

Front and rear planets— one path of 23 rollers (2.314 ¥ 20.574)

Low Int Rev

583

950

9.982

13.894

9.977

13.919

Front and rear planets— one path of 19 rollers (1.958 ¥ 18.923)

Low Int Rev

Life Factor

Slope

0.33 0.00028 0.39 0.00028 0.40 0.00028 Not Loaded Not Loaded 0.16 0.00062 0.32 0.00021 0.36 0.00022 0.40 0.00021 Not Loaded Not Loaded 0.15 0.00047 0.27 0.00078 0.24 0.00078 Not Loaded 0.29 0.00078 0.21 0.00162 Not Loaded 0.32 0.00092 0.36 0.00092 0.40 0.00092 Not Loaded Not Loaded 0.16 0.00203 0.26 0.00032 0.39 0.00024 0.31 0.00032 Not Loaded Not Loaded 0.18 0.00052 0.32 0.00085 0.36 0.00085 0.38 0.00085 Not Loaded Not Loaded 0.17 0.00165

+ Transmission input (converter output) taken from critical pin on converter curve—see Fig. 5.4.1.

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5.4.2.2  Thrust Needle Roller Bearing Design

transmission. As a matter of fact, thrust needle roller bearings can carry momentary overloads as high as their static load rating (Coa) without any detrimental effect.

A thrust needle roller bearing consists of a cage and roller assembly and two raceways. The needle roller thrust bearings used in all production automobile automatic transmissions have hardened steel cages. While polymer cages have been used successfully in radial bearings, only a hardened steel cage has demonstrated the strength, wear resistance, and lube flow paths to assure reliability under the load, speed, and temperature conditions encountered in automatic transmissions. End faces of gears or similar surfaces that can be hardened to Rc 58 minimum and finished to 0.5 μm Ra maximum make satisfactory raceways for needle thrust bearings. If such surfaces are not available, hardened thrust washers must be used. 5.4.2.3  Thrust Washers

Fig 5.4.11  Needle thrust bearings.

Again, for reasons of space, thrust washers are kept as thin as possible. Where the washer can be backed up by a surface giving full support along the roller length, it may be as thin as 0.75 mm, or sometimes even thinner. These thin washers are made from SAE 1074 modified, through-hardened steel. Washers up to 1.5 mm thick are not surface-ground. These washers may not be flat after heat treatment, but are designed to flatten under a 2000-N load. The bearing rollers operate directly on the as-rolled surface of the material. Thus, both surface finish and tolerances demand the best in steel rolling techniques.

5.4.2.1  Speeds and Loads This section will make no attempt to give a detailed analysis of thrust bearing speed and load calculations. The loads and speeds handled by thrust bearings due to gear mesh are easily calculated. However, other thrust loads that occur are very hard to evaluate. The procedure for determining the thrust loads caused by converter hydraulic forces, for example, is very involved. The transmission output shaft for a rear-wheel-drive transmission anchors one end of the propeller shaft and absorbs the forces necessary to slide the splines at the universal joints. The rapidly reversing spline forces are impact in nature and must be absorbed by the same thrust bearings that handle gear thrust loads. These impact forces are also very difficult to determine. For these reasons, the ability of a thrust bearing to operate satisfactorily in a particular location is usually determined by vehicle test.

Washers above 1.5 mm thickness require more pressure to flatten and, therefore, are surface-ground after heat treatment to ensure flatness. Washers above 2.25 mm thickness are made from carburized SAE 1018, through-hardened SAE 1074 modified, or SAE 52100 steel. The washer backup surfaces must be square with the axis of the transmission to give good load distribution on the rollers.

The complete range of operating speeds and loads for the thrust bearing also needs to be examined for potential highspeed no-load conditions and back-up surface separation.

When good alignment between parts is impossible due to tolerance stackup or deflections, it has sometimes proved beneficial to provide backup surfaces narrower than the roller length, but centered at the pitch diameter of the roller path. This prevents the load from being concentrated at either the inside or outside end of the roller path.

Axial space is usually limited. Most thrust needle roller bearings use the smallest practical roller diameter, only 1.984 mm. If increased capacities are necessary and radial space is limited, greater dynamic load ratings are obtained by using bearings with larger roller diameters. This procedure has been followed in several transmission designs.

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If possible, the thrust washer should be piloted (located radially) by the member with which it has no relative motion. When a washer must be piloted from a part with which it has relative motion, the piloting surface must be hardened to Rc 58 minimum. The bore of the thrust cage and roller assembly may be piloted on a surface having a hardness of only Rc 45 minimum. If it is piloted on its OD, however, the piloting surface must be hardened to Rc 58 minimum. Quite often such a hardened surface is provided by the use of a formed washer. Figure 5.4.13 shows examples of various types of special washers and how they provide the necessary piloting for the cage and roller assembly. Fig. 5.4.12  Permissible partial race support.

A thrust cage and roller assembly, or its washer, may drop off of what appears to be a suitable pilot because of axial play due to the accumulation of tolerances when the bearing is unloaded. Therefore, it is necessary that the pilot length be sufficient to maintain its piloting ability under extreme conditions.

Partial backups are common in many applications. Analytical tools that can determine the success of partial or interrupted backups are limited. These are usually modeled using contact pressure analyses or by downgrading the capacity based on the number of rollers that are unsupported. Approximations based on these methods should be verified with testing. A simpler, though riskier, method would entail a review of successful applications that incorporate a similar type of backup. Below are some suggestions for minimizing risk for some typical interrupted backup conditions:

Processing considerations limit the length of an ID lipped washer to 20% of the bore diameter, and length of an OD lipped washer to 30% of the outside diameter. Designers should be aware of this feature whenever they use a lip on a washer to pilot a thrust cage and roller assembly. When sufficient pilot length cannot be provided due to space limitations or to the impracticability of manufacture of the thrust washer itself, assemblies have been developed, as shown in Fig. 5.4.13 [3], which restrict the axial movement of the cage and roller assemblies in the unloaded condition so that they will not drop off the piloting surface. Some of these assemblies also include features to ensure one-way assembly to avoid the possibility of cross-piloting or improper lube flow.

5.4.2.3.1  Grooves (e.g., Torque Converter Applications)

• A larger number of thinner grooves is better than a few large ones. • Angled or tangentially oriented grooves are better than radial grooves. • A thick race material should be added for highly loaded thrust bearings that run against grooves. 5.4.2.3.2  Holes

• Between or adjacent to planetary carriers it is often necessary to run a thrust bearing over pinion pin or dowel pin holes. A thicker race material should be used. 5.4.2.3.3  Partial Backups

• The portion of a roller path that can be completely unsupported is very dependent on the load and backup surface design. • Bearings with roller paths supported by the face of gear teeth can be successful when sufficiently thick race material is used and the gear face geometry is well controlled.

Fig. 5.4.13  Bearing and formed race thrust applications. As mentioned earlier, thin thrust washers should be backed by a surface lying directly behind the raceway area. If such

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backing is not possible, washers of a greater thickness must be used. They must have enough structural strength to allow the thrust force to be transmitted from the roller contact to the backup surface without undue coning or deflection.

In addition to customary uses, thin-cross-section drawn-cup bearings have been used to replace bushings in applications where relative component speeds are high and lubrication flow is minimal, thus substantially reducing friction and heat generation. The drawn cup bearing is installed into the application by means of an interference fit between the drawn cup raceway and the housing. This process locates and fixes the bearing axially and radially without the need for additional retaining components, such as snap rings or end caps. However, the transmission designer needs to provide a bearing-quality shaft for the rolling element contact raceway surface.

5.4.2.4  Lubrication Because their rollers slide as well as roll, thrust needle bearings require more oil than might be expected for rolling element bearings. Fortunately, these bearings are usually located where pressurized oil can be delivered to them. Oil should be introduced at the bore. Centrifugal force takes care of the required circulation. Although the cages are only slightly narrower than the roller diameter, sufficient oil will pass to take care of bearing lubrication. Heat generation and lubricant flow requirements are now influencing thrust bearing designs in several types of applications. Transmissions in particular are operating at higher speeds and torques, warranting a review of the lubrication circuit, the physical limiting speed of the bearing, and the amount of lubricant flowing through the position. In designing assemblies such as those shown in the application in Fig. 5.4.10, openings are provided in the vicinity of the bore and OD to allow the oil to flow through the bearing. 5.4.2.5  Bearing Capacity and Life Factors The dynamic load rating (Ca) of a thrust needle roller bearing is calculated in a similar manner to radial bearings using the ISO Standard 281 formula with different coefficients. Once the load and speed conditions for the bearing position are determined, the speed and life factor calculations can be used to determine the required load rating for the bearing. Just as with radial bearings, the static load rating (Coa) should not be exceeded in order to avoid bearing damage.

Fig. 5.4.14  FWD transmission. 5.4.3.2  Typical Positions and Bearing Types Used 5.4.3.2.1  Sprocket Supports

Sprocket support bearings (for chain-driven front-wheeldrive (FWD) transmissions), as shown in Fig. 5.4.14 [5], are loaded in every gear when the chain is under torque load conditions in drive and coast modes. To ensure maximum bearing life, care must be taken to center the load over the support bearing rather than allow a cantilever mounting which can produce an undesirable moment load. Caged style drawn cup bearings are used here. History shows that normal minimum diametral clearance (D.C.) recommendations of 0.013 mm have been successful. When aluminum sprocket supports are used, the minimum D.C. is often larger than catalog recommendations to allow for clearance at low extremes of the operating temperature (usually –40°C) due to the differential thermal expansion. The drawn cup bearing must also be evaluated to ensure that press fit in the aluminum housing will be adequate at the high temperature

5.4.3 Other Bearing Applications 5.4.3.1  Drawn Cup Radial Bearings Drawn cup radial bearings are applied to various support positions within automatic transmissions. The drawn-cup radial bearing can offer advantages over bushings or other types of bearing products by its compact envelope size, load rating capabilities, and relatively low cost. They are often used in planetary-type transmissions as sprocket supports, pump shaft support bearings, and miscellaneous components to shaft supports. In automatically shifted manual (ASM) and continuously variable (CVT) type transmissions they are found in countershaft, pilot, and sheave support positions.

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5.4.4 Keys to Successful Applications—Selection Criteria

extreme. Quite often these sprocket support bearings run on bearing-quality inner rings, which are installed with a press fit onto the sprocket hub. Because of the stack-up of tolerances, the OD of these inner rings is often hard turned and polished, or ground after assembly onto the sprockets. This leads to a tighter overall range of D.C., which has a positive effect on bearing fatigue life and bearing noise.

5.4.4.1  Applied Loads Less Than ½ of Basic Dynamic Load Rating Drawn cup needle bearing life predictions are based on the premise that the maximum dynamic load applied does not exceed half the dynamic load rating. If your application exceeds this parameter, select a larger bearing or consult the bearing manufacturer for detailed analysis and recommendations.

5.4.3.2.2  Pump Shaft Supports

Pump shaft support bearings are generally caged type drawn cup bearings, and in some cases they are provided with integral lip seals. Pump shaft support bearings are normally located in the valve body of automatic transmissions and support the shaft that drives the variable displacement vane pump (VDVP). Drawn cup bearings used in this position can often be subjected to severe shaft slopes (resulting from the long slender shaft) and marginal lubrication flow. Because this position has high shaft slopes, D.C. is normally increased significantly to avoid cross loading. Because most valve bodies are aluminum, the minimum D.C. must be designed to allow for minimum clearance at minimum operating temperatures. Relieved end rollers are typically used to accommodate the shaft slope.

5.4.4.2  Lubrication Radial bearings exhibit nearly pure rolling characteristics during operation. However, heat generation and methods of reducing it should be considered during the design of the application. Optimization of the lubricant flow to and through the drawn-cup needle bearing should be exercised to avoid excess heat generation. A design target of 950 mL/ min for each bearing position should be a starting point to ensure proper bearing lubrication. The drawn-cup bearing design can be enhanced to add features that allow the bearing to increase or reduce lube flow. Features like open-end flanges and radial oil holes through the cup wall are examples of flow enhancements. An integral lip seal is an obvious flow restrictor.

Some applications have used full-complement drawn cup bearings in this position. Although loading calculations may indicate that a full-complement drawn cup is required to obtain adequate life, there is experience that proves a caged bearing may function better due to the marginal lubrication in this position. Caged drawn cup bearings in these positions often use a modified lip bore for lubrication flow enhancement.

5.4.5 Typical Applications Figure 5.4.13 illustrates bearing applications in a compound planetary gearbox. Note that the long planet pinions use two paths of rollers to resist the over-turning couple loads from the helical gear teeth, while the short planet pinion uses a single roller path. This design is used for a family of transmissions which feature various planetary set combinations based on the speeds desired and torque requirements. The lower-torque version uses a Ravingeaux arrangement, while the higher-torque versions use a simple and compound type double deck carrier. This provides a center support for the long pinion pin and increases the stiffness, thereby reducing deflection through the bearings.

5.4.3.2.3  Miscellaneous Component-to-Shaft Supports

Supports for sun gears, carriers, and output shafts are examples of some other possible bearing applications. These are typically lightly loaded bearing positions that were traditionally supported by bushings. Higher application speeds, for transmission use in all world markets, have resulted in high speeds between these components which are best resolved by the use of thin-cross-section drawn cup caged bearings. These bearing positions typically have radial sections of 1.5 to 2.5 mm. The D.C. selected for use in these positions is 0.013 mm minimum, unless nonferrous housings are employed and thermal expansion differentials require temperature range effect analysis similar to the sprocket support positions. Inverted bearing designs, where the drawn race is on the inner diameter of the bearing assembly, can be utilized here if the housing bore can be more easily adapted to a bearing-quality surface than the shaft.

A drawn-cup needle roller bearing is used in this gearbox as one of the supports for the carrier. Figure 5.4.15 shows the use of a thrust bearing with 3.175-mm-diameter rollers in a hydraulic torque converter. The large rollers in this bearing were necessary to obtain sufficient bearing capacity to withstand the considerable forces encountered in such applications.

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Instead of a clutch release mechanism to connect the engine to the gearbox, the countershaft automatic uses a torque converter. It also has a high-pressure pump to pressurize the hydraulic clutch packs. The torque converter, pump, and clutches can reduce efficiency during shifting. Some automotive companies have developed a twin-clutch, dual-input shaft system in order to eliminate the efficiency losses from torque interruption during shifting. Generally, the countershaft arrangement consists of an input shaft, a countershaft, and a secondary (output) shaft. The input shaft receives pure torque from the torque converter or input clutch and passes it along to either the main shaft in direct (1:1) mode for rear-wheel-drive (RWD) transmissions, or the countershaft in all other modes for both front-wheeldrive (FWD) and RWD. The countershaft is responsible for torque and speed modification required to propel the vehicle by overcoming any resistance to its motion. Gears on the countershaft can be an integrally machined part of it, splined to the shaft, or supported by bearings and activated by synchronizers or hydraulic clutch packs. These gears are usually in constant mesh with the gears on the output shaft. In some FWD transmissions, the countershaft is the output shaft, but typically a separate output differential is used, as shown in Fig. 5.4.16 [6]. Since the torque is transmitted through a single gear mesh location, the tooth forces can be higher than those in planetary gearsets, which have several gears sharing the loading.

Fig. 5.4.15  Hydraulic torque converter.

5.4.6 Summary Most rolling element bearings in light vehicle automatic transmissions were initially either complements of needle rollers, used in the bore of planet pinions; or thrust needle roller bearings, used along the main axis of the converter and gearbox sections of the transmission. Developments over the years have added drawn-cup radial bearings in several positions, and cage and roller planetary bearings. This section of the bearings chapter establishes guidelines for the application of these bearings. The designers should expect to modify their designs as their test work dictates. There is no substitute for an imaginative, comprehensive test program.

5.4.7 Countershaft Arrangements, Auto Shifted Manuals (Manuals) 5.4.7.1  Introduction Some automatic transmissions for passenger cars use a countershaft arrangement typically found in manual transmissions. This type of “manual-layout automatic” design and the traditional manual transmission both have a set of fixed gear ratios in constant mesh, activated by locking the gears to their respective shafts. While a particular gear is engaged by a synchronizer mechanism in a manual transmission, multi-plate clutch packs are hydraulically activated to change gears in a manual-layout automatic.

Fig. 5.4.16  Countershaft layout automatic transmission. 5-50

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Bearings

To illustrate the operation of a manual-layout automatic transmission, consider 4th gear in Fig. 5.4.16. The speed gear for the 4th gear ratio is clutched to the input shaft. It is free-spinning and will not transmit any torque until it is locked to the input shaft via the 4th clutch. It is also in constant mesh with a smaller gear on the countershaft which is always engaged.

the raceway for the most heavily loaded contact. The value comes from the load applied to the roller divided by the area created by the deformed region of the bodies in contact. This can then be used as a boundary condition to determine the actual stresses in the material below the point of contact. The other criterion that is considered when selecting the appropriate bearing is the typical failure mode for speed gears, false brinelling (fretting corrosion). False brinelling is recognized by evenly spaced depressions or wear marks on the shaft that correspond to the roller spacing of the bearing assembly. In some rare instances the failure mechanism will occur in the gear bore. False brinelling is not a plastic deformation of the raceway, but rather wear of the raceway. Although speed gears are only loaded statically, the rollers will still vibrate due to gear tooth tolerances and other imbalances in the transmission, allowing a possible fretting corrosion condition to exist. As the rollers in the bearing oscillate slightly from side to side, they will squeeze lubricant out from between the rollers and raceways and cause steelon-steel wear, the basis for false brinelling.

The 4th gear on the input shaft is locked by means of hydraulically engaged multi-plate clutches. The clutch inner hub is welded to the gear, while the clutch outer hub is splined to the shaft. When the hydraulic pressure is applied and the clutch plates are forced together, the gear becomes locked to the shaft and is able to transmit torque to the countershaft which is reacted by the differential, and eventually the wheels on the road surface. Torque is transmitted to the differential by means of a small output gear on the countershaft, which is in constant mesh with the differential ring gear transferring torque to the front axle.

The rate at which false brinelling will occur is heavily dependent on the amount of loading, the duration the bearing experiences that loading, and the lubrication conditions. For instance, in agriculture and construction applications where a majority of transmission time is spent in low gear, there is a greater probability of false brinelling occurring. Providing a good oil supply to the speed gear bearings can alleviate this problem.

5.4.8 Analysis Procedures and Results 5.4.8.1  Speed Gear Needle Bearings If in the example above, the 4th gear is locked to the shaft and transmitting torque, the bearing supporting that gear is statically loaded. This is because the bearing is loaded from the tangential, separating, and thrust gear mesh forces, but there is no relative motion between the bearing raceways (shaft and gear bore). Bearing reactions to these forces are calculated in a similar manner to the planetary gear sets in Appendix A. The only difference is the single point of gear mesh [7].

From many years of experience, it has been determined that if the maximum static load is below 10% of the bearing’s static load rating, the process of false brinelling is greatly slowed—to the point where it occurs well after reasonable transmission life has been achieved.

To select an appropriate bearing for any of the many speed gear positions in a countershaft automatic transmission, the style and static load rating of the bearing must be considered. The general layout of a countershaft transmission usually dictates that small cross-section bearings be used underneath the gears. In some lightly loaded applications and older manual transmissions, the speed gears were supported by journal bearings (hydrodynamic lubrication). A bushing is sometimes used when the loads are very high and time in gear is very long. In most current automotive transmissions, cage and roller assemblies support the speed gears. The cage and roller assembly is advantageous when the lubrication is limited, the speeds are high, or the oil is contaminated.

Cage and roller assemblies are well suited for the high-speed conditions when the speed gears are free-spinning. They also better tolerate slope from gear tilt than full-complement bearings, and are easy to handle and assemble into the transmission. In addition to these benefits, the cage can be designed to prevent false brinelling. By using a roller-piloted, split polymer cage design, false brinelling can be prevented in high-use gears. The failure mode is avoided by making the bearing precess around its center when under load. The single-split design feature along with the glass fiber content cause the cage to be in tension, wanting to spring open. The cage pocket retention tabs, which cause the cage to pilot on the rollers, resist the cage’s inclination to spring open. Because the linear speed of the roller center lags behind the outer raceway and advances relative to the inner raceway, the few rollers in the load zone rotate about their own centers. This movement of a few ­rollers

The static load rating of the bearing must be, at a minimum, equal to or greater than the maximum calculated load. In addition, the contact stress should be calculated and not exceed the recommended ISO 76:2006 limit of 4000 MPa for roller bearings. Note that this value is not an actual material stress, it is the pressure at the contact between the roller and 5-51

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Design Practices: Passenger Car Automatic Transmissions

5.4.8.4  Drawn-Cup Shaft Supports

in the load zone is transmitted to the cage body because of the roller piloting and cage tension, thereby causing the cage to rotate.

Drawn-cup needle bearings are used in numerous positions in countershaft transmissions. Their small radial cross-section and width make them ideal as a shaft support, providing a higher dynamic capacity than other styles of bearings (cylindrical roller, ball, tapered roller) of the same radial space. In addition, the press fit of the bearing in its housing requires that no other components (snap rings, etc.) be used to axially locate it. However, the drawn-cup bearing is not meant to locate the shaft. Therefore, a drawn-cup bearing is usually used on one end of a shaft that is supported by a ball or duplex tapered roller bearing on the other end to resist axial motion.

There are many engineered polymers suitable for transmissions using ATF or gear oil. The most common cage polymer used in countershaft transmissions is glass-reinforced polyamide (PA) 6-6, with a continuous use temperature limit of 120°C (250°F). However, polyamide (PA) 4-6, polyethersulfone (PES), polyetherimide (PEI), and polyetheretherketone (PEEK) are polymers with higher temperature limits available for more demanding applications. For speed gear positions that are unlikely to false brinell, standard catalog cages can be used. These catalog bearings are particularly suitable for lower gears such as 1st and reverse, where relatively short time is spent in gear. A very functional solution is to use two narrow single-row bearings per speed gear. The separate cages can rotate at different speeds if necessary, and better tolerate the slope induced from gear tilt. However, a more economical solution may be to use a double-row wrapped and welded steel cage, or double-row polymer cage.

The load on the bearing is determined by a static analysis of the shaft, using two simple supports (for a shaft supported by two bearings), and forces and moments produced from each gear mesh. Once bearings and speeds are determined for each gear, an equivalent load and speed can be calculated based on the time in each gear from the duty cycle. With the equivalent load and speed, and the L-10 life target, a required dynamic load rating can be calculated which will allow a bearing of the appropriate size to be selected.

5.4.8.2  Reverse Idler Support Bearings

5.4.9 Summary

When reverse mode is selected, the idler shaft comes into play. As shown in Fig. 5.4.16, the idler shaft supports only the reverse idler gear, which meshes both with a gear on the countershaft and one on the input shaft. The idler gear provides a change in rotational direction. Because it is in mesh with two other gears during reverse mode, it is the only gear in a countershaft arrangement where dynamic loading of the gear support bearings occurs. For this position, select the bearing based on the dynamic load rating required to achieve the L-10 life target for the duty cycle. Standard catalog cage and roller assemblies are routinely used in reverse idler positions in most transmission applications.

While the countershaft type of automatic transmission uses many of the same kinds of bearings as the planetary type, the loading conditions and failure modes of concern for bearing selection are quite different. Bearings under speed gears are usually loaded in a condition with no relative rotation between the inner and outer races, although the entire assembly is rotating. For this reason the bearings are selected based on static load rating and avoiding false brinnelling. The main and countershaft support bearings must react loads which change location along the shaft depending on the gear engaged and are selected based on the typical rolling contact fatigue methods for rolling element bearings. Just as in the previous section on planetary automatic transmissions, a well-designed and comprehensive test program should be used to verify that the conditions used for bearing selection were appropriate to ensure proper bearing performance in the application.

For cage and roller assemblies in speed gear and reverse idler positions, h5 and G6 ISO tolerances are generally used for the shaft and gear bore, respectively. 5.4.8.3  Thrust Bearings for Countershaft Transmissions Many transmission manufacturers today use thrust needle bearings and washers on both sides of the floating helical gears for axial location purposes. The outboard thrust washers are then grounded to the shaft by means of snap rings. The thrust bearing is only loaded statically when the speed gear is transmitting torque. However, the use of thrust bearings can reduce spin losses and improve transmission efficiency during the free-spinning conditions. If the application provides sufficient back-ups, a thrust bearing assembly can be employed, which combines the thrust bearing and washers into one assembly.

5.4.10 References 1. Takemura, H., Y. Matsumoto, and Y. Murakami, “Development of a New Life Equation for Ball and Roller Bearings,” SAE Paper No. 2001-01-2601, SAE International, Warrendale, PA, 2001. 2. Chiu, Y. P. and M. Myers, “A Rational Approach for Determining Permissible Speed for Needle Roller Bearings,” SAE Paper No. 982030, SAE International, Warrendale, PA, 1998. 5-52

Bearings

3. Baran, J., J. Hendrickson and M. Solt, “General Motors New Hydra-Matic RWD Six-Speed Automatic Transmission Family,” SAE Paper No. 2006-01-0846, SAE International, Warrendale, PA, 2006. 4. Chen, J., N. Anderson, and M. McKenzie, “Effect of Planetary Bearing Lubrication Methods on Operating Temperature and Life,” SAE Paper No. 981096, SAE International, Warrendale, PA, 1998. 5. Thompson, P., J. Marano, J. Schweitzer, S. Khan, and J. Singh, “General Motors 4T65-E Electronic Four-Speed Automatic Transaxle,” SAE Paper No. 980821, SAE International, Warrendale, PA, 1998. 6. Ohashi, T., S. Asatsuke, and H. Moriya, “Honda’s 4 Speed All Clutch To Clutch Automatic Transmission,” SAE Paper No. 980819, SAE International, Warrendale, PA, 1998. 7. Smith, K. and J. Hilby, “Analysis of Roller Bearings Under Transmission Gears,” SAE Paper No. 871684, SAE International, Warrendale, PA, 1987.

The ring gear is stationary. The input is through the sun, at 2740 r/min, the output through the carrier. To solve for speeds: 1. Construct a speed table having a column for each individual gear and the carrier, as in Table A-1. 2. Consider all elements of the train locked together. Rotate the entire mass plus one turn about the centerline of the geartrain. Enter this +1 in each column of the table, as shown in row 1 of Table A-2. 3. Consider the carrier fixed, give the stationary member (in this case the 90-tooth ring gear) a minus one turn. Determine the revolutions of each of the other gears about their own axis, as is done in a simple geartrain (row 2 in Table A-2). Note that this gives the speed ratio of each gear relative to the carrier. 4. Add algebraically the first and second rows to give the speed ratio of each gear and the carrier relative to the ground (row 3 in Table A-2). 27 5. The actual input speed 5 speed of the carrier is ¥ 117 2740 = 633 r/min. The speed of the 90T ring is zero because it is stationary (row 4 in Table A-2). 6. We are interested in the speed of the planet gear relative to the carrier because this gives the true planet gear bearing speed. From row 2 of Table A-2 we note the speed 90 of the 31-tooth planet relative to the carrier is – . 31 Since the actual speed of the carrier from row 4 is 633 r/min, then the actual speed of the 31-tooth planet rela90 tive to the carrier must be ¥ 633 or 1840 r/min (row 5 31 in Table A-2).

5.4.11 Appendix A Determining Planetary Bearing Speeds In a planetary or epicyclic train of gears, some of the members (sun, ring, carrier) turn on fixed axes, while others (planets) turn on axes which are themselves in motion. A means of determining the speed ratio or train value, the planet bearing speeds, and the speed and direction of rotation for each component part is known as the tabular method of solving planetary geartrains. This method assumes that the motion of the planets and the carrier take place successively instead of simultaneously. Also, while either direction may be assumed as positive (+), rotation in the opposite direction must be considered as negative (–).

Solution of the speeds of a compound planetary is illustrated in Appendix B.

To illustrate the tabular method of obtaining bearing speeds, consider the simple planetary set shown in Fig. A-1.

Occasionally a planetary train of gears may have none of its elements held stationary for a particular speed ratio. When this occurs, a speed table is constructed in the same manner as outlined previously for the planetary with the fixed member. However, because none of the members of this latter train is fixed, the rows in the table are first computed in terms of the unknowns x and y. The geartrain shown in Fig. A-1 can be used once again as an illustration. In this case, however, the input is to both the 90-tooth ring (at 1000 r/min) and the 27-tooth sun (at 2000 r/min) and the output through the carrier. To solve for speeds: 1. Construct a speed table similar to Table A-1. 2. Consider all elements of the train locked together. Rotate the entire mass x turns about the centerline of the geart-

Fig. A-1  Simple planetary set. 5-53

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Design Practices: Passenger Car Automatic Transmissions

3.

4. 5.

6.

Table A-3  Speed Table

rain. Enter this x in each column of the table, as shown in row 1 of Table A-3. Consider the carrier fixed, and rotate any one of the gears y turns. Determine the revolutions of each of the other gears about its own axis, just as if this were a simple geartrain (row 2 in Table A-3). Note that, as in the previous example, this gives the speed ratio of each gear relative to the carrier. Add algebraically the first and second rows (row 3, Table A-3). The actual input speed to the 90-tooth ring is +1000 r/min and the speed of the 27-tooth sun is +2000 r/min. Enter these speeds in row 4, Table A-3. Equate the algebraic speed of the 90-tooth ring and the 27-tooth sun to their known speeds: x + y = 1000 ⎛ 90 ⎞ x − ⎜⎝ ⎟⎠ y = 2000 27

90T Ring

27T Sun

27T Sun

Carrier

Row 1

+1

+1

+1

+1

Row 2

–1

−

Row 3

0

59 − 31

Row 4 Row 5

0

90 31

+

90 27

x

x

x

x

Row 2

y

⎛ 90 ⎞ ⎜⎝ ⎟⎠ y 31

⎛ 90 ⎞ −⎜ ⎟ y ⎝ 27 ⎠

0

Row 3

x+y

90 x + ⎛⎜ ⎞⎟ y

90 x − ⎛⎜ ⎞⎟ y

x

Row 4 Row 5

+1000

⎝ 31 ⎠ 670

⎝ 27 ⎠

+2000

1. Input Engine torque = 500 N-m at 1900 r/min. Critical torque converter output = 750 N-m   at 950 r/min. Transmission input = 750 N-m at 950 r/min. 2. Gear data—See Table B-1. 3. Planetary layout—See Fig. B-1.

Setting the helix hand of any one element fixes the helix hand of all the others. Therefore, the l9T long planet will be right hand while the 31T short planet will be left hand, or the l9T long planet will be left hand while the 31T short planet will be right hand. Also, the 19T long planet can lead or lag the 31T short planet. 4. Power flow Low gear—Input through 36T input sun, 27T reaction sun held stationary, output through carrier. Reverse gear—input through 36T input sun, 90T ring gear held stationary, output through carrier.

Table A-2  Speed Table 31T Planet

Row 1

Given:

Carrier

90T Ring

Carrier

5.4.12.1  Typical Planetary Bearing Calculations

Table A-1  Speed Table Layout 31T Planet

27T Sun

5.4.12 Appendix B

7. Solving simultaneously, we find that x = 1230 r/min and y = –230 r/min. 8. Substitute the value of y into the formula for the speed of the 31-tooth planet in row 2. The actual speed of the 31-tooth planet, relative to the carrier or the bearing 90 speed, becomes ¥ (–230) = 670 r/min (row 5 in Table 31 A-3).

90T Ring

31T Planet

Table B-1  Gear Data

0

117 + 27

+1

Gear

2740

633

Reaction Sun Ring Gear Short Planet Long Planet Input Sun

1840

Pitch Dia. Teeth (mm) 27 90 31 19 36

44.55 148.49 51.16 31.72 59.39

Normal Pressure Angle (°)

Helix Angle (°)

20 20 20 20 20

15.8 15.8 15.8 15.8 15.8

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Bearings Reverse Gear Bearing Speeds:

19T planet = 90/19 ¥ 633 = 3000 r/min 31T planet = 90/31 ¥ 633 = 1840 r/min Separating (S) =  F ¥ tan NPA/cos HA = 8417 ¥ tan 20°/cos 15.8° = 3184 N Thrust (T) =  F ¥ tan HA = 8418 ¥ tan 15.8° = 2382 N

Tables B-2 and B-3 show speeds for low and reverse gears, respectively.

19T LONG PLANET—Assume two paths of 23 rollers (1.984 ¥ 19) Distance between centers of roller paths = 43.2 mm Shaft diameter = 12.603 to 12.596 mm Gear bore = 16.579 to 16.591 mm Effective roller length (leff ) = 19 – 0.50 – 1 = 17.50 mm Basic load rating (C) per path = A · leff7/9D29/27 C = 676 ¥ 9.26 ¥ 2.09 = 13100 N

Table B-2  Speed Table Low Gear

Speed factors (SF) from Eq. 5.4.6:

Fig. B-1  Planetary layout. Solutions

36T Sun +1

+

27 31 19 · · 31 19 36

–

+1.75 +950

19T Planet

31T Planet

90T Ring

Carrier

+1

+1

+1

+1

–1

0

0 0

+1 +543

27 31 · 31 19

771

+

27 31

473

SF for 771 r/min = 2.57 SF for 3000 r/min = 3.86

31T SHORT PLANET—Assume two paths of 29 rollers (1.984 ¥ 12.7) Distance between centers of roller paths = 17.3 mm Shaft diameter = 16.383 to 16.375 mm Gear bore = 20.358 to 20.371 mm Effective roller length (leff ) = 12.7 – 0.50 – 1 = 11.2 mm Basic load rating (C) per path = A · leff7/9D29/27 C = 780 ¥ 6.55 ¥ 2.09 = 10700 N

Low Gear Bearing Speeds:

19T planet = 27/19 ¥ 543 = 771 r/min 31T planet = 27/31 ¥ 543 = 473 r/min

Speed factors (SF) from Eq. 5.4.6:

SF for 473 r/min = 2.22 SF for 1840 r/min = 3.34

Tooth Forces:

Tangential (F) =  input torque/(No. of planets ¥ PR36T) = 750 ¥ 103/(3 ¥ 29.70) = 8417 N

Table B-3 Speed Table—Reverse Gear

–

36T Sun

19T Planet

31T Planet

90T Ring

Carrier

+1

+1

+1

+1

+1

90 31

–1

0

0 0

+1 +633

90 31 19 · · 31 19 36

+

90 31 · 31 19

–

–1.50 –950 3000

1840

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Design Practices: Passenger Car Automatic Transmissions Loads in Low Gear

Fig. B-3  19T LONG PLANET—Position 2.

Fig. B-2  19T LONG PLANET—Position 1.

F = 8417 N   S = 3184 N   T = 2382 N

F = 8417 N   S = 3184 N   T = 2382 N

Transposing F and S forces into V-V¢ and H-H¢ planes:

Transposing F and S forces into V–V¢ and H–H¢ planes:

V=  8417 cos 33.5° + 3184 sin 33.5° = 7019 + 1757 = 8776 N H=  8417 sin 33.5° – 3184 cos 33.5° = 4645 – 2655 = 1990 N Moment arm for thrust (T) forces = 31.72 sin 33.5° = 17.5 mm

V = 8417 cos 33.5° – 3184 sin 33.5° = 7019 – 1757 = 5262 N H = 8417 sin 33.5° + 3184 cos 33.5° = 4645 + 2655 = 7300 N Moment arm for thrust (T) forces = 31.72 sin 33.5° = 17.5 mm

Load per bearing when right-hand helix is used:

Load per bearing when right-hand helix is used:

Horizontal = 1990 N  8776 × 33 2382 × 17.5 Vertical = + 43.2 43.2 = 6705 + 965 = 7670 (c left, T right) Resultant = 7910 N

Horizontal = 7300 N  17.4 5262 × 33 Vertical = − 2382 × 43.2 43.2 = 4020 – 965 = 3055 (T left, c right) Resultant = 7910 N

Load per bearing when left-hand helix is used:

Load per bearing when left-hand helix is used:

Horizontal = 1990 N  8776 × 33 2382 × 17.5 Vertical = − 43.2 43.2 = 6705 – 965 = 5740 (c left, T right) Resultant = 6075 N

Horizontal = 7300 N  17.5 5262 × 33 Vertical = + 2382 × 43.2 43.2

= 4020 + 965 = 4985 (T left, c right)

Resultant = 8340 N

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Bearings

Fig. B-4  31T SHORT PLANET—When 19T gear is in position 1.

Fig. B-5  31T SHORT PLANET—When 19T gear is in position 2.

F = 8417 N   S = 3184 N   T = 2382 N

F = 8417 N  S = 3184 N  T = 2382 N

Transposing F and S forces into V-V¢ and H-H¢ planes: V = 8417 cos 30° + 3184 sin 30° = 7290 + 1590 = 8880 N (cancel out) H = 8417 sin 30° – 3184 cos 30° = 4207 – 2757 = 1450 N Moment arm for thrust (T) forces = 51.16 sin 30° = 25.58 mm

Transposing F and S forces into V-V¢ and H-H¢ planes: V = 8417 cos 30° – 3184 sin 30° = 7290 – 1590 = 5700 N (cancel out) H = 8417 sin 30° + 3184 cos 30° = 4207 + 2757 = 6964 N Moment arm for thrust (T) forces = 51.16 sin 30° = 25.6 mm

Load per bearing when left-hand helix is used: Horizontal = 1450 N  2382 × 25.58 Vertical = 17.3 = 3520 N (c left, T right) Resultant = 3810 N

Load per bearing when left-hand helix is used: Horizontal = 6964 N  2382 × 25.6 Vertical = 17.3 = 3520 N (c left, T right) Resultant = 7800 N

Load per bearing when right-hand helix is used: Horizontal = 1450 N  2382 × 25.58 Vertical = 17.3 = 3520 N (T left, c right) Resultant = 3810 N

Load per bearing when right-hand helix is used: Horizontal = 6964 N  2382 × 25.6 Vertical = 17.3 = 3520 N (T left, c right) Resultant = 7800 N

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Design Practices: Passenger Car Automatic Transmissions Loads in Reverse Gear

19T LONG PLANET—Loads will be the same as in low gear

Fig. B-7  31T SHORT PLANET—When 19T gear is in position 2. F = 8417 N  S = 3184 N  T = 2382 N Transposing F and S forces into V-V¢ and H-H¢ planes:

Fig. B-6  31T SHORT PLANET—When 19T gear is in position 1.

V = 8417 cos 60° + 3184 sin 60° = 4208 + 2758 = 6966 N (cancel out) H = 8417 sin 60° – 3184 cos 60° = 7290 – 1590 = 5700 N Moment arm for thrust (T) forces = 51.16 sin 60° = 44.3 mm

F = 8417 N  S = 3184 N  T = 2382 N Transposing F and S forces into V-V¢ and H-H¢ planes: V = 8417 cos 60° – 3184 sin 60° = 4208 – 2758 = 1450 N (cancel out) H = 8417 sin 60° + 3184 cos 60° = 7290 + 1590 = 8880 N Moment arm for thrust (T) forces = 51.16 sin 60° = 44.3 mm

Load per bearing when left-hand helix is used: Horizontal = 5700 N  2382 × 44.3 Vertical = 17.3 = 6100 N (T left, c right) Resultant = 8320 N

Load per bearing when left-hand helix is used: Horizontal = 8880 N  2382 × 44.3 Vertical = 17.3 = 6100 N (c left, T right) Resultant = 10770 N

Load per bearing when right-hand helix is used: Horizontal = 5700 N U 2382 × 44.3 Vertical = 17.3 = 6100 N (c left, T right) Resultant = 8320 N

Load per bearing when right-hand helix is used: Horizontal = 8880 N  2382 × 44.3 Vertical = 17.3 = 6100 N (T left, c right) Resultant = 10770 N

Bearing Life Factor

Life factors for planet bearings are listed in the section on Calculation Summary.

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Bearings Shaft Slopes

Shaft slope through right bearing position (θRB): Due to P1(x > a) =

19T LONG PLANET—Formulas (Fig. B-8) x = distance from the left support to point where slope θ is to be found a = distance from left support to point of load application on shaft b = distance from point of load application on shaft to right support

=



= 4.1 P1 × 10–7



=

P1 × 10.9 × 54.1 × 43.2 3 × 65 × (207 × 103 ) × 1237



= 5.1 P1 × 10–7

Due to P2(x < a) =

Pb[a(L + b) – 3x 2] 6LEI



=

P2 × 10.9[54.1 × 75.9 – 3(10.9)2] 6 × 65 × (207 × 103 ) × 1237



= 4.1 P2 × 10–7

P1 × 10.9 × 54.1 × 43.2 3 × 65 × (207 × 103 ) × 1237



=



= 5.1 P1×10–7

Fig. B-9  Values for shaft slope calculation for 31T Short Planet.

Shaft slope through left bearing (θLB): Pab(b − a) 3LEI

Pab(a − b) 3LEI

31T SHORT PLANET—Formulas (Fig. B-9)

Shaft diameter = 12.6 mm L = a + b = 65 mm E = modulus of elasticity = 207 ¥ 103 MPa π I = moment of inertia of shaft = ¥ (12.6)4 64 4 = 1237 mm

Due to P1(x = a) =

P1 × 10.9[54.1 × 75.9 – 3(10.9)2] 6 × 65 × (207 × 103 ) × 1237



Due to P2(x = a) = Fig. B-8  Values for shaft slope calculation for 19T Long Planet.

Pa[b(L + a) – 3(L − x)2] 6LEI

x = distance from the left support to point where slope θ is to be found a = distance from left support to point of load application on shaft b = distance from point of load application on shaft to right support Shaft diameter = 16.38 mm: L = a + b = 65 mm E = modulus of elasticity = 207 ¥ 103 MPa π I = moment of inertia of shaft = ¥ (16.38)4 64 4 = 3534 mm

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Design Practices: Passenger Car Automatic Transmissions

Shaft slope through left bearing position (θLB): Due to P1 (x = a) =

Pab(b − a) 3LEI P1 × 7.9 × 57.1 × 49.2 3 × 65 × (207 × 103 ) × 3534



=



= 1.6 P1 × 10–7

Due to P2(x < a) =

19T LONG PLANET—Position 1—Low gear and reverse gear (Figs. B-10 and B-11)

Pb[a(L + b) − 3x 2] 6LEI

Fig. B-10  Values for shaft slope calculation for 19T Long Planet—Position 1—Low gear and reverse gear— right hand helix.

P2 × 39.9[25.1 × 104.9 − 3(7.9)2] 6 × 65 × (207 × 103 ) × 3534



=



= 3.4 P2 × 10–7

 (5.1 ¥ 3050 – 4.1 ¥ 3050) ¥ 10–7 θLB–V = = 0.00155 – 0.00124 = 0.00031 θLB–H =  (5.1 ¥ 7290 + 4.1 ¥ 7290) ¥ 10–7 = 0.00372 + 0.00299 = 0.00671

Shaft slope through right bearing position (θRB): Due to P1 (x > a) =

Pa[b(L + a) − 3(L − x)2] 6LEI P1 × 7.9[57.1 × 72.9 − 3(39.9) ] 6 × 65 × (207 × 103 ) × 3534



=



= –0.17 P1×10–7

Due to P2 (x = a) =

Resultant θLB = 0.00671:1

2

 (4.1 ¥ 3050 – 5.1 ¥ 3050) ¥ 10–7 θRB-V = = 0.00124 – 0.00155 = 0.00031 θRB-H =  (4.1 ¥ 7290 + 5.1 ¥ 7290) ¥ 10–7 = 0.00299 + 0.00372 = 0.00671

Pab(a − a) 3LEI

Resultant θRM = 0.00671:1

P2 × 25.1 × 39.9 × 14.8 3 × 65 × (207 × 103 ) × 3534



=



= 1.0 P2×10–7

Procedure in Calculating Shaft Slope Values

Forces on the shaft are shown in two planes: one in the plane of the paper (vertical plane) and the other perpendicular to the plane of the paper (horizontal plane). The intersection of these planes coincides with the shaft centerline.

Fig. B-11  Values for shaft slope calculation for 19T Long Planet—Position 1—Low gear and reverse gear— left hand helix.

The amount of shaft slope due to the set of vertical forces and the set of horizontal forces at each bearing position is found. Then the vertical shaft slope value and the horizontal shaft slope in each case are combined vectorially to give the resultant shaft slope at the respective bearing positions.

 (5.1 ¥ 4982 – 4.1 ¥ 4982) ¥ 10–7 θLB-V = = 0.00254 – 0.00204 = 0.0005 θLB-H =  (5.1 ¥ 7290 + 4.1 ¥ 7290) ¥ 10–7 = 0.00372 + 0.00299 = 0.00671 Resultant θLB = 0.00671:1

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θRB-V =  (4.1 ¥ 4982 – 5.1 ¥ 4982) ¥ 10–7 = 0.00204 – 0.00254 = 0.0005 θRB-H =  (4.1 ¥ 7290 + 5.1 ¥ 7290) ¥ 10–7 = 0.00299 + 0.00372 = 0.00671

θLB-V =  (5.1 ¥ 5738 – 4.1 ¥ 5738) ¥ 10–7 = 0.00293 – 0.00235 = 0.00057 θLB-H =  (5.1 ¥ 1988+ 4.1 ¥ 1988) ¥ 10–7 = 0.00101 + 0.00082 = 0.00183

Resultant θRB = 0.00671:1

Resultant θLB = 0.00192:1  (4.1 ¥ 5738 – 5.1 ¥ 5738) ¥ 10–7 θRB-V = = 0.00235 – 0.00293 = –0.00058 θRB-H =  (4.1 ¥ 1988 + 5.1 ¥ 1988) ¥ 10–7 = 0.00082 + 0.00101 = 0.00183

19T LONG PLANET—Position 2—Low gear and reverse gear (Figs. B-12 and B-13)

Resultant θRB = 0.00192:1 31T SHORT PLANET—19T gear in position 1—Low gear (Figs. B-14 and B-15) Shaft slope values for the respective bearings when the 31T short planet has a left-hand helix will be the same numerically as those when the gear has a right-hand helix.

Fig. B-12  Values for shaft slope calculation for 19T Long Planet—Position 2—Low gear and reverse gear— right hand helix.  (5.1 ¥ 7670 – 4.1 ¥ 7670) ¥ 10–7 θLB-V = = 0.00391 – 0.00314 = 0.00077 θLB-H =  (5.1 ¥ 1988 + 4.1 ¥ 1988) ¥ 10–7 = 0.00101 + 0.0082 = 0.00183

Fig. B-14  Values for shaft slope calculation for 31T Short Planet—19T gear in position 1—Low gear—left hand helix.

Resultant θLB = 0.00198:1  (4.1 ¥ 7670 – 5.1 ¥ 7670) ¥ 10–7 θRB-V = = 0.00314 – 0.00391 = 0.00077 θRB-H =  (4.11 ¥ 1988 + 5.1 ¥ 1988) ¥ 10–7 = 0.00082 + 0.00101 = 0.00183 Resultant θRB = 0.00198:1

Fig. B-15  Values for shaft slope calculation for 31T Short Planet—19T gear in position 1—Low gear— right hand helix.  (1.6 ¥ 3527 – 3.4 ¥ 3527) ¥ 10–7 θLB–V = = 0.00056 – 0.00120 = 0.00064 θLB–H =  (1.6 ¥ 1450 + 3.4 ¥ 1450) ¥ 10–7 = 0.00023 + 0.00049 = 0.00073

Fig. B-13  Values for shaft slope calculation for 19T Long Planet—Position 2—Low gear and reverse gear— left hand helix.

Resultant θLB = 0.00097:1

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 (0.17 ¥ 3527 – 1.0 ¥ 3527) ¥ 10–7 θRB–V = = 0.00006 – 0.00035 = 0.00029 θRB–H =  (0.17 ¥ 1450 + 1.0 ¥ 1450) ¥ 10–7 = 0.00002 + 0.00015 = 0.00017

31T SHORT PLANET—19T gear in position 1—Reverse gear (Figs. B-18 and B-19) Shaft slope values for the respective bearings when the 31T short planet has a left-hand helix will be the same numerically as those when the gear has a right-hand helix.

Resultant θRB = 0.00034:1 31T SHORT PLANET—19T gear in position 2—Low gear (Figs. B-16 and B-17) Shaft slope values for the respective bearings when the 31T short planet has a left-hand helix will be the same numerically as those when the gear has a right-hand helix.

Fig. B-18  Values for shaft slope calculation for 31T Short Planet—19T gear in position 1—Reverse gear—left hand helix.

Fig. B-16  Values for shaft slope calculation for 31T Short Planet—19T gear in position 2—Low gear—left hand helix. Fig. B-19  Values for shaft slope calculation for 31T Short Planet—19T gear in position 1—Reverse gear— right hand helix.  (1.6 ¥ 6095 – 3.4 ¥ 6095) ¥ 10–7 θLB–V = = 0.00098 – 0.00207 = –0.00109 θLB–H =  (1.6 ¥ 8875 + 3.4 ¥ 8875) ¥ 10–7 = 0.00142 + 0.00302 = 0.00444

Fig. B-17  Values for shaft slope calculation for 31T Short Planet—19T gear in position 2—Low gear—right hand helix. θLB–V =  (1.6 ¥ 3527 – 3.4 ¥ 3527) ¥ 10–7 = 0.00056 – 0.00120 = 0.00064 θLB–H =  (1.6 ¥ 6957 + 3.4 ¥ 6957) ¥ 10–7 = 0.00111 + 0.00237 = 0.00348

Resultant θLB = 0.00457:1  (0.17 ¥ 6095 – 1.0 ¥ 6095) ¥ 10–7 θRB–V = = 0.00010 – 0.00061 = –0.00051 θRB–H =  (0.17 ¥ 8875 + 1.0 ¥ 8875) ¥ 10–7 = 0.00015 + 0.00089 = 0.00104

Resultant θLB = 0.00349:1

Resultant θRB = 0.00116:1

 (0.17 ¥ 3527 – 1.0 ¥ 3527) ¥ 10–7 θRB–V = = 0.00006 – 0.00035 = 0.00029 θRB–H =  (0.17 ¥ 6957 + 1.0 ¥ 6957) ¥ 10–7 = 0.00012 + 0.00070 = 0.00082 Resultant θRB = 0.00087:1

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θLB–V =  (1.6 ¥ 6095 – 3.4 ¥ 6095) ¥ 10–7 = 0.00098 – 0.00207 = –0.00109 θLB–H =  (1.6 ¥ 5690 + 3.4 ¥ 5690) ¥ 10–7 = 0.00091 + 0.00193 = 0.00285

31T SHORT PLANET—19T gear in position 2—Reverse gear (Figs. B-20 and B-21) Shaft slope values for the respective bearings when the 31T short planet has a left-hand helix will be the same numerically as those when the gear has a right-hand helix.

Resultant θLB = 0.00305:1  (0.17 ¥ 6095 – 1.0 ¥ 6095) ¥ 10–7 θRB–V = = 0.00010 – 0.00061 = –0.00051 θRB–H =  (0.17 ¥ 5690 + 1.0 ¥ 5690) ¥ 10–7 = 0.00010 + 0.00057 = 0.00067 Resultant θRB = 0.00084:1

Fig. B-20  Values for shaft slope calculation for 31T Short Planet—19T gear in position 2—Reverse gear—left hand helix.

5.4.12.2  Calculation Summary 19T LONG PLANET—Bearing: Two paths of 23 rollers (1.983 mm diameter by 19 mm long). Loads, speeds, capacities, factors, and slopes for each bearing are similar. Figures listed in Table B-4 are for each bearing in the planet. 31T SHORT PLANET—Bearing: Two paths of 29 rollers (1.983 mm diameter by 12.7 mm long). Loads, speeds, capacities, and factors for each bearing are similar while slope values differ.

Fig. B-21  Values for shaft slope calculation for 31T Short Planet—19T gear in position 2—Reverse gear—right hand helix.

Figures listed in Table B-5 (irrespective of slopes) are for each bearing in the planet, while the slope listed is the higher value of the two that are present in each planet (θLB).

Table B-4  Long Planet Specifications 19 T Location Position 1

Helix

Gear

r/min

Speed Factor

Capacity, N

Load, N

Life Factor

Slope

RH

Low Rev Low Rev Low Rev Low Rev

  771 3000   771 3000   771 3000   771 3000

2.57 3.86 2.57 3.86 2.57 3.86 2.57 3.86

13100 13100 13100 13100 13100 13100 13100 13100

7910 7910 8340 8340 7910 7910 6075 6075

0.64 0.43 0.61 0.41 0.64 0.43 0.84 0.56

0.00671:1 0.00671:1 0.00671:1 0.00671:1 0.00198:1 0.00198:1 0.00192:1 0.00192:1

LH Position 2

RH LH

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Table B-5 Short Planet Specifications 19 T Location Position 1

Helix

Gear

r/min

Speed Factor

Capacity, N

Load, N

Life Factor

Slope

LH

Low Rev Low Rev Low Rev Low Rev

  473 1840   473 1840   473 1840   473 1840

2.22 3.34 2.22 3.34 2.22 3.34 2.22 3.34

10700 10700 10700 10700 10700 10700 10700 10700

  3810 10770   3810 10770   7800   8320   7800   8320

1.26 0.30 1.26 0.30 0.62 0.39 0.62 0.39

0.00097:1 0.00457:1 0.00097:1 0.00457:1 0.00349:1 0.00305:1 0.00349:1 0.00305:1

RH Position 2

LH RH

5.4.13 Conclusions

Since a left-hand helix is preferable for the 19T long planet, we should use a right-hand helix for its mating 31T short planet as the most ideal arrangement from a bearing standpoint.

19T LONG PLANET—Use two paths of 23 rollers—1.983 mm diameter by 19 mm long. The factors in all cases are satisfactory. Refer to Fig. B-22 for 19T long planet positions discussed below. The shaft slope values for position 1 are excessive in both low and reverse gear, irrespective of what helix hand might be used in the planet. Therefore, position 2 only should be considered. With position 2, use of a left-hand helix is preferable since this arrangement results in higher bearing life factors (in particular, the life factor for the more frequently used low gear ratio) and somewhat lower shaft slope values. 31T SHORT PLANET—Use two paths of 29 rollers—01.983 mm diameter by 12.7 mm long. Because of the high slope values of position 1 for the 19T long planet, we will consider position 2 only.

Fig. B-22  Planetary layout showing preferred position #2 for 19T long planet.

The factors and slopes are similar, irrespective of the helix hand that might be used and are satisfactory in each case.

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5.4.14 Appendix C

increasing oil flow through the bearing and reducing contaminants. Bearing Lock-Up—can be caused by improperly installing a full-complement or caged drawn-cup bearing. If an improper assembly tool is used, the cup flanges can be deformed, removing the axial free play in the assembly. With full-complement bearings, the rollers can skew and lock in the cup if a means of separating them and aligning the rollers in the bearing is not employed during installation. Adding a ball detent to the assembly tool is a suitable method to avoid this problem. Lube starvation at application start-up can also result in lock-up of the bearing assembly. Precautions should be made to provide pressurized lubricant to all bearing positions to avoid this failure mode. Brinelling—results from a static overload or sudden shock. The rollers are forced into the raceways and exceed the yield strength of the material. This leaves denting of the raceway and can possibly fracture the race. False Brinelling—can occur when a bearing experiences vibration or cyclic load without rotation. As the rollers in the bearing oscillate slightly from side to side, they will squeeze lubricant out from between the rollers and raceways and cause steel-on-steel wear, which eliminates the original raceway surface. The rate at which false brinelling will occur is heavily dependent on the amount of loading, the duration that the bearing experiences that loading, and the lubrication conditions. Bearing Flange Fracture—can be caused by improperly installing a full-complement or caged drawn-cup bearing. If an improper assembly tool is used, the cup flanges can be deformed, resulting in deformation and fracture of the case-hardened cup lip or flange. Always use a proper assembly tool.

5.4.14.1 Failure Modes—Examples by Bearing Type or Application 5.4.14.1.1 Planetary

Roller “penciling” wear—can result from high-speed operation with little or no gear tooth loading. Because the rollers are not loaded sufficiently, they can skew and skid along the raceways and wear. Sometimes increased lubricant flow can reduce the occurrence of this problem, but the operating condition should be avoided or minimized. 5.4.14.1.2 Radial

Cup Rollout—can result from dynamic overload conditions in an application. These conditions can simply be an applied application overload, or overload due to shaft misalignment conditions that edge-load the rolling elements. In either case, yielding of the drawn-cup core results in insufficient support for the hardened case structure, resulting in a thinning of the cup wall and surface fractures of the cup. Loss of press fit in the housing generally results. Drawn-Cup Bearing Walking—results from an inadequate press fit of the bearing cup into the application housing. This can be caused by not following manufacturers’ recommendations or by improperly sizing a low-tensile-strength (nonferrous) housing and operating throughout an extreme temperature range. Poor housing geometry, such as taper, roundness, and surface finish can also influence this condition. A bearing that walks in its housing is likely to move axially into counter-rotating components or will run unsupported by a portion of the housing or shaft. Shaft, Needle, and Cup Raceway Fatigue Spalling—is characterized by a coarse grain appearance in the failed areas on the raceways. This condition results from the raceway meeting its rolling fatigue limit. The failure is a subsurface fatigue of the raceway material. The cause can simply be operation beyond the predicted life and/or dynamic overload. Shaft, Needle, and Cup Raceway Surface Flaking/ Spalling—is characterized by a fine grain appearance in the failed areas on the raceways. This condition results from the raceway being influenced by inadequate lubricant film or contamination. The failure is a mico-welding of asperities on the surface of the raceway material. The cause can be addressed by

5.4.14.1.3 Thrust

Cage Fatigue—is another failure mode related to speed in thrust bearings. When bearing piloting loads due to friction (pressure ¥ velocity, or PV) become significant and rollers drive the cage bars with more force than normal, significant stress/strain can occur in the cage. Cracks may develop (usually beginning at the pocket corner, which is a stress concentration) and lead to breakage of the cage. Heat generation related to piloting and cage fatigue problems can both be improved by increasing the area in piloting contact (to reduce the contact pressure).

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5.5 Design and Selection Factors for Automatic Transaxle Tapered Roller Bearings

bearings must enhance the design of the transaxle by offering good rigidity for improved gear mesh. Selection and testing of tapered roller bearings include the effects of the following environmental conditions:

B. Martin Chrysler Corporation

• • • • •

H.E. Hill The Timken Company Automatic transaxle components are subjected to a very demanding environment, presenting a challenge when designing for good performance and efficiency. Designers must pay very close attention to the details of the automatic transaxle design during development and testing to meet maximum power requirements and to provide a design with desirable power/weight ratios. Refinements to the design are made based on the results of very extensive dynamometer durability and vehicle durability testing of the transaxles.

Demanding variable load and speed conditions Lightweight aluminum housings Large range of operating temperatures Automatic transmission fluid Thermal expansion effects between aluminum housing and steel shaft, gears, and bearings

This paper covers these environmental parameters and their effects on the selection and design of tapered roller bearings for Chrysler automatic transaxle models 31TH and 41TE, as shown in Figs. 5.5.1 and 5.5.2, respectively. These transaxles incorporate tapered roller bearings at six positions on the output, transfer, and differential shafts.

Tapered roller bearings must perform with good reliability, durability, and efficiency in a small amount of space. The

Fig. 5.5.1  Model 31TH three-speed automatic transaxle. 5-66

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Fig. 5.5.2  Model 41TE four-speed electronic shift automatic transaxle.

5.5.1 Nomenclature 2b d Dc dco dcu dh Ds dsi dso f fi fo

Fi

Contact width formed by two moving surfaces and in the direction of motion, mm Cup outside diameter, mm Distance between housing shoulders, mm Cone mean outside diameter, mm Cup mean inside diameter, mm Housing outside diameter, mm Distance between shaft shoulders, mm Shaft inside diameter, mm Shaft outside diameter, mm Lubricant flow rate, L/min Coefficient of friction between cone and shaft Coefficient of friction between cup and housing

F1i Fo F1o Fa Fr h k5 L

Required push-up or push-off force of cone, through the cone, N Required push-up or push-off force of cone, through the cup, N Required push-up or push-off force of cup, through the cup, N Required push-up or push-off force of cup, through the cone, N Total thrust (axial) force on bearing, N Bearing radial load, N Central or plateau lubricant film thickness, mm Dimensional factor to calculate heat carried away by petroleum oil, 28 for metric units Cutoff length used in making the roughness measurements Ra1 and Ra2, mm

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5.5.2 Critical Point Loading

Li

Bearing catalog rated L10 life calculated with torque (Ti) and speed (Si) for condition (i), hr LDR Life depletion rate L10 Bearing life associated with 90 % reliability, hr Lwtd Weighted bearing catalog rated L10 life for a cycle, hr Pi Contact pressure between tight fitted cone and shaft, MPa Po Contact pressure between tight fitted cup and housing, MPa Qoil Heat dissipation rate of circulation oil, watts T1 Transaxle input torque for condition 1, N∙m Tmax Transaxle maximum input torque for each speed, N∙m Tn Transaxle input torque in condition n, N∙m Twtd Transaxle weighted average input torque for conditions T1 through Tn, N∙m t1 % time/100 for T1, of all torques at same speed as T1 ti % time for condition i tn % time/100 for Tn, of all torques at same speed as Tn Wi Cone width, mm Wo Cup width, mm α ½ included cup angle, degrees αal Coefficient of thermal expansion of aluminum housing αst Coefficient of thermal expansion of steel shaft β ½ included cone angle, degrees ΔT Difference in setup versus operating temperature, °C Δi Interference fit of cone bore on shaft, mm Δo Interference fit of cup O.D. in housing, mm λm Modified lambda ratio ∑ΔB Summation of bearing width changes, mm υ ½ included roller angle, degrees σa Composite surface roughness using Ra1 + Ra2, mm θ Gear misalignment, radians θi Oil inlet temperature, °C θo Oil outlet temperature, °C ΔScone Axial deflection of cone due to contraction of bore, mm ΔScup Axial deflection of cup due to expansion of O.D., mm ΔS ΔScone + ΔScup, mm

A convenient starting point in matching bearing requirements to a specific powertrain is the critical point loading method. Used by Hull [1] extensively in planetary gear needle bearing design, this method has been extended to tapered roller bearings in automatic transaxles. Applied in combination with a mathematical analysis of the radial and thrust load requirements of a new transaxle design, critical point load calculations may be related quickly to bearing life from actual dynamometer and vehicle results in previous systems. From many years of engine dynamometer experience, it was determined that a critical point calculation of 60 hours of life yielded excellent field experience for planetary needles. This life figure has served successfully as a departure for screening of tapered roller bearings. Figure 5.5.3 is a graph of the torque converter output or transaxle input, torque, and speed conditions for one automatic transaxle. The lower curve is the converter output torque to the transaxle versus output rpm of the torque converter turbine into the transaxle. The upper curve is a plot of the converter output rpm times (torque)10/3 versus converter output rpm. At the first peak of the upper curve, the life of the transaxle bearings is at a minimum. It is the combination of torque and speed at this peak (466 N∙m @ 1037 rpm), called the critical point, that is used as a basis for calculations and bearing selections. Table 5.5.1 shows the type of correlation achieved in testing. The initial bearing selections were analyzed for the critical point loading conditions, using a sophisticated computer program to show correlation with actual test data. It will be observed that one bearing, the rear transfer shaft bearing, appears greatly overdesigned in this estimate, but envelope constraints of the transaxle design dictated the bearing size.

Fig. 5.5.3  Transaxle critical operating point for bearing life estimate. Illustrated is an engine shifting above 6000 rpm.

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Fig. 5.5.4  Model 41TE electronic automatic transaxle—2.5-L TC (285 N∙m)—transfer shaft torque—engine rpm—seconds matrix 12,000 dynamometer cycles (WOT—1, 2, 3, 4, coast).

5.5.3 Load and Speed Histograms

As mentioned in Hull’s paper, the critical point method should only be considered as a starting point because deflection, lubrication, and many other factors influence bearing life. Selection and design of bearings based only on the worst condition are not properly defined without considering the effects of the overall loading cycle. To properly evaluate variable gear loading and shaft speed effects on the fatigue life of the bearings, a load-speed histogram of all conditions in the loading cycle should be used in the analysis.

Load/speed/time or torque/speed/time histograms will often contain a hundred or more conditions. A torque/speed/time matrix representing digitized histogram data from wide open throttle (WOT) dynamometer testing of Chrysler automatic transaxle model 41TE is illustrated in Fig. 5.5.4. Each value represents the time (sec) for each condition of engine speed (rpm) and transfer shaft torque (N∙m). There are over 90 different torque/speed/time conditions in this particular dynamometer test cycle. The time and effort required to conduct a bearing life analysis would be minimized if the number of histogram conditions were reduced. Of course, this must be accomplished without affecting the accuracy of the analysis.

Table 5.5.1  Calculated Bearing Life at Critical Point of Loading Life Based on Timken Equivalent Radial Load Method

Location Output Shaft   Front   Rear Transfer Shaft   Front   Rear Differential   Left   Right

Bearing Selection (Series)

Calculated Life (hrs)

Bearing Performance

L69300 LM300800

131 243

A-L A-L

13600 LM501300

45 2289

A A

L69300 L69300

137 47

A life depletion rate (LDR) method, as discussed by Bhatia and Springer [2], will reduce the number of conditions in the histogram that need to be analyzed. The life depletion rate is a method of reducing the number of conditions by selecting only the conditions in the cycle that have the most affect on bearing life, but still give a high level of accuracy in the bearing life analysis. The LDR formula is shown here:

A-F, D A-F

LDR = Lwtd ¥

ti Li

(5.5.1)

Selecting the highest values of LDR to reduce the number of conditions results in only 27 conditions, as shown in Fig. 5.5.5. The time for each condition has been converted to percent time. Further consolidation of the cycle, maintaining the same high level of accuracy, by combining similar conditions of speed, reduces the number of conditions to ten,

A—Acceptable in all vehicle endurance and dynamometer endurance D—High relative deflection generally makes the left bearing show heavier use even though the right bearing calculates a much lower life F—Occasional fit related failures of cone spinning on undersize hubs L—Occasional lube related failures-subsequently fixed

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as shown in Fig. 5.5.6. This consolidation uses the following equation to determine weighted average torque for similar speed conditions: 10/3 ⎡ ⎛ T ⎞10/3 ⎛ T ⎞ ⎤ Twtd = Tmax ⎢⎢ t1 ⎜⎜ 1 ⎟⎟⎟ +… tn ⎜⎜ n ⎟⎟⎟ ⎥⎥ ⎜ ⎜⎝ Tmax ⎠ ⎥⎦ ⎢⎣ ⎝ Tmax ⎠



10/3

(5.5.2)

Fig. 5.5.6  Consolidated transfer shaft torque – speed – % time cycle using equation 5.5.2.

5.5.4 Transaxle Housing and Shaft Design In a bearing life analysis of an automatic transaxle, the material properties, stiffness values, and cross-sectional design of both the shaft and housing play an important role in how the bearings perform and, in turn, influence the performance of the transaxle. Under axial loading, the bearing outer race, or cup, will expand radially into the housing cup seat. Resistance to bearing radial expansion is dependent on the housing material modulus of elasticity, housing cross-sectional design, cup fit, and bearing outer race design. Radial expansion of a tapered roller bearing cup causes an axial movement, ΔScup, as illustrated in Fig. 5.5.7. Excessive expansion of the cup could necessitate redesign of the housing section supporting the bearing.

Fig. 5.5.5  Transfer shaft torque – speed – % time cycle calculated from dynamometer WOT matrix using life depletion rate analysis, using equation 5.5.1. The cycle in Fig. 5.5.6 uses only about 15.5% of the loading conditions from the histogram, but will account for almost 94% of the total effect on bearing life. This greatly simplifies bearing life analysis without greatly sacrificing the accuracy of the results.

Fig. 5.5.7  Cone contraction and cup expansion due to applied thrust load Fa. Housing and shaft deflections not shown.

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The bearing inner race, or cone, will similarly contract under load depending on the shaft material, shaft cross-sectional design, cone fit, and cone design. The amount of contraction will be more if the cone is mounted on a hollow shaft similar to the automatic transaxle differential carrier. Radial contraction of the cone results in an axial movement, ΔScone, shown in Fig. 5.5.7.

Tight cone fits are suggested for all rotating shaft applications. Experience has shown that the fit should be tighter when the bearing is mounted in a differential, due to the hollow section of the carrier under the cones. For the same dimensional fit, contact pressure between the cone and a hollow shaft is lower than it would be for a solid shaft, as illustrated in Fig. 5.5.9 for bearing JL69348/310 used in model 41TE transaxle. The tight fit of the cone on the hollow shaft should be increased to improve the holding power or resistance of the cone to rotate relative to the shaft. Refer to Appendix 1 for calculation of the contact pressure of the cone when mounted on hollow and solid shafts.

Figure 5.5.8 shows the calculated change in bearing setting due to expansion of the cup in the housing and contraction of the cone on the differential carrier as an axial load is applied. Bearing life is a function of operating setting, as will be demonstrated later in the paper.

Fig. 5.5.9  Comparison of contact pressure between cone bore and shaft for solid and hollow shafts for tight fits.

Fig. 5.5.8  Change in bearing setting due to contraction of the cone and expansion of the cup under loading.

Fig. 5.5.10  Housing stiffnesses required for a total bearing systems analysis.

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The bearing cup should also be mounted tight in the aluminum housing, if possible, to prevent it from creeping. The amount of tight fit depends on the size of the cup, housing cross-section, and thermal effects. Thermal effects are discussed later in the paper. Appendix 1 provides the equation to calculate the contact pressure, or holding pressure, between the cup O.D. and housing I.D. due to a tight fit. Appendix 2 provides equations for the required forces to install and remove cones and cups when mounted tight on the shaft and in the housing, respectively. Fig. 5.5.11  Setup for housing spring rate test of Model 31TH automatic transaxle.

5.5.5 Housing Rigidity Effects The stiffness of the transaxle housing can significantly influence bearing life and gear performance. There are three different housing stiffnesses considered in a total bearing systems analysis: axial, radial, and tilting, as illustrated in Fig. 5.5.10. Values of stiffness used in a bearing analysis should be determined through testing of the transaxle housing, if possible, to provide accurate predictions of bearing life. Measurements of housing axial spring rates have been made for one of the transaxles, but radial and tilting stiffnesses were not tested. Actual values for axial stiffness for model 31TH automatic transaxle were determined through testing in the bearing supplier’s application testing laboratory. Figure 5.5.11 illustrates the test setup used to determine characteristics of the final drive portion of the transaxle. A hydraulic cylinder was placed between the bearings in place of the differential carrier. Load was applied in 2200-N increments to 13 300 N while measuring axial deflection of the housing walls. A graph of these test results is shown in Fig. 5.5.12. The deflection curve is linear and shows a total housing axial stiffness of 40 415 N/mm.

Fig. 5.5.12  Housing axial stiffness test results for Model 31TH automatic transaxle.

Housing axial stiffness is a measure of the housing’s resistance to axial deflection under thrust loading conditions. Shaft and bearing axial deflections also cause a change in the bearing system initial setting, which could affect bearing life. Figure 5.5.13 illustrates a typical two-tapered roller bearing mounting arrangement. One bearing is considered the seated bearing and the other the set-up bearing. Generally, the seated bearing carries external gear thrust plus thrust induced by the radial loading of the set-up bearing. The set-up bearing usually only carries the thrust induced by its own radial loading.

Fig. 5.5.13  Typical mounting arrangement of tapered roller bearings. Bearing setting can be discussed in terms of the load zone in both bearings for the operating condition, as illustrated in Fig. 5.5.14. The seated bearing will more than likely have a load zone similar to that shown as preload in diagrams (c) and (d). The set-up bearing would have an operating load zone depending on, among other parameters, housing axial stiffness. Increased load zones using a stiffer housing can improve bearing life by distributing the applied load on more of the rollers. 5-72

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Bearings

Figure 5.5.15 provides calculated bearing relative life versus setting curves for different values of housing axial stiffness for differential bearings JL69349CP/310P for automatic transaxle model 31TH. It can be seen that the stiffer housing provides better system life for the dimensional setting range considered. Life versus setting values were calculated for dynamometer test conditions.

Recorded deflection measurements at various locations around the circumference of the differential cup backface and cone frontface, as shown in Fig. 5.5.17, were used to predict bearing relative misalignment. The Timken Company’s Select-A-NalysisSM computer program used these misalignment values in the bearing design and life evaluations. To illustrate the importance of using accurate values of housing radial and tilting stiffnesses in predicting bearing relative misalignment in the analysis, refer to Fig. 5.5.18. This graph provides curves of calculated bearing life versus housing radial and tilting stiffnesses. Housing axial stiffness was assumed constant at the measured value of 40 415 N/ mm. It is shown that the stiffer housing in this case provides improved system life.

Fig. 5.5.14  Examples of typical load zones of tapered roller bearings.

Fig. 5.5.16  Tapered roller bearing misalignment.

Fig. 5.5.15  Calculated differential bearing life versus bearing setting for Model 31TH automatic transaxle for different values of housing axial stiffness. The major effect of housing radial and tilting stiffnesses on bearing life is misalignment through the bearing. See Fig. 5.5.16 for illustration of exaggerated bearing misalignment. Bearing relative misalignment can result in stress concentrations at the edge of contact between the roller and raceway, causing a reduction in bearing life. Housing radial and tilting stiffnesses were not directly determined through measurements. However, bearing relative misalignments have been predicted from measurements taken during deflection testing of the differential housing for transaxle model 31TH. Housing deflection testing was conducted for various dynamometer WOT conditions.

Fig. 5.5.17  Measurements recorded during transaxle deflection testing to determine differential bearing misalignment.

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Fig. 5.5.18  Calculated differential bearing life versus setting for Model 31TH automatic transaxle for different values of housing radial and tilting stiffness.

Fig. 5.5.20  Calculated effects of housing stiffness and bearing setting on differential gear misalignment for Model 31TH automatic transaxle.

Misalignment of the gear, as shown in Fig. 5.5.19, will influence transaxle performance and is a function of total housing rigidity and bearing setting. Rigidity and setting effects are illustrated in Fig. 5.5.20 for transaxle model 31TH by analyzing the misalignment angle, θ, of the differential gear for various radial and tilting stiffness values. A constant axial stiffness of 40 415 N/mm was used. It is shown by the graph that a stiffer housing would improve gear mesh by minimizing misalignment of the gear under loading. Misalignment of the gear centerline is provided in radians for the worst condition in the loading cycle.

5.5.6 Lubrication Chrysler automatic transaxles use an automatic transmission fluid having a viscosity of 43 cSt @ 40°C and 7.2 cSt @ 100°C. This lightweight lubricant provides good transaxle efficiency but challenges the bearings to provide good performance under very demanding operating environmental conditions. Special attention to the effects of lubrication on bearing performance was required by the transaxle builder. Bearing fatigue life, as affected by lubrication, depends on oil viscosity, operating temperature, speed, load, and bearing design, and is discussed by Moyer [3] as a function of the modified lambda ratio (λm). Life is proportional to the modified lambda ratio, as shown in the following equation:

Axial deflection at the gear mesh can be calculated by multiplying the angular misalignment in radians times the gear pitch radius.

1/2



lm =

h ⎛⎜ 2b ⎞⎟ ⎟ sa ⎜⎜⎝ L ⎟⎠

(5.5.3)

The elastohydrodynamic oil film thickness (h), as shown in Fig. 5.5.21, is dependent on speed, load, and oil viscosity at operating temperature. The composite surface roughness (σa) is the arithmetic average of the bearing rollers and raceway in contact. The contact width (2b) between the roller and raceway is a function of load and bearing geometry. Moyer’s paper contains a table relating ranges of λm to bearing contact fatigue modes, and the influence of surface roughness, material, and geometry on improved performance. For λm values less than 0.3, surface roughness improvement will be most beneficial.

Fig. 5.5.19  Misalignment of differential gear due to loading.

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3. Downsizing an application for better reliability and durability in a smaller package Using cleaner steels and providing enhancements to the internal design of tapered roller bearings, such as The Timken Company’s P900TM bearings, will meet the above requirements. These bearings provide enhancements to the internal design through special profiling of the raceways and rollers, as discussed by Hoeprich [4], and super finishing of the contacting surfaces of the cone, cup, and rollers. A numerical procedure as a function of a load cycle, as presented by Hoeprich, is a state of the art technique for designing the contact geometry of P900 tapered roller bearings to maximize fatigue life. A typical cone raceway profile using this technique is illustrated in Fig. 5.5.22. The enhanced profile is designed to provide a more favorable distribution of stress along the contact between the rollers and raceways and to reduce high stresses caused by high loading and misalignment.

Fig. 5.5.21  Tribology model of line contact of tapered roller bearing. For λm of 1.0 to 0.3, material and surface roughness are both important. Reducing composite surface roughness to be within this range may show the most dramatic performance improvement, since increases into this range may also provide a change in damage mode, especially if a cleaner steel is used. For λm above 1.0, material influence is expected and surface roughness only has influence if asperities have immoderate sharpness. Geometry influence can occur at any λm and is related to those conditions in which improved profile across a contact leads to more uniform line contact stress. In the analysis of performance for differential bearings used in the Model 31TH automatic transaxle, the lambda ratios were evaluated for the ten conditions representing the dynamometer cycle. Refer to the next section on bearing internal design for comparisons of λm and life for bearing JL69349H/310 versus the same series bearing with enhanced surface finishes for an upgraded transaxle design.

Fig. 5.5.22  Typical cone raceway profile using numerical procedure. Automatic transaxle model 31TH has been upgraded for a 2.5-L (285 N.m torque) turbocharged engine. Minimum overall design changes to the transaxle were desired for the upgraded model, including using existing tapered roller bearings, if possible. Bearing JL69349H/310 was used at both positions on the differential. A loading cycle, similar to the one shown earlier in Fig. 5.5.6, was the basis for evaluating the differential bearings. Figure 5.5.23 illustrates calculated stress distribution across the raceways for this bearing under a heavily loaded condition of the loading cycle. The center stress of the cone raceway exceeds 4.8 GPa and uses only a small portion of the available contact length. Although the raceway of cone JL69349H is profiled based on past design practices, it is evident from the graph of stress distribution

5.5.7 Bearing Internal Design Today’s vehicles demand transaxle bearings that will meet the following requirements: 1. Increased allowable power to the transaxle using existing bearings 2. Increased bearing reliability and durability of an existing design for the same power conditions

TM

Trade mark of the Timken Company

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that an enhanced profile based on the numerical procedure should be considered for improved performance.

which show life improvements for the P900 bearing of 140% over the standard bearing for the assumed loading cycle. (See Fig. 5.5.25.)

This bearing was redesigned with profile enhancements based on the numerical approach. For comparison to Fig. 5.5.23, stress distribution for the P900 bearing (JL69349CP/310P) was generated, as shown in Fig. 5.5.24. This shows a more uniform distribution across the raceways using more of the available contact length, and maximum contact stress has been reduced under 3.5 GPa.

Fig. 5.5.25  Calculated life comparisons between standard and P900 differential tapered rolling bearings for Model 31TH automatic transaxle.

Fig. 5.5.23  Raceway contact stresses for bearing JL69349H/310.

5.5.8 Dynamometer Durability Testing Engine dynamometer testing serves both as a screening test for transaxle bearings and as a tool to verify ongoing production quality. Chrysler transaxles are subjected to wideopen-throttle testing that simulates vehicle operation from a standing start to near 160 km/h. Each bearing must pass through critical load points in addition to the high-speed operation in lower load phases of the test. The critical point loading typically occurs around 1000 rpm and 340 N.m at the transaxle input shaft for front-wheeldrive powertrains.

Fig. 5.5.24  Raceway contact stresses for bearing JL69349CP/310P.

Tapered roller bearing selections and designs are proven through many hours of accelerated testing of many transaxles. Testing is the ultimate measure of the sophisticated computer tools used by the bearing supplier to select and design the bearings. For upgraded transaxles with increased power, testing has been conducted to evaluate the performance benefits of using enhanced quality (P900) versus standard quality tapered roller bearings. Test results for the performance of the differential bearings for the upgraded Model 31TH transaxle are shown in the following tables.

Superfinishing of the rollers and raceways of P900 bearings will improve bearing performance through the reduction of the modified lambda ratio (λm) value, as provided by Eq. (3). Due to relatively slow speeds, high operating temperatures, and low oil viscosities for the transaxle differential bearings, super finishing of the cone and cup raceways and rollers was determined to be beneficial for the upgraded transaxle. Bearing JL69349H/310 (standard product) calculated to have a range of λm values of 0.05 to 0.53 for the dynamometer cycle conditions. Improvements to the surface finishes of P900 bearing JL69349CP/310P results in increased λm values in the range of 0.10 to 1.06.

In the initial design stages of the upgraded transaxle, differential bearings JL69349H/310 were evaluated for performance in dynamometer endurance testing. Table 5.5.2 provides the results of these tests. The life bogey for the transaxle at the

Using the Select-A-NalysisSM program that takes into account the total environment, theoretical calculations were made

SM

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time of testing was 12,000 cycles at WOT conditions. Three transaxle tests were conducted using the standard bearings with one early failure, one failure exhibited at the completion of the test, and one bearing passing the test. This trend of bearing performance indicated that bearing JL69349H/310 would not provide adequate performance in the upgraded transaxle. To provide the power density requirement for the upgraded transaxle, P900 bearings would be required.

between the rollers and raceways. Thus, it was shown in the testing that a larger standard bearing does not always provide the best results. A smaller tapered roller bearing with proper internal design could offer good performance and provide downsizing of the overall transaxle design. During early design stages of the bearing internal geometry, visual examination of the bearing internal contact patterns between the rollers and raceways after partially conducted dynamometer testing is important. This will give the designer good indication of whether the theoretical profiling is actually suited to the high loading and misalignment for the operating cycle and environmental conditions.

The results for ten different transaxle dynamometer tests are shown in Table 5.5.3 for differential bearings JL69349CP/310P (P900). All ten tests show good performance without any failures. Some of the tests were completed, while some were suspended due to component failures other than the bearings.

Dynamometer testing is a good measure of the strength of the housing section around the bearing. Testing will prove out the theoretical finite element analysis (FEA) conducted early in the design stages. Test results may require a redesign of the section in this area to provide adequate strength for trouble-free operation.

Table 5.5.2  Differential Bearing Jl69349H/310 (Standard Product) Test

Life (Cycles)

Bearing Condition

1 2 3

10,913 12,000* 12,000*

Failure-heavy spalling Failure-heavy spalling Good condition

5.5.9 Vehicle Durability Testing

*Test completed

Vehicle testing of Chrysler transaxle tapered roller bearings normally is accomplished within a general vehicle endurance test or a more specific powertrain endurance test. Both are accelerated test schedules. In the vehicle endurance test of 48,280 km of high-speed and high-load driving, emphasis is placed on a total system and component function; in the powertrain endurance test of 40,235 km, the focus is on the propulsion system itself and thus in this case, more specifically on tapered roller bearing endurance. Nevertheless, the bearings must pass both vehicle tests.

Table 5.5.3  Differential Bearing Jl69349H/310 (Standard Product) Test 1 2 3 4 5 6 7 8 9 10

Life (Cycles) 12,000* 12,000** 19,123*** 12,000** 42,554* 40,235 km PTE + 12,000 cycles* 21,379*** 17,009*** 14,703*** 12,000***

Bearing Condition Good condition Good condition Good condition Good condition Good condition (minor bruising) Good condition

The powertrain endurance test at Chrysler includes 2000 wide-open-throttle (WOT) accelerations up a 20% grade or 4000 WOT accelerations up a 15% grade, or a combination of the two, depending on weather conditions. These grade conditions, performed from a standing start at the bottom of the grade, are key elements in successful vehicle testing of bearings because they closely duplicate critical point loading.

Good condition Good condition Good condition Good condition

* Test completed ** The bearings in Test No. 2 were placed in the transaxle in Test No. 4 for an additional 12,000 cycles for a total of 24,000 cycles. *** Tests suspended due to other transaxle component failures.

Typically, vehicle speed up the grade is such that much of this test phase occurs at or near the critical point for bearing life. For common powertrains in passenger cars, the critical point is at 8 to 16 km/h at maximum engine load. In this sense, a vehicle testing cycle is more severe than a WOT engine dynamometer cycle because the dynamometer passes through the critical point comparatively quickly. This difference is made up by running a larger number of dynamometer cycles, now typically 24,000.

It should be mentioned that very early in the transaxle design phase, a larger bearing was considered for the differential positions. Bearing LM501349/310 (standard product) was thought to offer adequate performance, because its rating is 47% greater than bearing JL69349/310, resulting in a catalog life improvement of 261%. This larger bearing was tested under WOT test conditions, and early failures were experienced. The high bearing loading and misalignment caused geometric stress concentration failures at the edge of contact

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5.5.10 Thermal Effects on Performance

Change in cup fit due to thermal effects also has minor effects on bearing setting and is accounted for in the term ∑ΔB in Eq. (5.5.4).

The coefficient of thermal expansion of the transaxle aluminum housing is approximately twice that of the steel shaft, bearings, and gears, causing a change in the initial tapered roller bearing setting, as temperature varies. The total bearing setting change as a result of thermal effects is discussed by Dickerhoff, Hill, and Kreider [5] as: Setting Change = [(Dc α al) – (Ds αst)]ΔT – ∑Δ B

5.5.11 Solution to a Noise Problem Testing of automatic transaxle upgraded Model 31TH indicated an unacceptable noise level. It was determined that the noise was the result of the gear mesh between the output and intermediate shafts. It was found that by increasing the helix angle of the gearing from 27.5° to 32° the noise could be eliminated. However, increasing the helix angle of the gearing would impose higher loading on output bearings L68149/111.

(5.5.4)

For example, the initial endplay setting for the transfer shaft bearings in Model 41TE transaxle will be reduced when the transaxle heats up during operation and will increase at colder temperatures. Figure 5.5.26 illustrates bearing setting changes versus operating temperature. A total range in bearing setting of 0.43 mm is calculated for an operating temperature between −34°C and +120°C. The designer generally accounts for these thermal effects in specifying the bearing initial (room temperature) setting to give the desired setting at operating temperature.

The bearing life analysis for the increased helix angle indicated that the output shaft bearings should be of P900 quality to provide improved performance. Figure 5.5.27 illustrates bearing life improvements using P900 quality bearings (L68149P/111P) for the increased helix angle.

5.5.12 New Design Eliminates Cup Creep Assembly of the transfer shaft in Model 41TE automatic transaxle warrants a loose cup fit in the aluminum housing, front bearing, for ease of shaft assembly. Dynamometer testing showed that the loose cup “crept,” or rotated, in the housing. A tight fit would not permit the ease of assembly desired, so a new bearing cup design was developed to prevent the loose fitted cup from turning in the housing. A new cup is produced that incorporates a groove in the cup O.D. and is fitted with an “O” ring (see Fig. 5.5.28). This design has proven successful to eliminate cup “creep” in the aluminum housing, thus maintaining ease of assembly without sacrificing performance.

Fig. 5.5.26  Tapered roller bearing setting change versus operating temperature calculated for transfer shaft of Model 41TE automatic transaxle. Differential coefficients of thermal expansion between the aluminum housing and steel bearing cup are considered in determining the desired cup fit in the housing. As the temperature increases during operation, the initial cup fit will be relieved, because the housing bore grows faster with temperature changes than the cup O.D. A simple equation for determining temperature effects on cup fit in aluminum housings is shown here.

Change in Cup Fit = ΔTd(αal – αst)

(5.5.5)

As an example, the fit of differential bearing cup JL69310 changes about 0.9 μm/°C. This change in cup fit due to temperature should be considered so that a tight fit is always provided, preventing cup creep, or rotation, in the housing.

Fig. 5.5.27  Calculated life improvements using P900 tapered roller bearing on output shaft of Model 31TH automatic transaxle. 5-78

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Bearings

Fig. 5.5.28  “O” ring groove cup on transfer shaft to prevent cup “creep” in aluminum housing.

5.5.13 Oil Flow Test Improves Performance The bearings in the transaxle must receive a good supply of oil to give good performance. An inadequate supply of oil will not provide lubricant to the critical contact between the roller spherical end and cone large rib surface (see Fig. 5.5.29). This situation may cause the bearing to run hot or even burn up. The design of the transaxle must provide means for supplying lubricant to the bearings by splash and gravity feed, or by some type of pump. Testing may be required to prove out the lubrication system.

Fig. 5.5.30  Output shaft bearings oil supply for Model 41TE automatic transaxle.

5.5.14 Summary Automatic transaxles for today’s passenger cars and light trucks require bearings that will provide good life and reliability and improve the overall performance of the transaxle. Tapered roller bearings provide these features and have proven themselves in Chrysler’s automatic transaxles. Selecting a larger bearing with higher capacity for increased power does not always provide the best results. A smaller bearing with enhanced internal design could offer good performance and provide downsizing of the overall transaxle design.

Fig. 5.5.29  Typical oil flow through a tapered roller bearing.

Tapered roller bearing selection and analysis to improve the performance of automatic transaxles are accomplished through the use of computer programs such as The Timken Company’s Select-A-NalysisSM program. Other computer programs make it possible to design enhanced geometry for existing bearings and new bearing designs. Advanced manufacturing capabilities enable production of quality bearing components to provide good performance.

An oil flow test was conducted for output shaft bearings of Model 41TE transaxle that had experienced bearing overheating in vehicle and dynamometer tests. See Fig. 5.5.30 for the output shaft mounting arrangement and inlet oil supply. It was theoretically determined that an oil flow of 0.25 L/ min would be required to maintain a safe bearing operating temperature of 93°C. This was determined from the following equation, which assumes that all the generated heat is dissipated by the oil.

Qoil = k 5f (θo – θi)

Accurate values of transaxle housing axial, radial, and tilting spring stiffness are critical for accurate evaluation of bearing design and selection. Actual testing in the transaxle builder’s laboratory and in the field is essential to verify and support the analytical tools used to select and design bearings. Testing also reveals areas for transaxle improvement that cannot be totally designed through analytical methods. New bearing designs must also be tested to ensure good performance in the production units.

(5.5.6)

Testing shows that a 0.028 MPa oil pressure would be required to provide the 0.25 L/min calculated oil supply to maintain a stable operating temperature at 3000 rpm. It was also learned that an oil diversion device will be necessary to equally distribute the oil supply to each bearing.

SM

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5.5.15 Acknowledgments

bearing manufacturer’s drawing manual, and is the cone outside diameter at the midpoint of the raceway.

The authors wish to thank F. J. Schlueter, W. G. Teer, and D. H. Black of Chrysler Transmission Development for use of the vehicle and dynamometer endurance data. Also, thanks to the many colleagues at The Timken Company, especially at the Technology Center.

5.5.16 References 1. Hull, J. R., “Rolling Element Bearings in Passenger Car Automatic Transmissions,” SAE Design Practices, Passenger Car Automatic Transmissions, Volume 5, Chapter 26, SAE International, Warrendale, PA, 1973. 2. Bhatia, R. R. and T. E. Springer, “Using Histograms in the Selection Process for Tapered Roller Bearings,” Paper 810993, Proceedings of the SAE International Off-Highway Meeting and Exposition, Milwaukee, WI, September 14–17, 1981. 3. Moyer, C. A., “Using the Modified Lambda Ratio to Advance Bearing and Gear Performance,” Paper 901625, Proceedings of the SAE International Off-Highway and Power Plant Congress and Exposition, Milwaukee, WI, September 10–13, 1990. 4. Hoeprich, M. R., “Numerical Procedure for Designing Rolling Element Contact Geometry as a Function of Load Cycle,” Proceedings of the SAE Earthmoving Industry Conference, Peoria, IL, April 15–17, 1985. 5. Dickerhoff, R. P., H. E. Hill, and G. E. Kreider, “Thermal Compensating Tapered Roller Bearing for Enhancement of Transmission and Transaxle Performance,” Paper 910799, Proceedings of the SAE International Congress and Exposition, Detroit, MI, February 25–March 1, 1991.

Fig. 5.5.31  Dimensions for calculating cone/shaft contact pressure and required push-up or push-off force. 5.5.17.1  Contact Pressure Pi a.  Hollow Steel Shaft di dso P1 = 2⎤ ⎡ ⎛ d ⎞2 ⎢ 1+⎜⎜ so ⎟⎟ 1+⎛⎜⎜ dsi ⎞⎟⎟ ⎥ ⎢ ⎜⎝ dco ⎟⎠ ⎜⎝ dso ⎟⎠ ⎥ 1 ⎥ ⎢ 4 ⎢ 2 + 2⎥ 20.68×10 ⎢ ⎛ dso ⎞ ⎛ ⎞ d ⎜ ⎟ ⎜ si ⎟ ⎥ ⎢ 1−⎜⎜⎝ d ⎟⎟⎠ 1−⎜⎜⎝ d ⎟⎟⎠ ⎥ co so ⎦ ⎣

(5.5.7)



b.  Solid Steel Shaft ⎛d ⎞ 20.68×104 ⎜⎜ i ⎟⎟⎟ ⎜⎝ dso ⎠ P1 = ⎡ ⎛ d ⎞2 ⎤ ⎢ 1+⎜⎜ so ⎟⎟ ⎥ ⎢ ⎜⎝ dco ⎟⎠ ⎥ ⎥ 1+ ⎢⎢ 2⎥ ⎢ 1−⎛⎜ dso ⎞⎟⎟ ⎥ ⎢ ⎜⎜⎝ d ⎟⎠ ⎥ co ⎦ ⎣

(5.5.8)



Contact Pressure Between Tight Fitted Cup and Housing— Fig. 5.5.32 illustrates the cup of a tapered roller bearing mounted in an aluminum housing. The contacting pressure between the cup O.D. and housing I.D. depends on the interference fit, bearing design, and housing cross-section, and can be calculated using Eq. 5.5.9. The dimension “dcu” can be scaled from the bearing manufacturer’s drawing manual.

5.5.17 Appendix 1 Contact Pressure Between Tight Fitted Cone and Shaft—Fig. 5.5.31 illustrates the cone of a tapered roller bearing mounted on a shaft. The contacting pressure between the cone bore and shaft O.D. depends on the interference fit, bearing design, and shaft cross-section. For a given bearing, the maximum pressure would be when the cone is press fitted on a solid shaft. For a hollow shaft, as in a differential mounting arrangement, the interference fit would have to be increased to provide the same contact pressure as when the cone is mounted on a solid shaft. Experience has shown that the cone interference fit should be increased on the differential shaft to give good holding power against cone creep. Equations 5.5.7 and 5.5.8 will give the contact pressure between the cone bore and hollow shaft and solid shaft, respectively. The dimension “dco” can be scaled from the

Fig. 5.5.32  Dimensions for calculating cup/housing contact pressure and required push-up or push-off force. 5-80

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5.5.17.2  Contact Pressure Po (Cup)

Through Cup (Fi1)

Finite Aluminum Housing O.D.

1 1 = − Fi1 Fi

⎡ ⎤ ⎡ ⎛ d ⎞2 ⎢ ⎥ ⎢ 1+⎜⎜ ⎟⎟ ⎥ ⎢ ⎜⎝ dh ⎟⎠ 1 do ⎢⎢ ⎥ ⎢ P0 = ⎢ 4 ⎢ 2 +0.33⎥ + d ⎢ 6.89×10 ⎥ ⎢ 1−⎛⎜ d ⎞⎟⎟ ⎢ ⎥ ⎢ ⎜⎜⎝ d ⎟⎠ h ⎢⎣ ⎦ ⎣



⎤⎤ ⎡ ⎛ d ⎞2 ⎥⎥ ⎢ 1+⎜⎜ cu ⎟⎟ ⎥⎥ ⎢ ⎝ d ⎟⎠ 1 ⎥⎥ ⎢ 4 2 −0.30 ⎥ ⎥ 20.68×10 ⎢ ⎛ dcu ⎞ ⎟ ⎜ ⎥⎥ ⎢ 1−⎜ ⎟ ⎥⎦ ⎥⎦ ⎢⎣ ⎝ d ⎟⎠

(5.5.11)

where Fi is obtained from Eq. 5.5.10. 5.5.18.2  Push-Up or Push-Off Force (Cup)

−1

Through Cup (Fo)

(5.5.9)

Fo = fo πdWoPo





(5.5.12)

where Po is obtained from Eq. 5.5.9 Through Cone (Fo1)

5.5.18 Appendix 2

1 1 = − Fo1 Fo

Force Required to Push-Up or Push-Off the Cone and Cup— To assemble or disassemble a cone on a shaft or cup in a housing, the force required to accomplish this, when the cones and cups are mounted with tight fits, can be calculated using the following equations. These equations are for a steel shaft and aluminum housing. Refer to Figs. 5.5.32 and 5.5.33 in Appendix 1 for the required dimensions for these equations. As shown in Appendix 1, Eqs. 5.5.7 and 5.5.8 are used to calculate the contact pressure between a tight fitted cone on a shaft, and Eq. 5.5.9 should be used to calculate the contact pressure between a tight fitted cup and aluminum housing.

⎡ d d ⎤ (20.68×10 )pdo Wo tana ⎢⎢ d − dcu ⎥⎥ ⎦ ⎣ cu 4

;

(5.5.13)

5.5.19 Appendix 3 Example calculations of tapered roller bearing loads and catalog lives are provided for the output, transfer, and differential shafts for automatic transaxle model 41TE. These example calculations are for only one condition of the loading cycle. Calculations for the other conditions would be similar. Bearing life calculations shown below are based on a catalog approach and should be adjusted for the environmental effects of load zone (a3k), lubrication (a3l), and alignment (a3m). Refer to The Timken Company Bearing Selection Handbook, copyright 1986. Also refer to The Timken Company Bearing Selection Handbook for basic dynamic bearing load ratings and formulas for dynamic equivalent radial loads and bearing life calculations. 5.5.19.1  Nomenclature for Appendix 3

5.5.18.1  Push-Up or Push-Off Force (Cone)

C90 Basic dynamic radial load rating of a single-row tapered roller bearing for an L10 of 90 million revolutions or 3000 hours at 500 rpm, N Fae External applied thrust force, N FaG Thrust force on gear, N FaP Thrust force on pinion, N FsG Separating force on gear, N

Through Cone (Fi)  fi πdsoWiPi ; where Pi is obtained from Eqs. 5.5.7 Fi = or 5.5.8, Appendix 1

2

where Fo is obtained from Eq. 5.5.12

There are two different methods of pressing the cone on the shaft and cup in the housing. The easiest way to press the cone on the shaft is through the cone, and the least force required to press the cup in the housing is through the cup. These forces can be calculated using Eqs. 5.5.10 and 5.5.12. For the case when the cone has to be pressed off the shaft through the cup, Eq. 5.5.11 should be used. When the cup has to be pressed from the housing through the cone, Eq. 5.5.13 is used to calculate the force. The latter two methods of pressing the cone and cup are not recommended due to possible damage to the rollers and raceways. Also, depending on bearing geometry, it may be theoretically impossible to remove the cones and cups in this manner.



2cos2y cosb ⎛d d ⎞ (20.68×104 )(pdi Wi )⎜⎜⎜⎝ dco − dso ⎟⎟⎟⎠sina so co

(5.5.10)

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FsP FtG FtP Fr FrX

Separating force on pinion, N Tangential force on gear, N Tangential force on pinion, N Bearing radial load on bearings A, B, C, D, or E, N Bearing radial loading along x-axis on bearings A, B, C, D, or E, N FrY Bearing radial loading along y-axis on bearings A, B, C, D, or E, N K K-factor. Ratio of basic dynamic radial load rating to basic dynamic thrust load rating in a single-row bearing L1 L10 life for load condition 1, hours L2 L10 life for load condition 2, hours L10 Rating life. The bearing life expectancy associated with 90% reliability, hours Ln L10 life for condition n, hours L10 Weighted life. The bearing life expectancy (weighted) associated with 90% reliability for varying load, or speed conditions, or both, hours P Dynamic equivalent radial load, N P.D. Gear or pinion pitch diameter, mm S Bearing speed, rpm t1 % time/100 for condition 1 t2 % time/100 for condition 2 tn % time/100 for condition n

Summation of Moments about Bearing B: FrXA =

7.3×FtP 7.3×4920 = = 930N 38.6 38.6

FrYA =

7.3×FsP Pinion P.D.×FaP = 38.6 2×38.6

=

7.3×1590 129.7×2555 + = 4595N 38.6 2×38.6 1/2

1/2 2 2 FrA = ⎡⎢(FrXA ) +(FrYA ) ⎤⎥ = ⎡⎣(930)2 +(4595)2 ⎤⎦ = 4690N ⎣ ⎦

Summation of Moments about Bearing A: FrXB =

45.9×FtP 45.9×4920 = = 5850N 38.6 38.6

FrYB =

45.9×FsP Pinion P.D.×FaP = 38.6 2×38.6

=

45.9×1590 129.7×2555 + = 6184N 38.6 2×38.6 1/2

1/2 2 2 FrB = ⎡⎢(FrXB ) +(FrYB ) ⎤⎥ = ⎡⎣(5850)2 +(6185)2 ⎤⎦ = 8515N ⎣ ⎦

Dynamic Equivalent Radial Loads: ⎤ ⎡⎛ 0.47×Fr ⎞ B ⎟ PA = 0.4×FrA +KA ⎢⎜⎜ ⎟+F ⎥ ⎢⎜⎝ KB ⎟⎠ ae ⎥ ⎦ ⎣ ⎛ 0.47×8515 ⎞ = 0.4×4690+1.40⎜⎜ + 2555⎟⎟⎟ = 8790N ⎝ 1.68 ⎠

5.5.19.2  Output Shaft

PB = FrB = 8515N Bearing Life Calculations—Condition 1: 10/3 ⎛1.5×106 ⎞⎟ ⎛C ⎞ ⎟ L10 = ⎜⎜ 90 ⎟⎟⎟ ×⎜⎜ ⎜⎝ S ⎟⎟⎠ ⎝ P ⎠ 10/3 ⎛1.5×106 ⎞⎟ ⎛10,300 ⎞⎟ ⎜⎜ ⎟ = 560 hours L10A = ⎜⎜ × ⎟ ⎜⎝ 4,567 ⎟⎟⎠ ⎝ 8,790 ⎟⎠ 10/3 ⎛1.5×106 ⎞⎟ ⎛12,000 ⎞⎟ ⎟ =1,030 hours L10B = ⎜⎜ ⎟⎟ ×⎜⎜⎜ ⎝ 8,515 ⎠ ⎝ 4,567 ⎟⎟⎠

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Bearings

Weighted Average Bearing Life: −1

⎛t t t ⎞ L10(weighted ) = ⎜⎜ 1 + 2 +… n ⎟⎟⎟ ⎜⎝ L1 L2 Ln1 ⎠

−1

⎛ 0.0385 t2 t ⎞ L10(weighted )A = ⎜⎜ + +… n ⎟⎟⎟ ⎜⎝ 560 L2 Ln1 ⎠

−1

⎛ 0.0385 t2 t ⎞ L10(weighted )B = ⎜⎜ + +… n ⎟⎟⎟ ⎜⎝ 1020 L2 Ln1 ⎠

5.5.19.3  Transfer Shaft

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Design Practices: Passenger Car Automatic Transmissions

Summation of Moments about Bearing D: FrXC = = FrYC = =

6.1×FtG 234.7×FtP 234.7×FsP Pinion P.D.×FaP − sin18°+ cos18°− cos18° 211.4 211.4 211.4 2×211.4 234.7×3680 51.3×5915 6.1×4920 234.7×11380 − sin18°+ cos18°− cos18° =−560N 211.4 211.4 2×211.4 211.4 6.1×FsG Gear P.D.×FtP 234.7×FsP 234.7×FtP Pinion P.D.×FaP − + sin18°+ cos18°− sin18° 211.4 2×211.4 211.4 211.4 2×211.4 234.7×11380 51.3×5915 6.1×1590 118.7×2555 234.7×3680 − + sin18°+ cos18°− sin18° =12385N 211.4 211.4 211.4 2×211.4 211.4 1/2

1/2 2 2 FrC = ⎡⎢(FrXC ) +(FrYC ) ⎤⎥ = ⎡⎣(−560)2 +(12385)2 ⎤⎦ =12400N ⎣ ⎦

Summation of Moments about Bearing C: FrXD = = FrYD = =

217.5×FtG 23.3×FtP 23.3×FsP Pinion P.D.×FaP − sin18°+ cos18°− cos18° 211.4 211.4 211.4 2×211.4 23.3×3680 51.3×5915 217.5×4920 23.3×11380 − sin18°+ cos18°− cos18°= 4380N 211.4 211.4 2×211.4 211.4 217.5×FsG Gear P.D.×FaG 23.3×FsP 23.3×FtP Pinion P.D.×FaP − + sin18°+ cos18°− sin18° 211.4 2×211.4 211.4 211.4 2×211.4 23.3×11380 51.3×5915 217.5×1590 118.7×2555 23.3×3680 − + sin18°+ cos18°− sin18°= 2015N 211.4 211.4 211.4 2×211.4 211.4 1/2

1/2 2 2 FrD = ⎡⎢(FrXD ) +(FrYD ) ⎤⎥ = ⎡⎣(4380)2 +(2015)2 ⎤⎦ =1840N ⎣ ⎦

Dynamic Equivalent Radial Loads: ⎛ 0.47×FrD ⎞ PC = 0.4×FrC +KC ⎜⎜ +Fae ⎟⎟⎟ ⎜⎝ KD ⎠ ⎤ ⎡ 0.47×4820 +(5915−2555)⎥ =12080N = 0.4×12400+1.44 ⎢ ⎥⎦ ⎢⎣ 1.46 Use PC = FrC =12400N PD = FrD = 4820N

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Bearings

Bearing Life Calculations—Condition 1: 10/3 ⎛1.5×106 ⎞⎟ ⎛C ⎞ ⎟ L10 = ⎜⎜ 90 ⎟⎟⎟ ×⎜⎜ ⎜⎝ S ⎟⎟⎠ ⎝ P ⎠ 10/3 ⎛1.5×106 ⎞⎟ ⎛13600 ⎞⎟ ⎜ ⎟ = 410 hours L10C = ⎜ ⎟⎟ ×⎜⎜⎜ ⎝12400 ⎠ ⎝ 4990 ⎟⎟⎠ 10/3 ⎛1.5×106 ⎞⎟ ⎛15100 ⎞⎟ ⎟ =13520 hours L10D = ⎜⎜ ⎟⎟ ×⎜⎜⎜ ⎝ 4820 ⎠ ⎝ 4990 ⎟⎟⎠

Weighted Average Bearing Life: −1

⎛t t t ⎞ L10(weighted ) = ⎜⎜ 1 + 2 +… n ⎟⎟⎟ ⎜⎝ L1 L2 Ln1 ⎠

−1

⎛ 0.0385 t2 t ⎞ L10(weighted )C = ⎜⎜ + +… n ⎟⎟⎟ ⎜⎝ 410 L2 Ln1 ⎠

−1

⎛ 0.0385 t2 t ⎞ L10(weighted )D = ⎜⎜ + +… n ⎟⎟⎟ ⎜⎝ 13520 L2 Ln1 ⎠

5.5.19.4  Differential

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Design Practices: Passenger Car Automatic Transmissions

Summation of Moments about Bearing E: FrXF = = FrYF =

Bearing Life Calculations—Condition 1:

111.3×FsG Gear P.D.×FaG = 124 2×124

10/3 ⎛1.5×106 ⎞⎟ ⎛C ⎞ ⎟ L10 = ⎜⎜ 90 ⎟⎟⎟ × ⎜⎜ ⎜⎝ S ⎟⎟⎠ ⎝ P ⎠

111.3×3680 192.6×5915 + =−1290N 124 2×124

10/3 ⎛1.5×106 ⎞⎟ ⎛10,300 ⎞⎟ ⎜ ⎟ = 310 hours L10E = ⎜ ⎟⎟ × ⎜⎜⎜ ⎝ 15,160 ⎠ ⎝ 1,329 ⎟⎟⎠

111.3×FtG 111.3×11380 + =10215N 124 124

10/3 ⎛1.5×106 ⎞⎟ ⎛10,300 ⎞⎟ ⎟ =1,130 hours L10F = ⎜⎜ ⎟⎟ × ⎜⎜⎜ ⎝10,295 ⎠ ⎝ 1,329 ⎟⎟⎠

1/2

1/2 2 2 FrF = ⎡⎢(FrXF ) +(FrYF ) ⎤⎥ = ⎡⎣(−1290)2 +(10215)2 ⎤⎦ =10295N ⎣ ⎦

Weighted Average Bearing Life: −1

⎛t t t ⎞ L10(weighted ) = ⎜⎜ 1 + 2 +… n ⎟⎟⎟ ⎜⎝ L1 L2 Ln ⎠

Dynamic Equivalent Radial Loads: ⎛ 0.47×FrF ⎞ PE = 0.4×FrE +KE ⎜⎜ +Fae ⎟⎟ ⎟⎠ ⎜⎝ KF

−1

⎛ 0.0385 t2 t ⎞ L10(weighted )E = ⎜⎜ + +… n ⎟⎟⎟ ⎜⎝ 310 L2 Ln ⎠

⎤ ⎡ 0.47×10295 +5915⎥ =15160N = 0.4×5105+1.40 ⎢ 1.40 ⎥⎦ ⎢⎣

−1

⎛ 0.0385 t2 t ⎞ L10(weighted )F = ⎜⎜ + +… n ⎟⎟⎟ ⎜⎝ 1,130 L2 Ln ⎠

PF = FrF =10295N

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Chapter 6

Friction Clutches Anthony J. Grzesiak , Robert C. Lam, Donn K. Fairbank, and Keith Martin BorgWarner Transmission Systems

and analysis of multi-plate friction clutches are presented. In Section 6.3, the band clutch is discussed in detail. Many people have contributed to our current understanding of wet friction systems over the years. Some of these people are specifically acknowledged through their inclusion in the references at the end of this chapter. We also need to give special recognition to the authors of the previous Advances in Engineering publications, AE-5 and AE-18, for their contributions: R. J. Fanella, AE-18 Chapter 6, Friction Elements; L.E. Froslie, T. Milek, and R.W. Smith, AE-5 Chapter 11, Automatic Transmission Friction Elements; G.R. Smith, W.D. Ross, P.L. Silbert, and W.B. Herndon, AE-5 Chapter 12, Putting Automatic Transmission Clutch Friction Researchers on Speaking Terms; and W.D. Ross, E.M. Sharer, A.P. Blomquist, and W.B. Herndon, AE-5 Chapter 13, Measuring Friction of Single- and MultipleWrap Transmission Bands.

Ted D. Snyder Ford Motor Company Transmission & Driveline Engineering

Introduction The function of wet clutches and bands in the automatic transmission is to connect and disconnect torque-carrying elements to provide power to the driving wheels. The selective coupling of the torque-carrying elements of the planetary gear train creates different torque and speed ratios between the input and the output of the transmission. The shift from one ratio to another must be non-abrupt with, in today’s market, nearly imperceptible engagement or shift feel. To make the shift smooth, the friction element slips during the shift event, absorbing energy in the form of heat. When the friction elements are disengaged, drag torque must be minimized to maintain good fuel economy. In this chapter, two general types of friction systems are discussed: the multi-disc wet clutch, and the wet band. From a functional perspective, a friction system brings into contact two or more surfaces between the driving and driven members. The normal contact forces generated between these surfaces generate frictional forces that transmit torque from member to member. Paperbased friction materials are typically employed to enhance the interface frictional characteristics.

This chapter is the collective work of several people who have assembled references and personally contributed their knowledge in writing the subsections of this chapter. Section 6.1, Evolution of High-Energy Wet Friction Materials, was compiled and written by Robert C. Lam, BorgWarner Transmission Systems. Section 6.2, Multi-Plate Friction Clutch, was written by Donn K. Fairbank, BorgWarner Transmission Systems, with help on the mechanical components by Keith Martin, also with BorgWarner Transmission Systems. The final part, Section 6.3, Bands, was prepared by Ted D. Snyder, Ford ATN-PC, and Anthony J. Grzesiak, BorgWarner Transmission Systems.

This chapter is organized in three major sections. In Section 6.1, the evolution and application of paper-based friction materials are discussed. In Section 6.2, details on the design

Donn K. Fairbank BorgWarner Transmission Systems 6-1

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Design Practices: Passenger Car Automatic Transmissions

6.1 Evolution of High-Energy Wet Friction Materials

process, was readily accepted by the transmission developers because of its excellent shift qualities, high friction, and low cost [1].

6.1.1 Introduction and History of Early Development

Considerable efforts by the friction industry were used in the 1970s and early 1980s to develop a replacement for asbestos fibers because of its health issues. No single material has been found to be equivalent to asbestos in wet friction applications. However, elimination of asbestos fibers in wet friction materials was achieved by using combinations of several materials in formulations and papermaking process changes to satisfy the required friction performance of today’s applications. Advances in thermosetting resin technology and numerous improvements in resin saturating and material processing steps have also aided in meeting these performance requirements [2]. Of major importance was the introduction of new synthetic fibers, such as aramid, into the paper formulations in the 1980s and 1990s to improve performance, durability, and reliability of vehicle transmissions and limited slip devices. Most of today’s passenger car transmissions use paper-based friction materials containing cellulose, mineral and synthetic fibers, and organic and inorganic particles. These are bonded with a thermoset resin. Figure 6.1 is a timeline on the history of the development of materials for wet friction applications.

One of the earliest commercial uses of wet friction material was in a 1938 General Motors automatic transmission. Sintered metal was used as the shift clutches and woven material as the bands [1]. As the demand for automobiles and automatic transmissions grew after World War II, better wet friction materials were developed. Semi-metallic materials began to replace sintered bronze. These semi-metallic materials consisted of metal powders molded together with resin and friction particles such as asbestos and graphite. Both sintered and molded semi-metallic materials were plagued with low friction coefficients. To increase the coefficient of friction, softer and more flexible materials such as cork and Krafelt began to replace the hard sintered metal and molded semimetallic materials in the late 1940s [1]. However, high compression set and low durability with cork and Krafelt led to the blending of a newly discovered phenolic resin, Bakelite®, with asbestos fibers. This combination of Bakelite resin along with asbestos fibers allowed more durable, higher-strength, and higher coefficient-of-friction wet friction materials to be introduced in the early 1950s as a molded product. In 1957, the first paper-based wet friction material was introduced, which consisted of asbestos, cellulose fibers, and fillers on a Fourdrinier papermaking machine. The key features of this phenolic-saturated asbestos paper were high dynamic coefficient, low static/dynamic ratio, good heat and chemical resistance, and good tensile strength and flexibility. Paper also had more porosity than molded or extruded friction materials. Asbestos friction material, made with the papermaking

6.1.2 Evolution of Present Paper-Type Friction Materials Since the 1980s, the popularity of automatic transmissions has grown at a tremendous rate. With this growth have come the stringent requirements for designers to provide transmissions with better shift quality, longer life, and more fuel efficiency. These requirements of the transmission system drove

Fig. 6.1  History of the development of materials for wet friction applications. 6-2

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Friction Clutches

the development of high-heat-resistance and high-performance wet friction materials during the 1980s and 1990s. In addition to high temperature resistance and durability, current and future applications require wet friction materials to have consistent µPVT curves (friction coefficient (µ) at various pressure (P), velocity (V), and temperature (T) conditions), positive µ-V slopes, and high coefficient of friction. Current trends and requirements of today’s transmission systems and the necessary friction materials requirements are summarized in Table 6.1.

optimization of the several factors that control the performance of wet friction materials, as outlined in Table 6.2.

6.1.3 High-Energy Materials with Good Friction Characteristics The early focus of modern paper-type wet friction material was on providing better shift quality with acceptable heat stability to meet the demands of the transmission design. Cellulose was often the fiber of choice for its desirable friction characteristics. Cellulose fibers used in these friction materials include wood, cotton, linen, or rag, with cotton

To meet current transmission trends as outlined in Table 6.1, many friction characteristics must be met. This requires the

Table 6.1  Current Trends in Transmissions and Requirements of Wet Friction Materials Transmission Trends

Wet Friction Material Requirements

Higher pressures

Lower deformation, low thickness loss

Smaller pump, lower ATF flow High-energy material, higher heat resistance at low lubrication flow Reduced drag loss

Improved groove pattern design

Reduced size/weight

Higher µ2 increased heat resistance

Higher speeds, higher energies

Stable coefficients of friction, hot spot resistance

Continuous slip clutches

Good µ-V; no shudder, no noise

ATF compatibility Inert to chemical and physical interactions with fluids Better consistency of shift quality

Better µPVT consisntency, positive µ-V slope.

Table 6.2  Development of Today’s High-Heat-Resistance and High-Performance Friction Materials Friction Property

Wet Friction Material Controlling Factors

µ0, low-speed dynamic coefficient Friction material ingredients and ATF additives adsorption µ0, initial dynamic coefficient at high speed

Hydrodynamic effects/porosity/compression/ roughness

Mechanical strength Fiber type, fiber fibrillation, fiber/resin bond strengths Heat resistance More synthetic fibers (aramid, carbon), higher porosity Positive µ-V slope Balance of paper ingredients with ATF additives adsorption and pore size Hot spot resistance

Resiliency

Glazing Ingredient compatibility with ATF additives, pore size Compression set Optimization of fiber, filler, and resin types and ratios

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Design Practices: Passenger Car Automatic Transmissions

being the predominant component. Wet friction materials made with cellulose fibers have a relatively high coefficient of friction and low static/dynamic friction ratio for smooth shifting properties. Unfortunately, cellulose fibers lack high heat resistance. Under high-temperature conditions, the cellulose fiber breaks down, causing material break-out, high friction lining thickness loss, and eventual loss of good friction characteristics.

More stringent application demands for high energy and durability placed on wet friction materials by customers during the 1990s and into the twenty-first century drove the development of materials toward significantly reducing or eliminating cellulose fibers from formulations. Friction facings made with a high content of synthetic fibers offer superior heat, chemical, and mechanical durability to ones containing cellulose, but at a premium price. Both aramid and carbon fibers have proven to be effective in these highenergy applications [3, 9–11].

Heat resistance of papers can be improved by increasing porosity of the fiber network. Increasing porosity of the lining allows for more ATF storage and flow for cooling the material by convection. Material with increased porosity is also more effective in clearing the oil film and raising the dynamic coefficient of friction [3–5]. Because of their lack of good heat and chemical stability, friction materials with relatively high cellulose fiber content are primarily used for low- and medium-energy applications.

One of the process steps used in the manufacturing of friction material is fiber fibrillation, which helps control the strength, porosity, pore size, and density of the paper. Increasing the degree of fiber fibrillation of both the synthetic and cotton fibers improves mechanical strength while reducing the liquid permeability of the friction material and reducing the initial dynamic coefficient of friction [3, 12, 13]. Figure 6.2 shows low and high degrees of fibrillation on a porous network of friction materials. The degree of fiber fibrillation affects the liquid permeability and the hydrodynamic film, which in turn affects the initial dynamic coefficient of friction. High paper porosity and liquid permeability are desired to provide for high oil flow by convection for better cooling of friction material. This increased fluid flow also reduces the accumulation of degraded ATF additives on the surface, commonly referred to as glazing [5, 10]. Figure 6.3 shows an example of a glazed surface. However, extreme friction material porosity can result in dominant hydro­dynamic effects and too high an initial dynamic coefficient, thus resulting in an abrupt shift feel. Thus, the porosity and liquid permeability for oil flow through and along friction surfaces must be properly optimized and controlled to result in optimum heat dissipation and frictional characteristics. This can be done by proper

The addition of graphitic particles is also used to extend cellulose and cellulose/synthetic-based friction materials into wet friction applications requiring high thermal stability, high energy absorption, and/or low cooling oil flow [6–8]. Because graphite can act as a high-temperature lubricant, high coefficients of friction often are hard to achieve with high-content graphitic papers. In addition, graphitic material has a relatively high static/dynamic ratio, resulting in poor shifting quality. Thus, both good thermal properties and high-coefficients-of-friction papers are difficult to achieve by only increasing the graphite content of friction material. High-content graphitic-type papers are commonly used in heavy-duty areas where extra friction surfaces can be engineered into the application and where shift quality requirements are not stringent [9].

Fig. 6.2  Example of friction materials with (a) low and (b) high fibrillated fibers. 6-4

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Friction Clutches

Fig. 6.3  Example of (a) non-glazed and (b) glazed friction material surfaces. or eliminated by using high-resiliency materials. However, the use of high-resiliency materials may result in excess compression set and deformation under high-pressure conditions.

controls of fiber types and fibrillation, fiber/filler network structure, surface texture, and groove design. Figure 6.4 shows the controlling factors for engagement torque curve slope. Designing friction materials with proper selection and processing steps of the ingredients and their ratios has allowed friction material manufacturers to meet most of the higher energy needs of friction material users during the last decade. Table 6.3 shows some of the typical ingredients used in present wet friction papers for automatic transmissions.

6.1.4 Friction Materials with High Mechanical Strengths During a clutch engagement, the friction material is subjected to high heat and mechanical stress. Recent trends in transmission design have generated the need for friction materials to withstand more clutch engagements for longer life and to endure lower ATF flows, higher surface speeds, and higher torque demands for more fuel efficiency. Thermal degradation is one of the major factors for determining the life cycle of friction material [16]. Replacement of cotton fibers with aramid fibers and control of material porosity by fiber fibrillation and lining thickness have been the main approaches to improve heat, chemical, and mechanical strength ­durability.

Optimizations of type, location, and amount of frictionmodifying particles added to synthetic fiber formulations are made to meet the needs for desirable and stable friction characteristics, including µ-V characteristics at various operating conditions [10, 14]. In addition to selecting proper ingredients, porosity of synthetic fiber networks can be optimized to meet the transmission designer’s requirements for both higher friction coefficient and more durable materials [5].

Table 6.3  Typical Ingredients for Paper-Type Friction Materials

Modern friction materials have also been developed to resist hot spot formation on separators. The hot spot formations are particularly severe under high-speed, high-power, and low-lubrication conditions. Hot spots are discussed in more detail in Section 6.2.4.5, Hot Spots and Other Thermal Gradient Effects. Based on theoretical and experimental studies, hot spot formation has been shown to be significantly affected by friction material resiliency and, to a lesser extent, by ATF additive chemistry [15]. Hot spots can be minimized

Fibers Cellulose, mineral, aramid, carbon, glass Friction modifiers Diatomaceous earth, cashew nutshell oil, carbon, mica, calcium Solid lubricants

Graphite, molybdenum disulfide

Typical binders

Phenolic resin, silicone resin

6-5

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Design Practices: Passenger Car Automatic Transmissions

Fig. 6.4   Controlling factors for engagement torque curve slope. Increasing the amount of fiber fibrillation decreases porosity and increases mechanical strength of the material if ingredients and other processing steps are constant [13]. However, decreasing porosity or pore size reduces the ability of a material to cool itself by reducing the flow of ATF fluid away from the separator plate interface. Careful balancing of the degree of fiber fibrillation is required to have the optimum pore size and optimal mechanical strength while ensuring sufficient porosity exists for adequate heat convection by ATF flow. Furthermore, the mechanical strength of friction materials can be affected by resin bonding strength, resin distribution, fiber network orientations, and fiber/filler bonding strength.

6.1.6 New-Generation Material Trends and Directions In addition to using significant amounts of synthetic and carbon fibers to handle the high surface temperatures generated by today’s advanced transmissions, designers of friction materials have developed methods to surface apply frictionmodifying agents [19]. A variety of friction-modifying particles is being applied to improve coefficient of friction and optimize shift quality [19]. More porous and elastic substrates for surface-applied materials are also being developed to meet the requirements of advanced transmission systems for increased heat resistance, higher and more stable friction coefficients, reduced hot spotting, and improved mechanical strength durability. These particles can be applied to paper, non-woven, and woven substrates. This variety of substrates affords a wide range of porosity, pore size, compressibility, mechanical strength, and other internal properties of the friction material to be incorporated into its design. Size, shape, and type of the surface-applied material influence surface texture and voids; thus, determine how the hydrodynamic oil layer is cleared, and control the boundary oil film and coefficient of friction [20]. Surface structure and materials in these new concept facings provide uniform surface contact, high torque capacity, less thermal degradation, and good resistance to ATF interactions [19]. New-generation materials are being developed with superior surface and frictional properties on a variety of strong, durable, porous base substrates using surface application technologies [10, 19].

6.1.5 Friction Materials with Good μ-V  Characteristics for Slipping Applications During low-velocity slip operations, torsional vibrations can cause unpleasant noise or shudder. Two types of shudder exist in continuous slip clutches: initial, and long term [17]. Shudder occurs when dµ/dV in the µ-V curve is negative [18]. The vibration when the system is new is typically referred to as initial shudder. “Long term” refers to shudder occurring after the system has been continuously slipping for a time. Friction modifiers in the ATF, mechanical design, and the friction material properties affect initial shudder in torque converter systems. Surface treatments to friction materials have been shown to reduce both initial and long-term shudder by improving the µ-V relationship (Fig. 6.5). 6-6

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6.1.7 Development of Non-Papermaking Technologies for Wet Friction Applications

carbon fibers to manage surface texture and internal flow channels for managing oil flow [21]. Carbon fabrics are more flexible and porous while providing small surface voids of texture to prevent hydrodynamic films. This provides a wet friction material capable of continuous slip performance at very low speeds [22]. Controlling the resin impregnation of the fabric improves the compressive strength and the energy density capacity [23].

Woven carbon fiber fabrics are used in some of the most demanding friction applications requiring high heat resistance. However, high cost is a major factor limiting their use in today’s automotive transmissions. While carbon fibers typically have a lower coefficient of friction than most other synthetics, the coefficient remains very stable over a wide range of speed and pressure (Fig. 6.6). This simplifies the control of continuous slipping torque converter clutches. Improvements are being made in the methods of weaving

Non-woven textile technology offers the friction material formulator an alternative way to increase resiliency and porosity with minimal loss of mechanical strength [24]. Long stable

Fig. 6.5  Effect on μ-V by surface enhancement.

High-Energy Paper Material

Carbon Woven

Fig. 6.6  Comparison of μ-PV characteristics of paper-based friction material with woven carbon. 6-7

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Design Practices: Passenger Car Automatic Transmissions

requires the clutch be engaged for most of its life. There have been only a few clutches of this design in production automatic transmissions.

fibers are more easily processed with the non-woven process than with papermaking equipment. Structures formed with long fibers provide a very porous structure of interlocked and entwined fibers with good strength properties [10]. In particular, mechanical fatigue properties are good with this type of entwined long-fiber matrix, making it appropriate for heavy-duty applications. Particles can be added to the surface of these materials to enhance friction properties. However, the extreme porosity in these materials can result in hydrodynamic effects causing large variations of friction properties at various temperatures, pressures, and velocities.

6.2.2 Clutch Components The multi-plate friction clutch system can consist of many components. The existence and quantity of a given component is dependent on the application. For reasons of simplicity, each of these components will be described in turn and will be referenced back to Fig. 6.7 for illustration.

6.1.8 Summary of the Evolution of High-Energy Wet Friction Materials Current trends in the automotive industry are to develop transmissions with reduced weight, higher operating pressures, lower oil flows, longer life, and more fuel efficiency, while improving the consistency of the shift quality. To meet these requirements, wet friction materials must strike a balance among energy capability, higher coefficient of friction, stable friction characteristics, positive µ-V slopes, shudder, hot spot resistance, and fluid compatibility over a wide range of speeds, temperatures, oil flow, and operating pressures. Much progress has been made during the last two decades to understand the relationships of friction materials with wet clutch systems. This better understanding of the interactions among friction material ingredients, ATF additives, groove pattern designs, resin technology, and material processing steps, along with emerging technologies, will provide the development path for next-generation high-performance friction materials.

Fig. 6.7  Illustration of a hydraulic-apply, spring-release clutch. 6.2.2.1 Friction and Separator Plates [25] Friction and separator plates are critical components to the clutch. They have multiple requirements, including the following:

6.2 Multi-Plate Friction Clutch 6.2.1 Introduction

• • • •

At the core of the multi-plate friction clutch design are the plates. These interleaved plates transmit the torque between the housing and the hub. This torque transmittal is created by axially clamping the plates through a hydraulic-apply, springrelease system. In this system, depicted in Fig. 6.7, pressurized hydraulic fluid is used to squeeze the plates together and thereby transmit torque through them. Upon release of the hydraulic pressure, the spring returns the piston to its disengaged position.

Providing a pleasing shift feel Transferring torque Absorbing/dissipating heat created during a shift Minimizing drag when the clutch is disengaged

Two types of friction plates are typically used in automotive transmissions: double sided, and single sided. By far, the most widely used is the double-sided design. The doublesided plate consists of a steel core plate with friction material bonded to both sides. The core plate most commonly has a spline at its ID; however, in some designs, the spline is at the OD. The splines are typically straight sided or involute. OD-splined double-sided friction plates are usually the result of the designer trying to manage lube, packaging, or possibly spline integrity. To function properly, the pack must be built up by alternating friction plates with steel separator plates

Another hydraulic-mechanical means of clutch actuation is with a mechanical apply and a hydraulic release of the clutch. The apply force is provided by a spring (typically a Belleville). This type of clutch can be considered when the duty cycle

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Friction Clutches

• Minimizing ripple—Ripple is circumferential waviness of the separator surface near the area of the splines that is induced during the blanking process. Depending on its magnitude, ripple can affect shift quality and can cause hot spotting (i.e., dark spots on the surface of the separator caused by localized heating). • Surface finish—Surface finish of a separator is a function of the surface finish of the steel used to blank the plates and the process used to deburr the plates after blanking. Typical surface finishes range from 0.1 to 0.6 micrometers. The finish can affect frictional characteristics. In general, once the deburring process is established for a specific separator/application, it should be maintained in order to not introduce variables that could affect performance. • Thickness—Factors that influence the designed thickness include axial space available, heat sink requirements, and stress on the separator splines and mating splines.

(sometimes referred to as reaction plates). During an engagement of a double-sided clutch, torque is transferred between the friction plates and the separator plates. Conversely, the single-sided friction plate consists of a core plate with friction material bonded to only one side. A singlesided clutch pack is built up by alternating OD-splined and ID-splined single-sided plates. Assembling in this fashion allows the interface between each ID- and OD-splined plate to be the torque transfer location. The steel core plate in a single-sided design functions as both a core plate and a separator plate. Some of the advantages of single-sided plates are that all of the steel in the clutch pack is available for heat sink (i.e., can absorb the heat created at the interface of the friction material and the steel interface). In a doubled-sided clutch pack, the separator plate provides the only heat sink. The steel that is used in the double-sided core plate is insulated by the friction material and therefore provides only minimal heat-sink benefits. A designer of a single-sided clutch pack can take advantage of the additional heat sink and, as a result, can create a clutch that is shorter in length but can carry an equivalent amount of torque.

The diameter of a clutch pack is usually determined by the configuration of the planetary gear set and/or dictated space available within the automatic transmission. Space, thermal, and torque capacity requirements, as well as unit loading of the friction material, determine the clutch length or number of plates in the clutch pack. In some applications, unit loading on the friction material can exceed 7 MPa. For these applications, the designer should ensure that the friction material selected can sustain the high unit loading.

Some disadvantages of the single-sided clutch pack include the thermal limitations of this design. The thermal limitations are a function of the power flux during an engagement, engagement speed, and geometry of the clutch. By design, heat enters only the core plate from the reaction side, thereby creating non-uniform thermal stresses. Unlike double-sided friction plates, single-sided plates also expose the friction material at the core plate bond line to nearly the full interface temperature. Because the friction material acts as an insulator, the double-sided plate bond line remains relatively cool. This mechanism also results in higher temperature internal to the friction material because it is heated from both sides. While the interface temperature may remain lower in the single-sided designs, additional heat exposure on the bond side can lead to an earlier than expected thermal failure of the friction material. The designer should ensure that these limitations are evaluated through a proper design verification plan. Exceeding the limits can result in a catastrophic thermal failure of the clutch (i.e., coning of the core plate, severe hot spotting, bond failure). Assembly of a single-sided clutch pack is also more complicated, in that the assembler must ensure that the plates are all oriented correctly.

The loading on the clutch splines or lugs not only must preclude shearing, but also must prevent permanent deformation of the mating spline in the cylinder or on the hub. Distress on the splines of the mating component (typically a hub) will interfere with free axial movement of the plates. This can have a negative effect on shift quality. Clearance between mating splines for manufacturing tolerances, thermal expansion, and free axial movement of the plates must be provided. This is true for both friction plates and separator plates. Spline stress is also discussed in Section 6.2.3.4, Spline Tooth Stress. When designing a clutch, both breakaway torque (holding) capacity and dynamic torque (engaging) capacity must be considered. For most friction materials and applications, breakaway and dynamic coefficients of friction will be different. Many clutch design variables can affect the torque and energy capacity of a clutch. Not all of these variables are easily adjustable because of cost, packaging, and other constraints. These variables include:

The separator plate used in double-sided designs is typically blanked from cold rolled steel. It plays a critical role in the absorption of heat during a clutch engagement and is the reaction torque member of the clutch pack. Special considerations for separator plates include the following:

• Breakaway and dynamic coefficients of friction • Piston apply force • Number of active friction surfaces 6-9

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molded or cut into the friction material. Some designs use multi-segmented friction material to provide efficient use of the friction material and to form the grooves by leaving space between the segments. Adding grooves to a friction plate design reduces the amount of area that is in contact with the separator plate and, as a result, increases the unit loading on the friction material. The designer must ensure that the unit loading does not exceed the design limits of the friction material. Analysis of the loading must consider deflections that may cause non-uniform loading and higher local pressure.

• Material properties • Effective radius of clutch • Geometry of apply, backing, friction, and separator plates • Compliance of the clutch pack • Piston radial apply point • Boundary conditions (e.g., simply supported or can­ti­ levered backing plate) • Young’s modulus of the friction material • Heat sink mass • ATF coolant flow • Ambient temperature • Interface temperature • Transmission fluid characteristics

Waved friction plates are used for two reasons: • To reduce spin loss—The slight wave in the friction plates (typically around 0.2 mm in height) helps to separate the friction plates and separator plates when the clutch is disengaged. This helps break up the oil film between the friction plates and the separator plates. It is an effective method to reduce open pack drag. • To improve shift quality—During an engagement, a slight amount of torque is created as soon as the piston starts to move forward and the waved friction plates make contact with the separators. This slight amount of torque helps to bias the rotating components in the drivetrain that are associated with upcoming shift. By the time the friction plates go flat and start to carry significant torque, the lash is taken out of the system, and the shift quality is improved.

Most of these are obvious from the torque energy equations discussed in Section 6.2.3, Clutch Design and Analysis, while compliance or spring rate of the clutch pack and load distribution can be predicted using finite element analysis. The importance of uniform clutch lining (friction material) load distribution is: • Slight torque capacity effect due to the effective radius • Ability to design higher-energy-capacity clutches by avoiding hot spots • A more compact, space-efficient design • Potential reduction in spin loss, by minimizing the friction lining through optimization of the clutch for torque and energy capacity

The drawback to waved plates is that they take up additional axial space, thus increasing piston stroke and causing application delay. The trade-offs for space versus spin loss or shift quality must be assessed at the time of design. Depending on the geometry of the friction plate and the application, grooves can be as effective as waves in reducing open pack drag.

Clutch design variables have been listed. Not all of these design variables can always be adjusted due to constraints such as package size, cost, and other considerations.

A good rule for clutch pack clearance is a minimum of 0.13 mm per friction plate facing. For example, for a clutch pack with five double-sided friction plates, the minimum clearance should be 1.3 mm (0.13 mm × 5 friction plates × 2 facings per friction plate). If pack clearances become smaller than this, there is a potential for the clutch pack to have high drag and to develop hot spots, especially at higher rotational speeds. If the clutch pack clearance is too great, shift response times can become excessive, and an abrupt shift feel may occur. Drag (spin loss) is discussed in detail in Section 6.2.4.1, Open Clutch Drag Torque in a Wet Friction System.

Grooving plays an important role in the energy capacity of a clutch. The selection of the type of grooving to be used must take into account both the cooling desired and the drag torque produced by such grooving. From a cooling perspective, adding grooves to a friction plate provides channels through which ATF lube can flow when the clutch pack is engaged. Oil flow through the pack removes heat from the interface. From an open pack parasitic drag perspective, adding grooves breaks up the laminar film of oil that exists between the friction plate and separator plates, thereby reducing the viscous drag of the clutch. Radial grooves are probably the most common design because they provide an acceptable combination of cooling and spin loss. Other groove designs can be the result of special requirements of the clutch pack (e.g., shift quality, maximum cooling) or by the equipment that is available to the friction plate manufacturer. Grooves are typically

6.2.2.2 Clutch Housing The clutch housing is the largest component of a clutch system. The main inputs concerning the housing configuration 6-10

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Friction Clutches

balance dam is incorporated into the clutch design. Typical piston forces are on the order of 5,000 to 15,000 N. Good distribution of this force across the friction plates of the clutch pack is important for long clutch life. Pistons should be designed to minimize clutch fill volume, especially when the clutch is used with the adaptive shift controls. (Note that fill volume is defined as the amount of oil behind the piston before the beginning of the piston stroke.) Stops or bumpers should be used to ensure that oil can easily work against the entire area of the piston during the initial clutch fill.

are the required torque capacity, the apply pressure available, and the rotation speeds. Clutch housings may be manufactured a number of ways. Because the manufacturing method is one of the most influential factors in the design process, it is advised that no production housing design be attempted outside a concurrent engineering environment. Some of the more common manufacturing methods are aluminum die casting, cold forming, cold reduction, flow forming, shear forming, die forming, and combinations or hybrid methods. Weight, space, geometry, strength, and cost concerns drive the decisions as to which manufacturing method is most advantageous for a particular application at any particular production volume.

Piston seals are used to create a seal between the piston bore and the piston. There are many different types of seals for pistons. They include O-ring, D-ring, rectangular, short and long loose lip, and bonded. When using a bonded piston seal, a seal groove is not required in the piston because the seal is molded onto the piston. All other designs require a seal groove. Lip seals reduce seal drag in the release direction but are not usable if they must seal in both directions. Lip seals can also add to clutch hysteresis. For dual direction sealing, D-rings are preferred. Design practices, product testing, manufacturing technology, quality control, and materials are detailed by Oshanski, Barrons, and Martek [26].

There are three sections of a housing to consider. The drum portion is the outermost part of a housing. It contains the spline for the separator plates and usually a piston seal bore. The housing hub is the innermost part of the housing. It usually contains the spline for torque transmittal to the shafting, holes for clutch lube and feed, and an inner piston seal diameter. Ball bleed valves and air bleeds may also be incorporated into the housing. The section of the housing between the drum and the housing hub is called the web. Although it is common to think of the aforementioned manufacturing processes as the only ones necessary to produce a complete housing, they in fact produce only the drum portion.

6.2.2.4 Piston Return Springs The function of the return spring(s) is to return the piston to its unloaded position upon removal of the hydraulic pressure. In this position, the clutch clearances are at a maximum. The return spring pressure must be high enough to overcome seal drag and any centrifugal induced pressure head. In some cases, the return spring(s) must also provide force that creates a minimum controllable pressure for adaptive controls. Some common return spring designs are Belleville, singlecoil, and multiple-coil spring packs. Multiple loose springs are rarely used these days because of the assembly issues. A cost/benefit analysis and the space available usually dictate the spring design for a particular application.

The clutch housing is the container of the clutch system components and provides a convenient means to handle the clutch assembly. Areas of major design in the housing consist of the piston bores, where the finish and diameters must be specified to prevent piston seal wear or failure; the length of the piston bore, which must accommodate the piston stroke; the spline for strength, deflection, and wear; the web for pressure loading and thrust; the bearing surfaces for radial and thrust loads; the snap ring groove for strength and deflection; and the drum and web for centrifugal loading. In some cases, spline stresses will require that the spline be hardened.

With a multiple-coil spring pack, the springs should be piloted on the ends to limit undesired movement. This is especially true for rotating clutches where centrifugal forces are of concern. In rotating clutches, the spring pack can be designed to radially retain the pack’s snap ring in its groove. In rare cases where rotational speeds are low, high-force return springs may be used instead of traditional ball bleeds or balance dams to offset the centrifugal effect on the oil (see Section 6.2.3.3, Centrifugal Loads).

6.2.2.3 Clutch Piston and Seals Like the housing, clutch pistons can also be manufactured by many methods. Although die cast aluminum is still very common, the one-piece bonded steel piston with molded-in seals is gaining popularity. Ball bleed valves and air bleeds may be incorporated into the piston. Areas of concern in the design are strength and deflection, where maximum travel of the piston takes into account all deflections of the system (i.e., the housing, friction material, friction plate wear allowances, piston, and seal) to ensure that the piston seal does not come out of the piston bore. In rotating clutch housings, piston design must take into account the centrifugal effects on oil pressure. These pistons also include a seal surface if a

6.2.2.5 Apply, Backing, and Cushion Plates The apply plate is typically the first plate in the clutch pack and comes in contact with the piston. The purpose of the 6-11

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the apply plate. The purpose of the cushion plate is to cushion the oncoming forces of the applying piston to avoid an abrupt initial feel of the clutch engagement. Cushion plates are typically made from high carbon spring steel that are heat set to establish the desired geometry. As discussed above, non-uniform loading from a cushion spring can also lead to hot spot formation.

apply plate is to assist in uniform load distribution from the piston through the entire clutch pack. In some designs, a separator plate will suffice as an apply plate (when there is uniform circumferential and radial contact of the piston, as an example). In other designs that may have interrupted pistons or ID/OD favored loading by the piston, or a highload waved (cushion) plate, a much thicker apply plate is required to improve the load distribution through the clutch. Tapered apply plates are also used to improve load distribution radially. Non-uniform loading will make a clutch particularly susceptible to hot spotting, even with a thick apply plate. Clutches with high-energy requirements or high-speed engagements should not use reach-through apply pistons. If non-uniform loading cannot be avoided, very heavy apply plates are called for.

There are two common designs of cushion plates: • Waved plate—A waved plate can have three or more waves evenly distributed circumferentially around the plate. Wave heights can range from 1 mm to several millimeters. (All waves in a single plate are designed to the same wave height.) Waved plates vary in thickness as well. Typically, the designer has a desired load at a given height requirement. After identifying axial space available for the waved plate, the material thickness, number of waves, and wave height can be optimized. • Belleville plate—The Belleville is different from the waved plate in that it provides contact with the apply plate at either the ID or the OD. The contact pattern is line contact until the Belleville gets compressed flat. Like the waved plate, thickness and height are determined by the amount of load that is desired. The use of a Belleville can change the load distribution of a clutch pack. Finite element analysis should be used to verify acceptable load distribution.

The backing plate or pressure plate provides the backstop for the clutch piston force. The piston clamps the clutch pack against the backing plate during clutch engagement. It is generally necessary to design for deflection rather than strength on this component to avoid non-uniform radial loading of the friction plates. Apply and backing plates are typically made from blanked cold rolled steel or powdered metal. Using powdered metal provides manufacturing solutions for designs that require a step, taper, or are too thick to blank. Powdered metal plates have some potential thermal issues in high-power-density applications. See the end of Section 6.2.4.5, Hot Spots and Other Thermal Gradient Effects, for an explanation.

Based on finite element analysis, several conclusions can be made: • It is important to match the compliance of the apply plate and backing plate to ensure parallel deflection. • The piston apply point location is an important clutch design variable. The radial location should be chosen to ensure even load distribution on the friction material. • Tapering the apply plate not only can improve the load distribution but also saves axial space. Similar results can be obtained by tapering the backing plate either independently or simultaneously with the apply plate. • Design standards can be used for initial clutch design, but the resultant clutch lining load distribution should be calculated using finite element analysis. The exact compliance of a clutch is very geometry specific and is difficult to predict by inspection. By combining load distribution information with clutch plate sliding surface speeds, localized surface heat flux and, hence, temperature distributions could be calculated. An excellent treatise of clutch pack deflections is presented by Solt [27].

Fig. 6.8  Friction clutch with a balance dam. A cushion plate, usually a Belleville or waved spring, is sometimes used in the front of a clutch pack to improve shift feel. The cushion plate is typically located between the piston and

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6.2.2.6 Snap Ring

ally resemble clutch pistons. The major difference is that they generally do not have a seal at the ID. Unlike a piston, balance dams do not move axially. Some balance dam designs also include features that retain the return spring.

A snap ring holds the backing plate in the housing. Because of the large piston apply forces (typically thousands of Newtons), snap ring deflection and retention are common problems in clutch system design. Many times, radial retention is built into the backing plate to hold the snap ring in the groove of the housing. If this is not possible, much attention must be placed on snap ring and groove deflection analysis to assure desired performance. In a rotating clutch, centrifugal forces must be included in the snap ring analysis.

6.2.2.9 Air Bleed Mechanism One problem common with stationary clutches is that they tend to act like variable accumulators. This is especially true with large stationary clutches. Because stationary clutches are normally filled from the bottom upward, they tend to trap air in the top of the piston cavity. The amount of trapped air depends on the geometry of the piston seals and on how long the clutch has been left unapplied. Because this time varies greatly, so does the amount of trapped air in a stationary clutch. To help eliminate this variability, designers have used air bleed mechanisms in stationary clutches (see Fig. 6.9). Some of the more common air bleed devices are orifices and spring-loaded check valves. Air bleed mechanisms are always placed at the top of the housing or piston because that is where the air is normally trapped in a stationary clutch. Because air bleed orifices are very small, filter elements or screens may be incorporated into them to help prevent plugging due to contamination.

It is possible to use the snap ring as the component whose thickness is varied in order to provide a specified amount of piston stroke. Part of the assembly process may include measuring the height of the clutch pack and then selecting the correct thickness snap ring based on the desired piston stroke specification. 6.2.2.7 Ball Bleed Valve In rotating clutches, centrifugal force acts on residual oil in the clutch piston cavity enough to cause a partial clutch apply even when the clutch pressure is exhausted. To prevent this, a centrifugal dump valve called a ball bleed valve is placed either in the piston or in the housing to centrifugally exhaust residual oil. To dump the maximum amount of oil, the ball bleed should be placed as near to the outer diameter of the piston cavity as possible. Although ball bleeds look like simple check valves, they are not. A change in the ball seat angle of only a few degrees can mean the difference between success and failure. Some manufacturers use reed valves oriented at specific angles instead of ball bleeds for this function. Ball bleeds can be unitized or machined into the housing. Because of quality problems and problems in reworking the valve seat, most ball bleeds used today are unitized. 6.2.2.8 Balance Dam Another way to prevent centrifugal apply in rotating clutches is to use a balance dam (see Fig. 6.8). In this arrangement, an oil dam is placed between the clutch pack and the piston so that centrifugal oil pressure on the front side of the piston balances or nearly balances the centrifugal oil pressure from residual oil on the apply side of the piston. Although this method of dealing with centrifugal apply may be more expensive than using ball bleed valves, it is becoming the preferred method of dealing with the centrifugal effects on the oil. With this method, there is no release lag from exhausting residual oil because residual oil is not exhausted. Clutch fill times are also shortened because the clutch cavity is always full. Balance dams are filled from the lube circuit and gener-

Fig. 6.9  Air bleed mechanism for stationary clutches. 6.2.2.10 Clutch Hub The two key functions of the clutch hub are to carry the torque from the friction plate splines and to distribute the oil flow across the clutch pack. The hub must have a hole pattern or slots located in a way to provide cooling flow to all friction surfaces. Clutch hubs may be manufactured a number of ways, similar to the housings. The manufacturing method is one of the most influential factors in the design process. 6-13

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6.2.3 Clutch Design and Analysis

The values for engine torque (Te) and inertia torque are then added to give the required clutch torque capacity (Tc)

6.2.3.1 Clutch Capacity [1, 28]



In many automatic transmissions, a splitting of the torque results from the planetary gearing arrangement. Thus, for each automatic transmission installation, an analysis of the gear ratio and gearing arrangement must be made to determine the amount of torque being transmitted by each clutch. In the following equations, it has been assumed that all the torque transmitted through the transmission is being transmitted through the one clutch unit.



where

(6.1)

⎛ rad ⎞ α = angular acceleration ⎜ 2 ⎟ ⎝ s ⎠ Re = effective converter ratio

where

ω1 − ω 2 t



rad ⎞ ω1 = initial angular velocity ⎛⎜ ⎝ s ⎟⎠



rad ⎞ ω2 = final angular velocity ⎛⎜ ⎝ s ⎟⎠



t

= = = = =

2

(6.5)

coefficient of friction force normal to the clutch face (N) outside radius of face in contact (m) inside radius of ‑face in contact (m) number of active interfaces

6.2.3.2 Shift Energy [25, 27, 28] Several other factors must be considered in this phase of the clutch design. The energy absorbed by the clutch must be dissipated as heat. There are two general sources of this heat. The first is the kinetic energy of the rotating masses. When considering a shift at a given speed in an automatic transmission (neglecting the effect of slip in other elements such as a fluid coupling or torque converter), the total quantity of heat absorbed as a result of the inertia factor is a constant and is not dependent on clutch torque or the engagement length. The value of this energy is a function of inertia and the square of the difference in speeds of the engaging elements.

The average angular acceleration is the change in speed during the engagement divided by the length of time for the engagement and can be expressed as α=

μ Fn Ro Ri n

(R o + R i )

When designing a clutch, both the breakaway torque (holding) capacity and the dynamic torque (engaging) capacity must be considered. For most friction materials and applications, breakaway and dynamic coefficients of friction will be different. Also note that the breakaway coefficient will vary significantly with the interface temperature in the clutch. Identifying a realistic interface temperature at the time of maximum holding torque requirements can be important to avoid over-design of a clutch.

Ti = torque resulting from inertia (N . m) I = moment of inertia for the rotating masses



Tc = µ ⋅ Fn ⋅ n ⋅



(kg . m2)

(6.4)

It can be shown that the average radius can be substituted for the mean radius with little error. If the average radius is used, the formula simplifies to

where

2 ⎛ R 3 − R 3i ⎞ Tc = µ ⋅ Fn ⋅ n ⋅ ⋅ ⎜ o2 3 ⎝ R o − R i2 ⎟⎠



The torque resulting from the inertia of the effective rotating masses of the engine and the transmission is determined by the formula Ti =(I . α) . Re

(6.3)

This required torque capacity can also be expressed as a function of clutch specifications and is calculated using

To calculate the torque capacity of a clutch used for dynamic engagements, engine torque, converter torque multiplication, and inertia torque must be considered. The engine torque may be obtained from engine performance data. The engine torque is usually either increasing or decreasing through the speed range traversed during a shift; therefore, an average value of engine torque is selected. This value must be multiplied by the effective converter ratio to obtain input torque to the clutch.



Tc = Te + Ti

(6.2)

The second source of heat results from the engine power, which, although not constant during the shift, is continuous and therefore is dependent on time. The length of engagement by necessity becomes a compromise between a short, positive shift with the minimum total energy absorption, and

= shift time (s, typically 0.4 to 1.0 seconds)

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a very smooth, stretched-out shift where the heat resulting from engine input becomes an almost insurmountable problem. Although a short shift requires a minimum total energy absorption by the clutch, it is possible to fail the unit with an extremely high rate of energy absorption. One means of containing the problem of heat generation while still providing a very smooth shift is through torque management. This approach is discussed in Chapter 8.

is to have a self-compensating system, such as that described in the section on balance dams.

The kinetic energy that is converted into heat energy during the shift can be computed using the average value of torque [27]. This “average” energy is given as



E=

where



E = Tavg = ω1 =



ω2

=



t

=

1 ⋅ Tavg ⋅ ( ω1 − ω 2 ) ⋅ t 2

If design constraints disallow this option, the force due to the centrifugally induced pressure must be determined, and the piston return spring must be designed to compensate for this load. The pressure generated by centrifugal acceleration (see Fig. 6.10) is given as [30] p=

ρ ⋅ ω2 ⋅ ( r 2 − r02 ) 2

(6.7)

(6.6)

the kinetic energy converted to heat during the ratio change (N . m) the average torque on the clutch during the ratio change (N . m) the slip speed across the clutch at the begin⎛ rad ⎞ ning of the shift ⎜ ⎝ s ⎟⎠ the slip speed across the clutch at the end of the shift ( rad ; note that ω2 = 0) s the time of the shift event (s)

Fig. 6.10  Dimensions used in the computation of the centrifugally induced pressure head. where

Note that this equation assumes the slip speed across the clutch changes linearly during the event.



“Friction-Clutch Transmissions,” by Z.J. Jania, is an excellent guide for basic design and analysis of thermal problems in friction clutch design [29]. Thermal issues are also discussed in more detail in Section 6.2.4.2, Thermal Considerations in a Wet Friction System. Final design is still an inexact science because of the many variables during an engagement cycle. In fact, every value that determines the required torque capacity of a clutch is a variable, except the number of faces in contact. The values for coefficient of friction vary with speed, unit loading, temperature, and fluid. The axial force on the plates is not a constant, because of the planned schedule of pressure application during the engagement. Even the effective inside and outside radii of the friction contact surface may vary as a function of clutch compliance at various apply pressures.



p = the centrifugally induced pressure (Pa) ⎛ kg ⎞ ρ = the mass density of the fluid ⎜ 3 ⎟ ⎝m ⎠ rad ⎞ ω = the angular velocity of the clutch system ⎛⎜ ⎝ s ⎟⎠ r0 = the minimum radius at which the fluid is con strained to rotate with the clutch (m) r = the radius at which we desire the computed pressure (m)

We can note from this equation that the pressure will vary according to the distance r from the center of rotation, increasing with increasing r. This pressure acts on the piston, tending to close the clutch pack. Our next step is to compute the resulting force due to this pressure. The force dF acting on a small area of the piston dA is given as

6.2.3.3 Centrifugal Loads



As mentioned in Section 6.2.2.8, Balance Dam, centrifugal forces act upon the oil in the clutch as well as on the clutch components themselves. When this occurs, the centrifugally induced hydraulic pressure must be dealt with. One option

dF = p ⋅ dA = p ⋅ 2 ⋅ π ⋅ r ⋅ dr

(6.8)

Substituting our expression for pressure into Eq. 6.8, and integrating over the area of the piston, we have

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teeth is usually not considered because it is typically low in magnitude. Many companies have established spline stress calculation methods and guidelines based on their experience. Readers are referred to their company guidelines and to the paper by Finkin [31].

Ro



F = π ⋅ ρ ⋅ ω 2 ⋅ ∫ r ⋅ ( r 2 − r02 ) dr Ri

=



(6.9)

π ⋅ ρ ⋅ ω2 ⋅ ⎡⎣R o4 − 2 ⋅ r02 ⋅ ( R o2 − R i2 ) − R i4 ⎤⎦ 4

where Ri is the inner radius of the piston and Ro is the outer radius of the piston as shown in Fig. 6.10. With Eq. 6.9, the additional piston return spring load that is required to compensate for centrifugal loading of the oil can be computed.

6.2.4 Friction System Design Considerations The wet friction system—consisting of the friction plates, the reaction surfaces including the separators and end plates, and the fluid—has inherent considerations that must be addressed in addition to the more basic design elements such as the torque capacity and unit loading. These considerations include parasitic energy loss in the open clutches, thermal degradation of the friction material and fluid, and hot spotting of the separator plates.

6.2.3.4 Spline Tooth Stress Multiple-plate packs, as used in brakes, clutches, and automatic transmissions, consist of annular discs in an alternating array. One set is internally splined, and the other set is externally splined. The choice of core plate or separator plate thickness is often based on what experience has shown will not lead to failure of the teeth on the plate periphery. In other words, the apparent state of stress in the teeth often serves as the criterion for determining plate thickness.

6.2.4.1 Open Clutch Drag Torque in a Wet Friction System While a wet clutch pack is open and has relative rotation across its elements, a parasitic torque is created that results in a loss of efficiency in the transmission. One study has shown that the losses in the open clutch packs can be as much as one-third of the total losses in a modern automatic transmission [32]. This parasitic energy loss, rejected as heat from the transmission, has an impact on the fuel economy of the vehicle.

In general, the designer is primarily concerned with contact stress caused by the normal loading of the mating splines. Contact stress can be determined by SC =



T N⋅z ⋅t ⋅L ⋅r

(6.10)

The shear stress on the teeth is also a consideration and can be determined from where



SS =

T N⋅z ⋅t ⋅w ⋅r

6.2.4.1.1 The Drag Torque Curve

The parasitic torque losses in open wet clutches are caused by laminar shear of the fluid in the annular space between the friction facings and the reaction surfaces. The drag torque as a function of speed has a characteristic curve that increases linearly with speed in Region I of the speed continuum as shown in Fig. 6.11. In Region II, the torque drops off from the linear rise and begins to descend. In Region III, the torque drops, and in Region IV, the torque flattens out at a negligible level.

(6.11)

SC = contact stress (Pa) SS = shear stress (Pa) T = torque into the clutch SC (N . m) z = number of spline teeth per plate t = tooth thickness (m) L = tooth contact length (m). Note that L is the difference between the minor diameter of the internal spline and the major diameter of the external spline less the tip radii on the teeth. r = radius at the center point of tooth contact (m) N = number of plates in the clutch pack w = tooth width at radius r (m)

These calculations are very basic. The contact stress calculations assume that there is 100% tooth contact in both the radial and axial directions. The calculation for bending stress also assumes 100% tooth contact. Bending stress of spline

Fig. 6.11  Typical drag torque curve shape with regions identified. 6-16

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The linear torque rise in Region I of the drag curve is caused by the laminar shear of the oil in the gap between the friction plates and the separators. At the low speeds of Region I, that gap is filled with a film of oil. The drag torque can be expressed by Eq. 6.12. The formula assumes that the fluid is Newtonian and that the laminar velocity is in the circumferential direction:

is much thicker than at the land areas, the centrifugal forces overcome the shear forces at a lower speed and begin to drain fluid from the interface. By draining the fluid from the groove, there is no fluid to feed the laminar film in the land area, and the film area decreases. As speed increases into Regions II and III, part of the groove is drained of fluid; thus, part of the land area is no longer fed with fluid. The laminar film is breaking up. At high speed, Region IV, the laminar film is completely gone. In experimental work by Kitabayashi, Li, and Hiraki, it has been shown that centrifugal forces drain fluid from the grooves, causing part of the laminar film to begin to break up where no fluid remains in the groove to feed and maintain the laminar film on the downstream side of the groove [33].

2π ro ⎛ dυ ⎞ Tloss = N ⋅ ∫ τ ⋅ r ⋅ dA = N ⋅ ∫ ∫ ⎜− µ ⋅ θ ⎟ ⋅ r dr dθ A 0 ri ⎝ dz ⎠ ro ω ⋅ r N ⋅ π⋅ ω ⋅ µ 4 ⋅ r 2dr = ⋅ ( ro − ri4 ) ≈ 2 ⋅ N ⋅ π ⋅µ ⋅ ∫ ri 2⋅h h (6.12) where



M = number of facings τ = viscous torque per unit area



⎛ kg ⎞ μ = fluid viscosity ⎜ ⎝ ( m ⋅ s ) ⎟⎠



h = oil film thickness (m)



m υθ = fluid angular shear velocity ⎛⎜ ⎞⎟ ⎝ s⎠



rad ⎞ ω = relative slip rotational speed ⎛⎜ ⎝ s ⎟⎠



ro = friction facing outer radius (m) ri = friction facing inner radius (m)

Fig. 6.12  Film break-up at grooves from centrifugal oil clearing.

Equation 6.12 shows that torque in this linear region, Region I, 4 4 is a function of the radial width of the facings ( ro − ri ). The drag torque is also a function of the viscosity of the fluid, which is an exponential function of temperature, dropping rapidly as temperature rises. Drag torque is proportional to the number of facings and the rotating speed, and is inversely proportional to the thickness of the fluid film. The average rotational speed of the fluid being sheared in the interface is the average of the friction plate speed and the separator speed.

6.2.4.1.2 Design Variables and Drag Torque

Experimental work has demonstrated how various design variables, including those in Eq. 6.12, affect the open pack drag behavior. By understanding the basic mechanisms of the drag torque curve noted above, the experimental results can be better understood. 6.2.4.1.2.1 Grooves

At the low speeds of Region I, the tangential shear of the fluid film is strong relative to the centrifugal forces acting on the fluid. As a result, the film remains intact with the fluid supplied to the ID of the friction plates being enough to replenish the fluid that is being moved radially by the centrifugal forces.

The addition of grooves to friction facings reduces the drag torque. Figure 6.13 shows typical effects from increasing the number of grooves (reducing the land width between grooves). While the slope of the drag torque curve remains essentially unchanged in Region I, the transition to Region II moves down the drag curve as the number of grooves increases, and the tail of the drag curve, Region IV, begins at a lower speed. (Actually, the Region I slope is reduced a bit because of the decrease in the total land area as the number of grooves increases.)

As the speed increases into Region II of the drag curve, the laminar film begins to break up (Fig. 6.12). As a result, the laminar shear area decreases, and the drag torque begins to fall away from the linear rise with speed that is represented by Eq. 6.12. Because the oil film thickness in the groove area 6-17

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of temperature, significant effects are seen on the drag curve. Unlike the feed rate and grooving effects that have a dominant effect on clearing the oil from the interface, temperature primarily affects the fluid’s resistance to shear. This results in a set of torque curves that show substantially different slopes in the linear, Region I, portion of the torque curve, but the Region II torque peaks occur at the same speed at all temperatures (Fig. 6.15).

Fig. 6.13  Effect from number of grooves on drag torque. 6.2.4.1.2.2 Waved Friction Plates

Adding waves to the friction plates has an effect similar to grooving the plates. The waves break up the laminar film, allowing the oil to clear the interface through centrifugal force. The taller the wave height, the earlier the transition into the Region II oil film. To get the benefit of the waves, additional open pack clearance is required to maintain clearance over the top of the waves. This results in additional length in the apply piston stroke, which can have a negative impact on the control of the clutch engagement.

Fig. 6.14  Effect of oil feed rate on drag torque.

6.2.4.1.2.3 Oil Feed Rate

The oil feed rate to the clutch pack has a significant impact on the point at which the transition from Region I to Region II occurs. Similar to increasing the number of grooves, reducing the feed rate of the oil to the clutch pack (conventional, non-pressurized center feed) results in the transition to Region II occurring at a lower speed (Fig. 6.14). As the feed rate decreases, there is less flow into the grooves, and the centrifugal force acting on the fluid in the grooves begins to empty the groove faster than it is being fed. Increasing the oil flow, of course, increases the maximum drag, but only to a point. As the oil flow to the rotating clutch increases, the transition to the Region II fall-off in torque moves up the linear part of the curve. At some increased flow rate, however, a limit will be reached where additional feed to the clutch ID cannot flow through the clutch and will be dumped without passing into the clutch interface.

Fig. 6.15  Effects of lube oil temperature on drag. 6.2.4.1.2.5 Radial Section

Reducing the radial width of the friction facing reduces the slope of the Region I drag torque linearly with the reduction in area (Fig. 6.16) [33]. The centrifugal forces remain nominally the same, resulting in the Region II peak torque occurring at the same speed.

6.2.4.1.2.4 Oil Temperature

As shown in Eq. 6.12, there is a viscosity effect on the drag torque. Because viscosity is close to an exponential function

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friction plates comes from having the grooves rotating. The average rotating velocity of the oil in the grooves is higher than the average velocity of the laminar shear oil in the land area. This causes the centrifugal force that clears oil out of the interface to be higher in the grooves and precipitates the earlier transition to Region II.

Fig. 6.16  Effect of radial section on drag curve. When designing a clutch, reducing the radial section can be used to reduce the drag torque, but the facing unit loading will increase and, if the separator radial section is also reduced, the heat sink available during an engagement is reduced. The reduced heat sink will cause the interface temperature to rise higher during an engagement. All of these factors must be balanced in the design.

Fig. 6.17  Drag torque of rotating separators and of poorly drained housing compared to a normal grounded clutch. When both the friction plates and separators are rotating in the same direction, the entire oil film is at a higher rotational speed. Because centrifugal force goes up by the square of the rotational speed, this results in a substantial reduction in the peak torque by causing the fluid to clear the interface at a lower relative speed.

6.2.4.1.2.6 Pack Clearance

Pack clearance has an impact on drag torque only if it is too small. Observations of a friction pack running in the open pack mode have shown that the pack clearance may not be fully used until the speed gets into Region IV. There is a Bernoulli effect between the friction facing and the separator plate in which the laminar shear film pressure drops with increasing velocity. That effect, similar to the phenomenon that creates lift on an airplane wing, pulls the rotating elements together. This leaves the rest of the total pack clearance as a gap between the apply plate and the piston. Analysis of the Region I slope in drag tests and back solving for the equivalent film thickness (h in Eq. 6.12) has shown the film thickness to be about 0.05 mm thick at 110°C and about 0.10 mm thick at 40°C. While there is a large amount of scatter in the data, these numbers should serve to estimate the drag torque in Region I and to be a guide for setting minimum open pack clearance.

6.2.4.1.3 Other Design and Test Issues

Other effects that come into play can either influence the drag results or have other impact on the friction system. 6.2.4.1.3.1 Housing Drainage

Inadequate provision for draining the oil after it passes through the clutch pack can result in elevated drag torque. If an annulus of oil remains trapped in the interface, drag torque curves may continue to rise past Region II (Fig. 6.17). This can be a particular problem in grounded clutch packs in which the outer housing is not rotating and, therefore, is not centrifugally expelling the oil from the clutch assembly. 6.2.4.1.3.2 Heat Transfer

6.2.4.1.2.7 Hub and Housing Rotation

As the clutch slip speed transitions into Region IV of the drag curve, there is no longer a laminar film of oil in contact with the separator plates. When that occurs, the heat transfer coefficient will drop by as much as a factor of ten. In a high-energy situation, this can mean that the separators may not return to sump temperature before the next energy event occurs. As a result, the temperature can

All of the above observations are based on the friction plates rotating and the separators being stationary. When the opposite is the case—friction plates stationary and the separators rotating—the Region II torque tends to occur at a slightly higher speed, and the fall-off in torque, the transition to Region III, is delayed (Fig. 6.17). The advantage for rotating

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ations such as torque capacity, friction material net facing pressure, and the temperature-time profile.

ratchet up with subsequent shifts resulting in higher friction material temperatures and premature failure of the friction system (Fig. 6.18).

6.2.4.1.3.4 Garage Shift Clunk

Neutral-to-drive engagements can result in an audible “clunk” from the transmission. This occurs when clutch drag causes components in the transmission to rotate while in neutral. If, when the clutches engage, there is a torque reversal as gear lash is taken up, clunk can occur. An analysis of the reflected balance of drag torques can be made to evaluate ways to correct the problem. Because any clutch is likely to be in the Region I mode under idle conditions, a reasonable estimate of the drag torque can be made using Eq. 6.12 and an analysis of the reflected torques through the gear train. 6.2.4.1.3.5 Idle Ticking

Another issue that is related to drag is idle ticking or rattle coming from the transmission. The issue occurs primarily in transmissions in which a clutch, grounded to the transmission case, has a significant arc of spline teeth missing, often because of the opening at the bottom of the transmission housing to the sump. Various factors can result in a laminar shear film that is not a full arc of the friction plate, particularly at low speeds and immediately after engine start-up. The resultant forces acting on the separator plates are no longer pure torsional load acting about the geometric center of the separator. As the asymmetric load from this shear force rotates, it can cause a rocking motion about the spline teeth at the end of the gap, causing the separator to knock. As speed increases, the noise goes away either because the laminar film becomes more symmetric or because torsional load increases enough to keep the spline teeth locked.

Fig. 6.18  High-speed cooling effects of Region IV drag. This temperature ratcheting can be a particular problem in component or transmission dynamometer testing where the frequency of engagements may be high. Elevated temperatures are one of the primary causes for clutch failures. Accelerating durability testing by keeping the time between shifts short can result in a misleading life result. Either the test cycle time can be increased, or a low-speed rotation can be added to the test cycle to accelerate the cooling between engagement events. Durability testing should mimic the elevated temperatures and exposure times of a service situation or, at least, the differences between the environments must be understood when analyzing the results of bench or dyno durability testing.

The problem can be minimized either by keeping the circumferential spline fit tighter (less backlash) or by providing a closer major or minor diameter fit. It can also be helped either by increasing the drag (not a generally good direction to go) or by minimizing the drag with a more efficient groove pattern.

6.2.4.1.3.3 Transmission Efficiency

When evaluating a clutch design in light of the desire to improve efficiency of the transmission, several issues should be included in the analysis. In terms of fuel efficiency, the primary concern is parasitic energy consumption within the normal operating conditions. Energy consumption is the product of torque, speed, and time. The analysis of the clutch within the context of the fuel efficiency must be viewed in this light. Clutches that are open in the higher gears are usually the main concern because of the time spent under those conditions. Grounded clutches are of more concern than clutches in which both elements are rotating in the same direction because the grounded clutches have less centrifugal clearing of the interface oil.

6.2.4.2 Thermal Considerations in a Wet Friction System High temperatures are one of the primary causes of wet friction system deterioration and failure. With each shift, the clutch friction system absorbs energy generated by the slipping of the clutch during the engagement. Nearly all of the shift energy is stored in the separator plates during the shift event as heat and is then removed from the friction system by the oil and through conduction through the separator spline teeth. Thus, there are essentially three elements to the

A balance must be struck among the design alternatives available to reduce the drag in the clutches and other consider6-20

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In a double-sided friction plate, the insulating property of the friction material causes a large temperature gradient across the friction material, preventing the mass of the core plate steel from acting as a significant heat sink. However, these same insulating properties keep the bond-line temperature between the friction material and the core plate at a temperature far below the interface temperature.

friction system energy balance: energy-in, energy-stored, and energy-out. 6.2.4.2.1 Energy-In

Energy-in occurs primarily during the engagement of an ongoing clutch during a shift. The total energy of the shift is the integrated product of the slip speed and the clutch torque over time. The energy input rate (power) during a shift typically is very high relative to the energy removal rate. As a result, the separator plates absorb 90% or more of the energy as heat [34].

Single-sided friction plates are used as a way to package more active heat sink in the same axial space or to put the same active heat sink into less axial space. In the case of single-sided friction plates, the same basic equation for peak interface temperature applies, except that the active steel heat sink, which is usually thinner than a separator plate, has energy input from only one facing. Therefore, the equation for a single-sided plate temperature rise becomes

6.2.4.2.2 Energy-Stored

A good first-level approximation of the peak interface temperature for the clutch can be made if 90% of the energy of the shift goes into the separator plates. Therefore, the interface temperature rise for double-sided friction plates can be estimated by ΔTds = 0.90 ⋅



2 ⋅ E Shift N ⋅ M ⋅ cs





ΔTds = EShift = N = M = cs =

E Shift N ⋅ M ⋅ cs

(6.14)

where ΔTss is the bulk temperature rise in the steel of a singlesided plate.

(6.13)

In a single-sided friction plate, the friction material sees, nominally, the same high interface temperature on both sides of the friction material. This results in bond-line temperatures at the full interface temperature and in higher temperatures in the single-sided plate friction material because it is being heated from both sides.

where

ΔTss = 0.90 ⋅

bulk temperature rise in the separators of a double-sided pack (°C) total energy of the shift (J) number of friction surfaces mass of one separator (kg) ⎛ ⎞ J specific heat of the separator ⎜ ⎟ ⎝ ( kg ⋅ °C ) ⎠

6.2.4.2.3 Energy-Out

Energy is removed from the friction system primarily by the oil that flows past the separators and by conduction to the hub and housings through the spline teeth.

The average specific heat of a low carbon steel increases significantly with temperature. A reasonable value to use 520 J is . That is the average specific heat of a low car( kg ⋅ °C ) bon steel (SAE1025) between the temperature of 100°C and 300°C.

While the clutch is applied, there is cooling oil flowing to the clutch. If the clutch is rotating as an assembly while locked, cooling flow is being centrifugally forced through the grooves in the friction facings, carrying heat away from the hot surfaces. In the case of a grounded clutch, the oil feed is not being centrifugally driven through the grooves, and most of the circumference of the clutch does not see direct cooling by the oil. In a grounded clutch, a high percentage of the heat removal will be by conduction through the spline teeth, and the cooling rate will typically be lower than for the rotating clutch assembly.

In the typical shifting clutch, the total mass of the separator should be used, including the spline teeth and any unswept area of steel that is outside the contact diameters of the friction facings. The thermal conductivity of the steel is high enough to rapidly carry the heat onto these areas. Temperature in the end plate or apply plate is not generally analyzed. These reaction surfaces do absorb energy but are receiving input energy from only one side and often have more thermal mass than the separators. The insulating properties of the friction facings minimize the axial flow of heat from the rest of the pack into these surfaces.

The cooling rate will be affected by the temperature differential and by the oil flow rate. Interestingly, the cooling rate does not double when the cooling oil flow rate doubles. Without increasing the volume of the grooves, increasing the flow rate decreases the time that the oil is in the hot zone. This results in less temperature rise in the oil as it flows, resulting

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in a much smaller increase in the cooling rate than might first be expected.

viscous shear, the heat of vaporization of the fluid, compression of the porous friction material and the flow of fluid through the friction material, non-uniform contact pressure in the radial direction, the effects of various groove patterns, and others.

During open pack operation, the cooling rate generated by the oil flow increases dramatically. The laminar film of oil that forms in the rotating interface creates a film of fluid in intimate contact with the entire swept area. That film of oil has a significant time in the interface to absorb heat, resulting in rapid cooling. However, as mentioned in the previous section on open pack drag, at higher slip speeds where the drag torque drops (Region IV of the drag torque versus speed curve), so does the cooling rate. The cooling rate will drop by an order of magnitude (Fig. 6.18). This impact on the cooling rate needs to be considered, particularly in the design of test procedures, where the frequency of engagements is often high. Ignoring this behavior can result in test procedures that are far more severe than realized, resulting in over-designed clutch systems. 6.2.4.3 Thermal Modeling High temperature is a major factor that limits the life of a wet friction system. Thermal failure of the friction material and of the oil is a function of both temperature and the time at temperature (discussed more thoroughly in the next section). An analysis of the clutch interface temperature is an important step in evaluating the durability of the friction system. Equation 6.13 gives a good first-cut analysis of the temperature. If the clutch will not be subjected to high-energy shifts that are closely spaced in time and the calculated bulk temperature by Eq. 6.13 is below about 230°C, clutch thermal durability should not be an issue. If, however, the calculated bulk temperature is higher or there are expected to be a series of energy events closely spaced in time, then a more thorough temperature analysis is called for. Closely spaced shifts will cause the temperature to ratchet up if the time between shifts is insufficient to return the friction system to the sump oil temperature. Figure 6.19 shows repeated shift events with time between shifts to get the temperature back nearly to sump, while Fig. 6.20 shows the effect of closely spaced shifts causing temperature ratcheting.

Fig. 6.20  Interface temperature with inadequate cooling time.

The temperature plots in Figs. 6.19 and 6.20 were created using a detailed finite differences model of the energy balance in a wet friction system [34]. The model uses experimentally determined heat transfer coefficients, evaluates the energy balance in each phase of the duty cycle, and can evaluate the effects of multiple engagements. The model includes a number of secondary factors that include the heating from

Figures 6.19 and 6.20 show the interface temperature at the radial center of the separator plate and of the friction facing, as well as the temperature of the core plate. The interface temperature facing and separator are the same while the clutch is applied. When the pack opens, the friction material temperature drops much more quickly than the separator temperature because of the low thermal mass of the friction material. The figures also show how the insulating property

Fig. 6.19  Interface temperature with adequate cooling time.

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The damage that occurs in a friction system from the temperature of high-energy shifts will be cumulative. Each excursion to high temperatures activates the damage mechanism and adds damage to that already done.

of the friction material moderates the rate at which the core plate temperature changes. 6.2.4.4 Thermal Degradation

By reducing the peak interface temperatures and by reducing the time above the activation temperature, the damage to the friction material is reduced and the useful life of the friction system can be increased. Reducing the interface temperature will also reduce the breakdown of the chemical constituents of the transmission fluid. Breakdown of the fluid chemistry can change the friction characteristics of the fluid (see Chapter 12, ATF and Driveline Fluids). Breakdown of the fluid can also create an ash that leads to glazing of the friction material surface, resulting in deterioration of the friction characteristics.

High temperatures will cause degradation and failure of wet friction systems [35–37]. Theoretical and experimental studies have resulted in a model that calculates the degradation of the friction material using the temperature history near the friction interface [38]. In this study, it was shown that for the least temperature-resistant component in the friction material studied, cellulose, the weight loss is a zeroth order ⎛ dW ⎞ = k ⋅ W 0 ⎟ . In other words, at a constant reaction ⎜ − ⎝ dt ⎠ temperature, the fraction of the original weight of the cellulose is reduced in a linear relationship to time and the reaction rate, or where

k⋅t W = 1− W0 W0

Applying this analysis to an application demonstrates how increasing the heat sink in a shifting system can increase the predicted friction material life. Figures 6.21 and 6.22 show the temperature versus time profile of the same duty cycle run with two different separator thicknesses. The temperature rise with 3.0-mm thick separators is less than with the original 2.0-mm separator plates because of the increased heat sink in the separator mass. The analysis is for a 1–2 upshift followed by a 2–3 upshift. The primary energy input comes with the 1–2 shift, but there is a significant, albeit smaller, energy input in the 2–3 synchronous shift as the clutch disengages. In the analysis, the 1–2, 2–3 shift sequence is repeated a second time before the friction system returns to the sump temperature. The predicted life increases from 2,000 of these stacked events to 10,500 by increasing the heat sink to reduce maximum temperatures.

(6.15)

W = remaining concentration of cellulose fiber (weight per unit volume) Wo = original concentration of cellulose fiber (weight per unit volume) t = time duration at isothermal condition k = rate constant for a given temperature

The rate constant is an exponential function of the temperature, increasing as the temperature rises. It is given by the Arrhenius equation as E ⎞ ⎛ k = k 0 ⋅ exp ⎜ − ⎝ R ⋅ T ⎟⎠



(6.16)

where

k0 = reaction rate constant E = activation energy of reaction (J) ⎛ J ⎞ R = Boltzmann constant ⎜ ⎟ ⎝ °K ⎠ T = temperature (°K)

If temperature (T) in Eq. 6.16 is not constant, the differential equation must be solved numerically. In essence, this means that up to the activation temperature, very little breakdown of the material is occurring. As the temperature rises above the activation temperature, the breakdown rate increases exponentially.

Fig. 6.21  2,000 full duty cycles life is predicted with 2.0mm separators.

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cally that the pressure variations that trigger TEI events can be very small, on the order of 0.1 kPa in a nominal system pressure of 3.4 kPa [39].

Fig. 6.23  Focal hot spots on a separator plate.

Fig. 6.22  10,500 full duty cycles life is predicted with 3.0mm separators.

A simplified explanation of the instability is illustrated in Fig. 6.24. An initial perturbation in the pressure distribution results in a higher local temperature (Fig 6.24(a)). The higher local temperature causes the perturbation to expand, increasing the local pressure both by the local expansion of the surface and by bending the separator plate (Fig. 6.24(b)). Both mechanisms increase the local pressure, and the local pressure increase will increase the local heat input. In a mild case of hot spotting, a focal hot spot stain will appear on the surface of the separator (Fig. 6.24(c)).

6.2.4.5 Hot Spots and Other Thermal Gradient Effects Hot spots are one of the more common manifestations of the issues that are related to thermal gradients in a wet clutch system. They will appear as dark spots on the surface of the steel plates. During the slip phase of a clutch engagement, large specific power conditions exist. This means a great deal of energy per unit area is being absorbed, primarily to the steel of the separators and end reaction plates, over a short period of time. Although steel has a very good thermal diffusivity, large thermal gradients will exist. The thermal gradients create stresses in the steel elements caused by thermal expansion. When the thermal stresses remain within the elastic range of the steel, everything returns to normal once the thermal gradients dissipate. If the thermal stresses exceed the local yield limit of the steel, keeping in mind that the yield strength is reduced at elevated temperatures, a permanent strain results. The deformed parts usually result in progressive damage and failure of the friction system. Focal hot spots are one of the more common forms of thermal stress failure modes (Fig. 6.23). Focal hot spots are a result of thermoelastic instability (TEI) that is triggered by an anomaly in the pressure distribution in a slipping clutch. The thermal energy that goes into any spot, i, on the separator plates, Qi, is a product of the coefficient of friction µ, the velocity V, and the local pressure pi:

Qi = μ . V . pi

Fig. 6.24  Hot spot initiation and growth. (Steps (a), (b), and (c) are explained in the text.) It has been demonstrated analytically and experimentally that the TEI can result in an anti-symmetric distribution of hot spots on either side of a thin element such as a separator plate or a brake disk [40]. The separator plate will form a multi-waved sinusoidal form around the circumference, resulting in focal hot spots at the peaks on both sides of the separator (Fig. 6.25). The hot spots will be out of phase from side to side. It has also been shown that the waves will be complementary from separator to separator through the

(6.17)

As can be seen in Eq. 6.17, variations in the local pressure will generate variations in the heat input to the separator. It has been demonstrated both experimentally and analyti6-24

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a shifting clutch. An interesting summary of earlier work on thermal deformations can be found in a 1980 paper by Burton [43].

clutch pack. That is, the peaks in the waves on either side of a friction plate will have peaks that squeeze the friction plate at the same spots. This symmetry imposes no bending on the friction plate during the TEI event.

Thermal gradients are also involved in several other types of damage. Brittle materials with low ultimate tensile strength such as some cast iron and sintered materials can develop heat checking from the same thermal gradient effects that were described above. Thermal gradients cause the material to yield in compression in the hotter areas while the thermal gradient exists. When the gradient dissipates, the resultant tensile stress exceeds the ultimate strength of the material, and local fractures form near the surface. This heat checking is fairly common in vehicle brake drums and disks. It occurs less frequently in transmission systems but can be seen occasionally in sintered apply plates or reaction plates in clutches.

If the growth of the hot spot becomes great enough, thermoplastic yielding will occur in the area of the hot spots. This condition is referred to as thermoplastic instability (TPI). In TPI, material in the hot spot yields in compression because of the restraining force of the cooler surrounding material. When the temperature gradient dissipates, the compressively yielded material shrinks, reversing the bend in the hot spot area. On a subsequent engagement, the new high spot is on the opposite side of the separator. This initiates a new set of hot spots aligned with the originals but on the opposite side of the separator and results in the appearance of symmetric hot spots. Thermoplastic instability events will usually result in the displacement of material on the separator surface. These displacements may appear as smeared surface material or as a small dimple in the middle of the hot spot where material may have been removed. The permanent distortions associated with TPI events can trigger additional hot spotting and will typically create secondary damage, often the result of diminished open pack clearance. Thermoelastic events, on the other hand, do not tend to be progressive or create secondary damage to the system.

Banding hot spots, in which a circumferential dark band appears near the radial center of the reaction plates, have also been observed and analyzed [44]. Under most operating conditions, the banding form of hot spots occurs at a higher critical speed than focal hot spots, making the focal hot spots more common. Both analytical and experimental work have demonstrated that the critical speed for hot spots can be increased by using more resilient friction material and thinner separator plates. Resiliency in the friction material can be increased in the design and processing of the friction material. Making the friction material thicker can also increase the resulting resiliency. It has also been shown experimentally that formulation of the additive package used in automatic transmission fluids can have an impact on the formation of hot spots [15]. In that study, certain formulations of anti-wear and extreme pressure additives were shown to increase the susceptibility to the formation of hot spots. These additives become surface active at high temperatures and are believed to increase the coefficient of friction as the hot spot begins to form. It can be seen, referring back to Eq. 6.16, that a higher local µ will also increase the heat generation that causes the growth of a hot spot.

Fig. 6.25  Anti-symmetric formation of hot spots, showing the waving of the separator and separation between the separator and friction plate. In addition to the papers already cited, other papers exist that have developed the mathematical analysis of hot spots for two-sided planes and specifically for applications such as disk brakes and friction plates [41, 42]. These papers have demonstrated that there is a series of critical speeds associated with integral numbers of waves forming around the circumference of a disk between two other disks. Many of the analyses apply to situations with a highly conductive disk between two less conductive plates. The lowest speed in which hot spots will form and grow is calculated for various integer numbers of waves. The lowest speed for the series of wavelengths is identified as the critical speed. Experimental work by Zagrodzki and Truncone [39] has demonstrated the ability to predict the speed and number of hot spots that will form in a transient speed condition as is seen in

The coning seen primarily on plates that are heated only from one side, such as single-sided friction plates and the end reaction surfaces in a double-sided pack, also result from the same basic mechanism. Cone-shaped distortions will always be concave toward the hot side of the plate after the thermal gradients dissipate, again because of the yielding in compression and resultant surface tensile stress on temperature normalization.

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Design Practices: Passenger Car Automatic Transmissions

lection, and reporting are all done in the same manner for each individual test. By using these methods, one can build a database of performance characteristics that can be readily compared. These data can be used to improve the initial selection of a friction system for an application, reducing the time to market.

One other set of conditions has been seen, related to thermal gradients. In a few applications, there are reaction plates (i.e., separator or end plates) in which a significant amount of the radial section may be located inside or outside the friction facing swept area. Under these situations, the thermal gradient in the radial direction can be large. When the friction surface is near the OD, the outer ring gets hot and yields in compression during an engagement. The hot area is restrained from radial growth by the cooler ID area and yields in the circumferential direction. When the thermal gradient is gone, the outer ring shrinks and creates a coned plate. Unlike coning from a single-sided application of heat, the coned plate from a shrunken outer ring tends to be bistable. The inner portion can be pushed through the cone and will cone equally well pushed in or out, similar to the bottom of an old-fashioned oil can. When the friction surface is at the ID, the ID yields in compression, restrained by the cooler outer diameter. The ID shrinks when the temperature normalizes and the disk becomes waved similar to a potato chip. Either failure mode will remove clearance during open pack running and has the potential to thermally destroy the friction material.

6.2.5.1 SAE #2 Inertia Stop Test Machine The SAE #2 style inertia stop test machine, described in SAE J286, SAE #2 Clutch Friction Test Machine Guidelines, uses a rotating inertia wheel mounted to one end of an electric motor shaft and a test head mounted to the other end (Fig. 6.26). Interchangeable inertia weights are used to allow a choice of test conditions. Within the test head is a rotating hub mounted to the motor shaft that mates with the internally splined friction elements. The outer housing of the test head is mounted on bearings to the motor shaft and is splined to the externally splined friction elements. The outer housing is prevented from rotating with a lever arm that bears on a load cell to measure the reaction torque during an engagement. An apply piston in the test head is pneumatically actuated to engage the clutch elements, clamping the rotating and stationary elements together between the apply piston and the cover of the test head. When actuated, the clutch brings the rotating inertia to a stop, absorbing the kinetic and converting it to heat.

When faced with a design that requires this sort of geometry, it may be necessary to design in relief holes or notches to relieve the stress during the thermal gradients. The deep gullets in a woodcutting combination circular saw blade are an example of notches in a disk to relieve the thermal gradient stress of a hot rim on a cooler disk.

6.2.5 Clutch Friction System Test Methods Dynamic testing of the friction system (friction plates, separator, and fluid) is most commonly done on an SAE #2 machine, using the kinetic energy of a rotating inertia to simulate the engagement energy of a shift in a transmission. Several standard test procedures have been written by the SAE Friction Standards Subcommittee using the SAE #2 test machine to characterize the friction characteristics of the friction system and to test for durability based on a standardsized test plate. The standard plate, agreed to by the SAE Friction Standards Subcommittee, has a facing OD and ID of 146.15 mm and 120.54 mm, respectively, and a parallel 25-groove pattern with 1.17-mm wide grooves on a 5.69mm pitch.

Fig. 6.26  SAE #2 test machine schematic cross section. In addition to the basic mechanical elements, there is a lubrication system for the test components. Today, the most commonly used lubrication system for friction plate testing is a center feed oil system that centrifugally distributes the fluid to the test components. This system is similar to the lubrication system in a transmission. It uses an external sump with heating and cooling systems to maintain the lube feed system temperature and a feed pump to feed the lube to the inside of the rotating hub. An alternative lube system uses

These standard test methods are not defined as a qualification test for a specific application. Rather, they have been designed as standard methods for characterizing wet friction systems for comparative analysis in the design of a specific application. The plate geometry, test procedure, data col-

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Friction Clutches

6.2.5.2 SAE J2490 Recommended Practice μPVT Test

a fixed fill system that does not include an external sump. Because of the lower volume of fluid, the fixed fill systems are frequently used for fluid durability testing. With the fixed fill system, fluid temperature is managed with a water jacket in the test head.

The SAE Friction Standards Subcommittee has released several recommended test procedures that have been designed to characterize the properties of a friction system using a standard friction plate and the SAE #2 test machine. The µPVT test, defined in SAE J2490, gives the design engineer coefficient properties (µ) of the tested friction interface/fluid combinations under a variety of pressure (P), speed (V), and fluid temperature (T) combinations. The only variables allowed for in the procedure are the friction material, the fluid, and the reaction (separator) plates. These three variables must be clearly identified when reporting the results of the SAE J2490 µPVT test.

In use, the SAE #2 machine is brought up to slightly above the test speed with an electric motor. After the electric power to the motor has been shut off, the speed is allowed to coast down to the test speed, and the pressure is applied. The torque of the applied friction elements brings the inertia to a stop. During the engagement phase of the test, speed, pressure, and torque are measured. Figure 6.27 shows a plot of the recorded parameters during a typical engagement. Using the basic torque equation (a variation of Eq. 6.4), T = µ ⋅ P ⋅ A ⋅ N ⋅ Rm = µ ⋅ P ⋅ A ⋅ N ⋅

2 ⋅( 3⋅(

R 3o R o2

− R 3i − R i2

) )

Use of this test procedure gives a fairly broad range of operating conditions upon which to compare the friction characteristics of different friction materials and fluids. It can give the friction system design engineer a good insight into how different combinations of materials are likely to compare for an application. A variation of this test is often used to evaluate other changes to the friction system, such as groove configurations, but cannot be referred to as the SAE J2490 procedure because the grooves are not per the standard.

(6.18)

The SAE J2490 procedure is run with four standard friction plates and consists of four 50-cycle break-in levels at 3500 r/min with increasing steps of apply pressure, followed by 16 test levels, each level consisting of 25 dynamic engagements and one breakaway following completion of the twenty-fifth dynamic engagement. A plot of the speed and pressure conditions is shown in Fig. 6.28. The total test, including the break-in, is 600 engagements. There are two low-energy blocks, identical except for the oil inlet temperatures, and two high-energy blocks, also identical and run at the two oil inlet temperatures of 50°C and 110°C. The eight different test levels are achieved by varying initial engagement speed, apply pressure, and oil sump temperature while the inertia is kept constant at 0.701 kg . m2. In the eight low-energy blocks, the net facing pressure is set at 295 and 591 kPa; the speeds of engagement are 750 and 1500 rpm. The high-energy conditions use net facing pressures of 886 and 1329 kPa and engagement speeds of 2700 and 3500 r/min. Gross power flux ranges from 0.12 to 2.54 W/mm2. The test is run with a center-feed oil supply of 1.0 L min. Standard test results for an SAE J2490 test are shown in Table 6.4 and include the basic test conditions. Figure 6.29 shows a standard plot for the same test.

Fig. 6.27  SAE #2 engagement plot. and solving for the coefficient of friction, 3 ⋅ T ⋅ ( R o2 − R i2 ) T µ = = P ⋅ A ⋅ N ⋅ R m 2 ⋅ P ⋅ A ⋅ N ⋅ ( R 3o − R 3i )



(6.19)

the coefficient of friction can be calculated at any instant during the engagement, where

T = µ = P = A = N = Rm = Ro = Ri =

measured torque (N . m) coefficient of friction apply pressure (Pa) piston area (m2) number of active friction interfaces mean radius of the friction facings (m) friction facing outer radius (m) friction facing inner radius (m)

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Design Practices: Passenger Car Automatic Transmissions

consisting of 200 engagements and one breakaway. Inspections of the friction plates and separators are made at the end of each level. The different power levels are achieved by increasing the effective inertia while the stop time and initial engagement speeds are kept constant. Stop time is held constant by increasing the pressure at each step. The test is run at increasing power steps until the friction system has completely failed. The inertia and energy for each step are shown in Table 6.5. These standard test procedures give an indication of the relative energy limits of different friction material and oil combinations in a test designed to always use common geometry and procedures. These two test procedures should be used to establish a starting point for the longer-term durability tests defined in the durability test procedure, SAE J2489, described in the next section.

Fig. 6.28  SAE J2490 μPVT test conditions plot. 6.2.5.3 Recommended Practices SAE J2487 (3600 r/min) and SAE J2488 (6000 r/min) Stepped Power Tests

6.2.5.4 Recommended Practice SAE J2489 Durability Tests

The stepped power tests, SAE J2487 and SAE J2488, were also agreed to by the SAE Friction Standards Subcommittee and released as SAE Recommended Practices. These tests are designed to evaluate relatively short-cycle energy limits of a friction system using three of the same SAE standard test plates that are used in the µPVT tests previously discussed. Each test consists of increasing steps of power, each level

Recommended Practice SAE J2489 is the durability version of the SAE J2487 and SAE J2488 Recommended Practices. It uses the test cycles defined in the previous two procedures as the basis for longer-term durability testing, recognizing that failure in the 200 cycles per level of the step level tests

Table 6.4  SAE #2 μ PVT Test Results

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Fig. 6.29  SAE J2490 μPVT test results plot. Table 6.5  SAE J2487 and SAE J2488 Step Level Test Inertias and Energies

may be from a different mechanism than long-term (5,000 to 20,000 cycles) durability failures. The user of this procedure selects a level from either SAE J2487 or SAE J2488 for the durability test. Level 1 from the step level test will be used as a 200-cycle break-in. The durability test is run by repeating a chosen 200-cycle step level block until either total failure occurs or until the chosen number of cycles has been completed. The step level tests can be used for guidance in selecting the level or levels to use for durability testing.

SAE J2487, 3600 r/min Test

Data reporting includes, for every twenty-fifth engagement cycle, the calculated midpoint dynamic coefficient, 50% µ d , and the calculated endpoint dynamic coefficient,
100ms µ d max . For every two-hundredth cycle, the breakaway coefficient, 1.0 µ s4.37 is to be recorded and reported. (See SAE J1646 for the definitions of the coefficient symbols.) The report is to also include a plot versus cycle number of midpoint coefficient. It is recommended to also plot the average thickness loss per plate, the endpoint/midpoint coefficient ratio, and the breakaway friction coefficient.

SAE J2488, 6000 r/min Test

Step Level

Total Inertia (kg . m2)

Energy (kJ)

Total Inertia (kg . m2)

Energy (kJ)

 1

0.213

15.13

0.142

28.08

 2

0.254

18.02

0.156

30.76

 3

0.294

20.91

0.169

33.43

 4

0.335

23.80

0.183

36.11

 5

0.376

26.69

0.197

38.78

 6

0.416

29.58

0.210

41.46

 7

0.457

32.47

0.224

44.13

 8

0.498

35.36

0.237

46.80

 9

0.538

38.25

0.251

49.48

10

0.579

41.15

0.264

52.15

11

0620

44.04

0.278

54.83

12

0.660

46.89

0.292

57.50

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Design Practices: Passenger Car Automatic Transmissions

6.3 Bands 6.3.1 Overview Conventional automobile automatic transmissions use two types of friction elements: plate clutches, and brake bands. Although both types have advantages and disadvantages, brake bands have some unique features that make them a sound engineering choice in a number of applications. Friction bands are used to either hold or release a drum that is joined to a planetary gear set [45]. As with friction plates, this action is used to accomplish the desired ratio change. One advantage of a brake band is the relatively large frictional surface area it provides while consuming very little axial space in the transmission. The space claim for a band, excluding application hardware, is the stack thickness of strap, friction material, and running clearance. The band, being a cylindrical element, has a large direct heat sink available in the reaction drum. This heat sink allows a band to tolerate higher energy input from a surface area viewpoint than equivalent friction clutches. In addition, the band can be completely disengaged from the drum, allowing for very low parasitic drag without compromising subsequent reengagement properties.

FR FA



eµβ =



TD = ( FA − FR ) ⋅ R D



1 ⎞ ⎛ TD = FA ⋅ R D ⋅ ⎜ 1 − µβ ⎟ ⎝ e ⎠ PL =



FA ⋅ eµβ W ⋅ RD

(Energized) (De-energized) (De-energized)

(Liner pressure)

(6.22) (6.23) (6.24) (6.25)

where

FA = FR = TD = RD = µ = β = PL = W =

apply force (N) reaction force (N) drum torque (N . m) drum radius (m) coefficient of friction angle of wrap (radians) liner pressure (Pa) band width (m)

Figure 6.31 displays the significance of the above relationships in terms of holding power. Particularly noteworthy is the directionality of capacity.

Control of the shift is complicated by the geometry of the band drum system [46]. An exponential relationship exists between the band apply force and the pressure exerted by the band lining on the drum, whereas in a plate clutch, this relationship of apply force to surface pressure is linear (Fig. 6.30 and Eqs. 6.20 through 6.25).

Fig. 6.31  Capacity difference between singleand double-wrap bands. In addition to control issues related to directionality, there are transmission case design compromises involved with band use. Transmission case complexity and design compromises are related to the fact that bands are point apply and point reaction members. Careful consideration must be taken to avoid issues with case deflection and reaction member fatigue. Apply cylinders require more complex die action, and, as noted, fill time can become another facet of the control issue. The volume of fluid required for actuation generally means that bands are not readily modulated. Figure 6.32 illustrates the hardware necessary for a use of a double-wrap band in a transmission environment.

Fig. 6.30  Band wrap angles.

TD = ( FR − FA ) ⋅ R D   (Energized)

(6.20)



TD = FA ⋅ R D ⋅ ( eµβ − 1)   (Energized)

(6.21)

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Band construction methodology is dictated by loading. The higher the anticipated load, the thicker the strap material needs to be. However, the thickness of the material is directly related to engaged conformity. The thicker the material, the more difficult it becomes to achieve good conformity under load. Drum designs range from carrier castings to stamped cups. During high-speed engagements, friction-generated heat can distort the surface away from its original cylindrical shape. The better the conformance of band to drum, the greater the heat transfer potential. The thickness of the strap and the band’s circumferential length, not the strength of the material, determine the degree of elastic stretch under load. The thinner the band, the greater the stretch and the more difficult it is to have acceptable load application control. Strength of the materials ranges from mild steel at Rockwell B levels to heat-treated/heat-set components at Rockwell C levels. Band strap thickness specification must be balanced between these conflicting requirements.

Fig. 6.32  Band application hardware.

6.3.2 Transmission Design Considerations for Band Use The question frequently arises when a grounding clutch is required in an automatic transmission design on whether a band or a plate clutch should be used. The major factors taken into account in the selection of component designs in the modern automatic transmission tend to follow this list:

Band friction materials at one time ranged from semi-metallic to organic; however, advances in friction technology have allowed bands and friction plates to use the same families of resilient materials [47]. Modifications are made in consideration of the higher unit loading, but the base material concepts are very similar. Coefficients seen with resilient materials are significantly higher than semi-metallics, meaning that legacy designs can often be performance optimized at lower weight. The control of drum finish is more important with the use of advanced friction materials. Where the semimetallics, similar to a brake shoe compound, could cause surface damage to the drum without liner distress, newer materials require finish control to nearly the same degree as friction separator plates. Semi-metallic materials, such as brake shoes, wore in operation. This meant that bands in a transmission design required adjustment mechanisms for wear, including, in some cases, brinelling of band load transition members or permanent stretch of softer band strap materials. Contemporary bands do not require adjustment for the life of the transmission; thus, case designs generally do not have this provision. Occasionally, an adjustment provision will still be included to facilitate initial installation.

• Available barrel and hydraulic control area packaging space and dimensional characteristics of the space— length versus diameter • Specific torque capacity or gain required • Required controllability of the clutch • Required efficiency of the clutch • Design cost target • Design mass or inertia target • Required useful life and expected duty cycle

6.3.3 Selecting a Band Type Two design characteristics are used to categorize bands into types. These are the number of wraps and the thickness of the band strap. The number of wraps generally defines the holding power and the application range. The wrap angle is the continuous angular distance of band contact with the drum between the apply and the anchor hardware. Single-wrap bands have a load path that wraps around the drum one time, less than 360 degrees. Multiple-wrap bands have segments with bridging elements that result in a strap load path that wraps around the drum more than one time. Single-wrap bands are used when required holding power is lower, such as reaction torque in second through fifth gear. Double-wrap bands are used when torque levels are higher, such as reaction torque in low or reverse gear.

6.3.4 Servo Apply and Anchoring the Band The band servo can be placed in several locations around the drum. However, the direction of apply force acting on the band bracket must be directionally tangential to the drum. The angular misalignment of the servo with the ideal tangential direction is referred to as “toe-in” or “toe-out.” Toe-in or toe-out will, respectively, increase or decrease the lining compression at the end of the band and the resulting aggressiveness of the engagement torque profile. Excessive positive

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Design Practices: Passenger Car Automatic Transmissions

or negative toe-in (beyond 2 to 3 degrees) can be detrimental to lining life and shift quality. Toe can occur at both the apply and anchor ends of the band, depending on servo and anchor linkage geometry. A toe-in example is shown in Fig. 6.33.

Fig. 6.34  Example of a strut to reduce misalignment. Anchor attachment configurations range from a simple radial pin pressed into the case reacting against a matching radial groove or extruded hole formed in the band bracket to a groove or hole machined into the case mating to a clevis pin and loop attached to the anchor end of the band. The clevis pin hinge arrangement at the anchor end of the band provides theoretically optimum tangential alignment to the drum. This hinge arrangement restricts the ability of the band to conform to the drum in the axial direction. This can cause large variation in the unit load distribution between the band lining and drum surface when the band is applied. This variation in unit loading then causes variation in shift quality and interface temperature.

Fig. 6.33  Band toe angles illustration. The ideal alignment at either end of the band is tangential when the band is being applied under load against the drum. Because the band moves around the drum with assembly tolerance and increased loading and wear, ideal alignment of the servo band and drum is a compromise best optimized on the design layout, taking into consideration lining wear and tolerance stack-up.

One must consider tolerance accumulation in the design of the servo, band, anchor, and linkage. Dimensional variation will occur in band seat to seat dimension, length, and location of other linkage pieces, and in the diameter of the drum itself. Another dimensional variation to consider is the compression set of the band lining over its lifetime. Any variation in the drum diameter from piece to piece or compression set in the lining translates into approximately three times the variation in servo travel. This variation in servo travel creates a variation in the cumulative flow required to move the servo piston into the applied position from the released position. Older control designs may not be able to adapt the control valve flow rate to changing demand at the servo, thus leading to degradation in shift response. Newer control system designs may be able to adapt to this increase in flow demand by dynamically extending control valve open time to compensate to a pre-set limit. This additional flow requirement consumes control valve flow capability, which, in cases where the control valve flow is marginal, can cause degradation in response or undesired variation in initial engagement torque profile.

One design technique that can be used to reduce error in apply force alignment is the strut. The strut is an extra link between the servo rod or anchor pin and the band bracket that will bisect the toe angle error. The disadvantage of the strut is the assembly required. The strut is an extra part that is usually hand-assembled in production. Few struts are used in new product design today for this reason. Elimination of these components is accomplished by alignment of the servo and anchor pin. Consider the traditional design where the servo is placed horizontally and tangentially to the drum at the bottom of the drum, and the hydraulic control labyrinth is also located horizontally at the bottom of the gear case. The servo piston area competes with the labyrinth for the same design space at the bottom of the case. If the servo could be placed higher on the case, the labyrinth, attached valve body, and oil pan could be more easily designed. A strut can be used to extend the servo rod and bisect the misalignment caused by moving the servo higher in the case and changing the angle of the rod to compensate (Fig. 6.34). This approach can also be used to compensate for an increase in drum diameter that may be required to increase torque capacity of the transmission in future derivations.

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Friction Clutches

To compensate for tolerance accumulation in the band servo system, an adjustment can be made during assembly at either the servo end or anchor end of the band. Selective servo rod lengths or a threaded adjustment at either the servo or the anchor end of the system can be used to improve servo piston stroke precision. Arguably the best location for this adjustment is at the anchor end. The anchor end adjustment is performed after all parts are assembled, including the servo cover. If the selective servo rod lengths are used for adjustment, several servo rods or piston assemblies must be stocked for production, and the servo cover is assembled after the adjustment is complete. This will potentially add uncompensated dimensional variation. This through-thecase adjustment creates a potential leak path that must be reliably sealed.

Sometimes, oil flow is routed through the center of the servo rod to the apply side of the piston when the servo is located outside the oil pan and inconvenient to the labyrinth circuit. The “valve-to-bore” clearance between the servo rod and its guiding bore serves as a seal for the apply circuit. However, this bore can wear over time due to side loading from the band bracket. The servo rod moves slightly in and out against the band with pressure changes while the band is engaged and during apply and release events. This movement under load can cause abrasive wear in the bore (Fig. 6.37).

There are three approaches to achieving adequate band apply force from the servo. The direct-acting servo force multiplier is set by the apply piston area. This can be adjusted by changing the outer diameter of the servo piston. The indirect-acting servo employs a lever arrangement to multiply piston force between the servo piston and the band (Fig. 6.35). A third type is a dual apply area-type piston that allows load to be varied over a wider range, common when the band has an energized and de-energized function (Fig. 6.36).

Fig. 6.36  Dual area servo.

Fig. 6.35  Lever used to multiply servo force. The direct-acting servo includes a piston, rod, and seals packaged in a cavity cast and machined into the gear case. The machined cavity includes a bored hole in the case wall through which the servo rod protrudes to reach the band bracket. If the band is involved in synchronous ratio changes, the servo will include a hydraulic area on the reverse side of the piston to provide hydraulically powered release action when energized by an additional control circuit (Fig. 6.36).

Fig. 6.37  Typical fluid apply and release path.

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Design Practices: Passenger Car Automatic Transmissions

6.3.5 Band Design Analysis In the usual design situation involving the use of a band, the factors that must be evaluated are as follows: • Magnitude and direction of torque input and band apply force • Magnitude of the loading at the reaction end of the band • Magnitude of the maximum unit pressure to which the lining material will be subjected Bands in use today include single-wrap flexible (Fig. 6.39), double-wrap rigid (Fig. 6.40), and double-wrap flexible hybrid types (Fig. 6.41). For single-wrap bands in use, the anchor force is approximately double the apply force when operating in an energized direction and approximately half the apply force when operating in a de-energized direction.

Fig. 6.38  Servo with cushion spring. The servo return spring is typically a single coil-type spring designed with an appropriate load to: 1. Set stroke pressure of the servo to be compatible with the control valve and logic design 2. Provide sufficient de-stroke force to overcome seal drag and push the fluid out of the apply circuit quickly and effectively throughout the operating temperature range of the system A cushion spring can be used between the piston and rod to attenuate servo force during critical apply and release times while the band is slipping. This can be particularly useful during synchronous shifts when band slipping torque is controlling shift feel in coordination with another clutch applying or releasing. The cushion spring design requires the piston to maintain a sliding seal to the servo rod. This is usually accomplished with a valve-to-bore fit between the rod and the piston (Fig. 6.38).

Fig. 6.40  Typical double-wrap rigid band.

Fig. 6.39  Typical single-wrap flex band. Fig. 6.41  Typical double-wrap hybrid band. 6-34

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Friction Clutches

Bands are complex structural elements. Where a plate can be considered a two and one-half dimension extruded form for analysis purposes, a band is three dimensional. Plate core designs are dictated by tooth strength and heat transfer considerations. Band design is a balance between the structure to support the varying strap loading between apply and anchoring (Fig. 6.42) locations and the liner pressure operating limits. Straps may have tapered cross sections to allow the liner loading to be more uniformly distributed, and strap tensile stresses to be equalized for structure fatigue purposes. Finite element analysis has been used extensively in band design to optimize the structural properties (Fig. 6.43).

• Drum radius, surface finish, and material type—The material of the drum will be a factor in durability through persistence of drum finish, interaction with fluid additives, and heat transfer properties. The thickness of the drum and manufacturing method also play a role in band performance. Solid drums will not deflect under band strap contact load, while drums made from drawn cups will flex considerably. This will lower band fatigue life and could change engagement properties because of elastic distortion or bell mouthing at higher drum speeds. • Wrap angle—Typically, this is approximately 320° for single-wrap bands and roughly 660° for double-wrap bands for initial calculations. As a rule of thumb, doublewrap bands take twice the apply stroke of single-wrap bands. In most transmission hydraulic apply systems, this translates directly into a doubling of time to apply. • Apply load available from the system and load application method—Apply force radius—the distance from the center of the drum to the point of contact of the apply bracket with apply pin, and with the band in the engaged position—should be provided. The radius of the tip of the apply pin, or the configuration of an apply strut, should be provided. Brinelling of the apply pocket must be considered. The deeper the potential penetration, the larger the possible end variation in stroke to apply. Apply pin end radius should match apply pocket radius if possible with consideration of overall stress levels. • The engine torque and inertia torque if available with ratios for the torque converter and different gear ratios—These can be used to generate the torque holding requirements of the band. • Projected duty cycle—What function is the band to perform? Is the band working both energized and de-energized? Is there a swap shift involved? Will the band be used for braking the transmission in a pull-in maneuver? The duty cycle can be used to project transmission band liner life and mechanical structure life. While a reverse band life of a few thousand cycles at maximum load is generally sufficient for successful transmission lifetime operation, a band that operates in shifting or forward holding positions needs lifetime at maximum load orders of magnitude higher. • Anchor force radius—The distance from the center of the drum to the point of contact of the anchor pin with the anchor bracket while the band is locked up around the drum should be provided. Some anchor pins hold the band in a tangential direction, while others hold the band perpendicular to the tangent. If the band is held the second way, the radial distance is measured to the end of the pin.

Fig. 6.42  Variation of load: double-wrap band energized condition.

Fig. 6.43  Typical finite element analysis.

6.3.6 Necessary Information for Band Design Before beginning the quantitative design of the band, the space claim envelope and performance expectations should be defined. This allows the band designer to make basic functional choices in such areas as materials and processing steps required. It also provides the potential end user with a better price/value comparison and clarifies the value analysis picture. 6-35

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• Expected running clearance—The lower the clearance, the higher the open running drag. There is a point of diminishing returns, in that the higher the running clearance, the longer the band will take to apply. In general, no benefit is seen with clearances beyond 0.5 mm. • Allowable width of the band—This can be initially estimated by 90% of the usable drum area. Width determines energy density in individual segments. Note that for double-wrap bands, there will be a loss in effective width because of the strap movement and processing clearances necessary. • Path to assembly into final position—Band features for orientation such as tabs or wings or cutouts necessary to clear transmission bore projections can complicate the band tooling and manufacturing methods. It is not sufficient that the band function when installed; it must

also be capable of being installed in an assembly-line fashion. In general, a band is installed as one of the first elements into a transmission case. It needs to hold position as other assemblies are added or moved. • Fluid type to be used—Different additive packages and base stock types will have a significant influence on the friction material used. Tables 6.6, 6.7, and 6.8 present a summary of design elements in the band system and present how those elements impact the function and performance of the system. Table 6.6 addresses the band, Table 6.7 the drum, and Table 6.8 the linkage. Figure 6.44 is a graphical representation of the interactions between the various transmission and vehicle systems and the band system. Figure 6.45 is an Ishikawa diagram of factors that impact the consistency of the band system performance.

Table 6.6  An Overview of Band Design Factors Affecting Dynamic Engagement/Disengagement Torque Design Factor

When Increased

When Decreased

Band strap thickness, rigidity

Reduced conformity to an imperfect drum.

Improves conformity to the drum. Tends to reduce variability. Increases band stress.

Band strap width

Reduces power density. Reduces lining/drum unit pressure. May reduce conformity to an imperfect drum. Due to increased friction contact area, careful design of grooves and drain holes through the strap is required to control hydrodynamic torque during engagement.

Increases power density, increasing interface temperature for the same power level. Can improve dynamic engagement controllability.

Wrap angle (number of wraps)

Increasing the number of wraps from one to two increases torque capacity and decreases dynamic engagement controllability, particularly in the “energized” direction.

Decressing the number of wraps from two to one will decrease torque capacity, thus requiring increased supply force or drum diameter for the same torque capacity, but will increase energized engagement controllability.

Toe angle

Toe-in concentrates lining unit loading at the ends of the band and can cause accelerated lining wear. Toe-in will cause a more aggressive initial engagement torque. Excessive toe-in (roughly beyond 2–3 degrees) will reduce dyamic torque profile controllability.

Toe-in causes a lack of oil film control during the hydrodynamic phase of engagement. This translates into loss of dynamic engagement controllability.

Lining grooves and strap drain holes

When carefully designed, can improve engagement/disengagement controllability.

Reduces controllability, particularly when wider straps are used.

Bracket to anchor contraint

Increasing the constraint to the grounded end of the band can have a large effect on the distribution of tension across the width of the strap, similarly affecting lining unit loading.

Decreasing the constraints at the end of the band improves the ability of the band to conform to drum imperfections and thermal distortions.

Can cause variability in dynamic torque profile.

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Table 6.7  Band Drum Design Factors Design Factor

When Increased

When Decreased

Diameter

Increses torque capacity linearly. Usually difficult to package.

Decreases torque capacity. This parameter is usually traded off with servo force, to control basic torque capacity and lining unit loading.

Axial width

Decreases power density. Can increase thermal distortion wen not constained. Can decress controllability due to increased interface area.

Tends to increase thermal disortion, particularly with deep drawn formed drum.

Rim wall thickness

Increases heat capacity of the drum. Decreases thermal distorton, which can improve controllability.

Tends to increased thermal distortion, particulary with deep drawn formed drums.

Drum surface finish

Increasing the roughness magnitude may improve fluid retention and consistency of hydrodynamic and asperity phases of engagement; however, if asperities are rapidly changing due to wear or are damaging to the friction material, durability can be negatively affected.

Decreasing the surface texture, particularly with relatively soft materials, may result in decreased “shift quality life.” Surface texture and finishing method can be tested effectively using benchtype friction testing machines, such as the SAE #2 machine.

Drum material

Drum hardness interacts with surface texture. When material hardness approaches that of the hardened steel, the surface roughness should be reduced. The surface texture of the harder surface finish should be less aggressive than that for a softer material so that the band lining will not be damanaged. With higher surface hardness, the texture will change less over its lifetime. When less porous materials are used, such as steel versus cast iron, a more aggressive surface finish, perhaps turned and polished, generally works well.

Drum raidal lube holes

Radial lube holes through the drum into the friction interface can help keep the surface of the band wet prior to an engagement. This will enhance durability and reduce variability of dynamic engagement torque profile. An alternate method of lubing the band prior to engagement is a lube stream from a pressurized source (such as a servo apply or release circuit) onto the drum between the ends of the band strap or through a “window” in the band strap.

Drum dimensional tolerances

Improving precision of the drum runout, mass balance, roundness, etc., will reduce the propensity of the band to shudder or vibrate during engagement and disengagement. This will also contribute to reduced variation of engagement and disengagement dynamic torque profile.

Drum mounting bearing tolerances

Reducing bearing radial clearance and improving bearing precision can reduce the propensity of the band to shudder or vibrate, similiar to the drum tolerances discussed above.

Table 6.8  Band Linkage Design Factors Struts—Can be used to bisect alignment error at servo and anchor points. Difficult to assemble in high production. Levers—Can be used to muliply servo force. Can cause alignment to change with band wear and variation in servo piston stroke. Can be difficult to assemble and may require strut to reduce inherent alignment error. Cleveis (hinge-type) attachement of band to anchor—This reduces variation in achor end force alignment. If not carefully controlled, it can cause variation in strap tension across the width of the strap. Eliminates the overturning couple associated with the other anchor design alternatives.

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Fig. 6.44  Band/drum/servo system interaction diagram for shift quality.

6.3.7 Testing of Bands 6.3.7.1 Friction Testing Several design features of the band and drum are critical to consistent engagement quality. The automatic transmission band/drum combination is a special configuration of the wet clutch. Similar to the disc clutch, the dynamic engagement torque profile is composed of the three phases of the wet clutch [48]: 1. Hydrodynamic phase—This is when the oil film between the band and drum is “squeezed” out from between the band and drum by initial servo force, bringing the band into initial contact with the drum. 2. Asperity contact phase—This stage of the engagement occurs when asperities at the friction material surface make contact with the counter surface and generate friction force. 3. Dry contact phase—This final stage of the engagement occurs when the fluid has been squeezed from the interface and full asperity contact has occurred.

Fig. 6.45  Ishikawa diagram of band shift quality variation.

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The basic wet friction system design approach and theory applies to the band and drum system the same way as the disc clutch.

The impact of the fluid supply on performance is not merely theoretical. In use, most transmissions do not have a dedicated supply of fluid to the band. The reliance on incidental lubrication means that bands have a wider span of application issues from compensation for hydrodynamic effects to compensation for running only with mist. The lack of a defined oil supply significantly contributes to the variability of performance. Figure 6.48 shows the impact of fluid flow on performance in a bench test; Fig. 6.49 shows the impact in vehicle performance [52].

SAE J1499 covers SAE band friction test machine guidelines. There is no generally accepted equivalent to plate µPVT (SAE J2490) or durability tests (SAE J2487 and J2488). The range of band application hardware and mating surfaces makes a useful benchmark test difficult to construct [49–51]. The question of lubrication level, easily defined in plate testing, is a major concern. Bands are typically splash lubricated with fixed fill or recirculating oil. Interface design—grooves, holes, and friction material—to deal with this complexity is a subject of considerable activity and speculation. Figure 6.46 shows a transmission installation. Figure 6.47 shows the equivalent fixturing for an SAE machine. There may be differences in load application stiffness that influence results, depending on the machine type used. Pneumatic apply is typical in SAE machines, while all transmission load apply is done hydraulically.

The friction performance level of the bands and clutch packs is influenced by the type of fluid used. Fluids in use today are designed for vehicle life and, thus, may be fully or partially synthetic and contain aggressive additive packages. Typically, bench testing of candidates and statistically analyzing results determines fitness for use. The band, drum, and fluid must be considered a system rather than individual components.

Fig. 6.48  Impact of fluid flow on SAE machine friction performance. Fig. 6.46  Transmission environment for CD4E band.

6.3.7.2 Fatigue Testing Because the structure of the band is complex, life testing is used in validation of the design. Depending on the application, this may be simple single-stage loading or combinations of apply load and torque. The fixturing used (an example is shown in Fig. 6.50) mimics the geometry of the apply and reaction hardware in the transmission. Development testing is done to failure, and lifetime projections are made using Weibull analysis. Slope and characteristic life in this analysis can then be used to project how the band will perform in the application environment. Rainflow analysis and cumulative damage theories have been used with some success in determining design fitness for production.

Fig. 6.47  SAE fixturing for CD4E band. 6-39

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Fig. 6.49  Impact of fluid on band shifts in a vehicle.

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Fig. 6.50  Fatigue test equipment.

6.3.8 Failure Modes 6.3.8.1 Friction Material Failure Friction material failure can occur from distress caused by interface temperature being beyond design limits for the formulation. It can also occur if the mating drum surface has runout sufficient to cause mechanical fatigue. Lobing of the mating surface causes, in effect, a wave or plowing distortion on each actuation. A third possibility is a drum finish that is incompatible with the friction material being used. Resilient friction materials used today will not tolerate rough turned finishes. Finish specification suitability is usually determined by bench testing rather than pure numbers because of the variety of drum and friction materials used. Ra surface finish roughness is not generally sufficient as a specification but is perhaps the most commonly used. An equilibrium finish will eventually be reached, and the friction material and drum come into compliance. However, roughness beyond 0.75 µm should be approached with caution because of the potential for unacceptable liner wear and debris generation. Measurement of bearing ratios, peak-to-valley height, and so forth are valuable in an investigative mode but are difficult to implement as a means of process control.

Fig. 6.51  Fatigue failure from torque cycling test. As noted earlier, bands undergo elastic deformation with each cycle. This deformation can be a significant part of the delay in shifting. Again, the deformation is a property of cross section, not material strength; hence, efforts to minimize this deflection will increase the weight of the band [53]. A double-wrap rigid band with a strap thickness of 3 mm will not stretch as much as a hybrid band with a strap thickness of 2 mm, but the hybrid band may be more than twice as strong because of the differences in construction and processes. There have been instances where the band undergoes a fretting-type failure due to drum runout. The finish of the apply or reaction pin acts as a file to erode the mating band surface. 6.3.8.3 Bond Failure A third failure mode type is that of the adhesive that holds friction material to the band. The adhesives used, usually phenolic resin based, are chosen for their high heat tolerance and chemical inertness. Once the thermoset adhesive has been cured using appropriate time, temperature, and pressure, it will resist high-temperature shearing action for the life of the band. The adhesives used are resistant to temperatures well beyond 200°C for long periods. Integrity of the bond line is determined in a number of ways. A typical quality check is done using a chisel to attempt to remove the lining from the band, monitoring the fracture pattern of the liner and looking for patches of bare metal. Other tests are used, including steam exposure tests; reverse bend tests, where the band is permanently deformed by bending

6.3.8.2 Mechanical Failure In operation, the band structure is subjected to a combination of axial and bending stresses. Because of weight considerations, it is impractical to have significant safety margins; hence, it is very important to carefully define end use conditions. A typical torque cycling test involves the band being applied and locked around the drum, the drum being torqued, the drum torque being released, and then the band released. This process is repeated until the band cannot hold the torque or apply load. Figure 6.51 shows a typical fatigue failure from a torque cycling test. 6-41

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Design Practices: Passenger Car Automatic Transmissions

The specific horsepower of the band/drum combination can be increased sometimes to twice that of the plate clutch. High interfacial temperature drives failure of the friction interface. The cylindrical drum usually provides more heat sink mass than the separator plates in a plate clutch. The larger mass heat sink will produce a lower interface temperature for the same power level. Also, because the fiber-based friction lining usually has low conductivity, much like that of an insulator, the band drum exposes much more convective surface area to the fluid than the multi-plate clutch, providing higher heat rejection rate from the heat sink mass (Fig. 6.53).

it backwards; thermal shock tests, where the band is moved from cold to hot environments; and special fatigue tests, where the drum is heated to elevated temperature. Adhesive quality, tested as an entity, involves viscosity and gap-filling checks. Potential strength of the adhesive is evaluated using ASTM D-2182-72 standard button and bar tests.

6.3.9 Clutch Pack Versus Band The question frequently arises when a grounding clutch is required in the automatic transmission design: Should I use a band or a plate clutch? Because automatic transmissions have been around for more than 50 years, all configurations of clutch and band systems have been tried to some degree of success or another. 6.3.9.1 Advantages of Bands with Respect to Plate Clutches With respect to the above requirements, the band brake and servo design has advantages and disadvantages over the plate clutch-type brake design. The band-and-drum arrangement has a distinct packaging advantage over the plate clutch in the barrel of the transmission. The band consists of a reinforcing strap with brackets on each end, wrapped around a cylindrical shell. The band/drum friction surface is coaxial with the shaft, taking up precious little radial space in the barrel. Other components can be conveniently placed inside the shell (drum). The multi-plate clutch requires substantial radial space because its many frictional surfaces are perpendicular to the shaft (Fig. 6.52).

Fig. 6.53  Clutch pack versus band drum heat sink. The band brake will be more efficient than the equivalentsized plate clutch when disengaged. When the servo piston is retracted, allowing the band to separate from the drum, the band strap will move away from the drum. The “free shape” of the band can be manipulated to cause the band lining to lightly contact the drum in two locations when installed in the transmission in the released state. The radial clearance between the band lining and the drum varies with angular location. This creates a wiping action of the lining on the drum, which results in lower viscous drag torques when the band is released. This type of clearance control is difficult to accomplish when using plate clutches, because the individual clutch plates are usually unconstrained in the released state. The plates can then move axially, resulting in unequal clearances between pairs of plates within the pack. Smaller clearance between plates causes high viscous drag in the pack [54].

Fig. 6.52  Clutch pack package versus band package.

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Fig. 6.55  Vertical versus horizontal servo placement. The disadvantages of a horizontally located servo are that a separate leak-proof servo cover is required on the outside of the transmission case. The addition of any external access through the transmission case containing pressurized fluid is usually considered a reliability or leakage risk by the transmission design engineer. If the servo can be contained inside the oil pan of the transmission, the external leak path due to a cut o-ring, torn gasket, or loose retention bolt is eliminated. The vertical servo contained within the oil pan, while eliminating the above leakage issue, provides the disadvantage of taking up space in the hydraulic control area. If the servo is located here, the hydraulic control may have to be designed around the servo, thus providing a less than optimum shape for machining and assembly processing (Fig. 6.56). An alternate method to accommodate the labyrinth-located servo is to place the hydraulic valve body below the assembled servo. Sufficiently rapid fluid drain-back paths from the barrel into the sump of the transmission are necessary to prevent excessive viscous drag.

Fig. 6.54  Open running drag of band versus equivalent capacity clutch pack. Figure 6.54 is an open system running drag comparison of equivalent torque capacities between a clutch pack and band. Disengaged separator plate spline rattle is a common occurrence in the grounded plate clutch [55]. This noise can irritate the occupants of the vehicle, particularly in rear-wheel-drive vehicles where the path from the transmission gear case to the vehicle cabin is short and direct up through the floor pan of the vehicle. In front-wheel-drive applications, this seems to be less of a problem because the transmission gear case is typically located in the engine compartment, fairly isolated from vehicle occupants. 6.3.9.2 Disadvantages with Respect to Plate Clutches There are packaging disadvantages with the band brake as compared to the plate clutch. The servo actuator for the band must be located perpendicular and offset to the transmission centerline. The servo may be located in any angular location; however, it is usually located on either side of the case below the drum and acts on a near horizontal axis. It may also be located in the hydraulic control area, pushing up on the band apply bracket (Fig. 6.55).

Fig. 6.56  Servo bores take up hydraulic control design space. 6-43

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Other manufacturing requirements can make the band and drum combination less desirable in high-volume manufacturing when compared to the plate clutch. In the automatic transmission, the plate clutch or band must consistently perform smooth engagements and disengagements for the shift quality to be adequate. Because the band constrains the drum radially while the drum is spinning, the mass distribution of the drum and the precision of the drum mounting become important to prevent unwanted torsional vibrations during engagement and disengagement. This housing precision is not as critical in plate clutches because the friction surface is normal to the axis of the piston apply force. Therefore, minor misalignments and imbalances have less chance of creating objectionable torsional vibrations. The assembly of the band and subassembly of the servo are restricted to the final assembly line in the transmission plant because the servo and band anchor attachments are traditionally installed directly into the case. Plate clutches can be subassembled on separate assembly lines or in suppliers’ plants and shipped as a subassembly. This can be an advantage for the plate clutch in crowded plant-floor situations.

Fig. 6.57  Energized and de-energized friction curves.

6.3.9.3 Controllability of Band/Servo Systems Versus Plate Clutch Systems

6.3.10 Summary Bands can be used interchangeably with friction plates if the transmission engineer takes careful account of the differences in design approach needed for successful implementation. They are single unit elements and, as such, are more demanding of both manufacturer and end user. They offer rewards in terms of heat capacity and no-compromise drag properties but require that consideration of directionality and transmission support be done with a diligent engineering approach.

In the automatic transmission, the plate clutch or band must consistently perform repeatable, controllable engagements and disengagements for the shift quality to be adequate. As the electro-hydraulic control system becomes more precise and responsive and the control software becomes more sophisticated, more precise engagement and disengagement dynamic response is expected of the clutch or band. A basic disadvantage of a brake band is the degree of control that can be maintained over the engagement when a band is used to accomplish a shift. The control problem, actuation time and response, is compounded by the fact that the band can be applied in either an energized or a de-energized mode, depending on the direction of drum rotation. The energized mode, typically used in vehicle upshifts, is defined as the direction of drum rotation that coincides with the direction of band apply motion. Application of a servo causes the band to be tightened around the drum. A direct result of this wrapping motion is that, in the energized mode, the band drum friction adds to the band apply force. In the de-energized mode, typical of vehicle downshifts, the two forces are subtracted. Band shift modes and differences in the resulting torque curves and capacity are qualitatively shown in Fig. 6.57.

6.4 References 1. Lloyd, F. A. and M. A. DiPino, “Advances in Wet Friction Materials—75 Years of Progress,” SAE Paper No. 800977, Society of Automotive Engineers, Warrendale, PA, 1980. 2. Tuck, R. M., R. E. Grambo, R. E. Dowell, and R. S. Frichette, “Progress in the Development and Manufacture of Heavy Duty Paper Friction Material,” SAE Paper No. 831314, Society of Automotive Engineers, Warrendale, PA, 1993. 3. Barker, K. A., K. Ito, S. Yoshida, and M. Kubota, “Designing Paper Type Wet Friction Material for High Strength and Durability,” SAE Paper No. 982034, Society of Automotive Engineers, Warrendale, PA, 1998.

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4. Lam, R. and S. Kowal, “Fluid Transport Phenomena During Engagement of Fiber-Reinforced Polymeric Friction Materials,” SAE Paper No. 922097, Society of Automotive Engineers, Warrendale, PA, 1990. 5. Matsumoto, T., “Influence of Paper-Based Friction Material Visco-Elasticity on the Performance of a Wet Clutch,” SAE Paper No. 970977, Society of Automotive Engineers, Warrendale, PA, 1997. 6. Nels, Terry E., “Properties of Automatic Transmission Friction Papers,” TAPPI Journal, Technical Association of the Pulp and Paper Industry, Atlanta, GA, 1978, p. 231. 7. Chuluda, P., “Carbon Fiber/Flame-Resistant Organic Fiber Sheet as a Friction Material,” U.S. Patent 4256801, United States Patent Office, Washington, DC, 1981. 8. Lee, J., “Friction Paper Containing Activated Carbon,” U.S. Patent 5989390, United States Patent Office, Washington, DC, 1999. 9. Anleitner, M. A., “Friction Material Failure Modes in Oil-Immersed Multiple Disk Brakes,” SAE Paper No. 841064, Society of Automotive Engineers, Warrendale, PA, 1984. 10. Ikawa, S., K. Ito, M. Kubota, T. Shibuya, and S. Yoshida, “Trend of Friction Materials Developments,” Tribology of Vehicle Transmissions Symposium, Yokohama, Japan, 1998. 11. Wagner, D., “Carbon Fiber for Wet Friction Applications,” SAE Paper No. 972754, Society of Automotive Engineers, Warrendale, PA, 1997. 12. von Drach, Volker and P. Drucker, “New Process and Reinforcement Fibers for Friction Materials Based on Renewable Raw Materials,” SAE Paper No. 2001-013129, Society of Automotive Engineers, Warrendale, PA, 2001. 13. Kitahara, S. and T. Matsumoto, “The Relationship Between Porosity and Mechanical Strength in PaperBased Materials,” SAE Paper No. 960982, Society of Automotive Engineers, Warrendale, PA, 1996. 14. Chen, Y.-F., R. C. Lam, and T. Newcomb, “Friction Material/Oil Interface for Slipping Clutch Applications,” SAE Paper No. 2001-01-1153, Society of Automotive Engineers, Warrendale, PA, 2001. 15. Fairbank, D. K., K. Maruo, S. Du, and T. P. Newcomb, “ATF Additive Effects on Hot Spot Formation in Wet Clutches,” SAE Paper No. 2001-01-3594, Society of Automotive Engineers, Warrendale, PA, 2001. 16. Yang, Y., et al., “Theoretical and Experimental Studies on the Thermal Degradation of Wet Friction Materials,” SAE Paper No. 970978, Society of Automotive Engineers, Warrendale, PA, 1997.

17. Lam, R. C. and Y.-F. Chen, “Friction Material for Continuous Slip Torque Converter Applications: Anti-Shudder Considerations,” SAE Paper No. 941031, Society of Automotive Engineers, Warrendale, PA, 1994. 18. Kamada, Y., et al., “Wet Friction Materials for Continuous Slip Torque Converter Clutch, Tribology for Energy Conservation,” Elsevier Science B.V., 1998. 19. Lam, Robert, et al., “Emerging New Friction Materials Technologies for Torque Capacity Prediction and Friction Materials Development,” Tribology of Vehicle Transmissions Symposium, Japan, 1998. 20. Wirth, J., “Research into the Use of Controlled Surface Technologies for Clutch Friction Surfaces,” SAE Paper No. 2001-01-1157, Society of Automotive Engineers, Warrendale, PA, 2001. 21. Nels, T. E., “Fabric Arrangement and Method for Controlling Fluid Flow,” U.S. Patent 5842551, United States Patent Office, Washington, DC, 1998. 22. Winckler, P. S., “Carbon-Based Friction Material for Automotive Continuous Slip Service,” U.S. Patent 5662993, United States Patent Office, Washington, DC, 1997. 23. Dowell, R. E., “High Energy Friction Product,” U.S. Patent 6277769, United States Patent Office, Washington, DC, 2001. 24. Bortz, D., “Friction Controlling Devices and Methods of Their Manufacture,” U.S. Patent 5646076, United States Patent Office, Washington, DC, 1997. 25. Fanella, R. J., “Design of Friction Clutches,” Design Practices: Passenger Car Automatic Transmissions, AE-18, Society of Automotive Engineers, Warrendale, PA, 1994, pp. 391–398. 26. Oshanski, J., G. Barrons, and K. Martek, “Design Practices for Reciprocating Clutch Seals in Automatic Transmissions,” SAE Paper No. 900334, Society of Automotive Engineers, Warrendale, PA, 1990. 27. Solt, M. B., “Optimizing Automatic Transmission Clutch Lining Load Distribution Using Finite Element Analysis,” SAE Paper No. 900559, Society of Automotive Engineers, Warrendale, PA, 1990. 28. Froslie, L. E., T. Milek, and R. W. Smith, “Automatic Transmission Friction Elements,” Design Practices: Passenger Car Automatic Transmissions, AE-5, Vol. 5, Society of Automotive Engineers, Warrendale, PA, 1973, pp. 106–124. 29. Jania, Z. J., “Friction-Clutch Transmissions,” Machine Design, November 13, 27 and December 11, 25, 1958. 30. Jania, Z. and A. Kushigian, “How Rotation Affects Hydraulic Pressures,” Machine Design, February 1955, pp. 180–188.

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31. Finkin, E. F., “Approximate Analysis of Stresses in Multiple Disc Clutch Teeth,” SAE Paper No. 680423, Society of Automotive Engineers, Warrendale, PA, 1968. 32. Park, D. H., T. S. Seo, D. G. Lim, and H. B. Cho, “Theoretical Investigation on Automatic Transmission Efficiency,” SAE Paper No. 960426, Society of Automotive Engineers, Warrendale, PA, 1996. 33. Kitabayashi, K., C. Y. Li, and H. Hiraki, “Analysis of the Various Factors Affecting Drag Torque in MultiplePlate Clutches,” SAE Paper No. 2003-01-1973, Society of Automotive Engineers, Warrendale, PA, 2003. 34. Yang, Y., R. C. Lam, Y. F. Chen, and H. Yabe, “Modeling of Heat Transfer and Fluid Hydrodynamics for a Multidisc Wet Clutch,” SAE Paper No. 950898, Society of Automotive Engineers, Warrendale, PA, 1996. 35. Osanai, H., K. Ikeda, and K. Kato, “Relations Between Temperature in Friction Surface and Degradation of Friction Materials During Engaging of Friction Paper,” SAE Paper No. 900553, Society of Automotive Engineers, Warrendale, PA,  1990. 36. Ohnuma, H. and K. Kato, “The Effect of Groove Pattern of Paper Friction Plate on Its Life,” SAE Paper No. 910804, Society of Automotive Engineers, Warrendale, PA, 1991. 37. Takezaki, K. and M. Kubota, “Thermal and Mechanical Damage of Paper Wet Friction Material Induced by Non-Uniform Contact,” SAE Paper No. 922095, Society of Automotive Engineers, Warrendale, PA, 1992. 38. Yang, Y., P. S. Twaddell, Y. F. Chen, and R. C. Lam, “Theoretical and Experimental Studies on the Thermal Degradation of Wet Friction Materials,” SAE Paper No. 970978, Society of Automotive Engineers, Warrendale, PA, 1997. 39. Zagrodzki, P. and S. S. Truncone, “Generation of Hot Spots in a Wet Multidisk Clutch During Short-Term Engagement,” Wear, Vol. 254, 2003, pp. 474–491. 40. Lee, K. and J. R. Barber, “Frictionally Excited Thermo­ elastic Instability in Automotive Disk Brakes,” ASME Journal of Tribology, Vol. 115, 1993, pp. 607–614. 41. Du, S., P. Zagrodzki, J. R. Barber, and G. M. Hulbert, “Finite Element Analysis of Frictionally Excited Thermoelastic Instability,” Journal of Thermal Stress, Vol. 20, 1997, pp. 185–203. 42. Zagrodzki, P. and J. P. Macey, “Theoretical and Experimental Study of Hot Spotting in Frictional Clutches and Brakes,” Proceedings of International Tribology Conference, Nagasaki, Japan, 2000, pp. 1931–1936. 43. Burton, R. A., “Thermal Deformation in Frictionally Heated Contact,” Wear, Vol. 59, 1980, pp. 1–20.

44. Zagrodzki, P. and T. D. Farris, “Analysis of Temperatures and Stress in Wet Friction Disks Involving Thermally Induced Changes of Contact Pressure,” SAE Paper No. 982035, Society of Automotive Engineers, Warrendale, PA, 1998. 45. Fanella, R. J., “Design of Friction Clutches,” Design Practices: Passenger Car Automatic Transmissions, AE-18, Society of Automotive Engineers, Warrendale, PA, 1994, p. 419. 46. Phelan, Richard M., Fundamentals of Mechanical Design, McGraw-Hill Book Company, New York, 1957. 47. Matsumoto, Takayuki, “A Study of the Influence of Porosity and Resiliency of a Paper-Based Friction Material on the Friction Characteristics and Heat Resistance of the Material,” SAE Paper No. 932924, Society of Automotive Engineers, Warrendale, PA, 1993. 48. Grzesiak, Anthony J. and Robert C. Lam, “Application of Fluid Transport Phenomenon to Transmission Band Friction Material,” SAE Paper No. 922098, Society of Automotive Engineers, Warrendale, PA, 1992. 49. Stebar, Russell F., Ellard D. Davison, and James L. Linden, “Determining Frictional Performance of Automatic Transmission Fluids in a Band Clutch,” SAE Paper No. 902146, Society of Automotive Engineers, Warrendale, PA, 1990. 50. Watts, R. F. and S. D. Sparrow, “Development of a THM 700-R4 Band Friction Test for the SAE #2 Machine,” SAE Paper No. 881675, Society of Automotive Engineers, Warrendale, PA, 1988. 51. Castanien, Christian J., “Control of Band/Drum Interface Temperature in Automatic Transmissions and the Impact Upon Friction System Durability,” SAE Paper No. 902147, Society of Automotive Engineers, Warrendale, PA, 1990. 52. Fujii, Yuji, Ted D. Snyder, Anthony J. Grzesiak, and Christopher C. Denault, “Fluid Influence on Shift Properties,” U.S. Patent 6,651,786B2, United States Patent Office, Washington, DC, 2003. 53. Juvinal, Robert, Stress, Strain and Strength, McGraw-Hill Book Company, New York, 1967. 54. Lloyd, F. A., “Parameters Contributing to Power Loss in Disengaged Wet Clutches,” SAE Paper No. 740676, Society of Automotive Engineers, Warrendale, PA, 1974. 55. Anleiter, Michael A., “Vibration and Noise in OilImmersed Friction Couples—A Basic Discussion,” SAE Paper No. 861202, Society of Automotive Engineers, Warrendale, PA, 1986.

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Chapter 7

One-Way Clutches John M. Kremer (Retired) BorgWarner Corporation

organized somewhat differently, each contains the essentials for system design and analysis: system equilibrium, system stresses, and system dynamics. Where a history of the clutch has provided application design knowledge and failure analysis, this has been provided, too.

Introduction A one-way clutch (OWC) is a mechanical device that has two basic modes of operation: (1) engaged, and (2) freewheeling (or overrunning). In its engaged mode of operation, the OWC “closes” a torque path, permitting torque to “flow through” it. In its freewheeling mode of operation, the torque path is “open,” allowing relative motion across the clutch. When the clutch is closed, one torque path is defined. When it is open, another is in effect. The essential purpose of the OWC is to allow a smooth, seamless, non-controlled transition between one torque path and the other. By “non-controlled,” we mean that the OWC system inherently responds to the change in the torque direction, requiring no external controls to effect the change in the functional mode of the clutch.

The wealth of information contained in this chapter does not arise from a single source. It has been compiled from various sources over the years. In recognition of these varied sources, a reference list has been provided at the end of this chapter. However, special recognition is due to the following authors of previous SAE Advances in Engineering publications: • C.S. Chapman—AE-5, Chapter 1: Introduction • E.A. Ferris—AE-5, Chapter 2: Automotive Sprag Clutches—Current Design and Application • R.E. Sauzedde and E.F. Bowie—AE-5, Chapter 3: Design of Roller One-Way Clutches in Current Passenger Car Automatic Transmissions • R.L. Merrell and E.F. Bowie—AE-5, Chapter 4: Roller One-Way Clutches for Today’s Passenger Car Automatic Transmissions • R.J. Fanella—AE-18, Chapter 7: One-Way Clutches, Section 1: Roller One-Way Clutches, and Section 2: Sprag One-Way Clutches

This chapter relates to the design and analysis of OWCs. There are three types of OWCs currently in use in automotive transmissions: 1. Roller 2. Sprag 3. Pawl

Their work provided a firm foundation upon which this chapter has been built.

Although the functioning of each of these types is the same, the way in which each achieves that functioning is different. To address the unique aspects of each type, this chapter has been divided into three major sections, one section for each type of OWC. Although each of these three sections is

John M. Kremer (Retired) BorgWarner Corp.

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7.1 Roller One-Way Clutches

coupling phase, overrunning automatically without controls to time the transition. When used with a gear set, the OWC improves shift quality because it eliminates the need to synchronize the applying and releasing friction elements.

7.1.1 Introduction 7.1.1.1 Roller One-Way Clutches [1] Roller-type one-way clutches (OWCs) have provided dependable low-cost service for decades in a wide variety of automotive automatic transmissions. Roller clutches were first used as grounding elements in torque converter stators. Soon afterward, higher-capacity roller clutches were successfully used to ground first-gear reaction torque in compound planetary gear sets. In recent years, roller clutches have also been used successfully in many overdrive applications, where OWCs are required to transmit torque, release, and re-engage while both drive and driven elements are rotating at several thousand revolutions per minute.

7.1.1.2 Types in Present Transmissions [2] There are four basic types of roller clutches: 1. 2. 3. 4.

Loose rollers—inertia or gravity energized Caged rollers—cage energized Loose rollers—individually spring energized Caged rollers—individually spring energized

Type 1 has no mechanical means of energizing the rollers but depends on centrifugal force to place all the rollers in contact with the races. If torque is applied at 0 rpm, only those rollers that will fall into the wedge due to gravity will take the load.

A roller OWC is defined as having an outer race and an inner race (one of which contains the cam profile), rollers, springs that activate the rollers, and a means of positioning the springs. Further, this section deals exclusively with clutches having individually spring-energized rollers, because this is the type being used today.

In Type 2, the rollers are energized by means of a springactuated cage. This requires close tolerances on the cam and cage dimensions to ensure that each roller will take its share of the load and thus utilize the full capacity of the clutch.

One-way clutches have found a home in torque converters and transmissions where an element must act as a reaction member and transmit or resist torque in one direction, yet must rotate freely when the direction of rotation reverses. The OWC does exactly that, transmitting torque in one direction and overrunning or rotating freely in the opposite direction. While performing these basic functions, the roller clutch has these advantages over other types of devices:

Types 3 and 4 have each roller independently energized to the races by a spring, thus ensuring that each roller is in position to take its share of the load when torque is applied. These two types are used in present automatic transmissions. One design of the loose roller clutch, commonly known as the leg type, is shown in Fig. 7.1. It has legs integral with the cammed race that project into the space between the rollers and provide a reaction for the spring. Another design (Figs. 7.2 and 7.3) uses a sheet-metal retainer properly indexed to the cams to provide a reaction for the spring. In these clutches, the rollers and springs are inserted between the races at the time of assembly into the transmission unit.

1. It puts a relatively large torque-carrying capacity in a given space. 2. There is no need for external control, for, by its nature, it will transmit or release torque at the exact instant it is required to do so. 3. When overrunning, the drag (or friction) is a small fraction of its torque-carrying capacity. 4. When the clutch is carrying the torque, there are no resultant axial forces that must be resisted by adjacent parts. 5. It has a tremendous reserve capacity for occasional overloads. These properties satisfy needed functions in two areas in today’s automotive transmission: (1) the stator, and (2) the gear set. Most hydrodynamic torque converters use the roller clutch in the stator position. The clutch grounds the stator when the converter is in its torque multiplication phase, and it allows the stator to rotate as the converter changes to its fluid

Fig. 7.1  Stator roller clutch: leg type with loose springs and rollers [2].

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Fig. 7.2  Stator roller clutch: loose springs and rollers with retainer [2].

Fig. 7.5  Planetary reaction roller clutch: concentricity control cage [2].

Fig. 7.3  Planetary reaction roller clutch: loose springs and rollers with retainer [2]. Fig. 7.6  Inner race cams: concentricity control cage [2].

In the caged roller, individually spring-energized type (Figs. 7.4 through 7.6), the rollers and springs are pre-assembled into the cage. This provides a package for ease of assembly into the transmission unit. In the particular case of a blind assembly, the cage will hold the rollers in position against one race while the other race is assembled. The cage also provides for a fixed location for the springs between the races, preventing rubbing of the spring loops on either race.

7.1.2 Design Considerations 7.1.2.1 Roller Energizing Springs The purpose of the energizing spring is to position the roller so that it is ready to engage and take its share of the torque load. In the caged type of clutch, springs also hold the rollers in place for ease of transmission assembly. Currently, the majority of roller OWCs used in automatic transmissions employ accordion-type or z-type springs and are made of 301 or 302 stainless steel. The nominal load and spring rate for these springs vary considerably and are dependent on the functional requirements of the clutch. These requirements will be addressed in later sections of this chapter. 7.1.2.2 Cage

Fig. 7.4  Caged-type roller clutch with individual springs [2].

The use of a cage in roller OWC design is not essential, as is evident from Figs. 7.1 and 7.2. Because the addition of a cage adds cost and consumes packaging space, the decision to use one must be based on the value it adds to the assembly. Functional features that a cage can provide include:

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• Unitized assembly —The cage holds the rollers, energizing springs, and possibly other components in a unit that facilitates assembly into the transmission. • Indexing—The cage indexes the assembly to the cammed race, thereby providing proper positioning of the springs and rollers. • Spring anchor—The cage provides a means of anchoring the energizing springs with respect to the cammed race, thereby providing the proper energizing force to the rollers. • Spring protection—The cage can provide solid-height protection for the energizing springs. In so doing, the OWC system is then more robust against roller pop-out related failures. • Concentricity control —Often, the concentricity between the inner and outer races of the clutch relies on the clutch itself. When this is a functional requirement, concentricity features can be built into the cage, or the cage can capture concentricity-controlling features such as bearing blocks.

7.1.2.3 Race Concentricity Control Concentricity control between the races of a roller OWC is very important. Any runout of one race with respect to the other can cause movement of the roller “up” and “down” its cam. (This topic is covered in more detail in Section 7.1.5, System Kinematics, and Section 7.1.6, System Dynamics, of this roller OWC section.) This cycling of the roller also cycles the energizing spring and can lead to a fatigue failure of the component. As stated in the previous subsection, the plastic roller cage itself can provide concentricity control. For the stamped steel roller clutch cage, bearing blocks can provide this control. These bearing blocks are typically made of plastic, bronze, or bronze-clad steel. Figure 7.8 shows an example of a plastic bearing block.

Cage design has evolved greatly over the past decade. Whereas stamped steel designs were state of the art in the early 1990s, plastic cage designs are now commonplace. Figure 7.7 shows an example of a plastic cage roller clutch. Note that the cage provides positive indexing of the clutch with respect to the cammed outer race and that it also provides concentricity control for the races.

Fig. 7.8  Outer cam roller OWC with stamped steel cage and plastic bearing block for concentricity control. When a roller clutch is used in the stator position of a torque converter, the outer race is generally pressed into or molded into the stator. End caps can then be provided to give concentricity control between the inner race and the stator (and sub-

Fig. 7.7  Inner cam roller OWC with plastic cage having integral concentricity control. 7-4

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One-Way Clutches

is recommended in determining race dimensions, and the concentrated load effect should be considered.

sequently the outer race). Figure 7.9 illustrates this method of concentricity control.

Because the strut angle materially affects the stresses, it should be carefully selected. The larger the strut angle, the smaller the stresses and vice versa. It should, therefore, be as large as possible for maximum clutch capacity but small enough to prevent slipping. If the tangent of the strut angle exceeds the coefficient of friction, slipping and pop-out will occur. For design and manufacturing purposes, included angles of 6 to 8 degrees (strut angles of 3 to 4 degrees) have been used successfully, but 7 to 8 degrees is most common in presentday clutches. The actual angles under load probably deviate from this due to various deflections present. 7.1.2.5 Material and Heat Treat [2] Table 7.1 summarizes the material and heat-treat specifications being used for roller clutch races in present passenger car automatic transmissions. As noted, both low-carbon steel with a carburized case and high-carbon steel with a flame or induction-hardened case are equally acceptable from an engineering standpoint. Economics usually decides and depends many times on race configurations such as size or cross-sectional shape, necessity for hardened serrations, or size and location of mounting holes.

Fig. 7.9  Stator roller OWC with end caps for concentricity control. 7.1.2.4 Stresses [2]

7.1.2.6 Surface Finish [2]

Two stressed areas should be investigated in the design of the roller clutch races: (1) the mean hertz stresses at the roller contact, and (2) the hoop stress in the outer race. A mean hertz stress in the range of 3792 MPa (550 kpsi) based on the calculated torque load has proven to be conservative for most applications. Where there is little likelihood of shock loads, this may often be exceeded.

The surface finish required on the stressed surfaces depends somewhat on the fatigue life desired at the roller contact, but also on conditions associated with overrunning. On the cams, we find little difference in the fatigue life of the surface for surface finishes between 1.02 to 3.05 µm (40 to 120 µin.). This is the range of surface finishes obtainable with a broach. We assume that smoother surfaces, such as a ground cam, might show longer life. With cylindrical races, because they are traditionally hardened and ground, the surface is always 0.76 µm (30 µin.) or better, giving excellent fatigue properties, everything else being equal. Therefore, if there is a need for a better surface, the need comes from the operation of the clutch in its overrunning mode. When the rollers are forced to slide on the cylindrical surface, permissible drag, roller scoring, and sound generation must be considered. Experience shows that 0.51 µm (20 µin.) is required in most cases and 0.25 µm (10 µin.) in some, to keep the drag at a minimum, eliminate any chance of roller scoring, and reduce the level of any forced sound generation to the point that will not excite undesirable noise in the transmission. If the clutch cage side rails are used as bearings, the surface finish should be smooth enough to minimize wear. This depends on the side rail design and the loads to be carried.

The outer race hoop stress is equally as important as the hertz stress. Because the roller clutch has a high cam rise, the roller can move into the wedge to compensate for race deformations. Therefore, the hoop stress rather than race deflections under load will become the limiting factor. While a hoop stress as high as 552 MPa (80 kpsi) has been recommended for some applications, this should be tempered with engineering judgment. The outer race may have non-uniform cross sections or may be a composite of two sections of different metals such as a steel race pressed into a cast iron or aluminum housing. The race may have a flange or web on one side, potentially resulting in bellmouthing of the other side while under load. Oil holes or mounting holes that will induce concentrated stress areas may be present. Most race applications today have one or more of these conditions; therefore, a hoop stress of 345 to 414 MPa (50 to 60 kpsi)

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Table 7.1  Material and Heat Treatment for Roller Clutches [2]

7.1.2.7 Oil Holes [2]

7.1.3 System Equilibrium [3]

Oil holes in one or both races are often a necessary evil to provide lubrication for the clutch and mating parts. In the cylindrical race, this hole is invariably in the load path. Therefore, the angle of the hole should be as nearly perpendicular to the race surface as possible. Angles less than 70 degrees for an inner race and 60 degrees for an outer race are not recommended. A shallow angle will produce a small, unsupported area in the load path, which can lead to premature spalling or cracking. The position of the oil hole as it breaks into the load path is also critical. Hole location tolerances, plus permissible axial float of the roller with respect to the race, should be checked to ensure that the oil hole does not reach the edge of the load path. Again, spalling or cracking can occur if the end of the loaded roller is too close to the hole.

7.1.3.1 Roller Forces The first step in understanding the stresses acting on a roller OWC is to understand the balance of forces and torques acting on an engaged roller. Figures 7.10 and 7.11 show the free body diagram of a roller in an outer cam and inner cam OWC, respectively. As shown, the geometry is slightly different because of the cam location; however, our free body analysis is fundamentally the same. The contact force between a roller and the races is on the order of several thousand Newtons. The spring force acting on the roller is generally less than 10 N. Therefore, without loss of accuracy, we can neglect the spring load in our equilibrium analysis. This is the underlying assumption used in the following analysis.

7.1.2.8 Lubrication [2] Because the roller clutch must operate in approved automatic transmission oils, it is fortunate that these oils are satisfactory. The clutch, during overrunning, requires an oil film at the sliding surfaces, that is, between the rollers and the cylindrical race, and at the bushing. A larger quantity of oil than is necessary to maintain this film may be passed through the clutch to lubricate other elements of the transmission without any harmful effects on the engaging ability. However, additives such as graphite or molybdenum disulfide, which significantly reduce the coefficient of friction, should not be used, as rollers may slip under load and pop out. Fig. 7.10  Free body diagram of the roller in an outer cam OWC [3]. 7-6

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7.1.3.2 Strut Angle Limits In the previous section, it was demonstrated that the strut forces F(i) and F(o) can be decomposed into their tangential and normal components, as shown in Eqs. 7.2 and 7.3, respectively. The basic relationship between the tangential and normal forces and the strut angle is obtained by dividing Eq. 7.2 by Eq. 7.3



The roller is in equilibrium; thus, the total force acting between the inner race and roller (F(i)) is equivalent to the total force acting between the outer race and roller (F(0)). That is, F(i) = F(0)

Ff(i) = F(i) . sin α



(7.1)

Fn(i) = F(i). cos α

T(i) = Ff(i) . OR(i) . N(r)

(7.2)

T(i) = F(i) . sin α . OR(i) . N(r)

(7.7)

Ff(i) £ μFn(i)

(7.8)

tan α £ μ

(7.9)

1. The race and roller surface finish 2. The lubrication fluid composition 3. The lubrication fluid temperature

(7.3)

The value of µ for hardened steel on hardened steel bathed in automatic transmission fluid is generally between 0.080 and 0.120. Using the lower limit of 0.080 as our value for µ, Eq. 7.9 yields a maximum strut angle value of

(7.4)



Equation 7.2 showed that the tangential force between the inner race and a roller (Ff(i)) is a trigonometric function of the total force between the inner race and a roller (F(i)). That is, Ff(i) = F(i) . sin α, and Eq. 7.4 becomes

= tanα

The coefficient of static friction μ of the clutch environment is not a single-valued variable but has a range of values. It depends on factors that can change during the life of the clutch. These factors include:

The total torque between the inner race and rollers (T(i)) for an outer cam roller clutch is the product of the tangential force between the inner race and a roller (Ff(i)), the moment arm (OR(i)), and the number of rollers (N(r))

F(i ) ⋅cosα

This expression sets the upper limit for the value of the strut angle α.

The final step in balancing the forces on a roller is to derive the normal force (Fn(i)) acting on the roller

F(i ) ⋅sinα

Equations 7.7 and 7.8 define the same system and therefore are interdependent. Substituting Eq. 7.7 into Eq. 7.8 and simplifying, we get

The tangential force acting between the inner race and roller (Ff(i)) is a trigonometric function of the total force between the inner race and roller (F(i)) and the strut angle (α)

Fn(i )

=

The tangential force Ff(i) is also the frictional force of the system. Its magnitude is dependent on the normal force Fn(i) and is limited by the static coefficient of friction µ. That is,

Fig. 7.11  Free body diagram of the roller in an inner cam OWC [3].



Ff (i )

α £ 4.574°

(7.10)

During operation of the clutch, the strut angle must never exceed this limit, or the rollers may slip when the clutch engages. Dimensional variations during component manufacture, or wear as a result of clutch operation, can cause the strut angle to deviate from the desired value. Therefore, it is prudent to specify a strut angle that is less than the maximum.

(7.5)

Solving Eq. 7.5 for the total force per roller F(i), rather than torque, results in T(i ) (7.6) F(i ) = N(r ) ⋅OR (i ) ⋅sinα

Equation 7.10 defines the upper limit of the strut angle. There are practical limits on the minimum strut angle also. For example, a strut angle of 1 degree is feasible; however, the release of the elastic strain energy in the clutch system (when the transmitted torque drops to zero) tends to trap the roller

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and prevent a smooth disengagement of the clutch. In addition, a greater normal force is required to transmit a given operating torque as the strut angle decreases, and this, in turn, increases the contact and hoop stresses generated in the races. Figure 7.12 exemplifies this relationship, wherein we have plotted the strut component force ratio versus the strut angle.

properties of the inner race and roller (ν(i), E(i), ν(r), E(r)), as follows:



Fig. 7.12  Ratio of the strut force components as a function of strut angle [3].

⎛ 1 1 ⎞ + 2⋅F(i ) ⋅ ⎜ ⎟ ⎝ OR (i ) OR (r ) ⎠ σ c( max ) = ⎛ 1− ν(2i ) 1− ν(2r ) + π ⋅L(r ) ⋅4 ⎜ ⎜⎝ E(i ) E(r )

(

) (

)

⎞ ⎟ ⎟⎠



(7.11)

Fig. 7.13  Geometry definition of outer cam roller clutch [3].

7.1.4 System Stresses

A commonly used derivation of Eq. 7.11 defines hertz stress in terms of its mean value (σc(mean)), rather than maximum value [5, 6], as

7.1.4.1 Contact Stress [3] Spalling and brinelling are two possible failure modes of a roller OWC. Both are contact-stress related. Computation of the contact stress and how it relates to OWC design is discussed in this section.



We assume that the roller OWC has multiple rollers, each carrying an equal portion of the load. Therefore, examining one roller is representative of all rollers within the clutch. The race/roller contact in a roller OWC is either concave/convex, as between the outer race and roller; or convex/convex, as between the inner race and roller. The former is referred to as conformal contact, whereas the latter is referred to as non-conformal contact. Non-conformal contact loads lead to higher contact stresses; therefore, we are concerned with only the inner race/roller contact stresses. The variables used in the following discussion are defined in Fig. 7.13.

⎛ 1 1 ⎞ + F(i ) ⋅π ⋅ ⎜ ⎟ ⎝ OR (i ) OR (r ) ⎠ 1 σ c( max ) = ⋅ ⎛ 1− ν(2i ) 2 1− ν(2r ) + L(r ) ⋅4 ⎜ ⎜⎝ E(i ) E(r )

(

) (

) ⎞⎟



(7.12)

⎟⎠

We use the equation for mean contact stress to derive an additional term for the total force per roller (F(i)). The constants and material properties from Eq. 7.12 (π, ν(i), ν(r), E(i), E(r)) are brought outside the radical and are named c1:

The equation to determine maximum hertz stress (σc(max)) between two convex surfaces is defined by Young [4] in terms of the resultant force between the inner race and roller (F(i)), the outer radius of the inner race (OR(i)), the roller radius (OR(r)), the length of the roller (L(r)), and the material

1 π c1 = ⋅ 2 2 ⎛ 4 1− ν(i ) 4 1− ν(2r ) + ⎜ ⎜⎝ E(i ) E(r )

(

) (

) ⎞⎟



(7.13)

⎟⎠

Then, Eq. 7.12 simplifies to



⎛ 1 1 ⎞ + F(i ) ⋅ ⎜ ⎟ ⎝ OR (i ) OR (r ) ⎠ σ c( mean) = c1 ⋅ L( r )

(7.14)

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magnitudes of length; therefore, only the positive root is considered.

Solving Eq. 7.14 in terms of total force per roller (F(i)) results in 2

⎛ σ c mean ⎞ L( r ) ⋅ ⎜ ( ) ⎟ ⎝ c1 ⎠ F(i ) = ⎛ 1 1 ⎞ ⎜ OR + OR ⎟ ⎝ (r ) (i ) ⎠



7.1.4.2 Hoop Stress

(7.15)

Contact forces between the rollers and races create a circumferential (hoop) stress in the outer and inner races. The hoop stress on the inner race is compressive, and steel does not typically fatigue due to compressive stresses. However, the outer race experiences tensile hoop stresses, which is a typical mode of fatigue failure for steel. Therefore, we consider hoop stress for only the outer race.

For an outer cam roller clutch, we now have two equations (Eqs. 7.6 and 7.15) that solve for total force per roller (F(i)). We set Eq. 7.6 equal to Eq. 7.15 and obtain 2

⎛ σ c mean ⎞ L( r ) ⋅ ⎜ ( ) ⎟ T(i ) ⎝ c1 ⎠ = N(r ) ⋅OR (i ) ⋅sinα ⎛ 1 1 ⎞ ⎜ OR + OR ⎟ ⎝ (r ) (i ) ⎠



There are two approaches to the problem of hoop stress in the outer race: (1) the uniform pressure approach, and (2) the discrete load approach. Each approach has its own advantages and limitations, and these will be discussed in the subsections below. Note that either method assumes smooth cylindrical surfaces at both the inner and outer diameters. If this is not the case, appropriate stress concentration factors must be applied to augment the results of these computations. The reader is directed to Ref. [4] for a discussion of stress concentration factors.

(7.16)

During the actual design process for an outer cam roller clutch, we want to determine the optimal inner race outer radius (OR(i)), given material property and loading characteristics. That is, Eq. 7.16 is solved in terms of the inner race outer radius (OR(i)). Equation 7.16 does not have a simple solution for the inner race outer radius (OR(i)); however, it is a quadratic equation in the form 2 ⎛ ⎛σ ⎞ ⎞ 0 = ⎜ OR (r) ⋅ N(r) ⋅ sinα ⋅ L(r) ⋅ ⎜ c(mean) ⎟ ⎟ ⋅ OR (2i) ⎝ c1 ⎠ ⎠ ⎝

(

)

(

+ −T(i) ⋅ OR (i) + −T(i)OR (r)

)

7.1.4.2.1 Uniform Pressure Approximation [3]

In the first approach, it is assumed that the discrete roller loads can be accurately approximated by a uniform pressure load on the inner surface of the outer race (see Fig. 7.14). If the number of rollers N(r) in the clutch is sufficiently high, the bending moments generated by the discrete loading are relatively low. Under such conditions, this method proves to be reasonably accurate. (Analysis indicates that under most conditions, for N(r) > 8, the bending moment contribution is negligible.) Employing this method of hoop stress analysis enables us to formulate design equations, as will be shown.

(7.17)



The quadratic equation that solves for the inner race outer radius OR(i) is 2 ⎛ ⎛ σ c mean ⎞ ⎞ T(i ) ± T(2i ) − 4⋅ ⎜ OR (r ) ⋅N(r ) ⋅sinα ⋅L(r ) ⋅ ⎜ ( ) ⎟ ⎟ ⋅ −T(i ) ⋅OR (r ) ⎝ c1 ⎠ ⎠ ⎝ OR (i ) = 2 ⎛ ⎛ σ c mean ⎞ ⎞ 2⋅ ⎜ OR (r ) ⋅N(r ) ⋅sinα ⋅L(r ) ⋅ ⎜ ( ) ⎟ ⎟ ⎝ c1 ⎠ ⎠ ⎝

(

)

(7.18)

That is, given load, material property, and roller parameters, Eq. 7.18 calculates the outer radius of the inner race for an outer cam roller clutch. Fig. 7.14  Uniform pressure approximation model.

To use Eq. 7.18, we must select an operating contact stress at which the roller OWC will operate. Application history has shown that limiting the mean contact stress to 3792 MPa (550,000 psi) is reasonable for roller OWC applications. Equation 7.18 yields two real roots: one negative, and one positive. The negative root is meaningless when discussing

The governing equation for the mean hoop stress in the outer race (σh(mean)), as defined by thick cylinder analysis, is a function of the pressure on the interior surface of the outer race

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the outer diameter, and (2) between the roller loads at the inner diameter. These locations, as well as other information pertinent to this analysis, are illustrated in Fig. 7.15.

(Q(o)) and the wall thickness of the outer race (OR(o) and IR(o)) [7, 8]:

⎛ OR (2o) + IR (2o) ⎞ σ h( mean) = Q(o) ⋅ ⎜ 2 2 ⎟ ⎝ OR (o) − IR (o) ⎠

(7.19)

The pressure on the inner surface of the outer race (Q(o)) of an outer cam roller clutch is a function of the radial force per roller (F(o) . cos α), the number of rollers (N(r)), and the total inner surface area of the outer race (2 . π . r . l = 2 .  π . IR(o) . L(o)):

⎛ N(r ) ⋅cosα ⎞ Q(o) = F(o) ⋅ ⎜ ⎟ ⎝ 2⋅π ⋅IR (o) ⋅L(o) ⎠

(7.20)

If we assume that the length of the roller is equal to the length of the outer race (L(r) = L(o)), and substitute Eqs. 7.1, 7.15, and 7.20 into Eq. 7.19, then the following equation is derived for the mean hoop stress (σh(mean)) in the outer race:



Fig. 7.15  Discrete load approximation model. The results that Sauzedde and Bowie obtained are summarized in the following two equations:

2 2 2 ⎛ σ c( mean) ⎞ ⎛ OR (o) + IR (o) ⎞ σ h( mean) = ⎜ ⋅⎜ ⎟ ⎝ c1 ⎟⎠ ⎝ OR (2o) − IR (2o) ⎠



(7.21)

⎛ OR ⋅OR ⋅N ⋅cosα ⎞ (r ) (i ) (r ) ⋅⎜ ⎟ ⎜⎝ OR (r ) + OR (i ) ⋅2⋅π ⋅IR (o) ⎟⎠

(

)

However, we want to assume the average hoop stress (σh(mean)) that the outer race will encounter and then calculate the outer radius accordingly (OR(o)). Note that the inner radius of the outer race (IR(o)) is determined based on the geometry of the inner race calculated via Eq. 7.18 and the geometry of the rollers.

OR (o) =

Q(o) ⋅IR (2o) + σ h( mean) ⋅IR (2o) σ h( mean) − Q(o)



⎛ 1 F(o) ⎡ 1 R m(o) − e(o) ⎞ ⎛ R m(o) ⋅ho(o) ⎞ ⎤ (7.23) −⎜ − ⋅ ⎥ ⎢ 2⋅A(o) ⎢⎣ tanφ ⎝ tanφ φ⋅R m(o) ⎟⎠ ⎜⎝ e(o) ⋅OR (o) ⎟⎠ ⎥⎦

σ h@2 =

⎛ 1 F(o) ⎡ 1 R m(o) − e(o) ⎞ ⎛ R m(o) ⋅h i(o) ⎞ ⎤ −⎜ − ⎢ ⎟ ⋅⎜ ⎟⎥ 2⋅A(o) ⎢⎣ sinφ ⎝ sinφ φ⋅R m(o) ⎠ ⎝ e(o) ⋅IR (o) ⎠ ⎥⎦



(7.24)

where F(o) is the contact force, A(o) is the cross-sectional area of the race, Rm(o) is the mean radius of the race cross section, e(o) is the distance from the mean radius to the neutral axis, hi(o) is the distance from the neutral axis to the inner surface, ho(o) is the distance from the neutral axis to the outer surface, OR(o) is the outer radius of the race, IR(o) is the inner radius of the race, and φ is the half angle between the loads, which is defined as π φ= (7.25) (radians ) N The cross-sectional area of the outer race is given as

Therefore, Eq. 7.21 is put in terms of the outer radius of the outer race, where the pressure on the interior surface of the outer race (Q(o)) was previously defined in Eq. 7.20, that is,

σ h@1 =

(7.22)



7.1.4.2.2 Discrete Load Approximation

The second method of hoop stress analysis assumes that the bending generated by the discrete loads is not negligible. The point load approximation for the computation of hoop stress in a thick-walled cylinder is based on Timoshenko’s formulation for curved beam analysis [8]. Application of this theory to the analysis of race stress in a roller OWC was presented by Sauzedde and Bowie [9]. Therein, two critical locations for stress were noted: (1) above the roller load at

(

)

A(o) = W(o) ⋅ OR (o) − IR (o)

(7.26)

where W(o) is the width of the outer race. The mean radius Rm(o) of the race is given as

R m(o) =

OR (o) + IR (o) 2



(7.27)

e(o) is the distance between the neutral axis and the mean radius, and is given as [10]

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⎤ ⎡ ⎥ ⎢ ⎢ OR (o) − IR (o) ⎥ e(o) = R m(o) − ⎢ ⎛ ⎞ ⎥ ⎢ ln OR (o) ⎥ ⎢ ⎜⎝ IR (o) ⎟⎠ ⎥ ⎦ ⎣

where δst is the deflection of the system due to a statically applied roller load F(i), and C is the spring rate of the system, we can conclude that our system is essentially the same as that investigated by Ugural and Fenster, and that the conclusions drawn by them are applicable to our system. Taking note that our roller load F(i) is proportional to the applied torque T (see Eq. 7.5), we conclude that only half the maximum statically applied torque can be applied under shock loading conditions.

(7.28)

The variables hi(o) and ho(o) are the distances from the neutral axis to the inner and outer surfaces of the race, respectively. These variables are given as

hi(o) = IR(o) – Rm(o) + e(o)

(7.29)

7.1.5 System Kinematics



ho(o) = OR(o) – Rm(o) + e(o)

(7.30)

7.1.5.1 Variation in Roller Space [2] The roller space is defined as that radial area between the cylindrical race and the cam. For an outer cam design, if the radial space is made smaller, the roller is forced outward from the center and up the cam. Conversely, as the radial space is increased, the roller is pushed inward toward the center and down the cam by the spring.

7.1.4.3 Shock Loading In the previous subsections, various methods of computing system stresses have been presented. For each of these methods, the applied torque is a given quantity. Under normal conditions, when the loads are applied relatively slowly, the dynamics of loading can be neglected, and the system stresses can be accurately computed using the static load. However, if the load is applied quickly, commonly known as impact or shock loading, computed stresses based on the static load condition could prove to be underestimates. When loads are applied suddenly, in a period of time less than or equal to the first natural period of the structure [11], shock loading occurs.

The variation in roller space as the clutch rotates may be caused by the following: 1. Dimensional tolerances of installed races 2. Clearance of mounting bearings 3. Eccentricity of components Due to the high cam rise, roller clutches may be designed for a large variation in roller space. This permits relatively liberal manufacturing tolerances. However, for each new design, the dimensions and tolerances must be controlled sufficiently so that when the clutch is overrunning, the roller is free to unlock, and when the clutch is engaged, the roller is unobstructed in its movement into the loading position. A design layout showing all parts in their extreme positions can guarantee a good design in this respect.

By examining the work done by a falling body onto a linearelastic spring, Ugural and Fenster [11] demonstrated that, in a conservative system, the maximum deflection δmax of the spring is related to the static deflection δst and the height h from which it is dropped as

δ max = δ st +

( δ st )2 + 2⋅δ st ⋅h

(7.31)

If the drop height h is zero, the problem then is one of shock loading, and Eq. 7.31 becomes

δmax = 2 . δst

A major factor in controlling the roller space is the concentricity control or positioning of one race with respect to the other during rotation. It may be accomplished in various ways. With the leg-type loose roller and spring clutch, the bore of the legs may, in some cases, be used as a bearing riding the inner race with a close fit (Fig. 7.16). Straddlemounted plain bearings (Fig. 7.17) or a plain bearing on only one side (Fig. 7.18) may be used. An axially compact design using a single plain bearing is accomplished by supporting the housing of one race under the ID of the other (Fig. 7.19). With the caged-type clutch, the side rails of the cage may be designed as bearings and provide the concentricity between races (Fig. 7.20).

(7.32)

Therefore, under shock loading conditions, we can expect a linear-elastic spring to have twice the deflections as that of a statically applied load of comparable magnitude. In other words, the magnitude of the maximum allowable shock load is half the magnitude of the maximum allowable statically applied load for a given stress and deflection condition. Noting that the deflections in an OWC can be written as

δst = C . F(i)

(7.33)

7-11

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Fig. 7.16  Concentric control at the bore of the legs [2].

Fig. 7.19  Plain bearing of an axially compact design [2].

Fig. 7.17  Straddle-mounted plain bearings [2].

Fig. 7.20  Cage side rails as bearings [2]. 7.1.5.2 Axial Space [2] One consideration that is often overlooked is the race width overlap required due to axial stack-up or float of one race in relation to the other. If this is ignored, and the axial space is a maximum, the rollers or cage may be positioned off the edge of one race. On the other hand, when the tolerances go the other way, the minimum axial space should be approximately 0.254 mm (0.010 in.) greater than the maximum width of the clutch to provide for running clearance.

Fig. 7.18  Plain bearing on one side [2].

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7.1.5.3 Roller Skew [12]

2. If the geometric axis of the race is skewed relative to the other axes, oscillating roller skew will take place. This can be destructive to the conventional style energizing springs in both centrifugally neutral and centrifugally disengaging clutches.

Any roller clutch design should be carefully reviewed for potential skewing between the cam and race. 1. If the geometric axis of the cam is able to skew relative to the other axes, a fixed roller skew can take place, which can be destructive in a centrifugally neutral design (i.e., an inner cam design).

7.1.5.3.1 Skewed Cam to Race

If the cam and race are skewed relative to each other, the axial roller space in the plane of skew will not be constant. A simplified example is shown in Fig. 7.22.

For the cam angles commonly used, the roller skew angle is approximately 7.5 times the cam-to-race skew angle. As can be seen from Fig. 7.21, the maximum coefficient of traction is essentially reached at 1 degree roller skew, which occurs at 0.133 degree cam-to-race skew. This very low cam-to-race skew angle requirement means that full roller thrust would be achieved with only 0.058 mm (0.0023 in.) radial running clearance between the race and cam per 25.4 mm (1 in.) of pilot length. This running clearance is tighter than those achieved by normal manufacturing tolerances. If the cam is attached to an overhung mass, great care must be taken to balance the assembly. Figure 7.21 shows that a moment of only 0.050 N-m (0.037 lb-ft) will produce cam-to-race skew angles sufficient to produce maximum axial roller thrust.

Consider the cam and race as two flat surfaces. If the two surfaces are not skewed relative to each other (Fig. 7.22(a)), the roller space between the cam and race will be constant in a plane through the geometric axis of the cam. By adding a skew angle θ between the surfaces (Fig. 7.22(b)), the roller space along the geometric axis is no longer constant. However, there will be a plane α (Fig. 7.22(c)) that will have a constant space. This plane is skewed from the geometric axis of the cam by the angle ψ. Plane α is parallel to line β, which is the line formed by the intersection of the extended cam and race surfaces. Because the roller is being pushed into the wedge between the cam and race, the axis of the roller will lie along plane α and will be skewed relative to the cam and race by the angle ψ.

Fig. 7.21  Cam-to-race compliance [12]. If any of the above conditions exist, the material used for the roller end restraint (i.e., the cage) becomes critical. While observed roller forces were in the magnitude of only 245 to 267 N, roller speeds of 20,000 rpm are not uncommon. Roller end configuration and lubrication must also be considered.

Fig. 7.22  Cam-to-race skew [12].

Roller rotation and side thrust is not a concern on centrifugally disengaging clutches. 7-13

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of rotation were skewed, the plane of maximum skew would remain fixed relative to the ground. If the geometric axis is skewed, the plane of maximum skew will rotate.

With the aid of Fig. 7.23, the derivation of the equations for this skewed condition is shown. tanψ =



b a tanθ tanθ = ⋅ = t tanφ a tanφ



(7.34)

⎛ tanθ ⎞ ψ = tan −1 ⎜ ⎝ tanφ ⎟⎠

(7.35)



ψ ≈ θ . contangent (φ)

(7.36)



ψ = 7.6 θ

(7.37)

If θ  φ, then

Fig. 7.24  Overhung out-of-balance mass [12]. 7.1.5.3.3 Types of Roller Skew

1. If the geometric axis of the cam is skewed and all other axes are aligned, the rollers in the plane of skew will assume a skew angle other than zero. Those rollers that are 90 degrees from the plane of skew will be straight. This is an example of where the plane of skew follows the cam. Because of this, the skew angle of any one roller will remain fixed during the clutch rotation. This condition is illustrated in Fig. 7.25.

Fig. 7.23  Relationship of roller skew to cam skew [12]. 7.1.5.3.2 Variations of Cam-and-Race Skew

On examining the behavior of roller skew, four axes must be considered: (1) cam geometric axis, (2) cam axis of rotation, (3) race geometric axis, and (4) race axis of rotation. Skewing of the cam and/or race geometric axis can be caused by: 1. Manufacturing variations, such as a supporting member being out of square with the axis of rotation 2. A loosely mounted cam or race with an overhung outof-balance mass (Fig. 7.24)

Fig. 7.25  Geometric axis of cam skewed [12]. The roller skew was verified experimentally by filming an open-ended clutch in operation at 9,000 frames per second. In this case, trunnion end rollers were used (Fig. 7.26). The camera lens was aligned with the fixture’s axis of rotation. By measuring the image on each frame of the film, it was possible to calculate the skew angle of each roller.

The significance of a skew moment from an overhung mass is illustrated in the experimental data plotted in Fig. 7.21. Here, the cam was rotating, and the outer race was stationary. A skewing moment was applied to the outer race with a torque arm and static weights. The skew angle was measured using a fiber optics technique. Results showed that if the axis

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2. If the geometric axis of the race is skewed and all other axes are aligned, the plane of skew of the race will rotate relative to the cam and rollers. Because of this, the raceto-cam skew of any one roller will oscillate between a right-hand and left-hand skew once per relative revolution, as illustrated in Fig. 7.28, that is, the roller.

Fig. 7.26  Trunnion end rollers [12]. Testing was done with the cam skewed at 0.75 degree and rotated at 2000 rpm. For this particular clutch, 0.75-degree cam skew theoretically would produce a roller skew of 5.7 degrees. The observed data are shown in Fig. 7.27. The discrepancy between the observed and theoretical values is attributed to the fact that random production parts were used. The difference is well within production tolerances.

Fig. 7.28  Geometric axis of the race skewed [12]. This phenomenon was also verified with high-speed camera studies. Figure 7.29 shows the angle, frame by frame, of one roller for one revolution of the race. Superimposed is the theoretical sine wave based on nominal part geometry. When modifying dimensions to obtain a true sine wave of best fit, the curve shown in Fig. 7.30 is obtained. The dimensional modifications used were well within the specified tolerances. The explanation of the flat spot at the top of the curve came only after carefully re-examining and measuring the frames of the film during this period.

Fig. 7.27  Effect of cam skew [12].

Fig. 7.29  Roller skew with the geometric axis of the race skewed [12]. 7-15

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When a roller is rotating against the outer race with a fixed skew, as shown in Fig. 7.25, it will want to “track” out of the clutch. This will generate a thrust against the end-restraining member. The magnitude of this end thrust was measured experimentally. A roller clutch was essentially converted to a caged roller bearing, using two cylindrical races and a series of precision cages. The cages were made with very close-fitting roller windows, and each cage had a specific skew angle for the windows. The bearing was run with a radial load of approximately 1000 N applied to the stationary outer race, and the inner race was rotated at 2000 rpm. The axial force generated was measured with a thrust transducer. The observed data were further reduced to obtain the axial coefficient of traction (Fig. 7.32).

Fig. 7.30  Roller skew (best-fit sine curve superimposed) [12]. The distance between the end of the roller closest to the camera and the hook on the cam was measured. When combining this with the observed skew angle and the length of the roller, it was determined that the end of the roller away from the camera was against the hook, thus preventing full travel of the roller. This is illustrated in Fig. 7.31.

Fig. 7.32  Coefficient of traction [12]. At low roller skew angles, the coefficient of traction is small. In this specific case, roller skew angles of 1 degree and higher caused the coefficient of traction to approach the sliding coefficient of friction. The coefficient of traction also varies with geometry and material. The change in the coefficient of traction is due to micro slip [13].

Fig. 7.31  Roller interference [12]. 3. If the two axes of the cam are aligned and the two axes of the race are aligned, but the race and cam are skewed relative to each other, the same roller behavior described in item 2 will take place. In this case, there will be one complete skew reversal of the roller per revolution of the cam. 4. Any other combination of skewed axes conditions will produce an oscillating skew with a fixed offset.

7.1.6 System Dynamics 7.1.6.1 Roller Float [3, 14]

7.1.5.3.4 Coefficient of Traction

Roller float is defined as a condition wherein the roller loses contact with the rollerway. In certain applications (e.g., in the torque converter), this is a design objective of the OWC engineer. However, in most applications, roller float is deleterious to the operation of the clutch, as will be explained later.

Centrifugally neutral clutches (i.e., those of inner cam design) have the potential of roller rotation at high cam speeds.

Two conditions may cause roller float. The first occurs in clutches of outer cam design and happens when the clutch

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and outer race are spinning. The centrifugal force acting on the roller as a result of this rotary motion “pulls” the roller away from the center of rotation and, hence, away from the rollerway. We refer to this condition as centrifugal roller float. In applications where the inner race is grounded, such as in the torque converter, this type of roller float is advantageous, in that the roller/inner race contact is lost, thereby reducing wear and spin losses. If, however, the clutch must be “engagement ready” with the outer race spinning, this type of roller float is detrimental because the clutch cannot engage unless there is contact between the rollers and the inner race.

Fig. 7.33  Forces acting on the roller for the centrifugal roller float analysis [3].

The second type of roller float can occur in clutches of either outer or inner cam design and is called eccentricity roller float. This type of roller float is the result of a rollerway that has a finite eccentricity (or runout) with respect to the cammed race. As one race rotates with respect to the other, the roller will travel “up” and “down” the cam surface while tracking the rollerway. If the overrunning speed is great enough and the eccentricity large enough, the race will “throw” the roller off the rollerway. During the operation of a roller OWC, either of these conditions can occur. In some cases, the inertia forces that lead to these float conditions can occur simultaneously. Should this happen, the effects are additive. Hence, each condition will be addressed separately in the following sections.

Fig. 7.34  Force triangle for the centrifugal roller float analysis [3].

⎡ sin( 2α ) ⎤ ⎡ sin( 2α ) ⎤ 2 Psp = Pcen ⋅ ⎢ ⎥ = m(r ) ⋅c ⋅ω (o) ⋅ ⎢ ⎥ ⎣ sin ( φ − 2α ) ⎦ ⎣ sin ( φ − 2α ) ⎦

7.1.6.1.1 Centrifugal Roller Float

(7.39)

In certain applications, the outer race of a roller OWC freewheels about its axis. If the clutch is an outer cam design, then the rollers of the clutch will revolve with the outer race. As a result of this motion, the roller must accelerate toward the center of rotation to maintain its position relative to the outer race. This is known as centripetal acceleration and, by Newton’s second law, the force needed to create this acceleration is

where φ is the angle between the line of action of the centrifugal force Pcen and the spring force Psp. Equation 7.39 is used to compute the spring force required to allow centrifugal roller float for a given clutch and outer race speed. Alternatively, we may rearrange Eq. 7.39 to obtain the roller float speed for a given spring load (Eq. 7.40) as





Pcen = m(r ) ⋅a = m(r ) ⋅c ⋅ω (2o)

(7.38)

where Pcen is the roller centrifugal force, m(r) is the mass of the roller, a is the acceleration of the roller, c is the distance from the center of the clutch to the center of the roller, and ω(o) is the angular velocity of the outer race. Figure 7.33 shows the resulting system of forces.

⎛ Psp ⎞ ⎡ sin ( φ − 2α ) ⎤ ω ( o) = ⎜ ⎟ ⋅⎢ ⎥ ⎝ c ⋅m(r ) ⎠ ⎣ sin( 2α ) ⎦

(7.40)

Another variation of this analysis (which actually is unrelated to roller float) is to develop a force triangle for the condition where the outer race is stationary, that is, ω(o) = 0. Performing this analysis, we obtain

There exists an outer race speed above which the centrifugal roller force Pcen overcomes the spring force Psp, and the roller loses contact with the inner race. This condition is called centrifugal roller float. As Pn(i) reaches zero, we have a condition of equilibrium in which the roller is acted upon by three forces: Psp, Pcen, and Pcam. Utilizing a force triangle for this condition (Fig. 7.34), the spring force can be derived using the law of sines, as follows:



Pn(i ) =

Psp

tan( 2α )



(7.41)

Using Eq. 7.41, we obtain the nominal contact force between the roller and the rollerway as a function of the nominal spring force.

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spring compression may result from this condition, which could possibly lead to spring fatigue.

The function of the energizing spring is to position the roller for proper clutch operation. In the following analysis, proper operation is defined as maintaining contact between the roller and the rollerway during the freewheel mode of operation. In the event that the rollerway has a finite runout with respect to the cammed race, the roller will travel up and down the cam surface with each rotation of the rollerway. The energizing spring will compress and extend with each rotation, keeping the roller and rollerway in contact. This condition is illustrated in Fig. 7.35, wherein the geometry of an outer cam OWC system has been utilized. We will examine the outer cam OWC in this section; however, the following analysis can also be applied to a clutch having an inner cam configuration.

Using the method of kinematic equivalence [15], the dynamics of the roller can be examined using the analysis methods established for the four-bar mechanism [16]. A synopsis of this analysis is presented in this section, and the reader is directed to Ref. [14] for a detailed discussion. In Fig. 7.36, the schematic of the clutch in the 0-degree orientation is shown. The eccentricity of the system has been exaggerated to help emphasize the definition of some of the parameters listed in the figure. It is our objective to define the position, velocity, and acceleration of point C(r), the centroid of the roller. To facilitate this, a number of derived dimensions are needed and are listed below without further elaboration.

b = R cam − OR (r )

(7.42)



c = OR (i ) + OR (r )

(7.43)



D = a 2 + f 2 − 2⋅a ⋅f ⋅cosθ(i )

(7.44)



⎛ a ⋅sinθ(i ) ⎞ δ = arctan ⎜ ⎟ ⎝ f − a ⋅cosθ(i ) ⎠

(7.45)



⎛ d 2 + b2 − c 2 ⎞ λ = arccos⎜ ⎝ 2⋅b⋅d ⎟⎠

(7.46)



β = δ + λ

(7.47)



⎛ b⋅sinβ − a ⋅sinθ(i ) ⎞ γ = arctan ⎜ ⎟ ⎝ f − b⋅cosβ − a ⋅cosθ(1) ⎠

(7.48)

Fig. 7.35  Roller motion due to rollerway eccentricity [3]. (a) θ(i) = 0°; (b) θ(i) = 90°; (c) θ(i) = 180°; (d) θ(i) = 270°. As the rotational speed of the rollerway increases, the translational inertia of the roller starts to play a significant role in the functioning of the clutch system. If the rotational speed is great enough and the eccentricity of the rollerway is large enough, the roller inertia force will overcome the energizing spring force, and the roller will lose contact with the rollerway. We call this condition eccentricity roller float. This condition is illustrated in Fig. 7.35(d), where the inner race is shown at an orientation of θ(i) = 270°. Elevated levels of

Fig. 7.36  Definition of the eccentricity roller float analysis variables [3]. Note that in Eqs. 7.42 through 7.48, the parameter a is the eccentric offset of the geometric center Cg of the inner race from the rotational center C(i). The parameter β is the angular

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coordinate of the roller centroid with respect to the center of curvature of the cam Ccam. Taking the derivative of Eqs. 7.47 and with respect to time, we obtain the angular velocities . 7.48 . β and γ, which are given as

(

) ⎤⎥ ⋅ θ

a ⎡ sin γ − θ(i ) β = ⋅ ⎢ b ⎢ sin ( γ + β ) ⎣



⎥⎦

(i )



(7.49)

= k γ ⋅ θ (i )

(7.50)

= k β ⋅ θ (i )

Equation 7.54 defines the contact force between the roller and the cam surface. The forces acting on the roller are depicted in Fig. 7.37.

and

γ =

(

) ⎤⎥ ⋅ θ

−a ⎡ sin β + θ(i ) ⋅⎢ c ⎢ sin ( γ + β ) ⎣

(i )

⎥⎦

. respectively. Therein, θ(i) is the angular velocity of the. rollerway (which is also listed in this section as ω(i)), and β is the angular velocity of the roller about the center of curvature of the cam. Note that in Eqs. 7.49 and 7.50, we have implicitly defined the coefficients kβ and k γ.

Fig. 7.37  Forces acting on the roller for the eccentricity roller float analysis [3].

Taking the derivative of Eq. 7.49 with respect to time, the angular acceleration of the roller about Ccam is obtained as

β = k β ⋅ θ(i ) + k ′β ⋅ θ (2i )

In the event of roller float, Pn(i) is equal to zero. As with the previous analysis, we can build a force triangle (see Fig. 7.38) from the remaining loads. Applying the law of sines to the force triangle and then substituting Eq. 7.53 and rearranging, we obtain the rollerway speed at which eccentricity roller float will occur for a specified spring force

(7.51)

where the coefficient k¢β is defined as

(

) (

) (

)

k ′β = k β ⋅ ⎡⎣ k γ −1 ⋅cot γ − θ(i ) − k γ + k β ⋅cot ( γ + β ) ⎤⎦

(7.52)



A study of the relative magnitude of each of the two components on the right side of Eq. 7.51 has shown that the term . k β ⋅ θ(i ) is insignificant when compared to k¢β . θ2(i), especially at the critical orientation of θ(i) = 270° [14]. Hence, with little loss of accuracy, the angular acceleration of the roller . β¨ can be approximated by k¢β . θ2(i). The tangential component of the roller inertia force is then given as . Pt(r) = m(r) . b . β¨ = m(r) . b . k¢β . θ2(i) (7.53)

Psp ⋅sin ( φ − 2α ) = ω (i ) θ (i ) = m(r ) ⋅b⋅ k ′β



(7.55)

As you may note from Figs. 7.37 and 7.38, we are neglecting the frictional forces that act between the roller and the spring, outer race, and inner race. It can be shown that by ignoring the frictional forces, we compute a more conservative roller float speed. As an alternative analysis, we can rewrite Eq. 7.55 to give us the spring force required to prevent eccentricity roller float for a given clutch having a given inner race overrunning speed. This is given as

Equation 7.53 yields the eccentricity roller float force, Pt(r). We may say that Pt(r) is the force that we must supply to the roller for it to remain in contact with the inner race rollerway. This force is supplied via the energizing spring.



Another component of the roller inertia force is due to the angular velocity of the roller about the center of curvature of the cam. This force is given as 2 2 .2 Pn(r) = m(r) . b . β = m(r) . b . k β . θ (i) (7.54)

Psp =

m(r ) ⋅b⋅ k ′βω (2i ) sin ( φ − 2α )



(7.56)

wherein we have substituted ω (i ) = θ (i ) . With the spring force obtained via Eq. 7.56, the OWC engineer can compute the stress level in the selected energizing spring. This, in turn, can be compared to the endurance limit of the selected

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resonant response of the spring/mass system. This radial vibration of the races is the resonance under examination in this study, and the analysis model employed is illustrated in Fig. 7.40.

spring material to evaluate the spring fatigue life for the application.

Fig. 7.39  Depiction of a roller OWC with relatively large radial clearance [17]. Fig. 7.38  Forces triangle for the eccentricity roller float analysis [3]. 7.1.6.2 System Resonance [17] 7.1.6.2.1 One-Way Clutch System Operational Modes

The roller OWC has two basic modes of operation: (1) the engaged mode, and (2) the freewheel mode. In the engaged mode, the clutch system acts essentially as a single body. Its torsional and radial stiffnesses are extremely high [18], which leads to a very high natural frequency for the system. This mode of operation is not the focus of this study.

Fig. 7.40  The analytical model of the roller OWC [17].

Figure 7.39 depicts a roller OWC with relatively large radial clearances. In the freewheel mode (ω(i) > ω(o)), the races are allowed to rotate with respect to one another. In the applications of interest, the energizing springs are designed to keep the rollers in contact with both races during freewheeling. If sufficient radial clearance exists in the system, one race is “sprung” on the other by way of the rollers and springs. In this situation, we essentially have a two-mass system connected via N spring-energized rollers. The N roller/energizing spring subsystems work in concert and constitute the OWC spring system.

7.1.6.2.2 One-Way Clutch System Analysis 7.1.6.2.2.1 Basic Assumptions

In the formulation of an analytical model, assumptions are often made to facilitate or expedite results. The accuracy of the results is then dependent on the validity of the simplifying assumptions employed. The following are simplifying assumptions employed in this analysis. In any application of this analysis method, the engineer should assure himself or herself of the validity of these assumptions.

For the purpose of radial vibration analysis, the roller OWC system can be approximated by two annular rings connected through N radial springs. A net spring force results if the two rings are eccentric, and the system is pushed into motion by this resulting force. The subsequent oscillations will be the

1. All energizing springs are assumed to be linear and to have the same spring rate k, free height Hf, and working height Hw. 2. The roller mass m(r) is negligible.

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3. Frictional forces are negligible [19]. 4. The strut angle α is assumed to be constant. 5. The rollerway eccentricity e is given as e ≤ 0.01 . Rway , where Rway is the rollerway radius (see Fig. 7.39). e⋅cos( θ ) 6. The roller displacement function is given as δ = , tan( 2⋅α ) where θ is the global orientation of the eccentric rollerway center. (See Section 7.1.6.2.2.3, System Deflections, for further discussion.) 7. The rollers are evenly distributed about the clutch. 8. The global roller position is unaffected by roller displacement. 9. The outer race of the OWC system is fixed rotationally. 10. The excitation signal for our system is either a periodic external force or a periodic internal displacement.

Fig. 7.41  An examination of the rollerway eccentric center with respect to the rollers of the clutch [17]. 7.1.6.2.2.4  Roller One-Way Clutch System Spring Rate

The energizing spring force Fsp–j for roller position j subject to an arbitrary eccentric rollerway condition is given as

7.1.6.2.2.2  Spring Force

(

Fn =



Fsp

tan( 2α )



)

Fsp−j = k ⋅ ⎡⎣Hf − H w − Δ j ⎤⎦

The objective of this study is to investigate the resonance of the OWC system. Herein, one race is viewed as being sprung on the other via the N roller/energizing spring subsystems. The net radial force Fn acting on the races from one roller is [3]

= k ⋅ ( H f − H w ) + k ⋅Δ j

(

⎛ e⋅cos θ − Φ j = k ⋅(Hf − H w ) + k ⋅ ⎜ ⎜⎝ tan( 2α )



(7.57)

) ⎞⎟

(7.60)

⎟⎠

= f j + k ⋅Δ j = f j + δf j

where Fsp is the spring force, and α is the strut angle. After computing Fn, we can apply it to the dynamic analysis of either the inner or outer race systems.

That is, the spring force at position j is the sum of the nominal spring force fj and the change in the spring force δfj due to the change in the deflection of the spring. The roller/rollerway contact force is then given as [3]

7.1.6.2.2.3  System Deflections

Fn−j =

To explore the deflection within the OWC system, we will assume that the geometric center of the rollerway Cg is eccentric to its center of rotation Cr by an amount e, and that the orientation of this center with respect to the x-axis is given as θ. As shown in Fig. 7.41, the clutch has N rollers, evenly distri­buted about the clutch at a relative orientation 2⋅π of Φ = . As the rollerway rotates about Cr, its surface will N move “in” and “out” with respect to the rollers. The radial displacement εj of the rollerway at roller j is given as

(



)

ε j = e⋅cos θ − Φ j

Δj =

εj

tan( 2α )

=

(

e⋅cos θ − Φ j

(7.58)

tan( 2α )

)

tan( 2α )

=

1 ⎡ f j + δf j ⎤⎦ = f n−j + δf n−j tan( 2α ) ⎣

(7.61)

where fn–j is the normal contact force between the rollerway and roller at roller j, and δfn–j is the change in the contact force due to eccentricity e. Because we are dealing with a symmetric system, the radial direction that we choose for our investigation on the effects of contact force Fn–j is immaterial. Choosing to examine the motion of the system in the x-direction, we first project the roller contact force onto the x-axis and then sum the contact forces over the N rollers. If the rollerway is in its centered position, the forces acting on it sum to zero. This means that the nominal contact forces Fn–j acting on the rollerway will sum to zero, which leaves us with

where Φj is the global orientation of roller j. The displacement Δj of roller j at this position is defined as

Fsp−j

N

( )

Fx = ∑ δf n−j ⋅cos Φ j

(7.59)

j=1

( (

) ( ))

⎛ k ⋅e ⎞ N ⋅ ∑ cos θ − Φ j ⋅cos Φ j =⎜ ⎝ tan 2 ( 2α ) ⎟⎠ j=1

(7.62)

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where Fx is the net spring force in the x-direction for the OWC system. Applying the trigonometric function-product relations to the second half of Eq. 7.62 and then simplifying the expression, we get ⎛ k ⋅e ⎞ ⎧⎪ N 1 N ⎡ ⋅ Fx = ⎜ ⋅cos θ + ⋅ ∑ cos θ − 2Φ j ( ) ⎨ 2 j=1 ⎣ ⎝ tan 2 ( 2α ) ⎟⎠ ⎪⎩ 2

(

)

⎫ ⎤ ⎪⎬ ⎦⎪ ⎭

where m1 is the mass of one race, and m2 is the mass of the other.

7.1.7 Energizing Springs

(7.63)

There are two common types of energizing springs used in automotive roller OWCs: (1) the accordion spring (see Fig. 7.42(a) ), and (2) the z-spring (see Fig. 7.42(b)).

It can be demonstrated that

1 n ⋅ ∑ cos θ − 2Φ j = 0 2 j=1

(

)

(7.64)

which, after rearranging, leaves us with

⎞ ⎛ N⋅k ⋅ ( e⋅cos( θ )) Fx = ⎜ 2 ⎝ 2⋅tan ( 2α ) ⎟⎠

(7.65)

Note that in Eq. 7.65, the force on the system Fx is given as the product of the system displacement (e . cos(θ)) and the system spring rate, which is identified as

⎞ ⎛ N⋅k k owc = ⎜ 2 ⎝ 2⋅tan ( 2α ) ⎟⎠



(7.66)

The accordion spring has its beams oriented, more or less, in the radial direction with respect to the clutch. Because of this, the height of each beam is limited by the radial space between the races. The width of the spring is limited only by the available axial length of the clutch. A spring with a high relative spring rate and high nominal spring load is usually the result of an accordion spring design. In the accordiontype design, the loops of the spring, which are under high stress, are in close proximity to the overrunning race. If contact should occur between the spring and the overrunning race, material at the loop will be abrasively worn away, making the loop weaker. Early fatigue failure could be a result of this situation.

7.1.6.2.2.5  System Natural Frequency

There are two ways by which the OWC system can vibrate. First, one race may be firmly fixed to the transmission case or a well-supported shaft, and the second race is then sprung to the first. In this scenario, the second race would be able to vibrate with respect to the first at a circular frequency ωn, where ωn =

k owc (rad/sec) m

In the z-spring type of design, the beams of the spring are oriented, more or less, to the axial direction of the clutch. In this situation, the width of the spring is confined by the radial space between the races, while the height of the spring is bound by the axial length of the clutch. A resulting z-spring design will typically have a lower nominal load and a lower spring rate as compared to an accordion spring design. Because the beams of the spring are oriented to the axial direction, the loops are not subject to the relative motion of the overrunning race and, hence, are not subject to abrasive wear.

(7.67)

where m is the mass of the sprung race. A second scenario would be if both races were free to move radially. In this case, the resulting system resonance equation is given as

⎛ m + m2 ⎞ (rad/sec) ω n = k owc ⎜ 1 ⎝ m1m 2 ⎟⎠

(b)

Fig. 7.42 (a) The accordion spring design, and (b) the z-spring design.

From this analysis, we can see that the system spring rate kowc is a constant times the rate of the energizing spring k. It also is important to note that because k is assumed to be linear, our system spring rate kowc also will be linear.



(a)

(7.68)

Proper design of the energizing spring is essential to the performance and robustness of the roller OWC. If a spring is designed with too light a nominal load, the roller may experi-

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3. The roller end—This “inactive” beam is formed in such a way as to enhance its interface with the roller. Note that the fundamental geometry and list of features for the z-spring are common with those of the accordion spring. Because of this, we can apply a comparable analysis method (if not the same analysis) to the accordion spring.

ence roller float (see Section 7.1.6, System Dynamics). This is detrimental to the spring because greater than nominal deflections will occur, possibly leading to fatigue failure of the spring. If the spring load is too large, greater freewheel drag torques result, and accelerated clutch wear can occur. If the spring rate is too high, the resulting range of maximum stresses in the spring is very high, and the spring is likely to suffer a fatigue failure. These are only some of the reasons why the design of the energizing spring should be scrutinized.

In a linear rate spring, the geometry of one active beam is shared by all beams. This greatly simplifies the analysis, in that we need to analyze only one beam, and the results can be applied to all. Figure 7.44 shows the geometry of one beam of a linear rate spring. The terminology and variable definition given therein are consistent throughout this section. Note that planes A-A and B-B are planes of antisymmetry for the beam. If we reflect the upper half of the beam about A-A and then about B-B, we “produce” the geometry of the bottom half. By applying correct boundary conditions, this allows us to analyze only half of the beam.

Figure 7.43 depicts the geometry of a typical z-spring used in roller clutches today. The spring is composed of three distinct parts:

The geometry with which we will be working is shown in Fig. 7.45, wherein we have further divided the half beam into its three major components. Applying the proper boundary conditions, we compute the loads, deflections, and stresses [21] in each segment. These are summarized in Table 7.2. Note that the results presented in this table are for either an accordion spring or a z-spring possessing the beam geometry shown in Fig. 7.45. Should your energizing spring geometry be different than that shown, you should derive the appropriate expressions for your application.

Fig. 7.43  A typical linear rate z-spring [20]. 1. The anchor end—This component secures the spring to the cage or bearing block. 2. The active beams—The geometry and number of active beams dictate the characteristics of the spring.

Fig. 7.44  One z-spring beam.

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Fig. 7.45  Loads on each beam segment.

Table 7.2  Summary of Loads, Deflections, and Stress in the Roller OWC Energizing Spring

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The definitions of the variables used in the equations of Table 7.2 are provided in Figs. 7.44 and 7.45 and in the following list. To simplify this list, the subscript “seg” has been used. This subscript takes on the value θ (the loop segment), Z2 (the flat segment), or Z1 (the leaf segment). P0 Pseg N Mseg T W A

Am I

Rc R K E G σ1 δseg–b δseg–n δseg–s

where Nbeams is the number of active beams in the spring. Dividing the applied load P0 by the deflection of the spring, we obtain the spring rate

Applied load Internal force on the spring segment Internal normal force on the spring cross section Internal moment on the spring segment Spring material thickness Spring material width Spring material cross-sectional area (A = T . W)

Most laboratory testing, both in development and reliability efforts, is concentrated on examining fatigue characteristics of races and rollers, because experience shows this is the most likely cause of failure. Such testing shows the weakest link to be the cam race, where most of our test spalling occurs. The cylindrical race is the next weakest link where there is occasional test spalling, usually near the oil hole. Standard torque and cyclic endurance tests seldom produce a roller or spring failure. Extensive testing of one roller clutch package has produced some reliable test data relating to the spalling of the cams on the outer race. The clutch tested has the following characteristics. It is designed to carry 1627 N-m (1200 ft-lb) (the peak engine torque times torque converter ratio times the appropriate transmission ratio). The mean hertz stress at the inner race and roller contact is calculated to be 3.7 GPa (540 kpsi), and the hoop stress is 352 MPa (51 kpsi). The cams are on the outer race. The clutch contains sixteen 7.874 mm (0.3100 in.) diameter rollers by 12.4 mm (0.490 in.) long on a 111.1 mm (4.374 in.) diameter pitch-circle. The test procedure calls for stroking of the races at 520 cycles/minute for 200,000 cycles at 1627 N-m and recording the number of cams spalled per race at the completion of the test. The test is designed to challenge the fatigue life of the races in order to give some spalling, but not be so severe as to cause the clutch to lose its torque-carrying capacity. The results of these tests show an interesting distribution of cam spalling.

Radius of curvature of the spring loop at its mid-plane Radius of curvature of the spring loop at its outer surface Cross-section shear factor [10] (K = 1.5 for rectangular cross sections) Modulus of elasticity of the spring material Modulus of rigidity of the spring material Maximum principal stress (evaluated at points a, b, and c) Segment deflection due to bending load Segment deflection due to normal load Segment deflection due to shear load

We have applied a version of a statistical failure theory to the data, resulting in the curves shown in Fig. 7.46. The plot represents the use of the Weibull function to describe the life probability of the race. The vertical axis shows the life probability function or rank in percent.

δ = δ θ + δ Z 2 + δ Z1 = ( δ θ−b + δ θ−n + δ θ−s ) (7.69)

= ( δ Z1−b + δ Z1−n + δ Z1−s )

The horizontal axis shows the number of cams spalled per race. Plotted as “normal population” are the results of testing 140 races taken from production over a one-year period. Examining this curve shows the statistical probability of cam spalling. For instance, at the 10% level, there are four spalls, meaning that 10% of the races tested had four or more spalls. Another way of putting it is that 90% had four cams spalled or less. At another point, the curve shows that 50% of the

and two times δ is the deflection for the full beam. Summing the deflections of all the active beams (and any active parts thereof), we obtain the deflection ∆ for the spring subject to the applied load P0. For the springs that are shown in Fig. 7.42, we get

Δ = 2⋅N beams ⋅ ( δ θ + δ Z 2 + δ Z1 ) + 2⋅δ θ

(7.71)

7.1.8.1 Fatigue

⎛ +T⎞ Rc 2⎟ A m = W ⋅ ⎜⎜ T⎟ ⎜⎝ R c − ⎟⎠ 2 ⎛ W ⋅T 3 ⎞ Cross section area moment of inertia ⎜ I = ⎝ 12 ⎟⎠

= ( δ Z 2−b + δ Z 2−n + δ Z 2−s )

P0 Δ

7.1.8 Failure Analysis [2]

The total deflection δ of the half beam can be expressed as the sum of the contributions from each beam segment. In doing so, the total deflection of the half beam is written as



k=

(7.70) 7-25

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races had one spall or less. Our curve hits the zero spall at 62%, telling us that 62% of the clutches will spall at least one cam, and 38% will not spall at all.

race of the above type spall due to operation in a passenger car.

This curve is not a general one. It applies only to one clutch assembly tested in one particular manner. However, when this clutch is in the transmission of your vehicle and the test specifications relate to your application, then this curve is essential to fully evaluate any engineering or processing change being made. As can be seen from the curve, testing one assembly means little because sample-to-sample variation may affect test results. However, by testing several assemblies of a new configuration and thus determining a life curve, it is much easier to estimate whether these new races are better, the same, or worse than the normal population.

7.1.8.2 Load Patterns on Cams A great deal can be told about the function of a clutch, the manufacture, and the application by studying the load pattern on the cam and the load path on the race. This is true whether these patterns are the result of operation on a test fixture, on the dynamometer, or in the car. Figures 7.47 to 7.56 will show some of these results.

As an example, Fig. 7.46 shows a plot of seven races tested from a lot with a special heat treat. The curve, due to its slope, falls to the left of the normal population, showing a greater tendency to spall. The 10% rank shows nine cams spalled compared to the four normal. However, if the first race tested were the one that showed no spalls, the natural conclusion would be that the new process was as good as the old. Fig. 7.47  Normal load pattern after 200,000 cycles at 1627 N-m [2]. The width of the load pattern can be an indication of the load being applied. For instance, Fig. 7.47 is the load pattern on an outer race cam subjected to the 1627 N-m torque of 200,000 cycles. It measures 2.44 mm wide. Figure 7.48 shows the cam after 200,000 cycles at 1627 N-m plus 20 applications of a shock load to 2983 N-m. Two load patterns are visible. The one nearest the hook is the result of the stroking at 1627 N-m. Then, as the shock load of 2983 N-m was applied, the roller moved down the cam due to the deflections of the parts, causing the second load pattern. The initial pattern measures 2.41 mm wide, while the shock load pattern measures 3.45 mm (0.136 in.).

Fig. 7.46  Fatigue life characteristics of the roller clutch outer race [2]. It should be emphasized here that the test conditions are designed to cause spalling, in order to have an engineering tool to measure reliability and progress. We have yet to see a

Fig. 7.48  Normal load pattern after 200,000 cycles at 1627 N-m plus 20 cycles at 2983 N-m [2].

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Figure 7.49 shows the load track on a cam from a race having completed 80,450 km (50,000 miles) in a passenger car with a high-torque engine. This cam shows a bright area where the roller rides during overrunning, plus a very faint, lightly worked area, which is the load pattern. This pattern measures 1.78 mm wide. For comparison, Fig. 7.50 shows the race after 200,000 cycles at 1220 N-m. The width of this heavily worked load pattern is 2.03 mm. The design torque is 1627 N-m.

Figure 7.52 shows a load track that is not square with the race. This can be caused by a cam surface that is tapered or a race that becomes bellmouthed under load. A bellmouthed condition can result when the race is supported by an improperly designed housing, thin at one side of the race and flanged at the other side.

Fig. 7.49  Normal load pattern after 80,450 km [2].

Fig. 7.52  Abnormal load pattern: tapered cam [2]. Figure 7.53 shows severe roller end loading. The areas at the ends of the pattern are much more heavily worked than the center, even showing brinelling at the extremities. This can be caused by a concave cam or roller but is more likely due to an improper radius between the OD and the end of the roller.

Fig. 7.50  Normal load pattern after 200,000 cycles at 1220 N-m [2]. The previous load patterns are considered normal for a welldesigned clutch operating at various levels. Figures 7.51 to 7.56 show some patterns that signal abnormal operation calling for a design or manufacturing change. Figure 7.51 shows a severe convex condition in the cam surface or on the roller. This greatly overstresses the center of the load pattern and could lead to early spalling.

Fig. 7.53  Abnormal load pattern: roller end loading [2]. Figure 7.54 shows a phantom load pattern and is a signal that the roller has popped or slipped under load and has violently squirted into the clearance area of the cam. Many times, this results in a damaged spring. The hook of the cam shows where the roller has hit. Roller popping, in this case, was caused by a badly spalled inner race at the oil hole.

Fig. 7.51  Abnormal load pattern: convex cam or roller [2].

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Fig. 7.57  Load paths: roller end loading [2]. Fig. 7.54  Abnormal load pattern: roller popped [2].

Figure 7.58 shows a scuffed load path due to abnormal contact between the rollers and the inner race during overrunning. The scuffing is characterized by circumferential grooves scored into the load path. In this part, the cross-race surface finish increased from 0.254 to 0.762 µm (10 to 30 µin.), and further scoring could result in a failure.

Figure 7.55 shows a typical spalled area that does not affect the torque-carrying capacity of the clutch; Fig. 7.56 shows a massive spall that has so distorted the cam surface that the roller cannot take its share of the load. The roller has popped, as evidenced by the phantom load track and evidence of contact at the hook.

Fig. 7.58  Scuffed load path [2]. Contamination on the inner race surface might cause this, as can marginal lubrication. Having too high an energizing spring force on the rollers often coupled with too rough a surface finish on the race could also be blamed.

Fig. 7.55  Abnormal load pattern: slightly spalled cam [2].

Figure 7.59 shows a spall at the oil hole. The oil hole that interrupts the load path is a likely place for spalling to begin. Figure 7.60 shows the uneven scuffing of the load path due to the popping of rollers. In this case, the outer race cams were spalled badly enough to cause several rollers to pop.

Fig. 7.56  Abnormal load pattern: severely spalled cam [2]. 7.1.8.3 Load Path on Cylindrical Races Similarly, the load path can tell us about the design and application of a clutch. Figure 7.57 shows the results of roller end loading. The outer edges of the load path are much more heavily worked, showing as dark bands in the photograph. These areas are likely places for spalling to begin. Fig. 7.59  Load path: spall at the oil hole [2]. 7-28

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One-Way Clutches

to the problem at hand, the application of the methods presented should be done with caution. That is, the analysis expressions presented are not linked to any one measuring system. This makes the equations more versatile but requires the engineer to pay close attention to the units of measure. It is strongly advised that one system of measure be adopted and then rigidly adhered to throughout. Fig. 7.60  Load path: rollers popped [2].

7.2 Sprag One-Way Clutches

Figure 7.61 shows that brinelling can be caused by overloads. However, if properly designed for fatigue characteristics, the overload required to cause a harmful brinell is usually well beyond that encountered in the application. Soft races—say, a surface hardness below Rc 58—are liable to brinelling when subjected to shock loads. Finally, Fig. 7.62 shows the race after 80,450 km passenger car endurance with no abnormal wear evident.

7.2.1 Introduction 7.2.1.1 Sprag One-Way Clutches [1] The original concept of the sprag clutch was developed in the late 1940s. The chief attribute of this OWC design is its high load-carrying capacity to size ratio relative to a roller clutch. Because of torsional dephasing problems, sprag clutches were not utilized extensively until the early 1950s when a fully phased design became available. Since that time, sprag clutches have been used as driving and grounding members in many automatic transmissions worldwide. 7.2.1.2 Function and Operation of a Sprag Clutch [1, 22] The geometrical design and dynamics characterizing sprag operation basically involve unidirectional wedging of the surfaces of multiple-cam structures, denoted as sprag elements, between two races that enclose the elements. The primary components of the test sprag clutch, shown in Fig. 7.63, consist of a sprag assembly, two races, two bearings (both are shown in the figure), and two snap rings (only one is shown in the figure). The most complex piece is the sprag assembly, which consists of 22 sprag elements held in place by two cages positioned between the inner and outer races. A stamped, spring-steel ribbon located between the cages pre-loads the elements evenly to distribute the load during engagement. This is accomplished by 22 spring tabs formed on the ribbon, each of which is in constant contact with an element. The end bearings and snap rings align the sprag assembly axially between the races.

Fig. 7.61  Load path: brinelled [2].

Fig. 7.62  Normal load path after 80,450 km [2].

7.1.9 Summary In this section, we have presented design considerations, design methodologies, and analysis techniques for the design of roller OWCs. The information given herein has been used in the design and development of roller clutches for years. However, it is left to the reader to apply this information properly. In so doing, it is always prudent to review the underlying assumptions upon which these techniques are based. If the assumptions do not apply to the problem at hand, alternative methods should be sought (e.g., the finite element method of analysis). If the assumptions do pertain

Sprag clutches are a specific class of OWCs. The unique feature of OWCs is that they can maintain a high torque capacity in one direction and no capacity in the other direction. This provides optimum timing when shifting. In particular, sprag clutches can be fully phased to distribute the contact load equally for all elements. Because there is relatively little, if any, sliding speed differential in the drive mode, little wear occurs when the sprag clutch is engaged.

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The primary role of the sprag clutch in the specific application studied is to allow the input planetary sun gear to be driven by the torque converter in only one direction. This occurs in first and reverse gears during which the sprag elements are “wedged” (locked) in the “drive” mode to prevent relative motion between the inner and outer races. In this mode and during the transition to engagement, the wedged sprag elements transmit torque directly from the outer race to the inner race (see Fig. 7.65). In second gear, the inner race overruns the outer race in the same direction at 1.86 times the outer race speed. Because no load is applied to the sprag, this condition is regarded as freewheeling. The ribbon spring just described keeps each element in constant contact with the inner race surface so that, when required, engagement (and torque transfer) can be both rapid and coincident for all elements.

Fig. 7.63  Sprag clutch components [22].

As a consequence, multiple forces act upon the sprag. In the drive mode, the inner race experiences the wedging force transmitted by the sprag assembly from the outer race. In the freewheeling mode, the inner race experiences a net force from two sources. With the sprag clutch design chosen for this test development, the primary freewheeling force results from the requirement that the sprag be “centrifugally engaging.” This is accomplished by offsetting the centers of rotation and mass of the element in a specified orientation relative to the strut angle. The resultant centrifugal force acting on the sprag assembly, mostly during high differential speeds, tends to load the elements against the inner race, which contributes largely to the total drag force. An additional, secondary force is produced by spring tabs acting on the 22-sprag elements, which generates frictional drag on the inner race. This secondary drag force also contributes to inner race wear.

Figure 7.64 shows the sprag assembly and an enlarged view of one sprag element in an assembled clutch. In the enlarged view, the end bearing was cut away to expose the assembly and identify the cages and ribbon spring relative to the sprag element. Not shown are the tabs on the ribbon spring.

Considerable experience has been accumulated in the engineering of sprag clutches for the demanding requirements of a large percentage of all of the automotive automatic transmissions existing today, as well as in a number of aircraft, truck, and farm equipment applications. The high points of

Fig. 7.64  Sprag assembly components [22].

Fig. 7.65  Sprag clutch engaging action [1]. 7-30

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One-Way Clutches

as is illustrated in Fig. 7.68. Therein, h1 represents the sprag in the minimum radial sprag-space position, h2 the nominal freewheel position, h3 the “normal” engaged position, and h4 the position just prior to rollover. (See Section 7.2.6, System Deflections, for a discussion of rollover.) Note that position h1 could also be interpreted as the position just after rollover.

this experience have emphasized the following design points for successful and reliable sprag clutch operation. For full torque capacity and long service life: 1. The clutch design must force all of the sprags to work together in phase throughout their operating range (socalled “phasing”), so that the sprags equally share the load within small tolerance variations. 2. All sprags should be individually energized, axially aligned, and as free as possible of parasitic friction that subtracts from the normal energizing forces. 3. Adequate race proportions, concentricity, material, heat treatment, and surface finish are essential. The clutch is no better than the races used. 4. The clutch must be adequately lubricated. Lubrication requirements will vary significantly, depending on application details.

7.2.2 Theory of Operation [23] Both roller and sprag OWCs are friction-dependent devices that wedge a loading element between concentric races and thereby transmit a torsional load. In the case of a roller OWC, the roller acts as the loading element and friction wedges it between the rollerway of one race and the cam surface of the other race (see Fig. 7.66). If an offset circular arc is used in the design of the cam surface, the strut angle of the clutch remains essentially unchanged throughout the range of motion of the roller.

Fig. 7.67  Offset roller halves define a rudimentary sprag geometry [23]. As Fig. 7.68 illustrates, the dimensions h1 through h4 progressively increase. When a sprag engages and begins to carry a torque load, the races deform elastically and the space between them increases. Subsequently, the sprag rotates and fills the gap between the races. The strut angle α of the system is defined as the angle between a radial line drawn through the sprag/race contact point and a strut line drawn between the two contact points, as shown in Fig. 7.67. A sprag has two functional strut angles: one at the inner race contact point α(i), and the other at the outer race contact point α(o). These two strut angles differ by an amount γ, which is also the angle between the two radial lines drawn through the two contact points. The relationship between α(i) and α(o) is given as

Fig. 7.66  Definition of roller OWC terminology [23]. In a sprag OWC, the sprag acts as the wedging element and the cam surface. This is accomplished through the utilization of two cam surfaces within a single sprag and is most easily understood by visualizing a roller split in two, with the two halves offset by an amount e (see Fig. 7.67). This design gives the sprag an infinite number of tangent-to-tangent heights hs,



γ = α(i) – α(o)

(7.72)

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Fig. 7.68  A sprag operates under an infinite number of “heights” [23]. As the sprag rotates into position under load, the strut angles of the sprag increase. Hence, a sprag can be designed to have a low strut angle (which is good for “cutting” through a film of oil) at low torsional loads, and a high strut angle (which is good for minimizing hoop and contact stresses within the races) at high torsional loads. This change of strut angles as a function of sprag height is illustrated in Fig. 7.69. Therein, three data curves are shown that represent the outer strut angle α(o) (dashed line), the inner strut angle α(i) (dotted line), and the mean strut angle α(m) (solid line). The distance between the dashed and dotted lines represents the angle γ. It is important to note that the angle γ decreases with increasing clutch size. As the clutch gets very large, the radius of curvature of the races approaches infinity (i.e., flat plates), and the angle γ approaches zero. In this situation, the outer and inner strut angles are equivalent and are equal to α(m). It is by this method that the strut angle of a sprag is experimentally determined.

Fig. 7.70  The geometry of a typical sprag incorporates the concept of the offset roller halves [23]. In application, the sprag OWC assembly is composed of an inner race, an outer race, multiple sprags, cages, and energizing springs. Figure 7.71 shows these components and several variables. These variables are used throughout this section.

Fig. 7.71  Geometry definition of a sprag OWC [23].

7.2.3 Sprag Cam Design [24, 25] The engagement and load-bearing characteristics of a sprag are heavily dependent on its strut angle curve. The strut angle curve shown in Fig. 7.69 is easily attainable and has some useful attributes. However, many other strut curve designs have successfully been employed. Others have been investigated and dismissed.

Fig. 7.69  The sprag strut angles increase as the sprag height increases [23]. The split roller concept is useful in defining the nature of a sprag. However, the utility of such sprag geometry is limited. Ideally, the sprag geometry is tailored to optimize space, facilitate component interaction, and optimize inertia properties (see Section 7.2.8, Sprag Dynamics). A typical geometry resulting from a real-world application is depicted in Fig. 7.70.

For example, sprags have been designed to give a constant 2-degrees strut curve. These designs, however, were discarded due to a lack of cam rise. Other sprags have been designed to give a constant 4-degrees strut angle, but these had exhibited

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One-Way Clutches

poor cold-oil engagement characteristics and had a distinct lack of margin for wear.

With these two angles defined, the inner cam strut angle is given by Eq. 7.72.

When designing a new sprag, the engineer must first select the desired strut angle curve. This will depend on the operating environment, the duty cycle, and the desired attributes. Next, the engineer must relate these characteristics back to the geometry of the sprag geometry. We accomplish this through the aid of Fig. 7.72. Therein, the point Ci represents the center of curvature of the inner cam profile. The radius of this cam is defined as Ri(s). Likewise, point Co is the center of curvature of the outer cam profile, which has a radius of Ro(s). A line drawn between these two centers has a length Z and makes the angle β with respect to the horizontal.

The distance between the races (J) can be obtained in terms of the race radii as (7.75) J = IR (o) − OR (i ) or as a function of the cam radii as

(

A plot of the strut angle versus sprag height of a typical 8.38 mm sprag is shown in Fig. 7.73. Theoretically, a special sprag section should be used on each race diameter if identical conditions are to be maintained. Because of economics, however, the number of sprag sections has been reduced to a minimum, with the resultant compromises. What we are leading up to is the fact that the strut angle curve is plotted for flat races (infinite radii), and the necessary correction factors must be made to find the actual strut angles of a given sprag on a given race. The angle can be increased as much as 1 degree when going from flat races to a 25.4 mmdiameter race.

The forces Ff(o) and Ff(i) are the tangential components of the contact force. Forces Fn(o) and Fn(i) are the normal components of the contact forces. These forces are normal to the cam and race surfaces at the point of contact and have a line of action that passes through the center of the clutch. (Note that by this statement, we are assuming that the inner and outer races are concentric.) The line drawn between the two contact points is termed the strut. The angle between the strut line and the normal component of the contact force is called the strut angle. As noted earlier, the sprag has two strut angles, α(o) and α(i). The expression for the angle γ (see Fig. 7.67) is given as ⎛ Z ⋅cos (β ) ⎞ γ = sin −1 ⎜ ⎟ ⎝ OR (i ) + R i( s) ⎠

Fig. 7.73  New sprag strut angle curve [24].

(7.73)

The advantages of using flat races are that there is a common baseline for comparison, the calculations are simpler because angles α(i) and α(o) are equal, and a gage with flat races has been developed which very accurately and conveniently measures and plots the strut angle of an individual sprag.

(7.74)

The normal overrunning (or engagement) point for the sprag represented by this curve is at a strut angle of approximately 2.25 degrees. This angle is then increased to approximately

The equation for the outer cam strut angle is given as

⎛ OR (i ) ⋅sin ( γ ) ⎞ α(o) = tan −1 ⎜ ⎟ ⎝ IR (o) − OR (i ) ⋅cos ( γ ) ⎠

(7.76)

Having defined Eqs. 7.72 through 7.76, it is now a matter of determining the correct values for the geometry variables to achieve the desired strut angle curve. This is an iterative procedure and is expedited through experience. Often, it is easier to assume that the races are flat plates (i.e., having infinite radii) in order to expedite the first few iterations.

Fig. 7.72  The sprag geometry.



)

J = R o( s) + OR (i ) + R i( s) ⋅cos ( γ ) − Z ⋅sin (β ) − OR (i )

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Design Practices: Passenger Car Automatic Transmissions

of several thousand Newtons. The spring force Fsp acting on the sprag is generally less than 10 N. Therefore, without loss of accuracy, we can neglect the spring load in the equilibrium analysis.

4.5 degrees as the sprag is loaded. At angles higher than this, there is evidence that sprags will slip when loaded rapidly. The accepted design philosophy, however, does not permit any slipping of the sprags under load because it is unpredictable and too destructive to the sprags, the race surfaces, and the cage structure containing the sprags. As the sprag wears at the overrunning position, its strut angle will increase. A typical plot of an actual worn sprag is shown in Fig. 7.74. When the engaging strut angle has approached 4.5 degrees, the clutch engaging performance will become erratic.

Fig. 7.75  Equilibrium reaction forces acting in a single sprag [23].

Fig. 7.74  Worn sprag strut angle curve [24].

The sprag is in equilibrium; thus, the total force acting between the inner race and sprag F(i) is equivalent to the total force acting between the outer race and sprag F(o).That is,

If the sprag were made up of only two eccentric radii, the strut angle curve to the left of the freewheeling point would drop sharply as the sprag height decreased, as was illustrated in Fig. 7.69. What this means in actual practice is that the race eccentricity that can be tolerated by the sprag is rather limited because a large angular sprag rotation is needed to accommodate a small amount of race eccentricity. To alleviate this situation, another small radius was introduced in one of the cams so that more change in sprag cam height was realized for a given angular movement.



F(i) = F(o)

(7.77)

The tangential force acting between the inner race and sprag Ff(i) is a trigonometric function of F(i) and the inner strut angle α(i)

Ff(i) = F(i) . sin α(i)

(7.78)

This second radius accounts for the rise in the strut angle curve to the left of the engaging or freewheeling line, and permits the sprag and clutch to accommodate more race eccentricity so that larger tolerances can be used on the races and bearings making up the clutch package.

The final step in balancing the forces on a sprag is to derive the normal force Fn(i) acting between the sprag and the inner race

7.2.4 System Equilibrium [23]

The total torque T(i) transmitted through the OWC system is based on the tangential component of the strut force and is given as



7.2.4.1 Sprag Forces



The first step in understanding the stresses on a sprag OWC is to understand the balance of forces and torques acting on an engaged sprag. Figure 7.75 shows the free body diagram of an engaged sprag between an inner and outer race. The contact force between a sprag and the races is on the order

Fn(i) = F(i) . cos α(i)

T(i) = Ff(i) . OR(i) . N(s)

(7.79)

(7.80)

where OR(i) is the moment arm (i.e., the outer radius of the inner race), and N(s) is the number of sprags in the OWC. However, Eq. 7.78 showed that the tangential force Ff(i) is a

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One-Way Clutches

trigonometric function of the total force between the inner race and a sprag. Substituting Eq. 7.78 into Eq. 7.80 yields

T(i) = F(i) . sin α(i) . OR(i) . N(s)

If the strut angle exceeds this limit during operation, the sprag is prone to slipping and/or popping. Popping is a phenomenon wherein the sprag begins to engage and carry a load, but, because of the violation of Eq. 7.86, the load is suddenly released. The elastic strain energy stored in the system is converted into kinetic energy of the sprag, which subsequently impacts adjacent clutch components. Severe damage may result from this phenomenon.

(7.81)

Solving Eq. 7.81 for the total force per sprag F(i), rather than torque, results in

F(i ) =

T(i ) N( s) ⋅OR (i ) ⋅sinα(i )



(7.82)

7.2.5 Effective Race Width [23] In certain applications, the race widths (w(o), w(i)) are much greater than the sprag width (w(s)), as depicted in Fig. 7.76. Under such conditions, the greatest deflections in the race will occur at the location of the sprag, and the deflection will decrease as we move toward either edge of the race. These non-uniform deflections also induce non-uniform stresses in the race cross section. In essence, the entire race is not being utilized to support the sprag load, resulting in elevated stresses and deflections. This is illustrated in the stress contour plots shown on the outer race of Fig. 7.76.

7.2.4.2 Strut Angle Limit As with all friction-dependent OWC devices, the magnitude of the strut angle is limited by the coefficient of static friction μs between the sprags and each race. Because the inner race strut angle α(i) is always larger than the outer race strut angle α(o) by an amount γ, we need look only at α(i). The fundamental relationship between μs and α(i) is derived by first taking the ratio of the tangential force Ff(i) and the normal force Fn(i)

Ff (i ) Fn(i )

=

F(i ) sinα(i ) F(i ) cosα(i )

= tanα(i )

(7.83)

The tangential force Ff(i) is also the frictional force of the system, and its magnitude is dependent on the normal force Fn(i) but is limited by the coefficient of static friction μs. Algebraically, this is expressed as

Ff(i) £ μs Fn(i)

(7.84)

Equations 7.83 and 7.84 define the same system and therefore are interdependent. By substituting Eq. 7.83 into Eq. 7.84, we get

tan α(i) £ μs

Fig. 7.76  Relatively wide races (W(o), W(i)), compared to sprag width (W(s)), can result in non-uniform stresses [23].

(7.85)

One method of dealing with non-uniform loading on long cylindrical shells uses the actual widths of the race and sprag to determine effective race width We.

This expression defines the upper limit for the value of the strut angle. The coefficient of static friction μs within the clutch environment is dependent on many factors, all of which have a prescribed range of acceptable variation. Because of this, μs has a range of values. In addition, these factors change as the system wears, thereby influencing the value of μs. For hardened steel on hardened steel bathed in automatic transmission fluid, μs is between 0.080 and 0.120. Taking the conservative value of 0.080, Eq. 7.85 yields a maximum strut angle of

α(i) £ 4.574°

If

W ≥ W( s) +1.7⋅h,

then

We = W( s) +1.7⋅h

If

W < W( s) +1.7⋅h,

then

We = W



(7.87)

where W(s) is the sprag width, W is the race width (either W(i) or W(o)), and h is the radial race thickness (either h(i) or h(o)). This effective race width replaces the actual race width in the stress and deflection equations.

(7.86)

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7.2.6 System Deflections [23]

7.2.6.1 Contact Deflections

The sensitivity of a OWC to elastic deflections is dependent on the design of the system. A roller OWC, for example, can be designed to be very insensitive to deflections by making the cam rise of the clutch relatively large. (The cam rise of a roller OWC is defined as the allowable radial travel of the roller on the cam surface while under load.) A large cam rise is attainable because the cam is an integral part of the race instead of the loading element. It can be shown that the cam rise in a roller OWC can approach the diameter of the roller. An example of the cam rise in a roller OWC is given in Fig. 7.77.

Contact deflection computations are based on the loads applied to an individual sprag. The equation used to compute the radial contact deflection is given by Harris [26] as

δ = C⋅

Fn0.9(o) W(0.8 s)



(7.88)

where C is a constant that depends on the units used for the sprag load Fn(o) and the sprag width W(s). Note that Eq. 7.88 uses the normal force on the outer race. Table 7.3 [23] summarizes the input requirements for Eq. 7.88. Table 7.3  Input Requirements for Eq. 7.88 [23]

7.2.6.2 Hoop Deflections

Fig. 7.77  Definition of a roller OWC system cam rise [23].

In the following two subsections, the definition of each of the variables depends on whether we are referring to the inner race or the outer race. Table 7.4 [23] indicates these differences. This approach was adopted to eliminate the apparent repetition of including very similar equations.

In Fig. 7.78, the cam rise for a sprag OWC system is graphically defined. In contrast to the roller clutch, the cams in a sprag OWC system are an integral part of the loading element (see Section 7.2.2, Theory of Operation). For a typical sprag, the cam rise is limited to approximately five percent of the nominal sprag space, hnom. Because of a relatively small cam rise, the sprag OWC is generally considered more sensitive to system deflections than is a roller OWC.

Table 7.4  Hoop Deflection Variable Definition [23]

Fig. 7.78  Definition of a sprag OWC system cam rise [23]. Unlike system stresses, where we need look only at the outer race for hoop stresses and the inner race for contact stresses, we need to look at the entire sprag OWC system when determining deflections. This is because each clutch component contributes to the overall deflection of the system. Deflections are computed using either a uniform pressure approximation or a discrete load approximation. Because of greater accuracy, the discrete load approximation is always preferred. 7-36

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One-Way Clutches 7.2.6.2.1 Discrete Load Approximation

The radial deflection of the spragway is computed by substituting the applicable variables from Table 7.4 into the following equation [11]:

Using discrete load approximation, the expression for the radial deflection of the race at the point of contact with each sprag is given as [4] ⎡ F ( R − e )3 ⎤ ⎡ K1 ( φ − sinφcosφ ) K2 K2 ⎤ ΔR 1 = ⎢ n m + − 2⎥ ⎥⎢ 2 E ⋅I 4sin φ 2tanφ 2φ ⎦ ⎢⎣ ⎥⎦ ⎣



(7.89)

ΔR 1 =

⎡ Q ⋅R 13 R 22 ⎤ (7.96) ⋅ 1− ν + 1+ ν ⋅ ( ) ( ) R 12 ⎥⎦ E ⋅ ( OR 2 − IR 2 ) ⎢⎣

7.2.6.3 Rollover Torque

and φ is the half angle between the loads. The race deformation correction factors, K1 and K2, are defined as [4]

During the torque transmittal mode of operation of the sprag OWC, it is necessary to limit the system deflections. Should the sprag rotate too far due to system deflections, the sprag will “roll over” and permanently wedge itself between the outer surface of the inner race OR(i) and the inner surface of the outer race IR(o). Rollover is shown as position h1 in Fig. 7.68. This is a condition that is non-reversible and is detrimental to the function of the transmission. To avoid rollover, we must design the clutch so that the system deflections are less than the cam rise of the sprag. In other words, at the maximum applied torque, we must have



K1 = 1 – acf + bcf

(7.91)





K2 = 1 – acf

(7.92)

where e is the distance from the mean radius to the neutral axis, which is given as [10]



⎡ ⎤ ⎢ OR − IR ⎥ e = Rm − ⎢ ⎥ ⎢ ln ⎛⎜ OR ⎞⎟ ⎥ ⎢⎣ ⎝ IR ⎠ ⎥⎦

(7.90)

and

e Rm

(7.93)

2(1+ ν ) ⋅S⋅e Rm

(7.94)

a cf =

bcf =

7.2.7 System Stresses [23] 7.2.7.1 Contact Stresses There are two possible forms of contact between a race and sprag: (1) concave/convex, as between the outer race and sprag, and (2) convex/convex, as between the inner race and sprag. The former is referred to as conformal contact, whereas the latter is referred to as non-conformal contact. Non-conformal contact loads lead to higher contact stresses; therefore, we are concerned with only inner race/sprag contact stresses.

where ν is the Poisson’s ratio for the race material, and S is the shape factor for the race. For a race having a rectangular cross section, S = 1.2 [10]. 7.2.6.2.2 Uniform Pressure Approximation

The equation to determine maximum hertz stress σc(mean) between two convex surfaces is defined by Young [4] in terms of the resultant force between the inner race and sprag F(i), the outer radius of the inner race OR(i), the sprag cam radius in contact with the inner race Ri(s) , the width of the sprag W(s), and the material properties of the inner race and sprag (ν(i), E(i), ν(s), E(s))

In the uniform pressure approximation, we assume that the sprag contact forces act uniformly on the contact surface of the race. Therefore, to apply this method, we must first compute an equivalent pressure on the spragway of each race. (The spragway is the smooth cylindrical surface upon which the sprag contacts the race, that is, OR(i) and IR(o).) This equivalent pressure is given as

Q=

Fn ⋅N( s) 2⋅π ⋅R 1 ⋅W



(7.97)

to assure that the system will not roll over. Note that in Eq. 7.97, the variable Kc is the radial stack-up of clearances in the clutch system.

where acf is the hoop deformation factor and bcf is the shear deformation factor. For thick-walled cylinders, these factors are defined as [4]

Cam rise ≥ ΔOR (1) + ΔIR (o) + δ + K c

(7.95)



⎛ 1 1 ⎞ + 2⋅F(i ) ⋅ ⎜ ⎟ ⎝ OR (i ) R i( s) ⎠ σ c( max ) = ⎛ 1− υ(2i ) 1− υ(2s) + π ⋅W( s) ⋅4⋅ ⎜ ⎜⎝ E(i ) E( s)

(

) (

) ⎞⎟

(7.98)

⎟⎠

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erty and loading characteristics. That is, Eq. 7.104 is solved in terms of radius OR(i). Equation 7.104 does not have a simple solution for the inner race outer radius, however. It is a quadratic equation in the form of

where Ri(s) can be simplified as half of the nominal sprag height for our preliminary computations R i( s) =



h nom 2

(7.99)

A commonly used derivation of Eq. 7.98 defines hertz stress in terms of its mean value σc(mean) rather than maximum value [5, 6]

2 ⎛ ⎛ σ c( mean) ⎞ ⎞ 2 0 = ⎜ R i( s) ⋅N( s) ⋅sinα(i ) ⋅W( s) ⋅ ⎜ ⎟ ⋅OR (i ) ⎝ c1 ⎟⎠ ⎠ ⎝

(

)

(

+ −T(i ) ⋅OR (i ) + −T(i ) ⋅R i( s)

⎛ 1 1 ⎞ + F(i ) ⋅π ⋅ ⎜ ⎟ ⎝ OR (i ) R i( s) ⎠ 1 σ c( mean) = ⋅ ⎛ 1− υ(2i ) 2 1− υ(2s) + W( s) ⋅4⋅ ⎜ ⎜⎝ E(i ) E( s)

(

) (

) ⎞⎟



2 ⎛ ⎛ σ c mean ⎞ ⎞ T(i ) ± T(2i ) − 4⋅ ⎜ R i( s) ⋅N( s) ⋅sinα(i ) ⋅W( s) ⋅ ⎜ ( ) ⎟ ⎟ ⋅ −T(i ) ⋅R i( s) ⎝ c1 ⎠ ⎠ ⎝ OR (i ) = 2 ⎛ ⎛ σ c mean ⎞ ⎞ 2⋅ ⎜ R i( s) ⋅N( s) ⋅sinα(i ) ⋅W( s) ⋅ ⎜ ( ) ⎟ ⎟ ⎝ c1 ⎠ ⎠ ⎝

(

⎟⎠

1 π c1 = ⋅ 2 ⎛ 4 1− υ(2i ) 4 1− υ(2s) + ⎜ ⎜⎝ E(i ) E( s)

(

) (

) ⎞⎟



(7.101)

To use Eq. 7.106, we must select an operating contact stress at which the sprag OWC will operate. Application history has shown that limiting the mean contact stress to 3.45 GPa (500,000 psi) is reasonable for sprag OWC applications. Note that the actual contact stresses vary with strut angle and are determined iteratively. Equation 7.106 yields two real roots: one negative, and one positive. The negative root is meaningless when discussing magnitudes of length; therefore, only the positive root is considered.

⎟⎠

⎛ 1 1 ⎞ + F(i ) ⋅ ⎜ ⎟ ⎝ OR (i ) R i( s) ⎠ σ c( mean) = c1 ⋅ W( s)

(7.102)

Solving Eq. 7.102 in terms of total force per sprag F(i) results in the following equation

7.2.7.2 Hoop Stress

2



⎛ σ c mean ⎞ W( s) ⋅ ⎜ ( ) ⎟ ⎝ c1 ⎠ F(i ) = 1 1 + R i( s) OR (i )

7.2.7.2.1 Uniform Pressure Approximation

(7.103)

Contact forces between the sprags and races create a circumferential (hoop) stress in the outer and inner races. The hoop stress on the inner race is compressive, and steel does not typically fatigue due to compressive stresses. However, the outer race experiences tensile hoop stresses, which is a typical mode of fatigue failure for steel. Therefore, we consider hoop stress for only the outer race.

For the sprag clutch, we now have two equations that solve for F(i), Eqs. 7.82 and 7.103. We set these equations equal to one another and obtain the following 2



)

(7.106) That is, given load, material property, and sprag parameters, Eq. 7.106 calculates the outer radius of the inner race for a sprag clutch.

Then, Eq. 7.100 simplifies to



)

and the quadratic equation that solves for OR(i) is

(7.100)

We use the equation for mean contact stress to derive an additional term for the total force per sprag F(i). The constants and material properties from Eq. 7.100 (π, ν(i), ν(s), E(i), E(s)) are brought outside the radical and named c1

(7.105)

⎛ σ c mean ⎞ W( s) ⋅ ⎜ ( ) ⎟ T(i ) ⎝ c1 ⎠ = 1 1 N( s) ⋅OR (i ) ⋅sinα(i ) + R i( s) OR (i )

The discrete nature of the contact forces also creates bending stresses. If the number of sprags is very low, then the bending has a significant contribution to the circumferential stress. However, if the number of sprags is relatively large (greater than eight), then the circumferential stresses in the outer race are predominantly hoop stresses [23]. Therefore, in the ­following discussion, we assume the number of sprags

(7.104)

In the design of a sprag clutch, we want to determine the optimal inner race outer radius OR(i) given the material prop-

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magnitude of the hoop stress: (1) the outer radius directly above a sprag (location 1), and (2) the inner radius midway between two sprags (location 2).

is greater than eight, and we use the uniform hoop stress equation. The governing equation for the mean hoop stress in the outer race σh(mean), as defined by thick cylinder analysis, is a function of the pressure on the interior surface of the outer race Q(o) and the wall thickness of the outer race (OR(o) and IR(o)) [7, 8]

⎛ OR (2o) + IR (2o) ⎞ σ h( mean) = Q(o) ⋅ ⎜ 2 2 ⎟ ⎝ OR (o) − IR (o) ⎠

(7.107)

The pressure Q(o) on the inner surface of the outer race of a sprag clutch is a function of the radial force per sprag (F(o) . cos α(o)) , the number of sprags N(s), and the total inner surface area of the outer race (2 . π . r . l = 2 . π . IR(o) . W(o)):

⎛ N( s) ⋅cosα(o) ⎞ Q(o) = F(o) ⋅ ⎜ ⎟ ⎝ 2⋅π ⋅IR (o) ⋅W(o) ⎠

Fig. 7.79  Discrete load approximation model.

(7.108)

The angle φ shown in Fig. 7.79 is the half angle between the sprags and is given as

If we assume that the width of the sprag is equal to the width of the outer race (W(s) = W(o)) and substitute Eqs. 7.77, 7.103, and 7.108 into Eq. 7.107, then the following equation is derived for the mean hoop stress σh(mean) in the outer race:



2 2 ⎛ σ c( mean) ⎞ ⎛ OR (o) + IR (o) ⎞ ⎛ R i( s) ⋅OR (i ) ⋅N( s) ⋅cosα(o) ⎞ σ h( mean) = ⎜ ⋅⎜ ⎟ ⎟ ⋅⎜ 2 ⎟ ⎝ c1 ⎠ ⎝ OR (o) − IR (2o) ⎠ ⎜⎝ R i( s) + OR (i ) ⋅2⋅π ⋅IR (o) ⎟⎠

)

(7.109) However, we want to assume the average hoop stress σh(mean) that the outer race will encounter, and calculate the outer radius accordingly OR(o). Note that the inner radius of the outer race IR(o) is determined based on the geometry of the inner race that was calculated earlier via Eq. 7.106 and the geometry of the sprags. Therefore, Eq. 7.109 is put in terms of the outer radius of the outer race, where the pressure on the interior surface of the outer race Q(o) was previously defined in Eq. 7.108.

OR (o) =

Q(o) ⋅IR (2o) + σ h( mean) ⋅IR (2o) σ h( mean) − Q(o)



2⋅π π = N( s) N( s)

(7.111)

where N(s) is the number of sprags in the clutch. Another variable to be defined is the offset between the neutral axis and the mean radius for the outer race e(o). The general expression for this variable is given in Eq. 7.90, and the specific form for the outer race is given as

2

(

φ = 0.5⋅



⎤ ⎡ ⎥ ⎢ ⎢ OR (o) − IR (o) ⎥ e(o) = R m(o) − ⎢ ⎛ ⎞ ⎥ ⎢ ln OR (o) ⎥ ⎢ ⎜⎝ IR (o) ⎟⎠ ⎥ ⎦ ⎣

(7.112)

The hoop stress at the outer radius of the outer race above the sprag is a function of the normal force Fn(o), the mean radius Rm(o), the cross-sectional area A(o), the half angle between sprags φ, the offset e(o), and the outer radius of the outer race OR(o).

(7.110)

⎛ 1 Fn(o) ⎡ 1 R m(o) − e(o) ⎞ ⎛ R m(o) ⋅h o(o) ⎞ ⎤ σ h@1(o) = ⋅⎢ −⎜ − ⎟ ⋅⎜ ⎟⎥ 2⋅A(o) ⎢⎣ tanφ ⎝ tanφ φ⋅R m(o) ⎠ ⎝ e(o) ⋅OR (o) ⎠ ⎥⎦

7.2.7.2.2 Discrete Load Approximation

(7.113)

The equations used for discrete load approximations are significantly more complex than the uniform pressure approximation and are included for the cases when the uniform pressure approximation is inadequate. Figure 7.79 shows the model used to develop the stress equations. Two locations on the outer race are of particular interest because of the high

The hoop stress at the inner radius of the outer race midway between the sprags is a function of similar variables but also includes the inner radius of the outer race IR(o).

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Design Practices: Passenger Car Automatic Transmissions

sprag, and ω(o) is the angular velocity of the outer race, which is defined in radians per second. As shown, the center of gravity Cg is offset to the left from the outer sprag cam center Co. Because of this offset, the centrifugal force Fcen induces a moment on the sprag, tending to lift it from contact with the inner race (i.e., tending to disengage the sprag). This type of sprag is known as a centrifugally disengaging sprag. As can be seen, only the spring force Fsp is keeping the sprag in contact with the inner race. Note that a disengaging-type sprag will never disengage as long as it is carrying a small amount of torque (on the order of 14 N-m).

⎡ 1 ⎛ 1 R m(o) − e(o) ⎞ ⎛ R m(o) ⋅h i(o) ⎞ ⎤ ⋅⎢ –⎜ − σ h@2(o) = ⎟ ⋅⎜ ⎟⎥ 2⋅A(o) ⎢⎣ sinφ ⎝ sinφ φ⋅R m(o) ⎠ ⎝ e(o) ⋅IR (o) ⎠ ⎥⎦ Fn(o)

(7.114)

7.2.8 Sprag Dynamics [23] In evaluating a sprag OWC design, one must venture beyond static analysis of the clutch and examine the dynamic, freewheel behavior of the clutch system. Often, the success or failure of a design is dictated by the dynamic or dynamic transient performance rather than the static performance. Because the dynamic behavior of a sprag OWC is highly dependent on the sprag and spring design, an analysis methodology is offered in this section rather than a rigorous analysis.

If the sprag Cg is located to the right of the outer cam center Co, the centrifugal force Fcen tends to increase the sprag/ inner race contact force. This type of sprag is shown in Fig. 7.81 and is known as a centrifugally engaging sprag. As can be deduced, the net moment created by Fsp and Fcen tends to increase the contact force between the sprag and the inner race.

During the freewheel mode of operation of an OWC, the sprags tend to rotate with the outer race. This is due to the inertia load on the sprag increasing the contact force between the sprag and the outer race. Forcing the clutch to rotate with the outer race is often a design objective due to the possibility of wear on the outer cam surface of the sprag. In Fig. 7.80, we show a typical sprag. Assuming that the sprag is spinning along with the outer race, the centrifugal force Fcen acting on the sprag is defined as

Fcen = m( s)rcg( s)ω (2o)

(7.115)

Fig. 7.81  Defining a centrifugally engaging sprag [23]. Although the bulk of sprag OWC applications use either an engaging or disengaging sprag design, there is a third alternative. If the center of gravity Cg is coincident with the outer cam center Co, the centrifugal force Fcen tends to neither engage nor disengage the sprag from the inner race. This type of sprag is known as a centrifugally neutral sprag. A sprag of this type is rarely used because of the difficulties of assuring the coincidence of the two centers. Fig. 7.80  Defining a centrifugally disengaging sprag [23].

These three “inertia designs” of the sprag give the designer a degree of flexibility when designing the OWC for a specific application. For example, in the torque converter stator position where the clutch is not expected to engage at speed, the

where m(s) is the mass of the sprag, rcg(s) is the radial distance from the center of rotation to the center of gravity of the

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and energizing means. The axial alignment and parallelism of short sprags is also more difficult to maintain with the tolerances ordinarily used.

designer may select a disengaging sprag to reduce the contact force between the sprag and the inner race, thereby reducing spin losses and sprag wear. In a shift position, however, the designer may apply an engaging sprag, because the clutch will be expected to engage at speed. Note that each application is unique and must be closely examined to determine which sprag type is most appropriate.

Table 7.5  Sprag Characteristics [24]

7.2.9 Design Considerations 7.2.9.1 Number of Sprags [24] The maximum number of sprags that can be used on a given race diameter depends on the size of the sprag section and the particular clutch design. Table 7.5 [24] lists a number of characteristics of the 8.38 mm sprag section, as well as the minimum circumferential pitch Pc. Knowing the inner or outer race diameter, the sprag section, or more precisely the mean radial height, and the minimum circumferential pitch Pc, then the maximum number of sprags possible in a given annulus can be easily arrived at N max =

7.2.9.3 Full Phasing [24] Despite the inference made in the basic theory that torque load was equally shared by all the sprags, it took a number of field failures, then considerable testing and close observation and analysis of results with the original non-phased designs, before the full impact of this simple requirement was realized.

mean circumference of sprag annulus (7.116) Pc

For economy reasons, it may be desirable to use the minimum number of sprags on a given diameter that will handle the load requirements. There exists no absolute minimum on the number of sprags that can be used for a given clutch. However, one-third of the maximum number possible has been used successfully and has been able to handle one-third the maximum rated torque capacity despite the chording effect on the races.

Some of the factors encountered that contribute to de-phasing of the sprag are: 1. Torsionals 2. Shock loadings or repeated high loading 3. Variable energizing force during re-engagement after being centrifugally disengaged 4. Friction—either inter-sprag or end plate 5. Inertia forces on sprags, especially with the outer race accelerating or decelerating 6. Stiff oil films or heavy anti-friction additives in oil 7. Rapid loading and unloading of the clutch such as could occur with a chattering friction clutch 8. Excessive race eccentricity

The more typical problem one may encounter is to achieve the greatest possible torque capacity in a minimum of space. Because maximum torque capacity is a function of OR(i) and the number of sprags, and the number of sprags is also a function of OR(i), then it follows that Tm is proportional to OR2(i). So the easiest way of getting more clutch capacity is to increase diameter. The only offsetting factors in this reasoning are the following: (1) the overrunning speed increases as the first power of diameter, and (2) the inertia effects vary as the square of diameter.

7.2.9.4 Full Phasing—With Caged Design [24] 7.2.9.2 Length of Sprags [24]

Although there are single-cage sprag clutch designs in production today, they are not numerous. The reasons for this include the inability to assure the phasing of the sprags. And without proper phasing, unequal load sharing among the sprags can arise. Assurance of phasing could not be accomplished until the advent of the dual-cage design.

The maximum and minimum sprag lengths given in Table 7.5 are usually governed by practical considerations. For example, the maximum is limited by the ability to heat-treat without distortion, and the minimum is governed by the inefficient division of the axial space available between sprag 7-41

Design Practices: Passenger Car Automatic Transmissions

it was possible for one sprag to release its load so violently that it would bind up between the two cages and hold the remainder of the sprags inoperative. Figure 7.84 shows a typical pop-out.

Figure 7.82 shows an exploded view of a high-production, double-caged, full-phasing sprag clutch. The phasing is achieved by the use of two cages that are held concentric by their respective races. One of the cages controls the sprags near their outer race contact, and the other cage controls the sprags near their inner race contact. By accurately sizing and spacing the cage holes, the sprags can be so contoured and fitted to the cage holes that they must move in unison throughout their entire operating range within the limits of the tolerances imposed by economical manufacturing methods. Figure 7.83 shows the relationship of sprags and cages during freewheeling and under different loading conditions.

Fig. 7.84  Pop-out in double-caged clutch. Fig. 7.82  Full-phased sprag clutch [24].

Overloading of a phased clutch seldom occurs if the clutch package is properly designed and the dynamic loads are accurately estimated. If overloading occurs, the only solutions are to either increase the size of the clutch or eliminate the unexpected source of the high load, such as a non-modulated and suddenly applied friction clutch or a chattering friction band or clutch. Although it is not obvious, most clutch damage is caused when the sprags are unloading very rapidly. Factors that have been found to contribute to sprags or clutches suddenly releasing their load are: 1. Improper sprag geometry (to be discussed later). 2. Loose or slippery foreign matter between the sprags and races. 3. Very coarse race grind. 4. Excessive levels of extreme pressure additives in oil, such as graphite, molybdenum disulfide, and so forth. 5. Excessive axial or torsional vibration when attempting to engage the clutch. The normal axial movement of a helical gear on taking up load (e.g., a sun gear) has not hampered the engagements of the clutch in a number of applications currently running. This is because ordinary gear backlash is taken up before the clutch is engaged and begins to transmit torque. 6. Improper energizing of sprags—broken or yielded springs—or when centrifugally disengaging sprags are

Fig. 7.83  Clutch phasing [24]. (a) freewheeling, (b) light load, and (c) heavy load. 7.2.9.5 Pop-Out [24] The only real disadvantage encountered in the experience with double-caged sprag clutches is the so-called pop-out trouble that plagued the earlier designs. When this occurred, 7-42

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One-Way Clutches

7.2.9.7 Races [24]

required to re-engage just below the speed they would normally disengage. 7. Load instantaneously removed from a highly loaded clutch, such as a chattering-plate clutch or a sudden break in the driveline.

A OWC of any type is no better than the races used with it. When the clutch is engaged and carrying a torque load, the races store energy via elastic deformation. (Viewed from a different perspective, a sprag clutch is merely a means of storing energy in a couple of ring-shaped springs that are called races.) Hence, the elasticity of these races is critical to proper clutch performance. Considerable attention must be given to the detailed race designs and their mounting if a successful clutch package is to be achieved.

By redesigning the sides of the sprags, increasing the OD of the inner cage, and even putting the inner cage holes at a slight angle with respect to a radial line for some sprag designs, the possibility of a pop-out occurring was made practically impossible without breaking up of the hardened steel cage. Excellent field experience is convincing evidence that pop-outs can be avoided through robust design.

7.2.9.7.1 Proportions

Early in the history of sprag OWCs, a series of tests was conducted on various-size clutches having varying race proportions. The objective was to determine the optimum race proportions. It soon became evident that it was not the stresses in the races that were critical, but rather the amount the races deformed elastically under load. This is attributable to the cam rise of the sprag, which is finite (see Section 7.2.6.3, Rollover Torque). The design “guidelines” derived from these tests are:

7.2.9.6 Concentricity [24] Another assumption made by the theory is that the clutch races are concentric when the sprags first engage and begin to transmit torque. Unfortunately, this condition is not easily realizable in practice. Depending on the clutch, sprag-strut angle, and energizing-spring design, experience has shown that under some conditions, the races are forced further eccentric, and a good percentage of the sprags never carry any of the torque. Therefore, the few remaining can be overloaded and rolled over. The effect of the eccentric push on bearings associated with the races is sometimes damaging to the bearings.

1. The length of the races should be at least 3.2 mm (0.125 in.) longer than the length of the sprag. 2. The outer race radial thickness should be such that the ratio of its inner diameter to its radial thickness should not exceed 8, and should preferably be approximately 6.5. 3. The inner race ratio of its outer diameter to radial thickness should not exceed 10, and should preferably be approximately 8.

One possible explanation for this phenomenon is the effect that race eccentricity has on a non-phased clutch. Eccentricity will create a condition wherein half of the sprags will be operating in a radial sprag space that is greater than the nominal, and the other half in a space smaller than the nominal. Those sprags in the larger radial space have an appreciably greater cam rise per degree of sprag rotation than do the sprags in the smaller space. Therefore, as the torque is increased, the races are held eccentric or are forced into a position of greater eccentricity, depending on the extent of the original offset.

These results were based on static and dynamic tests of symmetrical and plain cylindrical races. If flanges or other nonuniform race cross sections are used, some allowance must be made for the bellmouthing effect. (Note that bellmouthing reduces the effective length of the sprags and tends to skew them.) If fatigue is a problem, the appropriate analyses and/ or tests should be run to find the effect of the stress raiser.

With a double-caged phased clutch having reasonable control on the race eccentricity (see the limits given in Table 7.5), the side loading under eccentric conditions can be minimized. Tests have demonstrated that races held 0.127 mm (0.005 in.) eccentric with a 1334-N (300-lb) weight moved to within 0.025 mm (0.001 in.) of concentricity by the application of only 6.8 N-m (5 ft-lb) torque on a relatively small doublecaged clutch.

7.2.9.7.2 Material and Hardness

To avoid local brinelling and to minimize overrunning wear, the race surface contacting the sprags should have a minimum surface hardness of Rockwell C 60, and a case is usually extended to a minimum depth of 1.27 mm (0.050 in.). At this depth, the hardness should not be less than Rockwell C 50. To prevent excessive race yield under load, the hardness of the core of the race is held in the range of Rockwell C 35 to 45. Experience with excessively hard cores (i.e., greater

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Design Practices: Passenger Car Automatic Transmissions

below approximately 57.2 mm is usually held to about 0.013 mm (0.0005 in.) minimum tolerance.

than Rockwell C 50) has shown them to be very prone to cracking at the outer diameter and exceptionally sensitive to stress raisers.

Composite races made up of relatively thin, hardened-steel sleeves held in or over cast-iron carriers have been used with some success, but only if the sleeves are pinned or keyed to the cast iron. A plain press fit has been used, but it does have a tendency to slip occasionally and sometimes will gall and hold; other times, it continues to slip, especially after repeated heating and cooling.

Typical race materials that have been used successfully are SAE 52100, 1060, or 5060. These materials must be given double heat-treatment to get the desired case and core properties. Carburizing steels such as 8640, 4620, and 8620 have also been used successfully. A graph showing the relative static strengths of a variety of materials used in a typical outer race is included in Fig. 7.85.

With the race proportions suggested, it can be expected that the outer race expansion at the OD will be about 0.13 mm (0.005 in.) and the inner race contraction about 0.13 mm when the clutch is loaded to its rated torque capacity Tm. The relative rotation of the races will vary with clutch size but will be in the vicinity of 4 to 7 degrees at Tm. The torsional rate of the clutch will vary as indicated in Table 7.6 [24]. Table 7.6  Variance of Torsional Rate of Clutch [24]

Fig. 7.85  Effect of race material and heat treat on outer race yield [24].

Specific figures on any one of the quantities mentioned above should be determined for the particular configuration at hand because so many variables enter into the final answer. Some of the more obvious variables are:

The surface finish of the outer race sprag surface is generally not rougher than 0.76 µm (30 µin.) rms, and the spragway of the inner race, where overrunning usually occurs, is not rougher than 0.51 µm (20 µin.) rms. The taper per side of the race sprag surfaces usually should not exceed 0.0003 mm/mm for the length of the sprags. A slight chamfer of about 0.8 mm (1/32 in.) × 15 degrees on one end of the races will simplify assembly.

Sprag section used (especially strut angle) Number of sprags used Clutch diameter Outer and inner race proportions and cross-sectional shape 5. Means for transmitting torque to races 1. 2. 3. 4.

Tolerances on the race diameters, with the associated bearing clearances, tolerances, and eccentricities, should be adjusted to hold the possible variation in the radial sprag space between the races to within the limits shown in Table 7.5. The limits on radial sprag space given in Table 7.5 have been arrived at over a number of years and appear to be well within practical bearing clearances and manufacturing tolerances, but are not so great as to jeopardize good sprag performance. With these limits, the outer race ID usually has a minimum tolerance of about 0.025 mm (0.001 in.), the inner race OD above 57.2 mm (2.5 in.) also has a 0.025 mm (0.001 in.) minimum tolerance, and the inner race OD

7.2.9.8 Overrunning [24] Relative motion between the sprags and the races is usually at the inner race contact, for the clutch tends to stay with the outer race because of the centrifugal force acting on the sprags. However, if lubrication conditions dictate otherwise, the clutch can be held frictionally to a stationary inner race so the rubbing takes place between the sprags and the outer race.

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7.2.9.9 Drag Torque

the sliding between the sprags and race is occurring. This is a very important point and should not be overlooked. In most designs, centrifugal force tends to throw the oil away from the critical surface where sliding takes place, and this is a big factor as to why most splash lubricating systems are inadequate.

In the transition from the freewheel to the engaged modes of operation, the sprag clutch depends on the energizing spring to help initiate the engagement. This spring imparts a load to the sprag that properly positions it for the transient event. If the spring load is too great, accelerated wear of the sprag and/or races may result. If it is too small, some sprags may not engage, resulting in an uneven distribution of load among the sprags. To aid the engineer, an empirical formula has been derived that relates the needed drag torque to other clutch parameters. This formula is given as [24]

Td = K d ⋅N( s) ⋅D⋅L( s)

(7.117)

where Td is the needed drag torque for the clutch, N(f) is the number of sprags in the clutch, L(f) is the nominal length of the sprags, D is the spragway diameter of the inner race ( = 2 . OR(i)), and Kd is the drag constant. When applying Eq. 7.117, the engineer must select the value of Kd appropriate for the measurement system being used. Table 7.7 gives the value of Kd for three systems of measure. Note that the drag torque value given by Eq. 7.117 should be used as an objective in the preliminary clutch design, and that the final value of Td will be a result of the consideration of all functional aspects of the design. (It is interesting to note that if Td is desired in the units of inch-ounces, the value of Kd will be 1.0.)

Fig. 7.86  Straddle-mounted plain bearings (preferred) [24].

Table 7.7  Drag Torque Coefficient

Fig. 7.87  Plain bearing, one side only—simplest construction [24].

7.2.9.10 Mounting Provisions [24]

Figure 7.89 shows a compact, straddle-mounted, plain bearing design that has been used successfully. Here, two 3.2 mmlong bearings are obtained with an increase of overall clutch width of only 2.5 mm. These shell-type bearings also act as dams and help retain oil in the clutch cavity. As an example of their robustness, a static radial load of 4448 N has been imposed on a 71 mm-diameter clutch with two shell bearings, with no adverse effect on the bearings. These types of bearings are commonly fabricated from bronze, bronze-clad steel, or phosphate-coated steel.

Some of the conventional methods of mounting and lubricating sprag clutches are shown in Figs. 7.86 to 7.88. Straddle mounting is generally preferred, but a plain or needle bearing of sufficient length on one side of the clutch has proved adequate. A single plain (not preloaded) ball bearing on only one side of the clutch allows excess angularity of the race axes and is not recommended. In all of the constructions shown, an attempt has been made to divert or dam the oil so that oil is always available at the inner race OD where

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Design Practices: Passenger Car Automatic Transmissions

7.2.9.12 Built-In Drag [24] There is a means for obtaining greater overrunning life, especially under borderline lubrication conditions, and to assist in the engagement of the sprags under all loading conditions, whereby a controlled amount of friction drag is introduced between each cage of a double-caged clutch and its adjacent race. During freewheeling, the frictional forces oppose and subtract from the normal energizing spring force on the sprags and thereby reduce the unit loading between the sprags and races so that overrunning life is materially increased. Then, during engagement, the directionally sensitive built-in drag of the phasing cages adds to the energizing spring force and ensures more positive and uniform engagement. Figure 7.90 is a picture of a typical production clutch with built-in drag. Drag between the outer cage and the outer race is obtained either by slotting the side bar of the cage at two points and bending the T-bar thus formed so it is an interference fit in the outer race, or by the use of stainless steel sprag clips, as shown. Drag between the inner cage and inner race, where overrunning is expected to take place, is accomplished by beryllium-copper drag strips, which are clipped on and held in the cage holes by the sprags. The built-in drag also serves to overcome any adverse effects of cage inertia on the engagement of the clutch during rapid acceleration or deceleration of one of the races.

Fig. 7.88  Piggy-back races and clutches, shell-type end bearings [24].

Fig. 7.89  Sprag clutch with end bearings. 7.2.9.11 Lubrication [24]

Fig. 7.90  Phased sprag clutch with built-in drag.

Oils such as SAE 10 to SAE 80 are quite satisfactory, but oils with additives such as modern automatic transmission oils are superior. Oils with higher percentages of EP additives, graphite, molybdenum disulfide, or the like are not recommended. Although pressure lubrication is preferred, it is not necessary to flow a given quantity of oil through the clutch for cooling purposes. Rather, it is important to keep the rubbing surfaces constantly wet with oil during overrunning.

7.2.9.13 Sprags [24] Because the essential working element of a sprag clutch is a sprag, we must devote some discussion to it. Metallurgically, a sprag is a piece of cold-drawn and accurately shaped wire, usually SAE 52100 steel that is cut to length and properly hardened and drawn at about 163°C (325°F) to a final hardness of Rockwell C 60 to 64. By proper hardening, it is implied that no decarburization is permissible, and the sprags must be quenched with an absolute minimum of distortion.

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7.2.9.14 Strut Angle Gage [24]

The contribution of this strut angle gage to the development of the art cannot be overestimated, for it finally gave a quantitative tool that did not only measure the variables in the sprags, but automatically gave an answer as to the quantitative effect of these variables on the critical sprag strut angle. This device plays a large part in incoming sprag inspection as well as in the analysis of laboratory tests and field returns.

Figures 7.91 and 7.92 show an automatic gage developed to measure strut angles of sprags. This strut angle gage applies a known fixed vertical load to the sprag, which immediately tries to rotate. By applying a variable horizontal load to the sprag, a value of horizontal load can be found that will just balance the vertical load. The ratio of the horizontal load to the fixed vertical load is directly proportional to the tangent of the sprag strut angle. Therefore, by plotting continuously horizontal force versus sprag height, and rolling the sprag from the low to the high end of the cam, we can draw a continuous curve of the sprag strut angle. One of the amazing things about this gage is that it produced curves virtually identical to what had been calculated on the basis of a number of assumptions. The greatest assumption was no distortion under load of sprags or races. But even when the magnitude of the vertical load was appreciably increased, the curves changed negligibly.

7.2.10 Wear [22] Sprag clutch wear is of interest because of the close dimensional tolerances required for the various components of the clutch. Excessive wear can cause a rollover malfunction of the sprag clutch, which renders the transmission inoperative. Rollover can result from severe wear of the inner race at the line contact with the sprag elements. The propensity to wear can be influenced by the quality of the ATF. Supplemental surface roughness measurements on the inner race were conducted using the high-wear reference fluid, ATF09, to better understand the wear mechanism occurring in the sprag clutch. In this analysis, localized surface damage due to wear was confirmed by surface profilometry and related to Rt and Rp. Surface roughness data from special timed-interval tests provided additional information on the wear process and suggested a possible mechanism for initiation and propagation of wear between the inner race and sprag elements. These data involved roughness data collected at intervals from 2 to 48 hours during extended tests. Although the interrupted-test data provided insight as to the mechanism of wear initiation and propagation, inner race weight losses were reduced by a factor of 50 relative to those observed in uninterrupted, 18-hour sprag wear tests. This was believed to result from the associated cool-down events and repeated removal of wear debris from the sprag during solvent cleaning and drying.

Fig. 7.91  Sprag strut angle gage.

Because the sprag element surface is quite difficult to quantify, surface damage to the sprag elements was examined only in a generalized manner. Although the quantity of worn material was greatest for the inner race, sprag element contour is important to proper engagement and plays a definite role in the wear mechanism. Figure 7.93 depicts the generalized, wear-related deformation in surface contour. It was determined that the face along the sprag element width, initially considered as conforming to the inner race surface, was actually curved. The curvature was greatest near the sheared edges, forming a “cusp” (0-hour profile). Profilometer-based surface measurements revealed that the deviation in element contour ranged from 0.0020 to

Fig. 7.92  Close-up of a sprag strut angle gage. 7-47

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Although surface deformation was assessed on several sprag elements, it is difficult to numerically relate the impact of any one sprag element to the overall wear on the inner race. This apparent discrepancy may have resulted from face curvature and wear variations among the remaining elements. The formation of the ridge and groove on the inner race correlated best with inner race weight loss. The Rp parameter is similar to the ridge height; to an approximation, the subtraction of Rp from Rt represents the groove depth. Ridge formation probably is caused by displacement of metal outside the wear track due to plastic deformation. Another explanation may be axial plowing (normal to the direction of race rotation) by the sprag element edges. The two cages of the sprag assembly allow some axial motion of the individual sprag elements.

0.0025 mm (0.00008 to 0.00010 in.) at the midpoint of the sprag element. Although the overall load is relatively low during the freewheeling mode, the cusp-shaped contour of the element would be expected to produce localized high-stress areas at the contact points at the ends of the elements.

Fig. 7.93  Wear scar formation on sprag element surface [22]. As the test proceeded, the cusped regions began to wear away (about 1 mm from each edge) within the first two hours. The contact zone and surface damage then extended farther toward the mid-portion of the element face as testing continued (18-hour trace). After 48 hours, the element face had flattened across the full width.

Fig. 7.94  Recess formation on inner race surface [22].

Inner race wear progression was analyzed by the use of surface profilometry, as shown in Fig. 7.94. The variation in the topography of the inner race surface reflected the damage caused by the sprag elements at various test times. The concave shape at the top of the figure indicates the profile and relative positioning of the contacting sprag elements. Indeed, race wear appeared to originate at the sprag-element contact points. After two hours, surface roughness (Ra) increased to about two to four times that typically measured before the test. By eight hours, surface damage was apparent at each end of the wear track. As the test progressed, considerably deeper grooves formed. After the 48-hour period, a groove depth of 0.0020 to 0.0025 mm existed at the end of the wear track. Groove depths of 0.051 mm (0.002 in.) were typical with the use of the high-wear reference fluid and additivefree base stock.

Whatever the mechanism, the overwhelming evidence of surface damage was groove formation on the inner race surface along the region of sprag element contact. The pertinent point is that degradation of the sprag clutch resulted from the combined wear of the inner race and the sprag elements. Although inner race surface roughness and topographical characterization provide good insight to potential sprag failures in a transmission, the only technically based relationship to rollover has been strut angle variation, determined from the sprag strut angle gage described earlier. The curvature of the sprag element surface was considered to be crucial to groove formation. This implication was presented to the supplier, and the sprag element curvature was confirmed to be within manufacturing tolerances. The concavity was attributed to thermal distortion of the sprag elements during cool-down following the extrusion, shearing, and heat-treat steps. The surface curvature is reportedly unavoidable.

In the specific example illustrated in Fig. 7.94, groove formation (at the end of the sprag elements) apparently continued at 48 hours, even though the cusped regions on the sprag element (shown in Fig. 7.93) were removed by that time.

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positions of the transmission, where some have found their way into production.

Surface roughness measurements may be essential in discriminating among ATFs that exhibit very little wear. Weightloss determinations become questionable due to reliance on small changes in large initial tare weights. In comparing superior fluids under very mild wear conditions, a more comprehensive analysis may be required because it was observed in the latter portion of the SVVT procedure development that the initial inner race surface roughness among the same batch of new sprags varied from 0.13 to 0.38 mm (0.005 to 0.015 in.). Initial roughness variation and its impact on race wear are of considerable concern, especially if the relatively mild severity-level of the current SWT procedure is retained. Knowledge of the effects of initial roughness on wear, as well as frictional drag measurements, might be used to screen sprag clutches before testing by the SWT procedure. (Frictional drag was measured for some sprags and found to be well within the suppliers’ tolerances.)

As with the sprag and roller OWCs, the pawl clutch derives its name from the loading element used therein—that is, the pawl (also commonly called the strut). Fundamentally, the pawl clutch consists of an input member, an output member, and a plurality of pawls. Typically, the pawls will be nested in recesses in one of the two members and engage notches in the other to provide a positive locking between the two. The resolution of the clutch is defined as the number of engagement opportunities in one revolution. This “positive locking” aspect of the pawl clutch, by definition, does not rely on friction to transfer torque from the input to the output members. This is in stark contrast to the roller and sprag OWCs and represents one of the strong attributes of this type of design. However, because the pawl must engage at specific notch locations to transfer loads, the clutch has only a finite number of engagement opportunities in one full revolution. This, again, is in contrast to sprag and roller clutch designs and represents a weak point in the design, because a finite number of engagement opportunities means a finite backlash, which, in turn, translates to impact loads.

7.2.11 Summary In this section, we have presented design considerations, design methodologies, and analysis techniques for the design of sprag one-way clutches. The information given herein has been used in the design and development of sprag clutches for years. However, it is left to the reader to apply this information properly. In so doing, it is always prudent to review the underlying assumptions on which these techniques are based. If the assumptions do not apply to the problem at hand, alternative methods should be sought (e.g., the finite element method of analysis). If the assumptions do pertain to the problem at hand, the application of the methods presented should be done with caution. That is, the analysis expressions presented are not linked to any one measuring system. This makes the equations more versatile but requires the engineer to pay close attention to the units of measure. It is strongly advised that one system of measure be adopted and then rigidly adhered to throughout.

There are two basic types of pawl OWC devices: (1) the axialapply device, and (2) the radial-apply device. These names refer to the direction in which the pawls act, as will become evident in the coming sections. Each of these devices has its own set of attributes, which will also be discussed in the following sections.

7.3.2 Axial-Apply, Pawl One-Way Clutches 7.3.2.1 Clutch Operation [27] The performance of the axial-apply pawl OWC can be thought of as similar to that of a high-resolution planar ratchet. The device consists of two plates (or flanges) designated the pocket plate and the notch plate, respectively; one is attached to a driving shaft and the other to a driven shaft. The plates are arranged coaxially, as shown in Fig. 7.95, with the pocket plate containing recesses that house spring-loaded pawls that face the notch plate. The notch plate contains a series of projections that can engage the pawls in one direction, locking the plates together torsionally (see Fig. 7.96). In the other direction, the pawls are forced into the recesses of the pocket plate, allowing the plates to rotate freely relative to one another. The number of pawls and notches are so chosen that a single pawl takes the lock-up forces, and the multiplicity of pawls provides several engagement opportunities within one notch spacing. The resolution of the clutch is

7.3 Pawl One-Way Clutches 7.3.1 Introduction The use of pawl devices in automatic transmissions is nothing new. The parking pawl, which has been in use for decades, is a prime example. The use of a pawl-type device as an OWC is relatively new, however. In early applications, the pawl OWC found a home in the racecar, torque converter stator position. This was primarily due to its high load capacity, and was facilitated by the application’s lack of a noise requirement. Its success in this application prompted application investigations in the shift 7-49

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7.3.2.2 Pawl Equilibrium

equal to the product of the number of pawls and the number of notches.

When the clutch is carrying a torque, a single pawl is engaged and transmits the entire load from the pocket plate to the notch plate. The engagement of a pawl is depicted in Fig. 7.97, and the fully seated angle at which it acts is shown.

Fig. 7.97  The engaged pawl. In Fig. 7.98, the free body diagram of the pawl is shown, along with the forces acting upon it. Note that the spring force acting on the pawl is very small compared to the contact forces and can be neglected in our equilibrium examination.

Fig. 7.95  Axial apply pawl OWC assembly [28].

Fig. 7.98  The pawl free body diagram. The circumferential component Fc of the strut force Fpp is given as

Fc =

T ravg

(7.118)

where T is the transmitted torque, and ravg is the average radius at which the pawl is located, as shown in Fig. 7.95. The strut force Fpp is then given by Fig. 7.96  Function of the pawl [27, 28].



When overrunning at very low speeds, the ramp portions of the notch plate force the pawls down against their springs as each notch passes. At moderate to high relative speeds, the situation becomes very different, with each pawl assuming a position out of contact with the notch plate. At these higher speeds, the pawl position is determined by a balance between the spring force pushing the pawl toward the notch plate and the hydrodynamic forces on the pawl (from the oil or other working fluid) pushing the pawl into its pocket. Figure 7.96 shows the typical pawl overrunning position. The presence of a working fluid is essential for achieving this out-of-contact overrunning condition. Upon application of torque in the lock direction, the first available pawl is pivoted into a notch, creating a positive connection between the notch and pocket plates.

Fpp =

Fc cosφ

(7.119)

where φ is the fully seated angle at which the pawl works. Because the pawl is in equilibrium when under the influence of two forces, the forces must be equal in magnitude (Fnp = Fpp), opposite in direction, and co-linear in application. Finally, the “unproductive” portion of the strut force is given as Fa = Fc ⋅tanφ (7.120) where Fa is the axial portion of the strut force. This axial force tends to push the plates apart and must be supported elsewhere in the OWC system. Note that the majority of the strut force works in transmitting the torque load from the pocket plate to the notch plate.

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7.3.2.3 System Stresses

ances. To simplify the model and to take a more conservative approach, the column is modeled with pinned end connections, as shown in Fig. 7.99. This represents the worst-case scenario with regard to tolerances between the two plates affecting the behavior of the pawl as a column. To simplify the model, two other assumptions were made.

7.3.2.3.1 Strength Considerations

To explore the strength of the axial-apply pawl OWC, three different loading conditions were used in an experimental investigation. These are:

1. The load on the pawl is treated as a point load acting at the center of the column. 2. Only one pawl is engaged and carrying a load.*

1. Cyclic loading 2. Shock loading 3. Monotonic loading to failure Each of these loading conditions produced its own types of failures. For example, for the clutch tested, cyclic loading always leads to a fatigue cracking failure of the notch or pocket plate [27]. For the case of shock loading, a series of tests with various plate and pawl materials revealed a mixture of failure modes. With high-strength steel plates, the failure mode was invariably pawl buckling. With lowerultimate-strength material plates, such as PM steel, the failure mode was mixed, either plate cracking or pawl buckling [27]. Monotonic loading also indicated a variety of failure modes, each depending primarily on the design and material of the notch plate and pocket plate. With well-designed plates of appropriate strength, the failure mode was usually pawl buckling [27].

Fig. 7.99  Buckled pawl deformations [27]. The method used to calculate the force required to buckle the pawl is known as the tangent-modulus theory. Developed by F. Engesser [29], it is a useful analytical tool for estimating buckling loads in short, thick columns. The form of the equations is similar to those developed by Euler, but differs in that they use the “tangent-modulus” term, which takes into account the non-linearity of the modulus above the proportional limit.

7.3.2.3.2 Pawl Buckling Prediction [27]

The number of situations when pawl buckling was the determining factor in the ultimate strength of the clutch dictated that a method for analytically determining the buckling point for various pawl geometries be developed. A method for making this determination follows.

The relationship between the applied torque and the actual strut force is given in Eq. 7.118. As the torque load is generated, a compressive load on the pawl results. If the load becomes sufficiently great, a lateral deflection v(x) and bending moment M(x) will initiate,

The ultimate strength of the axial-apply clutch is a function of the ability of the pawl to resist buckling under the application of compressive loads. The pawl is situated between the notch plate and the pocket plate and provides a physical interference between the two plates so that the relative rotation between them can occur in only one direction.



F . v(x) = M(x)

(7.121)

Assuming that the material under load is linearly elastic, the material reaction to the applied moment is then equal to the basic differential equation for a beam in bending,

Because the magnitude of the torque that can be transferred from the input shaft to the output shaft is of practical interest, an analytical approach was used to better understand the response of the clutch to high loading conditions. Because the pawl is typically the component that fails first under ultimate torque loading, the model for determining the ultimate strength was devised to predict when the pawl should first begin to buckle.

E ⋅I⋅

d2v = −M ( x ) dx 2

(7.122)

where E is the elastic modulus and I the section modulus. By rearranging Eqs. 7.121 and 7.122, we can obtain the secondorder differential equation to relate the deflection of the pawl to the axial force applied to its ends, that is,

Because the ends of the pawl are neither truly fixed nor truly pinned at the notch and pocket plates, the degree to which the pawl buckles varies somewhat with the effect of toler-

d 2 v F⋅v ( x ) + =0 E ⋅I dx 2

(7.123)

The general solution to Eq. 7.123 then is *At the time of writing, the design philosophy was to have only one pawl engage. Since that time OWC systems have been designed and successfully applied that have two pawls engaging.

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v ( x ) = C1 ⋅sin

For typical clutch pawls, however, the slenderness ratio typically is much less than the critical value.

F F ⋅x + C 2 ⋅cos ⋅x (7.124) E ⋅I E ⋅I



where C1 and C2 are constant coefficients to be determined, and v(x) is the equation for the shape of the pawl in bending. Because the lateral deflection at the end points of the pawl must be equal to zero, the boundary conditions at x = 0 and x = L, where x is the distance measured along the axis of the pawl and L is the overall length of the pawl, are given as

v(0) = 0,   v(L) = 0



(7.126)



C1 = 1,   C2 = 0

(7.127)

⎛ n⋅π ⋅x ⎞ v ( x ) = sin ⎜ ⎝ L ⎟⎠

(7.128)

where n = 1, 2, 3 represents possible mode shapes for the deflection. Because n = 1 represents the lowest possible load required to buckle the pawl, we conservatively use it as the practical design rule. Solving for the load F required to first initiate bending in the pawl, the equation is

F=

n 2 ⋅π 2 ⋅E ⋅I L2



(7.129)

π 2 ⋅E ⎛ L⎞ = ⎜⎝ ⎟⎠ r c σ pl

σ=

Leff = L (both ends pinned) Leff = 1.2L (one end pinned)

(7.135)

The effect that this range has on the ultimate strength of the clutches tested is shown in the experimental results area. In our analyses, we have applied the mechanical properties of AISI 4340, quenched and tempered at 204°C. A compressive stress-strain curve for this material is shown graphically in Fig. 7.100. To simplify the analysis, a tangent modulus expression was developed from the curve of Fig. 7.100 using a least squares method. The results of this exercise are shown in Eq. 7.136. This approximated stress-strain equation was then used in conjunction with the buckling equations to determine when the onset of buckling should occur.

(7.130)

Equation 7.130 will hold true provided the term in the denominator is large enough that the compressive stress level within the pawl remains below the proportional limit of the material. Above this limit, the modulus term in the equation is non-linear, and, as a result, the stress becomes non-linear. This critical value for the slenderness ratio then is

(7.133)

To account for the differences in the end conditions of the pawl as a result of these tolerance variations, we use the standard practice of adjusting the “effective length” of the pawl. This range, based on experimental results, is between

If the equation is rewritten in terms of the slenderness ratio ⎛ L ⎞ , where r is the average radius of gyration, the axial stress ⎜⎝ ⎟⎠ r in the pawl due to compression is equal to F π 2 ⋅E σ= = 2 A ⎛ L⎞ ⎜⎝ ⎟⎠ r

dσ dε

Tolerances affect how well the pawl ends emulate pinned connections. The end connection behavior of the pawl determines the shape of the column while it is buckling. For example, columns that behave as having one end fixed and one end pinned typically will bend in the shape of an “S,” whereas columns with purely pinned ends will typically assume a “U”-shaped form. We often see this experimentally with buckled pawls. This is illustrated in Fig. 7.99.

When C1 and C2 are both zero, the solution is trivial. Therefore, the deflection curve for the pawl is then given as

Et =

F π 2 ⋅E t (7.134) = 2 A ⎛ L⎞ ⎜⎝ ⎟⎠ r Because the tangent-modulus term is variable above the proportional limit, a numerical, iterative process is used to solve Eq. 7.134.

By substituting the boundary conditions into the general equation, the unknown coefficients can be determined. The general equation is satisfied when either of the following conditions holds true: C1 = 0,   C2 = 0

(7.132)

For this reason, the tangent-modulus term Et is used in lieu of the elastic modulus term E, as shown in Eq. 7.134.

(7.125)



⎛ L⎞ ⎛ L⎞ ⎜⎝ ⎟⎠  ⎜⎝ ⎟⎠ r c r strut



σ = ( 256.19 +17.3ln765ε ) ⋅6.894

(7.136)

(7.131)

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and 7200 rpm resulted in no disruption of the lacquer film. This was true so long as the acceleration to and deceleration from the test speed occurred rapidly. Overrunning at speeds less than 200 rpm resulted in some disruption of the lacquer, indicating occasional pawl contact at low speeds. This, however, depended on the viscosity of the lubricant and the ambient temperature. 7.3.2.4.2 Transition from Overrunning to Lockup [28]

Complete engagement of pawls during lockup is also simply and routinely verified. Load cycles for production parts are generally run at torques that are equivalent to between 551 and 896 MPa apparent contact stress on the load-bearing ends of the pawl. Tests are run to destruction with inspection of the test parts at approximately 250-k, 500-k, and 750-k cycles. Inspection invariably reveals a polished appearance over virtually all of the contact surface of the pawl. This is a result of surface asperity yielding under these fairly high contact stresses. Also, the size of the contact patch indicates that the pawl finds its way into a fully engaged position during each load cycle.

Fig. 7.100  Compressive stress-strain curve for AISI 4340 [27]. In comparison with experimental data, the results of this analytical method of strength prediction appear reasonably accurate [30]. 7.3.2.4 Pawl Dynamics

In our examination of the overrunning-to-engaged transition, we assume that the pocket plate is stationary and that the notch plate is overrunning, but decelerating to a rotation direction reversal. At some point, a pawl-engaging notch edge will pass the pawl end. This is considered time zero for the analysis and for the following description of the transition. The transition from overrun to lockup can be described in three steps.

7.3.2.4.1 Overrunning Pawl Position [28]

Pawls in the axial-apply pawl OWC are positioned by cavities in the pocket plate and are driven by engaging notches in the notch plate, as illustrated in Figs. 7.95 through 7.97. The pawls in the clutch are shaped and positioned similarly to the articulated shoes in a Kingsbury-type thrust bearing. Semi-empirical relationships developed for Kingsbury bearings are used to calculate the separation of the pawl trailing edge from the notch plate during overrunning. The key relationship is given as

h=

ν⋅u ⋅l p



1. The first step begins at this time zero and ends when two conditions are satisfied: a. The notch plate decelerates to zero angular velocity, and b. The pawl moves from its overrunning position (separated a distance h from the notch plate) to a position at or past the outer surface of the notch plate. 2. The second step is reverse rotation (left to right in Fig. 7.96) until the locking edge of the notch encounters the tip of the pawl. 3. The third step begins at this pawl-to-notch contact and includes the pivoting of the pawl into full engagement under the influence of the applied torque that has caused the rotation reversal.

(7.137)

where h is the pawl trailing edge separation in millimeters (mm), ν is viscosity in Newton-seconds per meters squared (N-sec/m2), u is linear velocity in millimeters per second (mm/sec), l is the length of the pawl in millimeters (mm), and p is the average pawl pressure in Newtons per meters squared (N/m2). For a target threshold speed of 100 rpm, a trailing edge separation of 0.018 mm is calculated. During overrun, pawls are maintained in a stable, out-ofcontact position as described. Experimental confirmation of this behavior has proven to be quite straightforward. During sample preparation for routine overrun testing, the notch plate is sprayed with machinist’s bluing lacquer. Dry film thickness varies but is approximately 0.01 mm. With this clutch preparation, 24-hour continuous overrun tests at 3000

For purposes of the initial analysis described in this subsection, the following benchmark condition is considered. The notch plate passes the pawl end at a deceleration of 10,000 radians per second squared and at a speed of 100 rpm, which

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The simultaneous solution of Eqs. 7.138, 7.140, and 7.141 for this study yields a flow of 198 cc/sec. This, in turn, results in a time of 2.84 microseconds to move the pawl into the engagement position. This compares favorably with the 1.05-millisecond window previously computed for the benchmark condition. Similar times have been computed for pawls operating in fluids having 5 to 30 centipoise dynamic viscosity (which spans the viscosity range for most automotive applications). The times computed for the pawl movement vary non-linearly from 1 to 22 microseconds, as shown in Fig. 7.102. Therefore, for the benchmark, Step 1 is complete at a time equal to that required to achieve zero relative velocity between the notch and pocket plates.

gives us 1.05 milliseconds to decelerate to zero velocity. The operating fluid used to quantify the benchmark is ATF. 7.3.2.4.3 Spring-Induced Pawl Movement [28]

Based on observation of pawl motion, the governing mechanism for motion of the pawl under the influence of the spring is movement of the ATF from the top of the pawl to the bottom of the pawl, as the pawl rotates into the engagement position. The primary paths for this fluid flow are the two “D”-shaped flow section areas, which are illustrated in Fig. 7.101. In general, these flow sections will be different for each pawl pocket design.

Fig. 7.101  Flow section for ATF [28]. Movement of the fluid is estimated using a modified form of the Darcy equation for viscous flow L ρ⋅v 2 ΔP = f ⋅ ⋅ Dh 2



Fig. 7.102  Time to engagement versus viscosity [28].

(7.138)

Step 2 is simply the time required for the notch plate to travel back to the threshold position described at time zero and is not further considered in this analysis.

where ΔP is the pressure across the region of interest, f is the friction factor, L is the path length, ρ is the mass density of the fluid, v is the velocity of the fluid, and Dh is the hydraulic diameter for a non-circular flow cross section, which is given as

Dh =

4⋅A C

7.3.2.4.4 Movement from Initial to Full Engagement [28]

Step 3 is defined as the remainder of the movement of the pawl, which is a 2.39 mm-long slide into the bottom of the notch. The seating force is a function of the applied torque and is given as

(7.139)



where A is the cross-sectional area of flow and C is the wetted perimeter. The variable f is computed as 64 f= Re



Re =

ρ⋅v ⋅Dh v ⋅Dh Q ⋅Dh = = µ νk A⋅ν k

(7.142)

where φseat is the initial pawl seating angle, Fseat is the pawl seating force, and Fc is as given in Eq. 7.118.

(7.140)

The clutch used in this analysis is rated for 678 N-m, and the initial engagement angle for a standard pawl is given as 11.98 degrees. This provides a worst-case pawl seating force of 5542 N at the given 678 N-m torque. Figure 7.103 shows the pawl position at worst-case initial engagement and identifies the seating force vector.

where Re is the Reynolds number and is given according to

Fseat = Fc . tan φseat

(7.141)

where Q is the flow rate and νk is the kinematic viscosity, which is given in stokes.

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was assumed, and viscosity values for ATF at 120°F were used. The results are shown in Fig. 7.105. These results indicate a substantially more exponential shape to the torque curve than measured results have yielded [31]. This is believed to be largely the result of viscosity differences caused by underestimated internal fluid temperatures.

Fig. 7.103  Pawl position—worst-case initial engagement [28]. A worst-case static friction force is estimated as 4003 N based on a coefficient of 0.15. This leaves a net pawl seating force of 1539 N. Computing the time required to fully seat the pawl yields a value of 0.24 microseconds. 7.3.2.5 Drag Torque [31] The drag torque on an axial-apply pawl OWC during overrunning conditions has been estimated using a semi-empirical relationship [32]. In this analysis method, Reynolds number, over the speed range of interest, is determined according to

Rn =

r 2 ⋅ω ν

Fig. 7.104  Torque converter reactor pawl OWC [31].

(7.143)

where Rn is the Reynolds number, r is the radius of the disklike portion of the clutch, ω is the angular velocity of the clutch, and ν is the kinematic viscosity of the fluid. A dimensionless moment coefficient Cm is determined for three ranges of Reynolds number. For laminar flow, with Reynolds number less than 1 × 104, Cm is given as

Cm =

2⋅π ⋅R n s⋅r

(7.144)

where s is the average disk-to-housing gap. For transitional flow, with Reynolds numbers between 1 × 104 and 3 × 105, the expression for Cm is

2 C m = 2.67⋅R −1 n

Fig. 7.105  Predicted drag torque for reactor clutch [31].

(7.145)

7.3.3 Radial-Apply, Pawl One-Way Clutches

and for turbulent flow, with Reynolds numbers greater than 3 × 105, we have 5 C m = 0.0622⋅R −1 (7.146) n

7.3.3.1 Clutch Operation The radial-apply pawl OWC is a high-resolution ratchet-type device. A partially exploded view of the clutch is shown in Fig. 7.106. The clutch consists of an inner race, an outer race, a multitude of spring-energized pawls (springs are not shown), and two end plates. The resolution of the clutch (i.e., the number of engagement opportunities in one revolution) is a function of the number of pawls and the number of notch recesses in the inner race. Resolution of the clutch is important, in that it identifies the potential backlash that the system will see each time the clutch engages—the greater the backlash, the greater the impact loads.

Finally, the computed moment coefficients are reduced to estimated torque by applying the following definition: 2⋅M (7.147) 1 ⋅ρ⋅ω 2 ⋅R 5n 2 where ρ is the density of the lubricant, and M is the moment on the disk.

Cm =

This analysis methodology was applied to the clutch shown in Fig. 7.104. For this analysis, a nominal gap between the plates

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parity, the energizing springs force the pawls down into the notch recesses of the inner race. At the moment of speed parity, one pawl will be positioned in an inner race notch recess and be positioned to take the engaging load. When the reversal of relative rotation is effected, that pawl will slide into the notch and begin transmitting a load from one race to the other. These two modes of operation for the clutch are illustrated in Fig. 7.107.

The outer race has recesses (or pockets) that accept the pawls, and energizing springs that force the pawls into an engagement ready position. During the overrunning mode of operation, the pawl is forced up into this recess by the inner race, working against the load of the spring. When the function of the transmission dictates a change in the relative rotation between the inner and outer races, the clutch enters its engaged mode of operation. As the races approach speed

Fig. 7.106  Radial-apply pawl OWC assembly.

Fig. 7.107  Function of the pawl. 7-56

One-Way Clutches

7.3.3.2 Pawl Equilibrium

where φ is the angle at which the pawl operates when in its fully seated position. Because the pawl is in equilibrium when under the influence of two forces, the forces must be equal in magnitude (FOR = FIR), opposite in direction, and co-linear in application.

The radial-apply pawl clutch is designed so that one pawl supports the entire load of engagement. This is possible because the short, stout pawl supports load in compression. When operating in the engaged mode, the pawl makes an angle with respect to a line tangent to the outer surface of the inner race. This engagement angle is depicted in Fig. 7.108. Note that the spring force acting on the pawl is neglected in the following analysis. This is because of its diminutive magnitude as compared to the engaging forces.

Finally, the “unproductive” portion of the strut force is given as

7.3.3.3 System Stresses Loading in the radial-apply pawl OWC is very non-linear in nature. One pawl engages and generates a load between itself and each race. The races deform and move radially, and the pawl rotates to “make-up” the difference. The radial component of the pawl load drives the races eccentric to the extent that their tolerances allow. Approximately 180 degrees away from the engaging pawl, the two races come into contact and give support to this radial load. This two-point loading/ constraint on the races induces significant bending in the outer race. The deformation due to this bending can lead to contact between the races at approximately +90 degrees with respect to the loaded pawl.

Figure 7.109 shows a free body diagram of the engaged pawl. The tangential component Ft of the strut force FIR acting on the pawl is the “productive” component. That is, Ft is responsible for the transmittal of the torque from race to race. This force is given as Ft =

T ravg

(7.148)

All of these non-linear aspects of the system loading make a close-form solution impossible. To adequately analyze the pawl OWC, one must rely on numerical methods such as the finite element analysis (FEA) method. In doing so, a complete outer race-pawl–inner race model must be used, with contact elements prudently used to properly define the contact between the three bodies.

Fig. 7.109  The pawl free body diagram. where T is the transmitted torque, and ravg is the radius to the midpoint of the loading face at the inner race notch, as illustrated in Fig. 7.108. The strut force FIR between the pawl and the inner race is then given as

FIR =

Ft cosφ

(7.150)

where Fr is the “unproductive” radial component of the strut force. This radial force is supported by the inner and outer races and is inherently self-contained within the system. Note that the majority of the strut force works in transmitting the torque load from the inner race to the outer, making it a structurally efficient system.

Fig. 7.108  The engaged pawl.



Fr = Ft . tan φ

The results of one such analysis are shown in Figs. 7.110 and 7.111. In Fig. 7.110, the deformed shape of the outer race is shown. In Fig. 7.111, the stress contours within the race are illustrated. In each of these Figures, the effects of the pawlto-race and race-to-race contact can be observed.

(7.149)

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During the freewheel mode of operation of an OWC, the pawls rotate with the outer race. In Fig. 7.112, we show a typical pawl with inertia and reaction loads acting upon it. Assuming that the race and pawl are spinning, the centrifugal force Fcen acting on the pawl is defined as

Fcen = m( p)rcg( p)ω (2o)

(7.151)

Fig. 7.112  Defining a centrifugally disengaging pawl. where m(p) is the mass of the pawl, rcg(p) is the radial distance from the center of rotation to the center of mass of the pawl, and ω(o) is the angular velocity of the outer race, which is defined in radians per second. As shown, the center of mass Cg is offset to the right from the pawl pivot point Cp. Because of this offset, the centrifugal force Fcen induces a moment on the pawl, tending to lift it from contact with the inner race (i.e., tending to disengage the pawl). This type of pawl is known as centrifugally disengaging. As can be seen, only the spring force Fsp is keeping the pawl “engagement-ready.” Note that a disengaging-type pawl will never disengage as long as it is carrying a small amount of torque.

Fig. 7.110  Finite element analysis (FEA) deformation results for the outer race.

If the pawl Cg is located to the left of the pivot point Cp, the centrifugal force Fcen tends to increase the pawl/inner race contact force Fn(i). This type of pawl is shown in Fig. 7.113 and is known as centrifugally engaging.

Fig. 7.111  Finite element analysis (FEA) stress contour results for the pawl-race system. Fig. 7.113  Defining a centrifugally engaging pawl.

7.3.3.4 Pawl Dynamics

Although the bulk of pawl OWC applications would dictate the use of either an engaging or disengaging pawl design, there is a third alternative. If the center of mass Cg is radially in-line with the pivot point Cp, the centrifugal force Fcen tends to neither engage nor disengage the pawl from the inner race. This type of pawl is known as centrifugally neutral. A pawl of

In the area of dynamics, the pawl shares one attribute with the sprag clutch. By prudently tailoring its geometry, one can achieve a pawl that has desirable inertial characteristics. That is, the center of mass of the pawl can be located radially off center of the pivot point, yielding a pawl that is either centrifugally engaging or disengaging.

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One-Way Clutches

this type is rarely used because of the difficulties of assuring the radial alignment of Cg and Cp.

5. Jones, A. B., “New Departure Engineering Data; Analysis of Stress and Deflections,” New Departure Division, General Motors Corporation, 1946. 6. Kerendian, H., “Development of Roller Clutch Design Computer Program; Design Analysis Information,” Hydra-Matic Division, General Motors Corporation, May 6, 1985. 7. Juvinall, R. C., Engineering Considerations of Stress, Strain, and Strength, McGraw-Hill, New York, 1967. 8. Timoshenko, S., Strength of Materials, Van Nostrand Reinhold, New York, 1958. 9. Sauzedde, R. E. and E. F. Bowie, “Design of Roller OneWay Clutches in Current Passenger Car Automatic Transmissions,” Design Practices: Passenger Car Automatic Transmissions, AE-5, Vol. 5, Society of Automotive Engineers, Warrendale, PA, 1973, p. 17. 10. Boresi, A. P., O. M. Sidebottom, F. B. Seely, and J. O. Smith, Advanced Mechanics of Materials, 3rd Edition, John Wiley and Sons, New York, 1978. 11. Ugural, A. C. and S. K. Fenster, Advanced Strength and Applied Elasticity, Elsevier, New York, 1982. 12. Haka, R. J. and R. P. Michnay, “Roller Skewing as a Factor in One-Way Clutch Operation,” SAE Paper No. 840576, Society of Automotive Engineers, Warrendale, PA, 1984. 13. Johnson, K. L., “Tangential Tractions and Micro Slip in Rolling Contact,” Rolling Contact Phenomena, edited by Bidwell, J. B., pp. 6–28. 14. Kremer, J. M., “Roller Float as a Consideration in OuterCam, Roller One-Way Clutch Design,” SAE Paper No. 950670, Society of Automotive Engineers, Warrendale, PA, 1995. 15. Jensen, P. W., Cam Design and Manufacture, 2nd Edition, Marcel Dekker, New York, 1987. 16. Paul, B., Kinematics and Dynamics of Planar Machinery, Prentice-Hall, Englewood Cliffs, NJ, 1979. 17. Kremer, J. M. and P. Altidis, “Roller One-Way Clutch System Resonance,” SAE Paper No. 981093, Society of Automotive Engineers, Warrendale, PA, 1998. 18. Costin, D. P., “Analysis, Fabrication, and Preliminary Testing of the Hammerhead Sprag,” Technical Report 9513-R, Transmission Systems Inc., BorgWarner, 1995. 19. Shabana, A. A., Theory of Vibration, Vol. II, SpringerVerlag, New York, 1991. 20. Kremer, J. M., “Design Manual: Roller One-Way Clutch with Outer Race Cam,” Technical Report 9418-2R, Transmission Systems Inc., BorgWarner, 1994. 21. Sandor, B. I., Strength of Materials, Prentice-Hall, NJ, 1978.

These three “inertia designs” of the pawl give the designer a degree of flexibility when designing the OWC for a specific application. For example, in the torque converter stator position where the clutch is not expected to engage at speed, the designer may select a disengaging pawl to reduced the engaging force between the pawl and the inner race and thereby reduce spin losses and wear. In a shift position, however, the designer may apply an engaging pawl, because the clutch will be expected to engage at speed. Note that each application is unique and must be closely examined to determine which pawl type is most appropriate.

7.3.4 Summary In this section, we have presented design considerations, design methodologies, and analysis techniques for the design of pawl one-way clutches. The information given herein has been effectively used in the design and development of pawl clutches. However, it is left to the reader to apply this information properly. In so doing, it is always prudent to review the underlying assumptions upon which these techniques are based. If the assumptions do not apply to the problem at hand, alternative methods should be sought. If the assumptions do pertain to the problem at hand, the application of the methods presented should be done with caution. That is, many of the analysis expressions presented are not linked to any one measuring system. This makes the equations more versatile but requires the engineer to pay close attention to the units of measure. It is strongly advised that one system of measure be adopted and then rigidly adhered to throughout.

7.4 References 1. Fanella, R. J., “One Way Clutches,” Design Practices: Passenger Car Automatic Transmissions, AE-18, Society of Automotive Engineers, Warrendale, PA, 1994, p. 437. 2. Merrel, R. L. and E. F. Bowie, “Roller One-Way Clutches for Today’s Passenger Car Automatic Transmissions,” Design Practices: Passenger Car Automatic Transmissions, AE-5, Vol. 5, Society of Automotive Engineers, Warrendale, PA, 1973, p. 27. 3. Chesney, D. R. and J. M. Kremer, “Generalized Equations for Roller One-Way Clutch Analysis and Design,” SAE Paper No. 970682, Society of Automotive Engineers, Warrendale, PA, 1997. 4. Young, C. W., Roark’s Formulas for Stress & Strain, 6th Edition, McGraw-Hill, New York, 1989.

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960722, Society of Automotive Engineers, Warrendale, PA, 1996. 28. Fitz, F., “Lock Up Times in Mechanical Diode Type One Way Clutches,” SAE Paper No. 951054, Society of Automotive Engineers, Warrendale, PA, 1995. 29. Engesser, F., “Ueber die Knickfestigkeit gerader Stäbe,” Zeitschrift für Architektur und Ingenieurwesen, Vol. 35, No. 4, 1889. 30. Fitz, F., “Ultimate Strength Determination of One-Way Clutches Under Impact Loading,” SAE Paper No. 960722, Society of Automotive Engineers, Warrendale, PA, 1995. 31. Fitz, F., J. Blum, and P. Pires, “Effect of Overrunning Speed and Plate Gap on Power Dissipation in MD Type One Way Clutches,” SAE Paper No. 940730, Society of Automotive Engineers, Warrendale, PA, 1994. 32. Schlichting, H., Boundary Layer Theory, 7th Edition, McGraw-Hill, New York, 1979.

22. Caracciolo, F., “Development of a Sprag Wear Test Procedure for Evaluating the Anti-Wear Performance of ATFs,” SAE Paper No. 902149, Society of Automotive Engineers, Warrendale, PA, 1990. 23. Chesney, D. R. and J. M. Kremer, “Generalized Equations for Sprag One-Way Clutch Analysis and Design,” SAE Paper No. 981092, Society of Automotive Engineers, Warrendale, PA, 1998. 24. Ferris, E. A., “Automotive Sprag Clutches—Current Design and Application,” Design Practices: Passenger Car Automatic Transmissions, AE-5, Vol. 5, Society of Automotive Engineers, Warrendale, PA, 1973, p. 6. 25. Costin, D., “Sprag One-Way Clutch Design Manual,” Technical Report 9511-1R, Transmission Systems Inc., BorgWarner, 1995. 26. Harris, T. A., Rolling Bearing Analysis, 3rd Edition, John Wiley & Sons, New York, 1991. 27. Fitz, F., and C. T. Gadd, “Ultimate Strength of Mechanical Diode Type One-Way Clutches,” SAE Paper No.

7-60

Chapter 8

Automatic Transmission Controls Table of Contents—Automatic Transmission Controls 8.1 Introduction: This table of contents covers the entire controls chapter. Most sections will have their own, more detailed table of contents. 8.2 Basic Shift Processes: The “How” of Shifting—This section describes what must occur in upshifts and downshifts, both power-on and power-off. The equations that govern the output and response are presented; data for the different shifts are analyzed and presented. Some of the tools used for shift quality will also be discussed. 8.3 Shift Torque Analysis and the Continuously Variable Transmission: The SAE Paper, 2004-01-1634: Ratio Changing the Continuously Variable Transmission, applies the approach presented in Section 8.2 for stepped-ratio transmissions to the CVT and is included in this section. 8.4 Scheduling, Grades, Driver Preferences, and Driveability: The “When” of Shifting—The challenge of attempting to provide the correct gear for all situations is addressed. Several innovative approaches from recent papers are offered to indicate what is possible and to stimulate thought. 8.5 Transmission Control and Types of Controls: The development trends, the three kinds of solenoids

8.6

8.7

8.8

8.9

used, and the different types of controls are described for today’s automatic transmission. The capabilities and requirements for the different options are also reviewed. Transmission Operational Features: The features made possible with the use of electronic controls are categorized, and individual features are described as to their capabilities and requirements. Automatically Shifted Manuals: This relatively new type of transmission is discussed, including its requirements, advantages, limitations, and capabilities. The difference provided by the two-clutch approach is reviewed and some of the actuators are discussed. Control Components: The valve body and hydraulics are still crucial to transmission control, especially for pressure control, and their design and manufacture are covered here. Also described are the various sensors used in transmission control, including their analysis, capabilities, and development. The solenoids were covered in 8.5 to support the types-ofcontrols description. Development Technology: Vehicle development and calibration systems are described; and the use of the simulation tools, HIL (hardware-in-the-loop), MIL (model-in-the-loop), and RPC (rapid prototyping controller) are reviewed.

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8.1 Introduction

effects which every transmission engineer needs to know. An excerpt from that paper follows:

The focus of this chapter is on electronic controls because any new transmission developments will be based on this technology. Hydraulic control technology, which is considerable, is covered, but it is treated as a supporting component to the electronic controls. As powertrain technology develops, the functions, sensors, and actuators will change, but the use of electronics will only expand. The truly amazing capability that the electronic logic provides to vehicle control will continue to grow as engineers focus on the challenges ahead.

8.2.1

Nature of the Disturbance Resulting from a Ratio Change

To permit the engineer to best exercise his ingenuity, an understanding of the fundamental relationships in ratio changing is important. Perception of the shift involves two of the five senses: touch and hearing. (Any shift that is seen, smelled, or tasted is a lousy shift.) As with most things, the rate of change is more perceptible than the magnitude of the change. The change in acceleration during a power up or down shift is felt and is significant. In some cases, this is accompanied by a chirp or squawk of the friction elements. The power-off shifts are characterized by the audible “clunk” of the driveline.

The material in this chapter has been developed to give the engineering community the basics of transmission control and the current status of the state-of-the-art in automatic transmission controls. When appropriate, full papers or portions of papers are presented. When material could not be found, the committee developed the information presented here. Much of the material in this chapter has not been previously published. The following lists each of the persons who have contributed to the development of the chapter and their applicable professional responsibility: Dr. Gang Chen, Chrysler Senior Transmission Controls Specialist Ron Cowan, Ford Motor Company, Transmission Control Strategy, Retired Dr. Hussein Dourra, Chrysler Advance Transmission System Engineering, Senior Specialist

Fig. 8.2.1  Oscillograph traces of commercial disturbances.

Joseph Gierut, Honeywell, Marketing Director

In Fig. 8.2.1 are oscillograph traces of “commercial” disturbances. The traces are the record of the horizontal disturbance to an accelerometer attached to the vehicle floor. Both shifts involve a reaction band and a direct clutch, and might be called “average acceptable.” The time interval is of particular interest and represents the order of all friction clutch shifts. The fluid coupling, however, has the energy capacity to stretch the upshift transition to as much as three seconds and the downshift to something in the order of a half a second. These traces are shown for orientation purposes and are not to be any standard of acceptability. Instrumentation is useful in the understanding of the phenomenon but is not a substitute for the subjective evaluation of the shift in the vehicle.

Dr. John Kremer, BorgWarner Transmission Systems, Analysis Support Maurice Leising, Chrysler Transmission Control, Retired Charles Marshall, Ford Motor Company, Transmission Electronic Systems and Hardware, Retired John Titlow, Conxall Corp. and Honeywell Corp. (Retired)

8.2 Basic Shift Processes— The “How” of Shifting

Acceptability remains undefined and varies significantly between engineers and organizations. Little is really known about what the customer is willing to spend for minimum disturbance.

This subject received excellent treatment in a 1960 paper, SAE 311A—“Ratio Changing the Passenger Car Automatic Transmission,” by F. Winchell and W. Route. Although obviously dated somewhat in perspective, it highlights many basic

Among other things, acceptability depends on the:

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Expectation—The disturbance accompanying an expected shift is more acceptable than that occurring from an unexpected shift. For example, the disturbance consequent to the deliberate movement of the shift lever or downshift detent has a higher degree of acceptability than the disturbance arising from the automatic upshift scheduled by the transmission engineer. Sense—The disturbance must be positive and not negative; that is, increased not decreased acceleration when the driver expects acceleration and vice versa. For example, the driver depresses the throttle detent to downshift and experiences a momentary loss of power; or with the throttle adjusted for the desired acceleration, there is a momentary reduction in acceleration during the upshift. Environment—An acceptable disturbance for a wide open throttle upshift in the presence of a high level of engine and wind noise, combined with the driver’s attention to his speed, would be much greater than that deemed acceptable for the relatively peaceful environment of a light throttle upshift, or coast downshift.

8.2.2

= number of active faces = polar moment of inertia of input member = polar moment of inertia of reaction member = equivalent polar moment of inertia of vehicle on output member E = energy to clutch during ratio change n Ie Ir Iv

The purpose of the following mathematical analysis is to establish the general relationship existing between the output torque and the input and reaction torques during a transient. For this analysis, the arrangement of the gear trains and friction elements is an arbitrary one, because the characteristic torque disturbances and energy transfer associated with a ratio change are common to all arrangements. Therefore, the simple arrangement shown in Fig. 8.2.2 will be used. It consists of a planetary gear set, with the sun as the input, the carrier as the output, and the ring as the reaction element. The corresponding torques are identified by Qi, Qo, and Qr, respectively. The reaction element is held to ground through an overrunning clutch; the synchronizing element is a friction clutch between the input and reaction. When the clutch is open, the gear train is in low and the output torque, Qo, is equal to the sum of the input torque, Qi, and the reaction torque, Qr.

Mechanics of Ratio Changing

In the remaining paragraphs, the mechanics of ratio changing will be developed for a typical gear train. [Authors’ note: To improve clarity and for ease of reference, the definition of terms and the tables of equations (from the appendix of the original paper) are shown next.]

Sufficient application of the clutch will produce a direct drive; that is, Qr will be zero and Qi will equal Qo.

8.2.2.1  Definitions, Symbols, and Equations Listed below are the definitions of the symbols used in this paper. R = gear ratio, ratio of output torque to input torque Qo = output torque Qr = reaction torque Qe = input torque Qim = torque on input gear Qrm = torque on reaction gear Qb = torque on friction reaction element Qc = torque on clutch Ne = input speed No = output member speed Nr = reaction member speed Fa = apply force μ = friction coefficient rm = mean radius of clutch

Fig. 8.2.2  Simple planetary for analysis.

Fig. 8.2.3  Simple planetary with inertial components added.

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Table 8.2.1  Summary of Torque Equations—Overrunning Clutch Reaction Downshifted

Torque Phase A-B

Inertia Phase B-D

Upshifted

Symbol

Qe

Qe – Qc

⎡I ⎤ Q e + Q c ⎢ e (R − 1) − 1⎥ ⎣ Ir ⎦ Ie 2 (R − 1) + 1 Ir

Qe R

= Qim

⎛ R – 1⎞ Qe ⎜ ⎝ R ⎟⎠

= Qrm

Qe

= Qo

0

= Qr

⎛ R − 1⎞ ⎜⎝ ⎟ Qe R ⎠

= Qc

Qe R

= lim Q eIr ⇒ 0

⎛ R – 1⎞ Qc ⎜ ⎝ R ⎟⎠

= lim QrmIr ⇒ 0

Qe

= lim Q oIr ⇒ 0

Eq. (8.2.1)

Eq. (8.2.6) Qe(R – 1)

(R – 1)(Qe – Qc) Eq. (8.2.2)

⎧ ⎡I ⎤⎫ (R − 1) ⎨Q e + Q c ⎢ e (R − 1) − 1⎥⎬ ⎣ Ir ⎦⎭ ⎩ Ie 2 (R − 1) + 1 Ir Eq. (8.2.7)

QeR

R(Qe – Qc) Eq. (8.2.3)

⎧ ⎡I ⎤⎫ R ⎨Q e + Q c ⎢ e (R − 1) − 1⎥⎬ I ⎣ r ⎦⎭ ⎩ Ie 2 (R − 1) + 1 Ir Eq. (8.2.8)

Qe(R – 1)

(R – 1)(Qe – Qc)

0

Eq. (8.2.4) 0

≤

R –1 Q e and nFarmµ R

Eq. (8.2.5)

≥

R −1 Q e and nFarmµ R

Eq. (8.2.5)

When Ir is small compared to Ie, Eqs. 8.2.6, 8.2.7, and 8.2.8 can be simplified as follows: Qe

Qe – Qc Eq. (8.2.1)

Qc R −1 Eq. (8.2.9)

Qe(R – 1)

QeR

(R – 1)(Qe – Qc)

Qc

Eq. (8.2.2)

Eq. (8.2.10)

R(Qe – Qc)

⎛ R ⎞ Qc ⎜ ⎝ R − 1⎟⎠

Eq. (8.2.3)

Eq. (8.2.11)

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Table 8.2.2  Summary of Torque Equations—Friction Element Reaction Downshifted

Torque Phase A-B

Inertia Phase B-D

Upshifted

Symbol

Qe

Qe – Qc

⎡I ⎤ Q e + Q c ⎢ e (R − 1) − 1⎥ ± Q b (R − 1) ⎣ Ir ⎦ Ie 2 (R − 1) + 1 Ir

Qe R

= Qim

⎛ R – 1⎞ Qe ⎜ ⎝ R ⎟⎠

= Qrm

Qe

= Qo

0

= Qr

⎛ R − 1⎞ ⎜⎝ ⎟ Qe R ⎠

= Qc

Qe R

= lim Q eIr ⇒ 0

⎛ R – 1⎞ Qc ⎜ ⎝ R ⎟⎠

= lim QrmIr ⇒ 0

Qe

= lim Q oIr ⇒ 0

Eq. (8.2.1)

Eq. (8.2.6a) Qe(R – 1)

(R – 1)(Qe – Qc) Eq. (8.2.2)

⎧ ⎫ ⎡I ⎤ (R − 1) ⎨Q e + Q c ⎢ e (R − 1) − 1⎥ ± Q b (R − 1)⎬ ⎣ Ir ⎦ ⎩ ⎭ Ie 2 (R − 1) + 1 Ir Eq. (8.2.7a)

QeR

R(Qe – Qc) Eq. (8.2.3)

⎛ ⎞ ⎡I ⎤ R ⎜ Q e + Q c ⎢ e (R − 1) − 1⎥ ± Q b (R − 1)⎟ I ⎝ ⎠ ⎣ r ⎦ Ie 2 (R − 1) + 1 Ir Eq. (8.2.8a)

Qe(R – 1)

(R – 1)(Qe – Qc)

nFarmμ

Eq. (8.2.4) 0

≤

R –1 Q e and nFarmµ R

Eq. (8.2.5)

>

R −1 Q e and nFarmµ R

Eq. (8.2.5)

When Ir is small compared to Ie, Eqs. 8.2.6, 8.2.7, and 8.2.8 can be simplified as follows: Qe

Qe – Qc Eq. (8.2.1)

Qc ± Q b R –1 Eq. (8.2.9a)

Qe(R – 1)

(R – 1))(Qe – Qc) Eq. (8.2.2)

QeR

R(Qe – Qc) Eq. (8.2.3)

Qc ± Q b Eq. (8.2.10a)

(Q c ± Q b )

R R −1

Eq. (8.2.11a)

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Design Practices: Passenger Car Automatic Transmissions

phase in Fig. 8.2.4), torque changes occur on the elements without a speed change; thus, inertia torques do not exist. In the second part of the transient, which will be called the inertia phase (the B-D phase in Fig. 8.2.4), the input and reaction elements are being accelerated to their new speeds; inertia torques, therefore, do exist and must be considered.

Figure 8.2.3 is the same planetary arrangement shown in Fig. 8.2.2 with the addition of the polar moment of inertia of the engine; i.e., the driveline and vehicle equivalent polar moment of inertia, Iv, and the reaction element polar moment of inertia, Ir. To make a completely generalized schematic, a torque, Qv, representing a grade component of the vehicle weight or a towing load is shown, which, added to the vehicle inertia torque, makes up the output torque, Qo. Also shown is the engine torque, Qe. For clarity, the external torques are drawn as solid-line couples, while those which are internal are drawn as broken-line couples. For this analysis, the vehicle speed during the ratio change will be considered constant. With this assumption, the product of Iv and av will be zero, and Qo will equal Qv.

8.2.3

General Equation for Output Torque

For the planetary arrangement shown in Fig. 8.2.3, the output torque can be expressed as:



⎛ ⎡I ⎤⎞ R ⎜ Q e + Q c ⎢ e (R − 1) − 1⎥⎟ ⎝ ⎣ Ir ⎦⎠ Qo = Ie (R − 1)2 + 1 Ir

(8.2.8)

This equation (see footnote) defines the output torque before and after the transient, as well as during the ratio change. [Author’s Note: See full SAE 311 for derivation, or see Section 8.2.5.1.4 for equations developed from the lever analogy.] Before the ratio change, when the gear set is downshifted, Qc = 0 Also, factors in Eq. 8.2.8 containing the ratio Ie/Ir can be neglected because no acceleration of the input or reaction elements is occurring relative to the output. Therefore, when downshifted, Eq. 8.2.8 becomes the familiar:

Qo = R Qe

and after the ratio change, when the gear set is upshifted: Qc = Qe (R –1) R Here also, factors containing Ie/Ir can be neglected because no relative accelerations are occurring between the elements of the gear set, and Eq. 8.2.8 reduces to

Qo = Qe

Before applying Eq. 8.2.8 to the transient, it should be recognized that the shift transient consists of two parts. In the first part, which will be referred to as the torque phase (the A-B

Fig. 8.2.4  Characteristics of speed, torque, and pressure during a power-on upshift. 8-6

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8.2.4.1  Power-On Upshift

During the torque phase, when no relative accelerations occur between the input and reaction elements, Eq. 8.2.8 becomes: Qo = R(Qe – Qc)



In Fig. 8.2.4 are plotted the speeds and torques on the elements of Fig. 8.2.3, during a power-on upshift. The significant torques plotted in Fig. 8.2.4 are the output torque, Qo, the engine torque, Qe, (which is shown increasing during the transient so that the output torque, before and after the upshift, is equal), the reaction torque, Qr, and the clutch torque, Qc.

(8.2.3)

During the inertia phase, when accelerations relative to the output do occur, Eq. 8.2.8 describes the event. However, because Ir is generally small compared to Ie, an important simplification can be observed by considering the limit as Ir approaches zero. Equation 8.2.3 becomes: Qo = Qc



R (R -1)

It will be noted that the clutch torque begins to rise at A after the clutch pressure has overcome the return spring and stroked the clutch pack clearance. The increasing clutch torque causes the reaction torque to decrease. Since the output torque is the sum of the input and reaction torques, it also decreases. When the reaction torque has reached zero at B, the output torque is equal to the input torque.

(8.2.11)

Thus, a very important relationship is established: during the speed change, the output toque is dependent only upon the magnitude of the clutch torque.

The speed change cannot begin until Point B is reached because the reaction torque must first reach zero on the reaction element before it can begin to rotate in the same direction as the input and output members. If the reaction member is a friction element, its torque capacity should now be zero or the output torque will be reduced further. (See Eq. 8.2.8a, Table 8.2.2.)

The use of a friction element instead of an overrunning clutch complicates the output torque equation slightly. During the speed change, the overrunning clutch, with its admirable torque-direction-sensing properties, exerts no torque on the reaction element. But a friction element can exert a torque on the reaction member during the speed change if an apply force is acting on the element; in that case, Eq. 8.2.8 takes on another factor, or:

⎛ ⎡I ⎤⎞ R ⎜ Q e + Q c ⎢ e (R − 1) − 1⎥⎟ ⎝ ⎣ Ir ⎦⎠ Qo = Ie (R − 1)2 + 1 Ir



From B to C, the output torque can be seen rising with the increasing clutch torque (C indicates the point where maximum clutch pressure is reached). The output torque continues to remain at a value dependent only on clutch torque, until the synchronized speed is reached at D. When the speed change is accomplished at D, the output torque drops to the level of the input torque, Qe.

(8.2.8a)

where Qb is the torque on the reaction friction element.

The passengers, during this transient, will be conscious of the variation in output torque. First, they will sense the decreasing acceleration in the torque phase from A to B. This sensation is disagreeable because it is negative in sense and followed by an abrupt change to an increasing acceleration from B to C. If the clutch torque is not carefully limited, the change in output torque at D, when the speed change is accomplished, will also be sensed by the passengers as a decreasing acceleration. Thus the passengers, in something close to one second, have been rocked forward in their seats, rocked back in their seats, and again rolled forward. This is a kind of rock and roll that no one likes, and a great deal of attention has been given to reducing the conspicuousness of this disturbance. Some fundamental approaches to the problem of reducing the awareness of the output torque disturbance will be discussed briefly.

In Table 8.2.2, the expressions for the torques on the several elements of the gear train are summarized for the case where a friction element reaction is used.

8.2.4

Application of the Output Torque Equation

The equations listed in Tables 8.2.1 and 8.2.2 will now be used to construct or explain the output torque disturbance accompanying the following ratio changes: • • • •

Power-On Upshifts Power-On Downshifts Power-Off Upshifts Power-Off Downshifts

First, however, it should be understood that the decreasing torque from A to B is an inherent characteristic of the upshift, and is inescapable. This is the case even when the upshift is made at the speed where the tractive effort curves intersect, as

Some discussion will also be devoted to possible ways of minimizing the disturbance during each ratio change. 8-7

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8.2.4.1.1 Inertia Balance

for example at A in Fig. 8.2.5. Here, the output torque before the shift will equal the output torque after the shift; thus,

A precise inertia value can be assigned to the reaction member. Thus, if Ir = Ie (R-1), it can be seen from Eq. 8.2.8 that the output torque becomes independent of clutch torque capacity, and dependent upon engine torque. See Fig. 8.2.6a.

RQe (low) = Qe (high) = Qo = constant

It will be noted that the above relationship prevails in Fig. 8.2.4; at point A, during a power on upshift, output torque before and after shift will be equal.

8.2.4.1.2 Controlled Clutch Capacity In this approach, the clutch is applied rapidly at A and limited in capacity after C to the value equal to Qe (R – 1) (here Qe is the input torque before the shift). The object with this method is to first accomplish the disturbance from A to C at a rate greater than the response rate of the third member components so that a proportionate change in vehicle acceleration is not produced. The limited torque capacity after C produces an output torque during the speed change equal to the output torque before and after the shift. See Fig. 8.2.6b.

Fig. 8.2.5  Tractive effort curves. Referring to Fig. 8.2.4, before a speed change can begin, at point B, the output torque must decrease the entire ratio step. If the reaction to ground is other than an overrunning clutch, the output will drop an additional amount due to the overlapping torque capacity which must be designed into the reaction friction member. From B to D, the problem is one of providing sufficient clutch torque to accomplish the speed change of the engine. This necessitates an increase beyond the value required to balance the engine torque at B.

8.2.4.1.3 Limited Clutch Capacity With this method, the clutch capacity is slowly built up from A; its magnitude is limited so that it is just slightly greater than Qe (R – 1)/R. The transient from A to D then becomes relatively extended. See Fig. 8.2.6c. The approaches just discussed for minimizing the output torque disturbance present some problems. The inertia balance approach is not very attractive when it is realized that the reaction inertia must be nearly as large as the engine inertia. The controlled and limited clutch capacity approaches can have the common difficulty of exceeding the energy capacity of the clutch. This can best be explained by plotting the relationship between “heat energy to the clutch” and “clutch torque capacity,” as shown in Fig. 8.2.7.

Three fundamental approaches for reducing the awareness of the rising output torque during the B-D phase are apparent. These are as follows:

Fig. 8.2.6a  Inertia balance.

Fig. 8.2.6b  Controlled clutch capacity.

Fig. 8.2.7  Relationship between heat energy to clutch and clutch torque capacity. The energy is infinite when the clutch torque can just hold the engine, or when

Fig. 8.2.6c  Limited clutch capacity.

Qc = Qe (R –1) R

(8.2.5)

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and approaches a minimum limiting value as Qc approaches an infinite value; the useful range is somewhere between the arbitrary lines A and B drawn on the figure. The more heat capacity built into the clutch, the closer can line A be moved toward the least clutch torque value and the less aware is the passenger of the shift.

and will reach its ultimate value, R Qe, when Qc finally becomes zero.

The instantaneous horsepower to the clutch, which is a direct function of clutch torque, also has an effect on clutch durability and must be considered. While large values of clutch torque will reduce the energy to the clutch, the instantaneous temperature at the faces of the clutch plates must also be kept within an acceptable range. Thus, in the controlled or limited clutch torque approaches, the clutch torque must be between some rather close limits to ensure acceptable shift feel on the one hand and durability on the other. These limits are widened by increasing the heat capacity of the clutch. 8.2.4.2  Power-On Downshift In Fig. 8.2.8 are plotted the speeds and torques for the simple planetary arrangement, shown in Fig. 8.2.3, during a poweron downshift or kickdown. The same general equations used to define the torque during the power-on upshift are applicable to the downshift. Referring to Fig. 8.2.8, it will be noted that the clutch pressure begins to decrease with the triggering of the shift valve at A, but no speed change occurs until the static capacity of the clutch has diminished to the precise value, (R –1) Qc = Qe (8.2.5) R at D, whereupon the clutch begins to slide and its capacity is diminished abruptly to its dynamic value. The general equations for the output, reaction, and input member torques are as follows:

Qim =

Qc (R -1)

Qrm = Qc

Fig. 8.2.8  Characteristics of speed, torque, and pressure during a power-on downshift.

(8.2.9) (8.2.10)

The torque disturbance resulting from the power-on downshift is less offensive to the operator because it is a voluntary disturbance; that is, one which is accomplished by overriding the automatic controls. However, the decreasing output torque from D to B is directionally wrong because the operator is calling for increasing performance. Therefore, the D-B interval even with an overrunning clutch deserves some attention in calibration. Again, several fundamental approaches are apparent. These are:

R Qo = Qc (R -1)

(8.2.11) It is evident that all of these torques now approach zero as the clutch torque decreases during the speed change from D to B. If the clutch torque reaches zero before the speed change is accomplished, as in Fig. 8.2.8, the output torque goes to zero (or slightly negative because of drag torque). At B, when the overrunning clutch locks up, the output torque rises at a rate dictated by the elastic stiffness of the system. If the clutch torque prevails beyond the completion of the speed change, the output torque will be:

Qo = (Qe – Qc)R

8.2.4.2.1 Inertia Balance Like the upshift, if the reaction member inertia is designed so that Ir = Ie (R – 1), the output torque from D to B will be inde-

(8.2.3) 8-9

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pendent of the clutch torque and equal to the engine torque. See Fig. 8.2.9a. Objections to the inertia balance scheme have already been discussed. 8.2.4.2.2 Fast Clutch Exhaust With this scheme, if the clutch torque can be dropped to zero very rapidly, full engine torque will become available to accelerate the engine during the neutral interval. See Fig. 8.2.9b. If the interval D-B is short, due to a fast clutch exhaust and small engine inertia, the disturbance to vehicle acceleration will be small and the sense of decreasing output torque minimized. In estimating the neutral interval in Fig. 8.2.9c, it should be recalled that our modern V-8 engines have a neutral WOT acceleration of about 4500 rpm per second, and the in-line sixes accelerate at about 4000 rpm per second. At forty mph, with a 1.82 ratio, the neutral interval will be approximately 0.3 seconds. [Author’s Note: Neutral WOT accelerations of today’s engines vary from 4000 to 8000 rpm/second. Engine torque and inertia determine the potential rate; calibration determines the rate achieved.] The fast clutch exhaust approach presents some timing problems when an overrunning clutch reaction member is not used. Because the neutral interval, which is correct for a low speed downshift, is not a long enough interval for engine acceleration during a high speed downshift, the reaction member is applied “early” at high speeds unless timing valves are used. Figure 8.2.10 shows an idealized downshift using a friction element reaction which is “early,” that is, the element is applied before the synchronizing speed is reached. A is the point where the element should be applied, but its application at X has lowered the output torque to a negative value. During the speed change, the output torque is



Qo = (Qc – Qb)

R (R -1)

Fig. 8.2.9  (a) Inertia balance.

Fig. 8.2.10  Torque and pressure during an idealized poweron downshift with “early” friction element reaction. The term Qb, the friction element torque on the reaction member, is negative in sense (and in the de-energize direction if this element is a band). Here, an advantage of the multiple wrap band can be seen. Its de-energize torque is smaller than for a single wrap, causing the output torque to go less negative.

(8.2.11a)

(b) Fast clutch exhaust.

8.2.9 (c) Accumulator clutch exhaust.

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On the other hand, if the reaction member is late in its application, the resulting disturbance is even more objectionable because it results in engine “flare” followed by a transient output torque limited only by the torque capacity of the reaction member. See Fig. 8.2.11.

[Author’s Note: This is the end of the excerpt from SAE 311A—“Ratio Changing the Passenger Car Automatic Transmission” by F. Winchell and W. Route.]

8.2.5

A Modern Perspective on Upshift Ratio Changing

The authors will now address, in detail and with reference to current control techniques, how each portion of an upshift and a kickdown acts to affect the transmission’s output torque. The transmission’s output torque profile is the control engineer’s contribution to shift quality. The goal is to explain what parameters shape the transmission output torque so that the engineer knows which tools can be used to achieve a desired result. It should be noted that other important contributors to shift quality are the driveline, the powertrain mounting system, and the vehicle’s response to the various driveline inputs, including sound. The same engine/transmission system can give very different results in different vehicles; the transmission engineer needs some consideration and help from colleagues who are developing the other systems. The first requirement with any transmission arrangement is ensuring that the speeds of the critical elements can be measured or calculated. Many clutch and gear train arrangements make it difficult to access the input shaft with a speed wheel. Input speed can typically be determined by measuring the speed of reaction elements, but that may require knowing the direction of rotation. Determining rotational direction quickly can add significant complication. Resolution and accuracy must also be considered; sometimes a process, such as welding on the speed wheel, may introduce distortions that can make the signal unusable. The lever analogy will be used to develop some expressions to show how this tool is used effectively. For a full description of the lever analogy, please refer to Section 3.5 or SAE 810102. Once the lever is set up, all expressions are derived from two operations, a torque balance of the lever (i.e., all right/left horizontal forces must balance) and a moment balance of the lever (i.e., the moments about any point on the lever must balance).

Fig. 8.2.11  Torque and pressure during an idealized poweron downshift with “late” friction element reaction. 8.2.4.2.3 Accumulator Clutch Exhaust If the clutch exhaust has an accumulator effect built in so that the clutch torque is maintained at a value just slightly below Qc = Qe (R – 1)/R, then the output torque will remain close to Qe until the reaction member has stopped. See Fig. 8.2.9c.

8.2.5.1  Power-on Upshifts (2005 Perspective) Figure 8.2.12 shows torques and speeds for an upshift which has been divided into its significant parts. The lever diagram for the upshift is also included in Fig. 8.2.13. The upshift is a typical single-swap type of shift that involves two friction elements, a releasing element and an applying element; in this case both are clutches-to-ground, but the description applies

An accumulator on the clutch exhaust can produce nearly imperceptible downshifts, but the scheme has two objections: (1) it delays the speed change, which is contrary to driver command; and (2) it results in significant heat energy to the clutch.

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to all upshifts. The use of a one-way clutch is not addressed here, as the differences have been adequately discussed by the Winchell and Route paper.

torque equals the input torque times the initial gear ratio. Also, referring to Fig. 8.2.13, the lever drawing, the torque balance yields:

QC2 = Torque applied to the 2nd Gear reaction element, C2, the Apply element in the 1-2 shift QC1 = Torque applied to the 1st Gear reaction element, C1, the Release element in the 1-2 shift Q¢C1 = Torque capacity of C1; note that capacity exists for both positive and negative torques Qi = Torque capacity to input; assumed to be a constant 100 Nm for this study QO = Output Torque of the transmission Ni = Speed of the input shaft



QO = Qi + QC1

(8.2.12)

the moment balance about C1 yields:

QO = Qi (D1 + D2)/D2

(8.2.13)

the moment balance about the output point yields:

QC1 D2 = Qi D1

(8.2.14)

8.2.5.1.2 Torque Phase There are two basic ways of controlling the torque phase exchange of friction elements: designed overlap and designed underlap. The designed overlap method maintains some excess capacity in the releasing element until the applying element has enough capacity to hold engine torque; then the releasing element is removed. This approach is shown in Fig. 8.2.12 and will be described next.

8.2.5.1.1 Initial Gear The graph portion before point A is simply in the initial gear. The driving conditions, i.e., throttle, car speed, etc., have called for an upshift; and the apply element is filling but has not developed any torque. The release element is fully engaged, and, with a fully engaged element, i.e., not slipping, there are two torques of interest: torque capacity, Q¢C1 (net pressure * piston area * mean disc diameter * friction coefficient), and torque requirement, QC1 (or torque actually being carried by the clutch and applied to the gear train). With a slipping element, these two torques are the same; i.e., any net pressure will result in a comparable applied torque (net pressure is actual minus the return spring equivalent pressure, etc.). In this initial-gear portion, because the applying element has not developed any torque, the output

In the torque phase portion from A to B, the applying element begins to pick up torque, which means that output torque is falling and the shift is moving into Winchell-andRoute’s “inescapable drop” (Section 8.2.4.1). Referring to the lever diagram in Figure 8.2.13, it is obvious from observation that grounding the 1st Clutch gives the Input more leverage on Output than grounding the 2nd Clutch; i.e., (D1 + D2)/ D2 compared to (D1 + D2 + D3)/(D2 + D3). The solid arrows in the torque phase diagram represent the torques in

Fig. 8.2.12  Torque profiles during a 1-2 shift. 8-12

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1st gear at time A; the dotted arrows represent the torques at time B. B is the time when QC2 develops enough torque to support all of the reaction required by the input torque; i.e., QC2 = Qi (D1/(D2 + D3)), so that the releasing element torque, QC1, equals zero. The rate of torque change from A to B is controlled solely by the applying element; as long as the releasing element has excess capacity, the torque of the release, QC1, simply supports what reaction torque is needed after the apply element’s torque is satisfied. From a moment balance about the output point:

In the designed underlap method, the control system will drop the releasing element capacity, Q¢C1, below the level required by input torque, Qi, minus the amount already supported by the applying clutch, QC2. When that is done, negative slip occurs in the releasing element. Slip at this stage means that inertial torques are involved, and the torques of both the applying and releasing clutches will act to determine lever, i.e., gear train, motion (which is a limited amount of runaway of the input element). The controls, typically, will attempt to maintain a small amount of negative slip, and to maintain negative slip, the controls must continually adjust Q¢C1 downward as QC2 develops torque or slow the rate of increase of QC2. This control can minimize any excess release element torque and, thereby, minimize the torque loss during the “inescapable drop.” When negative slip occurs in the releasing element, however, the speed of the input will increase; and the output torque will be reduced, at least momentarily. For good shift quality, this torque disturbance must be minor, i.e., well controlled, or shift feel will be objectionable. If the controls can delay the occurrence of slip until the apply element has developed significant torque, then QC1 is low and the slip event can be undetectable. An output torque diagram has not been prepared for designed underlap because of the number of assumptions that must be made, but the overall profile would be very similar to Fig. 8.2.12.

QC1 = Qi (D1/D2) – QC2((D2 + D3)/D2) (8.2.15)

As long as the releasing element’s capacity exceeds the requirement, Qo = Qi + QC1 + QC2, where QC1 is just the torque requirement. When further increases are made in the applying element, QC2, after time B, QC1 becomes negative and output drops below the inescapable level. For good shift quality, it is essential that the releasing element torque capacity, Q¢C1, be removed at, or very soon after, B to minimize the drop in output torque. As long as Q¢C1 has excess capacity, i.e., before C, there will be no significant changes in any component speed. Note also that after C, in the speed-change phase, the torque change rate is higher because both the decay rate of Q C1, now a negative torque, and the buildup rate of QC2 contribute to the more-rapid increase in output torque. Under most conditions, the minimum output torque during a shift occurs at C, the beginning of the speed change.

8.2.5.1.3 Upshift Torque Management If engine T. M. (torque management) is used for upshifts, it is not typically activated until after the torque phase is complete, i.e., after C, because any reduction in input torque would increase the drop in torque which occurs inescapably during this phase. If any management were to be done in the torque phase, it would seem appropriate to use it to increase input torque to compensate for the inescapable drop that occurs as the apply element builds up torque.

It is also noted that the vehicle’s response system, i.e., driveline, mounts, body, steering column, etc., can hide from the occupants much of the torque loss in this phase. The rate of change of torque certainly affects the response, and, if high rates are desired, the use of an overrunning clutch for the releasing element makes the task easier because the need to accurately time the release of the 1st Clutch and the apply of the 2nd Clutch limits the achievable rates of the torque exchange.

8.2.5.1.4 Speed-Change or Inertia Phase The speed-change phase starts when slip occurs, at C above; or, if designed underlap is being used, when the input speed is less than the initial gear speed. The torque equations are relatively easy to derive from the lever diagram of the gear train during speed change (see Fig. 8.2.14). The inertia values of the components, i.e., input, 1st Clutch, and 2nd Clutch, are attached to the lever as shown, and lever rotation is about the output point because vehicle speed is assumed to be constant for the duration of the shift. The block arrows indicate lever motion about the output point, which is assumed to be at constant speed during the shift.

Fig. 8.2.13  Lever diagrams for a four-speed transmission in a 1-2 upshift.

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change, αi, but not the output torque. There is no general consensus on the optimum shape of this profile, and vehicle response parameters are certain to affect desired optimum for any given vehicle. The shape illustrated in Fig. 8.2.12 is close to that used in most automatic transmissions. Prior to the use of engine torque management during shifts, the transmission engineer was forced, at medium to heavy throttles, to find a compromise between shift quickness and the magnitude of the torque disturbance. For any shift, there is a given quantity of inertial energy that must be dissipated. If the speed change is spread out over a longer time, the disturbance is less but may lack the desired speed and crispness. If the speed change time is too long, the shift may be perceived as two events, the torque phase exchange and the end-of-speed change torque loss; that double-event feel can be objectionable. Some friction materials tend to develop a higher coefficient as the clutch slip speed approaches zero, point E in Fig. 8.2.12, and that can accentuate the inertial torque at the end of the shift and feel like a bump. The transmission engineer may soften the apply force near the end of the shift to compensate for this coefficient change or to simply ease the torque drop at the end of the shift.

Fig. 8.2.14  Lever torques during the speed-change phase of the 1-2 shift. The torque balance of the lever yields the following equation:

(

) (

) (

Q = Q – α I + Q − I α + Q – I α O i i i C1 C1 C1 C2 C2 C2

)

⎛ ⎞ D2 D2 + D3 = Q + QC1 + QC2 – α ⎜ I i – IC1 – IC2 ⎟ i i⎝ D1 D1 ⎠

(8.2.16)



As mentioned above, there is no consensus on the ideal profile for output torque during a shift; the shift feel is so dependent on other vehicle systems and the shift conditions that the torque profile alone cannot be used to judge acceptability. It is sometimes surprising to see that certain torque disturbances are not noticeable in shift feel, and at other times, shift feel is especially sensitive to other disturbances.

(The sign convention for torques is rightward for positive drive, typically clockwise from the front; the torque directions shown on the lever in Fig. 8.2.14 are for the speed-change phase only. Thereby, they include a negative αi and negative torque on QC1.) (All αi terms are expressed as a function of αi.) The moment balance about the output point gives the following equation:

(Qi – αiIi )D1 = (QC1 – αC1IC1)D2 + (QC2 – αC2IC2 )(D2 + D3)

8.2.5.1.5 Upshift Torque Management Many modern powertrains use engine T. M. (torque management) to improve shift control. T. M. can provide three types of shift improvements during the inertia or speed-change phase of the upshift:

(8.2.17)

Substitute the following α expressions to have only αi.

α C1 = –

D2 αi ; D1

α C2 = –

• Reduced energy dissipation in the shifting clutches • Reduced torque disturbance • Reduced time required to complete the shift

D2 + D3 αi D1 (8.2.18)

From these two basic equations, all operating conditions can be evaluated. This has been done, and the conclusion, discussed in the Winchell and Route paper, that the apply element defines the output torque during the inertia phase has been duplicated (again, assuming the inertias of the reaction elements are negligible). The equation shows that, after release element torque drops to zero (QC1 = 0), and with the IC1 and IC2 terms set to zero, the profile or shape of the transmission output torque is determined by the buildup rate or torque/time profile of the applying element (i.e., QC2 determines the profile of QO). Qi affects the rate of speed

Again, during the inertia phase, the output torque is essentially proportional to the apply element torque, with input torque having virtually no effect. When the input torque is reduced by T. M., no significant change occurs in output torque, assuming that the inertias of the 1st Clutch and the 2nd Clutch are relatively minor. The apply element torque, which was in the torque-phase-providing reaction for the full engine input torque, now provides reaction for a much higher inertial torque on the input element and a greatly reduced engine combustion torque. Without T. M., a typical WOT

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8.2.5.1.6 Adaptation or Learning of Shift Parameters

shift would involve input speed change rates of 4000–5000 rpm/sec; with T. M., the speed change rates may be twice that amount. This feature reduces clutch energy dissipation by completing the inertia phase of the shift in less time and typically with less clutch torque. In fact, very smooth shifts can be made with no engine combustion torque during most of the inertia phase of the upshift.

One of the most valuable features of electronic controls is their ability to adapt to the hardware or conditions under which they are operating. With electronic controls, it is not unusual to find transmissions with over 200,000 miles that shift like new units. If the mechanical integrity is acceptable, and the friction characteristics are reasonable, the parameter adaptation will compensate for the other changes that occur during the life of the vehicle as well as correct for the as-built variations that occur in normal production. Some examples of parameter adaptation are:

Good, high-speed communications and a sensor which provides an indication of the transmission input speed are typically necessary to make optimal use of T. M. The time of the speed-change event may be as little as 200–300 milliseconds. Preferably, the torque is not reduced before, and is fully restored by the end of, the speed-change event; therefore, high speed communication and precise knowledge of the beginning and ending of the speed change are essential. With a torque converter in the system, input torque is a function of converter slip (i.e., engine speed minus input speed). This means that engine torque needs to be restored a short time before the speed change ends so that the needed converter slip exists at the end of speed change. If full engine torque is not restored, the output torque will be low, and that can be objectionable.

The time-required-to-fill-a-clutch is learned after initial build by operating in Neutral, applying the clutch, and observing how long it takes before the input speed (which is spinning at about engine idle speed) is slowed by the torque of the applying element. The test sequence is programmed into the controller and performed at final assembly. Thereafter, during normal driving with each steady upshift, the time-to-fill is updated by observing when the apply element torque stops a small amount of backward slip, which the release element is attempting to maintain. Also, this value is stored in the controller, and can be accessed by a service technician to determine whether excessive clutch disc wear has occurred. In this example, the time-to-fill parameter is learned as a clutch circuit volume (this is the volume of oil that must be put into the circuit to begin to apply the clutch) and used with a flow coefficient (to get time); that coefficient varies with operating conditions such as line pressure, temperature, and shift.

As mentioned earlier, T. M. is not typically used during the torque phase of the shift, and that means that the apply element must have enough torque capacity to handle any possible torque-phase requirement. T. M. reduces the energy dissipation requirement of the apply element, but it has little or no effect on the torque capacity requirement of this element.

For the time-to-fill parameter, some controls look for a particular input speed profile to identify clutch application. With some controls, the time-to-fill parameter is only learned on low-torque shifts, and the start-of-speed-change is essentially used to identify time-to-fill.

The inertias of the clutch components do become more significant because of the higher speed-change rates involved with T. M. As discussed in the Winchell and Route paper, high inertias in the reaction elements can have a substantial effect on shift torques, and a study of these is warranted in any new transmission design. The lever equations make it easy to do this study or to add the inertia effects to a plant model.

The parameter that controls the “apply force appropriate for the apply element in a speed change” will have an initial calibration, but that value will be adjusted. The adjustment may be made by either observing shift time (or a related parameter) and increasing the calibration if the time is too long (or vice versa), or, if real-time feedback is being used, averaging the torque needed to achieve desired operation and adjusting the starting level accordingly. This parameter would be learned for each shift and for the current estimated torque or throttle level. Temperature compensation may also be included in the parameter. By continually updating the element apply force used during shifts, the controls accommodate changes in friction characteristics that occur during the life of the car.

Another area of concern is the effect the high rates of deceleration have on the engine’s accessory drive. These rates can play havoc with the drive belt because the inertia torques of the accessories result in two torque reversals in each upshift. One approach used to protect the accessory drive is to drive the belt’s pulley though a one-way clutch on the engine’s crankshaft; this prevents the accessories from putting a positive torque on the crankshaft during the upshift. Often, the belt drive can be beefed up, or the controls can soften the torque transitions so that acceptable performance is achieved.

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The time-to-slip for each releasing element is learned by comparing a calculated input speed (from output speed and gear ratio) to the measured input speed to identify the time from element vent to element slip. Time-to-slip, typically, is learned with respect to torque and temperature. A learned time-to-slip allows the controller to time the apply and release events so that apply/release torque overlap/underlap can be minimized.

zero with a quick snap of the throttle to a very high level with a slow crowd of the pedal. Additionally, the speed change can vary from a few hundred rpm to well over two thousand rpm. The push by car builders to provide responsive powertrains means that slow or delayed KD shifts are not desirable; therefore, the shift strategy is frequently based on the amount of speed change that is being made. For a KD at low speed with an open torque converter, the entire shift is best made under relatively high torque conditions because the high shifting torque will reduce the amount of the torque increase at shift completion. Also, at low speed, the high torque can be maintained without introducing any significant shift delay because the time needed for speed change is extremely short. As shown in Fig. 8.2.9c, the output torque can stay near the initial gear level and then rise to the target gear level at the end of the shift. For a double-gear KD at highway speeds, however, the output torque should be allowed to go very low so that the engine can use most of its torque to accelerate the rotating components up to the target gear speed (reference Fig. 8.2.9b). Additionally, the driver’s input is also likely to change in a KD; a call for a 4-3 shift can easily become a call for a 4-2, and that must be handled smoothly. Hardware—With the KD shift, the release element is the primary control member because only the release element can provide positive torque during the speed change; any torque from the applying element is negative until the input speed is greater than or equal to the target gear speed. Early application of the applying element (reference Fig. 8.2.10) generates a negative torque which pulls Nt toward N-target, and results in a sharp torque reversal as Nt reaches N-target. Proper timing of apply element application is crucial to a KD shift with a large amount of speed change. An overrunning clutch has been popular as the applying element for kickdowns because it does not apply any torque until input speed is up to target gear speed, and that provides an inherent ability to cope with the widely different conditions that occur with the KD shift. The cost, space, and weight of the overrunning clutches are issues, however, especially as the number of speeds in the transmission increase. Therefore, electronic timing of element application is becoming increasingly popular. As indicated by Winchell and Route (Section 8.2.4.2.2), a band is preferred as an applying friction element because of its asymmetric torque characteristics, which minimize any negative torque from an early apply application, but, with the precision of electronic controls, the preference is less important today.

These are just a few of many parameters that are learned during the normal operation of the vehicle. The quality of the adaptation algorithms is crucial to long-time performance of the vehicle.

8.2.6

Downshift Control Study

As might be expected, the downshift is in many ways the inverse of an upshift; and the relationships observed in an upshift are similar to the downshift but often inverted. There are three basic types of downshift conditions: power-on or kickdowns, power-off or pulldowns, and closed-throttle or coastdowns. Within each type, there are many important variations, and these variations frequently require different control strategies. The first two types occur in response to driver commands, and, therefore, are expected to give a significant torque response. The coastdowns, however, occur when the speeds are low, the vehicle is quiet, and the torque disturbance must be almost unnoticeable. 8.2.6.1  Power-on/Kickdown Shift Again, the Ratio Changing paper provides an excellent background for this discussion (Section 8.2.4.2). It also paints a clear picture of the limitation of hydraulic controls, which typically progress from one pressure level at the beginning of a shift to another level at the end. Accumulators or valves can pause the progression, but they cannot reverse the direction of the pressure change. The quality of the KD or kickdown shift improves significantly with electronic controls because the controls can react to shift events and provide a response that is tailored to the current shift. This frequently means both dropping and increasing pressures during a shift, and that was not possible with most hydraulic systems. Conditions—The KD shift controls have to contend with highly variable conditions. With upshifts, each shift typically occurs at the same speed for a given torque level; therefore, the speed change and timing are the same for all shifts at that torque level. The KD, however, can be made under vastly different conditions. The input torque at the beginning of the shift can vary from almost

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8.2.6.1.1 KD Control and Output Torque—Large-SpeedChange Shift

as release element pressure is reduced from 2 bar down to 1 bar, the output torque falls from 170 N. m to 70 N. m, and the rate of change of input speed increases. This occurred because, at the point of initial release slip, the release element is still carrying a substantial amount of input torque through to the output and not allowing the engine to use its output to accelerate. As the controls correct this by reducing release pressure, the desired engine/input speed acceleration is achieved. At the appropriate moment, the filling of the apply element begins; this is timed to achieved element fill shortly after the input speed, Nt, exceeds target gear speed (at the second cursor), thereby ensuring that both apply and release element torques give positive drive torques (the “t” in Nt refers to the turbine of the torque converter). Note also that release element pressure is increased to about 2 bar just as Nt approaches N-target; this slows the speed change for the handoff and increases the amount of input torque that is carried at previous gear torque multiplication (through the release element). It is important to note that the release element has first claim on the input torque (it is a slipping element; therefore, its torque is equal to its torque capacity).

Figure 8.2.15 shows a 4-2 kickdown shift at 90 kph; the upper graph shows throttle motion, and release and apply element pressures for two seconds (68.8 to 70.8 seconds). The throttle motion was slow, about 0.4 seconds from 8 to 82 degrees; this allows the engine to develop full torque before any slip occurs. Note from 69.18 to 69.23, the controls had started a 4-3 shift which has a different release element, but the same apply element. When the throttle had increased enough to call for a 4-2, at the first cursor; a different element was vented, and the filling of the apply element was delayed because a larger speed change would be needed for the 4-2 (i.e., more time is needed to allow the engine to achieve the higher target speed). The lower graph shows the target gear speed, engine speed, transmission input speed, and transmission output torque, labeled Trq Mtr. At 0.15 sec after the first cursor, release element slip occurs; engine and input speed begin to rise; output torque falls; and the speed change is underway. Note that,

Fig. 8.2.15  4-2 kickdown shift at 90 kph.

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After the second cursor when Nt = N-target and the apply element is engaged (i.e., no slip, and the apply element has two torques of interest, capacity and requirement), the apply element’s torque is “requirement,” which is that left over after the release element’s portion is removed. This characteristic means that the rise in output torque, at the second cursor, is a function of the venting of the release element. This feature gives the control engineer a means to soften the large increase in output that occurs with a double gear kickdown and avoid a harsh kickdown shift. In this particular shift, a control anomaly occurred in the release element pressure at 70.3 seconds; the brief rise in release pressure can be observed as a brief loss of output torque (the anomaly also caused the disturbances in the pressures of the applied clutches, but because these are fully engaged, that disturbance does not have any effect on output torque). This shift was chosen for discussion because it illustrated the torque effects.

torque somewhat. Thus, there is less need for torque control at shift completion. 8.2.6.1.2 KD Control and Output Torque— Small-Speed-Change Shift The lower-speed shifts typically have two notable differences from the higher-speed variety—first, the change in input speed, Nt, is less and second, the torque converter allows much larger differences between Ne and Nt. Note in Fig. 8.2.16 that at the start of the shift at 35 kph the difference between Nt and N-target is less than 1000 rpm, and the engine speed, Ne, is already above N-target so that even an instantaneous speed change would still have some positive torque. This means that, under low-speed conditions, it is not necessary to manage Ne during a shift, and the first requirement, above, is not applicable to low-speed kickdowns. As before, this shift at 46.2 sec initially calls for a 4-3 and quickly switches to a 4-2 call as the throttle increases from 17 to 52 degrees (note initial release, then reapply, of 4-3 release element pressure). The 4-2 release pressure falls enough to allow clutch slip at the first cursor. The logic then adjusts 4-2 release pressure to control Nt as it moves to N-target. This control keeps the pressure at a relatively high level which minimizes the loss of output torque, labeled Trq Mtr, (note: torque zero is moved to the midpoint of graph for improved readability). The apply element, as before, is filled so as to apply shortly after Nt exceeds N-target. Because the release element is carrying much more torque under these conditions, the rise in output torque is primarily a function of the venting of the release element pressure. The requirements for the “small speed change” shift are essentially the same as the second and third items of the “large speed change” shift.

The primary requirements for shift quality with a largespeed-change kickdown are: Release Quickly and Keep Release Element Pressure Low. Net release pressure should be low (not zero, to avoid backlash issues) to minimize any delay in response and achieve the requested increase in engine speed and drive torque quickly. Note, the illustrated shift could be improved by dropping release pressure further at 69.4 sec to achieve an Ne/Nt acceleration rate of 5000 rpm/sec rather than the 2600 rpm/ sec shown, thereby providing a faster response to the driver’s call for a KD. Time the Apply Element Application to Occur at or Slightly Above Target Gear Speed. An over-running clutch does this automatically; an increase in release pressure near target speed makes this easier by slowing the speed change rate. Any torque in the apply element with Nt < N-target will be negative and will result in a reversal of this torque when Nt = N-target.

Time the Apply Element Application to Occur at or Slightly Above Target Gear Speed. An over-running clutch does this automatically. For clutch-to-clutch shifts, good release pressure control of Nt, input speed, near target speed is essential. Both the logic and the mechanical system must perform well to control input speed under these high-torque conditions. Any torque in the apply element with Nt < N-target will be negative and will result in a reversal of this torque when Nt = N-target.

Incorporate Control Features to Soften the Torque Increase at Shift Completion. Release element torque can do this, but engine torque management can also soften the torque increase and is frequently used for this purpose. Torque management is typically achieved with engine spark retard because spark gives a quick response and has an adequate range of authority. It is typically requested just before Nt = N-target (when the torque being carried by the torque converter is low due to the engine using most of its output for acceleration). The spark is then ramped back in to spread out the rise in torque and avoid harshness in the kickdown shift. With an over-running clutch under high speed conditions, the torque converter torque may be low as the over-running clutch engages, and, because input torque is dependent on developing slip in the torque converter, the engine inertia will slow the onset of

Incorporate Control Features to Soften the Torque Increase at Shift Completion. This is required even with an over-running clutch because input torque is dependent on torque converter slip, and at low speeds, converter slip is likely to be high at shift completion. The sudden onset of kickdown torque, therefore, can result in kickdown harshness. As shown in the shift described, release element torque can soften the torque increase, and as noted earlier, engine torque management can also do this. It is essential to remember, however, that 8-18

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input torque is a function of converter slip, not instantaneous engine torque.

Figure 8.2.17, 4-2 pulldown at 65 kph, shows essentially the same parameters as Figs. 8.2.15 and 8.2.16 except that the time is stretched to 2.6 seconds to accommodate the longer speed-change time. This shift began as the 4-2 kickdown discussed earlier, with an initial call for a 4-3 and a quick switch to a 4-2. With this transmission, the line pressure is higher in 2nd gear; therefore, when the 4-3 pressure turns back on, it rises to a higher level (it is partially determined by the loss of 4-2 release, which explains its inverse appearance). By the time of the first cursor, 17.9 sec, the 4-2 release pressure had dropped to 0.5 bar and the element exhibited slip. Nt is less than N-initial, the speed calculated from No to represent the speed in the initial gear (4th). The turbine slows somewhat because of the negative torque from the torque converter. The control logic limits the negative slip by reapplying some pressure to the 4-2 releasing element. The logic started to apply the 2nd gear apply pressure at about 17.6 seconds; and at 18.2 sec the filling of the element was complete, and it started to develop torque, as indicated by the increase in negative torque in the Trq Mtr trace. The logic then controls the apply pressure to achieve a desired rate of change of Nt, turbine speed. This desired acceleration is typically low to

This discussion has covered a 4-2 shift to emphasize the challenges, but, just as with the upshifts, the effects and relationships discussed apply to any single-swap shift. The torque equations are not discussed here, but they can be developed as described in upshift Section 8.2.5.1.4. 8.2.6.2  Power-off Downshifts or Pulldowns This shift is typically used by the driver to obtain some vehicle braking torque from the engine, as when driving down a long grade towing a heavy load and wanting to avoid overheating the vehicle’s braking system. By downshifting to a lower gear, the engine speed is increased so that the motoring torque is maximized, and the additional torque ratio increases the relatively limited motoring torque enough to provide significant braking torques. Although most flatland drivers will never encounter a need for this shift, many others will use it frequently and will appreciate the smooth application of engine braking torque.

Fig. 8.2.16  4-2 kickdown shift at 35 kph. 8-19

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Fig. 8.2.17  4-2 Pulldown at 65 kph. provide only a modest increase in engine braking torque; that, of course, extends the shift time, as shown in this shift. The Apply element torque pulls Nt to N-target, and the negative drive torque is increased; through the negative slip in the torque converter, Ne, engine speed is pulled up to 2nd gear levels. At the second cursor, the 2nd gear apply element is fully engaged, and the negative drive torque is reduced due to the loss of the inertial torque from turbine inertia. The negative drive torque continues to be reduced (until 19.7 sec) as the torque from the torque converter is reduced due to the loss of engine inertial torque. The inertia phase of this shift is very much like an upshift, except the torque and speed directions are reversed.

events would not have been affected significantly by an earlier start of apply. If desired, engine torque management could be used to reduce the inertial torques in this shift. But there are a couple of considerations other than just shift quality. First, this is typically a manually selected shift, and with the throttle closed, the driver probably desires the braking torque, and he may not want to lose the higher braking torque that comes from the inertial effects. Second, the use of engine torque management for this shift would require an increase in engine throttle (to offset the inertial braking torques). That requires electronic throttle control for the engine and is likely to mean that additional safety features must be added to the transmission controller to ensure that an inadvertent power increase never occurs as a result of a failure.

This shift could have been quickened by about 0.25 sec if the logic had begun to apply the 2nd gear apply element that much sooner. The negative slip indicates that any objectionable overlap torque would not have occurred with a 0.25 sec earlier apply. The logic would normally do this, but this particular shift was run before adequate learning had occurred—in order to show the slip direction. All subsequent

This type of shift may also be used by some automatic controller programs, such as a cruise control downhill overspeed reduction feature. If the shift is requested by an automatic feature, the priority for good shift quality is higher, and engine torque management may be appropriate. 8-20

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8.3 Shift Torque Analysis and the Continuously Variable Transmission 8.3.1

8.3.3

The purpose of this paper is to provide an understanding of the ratio changing mechanics of the continuously variable transmission. The transmission output torque changes affect vehicle acceleration and driver awareness. The focus is therefore on what happens to output torque during the ratio changing transient. The methods can also be used to determine the speeds and torques of the engine and any member of the transmission. The ratio-changing mechanics of the step gear automatic transmission were presented in SAE Paper 311A at the 1961 SAE International Congress (see Fig. 8.3.1). This paper builds on that effort by showing how the principles can be extended to the CVT. The lever analogy was presented in SAE 810102. Knowledge of both these papers is of great use in understanding CVT ratio-changing mechanics. The step gear automatic transmission ratio changes have implicit torque and vehicle acceleration changes during the shift transient that have required engineering attention to make them acceptable to the vehicle operator. The CVT has advantages over the step gear transmission in the number of ratios available and the ability to change ratio in a continuous and smooth manner. The transmission engineer needs to know how these apparent advantages affect vehicle acceleration and how that understanding can be applied to improve operator acceptance. The lever analogy of gear sets and three approaches will be used to understand CVT ratio-changing mechanics:

Introduction

The extension of shift torque analysis to the Continuously Variable Transmission (CVT) was developed and presented in an SAE Paper, 2004-01-1634: Ratio Changing the Continuously Variable Transmission, written by John E. Mahoney, General Motors Corporation (Retired); and Joel M. Maguire and Shushan Bai, General Motors Corporation. As noted in the paper’s introduction, the torque analysis approach was based on the following two papers: SAE Paper 311-A, Ratio Changing the Passenger Car Automatic Transmission, 1961, and SAE 810102, The Lever Analogy, 1981 (included in this Edition as Section 3.5). This, of course, is the same base as was used in Sections 8.2.5 and 8.2.6. The paper is an appropriate and competent extension of that shift torque analysis, and it is included here. SAE Paper No. 2004-01-1634, Ratio Changing the Continuously Variable Transmission By John E. Mahoney, General Motors Corporation-Retired; Joel M. Maguire and Shushan Bai, General Motors Corporation

8.3.2

Introduction to Paper

Abstract

1. Comparison to the transients of step gear transmissions as the number of steps is increased. 2. Taking the step gear ratio-changing equations to a limit. 3. Differential calculus analysis.

The ratio changing mechanics of the continuously variable transmissions are developed. The lever analogy of gear sets, comparison to step gear transmission mechanics, differential calculus analysis, and the step gear ratio changing equations are used. Power on up-shifts, power on downshifts, power off up-shifts, and power off downshifts are analyzed. Approaches to minimize the disturbances are considered.

Fig. 8.3.1 8-21

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The techniques will be applied to the four main types of ratio changes: • • • •

Power on up-shifts Power on downshifts Power off up-shifts Power off downshifts

8.3.4

Fig. 8.3.3

Power On Up-Shift

For the speed ratio change to start, the oncoming element must apply additional torque. The amount of additional torque determines how high the output torque goes, how fast the speed ratio change is completed, and how much energy is turned to heat. See Fig. 8.3.4.

The power on up-shift is defined as changing ratio to a lower torque multiplication while a positive input torque is applied. Automatic transmissions traditionally change ratio with power on, while manual transmissions traditionally shift power off. During a step gear power on up-shift, there are two tasks: changing the torque ratio and changing the speed ratio. These two tasks do not occur simultaneously. SAE Paper 311A shows that the mechanics require the torque ratio change to complete before the speed change can start. The two processes are referred to as the torque phase and the speed or inertia phase. Transmission output torque is plotted versus time to show what happens during the transient from the downshifted gear ratio to the up-shifted gear ratio (see Fig. 8.3.2). Input torque is held constant for the analysis. The before shift torque is equal to the input torque multiplied by the initial gear ratio. The after shift torque is equal to the input torque times the lower after shift torque ratio.

Fig. 8.3.4 Up-Shifting the CVT To visualize the power on up-shift for the CVT we can observe what happens when a single step ratio up-shift is replaced equivalently by two, or three or more smaller step up-shifts. See Fig. 8.3.5.

Fig. 8.3.2 The ratio change is initiated by an oncoming element in the transmission that applies torque to the gear members that will provide the up-shifted ratio. Simultaneously, the element that is maintaining the initial ratio must be released. This must be coordinated to prevent engine run away (flair) or driveline tie-up. This torque application has the effect of reducing the output torque to the level of the up-shifted output torque with perfect element transition, less if imperfect. See Fig. 8.3.3. If the ratio change stopped at this point, the transmission would be in the up-shifted torque ratio, but the down-shifted speed ratio.

Fig. 8.3.5 As the number of shifts becomes larger and the steps become smaller, the torque phases become smaller and the inertia phases get shorter and closer to each other. The limit of this visualization is a torque phase disappearing and the inertia phases blending together with decreasing torque slope. The equation for the step ratio torque phase is:

To = TiD1 − Tc

D1 − D2 D2 − 1

(8.3.1)

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Where To is output torque, Ti is input torque, Tc is oncoming element torque, D1 is the initial ratio and D2 is the ending ratio. The limit of this equation as D2 approaches D1 is:

To = TiD1

The torque relationship for this system is:

D2 D2 − 1

The limit of this equation as D2 approaches D1 is:

(8.3.5)

Where I is the input inertia and α is the input acceleration. Dν is the variable ratio.

(8.3.2)

This indicates no preliminary torque phase, and the torque and inertia phases will proceed concurrently. The equation for the inertia phase is:

To = Tc

To = (Ti + Iα)Dν



Dν =

Ni No

(8.3.6)

Where Ni is input speed and No is output speed. Because:

(8.3.3)



Ni = Nii – αt

(8.3.7)

Where Nii is initial input speed and t is time elapsed.

D1 To = Tc D1 − 1

(8.3.4) The inertia phase output torque has a value determined by the ratio and the oncoming element torque. The torque ratio changes along with the speed ratio. The lever analogy for gear sets depicts the gear train as an equivalent lever and represents the torques on the gear train as forces. The value of the analogy is that the visualization and analyzing of linear motion is easier than rotary motion. A step ratio gear set is represented as a lever in Fig. 8.3.6.



Dν =

Nii − αt No

To = (Ti + Iα)

Nii − αt No

(8.3.8) (8.3.9)

If α is a constant, the output torque diminishes as the transmission is continuously up-shifted. This is shown in Fig. 8.3.8.

Fig. 8.3.8 The ratio change as shown in Fig. 8.3.8 might not be acceptable to the driver. This could be improved upon by lengthening the shift time, reducing the input torque during the transient with spark retard, or varying input acceleration with ratio control, as shown in Fig. 8.3.9.

Fig. 8.3.6 An input force, output force, and two reaction forces are shown acting on the lever. One reaction force represents the downshifted ratio and the other, the upshifted ratio. Which reaction is applied determines the current ratio. During the ratio change, both will be applied in proper amount to get the desired transient. Figure 8.3.7 shows a lever representation of a CVT. The two reactions of the step gear representation are replaced with a movable force.

Fig. 8.3.7

Fig. 8.3.9 8-23

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Simulation Insight

The positive inertia torque only appears when there is a negative engine speed change during up-shifting. Since this type of power-on up-shift creates an undesired jerky feeling, it is typically avoided by the ratio scheduling system. Figures 8.3.11 and 8.3.12 show the torque, speed, and ratio trace for a constant engine speed up-shift, and an upward engine speed up-shift at a constant throttle opening. It can be seen that the upward engine speed up-shift provides more performance (higher output torque).

In a step gear power-on up-shift, a large step of ratio change happens in a short period, in average about 1.5 ratio/second. In a CVT power-on up-shift, the ratio change is spread out over a longer time interval; a typical ratio change rate for a CVT power-on up-shift is 0.3 ratio/second. In addition, in step gear power-on up-shifts, the inertial torque is always positive. However, in CVT, depending on the way the CVT ratio change is carried out, the inertia torque of a power-on up-shift of CVT can be zero, positive, or negative. Most CVT ratio scheduling systems conduct a power-on up-shift with a zero inertia torque. That is, for a constant throttle opening, a predetermined corresponding engine speed is maintained. The CVT ratio is shifted up as the vehicle speed increases. Engine speed increasing up-shift has also been proposed to gain an enhanced performance feeling. That is, for a constant throttle opening, the predetermined desired engine speed increases as the vehicle speed increases. Because the engine speed is going up during the ratio change, this type of upshift has negative inertia torque (see free body diagram in Fig. 8.3.10).

8.3.5

Power On Downshift

The power on downshift needs to complete the speed change before the torque change. This is accomplished by reducing element torque capacity and allowing the input to increase speed. This acceleration and reduction of element torque reduces output torque. The amount of reduction depends on how fast the engine is allowed to accelerate and this, of course, affects the duration of the transient. Once the speed has reached the downshifted amount, the downshifted element can make the torque ratio change. The plot of output torque versus time during a power on downshift is shown in Fig. 8.3.13. The figure also compares the downshift with two and three steps to make the same overall change. The figure finally shows how this process taken to a limit would look for a continuously variable transmission. Looking at the downshifting mechanics and referring to Fig. 8.3.7, the equation for the power on downshift is:

Fig. 8.3.10

Fig. 8.3.11

Fig. 8.3.12 8-24

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To = (Ti − Iα)

Nii − αt No

(8.3.10)

If No and α are constant, the output torque during the transient would be less than the initial starting torque and increasing with time. This is shown in Fig. 8.3.13 and confirmed in Fig. 8.3.14.

Fig. 8.3.13 The CVT power on downshift as shown is not that much different from the step ratio power on downshift. Its disturbance can be lessened by lengthening the shift time, opening the engine throttle during the transient to increase the input torque, and varying input acceleration with transmission ratio control. The effects of these modifications are shown in Fig. 8.3.15.

Fig. 8.3.16

shift with a ratio change that is too fast. In this case, a negative output torque is observed. Figure 8.3.17 is a power-on downshift with a slower ratio change rate. The output torque smoothly increases.

Fig. 8.3.14

Fig. 8.3.15 Simulation Insight The shift feel of a power-on downshift is mainly determined by the rate of CVT ratio decrease. If the rate of ratio decrease is too great, a large negative inertial torque will be seen at the output shaft. If the rate of ratio decrease is too low, it will take more time to reach the desired engine power lever. Therefore, proper choice of ratio decrease rate is important. In many ways, this is analogous to the actions found in step gear transmissions. Figure 8.3.16 shows a power-on down-

Fig. 8.3.17 8-25

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8.3.6

Power Off Up-Shift

can be made coast-to-coast, drive-to-drive, or drive-to-coast with not enough CVT torque to reverse output torque, the transient can be improved.

The plot of output torque versus time for a CVT power off up-shift is shown in Fig. 8.3.18. A power off up-shift is usually initiated when the vehicle operator suddenly reduces the input power to the point that the output is driving the input and the input torque is negative. The plot shows the input torque becoming negative. The equation for the inertia phase is the same as for the power on up-shift and is controlled by the torque of the oncoming element. It will cause the output torque to go from negative to positive and back to negative when the change is completed.

8.3.8

Conclusion

The understandings of the ratio-changing mechanics of the continuously variable transmission were developed. They were applied to determine how transmission output torque changes during the ratio-changing transient. Methods of reducing the output disturbances were shown. The tools and equations developed in prior works for step gear transmissions were applied to the CVT. These tools can be applied to determine other torques and speeds of interest in the CVT drivetrain.

8.3.9

Fig. 8.3.18

References

Winchell, F. J. and W. D. Route, “Ratio Changing the Passenger Car Automatic Transmission,” SAE Paper 311A presented at the 1961 SAE International Congress, Detroit, Michigan, January 1961, Benford, Lesing, SAE Paper 810102, SAE International, Warrendale, PA, 1981.

If the shift can be made before the output torque goes negative, it can be made with less output torque disturbance and the output torque will not reverse under CVT force. This is shown in Fig. 8.3.19.

8.4 Shift Scheduling Table of Contents—Shift Scheduling

Fig. 8.3.19

8.3.7

8.4.1 Introduction 8.4.2 Shift Scheduling Control 8.4.3 Up Grade Road Problems 8.4.4 Down Grade Road Problems 8.4.5 Vehicle Mass Influence 8.4.6 Driver Classification 8.4.7 Shift Control Using Fuzzy Logic 8.4.8 Shift Schedule Control Using Information from the Vehicle’s Navigation System 8.4.9 Select Transmission Ratio Guarantees the Demanded Traction Power

Power Off Downshifts

The power off downshift is used to return the transmission to its initial gears as the vehicle and output speeds reduce toward a stop. As a vehicle decelerates, it is first driving the input and later being driven by the input. This is shown in the Fig. 8.3.20 plot of output torque versus time.

Fig. 8.3.20

8.4.1

The output torque starts negative and then becomes positive, and this is caused to be negative by the ratio change. This is known as a drive-to-coast power off downshift. The output torque equation is the same as for the power on downshift, with recognition of the sign of the input torque. The shift shown reverses the output torque under CVT force, which could cause driveline noise or a felt disturbance. If the shift

Introduction

It was recognized early in the development of the motor car that, unlike steam or electric power plants, an internal combustion engine of reasonable size and weight, directly coupled to the driven wheels, could not deliver the range of speed and power required of the passenger car. Starting

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from a rest position, a car has a wide range of speed and torque requirements. However, internal combustion engines have limited practical and usable speed ranges and could not simultaneously start themselves and put the car into motion from rest. In addition, vehicles usually demand the greatest torque at the driving wheels when starting from rest. The internal combustion (IC) engines, on other hand, produce their maximum torque at a relatively high speed. Moreover, a large engine capable of delivering the starting torque without a transmission would have to be larger and heavier than an engine and transmission system combined. Transmissions serve to increase the flexibility of the powertrain such that a reasonably sized internal combustion engine could provide the speed and torque characteristics required by a motor vehicle.

An understanding of the engine performance characteristics is a necessity to design a satisfactory shift schedule. The engine is the source of power needed to start, accelerate, and propel a vehicle. Otto cycle engines are used in most vehicle applications today. Otto cycle engines have zero power at zero speed, typically provide maximum power at speeds between 3500 and 6000 rpm, and have an optimum operating point for best fuel economy at any given power level. The torque of an engine is defined as the rotational force the engine produces, and the power of an engine is defined as the torque multiplied by engine speed. Figure 8.4.2 provides the engine wide-open throttle torque and horsepower curves for a 1.0-L engine. The engine torque peaks at 3500 rpm and the engine horsepower peaks at 5500 rpm. Figure 8.4.3 provides the torque and fuel consumption plot for the 1.0-L engine over a full spectrum of throttle settings. Since the most efficient point for the engine changes with the engine speed and power required, there is no way for a step transmission to let the engine operate always in the most optimized fuel economy condition since the requirements vary continuously as vehicle speed increases or decreases.

Because of easy operation and smooth shifting, the automatic transmission has now been widely used in cars since it was first introduced in the late 1930s. Traditionally, most of the transmissions were two, three, or four speed, and the shift schedule had been determined by two hydraulic pressures, one corresponding to the vehicle speed and the other to the engine’s output torque. Figure 8.4.1 shows a typical example of the shift schedules of a hydraulically controlled automatic transmission [1].

The criteria for establishing the gear ratios of a transmission are based on the function that each gear should perform. In first gear, the sufficient torque is required so that the vehicle can launch on a grade and accelerate at a reasonable rate. In the highest gear, enough torque should be available to keep

The shift schedules of automatic transmissions have been significantly improved through the application of electronic control since the late 1980s. With electronic control, there has been much greater flexibility available for programming the shift schedules based on the use of sensors to detect the vehicle speed and throttle valve opening. This has made it possible to achieve the best operating speed and torque of the engine under any given set of driver inputs and vehicle operating conditions. Modern automatic transmissions have become an integral part of the engine control strategy.

Fig. 8.4.1  Shift schedule of a hydraulically controlled automatic transmission (upshifts).

Fig. 8.4.2  1.0-L engine wide-open throttle torque and horsepower.

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However, even with all the potentials and possibilities for modern transmissions, automatic transmissions do not automatically provide good performance and fuel efficiency without a proper selection of gear ratio and shift timing. The time to make a shift, and the criteria to consider when making it, are always important concerns in automatic transmission controls.

8.4.2

Shift Scheduling Control

In the conventional system, the gear shift timing is determined to enable the throttle valve opening that meets best the driven shaft torque demanded by the driver. As the oil price rises, the fuel economy demand becomes an increasingly important factor in automatic transmission shift schedule determination. In the case where gear shifts are timed for fuel consumption, the shift points are usually at much lower vehicle speeds than when the timing is selected by conventional preferences. Under this condition, the driver will need to use much larger throttle openings and, therefore, will not obtain the desired feeling of vehicle acceleration capability. This means the optimal point of fuel economy is usually not at the same zone as the engine high-performance region as shown in Figs. 8.4.2 and 8.4.3.

Fig. 8.4.3  1.0-L engine torque and fuel consumption vs. throttle opening and engine speed.

the vehicle moving, and the engine speed should be kept in a range that is efficient for operation. In the interim gears, the gear ratio steps should be evenly distributed, or for the best driveability, the ratio steps for the lower gears are somewhat larger than those for the higher gears.

The typical principals for actual shift scheduling are more acceleration-based in higher throttle regions and more fueleconomy-based in the low throttle regions. Overall, driveability is generally given the first priority. A vehicle’s driving feeling is dramatically influenced by the shift schedule programmed into the vehicle’s electronic controller.

With more gear ratios available, the automatic transmission ratio spread will be increased. Higher ratio spread has the potential not only to increase the low gear ratio and decrease the high gear ratio, but also to reduce the speed change between gears. A higher low-gear ratio improves the launching performance, and a smaller high-gear ratio improves the highway fuel economy. With reduced ratio steps, the transmission will be able to make the shifts more smoothly because of the reduction in the inescapable torque drop during shift and the reduced change in engine speed; it also makes it possible to adjust engine speed closer to the optimum fuel economy condition.

A good-feeling shift schedule that balances fuel economy and driveability typically requires extensive calibration. Delaying upshifts too long can make a vehicle feel as though it is straining with too much engine speed to achieve the desired acceleration, while significantly hurting the fuel economy. Upshifting too early can produce a disconcerting feeling that the vehicle is lugging and/or is underpowered. Delaying a downshift event too long after a driver begins pushing the accelerator pedal or scheduling it too early, will likely be perceived negatively. In the first case, the driver may believe that the engine lacks power, and in the second case the driver may perceive that shifting is too volatile or “busy.”

In a quest for a new kind of competitive edge, auto makers are pouring billions of dollars into creating cars with five, six, or more forward speeds. The burst of investment in automatic transmissions with more than the traditional three and four gears is being driven by the growing demand for better fuel economy and overall powertrain performance, as well as car makers’ need to outdo rivals in a crowded market.

Figure 8.4.4 gives an example of an actual shift schedule that takes these factors into account. This shift schedule has been designed to provide an optimum balance of fuel economy and driveability, and it represents a typical shift schedule for today’s electronically controlled automatic transmissions.

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A fixed shift schedule does not present any major problems when a vehicle is operated under ordinary driving conditions, such as on a flat road without any steep gradients, at sea level, and under normal passenger and cargo loads. However, it often exhibits undesirable characteristics when driven up and down hills, winding roads, or when a vehicle is carrying a heavy load.

Another problem occurs on winding roads with uphill and downhill gradients. Consider a situation where a vehicle is traveling at an average speed of 60 km/h on a winding road that has an average uphill gradient of around 10%. Figure 8.4.6 compares which gears are used under these conditions with a four-speed automatic and a five-speed manual transmission.

Fig. 8.4.4  Shift schedule of electronically controlled automatic transmission (upshifts).

8.4.3

Up Grade Road Problems

An example of the shifting problem that occurs with this condition is the gear hunting sequence shown in Fig. 8.4.5 [1]. In this example, the operating point of a vehicle traveling in 4th gear is currently at point A. The road-gradient-demanded drive torque is indicated by the line X in the figure. The driver presses on the accelerator, and as a result the operating point moves from A to B and then on to C after the transmission downshifts. However, since the drive torque at C is excessively large and the vehicle begins to accelerate, the driver lets up on the accelerator. As a result, the operating point moves from C to D and then on to E after the transmission upshifts. At E, the vehicle begins to decelerate because of insufficient drive torque and so the driver again presses on the accelerator, moving the operating point to B. This frequent repetition of gear shifts (B→C→D→E→B) is typical of the gear hunting problem.

Fig. 8.4.6  Comparison of selected gears. The automatic transmission upshifts just before the corner because the driver lets up on the accelerator. However, when the driver again presses on the accelerator as the vehicle leaves the corner, the transmission downshifts. This same type of shifting action also occurs on an uphill road where there are slight changes in the road gradient. For example, in the middle of a down-hill stretch of the road the driver will let up on the accelerator even though he can see an uphill gradient ahead, and the automatic transmission will upshift as a result. In the case of a manual transmission, these unnecessary gear shifts do not occur because the driver judges the driving conditions and shifts gears accordingly. As a measure for preventing the situations, some vehicles mounted with an automatic transmission are provided with an overdrive cancel switch. The above-mentioned hunting problem can be resolved by setting the switch so that overdrive is not used. However, the benefit of this control switch cannot be obtained unless drivers have a good understanding of vehicle characteristics and use the cancel function appropriately. Another problem with this switch is that it can lead to a deterioration of fuel

Fig. 8.4.5  Gear hunting on a grade.

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economy if a driver forgets to turn the switch off or uses it when it is not necessary.

which permits achievement of the previous speed. When the throttle is reduced to simply maintain speed, a 3-4 shift would normally be made, and the cycle would repeat. The inhibit calculation, however, prevents a 3-4 shift until the grade climb is completed during time period (1). The acceleration level (αR) required to permit a shift is initialized at a normal value. Thereafter, it is increased somewhat during periods of “calculated negative 4th acceleration” and reduced during periods indicating at least moderate 4th acceleration capacity. This provides a natural hysteresis for the 3-4 inhibit function and accommodates brief reductions in grade without resulting in 3-4 busyness.

Although this condition can be improved somewhat by modifying the shift schedule, it must be done by lowering the throttle angle for 3-4 shift as shown in Fig. 8.4.7. Because the maximum engine torque is, for all practical purposes, already available at the 4-3 shift point, the hunting condition cannot be significantly improved by increasing the 4-3 kickdown line. To lower the throttle requirement for 3-4 shift line or to move the upshift 3-4 line to a higher speed range, however, causes the shift to seem excessively delayed on level roads. This driving torque relationship typically exists between any adjacent gears in a step-ratio transmission, but it only becomes annoying when the overall gear ratio causes it to occur on more-commonly encountered moderate grades.

8.4.4

When driving down a steep grade, the driver reduces the throttle opening and may actuate the brakes to achieve a desired maximum speed. The intention under these conditions should be to drive in a gear as low as possible to use the increased braking torque of the combustion engine. The transmission control system does quite the opposite. The shift pattern in Fig. 8.4.6 shows that the reduction of the throttle opening leads to a higher gear position. That means the braking torque of the engine is reduced and, therefore, the mechanical brakes have to compensate by absorbing more energy. This behavior is not desirable.

Fig. 8.4.7  Shift pattern for upshift driving.

An interesting solution to this and other problems is presented in the JSAE Paper 9538041 [3]. The following summarizes the authors’ comments. It is very difficult to optimize gear position with throttle angle and vehicle speed, even with the information of road gradient and engine torque, because drivers have individual preferences, especially regarding engine braking. Therefore, a brake signal is added to judge drivers’ dissatisfaction with engine braking in addition to throttle and vehicle speed signals, as shown in Fig. 8.4.9. Adaptation or learning control is used to correct down-shifting conditions that suit drivers’ wishes based on vehicle speed, throttle, and brake operations.

Various attempts have been made by different researchers to devise a method for estimating the road gradient on the basis of the drive torque generated by a vehicle, the resulting acceleration, and other factors. One of the approaches used to resolve the hunting condition was to make the 3-4 shift schedule adaptable to current vehicle operating conditions [2]. In 3rd gear, the controller calculates the level of acceleration that the vehicle would be capable of maintaining in 4th gear. If the level is too low (or negative), the controller inhibits the 3-4 shifts.

αo ≤

To3 − To4 + αR Io

Down-Grade Road Problems

(8.4.1)

If downshifting is provided when a driver does not desire engine braking, the driver will step on the accelerator, thereby lightening engine braking. In this case, the learning control slightly corrects the downshifting condition so that engine braking is suppressed. On the contrary, if downshifting is not provided to satisfy the driver needs, the driver will press the brake pedal frequently to inhibit increasing vehicle speed. Then the learning control slightly corrects the downshifting condition so that engine braking is more effectively applied. The design and calibration of this learning control is a significant challenge given all the possible driving conditions.

where αo is the transmission output acceleration, αR is required acceleration level, To3 is the transmission output torque existing in 3rd gear, To4 is the potential transmission output torque existing in 4th gear, and Io is the vehicle inertia. The relationships involved result in Eq. 8.4.1, as shown in Fig. 8.4.8. This graph shows how adaptive scheduling works for a vehicle climbing a grade. When the vehicle begins the climb, it loses speed, and the throttle is increased in an attempt to maintain speed. This results in a 4-3 downshift,

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Fig. 8.4.8  Acceleration-modified 3-4 shift scheduling.

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where va is vehicle speed, δ is coefficient of revolution mass conversion, ma is driving mass of vehicle, MeD is dynamic output torque of engine, rd is dynamic rolling radius of tire, ig is gear ratio, im is final ratio, η is the efficiency of powertrain, ψ is resistance coefficient of road, including the grade of road and rolling resistance coefficient, which may be a function of vehicle speed, CD is aerodynamic drag coefficient, and A is area. To exert the best vehicle performance, the acceleration is always the same after and before vehicle gear shifting.



⎛ dv a ⎞ ⎛ dv a ⎞ ⎜⎝ ⎟ =⎜ ⎟ dt ⎠ ing ⎝ dt ⎠ in+1 g



(8.4.3)

where va is vehicle speed, and n and n+1 refer to the nth and (n+1)th gear. The different shift points of adjacent gears related to driving mass can be obtained by properly solving Eqns. 8.4.2 and 8.4.3 (see detail from SAE Paper 2002-01-1258). Obviously, to apply the driving mass compensation for shift scheduling, a load detection feature must be included. With the dynamic tri-parameter method, it has the potential to compensate the grade and vehicle mass to achieve the best vehicle launch performance, especially during the 1-2 upshift. However, under the pressure of government regulations and oil price increases, transmission shift points have been increasingly under pressure to be more and more fuel-economy oriented. In the conventional system, the gear shift timing is determined to enable the throttle valve opening to meet the driven shaft torque demanded by the driver as much as possible. In the case of gear shift timing for fuel consumption, on the other hand, the shift point occurs much earlier relative to the vehicle speed as compared with the conventional condition. Under the fuel consumption optimized strategy, the driver will not obtain as much acceleration feeling.

Fig. 8.4.9  Engine braking judgment during downhill driving.

8.4.5

Vehicle Mass Influence

Another factor influencing shift point determination, which should not be neglected, is vehicle driving mass. As shown in Fig. 8.4.5, a similar hunting problem occurs during uphill road pulls with heavy vehicle loads. One way to resolve the hunting problem during heavy vehicle load is to apply Eq. 8.4.1 to make the 3-4 shift schedule adaptable to current vehicle operating conditions [2]. In 3rd gear, the controller calculates the level of acceleration that the vehicle would be capable of maintaining in 4th gear, and if the sensed level is too low (or negative), the controller inhibits the 3-4 shifts by using the criteria of Eq. 8.4.1.

To reduce the fuel consumption by making the gear shift timing for fuel consumption compatible with the acceleration feeling, as suggested by the authors in JSAE 9635674 [5], torque correction by electronic control of the throttle valve is indispensable. The proposed driven power control method using the throttle control of the target driven torque will be based on compensating for the torque reduction caused by the selection of gear shifting timing for minimum fuel consumption.

As suggested in SAE Paper 2002-01-1258 [4], another way to avoid the hunting problem is to use the calculated vehicle mass as a shift control parameter for selection of the shift point. Depending on vehicle driving mass, different shift points can be derived through “dynamic tri-parameter shift schedule” theory. Additionally, a dynamic vehicle model is used in definition of the shift points. Basically, in this method, the key criterion is to keep the vehicle acceleration always the same after and before vehicle gear shifting for the best vehicle performance.

8.4.6

In a dynamic vehicle model, under the drive of the powertrain, the vehicle overcomes the resistance force of rolling resistance, aerodynamic drag, and acceleration resistance.



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δma

Additionally, shifting sometimes does not match drivers’ intentions because there are various driving styles. For example, in sporty driving, a shift pattern which provides driving in lower gears is required because drivers need more driving force for acceleration.

D

C Av 2 dva M e i gi m ηT = − ma gψ − D a dt rd 21.15

Driver Classification

(8.4.2) 8-32

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8.4.7

Figure 8.4.10 shows the shift pattern which continuously moves the shifting lines depending on road gradient and driving style [3]. The driver is classified as being either moderate or sporty. Many methods with conventional control strategies are based on mathematical models, which describe and classify the behavior of human drivers. Thus, it is necessary to set up such a description model that attempts to provide targeted functionality.

Shift Schedule Control Using Fuzzy Logic

When considering the human thought process, decision making and the subsequent action taken do not rely on mathematical models. On the contrary, people understand and judge a situation before acting in a way regarded as the process of recognition → judgment → decision → action. Thus, it is possible to code this series of actions into IF-THEN rules. These rules represent knowledge acquired through personal experience and can provide and improve the quality of control based on human knowledge. In SAE Paper 905049 [6], the concept of using a fuzzy set was introduced to express a highly skilled, qualitative control technique for adapting the shift schedule to different driving conditions and drivers. To devise the fuzzy logic rules, statistical analyses were made of driving behavior data compiled on a large number of drivers under various types of road conditions. For example, the road conditions were recorded on video tape and at the same time recordings were made of the throttle valve opening, vehicle speed, brake operation, and steering wheel movement. Subsequently, the measured data were subjected to a comprehensive analysis while comparing them with the video tapes of the test roads. As introduced in SAE Paper 905049, fuzzy control implements fuzzy reasoning by determining the output and control of the system, on the basis of input control knowledge expressed by IF–THEN fuzzy production rules which code the recognition process. The rules can be expressed as follows:

Fig. 8.4.10  Continuous variable shift patterns. One example could be: Class driver = k1 ¥ throttle opening + k2 ¥ speed of throttle opening + k3 ¥ vehicle acceleration

Rule 1: Rule n:

Other well-known classification methods make use of threedimensional maps to combine two inputs and assign one result. Such a map has to be implemented by a complete data array. Such methods have poor capability in implementing rule-based knowledge in the form of “If. . . Then” premises.

IF(x1 is A11 AND, …, AND xk is Ak1) THEN y1 = b1 IF(x1 is A1n AND, …, AND xk is Akn) THEN yn = bn

where A is a fuzzy set expressed on R1 b is an output value (real number) x is an input variable, and y is an output variable

Various attempts have been made by different researchers to overcome this kind of methodology and introduce methods which do not force the implementation by a mathematical description, especially if there is no obvious physical background or description available. One of the popular approaches tried by many OEMs was based on the idea that the driving environment could be detected from the driver’s actions, assuming that the driver functioned as a single comprehensive sensor. A specific method examined applies fuzzy logic to derive a quantity corresponding to the road gradient. The method uses throttle valve opening and vehicle speed as the information inputs.

When x1 = x10, …, xk = xk0 (x10, …, xk0; singleton) is input, the truth value of Rule;[Rule] is calculated as follows

[Rule]= MIN {A1i (x10), …, Ak i (x k0)}

where A1i (x10) is the membership value in x10 of fuzzy set A1i. Then, the output value (control command) Y is calculated as follows:

Â[Rule ]¥ b Y= Â[Rule ] i

i



i

(8.4.5)

i

i



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Output Block—In this block, an over-revolution check is done by considering the gear position (determined through reasoning in the previous block). After determining the appropriate gear-shift position, a command is issued to the actuator.

The fuzzy shift scheduling system consists of four blocks as shown in Fig. 8.4.11: the input block, the reasoning block, the knowledge base, and the output block.

Note that the real number following THEN represents a shift variable value. The minus sign indicates down; the plus sign indicates up. In summary, the fuzzy systems calculate subjective quantities like the driver value and the load value, which are used as interpolation variables for shift line interpolation. This operation on the one hand combines the input signals in a desired way by the fuzzy rules. On the other hand, it allows one to carry out a nonlinear mapping by the design of the input membership functions. Therefore, the fuzzy systems simply play the role of a nonlinear interpolation function. By the tuning of the input membership functions, the sensitivity of the input quantities can be adjusted depending on the operating point.

Fig. 8.4.11  Fuzzy shift scheduling system. Input Block—In this block, input variables such as vehicle speed, throttle opening, engine speed, brake signal, and gearshift position are received, and then preprocessing is performed to determine the necessary control information. Reasoning Block—In this block, the appropriated gear-shift position is obtained by fuzzy reasoning with information from the input block, and rules of the knowledge base. Knowledge Base—This block stores knowledge based on personal experience learned as the object of a number of “IF–THEN” rules. The ambiguity in recognition is expressed by using fuzzy sets. Figure 8.4.12 lists the rules determined through driving behavior investigation, the computer simulation, and the corresponding fuzzy sets.

8.4.8

Shift Schedule Control Using Information from the Vehicle’s Navigation System

From previous discussions, it can be concluded that a smooth drive can be accomplished if the system understands the driving conditions of the vehicle. With the advent of recent electronic information technologies, many methods for detecting the driving conditions have been developed and put into commercial applications, such as navigation systems, radars, CCD cameras, etc. As an example of using information from navigation systems for shift control, the following is a summary of SAE Paper 2002-01-1254, which introduced the experimental application of coordinated navigation control on the fourspeed automatic transmission (4AT) in a mid-sized luxury sedan [7]. That system detects the road curvature ahead of the vehicle, the speed of the vehicle, and the brake application of the driver. As the vehicle approaches the curve, the system shifts the gears down from 4th gear to 3rd gear. After it determines that the vehicle has completed the curve by its operating condition, it shifts back to 4th gear. However, control of the system was applicable only to curvatures that are greater than a certain value. Another example, as shown in Fig. 8.4.13, is called the NAVI·AI-SHIFT in Toyota’s Mark-II model that affects shift control of a five-speed automatic transmission (5AT) in coordination with a navigation system [8]. This system estimates the contour of the road ahead from the road data, then affects shift control based on that information and the road gradient.

Fig. 8.4.12  Diagram of fuzzy sets and control rules. 8-34

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The navigation system determines the curvature of the road ahead in accordance with the four following classifications, starting with the mildest curvature: straight line, large radius corner, middle radius corner, and hairpin corner. Then, it determines the approach to the corner judgment area based on the contour of the road ahead, as shown in Fig. 8.4.14. This is for determining whether it is necessary to decelerate in order to smoothly turn the curve based on the curvature of the turn, the distance of the vehicle from the curve, and the vehicle speed. The Navi Electronic Control Unit (ECU) then transmits the results of this judgment to the automatic transmission (AT) ECU.

road contour direction (horizontal axis) that have been created for determining the recommended shift position. These maps enable the system to select the lower shift position as the road gradient and the curvature become more severe. When the system determines that the recommended shift position is lower than the vehicle’s current condition, the system checks the vehicle speed, the cornering judgment, and the vehicle conditions to determine whether it is appropriate to execute control. Then, the system selects a downshift command in accordance with the operation of the accelerator and brake by the driver. While the transmission is in 3rd gear or 4th gear, if the recommended shift position matches the shift position selected by the normal shift map, the system selects a hold control to prohibit the transmission from upshifting.

On an actual road, the engine brake force and the vehicle drive force desired by the driver vary by the gradient of the road, even if the vehicle is approaching a curve with a given curvature at a given speed. Therefore, shift control that better suits the intention of the driver can be accomplished by adding the road gradient information to the plane-surface navigation information, instead of using only the plane-surface navigation information. Thus, the recommended shift position can be determined through a three-dimensional assessment of the contour of the road. For this reason, the system determines the recommended shift position by combining the road curve information and gradient information (see Figs. 8.4.15 and 8.4.16).

The recommended shift positions have been determined with the greatest possible care so that all users can feel fully comfortable with a system that is not intrusive. The actual shift positions have been rendered as follows. To downshift

Figures 8.4.15 and 8.4.16 show the five-stage map for the gradient direction (vertical axis) and the four-stage map for the

Fig. 8.4.15  Down shift judgment map.

Fig. 8.4.13  Action of NAVI-AI-SHIFT.

Fig. 8.4.16  Up shift judgment map.

Fig. 8.4.14  Conceptual drawing of corner judgment logic. 8-35

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a vehicle that is in 5th gear as it approaches a curve, and the recommended shift position is 3rd gear, the transmission shifts sequentially 5th gear Æ 4th gear Æ 3rd gear so that the engine brake force increases smoothly. To upshift a vehicle that has completed the curve, the transmission shifts sequentially 3rd gear Æ 4th gear Æ 5th gear so that the drive force changes smoothly. As a result, the vehicle’s ride is extremely smooth and comfortable, both while approaching and exiting a curve.

2. Uncertainty for determining the present position (which occurs when there is a road that is adjacent to the road on which the vehicle is traveling) 3. Low accuracy of the present position judgment (which occurs immediately after recovering from a route deviation or immediately after passing an intersection) 4. Incorrect map data (which occurs when the vehicle has not turned even if the navigation system has output a deceleration requirement judgment)

In this system, the navigation system affects control by analyzing the contour of the road based on the database of the road ahead and transmitting this information to the AT ECU. If the system finds that the road intersects with another road, it cannot analyze the contour of the road ahead because the system cannot tell which road the vehicle will take. Therefore, the navigation system transmits the signals, which indicate that the vehicle is currently being driven in the vicinity of the intersection, to the AT ECU. Based on this information and the operating conditions of the vehicle, the AT ECU then affects control to hold the existing shift position and prohibit shifting at the intersection, as shown in Fig. 8.4.17. This measure enables the system to smoothly affect control even if the intended travel direction of the vehicle cannot be ascertained while the vehicle passes through an intersection. As a result, the system can be operated even if route guidance is not being implemented.

The Navi ECU constantly monitors whether conditions 1 to 3 are occurring, and if it determines the presence of any one of the conditions, it stops the operation of the NAVI. AI-SHIFT system or holds the existing shift position. In the case of condition 4, the Navi ECU learns that the map data for that location is incorrect, and prohibits the system from affecting control at that location. The self-diagnosis function prevents the NAVI. AI-SHIFT system from operating improperly when the navigation system is not showing the correct position of the vehicle or when the actual road differs from the road in the map data. As previously mentioned, this system uses the information from two systems for determining the recommended shift position. These systems provide road curve information from the navigation system and the road gradient information calculated by the AT. Because these two pieces of information are combined to determine the contour of the road, even if there is a slight error in one piece of the information, the judgment of the recommended shift position will not be extremely altered, so that the driver will not feel uncomfortable with the system. The next section includes discussion from [9], GALOP-IAV’s Universal Speed Ratio Selection.

8.4.9

Fig. 8.4.17  Conceptual drawing of intersection judgment logic.

Select Transmission Ratio Guarantees the Demanded Traction Power (summarized from SAE Paper 2002-01-1256)

Incidentally, if the current position information of the navigation system and the digital map data are used, the occurrence of errors in determining the present position and the actual contour of the road is unavoidable. These errors significantly alter the shift control, and in the worst case, they could cause the transmission to inadvertently downshift and make the driver uncomfortable. To resolve this problem, a self-diagnosis function has been provided in the system to address the following four situations:

Even though the shift strategy has been greatly improved with all the new technologies mentioned previously, the basic principle is still that the shift lines depend on load and speed. The special functions were realized by switching or interpolating between multiple sets of shift lines. This further aggravated the inherent problem of shiftline strategies: The large amount of calibration data and in-transparent behavior while interpolating entails long development times to ensure satisfactory vehicle behavior in the wide ranges of operating conditions.

1. Low precision of the sensors for determining the present position (which occurs when the reception of the GPS signals is poor or when the parameters for calculating the travel distance have been changed significantly)

In current transmission control units for four-speed automatic transmissions, up to eight of the shiftline maps, as shown in Fig. 8.4.4, are used. In addition, the same number 8-36

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of shiftlines for the lock-up-clutch control is necessary in automatic transmissions equipped with torque converters.

visualization, the above mentioned is shown in a common traction torque diagram in Fig. 8.4.18.

Since the introduction of electronic throttle control, additionally, the relation between the accelerator position (load) and the engine torque has become a variable, and thus a popular means of adjusting driveability late in the development process. With a classic shiftline strategy, this means permanent recalibration; e.g., it is possible that the torque at the engine speed after an upshift is reduced and the vehicle cannot maintain its speed as desired. Exchanging the accelerator position by the engine torque would be one option. With IAV’s GALOP [9], a completely different approach was chosen, which is applicable also to CVTs and allows for a substantial reduction of calibration data: the driver’s power request, determined by an engine or drivetrain management system, is interpreted directly and leads to a target engine speed, from which an optimal transmission ratio is derived.

For the use in a vehicle, it is necessary to have hysteresis between the up and downshifts. In case of no existing hysteresis, an upshift may be followed by an immediate downshift due to a small change of power request. Two new additional criteria have been defined and added to eliminate this problem. For upshifts, the Power Reserve Request (PRR), and downshifts, the Power Gap Limit (PGL), were introduced. The resulting imaginary shiftlines are visualized in Fig. 8.4.19. As in Fig. 8.4.18, the lines under maximum wheel torque curves at each gear represent the lines of constant traction power.

Since the accelerator pedal is the only possibility for the driver to give his traction power demand to the drivetrain, it is very important to use this value carefully. The input from the accelerator pedal can be a signal for many different values such as: • • • • •

Engine torque demand Acceleration demand Target speed demand Wheel torque demand Traction power demand

Fig. 8.4.18  Range of 2nd gear in traction torque diagram with torque request for down/up shifts.

While selecting one of the possible interpretations, it is necessary to focus on the likely use of the several demands. It appears logical that the driver has knowledge about the performance of the car at full throttle. The accelerator pedal movement represents the wish to use a specific part of that possible performance. An obviously related item is the traction power. It is also an illustrative input that is easy to analyze and not speed- or gear-dependent. It may be concluded that the gearshift decision as well as the engine load should be dependent on the traction power demand. In hybrid drivetrains, it is very practical to use an input like the wheel-torque demand or power demand to be able to split the requested power between the combustion engine and the electric motor. Battery management also will be much easier with a power-based system.

Fig. 8.4.19  Traction torque diagram with PGL and PRR. Upshifts are not requested when the target gear fulfills the power demand from the accelerator pedal (PPED) but the sum of the Power Reserve Request and PPED. Downshifts are performed when PPED minus PGL is greater than the maximum power at actual engine speed.

Upshifts or a lower ratio should be requested when the power demand can be fulfilled in the target gear; downshifts or higher primary engine speeds are necessary when the current gear is unable to fulfill the driver’s power request. For

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into a target engine speed. For all transmissions with fixed speed ratios, the requested engine speed can be converted into a target gear.

pedal movement. GALOP uses the power request and derivatives of this value to detect the real power request, which is responsible for the acceleration of the vehicle. The function’s main goal is to provide the driver with the necessary power without permanent shifting action. PPED is modified by adding a driver-dependent value, representing an additional power reserve; later functions use PDRIVE as the power demand value.

The flow of signals as shown in Fig. 8.4.20 provides transparency to the gear selection processes. Starting with the accelerator pedal, the detection of the power demand, the drivertype detection, and the hill-assistance function, modify this signal to provide the power request function with an input for the power request. After determining the Power Gap Limit and the Power Reserve Request, the minimum engine speed and the target speed for upshifts is calculated. Finally, the transmission ratio is selected in different functions for CVTs, ATs, and ASTs.

In case of a constant pedal value after a period of fast movement or movement with high amplitudes, the driver type detection should decrease the engine speed to a normal level. One target is to meet the usual, efficiency-optimized engine speed within approximately 30 seconds. Power Request for Upshifts and Downshifts—This section handles the modification of the power request for upshifts and downshifts separately. To have a power reserve after the target gear is engaged, the power request from the throttle pedal is added with a value from a calibration map, which determines the Power Reserve Request (PRR). The power demand for upshifts is called PRU. PRU = PDRIVE + PRR However, even in the case of a six-speed-transmission, the traction torque gap between two gears cannot be avoided. This leads to the conclusion that the power reserve at high engine speeds should be zero or less.

Fig. 8.4.20  Flow of signals in the transmission ratio selection process. Detection of Power Demand—Usually the communication between drivetrain components is based on the engine torque. This input is not suitable for the transmission ratio decision. A better choice is the power demand, because the engine power may vary from gear to gear depending on the actual engine torque. Best results are achieved with a speeddependent power or wheel-torque request derived from the accelerator pedal. The value for the power demand from the accelerator pedal is referred to as PPED in the following sections.

For the downshifts an accepted Power Gap Limit (PGL) is the opposite of the power reserve (PRR). The driver feels that a downshift seems reasonable after determining that the current gear cannot provide the requested power. Consequently, the PGL is lowering the power demand for downshifts (PRD). However, PRD is never lower than PHILL, the minimum power request resulting from the hill detection. PRD = PDRIVE – PGL As a result, the difference between PRD and PRU is the range of power request—and accelerator pedal movement as a side effect—that does not force a gearshift or transmission ratio variation.

Hill Assistance—Since GALOP is a power-demand-based structure, it is possible to drop the conventional structure of using special shiftlines for mountainous conditions. In this function the climbing resistance is calculated. The strategy is to provide the driver with a minimum engine speed that is sufficient to produce the power needed to drive with a constant speed at the detected incline. The result of this function is a minimum power request (PHILL) for the engine speed selection process.

Conversion of Power Request into Determined Engine Speeds—After the power request for upshifts and downshifts is determined, it is necessary to convert it into a value that is suitable to obtain a transmission ratio. An illustrative value is the engine speed or the primary speed. The power request for upshifts is converted into an engine speed which is the minimum speed for the target gear in case of an upshift (SPUP) or in case of a primary speed variation to lower speeds of a CVT.

Driver Type Detection—An automatic transmission ratio selection strategy should offer a driver type detection to prevent unwanted gearshifts as a result of dynamic accelerator

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Throughout a downshift, the power request is converted into a minimum engine speed request (SPMIN).

of the transmission ratio is executed in steps. Following such a downshift procedure, the engine speed increases depending on the vehicle velocity. The PRU- dependent engine speed is used as a target speed for emulating a “kind-of ” upshift procedure. Whenever the vehicle speed is changing, the engine speed is varying as well. Small power request changes and consequently small accelerator pedal movements do not lead to altering engine speed as long as SPUP and SPMIN are not changing; e.g., as a consequence of a changing traction resistance. Only in the case of high-value amplitudes is the engine speed allowed to vary with a change in power request. The redesign of the transmission ratio selection process was a useful step on the way to more efficient gear shifts. Even though fixed or variable shift schedules are still dominantly used in current-production vehicles, the structure of driverpower-demand-based transmission shift control could be a direction of future advanced shift scheduling. It is possible to include many functions for each special type of transmission. As an important side effect, it is possible to give every model in the manufacturer’s fleet the same perception and behavior concerning the transmission ratio selection. This may be important for product differentiation and establishing a clear profile in a market segment, regardless of whether the car is equipped with CVT, AST, or AT.

Fig. 8.4.21  Visualization of imaginary shift points in an engine speed/vehicle velocity diagram. In Fig. 8.4.21 the relationship of the calculated engine speed and the vehicle velocity is shown. The desired velocity for upshifts and downshifts is comprehensible in the diagram. Gear Selection for AT, AST, and AMT—The stepped transmissions can be easily handled by gear selection logic. If the actual engine speed is lower than the determined minimum engine speed, a lower gear is requested that provides this minimum speed. If the requested minimum speed for upshifts is lower than the engine speed in a higher gear, this higher gear is selected.

8.4.10 Wrap-up This completes the summary of the state-of-the-art of shift scheduling. The features discussed cover the shift scheduling controls for up-grade road problems, down-grade road problems, vehicle mass influence, driver classification, new shift scheduling methods by using fuzzy logic, using information from a vehicle’s navigation system, and guaranteeing traction power. Some of the features are mature products in current transmissions, and some of the features discussed have been implemented in only a few models and not necessarily with 100% success, but they indicate the extent of what is possible and point to the direction of future developments.

As a result, the provided possible engine power is not less than PRD but may be greater than PRU, depending on the real power reserve which is greater than or equal to PRR. Conventional automatic transmissions operating with a hydraulic torque converter need special focus on calculation of the engine speed under current load conditions in another gear. In such transmissions, not only the engine speed but also the efficiency of the torque converter has to be part of the gearshift decision. This can be made more complex by adding a lock-up clutch to the converter.

8.4.11 References

Transmission Ratio Selection for CVT—Up to the determination of the requested engine speed, the strategies for the CVT and the step-ratio transmission are equal. The calculated values for minimum engine speed SPMIN and target engine speed for upshifts SPUP are used in a ratiocalculating module that emulates the fixed steps. Because the minimum engine speed is already known, it is easy to ensure that the current engine speed never falls below this value. To provide a well-known behavior, the shortening

1. Yamaguchi, Hiroshi, “Automatic Transmission Shift Control Using Fuzzy Logic,” SAE Paper No. 930674, SAE International, Warrendale, PA, 1993. 2. Leising, Maurice B., Howard Benford, and Gerald L. Holbrook, “Adaptive Control Strategies for Clutch-ToClutch Shifting,” SAE Paper No. 905048, SAE International, Warrendale, PA, 1990.

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3. Kondo, Kaoru and Hitoshi Goka, “Adaptive Shift Scheduling Strategy Introducing Neural Network in Automatic Transmission,” JSAE 9538041. 4. Yong, Zhang, Song Jian, Wu Di, and Xu Chunxin, “Automatic Transmission Shift Point Control under Different Driving Vehicle Mass,” SAE Paper No. 2002-01-1258, SAE International, Warrendale, PA, 2002. 5. Minowa, Toshimichi, Hiroshi Kimimura, Naoyuki Ozaki, and Masahiko Ibamoto, “Improvement of Fuel Consumption for a vehicle with an Automatic Transmission using Driven Power Control with a Powertrain Model,” JSAE 9635674. 6. Sakai, I., Y. Arai, Y. Hasegawa, S. Sakaguchi, and Y. Iwaki, “Shift Scheduling Method of Automatic Transmission Vehicles with Application of Fuzzy Logic,” SAE Paper No. 905049, SAE International, Warrendale, PA, 1990. 7. Kawi, M., et al, “Development of Shift Control System for Automatic Transmission Using Information from a Vehicle Navigation System,” SAE Paper No. 1999-011095, SAE International, Warrendale, PA, 1999. 8. Inagawa, Tomokazu, Hideo Tomomatsu, Yoshikazu Tanaka, and Kazuyuki Shiiba, “Shift Control System Development (NAVI-AI-SHIFT) for 5 Speed Automatic Transmission Using Information from the Vehicle’s Navigation System,” SAE Paper No. 2002-01-1254, SAE International, Warrendale, PA, 2002. 9. Nasdal, Roland and Mathias Link, “GALOP-IAV’s Universal Speed Ratio Selection Strategy for ATs, CVT and Hybrid Drivetrains,” SAE Paper No. 2002-01-1256, SAE International, Warrendale, PA, 2002.

in solenoids and their drivers, and improvements in sensor capabilities. All of these enablers have been realized at everreducing cost. The most important targets of this trend include: • minimize total transmission cost and weight provide addition gears (ratios) and address the associated packaging challenges • facilitate more clutch-to-clutch shifting which, in turn, reduces the cost and package size • provide smoother and more consistent shift feel by using shift control strategies that are far more complex than were practical with hydraulic controls • improve fuel economy by using more complex and aggressive converter bypass clutch lockup strategies • improve driveability through the use of more-capable control logic and added transmission calibrations for better shift feel, lockup feel, and shift scheduling. Although there are several unique transmission control systems under development with some in use today, most of those found on the typical automatic transmission can be broken down into three major categories: 1. Hydraulic Control 2. Indirect Electronic Control 3. Direct Electronic Control As hybrid systems, auto-shift manual systems, electric power systems, etc., are developed, the types of controls are likely to change substantially. This section presents the status as of 2007.

8.5 Transmission Control and Types of Controls 8.5.1

Introduction

8.5.2

The trend toward increased electronic content in automatic transmission controls, which began in the early eighties, has continued through 2007. Most of the advancement in electronic transmission control development has occurred over the last two decades and since the third edition of “Design Practices: Passenger Car Automatic Transmissions” was written in about 1990. The pursuit of fuel economy, shift quality, and added functionality, all at reduced cost, weight, and package size, is driving this development. Although the types of controls and solenoids have been named, it is recognized that different folks call them by different names. The intent is to describe the category and its characteristics and not to be concerned about its name.

Hydraulic Controls

Pure hydraulic controls are becoming increasingly rare, and are limited to three-speed and some four-speed automatic transmissions. All of these have been in production for a relatively long time. Many elements of the hydraulic controls, however, continue to be used especially for flow control, gating, and pressure regulation. For shift control with hydraulics, two control pressures are generated: (1) a pressure, called governor pressure, which is a function of vehicle speed and is generated by a governor valve or pump on the output shaft, and (2) a pressure, called TV pressure (throttle valve), is used as an indication of input torque; the pressure is either a function of accelerator pedal position or an inverse function of engine vacuum. These two pressures are applied at opposite ends of two-position shift valves. The shift valves move according to the force-balance

The most influential enablers of this trend include increased processor memory and throughput capability, improvements

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of the opposing pressures as well as spring forces calibrated to define the shift schedule. When a shift valve moves, it triggers a shift by pressurizing complex hydraulic circuits containing orifices, regulating valves, and accumulators that ultimately pressurize and/or depressurize (vent) the oncoming and/or off-going friction element(s) for the shift. The orifices, regulators, and accumulators are calibrated to shape the dynamic pressure, force, and torque capacity profiles for smooth shift feel, while also keeping clutch energies in check. The TV pressure also controls line pressure via the main regulator valve. The Driving Range (Park Reverse Neutral Drive Low) is determined by a manual valve that is mechanically connected to the shift lever by a cable or linkage, and the manual valve pressurizes or vents forward or reverse circuits upstream of the shift valves.

8.5.3

The potential loss of electrical power in a failure makes it necessary to consider the normal state of the solenoid design because that can determine the “limp-home” capability of the transmission. Moreover, the dirt tolerance of a design can affect the ability of the solenoid to reach its “normal” state. A ball design solenoid is much more dirt tolerant than a spool valve type, but other solenoid features and circuit filters can have a significant effect as well. A full failure modes and effects analysis (FMEA) is a must with electronic controls. High flow rate is often a requirement achieved by incorporating another valve so that the flow through the actual solenoid is simply the amount needed to actuate some type of slave valve, which is also typically more dirt tolerant. This approach, however, can add failsafe and other complications that may lead to added complexity. The three types of electrohydraulic solenoids in general use today are the:

Electronic Controls

On/Off Solenoid—This type is the smallest, requires the least current (therefore, a cheaper driver), and is relatively slow in response. It can be designed for two-way action (i.e., to open or close a single passage) or three-way, which is used to pressurize or to vent a particular passage. Two-way use typically results in a design which has some oil leakage under some operating condition; therefore, the extra cost of the three-way is sometimes justified. The on/off solenoid has seen wide application for shift valve and converter clutch control. Figure 8.5.1 shows on/off solenoids.

The initial use of electronics in automatic transmission controls, which began and spread throughout the ’80s and early ’90s, was enabled by the then recently-adopted electronic engine controls which were essentially mandated by emissions regulations. The use of a microprocessor and electronic fuel control was required to improve the fuel/air mixture and spark timing control that was needed to meet the emissions regulations. The microprocessors in use then had, with relatively minor modifications, the ability to handle transmission controls that did not require fast response. The adequate and affordable rotational speed-sensing capability required for these engine controls was more than adequate to schedule shifts. The low-cost electro-hydraulic solenoid was the final enabler for the initial levels of electronic automatic transmission control. The next section will review solenoids because understanding their capability is essential to discussing the different types of electronic control. 8.5.3.1  Solenoids

Fig. 8.5.1  On/Off solenoids. (Courtesy of BorgWarner)

Although the on/off solenoid was the only low-cost type at the beginning of the transition to electronics, later development has reduced the cost and improved the performance of the other types. Since then, the use of the more-capable types of solenoids has increased substantially.

Pulse-Width-Modulated (PWM) Solenoid—The PWM solenoid is really just an on/off solenoid designed for fast response and, most frequently, with three-way action; two-way designs have also been used. The control frequency determines the time period of each on/off cycle; that time and the solenoid’s on/off response determine the range of authority that a PWM solenoid will provide. Typically, a constant control frequency between 30 and 100 Hz is used, and the percent-on (i.e., pulse width) is varied over the range of authority to achieve the desired control. Periods of full-on or full-off, of course, provide for apply and vent conditions. PWM solenoids are best suited for flow control, as in converter clutch control,

With all types of solenoids, adding flow rate, three-way action (i.e., more travel), or faster response will increase the size and cost because these features involve heavier wire, more magnetic flux area, and higher-current solenoid drivers to achieve the force, stroke, and speed needed. Those parameters—force, stroke and speed—are the most significant in determining the solenoid design and cost.

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but they have also seen extensive use for pressure control in direct clutch control systems that have adequate partadaptive algorithms. Most early versions produced some noise during PWM control, but development has virtually eliminated the noise. The pressure-to-duty cycle curve for this type of solenoid has significant part-to-part variation (repeatability, however, is excellent); if precise level control is required, a self-calibrating control algorithm can provide excellent results. An added-cost, high-current, fast turn-off solenoid driver is required for direct clutch control with this solenoid, unless a specific application does not require fast response or high flow, as when used for controlling a converter clutch or with some secondary valve. Figure 8.5.2 shows a PWM solenoid.

of course need more capable driver components and greater heat dissipating ability. A system problem that exists with both PWM and VFS (especially) is that the object of control is clutch pressure, but if there is significant flow from the solenoid to the clutch, the pressure at the solenoid will be significantly higher than clutch pressure. The control algorithms must carefully handle the transition from clutch filling (high flow) to clutch torque control (leakage flow only) to achieve a smooth buildup of torque. In the 80s and early 90s, the variable force solenoids used in transmission control had a relatively low force output which limited their use to the bleed-type or a small valvetype. The bleed-type design (which has been widely used for line pressure control) typically requires lower currents and uses a relatively small coil, so the costs are reasonable. But the output flow is very low, and there is some leakage required all of the time the solenoid is working at other than one limit. A downstream valve is required if any significant flow is needed. Use of a downstream valve has advantages of control flexibility and some claimed improved dirt tolerance, but a bleed-type valve system has continuous leakage (which affects pump requirements), and the two-component system can make failsafe design and part calibration/accuracy issues more difficult. Figure 8.5.3 shows a pressure and flow characteristic curve for a bleed-type solenoid.

Fig. 8.5.2  Pulse-width-modulated (PWM) solenoid. (Courtesy of BorgWarner) Variable Force Solenoid (VFS)—This solenoid, which is also called a linear solenoid or an analog solenoid, develops a magnetic force output which is proportional to the electrical current provided by the solenoid driver. This type can provide an accurate open-loop pressure curve which, typically, can be adapted with algorithms to correct for clutch friction variation. It is necessary, however, to address the items which affect the current; namely, part-to-part variation, temperature which causes coil resistance to change, and input voltage variation. Numerous driver designs have been used over the years to compensate for changes in these variables, and today, a full current feedback loop is frequently used at added cost to improve the accuracy. The solenoid driver is constructed to provide a proportional current response from 0% to 100%; the current signal consists of a pulsed duty cycle typically operating in a range from 300 Hz to 1000 Hz (some use a different form of switching which results in higher values). Development has shown that some improvement in hysteresis can be achieved by providing a variable duty cycle (i.e., a slower duty cycle at low control pressure and a faster duty cycle at higher control pressure). Solenoids requiring higher current levels, discussed in the next paragraphs, will

Fig. 8.5.3  Pressure/flow characteristic for a bleed-type VFS. (Courtesy of BorgWarner) The valve-type VFS requires the force to be applied over more distance, which compromises the force, and, since it also involves a spool valve rather than a ball, the design can have issues of dirt tolerance. Since the design uses an overlap spool valve, it has very low leakage at any control pressure, so the pump requirement can be less. The valve-type VFS has been developed to have sufficient output to supply all of the flow needed for direct clutch control. This requires more force

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or stroke, and the size of the solenoid and solenoid driver varies substantially with this change. Figure 8.5.4 shows a bleed-type VFS next to a larger valve-type, high-flow VFS (for direct clutch control). Both types are in wide use today in transmission control.

Indirect Shift Feel Control—Shift feel and energy control were typically accomplished via a network of orifices, regulators, and accumulators very similar to those which had been used in pure hydraulic controls. However, also included was the electronic capability to adjust the shift element torque based on control algorithms and observed performance. Variable-force solenoids were used to generate a throttle pressure or to control line pressure, and sometimes to control torque-converter clutch pressure. This later use has enabled some units to achieve controlled-slip operation. These VF solenoids provide the capability to indirectly control shift feel both adaptively and in real time. The throttle solenoid’s output pressure was in some cases applied to the accumulator so that the solenoid’s output pressure would adjust the clutch pressure as the accumulator strokes. In others, the system line pressure was adjusted to achieve the desired changes in shift torque. Thus, the clutch pressure-vs.-time profile is influenced by an electronically controlled throttle or line pressure. As the shift proceeds, speed sensors tell the microprocessor how quickly the ratio is changing, and real-time pressure corrections can be made for shift feel smoothness. The use of the control algorithms to adapt the shift torques to achieve the desired shift profiles has proven to provide a substantial improvement in overall shift quality.

Fig. 8.5.4  Variable Force Solenoid (VFS)—bleed-type and high-flow valve-type.

8.5.4

Indirect Electronic Controls

Most of the industry started using electronics by placing some electronic controls over a basic hydraulic control system in what is called here, “Indirect Electronic Controls.” This allowed their application to existing transmissions, thus avoiding the cost and development of a totally new approach. The hydraulic use of a governor pressure involved significant compromise because of its inherent parabolic curve, and the intricate hardware needed to generate the pressure. It was the first item to be replaced; the shift scheduling task was accomplished with speed and throttle signals which the engine controls had available and simple on/off solenoids. These solenoids were used to apply or release pressure at one end of the shift valves, which only had return springs at their opposite ends. The microprocessor used the output shaft speed and throttle position sensor signals to decide when to switch solenoids and trigger shifts. The ability to use electronic logic to schedule shift has provided a substantial benefit in overall powertrain driveability. It has allowed the schedule to be tailored better to individual vehicles, and driving conditions like grade climbing, low ambient temperature, etc.

As might be expected, the indirect-shift-feel control configuration has relatively limited influence over shift feel, when compared to direct clutch control described next. This level of electronic control has limitations in response, range-ofauthority, and time-of-control. Also, expensive hydraulic control elements such as accumulators with regulator valves are still used, and it is generally applied to nonsynchronous shift transmission designs, which require one-way and coast clutches. Figure 8.5.5 illustrates the indirect electronic control system concept.

To reduce the number of on/off solenoids, shift valves can be logically networked with other downstream switching valves so that, for example, in a four-speed transmission, each combination of states of two on/off solenoids commanded one each of the four transmission gears. This valve network can be designed so that a default forward ratio and reverse remain available via the manual valve (still mechanically connected to the manual lever) even with loss of power to all solenoids (limp home mode). Some transmissions also used on/off solenoids to engage and disengage the torque converter clutch.

Fig. 8.5.5  Indirect electronic shift control system. 8-43

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8.5.5

Direct Electronic Control of Shifting Elements

This method controls each shifting element directly with the electronic controls. The on/off flow to each element, the pressure level, the rate of change of pressures, and the steadystate operating conditions are almost solely determined by the controller. This provides significant opportunities for improvement, but it also places stringent demands on the controller and its software. Failsafe design, for example, becomes critical because a simple electronic failure can apply the wrong elements which can cause the driving wheels to lock up or the engine to overspeed or other undesirable happenings. The temperature range, the life requirements, and the modes of failure of many new components become critical, and maintaining proper control under all steady-state and state-changing conditions is a substantial challenge. The controller speed, the input sensor data, and solenoid driver capability must be improved The first use of Direct Control was in a four-speed unit described in a 1989 SAE Paper, #890529, The All-Adaptive Controls, etc. This unit demonstrated simplified hydraulics and mechanics by eliminating most of the hydraulic functions (only five valves; four solenoid valves) and avoiding the use of over-running clutches and engine-braking clutches for all shifts (the four-speed had fewer parts than a three-speed). Its use of high-flow PWM solenoids caused some concerns initially because they were audible outside the vehicle; later development eliminated the noise problem. Most of the later direct control designs use VFS solenoids because their cost/performance has improved substantially, the VFS open-loop pressure control can be more accurate, and they are not a noise problem. With morerecent five- to seven- speed transmissions, multiple-gear kickdowns become highly desirable, and these are difficult to accomplish well without direct clutch control. Moreover, with the additional gears, the complexity of control becomes difficult to manage without direct control. Multiplexing is frequently used to minimize the number of solenoids required, and it can also aid in providing failure mode control. Figure 8.5.6, Direct Electronic Shift Control, shows the system used in Direct Control.

Fig. 8.5.6  Direct electronic shift control. Other types of controls are in use or being developed for different classes of transmissions, e.g., the CVT, the DualClutch Layshaft transmission, and transmissions for hybrid powertrains. These controls present many new challenges, but the designs at this time are very design-specific, and are not covered in this edition. Maurice Leising, September 2007

8.6 Transmission Operational Features The introduction of electronic controls has led to a substantial increase in new transmission operational features. The low cost of incorporating electronic logic makes it practical to address issues which were previously just tolerated. These new features usually fall into one of the following categories: • • • • •

Shift Scheduling Quality Improvement Powertrain Efficiency Service Multiple System Features

The cost of providing the inputs needed for a feature is typically the major consideration. Features that need driver input face extra challenges. Driver interface elements must compete with entertainment systems, navigation systems, climate control systems, cruise control, etc. for space in the steering wheel/instrument panel area. Additionally, their function must also be simple and intuitive enough so that most drivers understand their purpose, which can be difficult with technology-intense powertrain features. The advent of high speed, inter-system communication links also makes some input data less costly and more available. It also makes it

Although beneficial for all types of controls, certain transmission hardware characteristics have proven to be crucial to control when using direct electronics. Examples of these characteristics include continuously filled hydraulic lines, fast-responding hydraulics and solenoids, friction element system gain control, and hydro-dynamically balanced rotating clutch apply chambers.

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possible to provide multiple-system features. As the different automotive systems add capability, the transmission controls engineer needs to continually examine the data and capability available to determine whether desirable new features can be developed. Some of the features discussed below could not have been achieved just five years ago.

8.6.1

include modifying the shift point based on time-in-gear (to avoid too-rapid upshifts) and based on estimatedtime-to-start-shift (to shift at a precise maximum engine speed). Stay-In-Gear on Turns—For improved driveability, the presence and severity of turns are determined by the use of additional sensor data, and the schedules are modified to reduce busyness and improve performance feel. Manual Gear Selection—A mechanism and/or switches are provided so that drivers can select an operating position where they can choose a gear higher or lower than the current gear, typically with a small, push-on gear lever. Logic is usually provided which can override the selected gear to protect against engine overspeed, excessive lugging, excessive clutch torque, etc.

Shift Scheduling Features

Section 8.4—Scheduling, Grades, Driver Preferences, and Driveability—presents a number of shift scheduling features, the logic for feature development, and a description of the feature operation. Some of those features are repeated briefly here just to complete the coverage. This category has had the most activity because the use of electronics enabled the capability and the shift scheduling task is very subjective in nature. Some examples are:

Other shift scheduling features could be developed which take advantage of GPS information in case such systems become available in enough volume to make the feature attractive to offer. This information could reduce shift busyness and provide additional engine braking if approaching curves and/or grades were known. Similarly, fuel economy could be improved with GPS information. Vehicle loading information could also be used to improve shift scheduling.

Gear Selection on Grades—Hunting between gears can occur under many load conditions at a constant speed on significant grades (ref. Section 8.4.3). A number of different approaches have been developed to resolve this objectionable operation; some adjust the shift schedules, and others calculate the ability to maintain speed before upshifting. Additionally, on downgrades, overspeed may occur; downshifts are sometimes made to increase engine braking and control overspeed. Performance/Normal/Economy Mode—A switch is provided for the driver to use to directly select from two or more different shift schedules. Switches have also been provided by some manufacturers to prevent “Overdrive” operation and to provide special schedules for “Trailer Towing.” Driver-Adaptive Shift Scheduling—Through rapid throttle movements and/or higher average throttle during accelerations, aggressive driving is observed. With this type of driving, upshifts are delayed and kickdown shifts are made more sensitive for a better performance feel. Conversely, with slower throttle movement and/or lower average throttle openings, the upshifts are earlier and kickdown shifts take more throttle movement (ref. Section 8.4.6), as with an “Economy” mode. This feature attempts to provide the merits of the previous feature without the use of a driver-operated switch. Condition-Sensitive Shift Scheduling—Special schedules are provided for cold ambient operation, warm-up, and hot oil temperature operation. Unique “Cruise Control” schedules are provided or the schedules are modified, with cruise operation to minimize shifting and reduce the torque disturbance with shifting. Other examples

8.6.2

Quality Improvement Features

The availability of electronic logic has provided substantial improvements in quality for many transmission functions. Several examples are described: Shift Torque Adaption for Speed Change Rate or Time—Shift quality is one aspect of transmission operation that has benefited greatly from electronic logic. Contributing to this is the fact that clutch frictional torque tends to vary significantly from part to part; additionally, clutch friction is subject to changes over the life of the transmission. Moreover, durability requirements meant that the design level of clutch torque for hydraulically controlled transmissions had to be adequate for the life of the transmission. These factors combined to cause most shifts to be calibrated with more torque than was desired for good shift feel. Electronic logic has the ability to measure the shift and use more or less torque, as required for shift feel and durability, thus allowing for the use of the correct torque for each shift. Good shift measurement, however, requires measuring the transmission input speed. Most gear train configurations in the late 80s had no sensor access to the input shaft, and, therefore, could not obtain an input

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speed measurement (determining input speed from measurements of other elements has been done by some successfully). Therefore, for most manufacturers, full use of this capability was not realized until a new or significantly modified transmission (which provided for measurement or determination of input shaft speed) was put into production. Some manufacturers use the rate-of-speed-change to control shift torque in real time; others use the total-shift-time to adapt a calibrated torque level for best shift quality. By adapting the torque level, shifts with high energy dissipation are avoided, and good shift quality for the life of the transmission is the typical result. Shift Torque Adaption for Oil Temperature, Low Range Selection, and Throttle Changes—The torque or oil pressure used for shifting is revised for cold and hot temperatures, for “low” range transfer case selection, for sudden changes in throttle level, and for other unique conditions that benefit from a different-than-normal torque for any given shift. The ability to adapt to different operating conditions has improved the overall quality significantly. Torque Management for Clutch Life and Shift Feel—Engine torque management was initially developed to reduce energy dissipation and, therefore, the size of the clutch pack needed to handle WOT upshifts for high-output, high-speed engines (ref. Section 8.2.5.1.5). The use of torque management, however, was also noted to be able to improve the shift feel, and it has since been applied to most upshifts and many other shifts as well.

8.6.3

thereby improve powertrain efficiency under many lightload and low-vehicle-speed conditions. The continuous slip in the clutch prevents the combustion-cycle-induced crankshaft speed variations from being transferred to the rest of the drivetrain where the speed variations will cause vibrations and noise. Torque converter clutch capacity is regulated to maintain the desired level of converter slip. This is a challenging feature for the powertrain and requires simultaneous development of the software, the converter clutch, the mounting system, and other hardware systems. The vibration isolation is effective, however, and has been used to prevent disturbances from A/C engagement, and other engine events such as switching the number of working cylinders. Neutral Idle—This feature detects the closed-throttle, stationary-in-Drive condition and places the transmission essentially in neutral to reduce engine load at idle for reduced fuel consumption. Providing a smooth subsequent drive-away torque and avoiding rollback are two major Neutral Idle controls challenges. Directional output speed sensing and brake pressure sensing may be required for Neutral Idle. Transmissions with direct electronic clutch controls have Neutral Idle hardware capability. Hydraulic changes are required to allow indirect electronic controls to disengage the necessary clutches while the manual valve is in Drive position. Deceleration Fuel Shut-Off—DFSO seeks to reduce fuel consumption by shutting off all fuel when the engine has sufficient speed that it will restart by simply turning on fuel, and spark when engine power is needed. By modifying converter clutch control and the shift schedule, the car speed range over which DFSO can be used is extended significantly. New control strategies are required to provide appropriate engine-braking and to avoid engine stall or hesitation during DFSO and power off/on transitions.

Transmission Efficiency Improvements

The capability provided by the electronics has led to the development of numerous ways to improve driveline efficiency; some of those are described: Adaptive Line Pressure—Driving the hydraulic pump is one of the major parasitic losses in an automatic transmission, and the loss is proportional to the pressure maintained. Steady-gear line pressure needs to be at the proper level for the current input torque, minimized for efficiency, but sufficient to prevent durability issues associated with excessive clutch slippage. Adaptive line pressure “learns” the optimum line pressure to command at each throttle and gear condition by allowing only a momentary slip when a throttle tip-in occurs from that operating condition. Controlled Slip for the Torque Converter Clutch—Maintaining a small amount of slip in the converter clutch can allow the clutch to be engaged at much lower engine speeds and

8.6.4

Service Improvement Features

The use of electronic controls increases the types of components that may require service, but the logic capability of the electronics can greatly improve the speed and accuracy of the service experience. Diagnostic Capability—Electronics provide the ability to identify out-of-range component data and store appropriate fault codes for retrieval by service personnel. They can also store the vehicle conditions existing at the time of the fault; this frequently will separate mechanical faults from electronic or data faults. Some even store a histogram of temperature and/or torque which can

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also be retrieved to improve diagnostic analysis. Some execute a brief test exercise when certain faults occur to identify whether the bad data is a correctable anomaly or a hard fault. Some run a model of certain parameters during vehicle operation and compare the measured data to the model to ensure that the data is reasonable. Failure Mode Management—The logic can evaluate failures that occur and select an operating mode which provides the greatest capability in the presence of that failure. This may avoid one gear, use of the converter clutch, or it may require a complete shut-down (which typically means a forward gear, neutral, and a reverse gear are available). The logic may also manage its way around a given failure by substituting model data or executing a function in a nonstandard manner. This ability provides safe and appropriate system function with identified failures that avoid stranding the customer whenever possible. Other Functions—Some run a program during the full vehicle operation which predicts the condition of the automatic transmission fluid (ATF). It bases the estimate on a formula that uses time, temperature, and operating conditions. Others implement a histogram to acquire data on oil temperature, torque, gear, operating condition, etc. The data can be retrieved to better identify the service condition and/or other special purposes.

8.6.5

dissipation needed by the brake system and amount of torque reduction required from the engine. Using all three systems typically allows the traction system to be used over the full range of vehicle speeds, rather than just at less than 20 mph. Stop/Start Operation—Stop/start operation involves stopping the engine during idle conditions to reduce fuel consumption. This requires a rapid restoration of power when the throttle is opened. This means that the transmission must be ready to provide drive when the engine re-starts. Therefore, the clutch is kept applied at very low capacity with some auxiliary power source. The transmission may also be used to supply some hill holding torque during the “idle” condition. Future feature developments will likely address issues such as vehicle systems’ temperature control, component failure management, hybrid drive management, etc. Only the limit of the engineer’s imagination will control the future of transmission feature development. Maurice Leising, September 2007

8.7 Automatically Shifted Manual Transmissions Most people know that cars come with two basic transmission types: manuals, which require that the driver change gears by depressing a clutch pedal and using a stick shift, and automatics, which do all of the shifting work for drivers using clutches, a torque converter, and sets of planetary gears, and some kind of control system. Each offers its own set of advantages: smoother and easier operation for the automatic versus better economy and more driver control for the manual. Recent emphasis on fuel economy and the increased logic capability of electronic control have led to explorations of the middle ground between these two types.

Multiple System Functions

The increased availability of high-speed, inter-system vehicle data links will lead to more system features in this category. Current examples include: A/C Clutch Engagement—In some applications, simply adjusting engine torque is not sufficient to hide the engagement bump of the A/C clutch when the converter clutch is engaged. By starting controlled-slip operation in the converter clutch before the A/C engagement occurs, the engagement disturbance is completely hidden. The complete event is typically accomplished in less than one second. Variable Displacement Engine—In a similar manner to the above feature, controlled-slip operation is used to hide the disturbance that occurs when the engine activates or deactivates cylinders. Certain transmission data may also be used to determine when deactivation is used, and the shift schedule may be adjusted as well. Traction Control Systems—These systems reduce wheel torque to prevent excessive tire slip. This torque reduction is achieved with brake application, engine torque reduction, and transmission upshifts. The upshifts reduce the heat

8.7.1

Automated Manual Transmissions (AMTs)

An automated manual transmission is simply a manual gearbox mated to an electronically controlled clutch and either a manual or automated shifting mechanism. They have not been covered in previous editions of this book because they were considered more Manual than Automatic. The Powershift transmissions, discussed below, are comparable to other automatics and are, therefore, included in this chapter. The control challenges with AMTs include proper use of the single input clutch during launch and shifts, positioning synchronizers, and coordinating engine speed and torque for

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optimum smoothness and durability. Control and actuation of the synchronizers may be via hydraulics or a mechanical system of cams and electric motor(s).

improvements. This, of course, is the primary drive behind this development. Figure 8.7.2.1 shows a simplified DCT schematic. The two clutches are linked to separate concentric input shafts. In this example the rear clutch is linked through the outer hollow shaft and drives gears 1, 3 and 5. The front clutch is linked through the inner solid shaft and drives the gears 2, 4, 6, and Reverse.

AMTs offer the fuel economy advantage of a fully manual transmission with the convenience of an automatic. The AMT is cost-effective because it is able to use a conventional transmission without modifications to the existing gears and shafts. However, it suffers from the manual transmission’s characteristic power interrupt during the shift. To shift, the clutch must disengage to remove the torque from the driving gears; then the synchronizer can move from the lower gear to the higher gear; and finally the clutch can re-engage to apply torque to the higher gear. This results in a noticeable dip in acceleration because there is no output torque for a significant period of time. Even with good control, shift feel is no better than that of a “well-shifted” manual with its neutral interval. AMT shifts are therefore not as smooth as a conventional automatic or the Powershift DCT concept discussed next.

8.7.2

With the DCT arrangement, all regular shifts must be from one clutch to the other; this means that a shift from 6th to 4th involves a 6-5 shift and a 5-4 shift because the front clutch drives both 6th and 4th. Some transmissions make the 6-5-4 shifts in one event, but it requires complex control logic and coordinated engine torque management. Patent # 6869382—Double-Downshift Gear Strategy for a Dual Clutch Automatic Transmission—describes one approach to accomplishing a 6-5-4 type shift.

Powershift Transmissions (Dual-Clutch Transmissions)

To achieve shift quality that can be comparable to an automatic, the dual-clutch transmission (DCT) configuration was developed to provide continuous power flow during shifts. The DCT is basically two manual transmissions “in parallel” with two input clutches. A six-speed consists of two manual transmissions, one will have the odd ratios and the other will have the even ratios. While in a given gear, the other box is synchronized for the next gear via either hydraulic actuation or cams and motor(s). The shift to the next gear is then accomplished via a controlled swap of input clutches. No neutral interval is involved because the synchronizer is engaged before the clutch swap begins.

Fig. 8.7.2.1  DCT schematic with dry clutches. The DCTs required some unique new strategy features: Launch Clutch Control The input shaft from the engine is connected through the damper with the outer plates of both clutches. When starting the engine or from a stop, the first gear is always engaged. Since the rear clutch is open, there is no torque transfer to the wheels. When the rear clutch is being closed, the outer plates of the clutch are getting into slipping contact with the inner plates, smoothly starting to transfer the engine torque through the hollow shaft, gear set, and synchronizers of the first gear to the differential and finally the wheels. The challenge is to coordinate clutch capacity, engine torque, and rpm to provide a creep feel and launch feel that is smooth, consistent, and “converter-like.”

The DCT control challenge is to achieve acceptable smoothness, response, and durability through the use of input clutches and synchronizers during launch and during shifts. This contrasts with the torque converter for launch and the continuously engaged planetary gearing of conventional automatics. Additionally, the DCT must deal with the rigid characteristics of a manual-type driveline without any fluid damping elements. With the use of a launch clutch instead of a torque converter, the efficiency losses of the torque converter are avoided, and the fuel economy is improved. Some are using dry launch clutches, rather than wet clutches, and this eliminates the need for any hydraulics so the parasitic losses of a hydraulic pump are also avoided, which gives further efficiency

Active Hill-Hold Control The control must determine when it is appropriate to use Hill-Hold, and provide sufficient torque to hold the vehicle

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8.7.3

stationary at closed throttle on hills up to certain grades. The grade is close to an equivalent grade which a torque converter would hold.

Powershift Concept Study

A recent SAE Paper, 2007-01-1096, “Double Clutch Transmission (DCT) using Multiplexed Linear Actuation Technology and Dry Clutches for High Efficiency and Low Cost,” presents a concept study of Powershift transmission design. Although as with any study of this kind, its long-term value is limited because of the lack of hard data, it does cover many issues related to the DCT concept, including the actuation hardware. It is presented here, not to endorse the concept selection, but to provide relevant information on the significant differences of the DCT concept to anyone interested in powershift transmissions.

Launch Clutch Energy Control The controls must detect extreme clutch energy conditions, such as extended steep hill-hold (using throttle), simultaneous brake and throttle application, and repeated high-energy launches. They must avoid launch clutch damage by taking actions to warn or discourage the driver from the current action, and/or to reduce energy input to the clutch. Such actions could be taken when the inferred or sensed clutch temperature approaches a permanent damage threshold.

Double Clutch Transmission (DCT) using Multiplexed Linear Actuation Technology and Dry Clutches for High Efficiency and Low Cost

Synchronizer Control With DCT, synchronizer control provides additional challenges. The synchronizers must be pre-positioned before the shift starts. The challenge is to predict the next gear as often as possible, and to also handle change-mind shifting correctly. Consistent and minimized average shift delays are the goals. Advancements in actuation systems that speed synchronization will continue to help with this challenge. As with launch clutch control, synchronization may be electro-hydraulically controlled or electro-mechanically controlled. Cost, speed, and accuracy are all critical factors.

SAE Paper No. 2007-01-1096 By J. C. Wheals, A. Turner, K. Ramsay, A. O’Neil, J. Bennett, and Haiping Fang, Ricardo Driveline and Transmission Systems, Ricardo Plc. 8.7.3.1  Abstract Stemming from predictions made for transmission adoption and subsystem volumes up to 2020 for the EU market, a concept study and recommendations are presented for a six-speed 200-N. m powershift transmission covering the following: specific new features for low cost and high efficiency applied to a DCT; novel, direct-acting electromagnetic linear actuators for modulation of clutches and shift rails; and mechanical multiplexing to allow control of both clutches and shift rails using two linear actuators only.

Although electro-mechanical actuation designs for DCT transmission are still in a relatively early stage of development, there are some general comments that can be made regarding the actuators. By their nature, dry clutch designs require simultaneous control of two clutch applications and the shift synchronizers to perform a shift. Small, compact brushed or brushless DC motor actuators can be used to perform clutch and shift synchronization control. In the case of the brushless motor approach, commutation is controlled by software and requires more complex electronic controls, increasing cost. Brushed motors use simplified electronic controls and are lower in cost, but long-term durability and generally a larger packaging envelope could be issues. Whatever the choice, the motor design needs to be optimized for electrical load efficiency and low power consumption. Figure 8.7.2.2 shows a typical brushless DC control motor.

8.7.3.2  Introduction The paper describes the technology options, both existing and novel, that were reviewed at the first stage in the definition of a powershift transmission product targeted at Bclass vehicles prior to the build of a demonstrator vehicle. A double clutch transmission (DCT) architecture was adopted in the first instance along with conventional shaft-operated synchronizer assemblies. This left the areas of actuation and the twin clutch module for investigation to achieve cost and efficiency targets relative to the successful hydraulic DCT fitted to VW vehicles. The VW transmission, known as DQ250, has been very thoroughly analyzed from both mechanical and control perspectives [1], allowing well-founded estimates to be made of relative performance and to judge which subsystems may be revised to meet the anticipated requirements in lower-cost vehicles. While primarily focused upon application to DCT architectures, subsystem alternatives are discussed with regard to their suitability for application with automatic transmissions (ATs).

Fig. 8.7.2.2  DCT actuator.

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8.7.3.3  Market Perspective

Figure 8.7.3.2 shows the results of scoring each of the transmission types for each of the attributes. Each transmission type was scored both for attributes and a cost estimate to include anticipated product evolution and improvements in manufacturing efficiency. Generally, it is seen that the overall score for each transmission declines. This arises from factors such as the likely decay of sub-brand cache associated with DSG™, as indicated.

Figure 8.7.3.1 shows a prediction of the market share of different transmission types within the EU up to 2020. Generally, MTs are seen to lose share to automated layshaft transmissions with either torque interrupt (AMT) or powershift (predominantly DCT) characteristics.

Fig. 8.7.3.1  EU transmission prediction (sales).

Fig. 8.7.3.2  Transmission ratings to 2020 EU.

However, with the DCT category, it can be strongly argued that subvariants will be developed to suit lower-cost vehicles in the EU, Asia, China, and Brazil. From discussion with OEMs and Tier-1 suppliers, Table 8.7.3.1 shows the anticipated change in emphasis that may be applied by end users to a range of weighted attributes relevant to the transmission. The attributes were selected to reflect the reason for choosing a particular transmission type for vehicles in which more than one option existed. In 2006 it is seen that ease of use provided by automation has the same emphasis as fuel economy and shift quality combined. However, by 2020 many attributes may become expected as standard and so drop out of the list of selection criteria, leaving fuel economy and shift quality as the only differentiators. Table 8.7.3.1

Of course, this is not an exact predictive process, but it is more substantiated than mere extrapolation from current sales trends; taken with the prediction of powershift transmissions in Fig. 8.7.3.1, it appears that a low-cost DCT is a suitable product to fill the highlighted gap. 8.7.3.4  Technical Approach The paper will argue a solution: features to reduce transmission length, novel electrical actuation for combined clutch modulation and gear engagement, dry clutch arrangements with novel latching devices, and anti-rollback features to reduce sustained clutch slip. The preferred solution is then supported by detailed simulation of fuel economy.

Transmission Attribute Weightings

Consumer/OEM Vehicle Attributes

Weightings

Anticipated Changes in FE Emphasis Fuel Economy Shift Quality (Comfort, Sporting) Ease of Use: Automation Ease of Use (Hill Start, Creep) Launch Performance Compatibility with Paddles/marketable HMI Consumer trans type recognition/preferences Number of gears: market appeal

8-50

Year 2006 EU

Year 2020 EU

0.15 0.15 0.3 0.05 0.15 0.1 0.05 0.05

0.7 0.3

Automatic Transmission Controls

8.7.3.5  Shaft and Gear Layout Figure 8.7.3.3 shows the layout of a typical MT with length dimensions to be used as a comparative reference for the powershift arrangements. The MT has an approximate length of 286 mm.

Fig. 8.7.3.5  Four-shaft DCT layout. Currently, a transmission with a length of 325 mm will fit many B-sector transverse powertrain vehicles, but as has been shown, this is a severe challenge for even high-cost wet clutch DCTs with four-shaft designs. Further, it is inevitable that further package reductions will result from even modest increases in the under-bonnet volume occupied by longitudinal crash members. For longevity of the design, an ambitious target of 310 mm for a double layshaft arrangement was adopted for the project, assuming use of conventional synchronizers and dogs, and avoiding highly compounded arrangements.

Fig. 8.7.3.3  Typical MT layout and dimensions. A typical DCT is shown in Fig. 8.7.3.4, and it is seen that the addition of a nested wet clutch and actuation increases the length to 351mm, even with slightly optimistic estimates of the axial size of the clutch module and its local actuation elements. This is an increase of 65 mm over the standard MT. Figure 8.7.3.5 shows a four-shaft DCT arrangement as a means of reducing the transmission length, albeit at considerable additional cost. Again with the same optimistic estimates for the clutch module and actuation, a length of 328 mm is achieved, which is 42 mm longer than the MT.

Further Design Considerations The following experience-based subtleties were considered during to the development: deviation from geometric ratio progression is required for optimized automotive applications. Specific features may appear advantageous in terms of reducing the number of meshes required, but this economy may reduce the flexibility to define gear ratios independently. The additional inertia of highly compounded gear trains will place additional load and thermal requirements upon synchronizers. Introducing multiple meshes also reduces efficiency and increases not only the absolute value of backlash, but more importantly the degree to which it is apparent to the driver. The mechanical shaft interface between the engine and transmission should be a torque-only coupling without radial, bending, or axial loads. A DMF is usually fitted to reduce longitudinal shuffle. Gear rattle may be reduced as a secondary function of the DMF. 8.7.3.6  FMEA and Safety Constraints

Fig. 8.7.3.4  Typical DCT layout and dimensions.

Review will be restricted to actuation of the clutches and actuation of the shift rails; specifically, the following concerns will be addressed: double gear engagement on the same 8-51

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shaft, and sudden loss of electrical power. In both these cases, physical trials have been undertaken to establish the probability of occurrence and severity.

belonging to one half of the transmission is not required. The actuation system for the clutches and rails substantially defines the shift quality and a large proportion of the transmission cost. Hydraulic control has been applied to the first mass-produced DCT, but as is discussed later, this attracts a high cost penalty. The paper will later describe how the shift processes may be achieved with just two main actuators and review the preferred solutions.

Double Gear Engagement Can two gears be engaged on the same shaft, and what is the consequence if it were to happen? Detailed simulation indicated that the phenomenon could arise, but engineers were skeptical as to the real likelihood. Full rail engagement force was applied to the open dog with representative tooth spacing within a transmission rig simulating a DCT. Several hundred engagements attempts were rejected prior to a successful engagement that resulted in the catastrophic fracture of the rig. As result of this work, it was judged that some form of interlock is required.

Actuation Load Requirements Clutch Actuation Appendix 1 shows a rudimentary calculation of the loads associated with a single-plate dry clutch, indicating that a clamp load of approximately 3 kN is required with a friction coefficient of 0.35. Various forms of mechanical advantage could be applied to reduce this load to ~1 kN, which as will be discussed, equates to a typical shift rail force. Depending upon the spring configuration, a dry clutch could be energize-to-open or energize-to-close. However, the full clamp load could be sustained by a substantially lower actuation load if a nonlinear application spring or other over-center device is applied.

Loss of Electrical Power One consequence of the loss of electrical power would be the inability to actuate the clutches or shift rails. The requirement for power shifting in which both clutches are simultaneously active precludes clutch interlocks, so a condition in which both clutches were closed with each shaft carrying an engaged gear is possible and must be considered. This could arise just prior to a shift when the next gear has been pre-engaged with its associated clutch in an open state. Physical tests showed that the clutch coupled to the higher gear (3rd) slipped, and that the clutch coupled to the lower gear (e.g., 2nd) remained clamped with no slip. While alarming to the driver, the vehicle remained marginally stable and came to a halt under control. However, in traffic conditions an accident was judged probable. In the fail condition, it is not possible to disengage a gear (even if the rail actuators were active) because the mechanical path between the clutch would be transmitting the torque equivalent to the lowest value of each clutch capacity and its associated gear ratio. Further, modulation of engine torque would have no influence and could not cause the dogs to be momentarily unloaded to allow disengagement. In summary, the use of clutches that fail closed can have a serious but not catastrophic consequence for DCTs using conventional positive gear engagement devices such as dogs. It is shown later in the paper that significant fuel economy advantages arise for clutch arrangements that are sprung closed or are in some way latched; for such systems the same arguments would apply.

Shift Rail Actuation Figure 8.7.3.6 shows a 1-3 gear cluster from a VW DQ250 with annotations of the elements and travel.

Fig. 8.7.3.6  Synchronizer assembly. Rig test data of a similar unit is shown in Fig. 8.7.3.7. During the main synchronization period, i.e., the region between the dashed lines, the force on the shift rail increases to ~1 kN. Throughout this period, the rail velocity is zero as the rail force is applied, via the selector fork, to the synchronizer to equalize the gear and shaft speeds before engagement. Thus, a linear actuator for controlling the shift rails is required to have a peak force capability of 1 kN and a maximum stroke of 16 mm.

8.7.3.7  Actuation Requirements The following actuation modes provide adequate DCT powershift functionality: simultaneous control of both clutches, simultaneous control of one rail for odd gears and one rail for even gears, simultaneous control of the clutch and a rail 8-52

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Fig. 8.7.3.7  Recorded synchronization data.

8.7.3.8  New Actuation Technology

8.7.3.9 is relatively flat over the rated stroke compared to, for example, solenoid-type actuators. The direction of the thrust force is determined by the polarity of the coil current, while the shaft is easily supported and the armature may rotate in its bearings without affecting performance.

Moving Magnet Linear Actuator Figure 8.7.3.8 provides a schematic of a novel electromagnetic alternative to hydraulic actuation, which has particular suitability for transmission applications. Defined as a singlephase moving magnet linear actuator (MMLA), it is able to provide proportional force control within its travel envelope and exceeds the objective of providing 16 mm travel at 1000 N within a volume of 100 mm axial length by 76 mm diameter from a 12-Vdc source. A tubular actuator topology was selected because it has no end-windings and zero end-leakage flux, which is an important consideration as the actuator is required to operate in an environment that may contain ferrous particles. Of the various short-stroke linear actuators that were investigated, single-phase, moving-magnet designs were shown to have the highest force density while also being robust (no flying leads) and offering a low thermal resistance path to ambient for the phase winding (coils mounted on the stator). Also, the actuator force displacement characteristic shown in Fig.

Fig. 8.7.3.8  Moving magnet linear actuator.

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Fig. 8.7.3.9  Force/travel characteristic. Rig Test of Actuator

Fig. 8.7.3.11  Actuator current and force on selector rail during a gear-to-gear shift event.

The control scheme was developed using a synchronizer durability test rig, as shown in Fig. 8.7.3.10. The total selector rail stroke of the rig was 16.6 mm (gear-to-gear), with a pair of triple cone synchronizers, each with mean cone diameters of 69.3 mm, 64.2 mm, and 57.2 mm, respectively, a cone angle of 7°, and a tooth chamfer angle of 44.5°. The engine input was represented by an induction machine, which drove a large flywheel to ensure constant input speed while synchronization was in progress. Figure 8.7.3.10 shows the test rig in which the left-hand synchronizer is connected to ground via a load cell and the right-hand synchronizer is connected to an inertia disk of 0.03 kgm2. In this configuration, by moving the selector rail to the right, the inertia disk is accelerated from standstill to the engine speed, and by moving the selector rail to the left, the inertia disk is accelerated from engine speed to standstill. A load cell, which is in series with the actuator, measures the force applied to the selector rail, while the selector rail displacement is measured via a linear variable displacement transducer (LVDT), and the actuator current is measured with a current transducer. Figure 8.7.3.11 shows the actuator force and current during a shift. Note that the peak force of 400 N is lower than would be required for a single-cone synchronizer.

8.7.3.9  Subsystem Solutions Having established outline requirements and constraints for the transmission, this section will discuss the main subsystems. Twin Dry Clutch Module The additional length of the second clutch was estimated at +65 mm, which would exceed the packaging targets. Nesting (concentric location) of the two clutches was investigated to assess the geometric and thermal feasibility. In such an arrangement, 1st and reverse gear would be on the layshaft coupled by the larger, outer clutch because that has the highest duty. Figure 8.7.3.12 shows a line diagram of a nested clutch module in which the clutches could be sprung open or closed.

Fig. 8.7.3.12  Nested twin dry clutch module. Fig. 8.7.3.10  Actuator on synchronizer rig. 8-54

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Although the duty of the inner clutch would be substantially lower than the outer, significant thermal dissipation must be ensured. Clutch cooling, especially of the inner clutch, has been considered, but this will not influence the size of the iron elements that are dictated by instantaneous sinking requirements. The following design variants may apply: a dual-plane driven plate has been applied to reduce length, but this could be single-plane instead. Actuation could be sprung open or sprung closed or a combination of the two. Application forces are reacted to the driven plate, which is reacted on DCT input 1 ensures no loads are applied to the engine crank. One or both couplings could include multiple plates. The arrangement could include an impeller and controlled louvers for cooling. To improve heat rejection, aluminum vanes may be fitted to rotating components and to the bell housing. Beyond the preceding review, the design should ensure that lube is prevented from contaminating the dry clutch facings. This may necessitate the use of deflecting shields to counter the possibility of leakage past the seals on the input shafts.

the clutch facings is dependent upon the shift quality target for the shift. A very smooth shift introduced more energy. In this case, given the target vehicle for application of this transmission, is would be possible to progressively reduce shift comfort to control the clutch temperature.

Design Considerations for the Clutch

Design Considerations for Clutch Control

Fig. 8.7.3.13  Interim design for compact nested twin dry clutch. Clutch Actuation The control requirements for wet and dry clutches are fundamentally different: pressure control is applied to wet clutch packs, positional control is applied to dry clutches controlled via long-travel diaphragm springs. Particularly with dry clutches, wear compensation and thermal expansion must be accommodated.

Appendix 1 gives dimensions for the inner and outer clutches and shows adequate torque capacity with a standard friction material that would exhibit the stable negative mu/ temperature characteristic required for good control. The unit pressure is within the capabilities of a standard facing material. Figure 8.7.3.13 shows an interim layout. A detailed model which includes thermal characteristics in addition to the dynamics of clutches and synchronizers shows that the thermal capacity of the inner clutch is marginal for the case of repeated full-power launch from rest to 100 kph. The test involved three repeats with a 10-second delay between each launch. As would be anticipated, the thermal limit of

Actuation Configurations The choice of MMLAs as actuators dictates that they may be preferably mounted remotely from the clutch module for the following reasons: higher currents would be required to counter elevated coil temperature, the choice of magnet tech-

Fig. 8.7.3.14  Clutch actuation using sealed hydraulic column. 8-55

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nology and associated cost changes according to the Currie point, assuming dual function (clutch and rails), the device may be located close to the shift rails to minimize linkages. This section of the paper now describes some alternatives. Lever Arm with Pivot The conventional arrangement of a lever arm and a nonconcentric actuator could be applied but would suffer compliance, hysteresis, and introduce additional components. Concentric Pistons Figure 8.7.3.14 shows an arrangement compatible with concentric pistons with a closed hydraulic linkage to the actuator. For this arrangement with a closed hydraulic column, sustained pressure may cause leaking of a sliding seal that has acceptable friction, leading to the suggestion that a fully closed column with a rolling membrane seal would be preferred.

Fig. 8.7.3.16  Twin dry clutch module. Shift Rail Actuation Multiplexed Actuator: “Crane” DCT Actuator

Sliding Pivot

Current DCTs use individual hydraulic actuators on each (of four) shift rails. This requires a large number of valves to operate such a system. This could be multiplexed to reduce the valve count and cost. Ricardo’s novel “crane” actuator significantly reduces actuator and valve part count and cost. This was successfully demonstrated on the Chrysler ME4-12 in 2005. The cross gate valve is used to locate the cross-gate position into which a pin is forced from the head of the rail actuator. The specific rail is moved, and when in position, the pin is withdrawn leaving the rail located under the action of simple spring detents. The actuator then moves to perform the next rail task. Figures 8.7.3.17, 18, and 19 show details of the arrangement and its application vehicle.

An ingenious arrangement using a moving pivot point has been proposed by LuK [3]. Figure 8.7.3.15 shows the actuator with a motor driving a power screw, which moves the radial location of a pivot element. In this way the actuator load to achieve a given clamp load is reduced. Another benefit appears to arise from the low energy requirement to maintain a chosen state. Figure 8.7.3.16 shows the installation of two such devices to control the apply/release bearings in a tandem dry clutch module. The following general comments may be made: power screws introduce backlash and friction, which are detrimental to control; a highly geared motor may not provide the high frequency modulation required to perform a smooth clutch-to-clutch shift; location of the motor in the high-temperature area of the bell housing may reduce motor performance; one motor, gearing, mechanism, and associated power electronics are applied for each clutch and appear to perform no other task, such as the control of shift rails. This redundancy appears inefficient.

Fig. 8.7.3.17  “Crane” shift actuator—hydraulic. Fig. 8.7.3.15  Clutch actuator. 8-56

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Fig. 8.7.3.20  Multiplexed actuator for gears and clutch.

Fig. 8.7.3.18  “Crane” shift actuator—rails, forks.

Figure 8.7.3.21 shows one complete half of the actuation scheme for the DCT comprised of the following: one actuator, hydraulic column to actuate the clutch with a remote latch (discussed later), and a means of shift rail selection. This minimum content arrangement contrasts with other approaches of locating medium performance actuators for each actuation task. Clutch Latching Technologies The use of an MMLA as the clutch actuator will require a latching arrangement to allow the device to be unpowered during vehicle usage except when modulating the clutches or actuating the shift rails. There are fundamentally two forms of mechanism which provide function equivalent to a latch: series clamps and parallel load path. Important subtleties such as latch release under failure modes must be considered. Further, the device may rotate with the clutch once set or it may be applied remotely via a continuously applied bearing. Figure 8.7.3.22 [4] shows a latch of category “set-reset series load clamp.” Although not a specific advantage for DCT application, the ability to control the latch by the same actuation source as the clutch piston may be preferred for applica-

Fig. 8.7.3.19  Chrysler ME4-12. (Courtesy of Ricardo DCT) Multiplexed Actuator Continuing the theme of hydraulic multiplexing, Fig. 8.7.3.20 shows an approach of selecting one of two rails under the action of two simple solenoids with no risk of double selection. Later, a preferred arrangement for selection of multiple gear and clutch elements is discussed using a low-torque rotary actuator attached to the linear actuator to move a selection finger.

Fig. 8.7.3.21  Overall scheme with clutch latch. 8-57

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tions in ATs where actuation access is often confounded by multiple rotating members. While enjoying this significant advantage, they do suffer the drawback that they fail to their current state if actuation pressure is lost. The device operates according to the following sequence similar to that of a Biro pen: the same mechanism applied to each clutch (press on, release momentarily to latch, press off), piston overtravel, for latching, is achieved with a “heavy duty” Belleville spring between piston and clutch plates; and a separate “light duty” conical spring is used for latch mechanism control. To modulate the clutch opening from a latched closed state, the control strategy would first apply pressure to unlock the clutch; once unlocked, pressure decay is controlled in the normal way.

Fig. 8.7.3.23  Clutch latch: marginally stable type.

Fig. 8.7.3.24  Clutch latch: electromagnet. Preferred Multiplexed Actuation of Clutch and Rails with Clutch Latching Figure 8.7.3.25 provides a scheme for the operation of a DCT comprised of four shift rails and two clutches using two linear actuators. This has been arranged as two similar modules with unspecified means of selectively connecting the actuators to the clutches or gear-shift rails.

Fig. 8.7.3.22  Press-on press-off clutch latch. An alternative approach applies a latching function at the remote end of the linkage (such as a closed hydraulic column, cable, or series of levers) and would therefore require the continuous running of an apply/release bearing. This would cause parasitic losses and would require that the bearing be sealed and of a higher life specification than intermittently operated release bearings found in MTs. Shown in Figs. 8.7.3.23 and 24 are two potential solutions, both of which fail open in the event of electrical power loss. Figure 8.7.3.23 shows the actuator acting upon a precompressed spring to transfer load to a closed hydraulic column. A prop or other marginally stable device is held in place by a small solenoid to allow the actuator to be de-energized. The spring would maintain clamp force in the latched state and would account for thermal contraction.

Fig. 8.7.3.25  Actuator multiplexing scheme. An implementation of a related scheme is shown in Fig. 8.7.3.26 in which a selection finger is rotated by means of a low-torque rotary actuator to engage with either the shift rails or a clutch-operating rail, which travels back through a bore in the combined roto-linear actuator assembly. The linear actuator then operates upon the clutch or one of the two shift rails. A DCT would require two systems to achieve full functionality.

Figure 8.7.3.24 shows a functionally similar arrangement, but with an electromagnet that is energized once the armature is pressed against the stator. With zero air gap, a comparatively small device is required. With respect to energy losses, various configurations are presented in Appendix 2. 8-58

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this is likely to provide a softer engagement and allows the device to be fitted within the transmission without concerns about sealing.

Fig. 8.7.3.26  Rail and clutch actuator.

Fig. 8.7.3.27  Anti-rollback device.

Rollback and Park

If a second spring element was added to prevent rollforward and so provide a bi-directional park brake, then a controlled interlock, potentially of the following types, would be required: A solenoid with a position switch. This could be controlled directly or by an intermediate electronic device that only provided an output when in receipt of an appropriate control signal sequence that could not arise from a simple short or wire fracture. An interlock pin controlled by a device requiring a specific sequence of electrical signals such as a stepper motor. Figure 8.7.3.28 shows an arrangement that combines a park function using the same principle. The spring coils are wound in cw and ccw senses and both have one end anchored to the central mount plate. An interlock device is shown to mitigate the risk of inopportune energizing of solenoid 2.

Rollback on a gradient is a frequent criticism of dry clutch AMTs; indeed, even wet clutch DCTs with cooling systems enter specific control modes to warn the driver that the thermal limit of the launch clutch has been exceeded and rollback may be experienced. Integration with the brake system (EPB) is probably the lowest-cost solution for the prevention of rollback, but for an R&D demonstrator an additional device would be introduced to avoid superfluous software integration work. Indeed, the likely requirements for application to a low-cost vehicle may preclude the addition of brake pedal pressure sensing and high-resolution velocity sensing (speed and direction), making the fitment of a transmission device the favored solution. The following selection criteria were applied: provision of smooth transition when positive drive torque equals and then exceeds gravitational torque when launching on an up-hill slope; only prevents rollback, not rollforward; drag loss in open state below 10 W; actuation energy below 12 W (i.e., 1 amp @ 12 V); and cost, mass, and package specification. Further, a robust solution must not be adversely influenced by the following: external shock loads (e.g., bumping a curb), thermal expansion, wear, and changes to lubrication regime. A conventional positive-engagement device such as an AT-type pawl is not suited for the following reasons: harsh transition with part load transition and durability under frequent part-load engagement/disengage transitions.

Fig. 8.7.3.28  Combined anti-rollback and park.

Proposed Solution

Lubrication

Figure 8.7.3.27 shows a wrap spring with a tensioning solenoid with positive actuation of the tang ring to reduce the potential for vehicle motion. Regarding lubrication, the arrangement could be wet or dry; wet is preferred because

The elimination of the lube oil pump is important to reduce cost and to improve efficiency, albeit with the potential durability risks to shaft bearings, under gear bearings, gear thrust

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bearings, and synchronizer elements. To ensure adequate lubrication, higher oil fill than would be required within a pumped system leads to less efficiency gain than might be anticipated due to churning losses. Experience suggests that oil may be carried to the upper portion of the casing by the final drive gear. This may then be collected in a reservoir feature (potentially a low-cost plastic gallery) from which it is guided toward the lubrication targets by gravity, as shown in Fig. 8.7.3.29. Specific additional features are required: gear meshes may be fed by a drip bar from the gallery or “stalactite” lobes, bearings and other gear/synchro features may be fed by centripetal effects on oil fed to bores within the shafts. Regarding application examples, many of these features are seen within recent transmissions [6]. A further potential benefit of a galleried arrangement arises when the vehicle is stationary and the gallery drains to the lower area of the casing, whereby idle rattle (an important refinement issue) may be reduced by locating the 1st gear lay shaft so that it is substantially immersed in oil, which acts to damp oscillation. At this stage of design, incline tests and starvation due to sustained high-speed cornering have not been explicitly considered.

Fig. 8.7.3.30  Combined roto-linear actuator applied to sixspeed transverse MT. Having satisfied the actuation requirement, the remaining element of the design with a high degree of novelty, the nested twin dry clutch, may be addressed. The analysis of detail elements of interim designs was ongoing at the time of writing, but rudimentary thermal requirements have been met. An interim version is shown in Fig. 8.7.3.31.

Fig. 8.7.3.29  Lubrication scheme. 8.7.3.10  Overall Design The application of the linear actuation technology was verified in conjunction with a rotary selection actuator, as shown in Fig. 8.7.3.30, which illustrates a transverse six-speed transmission with an interim design of mounting boss which also houses position sensors. Fig. 8.7.3.31  Nested twin dry clutch module.

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Simulation Details

The full transmission is shown in Figs. 8.7.3.32 and 33 and is illustrative of a design with all ratios synchronized, 200 N. m input capacity, and a length of 310 mm.

V-Sim™ software was used with a closed-loop driver algorithm applied to a warm-start NEDC test cycle. The vehicle chosen for simulation was a VW Golf 2.0 Tdi 6MT. All variants were controlled according to the normal mode shift map measured on the DSG vehicle. The AMT model accounted for the following: torque loss for gear meshes, bearings, seals as MT; actuation electrical load assumed active only during shifts; other electrical loads (TCU). Wet Clutch DCT model accounted for the following: torque loss for gear meshes, bearings, seals mapped from spin rig data for VW DQ250; changes for drag of open clutch mapped for speed; hydraulic pump mapped for speed and load; incremental mass (incremental cooling); incremental rotary inertia; electrical loads (TCU and valves); changes to vehicle CdA due to air flow to the transmission cooling radiator was ignored. Dry clutch DCT with electrical actuation and clutch latching: torque loss for gear meshes, bearings, seals mapped from spin rig data for DQ250; negligible drag of open dry clutch; clutch actuation bearing and seals drag; incremental mass (incremental cooling); incremental rotary inertia; lube by splash—small incremental drag applied to FDR gear; electrical loads (TCU). The data applied for the DQ250 simulation was extracted from a report [1] detailing the physical testing of a VW Golf 2.0 Tdi DSG derived by the following process to ensure its accuracy: instrumentation of a vehicle to allow measurement of operating conditions and CAN data during a suite of representative maneuvers on a chassis dynamometer; the data was processed and applied to the algorithms within a universal transmission controller to allow recreation of in-vehicle control outside the vehicle; the transmission alone was installed on a dynamometer with sensitive torque measurement on the input and output shafts to allow efficiency to be calculated while the transmission was subject to exactly representative control to ensure realistic pump load. The transmission is shown mounted on an efficiency rig in Fig. 8.7.3.34.

Fig. 8.7.3.32  Two-dimensional section of transmission.

Fig. 8.7.3.33  Schematic of six-speed DCT transmission. 8.7.3.11  Fuel Economy Simulation A comparative study is presented in this section to identify the vehicle economy changes arising from applying the discussed actuation and clutch systems to a DCT layout.

Fig. 8.7.3.34  VW DQ250 on test rig.

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Simulation Results and Comparison with Other Transmission Types

Contrasting the economy of the 6-eDCT to the 6AMT. a decline of 1.3% (13.5-12.2) is apparent; however, this variant is likely to achieve substantial market acceptance. Current DCTs (VW DQ250) are approximately 5.4% better than current ATs. If electrical actuation of the wet clutch module was possible, adoption of electrical actuation could improve this due to elimination of the parasitic torque required to drive the high-pressure hydraulic pump, although the drag loss of the open wet clutch would persist. The adoption of the actuation and clutch design described in this paper would provide a 6.8% improvement according to simulation, with all other factors held common.

Figure 8.7.3.35 shows an example of the simulated torque loss of the transmission for the AMT variant during an NEDC cycle. Applying the simulation results for all transmission variants, Fig. 8.7.3.36 was plotted relative to a 6AT with a torque converter. As would be anticipated, the automation of a manual transmission (AMT) gives best economy at 3.5% above a 6MT with fixed-cycle shift points—but shift quality and poor creep function make this unacceptable for mature AT markets.

Fig. 8.7.3.35  Simulation example: transmission torque loss.

Fig. 8.7.3.36  Fuel economy comparison. 8-62

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8.7.3.12  Cost

Combined Synchronization and Gear Locking

Reference [7] details a cost comparison based upon high-volume manufacture. This study provides a conservative saving estimate for the design described, including electromagnetic clutch latches and anti-roll features, of 22% versus the VW DQ250. Further reductions would involve gear compounding and associated ratio compromises.

A releasable gear engagement, that is one that would open under load unlike a conventional dog clutch, would mitigate the disadvantage of using two fail-to-close clutches within a DCT. Further, if such a device provided synchronization capability, then a further step reduction in cost and package, beyond that suggested for the concept described in this paper, could be achieved.

8.7.3.13 Alternative Configurations and Related Technologies

Alternative Transmission Architectures

The reader will be aware of the activity beyond the discussion of the DCT-related transmission concept presented here, including quasi-powershift alternatives to DCT. Some of the alternatives relate to enabling subsystem technologies or are more wide ranging and define a new type of transmission altogether.

Some alternative architectures include dual clutch multi-path with conventional synchronizers and dog clutches, a single synchronizer as found in some truck applications, and single clutch multi-path with switch couplers.

Dogs and Synchronizers

The paper has described the background review of the many alternative subsystem technologies to define a transmission to meet a specific application (powershift, 200 N. m, B-class); from this work the following conclusions are drawn: a solution based upon a DCT architecture has been discussed which involves the multiplexing of a novel electrical actuation system and dry clutches. A nested dry clutch module has been proposed which appears to meet the requirements for a 200-N. m application in terms of length, torque capacity, and thermal capacity using a standard friction facing. Simulation using a conservative subsystem model has shown that a fuel economy saving of 6.8% is possible relative to a current wet clutch DCT. A large proportion of the efficiency arises from the deletion of the hydraulic actuation system and the application of latching mechanisms to the clutches to virtually eliminate the energy required to maintain clamp forces. The other significant contributions arose from the avoidance of drag torque from the open clutch, and the deletion of the lubrication pump. A substantial element of the cost reduction was associated with the adoption of both the novel linear motor devices and the actuation connectivity in which two clutches and four shift rails are controlled by just two linear motors. Various solutions have been proposed for hill-hold functionality to overcome the current limitation of dry clutches. The requirement for a DMF or other dampers is the subject of continuing work not complete at the writing of this paper. Following the detail design of the transmission, the build of a collaborative demonstration vehicle is targeted at Q4/2007. While the paper has focused upon subsystem solutions relevant to DCT application, both transverse and in-line, certain approaches are also relevant for wider application; specifically, the series load path latch concepts are eminently suited to AT application.

8.7.3.14  Conclusions

Multiple conventional synchronizers account for a substantial portion of the transmission length and cost; some claimed alternatives are discussed below. Alternatives to Dog Conventional Engagement Devices • Zeroshift (www.zeroshift.com) • Switch Coupler [5] as shown in Fig.37

Fig. 8.7.3.37  Switch coupler. At the time of writing, the authors are unaware of conclusive published data relating to vehicle testing of such systems.

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8.7.3.15  References

319331; Mobile 0044 0789 9905157; Direct Fax 0044 (0)1926 319300; e-mail [email protected]; web: www.ricardo.com.

1. Fracchia, Marco, et al., Benchmarking Report VW DCT DQ250, Ricardo Driveline & Transmission Systems, Ricardo UK Ltd. 2. Turner, Andrew, Keith Ramsay, Richard Clark, and David Howe, Direct-Drive Electromechanical Linear Actuator for Shift-by-Wire Control of an Automated Transmission, Ricardo UK, Southam Road, Radford Semele, Leamington Spa, Warwickshire, CV31 1FQ, UK Department of Electronic and Electrical Engineering, University of Sheffield, Mappin Street, Sheffield, S1 3JD, UK. 3. www.LUK.de 4. O-Neill, A., W. Simpson, et al., Patent Application GB0521036.4, Latching Multi-Plate Clutches, Ricardo UK Ltd. 5. Burke, John, John Bennet, Patent Application GB0418645.8 and GB0419183.9, A novel Gear Engagement Device Providing Power Shifting for a Single-clutch Gearbox without Interruption of the Torque, Ricardo UK Ltd. 6. Fracchia, Marco, et al., Honda MT Benchmarking Report, Ricardo Driveline & Transmission Systems, Ricardo UK Ltd. 7. Analysis of DCT Architectures and Subsystems 2006, Ricardo UK Ltd.

8.7.3.19  Appendices Appendix 1  Clutch Actuation Calculations Clutch Calculation Twin Nested dry clutch module Outer Clutch Variable Cluth Torque OD Friction disk ID friction disk Radius-effective Equivalent tangential force Friction coefficient Clamp force to transmit torque   (single surface) Number of friction surfaces Clutch force Pressure on facing (average) Actuator piston   OD   ID   Active Area   Actuator pressure Inner Clutch Variable

8.7.3.16  Glossary DMF Dual Mass Flywheel DSG™ Direct Shift Gearbox MMLA Moving Magnet Linear Actuator (single phase)

Clutch Torque OD Friction disk ID Friction disk Radius-effective Friction coefficient Clamp force to transmit torque   (single surface) Number of friction surfaces Clutch force Pressure on facing (average) Actuator piston   OD   ID   Active Area   Actuator pressure

8.7.3.17  Acknowledgements The authors are suitably grateful to the Directors of Ricardo plc for their funding of this program and their permission to publish this paper. The following specialists are thanked for their contribution of original material and/or assistance: Shaun Mepham, John Burke: multiplexed hydraulic actuator; John Burke, Vojtech Rosol: DCT shaft and gear layouts; Pascal Reverault: Fuel Economy Simulation. 8.7.3.18  Contact Jonathan C. Wheals, Chief Engineer: Innovation Ricardo MTC, Southam Rd, Radford Semele, Leamington Spa, Warwickshire, CV31 1FQ, UK; Direct Tel. 0044 (0)1926

Value Units 200 240 190 107.5 1860.5 0.35 5315.6

Nm mm mm mm N [] N

2 [] 2657.8 N 0.03934913 N/mm2 115 100 0.00253291 1049310.2 10.5

mm mm m2 N/m2 (Pa) bar

Value Units 200 180 100 2857.1 0.35 8163.3

Nm mm mm N [] N

2 [] 4081.6 N 0.05800107 N/mm2 96 65 000391992 1041253.5 10.4

mm mm m2 N/m2 (Pa) bar

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Appendix 2  Power Losses for Different Types of Clutch Latch

8.8.2.3   Speed Sensing 8.8.2.4   Position Sensors 8.8.2.5   Pressure Sensing 8.8.2.6   Temperature Sensing 8.8.2.7   Barometric Absolute Pressure 8.8.2.8   Torque Sensing 8.8.2.9   EMC Considerations 8.8.2.10  Acronyms and Definitions 8.8.2.11  References

BIRO-type Latch Speed Speed Bearing torque Bearing Power Loss Seal Torque Seal Power Loss Total Power Loss

3000 314.1593 0 0 0 0 0

rpm rad/s Nm W Nm W W

12 3000 314.1592654 0.1 31.41592654 0.2 62.83185307 106.2477796

W rpm rad/s Nm W Nm W W

8.8.1

Remote—electromagnetic holder Solenoid power Speed Speed Bearing torque Bearing Power Loss Seal Torque Seal Power Loss Total Power Loss

Hydraulics and Valve Body

With the advent of today’s electronic transmission controls, the use of hydraulics in the automatic transmission has changed significantly, but hydraulics still provide the muscle and the cushion for most transmission functions. Their proper design and manufacture are crucial to the overall functioning of the automatic transmission. Most of the material in this section was prepared when hydraulics did everything, and therefore contains some dated components and comments, but the essential information is still current to the state-of-the-art. The three papers that comprise this section are “Hydraulic Control Systems,” “Design of Valve Body and Governor Systems,” and “Manufacturing Aspects of Valve Body Design.”

8.8 Control Components This section covers some of the components used in transmission control. The hydraulics and valve body, 8.8.1, and the transmission sensors, 8.8.2, are described in detail. The various types of solenoids are discussed in 8.5, Transmission Control and Types of Control, and some discussion of other actuators is available in 8.7, Automatically Shifted Manuals. There is no discussion of the electronic controller here; that is left to the electronics community. There are, however, several SAE papers that address on-board controllers and their issues.

8.8.1.1  Hydraulic Control Systems J. R. Doidge and C. W. Cline Hydra-Matic Div., General Motors Corp. Revised and Updated February 1971 by: L. E. Green Hydra-Matic Div., General Motors Corp. To the uninitiated, the control system for an automatic transmission presents such a maze of valves, channels, springs, and assorted devices that one often is discouraged from delving further into this subject. However, like many complex devices, the controls are a complicated sum of a number of basically simple units (Fig. 8.8.1.1.1). While it may take a number of years of experience before one feels entirely at home in this complex, a general understanding can be obtained in considerably less time.

Table of Contents—Control Components 8.8.1   Hydraulics and Valve Body 8.8.1.1   Hydraulic Control Systems 8.8.1.2  Design of Valve Body and Governor Systems 8.8.1.3  Manufacturing Aspects of Valve Body Design 8.8.2   Sensors 8.8.2.1   General Design Overview 8.8.2.2   Environmental and Test Conditions

An automatic transmission performs various jobs—some automatic, some not. The nonautomatic functions, referred to as manual shifts, provide a neutral, reverse, and forward range, and provide one or more ranges giving engine braking. Engine braking generally is provided by holding the transmission in reduction and engaging any units necessary to cause the transmission to carry coasting torque.

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Fig. 8.8.1.1.1  Hydraulic control system. The automatic function of the transmission is to provide high torque multiplication at low vehicle speed, decreasing the multiplication as the car speed increases. This operation is either inherent in the design and requires no control, as with the pure torque converter, or is programmed by the engineer in discrete steps according to the vehicle speed and the performance desired by the driver.

Hydrodynamic Fluid Coupling or Torque Converter—This unit usually is filled any time the engine is running and requires no control other than a pressure control. Some transmissions not currently in production have used the fill and exhaust of a fluid coupling, as a hydrodynamic clutch, to accomplish gear ratio changes. Hydrodynamic torque converter units with movable reactor blades have also been used to provide limited ratio change by changing the torque multiplication ratio of the converter. Clutches—Clutches are used in both manual and automatic shifting. Automatic shifting clutches are usually of the disc type, and the shift feel control system associated with them is called an accumulator. This produces a rather precise pressure-time control for clutch application. Clutches used only for manual shifts may be either multiple-disc or cone-type and usually have only a simple shift feel control.

A very general classification of the controls used would divide them into two groups: those that cause the shift to occur, which will be called shift point controls; and those that control the smoothness or quality of the occurrence, which will be called shift feel controls. The shifts themselves are caused by directing, through the hydraulic control system, oil pressure to various hydraulically applied and/or released units. For instance, a very common automatic upshift is to apply a disc clutch across two members of a planetary sun gear. The units that are usually used for changing gear ratios or hydrodynamic ratios are listed as follows.

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Fig. 8.8.1.1.2  Shift transition mechanisms.

Bands—Bands are used in manual and automatic shifting, in applications requiring the locking of a planetary reaction member to the transmission housing. A band is applied by a unit called the servo, and the shift feel controls associated with the apply and release of the band frequently are included in the servo itself. Servos usually require accurate timing controls and may require some pressure-time control during this shift. Bands may be single- or multiple-wrap, depending on the capacity required and the application.

One-Way Clutches—One-way clutches need no control. They are generally of the sprag or roller type, which through the geometry of the unit can hold torque in one direction only and free wheel when the torque is reversed. Figure 8.8.1.1.2 illustrates several typical arrangements of these units as used for ratio changing. The associated hydraulic control systems are shown for each combination of units.

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The several combinations of units in current use in passenger car automatic transmissions are listed in Table 8.8.1.1.1. Both the input and reaction units are shown for the manual shift functions, and the releasing and applying units are shown for the upshifts. Reaction units are shown for braking functions.

that it is normally not controlled by the driver, but rather by signal pressures. One of these signal pressures is generated by a governor, driven by the output shaft, and varies with vehicle speed. The other of these signal pressures, referred to as modulator pressure or throttle valve pressure, varies with the performance demanded by the driver. This is typically accomplished by mechanical linkage from the carburetor or by a vacuum modulator. Mechanical linkage actuated by the carburetor may act on a regulating valve train in the transmission, to generate a pressure that increases continuously as the throttle is opened. Frequently, this control also creates a discrete pressure at WOT, known as detent pressure, which is used to cause forced downshifts and provide desired WOT upshifts. The vacuum modulator in its simplest form consists of a diaphragm acted on by engine intake manifold vacuum, exerting a force that counteracts a spring load applied to a regulating valve in the transmission. At light throttle, the vacuum is high and the net force applied to the valve is low. As throttle opening increases, the vacuum drops, thereby increasing the net force on the regulating valve and increasing the signal pressure. In conjunction with a vacuum modulator, a mechanical control or electric solenoid control is usually used to actuate a detent pressure control at WOT for forced downshifts and WOT upshifts.

Table 8.8.1.1.1 Current Usage of Automatic Transmission Units Type of Transmission Operating mode Forward (input/ reaction) Reverse (input/ reaction) 1-2 shift (release/ apply) 2-3 shift (release/ apply) Second braking (reaction) First braking (reaction)

3-Speed and TC

3-Speed and TC

2-Speed and TC

3-Speed and TC

C/OC

C/OC

/B

C/OC

C/B

C/C

/C

C/B

OC/C

OC/C

B/C

OC/B

OC/C

OC/C

—

B/C

B

B

—

B

B

C

B

B

Shift valve trains are arranged so that governor pressure acts to push the shift valve in the upshifted direction, and throttle valve pressure tends to prevent this movement. The throttle pressure may be modified by additional regulating valves, or by governor pressure acting on the vacuum modulator valve, before acting on the shift valve system itself. In addition, springs generally are used on the shift valves as fixed loads, determining what is referred to as the closed throttle shift point or minimum speed shift point. Line pressure also acts on a small differential area of the shift valve, in the upshifted position only, to provide a hysteresis between upshift and downshift points. This provides a snap action valve motion, preventing a restricted feed or exhaust of the controlled unit, and preventing shift valve hunting at the shift point.

Note: TC = torque converter, C = disc clutch, B—band, OC = one-way clutch.

8.8.1.1.1 Hydraulic Shift Controls With these units in mind, we can discuss the hydraulic shift controls for the nonautomatic or manual functions. Neutral, reverse, and forward are selected by the driver by mechanical movement of the manual valve, located in the hydraulic control valve body, which directs oil pressure to the necessary units and exhausts those units not involved. Selection of a braking range requires that one or possibly two functions must take place. The first function is to override the automatic control system and hold the transmission in a lower gear ratio than would have been selected by the automatic controls.

Movement of the shift valve generally directs an oil pressure that is the prime mover for the entire shift, regardless of how many units are involved. It is at this time that the shift feel controls come into play. Typically, an automatic shift involving application of unit A and release of unit B must be accomplished by applying unit A with a controlled pressure, and by releasing unit B at the moment that unit A has reached a prescribed torque capacity. This prescribed torque capacity for timing of the releasing elements is not constant for all shifts, but depends on the engine torque at the moment of shifting. Likewise, the pressure used in applying unit A will be varied according to the engine torque at the moment of shifting.

The second function arises in transmissions that use oneway clutches to carry gear reaction torque. In these cases, it is necessary to apply a band or clutch that mechanically parallels the free-wheel unit and provides the overrun torque reaction required for the particular gear ratio that has been selected. The hydraulic controls for the automatic functions are the shift valves, also located in the hydraulic control body. These valves are similar to the manual valve in that they direct oil to the friction unit to be activated and cause a shift to occur. This function is different from the manual function in

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8.8.1.1.2 Accumulator The most commonly used device used to control the pressure for the application of unit A is an accumulator. An accumulator controls pressure for an interval of time, depending on its volume and the rate of flow into it. The engineer intends for the unit being activated to complete its engagement during the interval that the accumulator is controlling the pressure. At the end of this period, the pressure will jump to line pressure. This is a desirable safety feature, because it ensures that the unit will be engaged and prevents a failure in case something goes wrong.

Fig. 8.8.1.1.3  Simple accumulator.

A very simple accumulator is shown in Fig. 8.8.1.1.3. Oil being supplied to unit A is restricted by the orifice at 1. As oil flows through the orifice, it flows to unit A and into the accumulator where it builds up pressure and strokes piston 2 down the bore against spring 3. This results in the pressuretime curve a-b-c-d if the spring has no preload, or e-f-g-d if the spring has preload. The time from a to b depends on the size of the orifice and the volume of oil absorbed by the accumulator, and, to a certain extent, by the pressure differential across the feed orifice. The pressure rise is dependent on the rate of the spring; c-d is line pressure, which is reached after the piston has completed its stroke.

Fig. 8.8.1.1.4  Modifying pressure at accumulator.

This accumulator would suffice if all the shifts were made at the same engine torque. To vary the pressure at which the piston strokes, we complicate our accumulator by adding another pressure (Fig. 8.8.1.1.4). Oil pressure is introduced at 4, which opposes the stroking of the piston, thus changing the level a-b according to how much pressure is at 4 and the relative piston areas 2 and 4. This pressure may be the same throttle pressure that we used on the shift valves, or it may be desirable to modify this pressure somewhat for best shift feel. In this case, we may modify it with valves, as in Fig. 8.8.1.1.5. Without going into detail as to how these valves work, throttle pressure entering at 5, using line pressure entering at 6, generates the torque conscious pressure, which acts upon the accumulator piston. For purposes of comparison, curve a-b is a typical throttle pressure-versuscarburetor opening curve, and curve c-d is a typical torque conscious pressure-versus-carburetor opening curve.

Fig. 8.8.1.1.5  Accumulator with additional area.

Suppose that unit A is a clutch, and that as it is making its controlled engagement under the influence of our hypothetical accumulator, and a band is the unit B that is to be released when the clutch has reached a certain capacity. This certain capacity happens to correspond very nearly to the pressure at which the engineer wants the accumulator to begin its stroke. It can be convenient to the designer, therefore, to put a stem on the accumulator piston and use it to apply a load on the band. The accumulator thereupon becomes both servo and accumulator, as shown in Fig. 8.8.1.1.6.

Fig. 8.8.1.1.6  Accumulator as both servo and accumulator.

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The combination may become further complicated when a downshift, releasing A and applying B, must be made smooth. Orifices in the apply pressure passage may be added to delay the engagement of the band to some interval of time after the clutch has been exhausted. Where the downshift is a forced downshift, covering a wide speed range, the orificing may be made speed sensitive, through the action of a valve operated by governor pressure. The servo may be designed so that the piston acts on the pin through a spring, to cushion the band apply. On the other hand, the designer may choose to keep the servo as simple as possible and locate the shift feel controls in the main control assembly or valve body. In this case, the apply and release of the servo would be by valve control.

and factors: what material is most desirable for the main control body? Should the design be made to use existing manufacturing equipment? Is the cost of the system commensurate with its application? Should the control system be broken down into subassemblies for best utilization of space and ease of assembly? Since the same basic controls may be used in a wide variety of different vehicles, can they be adapted with minimum changes? 8.8.1.1.5 Testing The designer should also bear in mind that it is desirable to test the controls before they are assembled into the transmission to ensure proper function. In this case, the type of test and information required must be taken into consideration in the control system design.

8.8.1.1.3 Reliability A very important consideration, once the functions have been provided for, is the reliability of the controls. Aside from avoiding designs that are difficult to manufacture, or are extremely sensitive to production variations, it is wise to investigate the results of a partial failure of the controls. If any partial failure, such as a sticking valve, results in a total loss of drive, a burning up of one or more units, or a dangerous situation (such as downshifting to low gear at very high speed), then the designer should make every effort to circumvent this failure in his design.

8.8.1.2  Design of Valve Body and Governor Systems D. C. Hewitt and R. L. Leonard Transmission and Chassis Div., Ford Motor Co. The function of an automatic transmission valve body and governor system is to regulate pressure and direct fluid from a pump or pumps to transmission components such as the torque converter or fluid coupling, band servos, clutch cylinders, cooler circuits, and lubrication systems. The scope of this paper includes the following:

An accumulator to regulate clutch pressure, in place of a regulator valve, is an example of inherent safety of operation. If the accumulator sticks, the regulation is stopped and the shift is rough, but the clutch does not suffer. If the torque conscious pressure falls, the pressure regulated for the clutch may be too low, resulting in a slipping shift, but the clutch will slip only until the accumulator piston bottoms, at which time the clutch pressure will jump to line pressure, and the clutch will lock up before any damage has occurred.

1. Discussion of the factors affecting the design of the hydraulic control systems 2. Function of basic types of hydraulic valves and the accompanying circuits 3. Description of typical designs of automatic transmission hydraulic systems 4. Synthesis of a hydraulic control system for a hypothetical transmission by combining valves and circuits to meet specific functional requirements 5. Calculations of valve areas by solution of simultaneous equations

Sometimes, however, it is impossible to make a control failsafe, and in this case the effort is directed toward preventing the failure. Critical valves are designed to be operated by relatively high loads and thus reduce the possibility of valve sticking. Circuits may be added to cycle valves when not in use in order to prevent dirt collection and subsequent sticking. Filters are used in some transmissions, and additional screens can be placed in pressure lines that are feeding valves critical to the operation of the transmission.

8.8.1.2.1 Factors Affecting Control Design Each automatic transmission hydraulic control system is designed to accomplish specific functions in a certain transmission. This fact may be so obvious that stating it seems naive; however, it should be borne in mind that the transmission is not built around the hydraulic control system. If the latter were true, the problem of the control engineer would be greatly simplified, but perhaps at the expense of creating design problems in other areas of the transmission. Therefore, before a control system can be designed, it is necessary to ascertain exactly what functions are to be performed, as well

8.8.1.1.4 Cost The final consideration for the control system is, of course, that it must be made on a production basis at a reasonable cost. In this realm, the engineer is faced with many decisions

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parallel circuits for cooling and lubrication, a flow priority for these circuits must be established to ensure that the most essential functions will be maintained if the pump capacity is severely taxed under extreme operating conditions.

as the pressure and volume requirements of each hydraulic component. Of the many factors to be considered, perhaps a logical beginning is the pumping system, because all of the other hydraulic components are supplied with fluid from the pump or pumps. An automatic transmission may have both a front and rear pump, but each transmission must have at least one front pump. The front pump may be a constant displacement type, single- or two-stage, or a variable-displacement design. A front pump is driven by the engine and is therefore operative whenever the engine is running. The rear pump is driven by the output shaft and consequently functions only when the vehicle is in motion. The approximate flow from the pump or pumps must be considered so that the hydraulic passages can be designed with an adequate capacity.

Other factors for consideration in control design include the need for shift recalibration and the need for interchangeability of the components in several transmissions. If the system is to be used with only one transmission and engine installation, the need for flexibility of recalibration is minimal. On the other hand, if the controls are programmed for use in a series of transmissions with various engine displacements, provision should be made for major calibration modifications without expensive production and retooling problems. While it is usually more economical to make the control system with a minimum number of valve bodies, space limitations and flexibility requirements may dictate the use of several small subassemblies. When all the factors affecting the hydraulic control design are considered, it becomes apparent that there is no “best” hydraulic control system for all installations; each system must be designed and developed for a multiplicity of unique requirements.

The control engineer will also need to know the number of band servos and clutch cylinders that must be supplied, and the pressure requirements for these components in each range and for each speed and throttle opening. The pressure acting in these units must be sufficient to hold the band or clutch during the most severe loading condition. One example of an extreme loading condition would be that of a band holding a drum in the deenergized direction during the application of full-throttle engine torque acting through a torque converter. Another example would be a disc clutch holding full-throttle torque multiplied by the converter stall torque ratio with high-temperature fluid and the accompanying pressure loss resulting from leakage. If sufficient pressure to prevent band or clutch slippage under these severe conditions were maintained continuously by the regulating system, the pumping efficiency would be adversely affected. Another difficulty resulting from a constant high pressure would be incurred while attempting to calibrate friction elements for smooth engagements.

8.8.1.2.2 Design of Basic Valves and Circuits Before proceeding with an analysis of complete control systems, it will be necessary to understand the design of fundamental valve types and circuits used in current-production control systems. The basic valves that will be discussed are the regulating, check, and shifting or relay valves. Regulating Valve Design—To meet the requirements for precisely modulated pressures in various circuits, several regulating valves are used in each control system. Fig. 8.8.1.2.1 shows a basic regulator valve. In this simple circuit, the hydraulic line from the pump branches out to supply the main line and to pressurize the area on the end of the valve. When the pump begins to operate, fluid fills the line and exerts a pressure force on the end of the valve. This pressure acting on the end of the valve causes the valve to move upward and compress the spring. When the valve moves far enough, exhaust port X is opened. The pressure that this type of valve will maintain in the main line can be determined by balancing the forces acting on the valve:

The flow and pressure requirements of the hydrodynamic unit must be known to the control engineer. If a dump-fill coupling is used, the schedule for charging and discharging fluid is required, too. Transmissions that are air-cooled only will not require oil flow to an external cooler, but most automatic transmissions are now at least partially cooled by flowing fluid to an intercooler (heat exchanger) in the engine radiator and then back to the transmission. An estimate of the heat rejection requirement for the transmission is needed so that sufficient flow can be directed to the cooler. Cooler flow is usually between 1 to 3 gpm. In some cases, it is desirable to use the relatively cool fluid from the cooler system for the lubricating circuit. In other installations, the cooled oil is dumped into the transmission sump. When the fluid is returned directly to the sump, another branch of the circuit must be provided for lubricating oil. In cases where there are



PA – S

(8.8.1.2.1)

where: P = pressure A = area at end of valve S = spring load at working height

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Generally, this type of regulator valve effects a constant line pressure whenever the pump volume meets or exceeds the volume flowing through the main line plus the leakage through the regulator valve. If the pump capacity is less than the flow and leakage requirements, the pressure is determined only by pump capacity. The regulator valve ports must be designed to flow the maximum capacity of the pump, less the minimum flow through the main line, otherwise main line pressure will exceed the designed pressure because of restriction across the valve or at the exhaust port. Figure 8.8.1.2.2 shows another type of basic regulating valve where the primary function is to regulate at a specific pressure from the main line pressure supply. Unlike the valve discussed above, this valve does not exhaust large quantities of oil from the system. This is accomplished by giving proper consideration to valve overlap. Total valve overlap is the sum of A and B shown in Fig. 8.8.1.2.2. Although an attempt is made in the design of this valve to prevent exhausting of any more oil than necessary, paradoxically the function of the valve is dependent on leakage across the overlap areas. Assuming that there is no flow into the regulated line circuit, leakage from the main line through sealing area B will equal leakage into the exhaust port through area A. In actual installations, however, there is always some flow into the regulated line; therefore, the flow across area B is equal to the flow in the regulated circuit plus the leakage into the exhaust port.

Fig. 8.8.1.2.2  Low-flow regulator valve. A large overlap is desirable from a leakage consideration but not from the functional standpoint. Because the flow in the regulated line is subject to variations, the valve must quickly respond to transient conditions. As the valve moves, the spring load is changed due to the spring rate. If this movement is too great because of extensive overlap, the valve will tend to “hunt,” and the regulated pressure may pulsate. The design of the regulating valve spring is extremely critical if usable line pressure tolerances are going to be maintained. Because precise dimensional control of valve diameters is practical, tolerances in valve areas contribute little to line pressure variations. On the other hand, spring load tolerances can be a major factor in the total line pressure limits. The minimum and maximum spring loads on any regulating valve are a function of the spring (load) tolerances and the variations in spring height when the valve is at the regulating point. It is necessary to carefully dimension the important valve body parts and spring seats to prevent excessive stackup tolerance. In many applications, a low-rate spring is required so that load changes due to variations in the installed spring height and consequently the regulated pressure tolerances can be kept to a minimum. To install a low-rate spring usually necessitates additional space, and spring buckling problems may be aggravated. Some springs in the system may require closer tolerances than those considered commercial by the spring manufacturers; the cost of the springs will reflect this requirement for additional inspection work.

Fig. 8.8.1.2.1  Basic regulator valve. If the line pressure is 100 psi and a spring is used so that the regulated pressure will be 10 psi, the pressure drop through area B will be 90 psi, while the pressure drop across exhaust port (area A) is only 10 psi. Under these conditions, the valve will position itself so that more of the total overlap is at area B. Conversely, if a spring is used to regulate a pressure of 90 psi, the valve will move downward to provide more seal at the exhaust port.

Regulating springs are closed on the ends and ground flat to prevent any side loading of the valve. The spring must work freely in the bore or over a guide pin so that friction is kept to a minimum.

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Valve vibration is sometimes evidenced by an audible buzzing noise. The cause of valve buzz can frequently be traced to the transmission pump or pumps. Pumps used in automatic transmissions produce a series of pressure impulses as each gear tooth or vane discharges a pocket of fluid into the pump output port. The possibility of valve chatter is generally less in transmissions having pumps with a large number of teeth or vanes. This indicates that there is less tendency for valve vibration if the frequency of pressure pulses is at a level above which the valve has a tendency to vibrate. Other factors affecting valve vibration include fluid viscosity, valve mass, valve porting, resonance of pumps and pressure lines, and especially the natural frequency of the valve spring. The natural frequency of a spring can be computed as follows: where:

To = (Ti − 1α)

Nii – αt No

the annular port. Subsequent machining to eliminate this draft angle is not economically practical. In addition to this unbalance in the static forces on a valve, fluid flow across the valve may cause a significant side loading force. On valves whose function may be seriously affected by side loading, multiple annular grooves are incorporated in the valve lands, as shown in Fig. 8.8.1.2.5. When the annular grooves are incorporated, the fluid normally leaking between the valve land and the bore fills the grooves and exerts a separating pressure between the valve and the bore around the entire valve. This hydraulic centering action minimizes the side loading and thus reduces valve friction. Disadvantages to grooving the lands are cost and, under some conditions, increased leakage. An axial force on a valve may become a problem in valves that flow relatively large quantities of fluid at high pressures. This axial force is caused by a jet effect and the momentum of the fluid acting on a square land. If this force of fluid momentum acts in the same direction as the spring, the regulated pressure becomes higher as flow is increased. If the jet effect is in the opposite direction, the regulated pressure decreases with an increase in flow.

(8.8.1.2.2)

n = vibrations/min of spring vibrating between its own ends R = rate/in deflection, lb W = weight of active portion of spring, lb

Figure 8.8.1.2.6 shows a contoured valve and a porting design which may be used to offset the axial force caused by momentum. The combination of the contoured valve and special porting could actually result in a force tending to move the valve in a direction opposite to that caused by the inlet jet action.* The precise contour required to balance the force is dependent on the angle of entry of the jet, and the angle of entry is affected by the opening or axial clearance. Balancing of the forces on the valve may create an unstable condition that will cause hunting and a buzzing problem. The value of valve contouring and negative force porting in automatic transmission controls is somewhat controversial.

Frequently, in practice more effort is directed toward alleviating the disturbance than ascertaining all of the causes of the problem. A simple and generally effective method of attenuating valve buzz is the use of an orifice in the hydraulic line pressurizing the end of the valve. The circuits shown in Figs. 8.8.1.2.1 and 8.8.1.2.2 incorporate orifices for this purpose. This constriction reduces valve-sensitivity by dampening the pressure pulses from the pump. Another common solution to the problem is the use of “buzz flats,” or metering notches. These flats and notches may be cut in the valve land (Fig. 8.8.1.2.3) or cast in the valve body (Fig. 8.8.1.2.4). Although the cost is less if the notch is cast in the body, the function is the same; small quantities of fluid are permitted to flow through to the exhaust port without opening the entire periphery of the valve. Thus, a more gradual transition from fully closed to slightly open can be made.

*Lee and Blackburn, “Contributions to Hydraulic Control,” Transactions ASME, August 1952.

Another problem that must be considered is the effect of side loading of the valve. Side loading causes friction between the valve and the bore and tends to create sticky, erratic operation. To prevent side loading, insofar as possible, all porting is accomplished through annular areas surrounding the entire valve. With this design, a balancing effect results from hydraulic pressure acting on the entire periphery. To balance the static hydraulic forces completely, this annular port must, of course, be the same width all the way around the valve, but this is not feasible in production units. The requirement for draft angle on a die-casting blade affects the width of

Fig. 8.8.1.2.3  Regulating flats on valve.

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Poppet valve A, consisting of a flat disc and a spring, closes against a flat seat until the pressure force exceeds the force imposed by the spring and any opposing hydraulic force. The spring load is very low and is used primarily to prevent the valve from cocking in its bore. The valve usually seals on a steel plate to prevent brinelling during the frequent and rapid closing. One of the ball check valves shown (B) functions in the same manner as the poppet type of valve, except that a spring is not required to prevent cocking. A spring may be required if the ball is to unseal itself at some specific pressure. The ball may require a little more depth of pocket for operation than a poppet valve; however, the cost of the ball may be slightly less.

Fig. 8.8.1.2.4  Regulating notches in valve body.

Ball check valve C is used to direct fluid flow from either of two passages to a common line. Flow from port X will close port Y. However, if flow is from port Y, port X will be sealed off. At least one control circuit in use today uses ball check valves of this type as a fail-safe feature. If certain critical control valves stick in the wrong position, an alternate source of pressure is supplied to the necessary units so that the transmission continues to operate. A slightly different principle is used with ball check valve D. The ball seals at the O.D. by being designed with a minimum clearance between the ball and the bore. A valve seat is not required so that the ball may work in a soft metal bore where access to a steel plate is not possible. When the hydraulic force overcomes the spring force, the ball moves into the larger bore and allows fluid to flow. Because of the need for clearance between the ball and bore to allow free movement of the ball, this installation causes some leakage that will prevent its use in those cases where a positive seal is required.

Fig. 8.8.1.2.5  Annular valve grooves.

Check valve E operates similarly to valve A. The mechanical connection between the rubber valve and the spring is used to prevent the valve from moving into a position that would block the flow into port 2. The selection of check valves is based on the function, the space limitations, and the material available for the valve seat. Shift or Relay Valve Design—The shifting valves are also sometimes called two-position valves. This latter name describes the operation of the valve. Accumulative forces, hydraulic and spring, move the valve from one position to another and cause specific groups of friction elements to be applied or released.

Fig. 8.8.1.2.6  Contoured valve and negative force porting. Check Valve Design—There are many uses of check valves in automatic transmission control circuits, and they are finding greater use in each new design. In general, they prevent fluid flow until a specific pressure or pressure differential is attained and are also used to close different passages as flow direction is reversed. They are relatively trouble-free and can simplify circuit design with a minimum of cost. Several types of check valves are shown in Fig. 8.8.1.2.7.

Shift valves sense vehicle speed and throttle opening by means of pressures acting on opposing areas of the valve. A pressure signal indicating vehicle speed forces the valve in a direction to cause a shift, while another pressure signal

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indicating the throttle position tends to retard valve movement. Also retarding valve movement is a spring required to return the valve to the lower gear when speed is decreased or the operation of the vehicle is discontinued.

Now that the factors affecting control design have been considered and the basic valve types that are the building blocks of a control system have been analyzed, we can proceed to investigate complete hydraulic control systems.

Fig. 8.8.1.2.8  Typical shift valve. 8.8.1.2.3  Designing Hydraulic Control Systems It would be beyond the scope of any one paper to discuss in detail all of the control systems in current usage, and to discuss only one system would not be an adequate coverage of the subject. Therefore, for the purpose of this paper, a cross-sectional study of current usage will be attempted by designing a hypothetical control system. First, of course, it will be necessary to know the functional requirements of our hypothetical transmission. Let us assume that our objective is a control system design for a two-speed automatic transmission incorporating both a front and a rear pump. Furthermore, let us assume that the pressure schedule must be as follows:

Fig. 8.8.1.2.7  Typical check valves. A shift valve must be designed to effect a quick snap action once the valve has begun to move. This is accomplished by the elimination of one of the forces opposing valve movement just as the valve begins to stroke. For example, Fig. 8.8.1.2.8 shows a typical valve before and after shifting. Before the shift, the forces tending to affect the shift are a speed signal and the main-line pressure acting on area B. The forces opposing a shift are the throttle position signal, a spring, and the main line pressure acting on area A. When the valve moves slightly, the main line pressure to areas A and B is cut off. Because area A is greater than area B, the forces become unbalanced and a snap action results. At this point, it should be mentioned that the difference between areas A and B is termed the differential area. Thus, in this particular valve, the total effect of line pressure can be computed by multiplying the differential area by the pressure. In subsequent discussions of valve forces, only the differential area will be considered rather than the individual areas.

1. Full-throttle drive stall—160 psi minimum (drive range, low gear) 2. Full-throttle low gear stall—160 psi minimum (low range, low gear) 3. Full-throttle reverse gear stall—200 psi minimum 4. Torque converter charge pressure—75 psi maximum The stall pressures are based on the capacity of the friction elements used; however, to facilitate calibration and attain pumping efficiency, it is necessary to reduce or cut back from these full-throttle stall pressures when the throttle opening is decreased and/or the vehicle speed is increased. For the purpose of this paper, we have divided the control design problem into several individual systems as follows:

If the motion of a shift valve were not rapid, the transmission would hunt between gears, and a friction element failure would probably result. Once the valve has begun to move, the chain of action must be irrevocable until the shifting function has been completed. This requirement causes a hysteresis effect so that upshifts and downshifts do not occur with the same conditions of speed and throttle opening.

1. Part A—main regulator 2. Part B—throttle 3. Part C—governor

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4. Part D—manual 5. Part E—shifting or relay 6. Part F—special-purpose

A compact, positive-displacement, two-stage pump is in use today which uses the circuit feature of the two-pump system. However, two separate pump assemblies have the advantage that the rear pump is driven by the transmission output shaft and thus provides pressure during vehicle push starts. An approach that can increase system efficiency and supply a much greater volume of fluid when necessary is the use of a variable-displacement front pump. With this type of pump, displacement can be regulated to supply the exact oil volume requirements of the system throughout the transmission operating range.

In each of these parts, one or more approaches representing current practice will be discussed and then one design selected for the hypothetical system. Part A—Main Regulator System—Frequently, the front pump capacity requirement is established only after an experimental evaluation of the entire control system. Because leakage varies in different installations, the system requirements cannot be accurately predetermined. The pump capacity must be large enough to ensure an adequate pressure in the band servos and clutches at all times. Stall and low-speed operation impose the most severe conditions because the pressure requirements are high while the pump speed is relatively low. As the vehicle speed increases, the demands on the front pump are decreased, and at the same time the rear pump output increases. Ultimately, the rear pump may take over the system. At this point, the front pump operating pressure is reduced, thus increasing the transmission efficiency. When the rear pump supplies the system, the front pump output may be entirely bypassed or used to supply the converter, lube, and cooler circuits at pressures considerably lower than required by the other components in the system. If at any time the main line system requires more fluid than the rear pump can supply, a check valve system permits the larger pump to again supply the entire system.

The design parameters for the hypothetical system include the ability to start the vehicle by pushing; therefore, the twopump system shown in Fig. 8.8.1.2.9 will be adapted for our purpose. For simplicity, two constant-displacement pumps have been selected. Suitable converter or coupling charge pressures must be provided in all automatic transmission control circuits. Converter flow may be supplied from main line pressure at the main line pressure regulator valves, as shown in Fig. 8.8.1.2.10. In this valve circuit, fluid from the front pump flows around the valve, through the front pump check valve (not shown), and back to the valve at two locations. At one of these locations, there is a differential area, thus creating a hydraulic force to oppose the spring and affect the basic regulating function. The other location or port for fluid from the check valve provides for the converter charge. (The function of the compensator pressure acting on the end of the valve will be discussed later in Part A.) Converter charge pressure with this arrangement is full line pressure, except for the pressure drop resulting from flow across the orifice in the converter charge line. In cases where the lube system is supplied from the converter charge pressure line, consideration must be given to the effect this bleedoff has on the actual converter charge pressure. Converter charge pressure should be only high enough to prevent converter cavitation. Therefore, it may be desirable to regulate a separate converter charge pressure. This will require an additional regulating valve, but closer control of converter charge pressures is possible than with an orifice. It may be necessary to boost charge pressure to prevent converter cavitation to stall and to increase the flow of fluid through the converter to dissipate the generated heat. Figure 8.8.1.2.11 shows a converter regulator valve where the spring end of the valve is pressurized with line pressure until after the upshift into drive gear. This is controlled by the position of the shift valve. (Shift valves will be discussed in Part E.) This hydraulic force on the converter regulator valve aids the spring force in low gear to boost the converter charge pressure. When the transmission

A circuit affecting these regulating functions is shown in Fig. 8.8.1.2.9. Both pump outputs are connected to one common regulator valve. Fluid from the front pump flows directly to the regulator and also can flow through the front pump check valve to the main line, while the output from the rear pump must flow through the rear pump check valve to the main line and the regulator. When sufficient fluid pressure is generated by the rear pump to overcome line pressure force on the rear pump check valve, the valve is opened and the front pump check valve is closed. Note that the effective hydraulic area is larger on the spring side of this type of check valve, requiring that the secondary pump pressure be slightly higher than line pressure to open the valve. Once the rear pump check valve opens, the pressure drop across the valve will keep it open as long as the flow requirements of the system are supplied by the rear pump. When the rear pump supplies the system, the main regulator valve moves against the spring to the rear pump regulating land. Front pump volume is then directed into the pump suction line, minimizing the effect of oil screen or filter restriction. (In Fig. 8.8.1.2.9, the rear pump is supplying the line, and the front pump output is being bypassed.)

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is in drive gear, converter charge pressure is a function of the converter valve spring only.

charge port is closed to prevent further pressure increase. The desired pressure limits are set by designing the spring with a specific rate. If the transmission is to be air-cooled only by the use of converter fins, the radiator intercooler (heat exchanger) circuit is deleted from the system, and converter discharge is either exhausted to the sump or flowed directly into the lube circuit. Converter discharge is usually the highest sustained temperature location in the transmission, and maximum cooling will be affected by directing converter discharge to the cooler. This is, of course, because of the maximum temperature differential between the transmission fluid and radiator coolant.

Fig. 8.8.1.2.9  Two-pump regulating circuit.

Fig. 8.8.1.2.11  Converter regulator valve. Fig. 8.8.1.2.10  Converter charge from main regulator. For our hypothetical circuit, we will use the converter regulator valve shown added to the basic regulator circuit in Fig. 8.8.1.2.12. Initially, the spring moves the converter regulator valve to the left, preventing the flow of converter discharge oil. This also prevents the converter from draining when the vehicle is not in operation. The charge side of the converter is closed off at the main regulator valve. If the converter or fluid coupling were to drain whenever the engine was stopped and the pump became inoperative, an undesirable delay would be experienced when operation was resumed. We will design our circuit so that when converter discharge pressure reaches 30 psi, the hydraulic force on the end of the valve overcomes the spring force and allows oil to flow to the cooler and lube circuits. When converter discharge pressure reaches 75 psi, the converter

Fig. 8.8.1.2.12  Converter and line pressure regulating circuit. 8-77

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Figure 8.8.1.2.13 shows two views of a transmission cooler control valve assembly that permits fluid flow to the cooler only after a certain temperature has been attained. This feature not only increases transmission pumping efficiency, but also diminishes the time during which the transmission might function erratically because of viscous fluid. At temperatures below approximately 200°F, the bimetal thermostatic element closes the orifice in the body. As long as this orifice is closed, an equal pressure is maintained on each end of the valve, and the spring locates the valve such that fluid cannot flow through the ports to the cooler passage. Above 200°F, the thermostatic element opens and reduces the fluid pressure on the spring side of the valve. The valve now moves against the spring and allows oil to flow through the port’s opening into the cooler passage surrounding the valve body.

tion to engine torque. By causing throttle pressure (or a function of throttle pressure) to act on the main regulator valve, we can vary line pressure with engine torque (the source of throttle pressure will be explained in Part B). Figure 8.8.1.2.14 shows a family of regulated line pressure curves that can be obtained by modulation of line pressure with throttle pressure. Note that the minimum pressure curve must satisfy the drive range idle pressure requirements, and the maximum curve must meet the stall pressure requirements. To meet the requirement that line pressure be reduced with speed, we will cause a function of governor pressure to act on the main regulator valve (the source of governor pressure will be explained in Part C). Figure 8.8.1.2.15 shows a family of line pressure curves cut back with both throttles and governor pressures. With this family of curves, we have satisfied our need for relatively high pressures at stall and have also facilitated calibration and improved pumping efficiency by reducing the pressures under other conditions of torque and speed.

All transmissions require lubrication for bearings, thrust washers, friction materials, and gears. The control circuit must provide this pressure source to these areas. The usual method is to tap off from the converter discharge circuit either before or after the cooler, if a cooler is used. The place in the control circuit from which lube is supplied depends on the availability of the oil supply and the location of the lube requirements in the gearbox. If the converter is located at the front of the transmission, it may be convenient to supply lube oil to the front of the gearbox directly from the converter discharge line. On the other hand, lubrication to the rear of the transmission may be more conveniently supplied with cooler return oil if the return line is connected to the rear of the case.

It should be noted that not all current automatic transmission control circuits reduce line pressure with increasing speed, but current designs do vary line pressure with throttle pressure. One reason for this is that stall pressure requirements in drive range are not always greater than for normal operation. For example, transmissions incorporating fluid couplings rather than torque converters do not require pressure amplification at stall. In all transmissions, however, the pressure requirements are somewhat proportional to torque and are consequently varied with throttle pressure.

Our hypothetical system will include a series circuit. This means that the cooler and lubrication circuits are in series, and lube oil must first pass through the cooler. With this type of circuit, a blowoff valve may be placed between the cooler and the lube circuits so that cooler flow will not be excessively limited by restriction in the lube circuit. An alternate arrangement for cooler and lube circuits is the parallel system. In this system, the converter discharge branches into two separate lines for the two different functions. In either system, the lube pressure should be maintained at a minimum of approximately 10 psi; however, this may vary between transmissions depending on the lube system flow restriction and the oil volume requirements.

Let us now examine a main line regulating circuit that will produce the family of curves shown in Fig. 8.8.1.2.15. It was stated that functions of throttle and governor pressures act on the regulator valve because in most systems these pressures do not act directly on the regulator valve. (In one system, throttle pressure does act directly on the main regulator, but this system does not provide for pressure reduction with speed.) In several systems, the throttle and governor pressures act directly on an intermediate pressure-regulating valve. This valve, which we will call the compensator valve, regulates a pressure that acts on the main regulator valve. The resulting force opposes the main regulator spring, as shown in Fig. 8.8.1.2.16. Thus line pressure becomes an inverse function of compensator pressure. The complex relationship of typical throttle, governor, compensator, and line pressures will be clarified by studying the approximate values in Table 8.8.1.2.1.

A basic pressure-regulating valve has already been discussed in some detail and could be used if a constant line pressure satisfied the system requirements throughout the complete operating range. However, it is one of the requirements of our hypothetical system that line pressure must vary in propor-

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Fig. 8.8.1.2.14  Throttle modulated line pressure.

Fig. 8.8.1.2.13  Thermostatic valve. Table 8.8.1.2.1 Drive Range Pressures, psi Throttle

Governor

Compensator

Main Line

 0 65 65  0

 0  0 45 45

47 13 33 50

  60 160   90   50

Fig. 8.8.1.2.15  Typical line pressure curves.

Fig. 8.8.1.2.16  Regulator and compensator valve circuit.

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We have still another condition to satisfy the requirement of our hypothetical transmission: reverse stall pressure must be 200 psi minimum. To provide for this pressure, line pressure from the manual valve (when in reverse range) is directed to the end of the compensator valve, and this additional hydraulic force overcomes the compensator spring load and exhausts the compensator pressure passage. With zero compensator pressure, line pressure will then increase to 200 psi to produce a hydraulic force equal to the full load of the main line pressure regulator valve spring. If the drive and reverse stall pressure requirements are the same (as on some transmissions in use today), the aforementioned modification to the compensator valve is not required.

design due to a limited amount of spring space available for the load and low rate desirable. Throttle pressure acts on the spring end of the valve and aids the springs in opposing the hydraulic force due to line pressure acting on area A and differential area B. An orifice is used in line B to dampen pump impulses into the system that might cause valve buzz. As throttle pressure increases, line pressure must also increase to balance the higher hydraulic force; in this manner, regulated line pressure becomes a function of throttle pressure. Two line pressure-conscious areas are used so that a higher pressure may be regulated in reverse range than drive range. When both areas are pressurized in drive range, area B directly from main line pressure and area A from the manual valve, a lower pressure is required to balance the load of the springs and any throttle pressure force. In reverse range, area A is not pressurized.

Governor pressure acting on the short compensator valve shown in Fig. 8.8.1.2.16 aids the compensator spring in increasing compensator pressure to affect a cutback in line pressure. As governor pressure increases on the short compensator valve, the primary part of the line pressure curve is regulated according to Fig. 8.8.1.2.15. To prevent this curve from falling below an acceptable operating pressure, governor pressure is also supplied to the cutback valve. On the cutback valve, governor pressure opposes line pressure. When governor pressure is high enough to overcome the line pressure force and move the cutback valve into contact with the compensator valve, the effective governor area of the compensator valve train is reduced to the difference in the two governor areas. The three valves then regulate as one valve to give the secondary part of the line pressure curve. For our circuit, we have arbitrarily selected this method of obtaining the two-stage cutback required to obtain high stall pressure. The secondary part of the line pressure curve would be at a constant pressure if both governor pressure areas were equal.

Fig. 8.8.1.2.17  Line pressure regulator valve. Part B—Throttle Valve Systems—There are two methods of obtaining a throttle signal in current use today. One system uses a linkage actuated by the accelerator pedal movement to vary the spring load on the end of a hydraulic regulating valve, as shown in Fig. 8.8.1.2.18. Let us for the moment consider only the lower throttle valve and assume that the upper valve is only a mechanical connecting link between the throttle-actuating lever and the spring. As the throttle spring is compressed by a movement of the lever, throttle pressure acting on the end of the throttle valve will increase to balance the axial force imposed by the spring. Throttle pressure is then regulated from the line pressure supply. The design requires that close control of the spring rate and its free length be maintained. The start of throttle pressure buildup is determined by the free length when the lever movement first compresses the spring and imposes a load on the throttle-regulating valve. A low spring rate is desirable due to the regulating valve movement and the importance of close control of pressure for consistent line pressure regulation. This linkage-actuated throttle pressure system has certain

We have now completed the main regulating aspects of our hypothetical system; however, as previously mentioned, some control circuits do not reduce line pressure with vehicle speed. The valving arrangement for this type of system is somewhat less complicated, as shown in Fig. 8.8.1.2.17. Both the front and rear pumps, or both stages of a two-stage pump design, supply the main line at port C. When the system is initially pressurized by the pump, line pressure increases and moves the valve until port D is opened. This port pressurizes the hydrodynamic unit. A further increase in line pressure due to oil volume from the pumps will open port F to the pump suction port E. Port F is connected to the pressure side of the transmission front pump or the larger pump in a two-stage pump design. If excessive oil volume is present in the system, line pressure will increase further, depending on the spring rates, until the line pressure port C is opened to the pump suction port E. Two springs were used in this particular

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cost advantages over other means of throttle control. For example, if a linkage is required so that the driver can control downshifts with the accelerator pedal, this same linkage can also be used for actuating the throttle valve.

the diaphragm and the rod toward the valve; the third force, atmospheric pressure, acts on the diaphragm in a direction away from the valve. When the engine is inoperative, the air pressure is equal on each side of the diaphragm, leaving only spring force acting on the valve. When the engine is idling, the air pressure in the engine intake manifold is considerably less than the atmospheric pressure. Thus, the air pressure tending to move the rod toward the valve is diminished, and less force acts through the rod to the throttle valve. Little or no throttle pressure is regulated under this condition. When the throttle is opened, the absolute pressure in the intake manifold is increased and approaches the atmospheric pressure. This causes an increase to the force acting on the throttle valve. Note that throttle pressure is then directly proportional to the absolute pressure in the engine intake manifold.

A recent innovation is the use of a cable instead of a mechanical link between the carburetor and transmission. However, from the control circuit design standpoint, the function of the cable is fundamentally the same as with the linkage; that is, the movement of the throttle valve in proportion to the carburetor opening. If we now consider also the upper valve in Fig. 8.8.1.2.18, we have a throttle and downshift valve design both actuated with the same linkage. When the downshift valve is moved to a predetermined downshift position, throttle pressure is directed to the shift valve through the downshift pressure passage to signal the downshift. The downshift pressure line is exhausted between the two valves when the downshift valve is not in a kickdown position. In some current transmission designs, line pressure is directed through the downshift valve circuit to the shift valve instead of throttle pressure.

The required family of line pressure curves will dictate the amount of vacuum at which the throttle valve must start to regulate. This point where pressure regulation begins in one installation is approximately 15 in vacuum, although this value varies because of differences in engine manifold vacuum characteristics and light-throttle upshift pressure requirements.

In both designs, the basic purpose is to signal a transmission downshift. The shift valve design must, of course, take into consideration the difference in throttle or line pressure, depending on which is used. The throttle valve shown has one unusual feature. A bimetallic spring is located at the lower end of the throttle valve to compensate for the effects of temperature. During low-temperature operation, the element will expand and apply a load against the valve opposing the throttle spring. This will result in a lower throttle pressure and consequently an earlier upshift pattern. The thermostatic element is adjusted by a screw to give an accurate spring value at a given temperature.

The effect of altitude must be considered in designing a vacuum throttle control system. With increasing altitude, the atmospheric pressure falls while the absolute engine manifold pressure remains relatively unchanged. Referring to Fig. 8.8.1.2.19 again, it is apparent the throttle pressure will then increase with altitude. This increase in pressure, combined with the normal loss of engine power at higher altitudes, will tend to make the shift quality more positive. Another design problem must also be considered with vacuum control. The cause of this problem can be seen by studying the family of curves shown in Fig. 8.8.1.2.20. Note that there is little difference in engine vacuum for the 60° and 70° (wide-open) carburetor throttle plate angle curves. Because there is very little difference in engine vacuum at the larger carburetor openings and vehicle speeds, some means of magnifying this vacuum difference through this shift range is required to obtain a desirable throttle opening versus shift speed schedule. This magnification is accomplished by the use of a boost pressure.

A second method of throttle pressure control uses the engine intake manifold vacuum pot, as shown in Fig. 8.8.1.2.19. A spring in the airtight upper chamber acts downward on a flexible diaphragm; the lower chamber is vented to the atmosphere. The operation of the vacuum control will be discussed from two approaches, the first being more concise and the second being more technically accurate. 1. Engine intake manifold vacuum is inversely proportional to engine torque. A spring in the vacuum pot acts on the throttle valve and tends to increase throttle pressure. Opposing the spring is engine vacuum. When the vacuum is relatively high as at idle, throttle pressure is low, but when the carburetor throttle is opened, vacuum falls, and throttle pressure increases because of the spring force. 2. There are three forces acting within the vacuum pot. Air pressure resulting from the absolute pressure in the engine intake manifold and a spring tend to move

Throttle boost is only required for shift spacing at the upper end of the shift range and is used only for throttle control of the shift valves and not for line pressure regulation. Figure 8.8.1.2.21 shows a regulating valve for obtaining a throttle boost pressure. Until throttle pressure reaches the break point of the two curves shown in Fig. 8.8.1.2.22, throttle pressure is allowed to flow across the valve, with the spring offsetting 8-81

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the hydraulic force acting at the opposite end of the valve. At the break point of approximately 40 psi, the throttle pressure force overcomes the spring force and moves the valve. Sufficient movement of the valve opens the line pressure port and causes a throttle boost pressure to be regulated. Throttle boost pressure is higher than throttle pressure but always directly proportional to throttle pressure. The boosted throttle pressure is indicated by the upper portion of the solid line in Fig. 8.8.1.2.22. If the pressure were not boosted, it would be impossible to obtain a pressure much higher than 65 psi at the minimum vacuum. Boosted pressure at minimum vacuum (approximately 1 in Hg) is approximately 85 psi.

Fig. 8.8.1.2.20  Engine vacuum characteristics.

Fig. 8.8.1.2.18  Downshift and throttle valves.

Fig. 8.8.1.2.21  Throttle boost valve. There are some definite advantages of this vacuum control system over linkage. No adjustments are required after the transmission leaves the factory, and increased reliability can be expected in any mechanism that is not subject to periodic adjustments (or maladjustments). Another advantage of the vacuum system is that it is fail-safe. If the diaphragm fails or the vacuum line develops a leak, high pressure will result; a failed or maladjusted linkage can cause low pressure, and the low pressure may permit clutch or band slippage. Excessive slippage of friction elements not corrected immediately will cause a transmission failure. Another type of vacuum control in use actuates a throttle and kickdown valve train in the same manner as with the mechanical linkage. This is accomplished by having a solenoid integral with the vacuum pot. An electrical signal from a switch connected to the accelerator linkage triggers the solenoid and creates an additional force on the push rod to affect the kickdown shift. Because this particular vacuum control system was designed for incorporation with an ex-

Fig. 8.8.1.2.19  Vacuum-actuated throttle valve. 8-82

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isting valve body, a small reversing linkage mechanism is used to change the direction of the force from the vacuum pot. Because of tolerances in this internal linkage, an adjustment is required when the vacuum pot is assembled to the transmission case. This adjustment procedure positions the vacuum can relative to the case, and subsequent adjustments, although infrequent, can be made within prescribed limits by turning the threaded vacuum pot.

where:

P α N2 r

(8.8.1.2.3)

P = governor pressure N = rotational speed r = radius to c.g. of mass α = varies with Figure 8.8.1.2.23 shows a simple governor curve. Figure 8.8.1.2.24 shows a governor circuit that will give a single stage or simple curve. Because pressure is supplied to the governor from the rear pump, oil is not drained from the main line at low speeds or vehicle standstill. An orifice is placed in the line between the pump and the governor so that excessive amounts of oil are not exhausted at higher vehicle speeds when the rear pump is supplying the main control circuit. As the governor starts to rotate, oil is fed through the orifice to the top of the governor valve. As the valve moves out from the center of rotation due to centrifugal force of the valve mass, the valve regulates a pressure proportional to vehicle speed. At very high speeds, the rear pump supply pressure is not sufficient to balance the centrifugal force, and the governor valve grounds out on the governor body. Governor pressure is then equal to rear pump pressure or line pressure if the rear pump is supplying the system. All oil that flows through the orifice must be used to maintain governor pressure or be exhausted at the governor valve. The simplicity of the design and the self-cleaning action of the relatively high oil flow minimizes sticky governor problems.

Fig. 8.8.1.2.22  Throttle and throttle boost pressure.

When two shifts are required at relatively low speeds, as for the minimum throttle upshifts in a three-speed automatic transmission, a simple governor curve does not provide sufficient discrimination between the governor pressures at the 1-2 and the 2-3 shifts to ensure consistent shift spacing. This problem is overcome by the use of a two-stage governor. Figure 8.8.1.2.25 shows a typical two-stage governor curve. The two-stage curve not only provides higher governor pressure at the 1-2 shift, but it also permits the use of a smaller governor pressure area on the 1-2 shift valve. Generally, a two-stage curve is designed so that the minimum 1-2 shift will occur on the primary curve, and the minimum 2-3 shift will occur on the secondary curve. Because the governor is supplied by line pressure, governor pressure cannot exceed line pressure. Accordingly, the value of governor pressure required to signal for any shift must be less than line pressure at the shift point. A governor pressure approximately 20 psi below line pressure for the full-throttle 2-3 shift is a sufficient differential to ensure consistent upshift under conditions of high leakage and restriction.

A system with two separate throttle valves has also been used successfully for several years. The vacuum-controlled throttle valve (also conscious of governor pressure) regulates a pressure that in turn modulates the main line pressure. The other throttle valve is linkage operated and regulates the throttle pressure which acts on the shift valve. This throttle valve system has flexibility in that the line pressure and shift scheduling are independently controlled. Another advantage is that shift spacing is not affected by altitude as with other vacuum-modulated systems. Disadvantages are the requirement for an accurate linkage adjustment to ensure proper shift spacing and increased complexity because of the separate throttle valve circuits. Part C—Governor Circuit Design—There are many types of governor valve systems, but they all rely on the centrifugal effects of some mass to produce a force proportional to the square of the speed of a rotating member. All governor curves will therefore be parabolic in shape and will conform to the basic relation

Figure 8.8.1.2.26 shows a two-stage governor in which the regulating valve and the effective mass are located on opposite 8-83

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sides of the output shaft. The valve is connected to the weights by a rod passing through the output shaft. As rotation begins, the centrifugal force of the weights causes the valve to be drawn toward the center of rotation and regulate a pressure proportional to the speed. At a predetermined speed, the outer weight grounds out on the outer snap ring and then the inner weight becomes the controlling factor. The reduction in effective mass resulting from the grounding of the outer weight causes a slower buildup of governor pressure indicated by the secondary part of the governor curve. Some complications may exist in this design because of the connecting members required between the valve and the weights; however, there are also some definite advantages in having the valve and weights on opposite sides of the shaft. For example, less space is required for rotation of the unit and this compact design is desirable in automatic transmissions where space is vital. Also, note that the governor valve can be installed from the outside. When the valve and weights are located on the same side of the shaft, it is necessary that the effective hydraulic force on the valve be in a direction toward the shaft. To accomplish this requires a reversal of the valve from the position shown in Fig. 8.8.1.2.26; that is, the larger of the two valve lands must be nearer the centerline of rotation. Assembly of the unit then consists of installing the valve in the bore of a separate body, which is subsequently bolted to the governor counterweight.

Fig. 8.8.1.2.25  Two-stage governor curve.

Fig. 8.8.1.2.26  Typical two-stage governor. In the governor designs previously discussed, the governor valve and body rotate with the output shaft. Figure 8.8.1.2.27 illustrates a different approach. In this design, rotation of the output shaft causes weights to move away from the shaft, pivot about pins, and exert an axial force which is transmitted to the governor valve through a lever arrangement. The mechanical force on the valve is proportional to speed, and thus a conventional governor pressure curve is regulated. When the governor pressure supplied to the end of the second-stage valve is sufficient to overcome the spring force, the secondstage valve moves against the primary valve pin, and the two valves regulate as a solid body. The effective governor area is then the sum of the two areas, and the second stage of the governor curve is produced.

Fig. 8.8.1.2.23  Governor pressure curve.

This completes the discussion of the components in the regulating circuit. For our hypothetical system, we have selected a linkage throttle control system and the two-stage governor. Figure 8.8.1.2.28 shows our hypothetical system including the

Fig. 8.8.1.2.24  Single-stage governor. 8-84

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main regulator, the compensator train, the throttle, and the governor valves. Now that the regulating circuit is completed, we will consider means of transmitting regulated pressures to friction elements at the proper tune.

Part D—Manual Valve Design—The logical place to start with this portion of the control circuit is the manual valve. Manual valves derive their name from the fact that they are actuated manually by the driver of the vehicle through a linkage arrangement. Because of the inherent tolerances in any linkage system, proper positioning is a problem peculiar to the manual valve. There are several different designs currently used to obtain valve positioning, and a typical installation is shown in Figure 8.8.1.2.29. Precise locating of the valve is necessary to prevent counteracting friction elements from being engaged simultaneously and causing a tie-up with the ultimate failure of the transmission. The relative position of the manual valve is predetermined by the required ranges in the particular transmission (park, low, neutral, drive, etc.) and the sequence of these ranges on the selector quadrant on the steering column, instrument panel, or floor. Although the function of a manual valve is relatively easy to understand, the valve is among those most difficult to design. The required movement and functions usually dictate that the manual valve be relatively long. The optimum design is that valve which performs all the necessary porting functions with a minimum of length. The mechanical connection for valve movement will induce some side loading and possible bending of the valve. This problem is aggravated with the

Fig. 8.8.1.2.27  Non-rotating valve governor.

Fig. 8.8.1.2.28  Complete regulating circuit. 8-85

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longer valve designs. Thus, there are several design problems facing the control engineer even before he begins to establish lands and porting. There is one advantage with the manual valve that is common to no other valve in the system: if the valve sticks in the bore during operation, the driver will probably free it without knowing there was a malfunction. Consequently, the designer can permit less clearance between the valve and bore, and this helps reduce valve leakage. The basic function of the manual valve is to direct regulated line pressure to the various shift valves for clutch or band application, or in some cases, pressure is directed to a specific friction element. In each transmission range, only certain valves in the control circuit require pressurization for proper functioning; from a leakage consideration, it is desirable to pressurize only those necessary. When an oil passage is not pressurized, it is necessary to provide for an adequate exhaust so that leakage from adjoining pressurized areas will not build up any pressure. The manual valve can be used extensively for exhausting inactive lines.

Fig. 8.8.1.2.29  Manual valve locating device.

Figure 8.8.1.2.30 shows a typical manual valve porting design for a two-speed automatic transmission. The valve is composed of three lands that seal off pressurized ports from exhausted port areas as the valve is moved through the shift quadrant of park, reverse, neutral, drive, and low ranges. The valve is shown in the neutral position, and although line pressure is supplied to the manual valve at port C, no oil is allowed to flow to any other port. This same condition also exists in park range, as no transmission shifting is required. Note that all other ports are open to either exhaust port A or exhausted at the end of the body bore. Ports F and G are used to exhaust ports D and E, respectively, and are required only for that purpose in the system. In reverse range, port B is pressurized to engage the reverse friction element and to provide for high line pressure in reverse, in a manner described in Part A. In drive range, port D is pressurized to supply oil to the shift valve, downshift valve, and directly to the low-gear friction element. Port E is pressurized to supply oil to the shift valve to cause the transmission to downshift into low gear. If the transmission is in low gear, this pressure force prevents an upshift.

Fig. 8.8.1.2.30  Manual valve. Figure 8.8.1.2.31 shows our complete hydraulic circuit, including the manual valve discussed in Part D, and the shift valve that will be discussed in Part F. The shift valve train appears to be comprised of three valves and two springs. Actually, the small throttle-reducing valve at the right end of the train and the inner spring could be placed in a different location without affecting the basic function of the shift valve train. Governor pressure acting on the left end of the valve train forces the long shift valve in the direction to effect an upshift (to the right). Opposing the governor pressure force are the two springs and reduced throttle pressure force regulated by the throttle-reducing valve. The throttle-reducing valve reduces throttle pressure by some constant value; we will assume a reduction of 20 psi for our system. Thus, when throttle pressure reaches 30 psi, reduced throttle pressure will be 10 psi, and this resulting hydraulic force on the shift valve is designed to effect the proper delay in the upshift point to obtain an optimum shift schedule.

Part E—Shift Valve Design—To complete our control circuit, shifting valves are necessary to signal for the application of the friction elements. A minimum of one shift valve is required for each upshift to be effected. Most control systems, however, require more than this number to satisfy the various upshift and downshift requirements. The number and arrangement of shift valve trains depend on the number of friction elements and the sequence of apply and release actions required. Then, too, provision must be made for timing problems that are peculiar to the transmission design.

On a minimum or a very light-throttle upshift into higher gear, there is no throttle pressure and consequently no reduced throttle pressure in the system. The upshift point is determined by the spring load and the effective hydraulic force due to governor pressure. Part-throttle upshifts are af-

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fected by reduced throttle pressure only after throttle pressure has reached 20 psi. Prior to reaching 20 psi, throttle pressure is effective only in increasing the line pressure in the system to compensate for the increase in engine torque. As throttle pressure increases to 20 psi (the start of reduced-throttle pressure buildup), there is a slight delay in the upshift due to the increase in the reduced throttle valve spring load as the valve moves to its point of regulation. However, if the spring rate is kept low, the shift delay force will be slight.

This, in turn, permits the fill or exhaust of one or more of the band servos or clutch cylinders. Line pressure is used to help delay the upshift in some designs and in others to provide valve snap action. In the latter design, the line pressure will prevent the downshift from occurring until governor pressure is reduced because it (line pressure) is acting in the same direction on the valve as the governor force. Hydraulic forces that are used to effect a snap action of the valve will also cause a delaying action; therefore, these forces should act in the same direction on both shift valves in a three-speed transmission. By making the function of the forces the same on all shift valves, the possibility of shift pileup or excessive shift delay—which may occur when one shift is delayed and the other shift is not—is diminished. Pileup is a condition where the 1-2 upshift occurs at the same time or close to the 2-3 upshift. In severe cases of pileup, second gear mat be completely bypassed, resulting in 1-3 shift.

If the throttle-reducing valve were not used in this system, the minimum and light throttle upshifts would seem to delay the driver. As soon as the driver depressed the accelerator pedal, throttle pressure would increase and create a delaying force on the shift valve, thus delaying the upshift until a higher vehicle speed caused sufficient governor pressure to offset the throttle pressure. In our hypothetical system, the upshift occurs when the governor pressure force overcomes the spring and the reduced throttle pressure forces. The valve strokes to the right and allows oil to flow through the porting to the clutch as required for the shift. Note that proper timing between clutch application and band release is accomplished by using a common passage for clutch apply and band release pressure.

Part F—Special-Purpose Valve Design—There are many types of special-purpose valves in use; however, this discussion will be limited to the orifice control valve shown in Fig. 8.8.1.2.31. The purpose of this valve is to ensure shift smoothness during the closed-throttle, high-to-low gear downshift. Shift smoothness is affected by precisely timing the application of the low band with the releasing of the clutch. In Part E, it was stated that low servo release and the clutch apply are supplied from a common pressure line. Figure 8.8.1.2.31 illustrates this principle and also shows a ball check valve in the servo branch of the circuit. This ball check valve causes the orifice control valve to be bypassed during upshift but be functional during a downshift. The use of the orifice is required on a closed-throttle downshift to prevent a friction element tie-up and the subsequent clunk. A tie-up condition occurs when the low band applies before the high clutch released. This momentary lockup of the driveline may cause an audible and objectionable clunk. This servo and clutch tie-up occurs only at closed throttle because of the low engine torque output and the pressure relationship between the clutch apply and servo release. When the shift valve signals a coasting downshift from high gear, the pressure drops in both the clutch and servo release circuits to a point where the force on the apply side of the servo piston overcomes the release force. As the piston strokes, the release oil is forced out of the servo into the line. Without a pressure drop across an orifice such as that provided by an orifice control valve, a pressure would be maintained in the clutch feed line sufficient to keep the clutch engaged. The band would then apply before the clutch disengaged and a tie-up condition would exist until the clutch released.

To provide for the desired full-throttle shift point, the downshift valve is moved to the right, and the throttle pressure is supplied to the reduced throttle valve exhaust port preventing regulation. The reduced throttle pressure area of the shift valve is then conscious of throttle pressure. Throttle pressure is always greater than reduced throttle pressure by 20 psi. In this manner, a greater delay force acts on the shift valve, and the maximum throttle shift point is established. If engine vacuum were used for regulation of throttle pressure, it would be necessary to use boost pressure in place of throttle pressure for the reason stated in Part B. Reduced throttle boost pressure would be used for shift control in place of the reduced throttle pressure. A three-speed transmission would require that the control circuit provide for two upshifts: low-to-intermediate gear and intermediate-to-high gear. Two upshift valves would therefore be required. The intermediate-to-high upshift could be accomplished with a valve train similar to that used in the hypothetical system. A typical low-to-intermediate upshift valve was shown in Fig. 8.8.1.2.8. The same reduced throttle valve pressure is used on both shift valves to affect a delay in the upshift. Although upshift valves look completely different and are different with regard to valve diameters and spring size, they all function basically the same. As previously mentioned, a governor pressure force overcomes a spring force and a function of throttle pressure force to stroke the valve.

Under open-throttle downshifts, the engine torque is greater, and the pressure in the clutch maintained by the fluid being exhausted from the servo is not sufficient to keep the clutch

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Fig. 8.8.1.2.31  Complete hydraulic circuit. when the continuity of the driving force from the engine to the wheels is interrupted by an excessive slippage of a band or clutch, permitting a momentary, uncontrolled acceleration of the engine. It is therefore the function of the orifice control valve to restrict the flow of servo release oil, under certain specific operating conditions, until the clutch will release smoothly. Throttle pressure is applied to the orifice

applied long enough to create a tie-up. A similar condition exists on a closed-throttle, manual-drive-to-low coasting shift; however, in the latter case, it is output shaft torque rather than engine torque that tends to cause the clutch breakaway. Under open (engine) throttle conditions, the use of the orifice is undesirable because restriction of flow might result in engine cut loose. Engine cut loose occurs 8-88

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control valve so that, with open (engine) throttle conditions, a flow passage is provided to bypass the orifice. In a similar manner, line pressure in manual low gear, acting through the smaller valve, moves the orifice control valve and permits unrestricted exhausting of servo release oil during a manual drive to low shift. The function of the orifice control valve spring is to set a throttle pressure at which the orifice control valve will stroke and to ensure that the valve will return to the closed-throttle position.

where: PL = 160 Pt = 65 Pg = 0 Eliminating Pc,

This completes the plumbing phase of our control system. Although each of the components is representative of current practice, no system exactly like our hypothetical system has ever been built. If such a control system were to be constructed it would, of course, be necessary to determine valve areas, land diameters, and spring loads.

Idle Pressure: and

Based on the requirements for the hypothetical transmission stated previously, and shown by the family of line pressure curves in Fig. 8.8.1.2.15, the pressure values shown in Table 8.8.1.2.2 must be obtained.

S1 = 60 A1 + Pc A2

where: PL = 60 Pg = Pt = 0 Eliminating Pc,

Table 8.8.1.2.2 Pressure Values, psi

S1 = 60A1 +

A2 A4

(8.8.1.2.6)

Minimum Pressure:

65 psi 25 psi 45 psi

S1 = 50 A1 + Pc A2 where: PL = 50 Pc = PL Pt = 0 Eliminating Pc,

Seven equations for conditions of equilibrium may be written. Reverse Stall Pressure: S1 = 200A1

(8.8.1.2.5)

S2 = Pc A4

At this time, certain assumptions must be made based on experience and good practice. Subject to revision (if calculations indicate the necessity), we will assume the following:



A2 (S2 – 65A5 ) A4

The short compensator valve determines the intersection point of the primary and secondary line pressure curves but does not contribute to compensator pressure regulation on the primary curve.

Sample Computations for Regulated Line Pressure

Throttle pressure—maximum Governor pressure at 1000 rpm output Governor pressure at 2000 rpm output

S1 = 160A1 +

(8.8.1.2.4)

S1 = 50 A1 + 50 A2

(8.8.1.2.7)

The governor pressure when this condition occurs can be calculated after the compensator areas and spring valves have been determined. It is a function of point D in Figure 8.8.1.2.31 and cannot be set independently because a curve drawn through the break points in the family of line pressure curves will pass through the zero axis if projected beyond actual values. The curve swings about the zero axis and has already been determined by point D.

where: PL = 200 Pc = 0 Pc = 0 because S2 < PL A6. However, this should be checked after S2 and A6 have been determined Drive Stall Pressure: S1 = 160 A1 + Pc A2

Intersection of Maximum Primary and Secondary Pressure Curves:

and

S1 = 100 A1 + Pc A2

S2 = Pc A4 + 65 A5 8-89

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8.8.1.3  Manufacturing Aspects of Valve Body Design

where:

L. T. Szady and C. R. Moore Chevrolet Motor Div., General Motors Corp.

Pg = 25 Pt = 65 Eliminating Pc, S1 = 100A1 +

also

The valve body houses the control valves and provides the oil distribution passages that call the signals for automatic gear shifting. Scheduling complexities dictate an intricate control system. This makes the valve body a complicated assembly of precision parts.

A2 (S2 + 25A3 – 65A5 ) (8.8.1.2.8) A4

100 A7 = 25 A8

After determining the type, shape, and number of valve mechanisms required, the designer must arrange them in a subassembly that is trouble-free and economical to build. We will limit our discussion to the latter task.

(8.8.1.2.9)

Maximum Pressure at 2000 rpm Output:

S1 = 90 A1 + Pc A2

where:

8.8.1.3.1 Valve Body

PL = 90 Pg = 45 Pt = 65 S2 + 45 A3 + 90 A7 = Pc A4 +65 A5 + 45 A8

The most desirable valve body is one that is small enough and has a small number of valve bores so oriented that the valve body may have all bores finished in one clamping. Why is a small valve body desirable? In most manufacturing plants, the valve body is drilled and bored on an indexing table machine called a Kingsbury. This vertical machine has a central column to which individual vertical machining spindles are attached. In addition, horizontal machining spindles are attached to the circular periphery of the machine to drill, ream, and tap mounting holes, pressure taps, and orifices.

Eliminating Pc, S1 = 90A1 +

A2 [S2 + 45(A3 – A8 ) + 90A7 – 65A5] A4 (8.8.1.2.10)

We now have seven equations to use in solving for nine unknowns (seven areas and two spring loads). Based on experience, a diameter large enough to handle the pump capacity is arbitrarily established for the main regulator valve.

A1 + A 2 =

πd 2 4

If a valve body is designed with manufacturing in mind, a small valve body can be completely machined on one of these machines. Otherwise, two or three of these machines are necessary to complete one valve body.

(8.8.1.2.11)

If the valve body is large, the clamping fixture becomes large. With large fixtures, only eight stations can be nested around the vertical column of the machine. With small fixtures (small valve body), 12 stations can be nested around the vertical column. It may take two machines with large fixtures to do about the same number of operations as one machine with small fixtures. In round numbers, one of these machines completely tooled represents a cost close to $135,000. So there is a worthwhile saving to be made with a properly designed valve body.

where: d = large diameter of main regulator valve After substituting a value for d in Eq. 8.8.1.2.11, A1, A2, and S1 can be obtained from Eqs. 8.8.1.2.4, 7, and 11. There are now six unknowns (five areas and one spring load) and five equations. Based on experience, a tentative value is set for S2. Then A4 is obtained from Eq. 8.8.1.2.6, A5 from Eq. 8.8.1.2.5, and A3 from Eq. 8.8.1.2.8. Equations 8.8.1.2.9 and 10 can now be solved simultaneously for A7 and A8. The value of A6 can be selected to establish an optimum size for the compensator valve.

Two manufacturers prefer to machine the valve body on a transfer line, but the above facts apply here also. A small valve body means small fixtures, a shorter transfer line, and less capital investment.

Because S2 was selected on a trial-and-error basis, it may be necessary to repeat the computations if the calculated valve diameters are not feasible from a manufacturing standpoint or if the package size is not acceptable.

Completing all the important valve bores in one clamping is desirable. Reclamping always presents the possibility of distorting, warping, twisting, or bending of the precisely finished valve bores. 8-90

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The requirement for single clamping differs for the two machining methods. For single clamping on the indexing table machine, the bores must be basically complete from one direction, although under certain conditions two directions at 90 deg can also be machined in one clamping. For single clamping on the transfer line, the bores can be from two directions, 180 deg apart.

consisting of one wall and one oil passage requires 0.3 in, whereas the same in aluminum would require 0.25 in. On a volume basis, size for size, the aluminum valve body as die-cast would cost slightly less than cast-iron. However, this is offset by other items such as need for gun boring, anodizing, deburring, and burnishing, which probably make an aluminum valve body more expensive. The small difference in casting cost is explained by the fact that cast-iron weighs more but the cost per pound is less.

On the indexing table machine, when it is impossible to bore from one side only, it becomes necessary to rotate the valve body to a new position and reclamp. The second clamping can be in any position; therefore, the remaining bores can enter the valve body from either side or rear. Arranging some valves at 90 deg to the direction of the general axis of the valve body should not be overlooked, for the reward may be compactness. But making all bores from one side is still most desirable.

Normally, the machining of aluminum is faster than that of cast-iron if the same tools are used. However, in cast-iron conventional reamers are used, while in aluminum gun reaming is necessary to control size and finish. Gun reaming is slower than conventional reaming, with the net result that in this particular situation the cast-iron is machined in less time than the aluminum. The final cost in cast-iron is less than in aluminum.

8.8.1.3.2 Valve Body Bores

Gun reaming is used in aluminum because of the smaller bore tolerance required than in cast-iron. Although the drawings show the same bore tolerance for aluminum as for cast-iron, we will show later why manufacturing is producing bores in aluminum that are less than print tolerance.

Valve body bores should be kept as short as possible, because the machine cycle is proportional to the length of bore, and it is easier to make a straight bore. The longer the bore, the longer the time cycle on the machine, and the indexing time of the machine is geared to the longest machining cycle. To shorten a long machining time, the process man will, if possible, make two or more passes at the long bore, cutting the machine time proportionately.

Evidently, conventional reaming can be used in production if the hole tolerance is 0.001, but if the tolerance is less than 0.001 it becomes necessary to resort to gun reaming, which is more accurate but slower. Gun reaming does not require a guide bushing, because the gun reamer makes its own guide. Conventional reamers require a guide.

Whenever possible, a single-diameter valve and bore are most desirable because: 1. Runout problems between two diameters are eliminated. 2. A simple and inexpensive tool without steps can be used. 3. Cutting speeds (feet per minute) do not have to be compromised, particularly when a large step in diameters exists.

In aluminum, all bores are cored and have about 0.020 finish stock per side. In cast-iron, only the large bores are cored; all others are solid. In general, the aluminum valve body with cored valve holes is brought to size in two operations. The first operation consists of drilling or rough reaming, depending on the condition of the hole. The second operation is to final gun ream to size.

If single diameters cannot be used, make the step as small as possible so that a less expensive tool can be used with no surface speed compromise and perhaps better concentricity and straightness. It has been suggested that if the bore is 21⁄2-in long, do not go under 1⁄2-in diameter.

In general, the cast-iron valve body with solid holes or cored holes is finished to size by a rough drill operation to remove maximum material. This is followed by a rough ream to straighten out the drilled hole as much as possible. Then the cast-iron valve body is finish-reamed to size. The aluminum body requires two passes per bore, while the cast-iron body requires three passes per bore.

8.8.1.3.3 Cast-Iron Versus Aluminum Valve Body From what we have observed, the only advantage to an aluminum valve body is weight saving, because aluminum weighs one-third the weight of iron. Another slight advantage to aluminum is that the length of valve and valve bore can become somewhat shorter. For example, in cast-iron, one port

After finish boring of the aluminum body, most manufacturers anodize the valve body for two reasons (one manufacturer does not anodize):

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1. Chips and burrs become brittle and are more easily removed in subsequent hand deburring and shell blasting operations. 2. A harder surface permits freer movement of the valve in its bore.

facturing. The 0.0005 in minimum clearance does not include the possible runout in a stepped valve and bore. Considering the TIR on valve and bore, the minimum clearance becomes 0.0001 in: 1. 2. 3. 4.

We have observed a substantial amount of hand deburring with the aluminum bodies, whereas the cast-iron body has practically no hand deburring. Also, the aluminum bodies required a sizing operation after anodizing. This consisted of either a rotary bearing operation or a stationary burnishing. In cast-iron, burnishing is used only for repair work.

+0.0005 minimum diametral clearance (aluminum) −0.00015 (0.003 in TIR on valve) −0.00025 (0.0005 in TIR on valve bore) +0.0001 minimum diametral clearance including runout

By referring to Fig. 8.8.1.3.1, we can see that if we had a minimum clearance of 0.0001 in at 68°F, the valve would not want to move freely as a valve must move. After including runout, the minimum clearance of 0.0001 in leaves nothing to tolerate warping, bowing, or distortion of the valve body.

8.8.1.3.4 Leakage Versus Bore Clearance in Cast-Iron and Aluminum Figure 8.8.1.3.1 shows the diametral clearance of a steel valve in a cast-iron valve body and a steel valve in an aluminum valve body plotted against temperature. Because cast-iron and steel have the same rate of thermal expansion, the diametral clearance remains constant, independent of temperature. With an aluminum valve body, the diametral clearance increases with increase in temperature because aluminum has a rate of expansion twice that of steel—for aluminum, 0.0012 in/in/100 deg and for steel, 0.0006 in/in/100 deg.

In cast-iron, because the minimum diametral clearance is 0.001 in and after considering runout in stepped bore and runout on stepped valve, the minimum diametral clearance becomes 0.0005 in, which can tolerate some distortion without making a sticky valve: 1. 2. 3. 4.

Note that at 68°F, the minimum clearance is 0.0005 in with aluminum, while the minimum clearance is 0.001 in with cast-iron.

+ 0.001 minimum diametral clearance (cast-iron) −0.00025 (0.0005 in TIR on valve) −0.00025 (0.0005 in TIR on valve bore) + 0.0005 minimum diametral clearance including runout

In aluminum, to avoid minimum valve clearances, manufacturing is compelled to make valve bores to less than print tolerance, favoring the high side in the valve bores while favoring the low side on the steel valves. In cast-iron, full dimensional tolerances can be used.

With an aluminum valve body, it is necessary to keep the minimum clearance at 0.0005 in so that at about 200°F the clearance would be 0.001 as it is with cast-iron (Fig. 8.8.1.3.1). This is done to keep the oil leakage through diametral clearance the same for an aluminum and cast-iron body.

At 240°F (Fig. 8.8.1.3.1), the maximum valve clearance is the same for cast-iron and aluminum, and hence the oil leakage would be equal. To provide manufacturing with a full working tolerance with aluminum at 68°F would require that the clearance be made 0.001 minimum, 0.0025 maximum. This would now increase the maximum valve clearance at 200°F to 0.0029 in for aluminum, as compared with 0.0025 maximum for cast-iron. This slight increase in valve clearance may not appear very much, but it does increase the oil leak by 65%, as shown in Table 8.8.1.3.1. This increased oil leakage would occur only if in aluminum the valve clearance was made 0.001 minimum and 0.002 maximum at 68°F. If the clearance is kept at 0.0005 in minimum and 0.002 maximum, as it is currently in aluminum valve bodies, the oil leakage is exactly the same as in cast-iron at 200°F. But this condition presents a hardship to manufacturing because:

Fig. 8.8.1.3.1  Clearance versus temperature (0.500 diameter steel valve). The 0.0005 in minimum diametral clearance when using aluminum presents more demanding requirements on manu-

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Table 8.8.1.3.2 Rates of Leakage

1. Under minimum limit stack including runout in a twostep valve, the minimum clearance is 0.0001 in at 68°F, which is inadequate and leaves no clearance to tolerate any bowing or distortion. 2. Manufacturing is forced to work to tolerances less than shown on drawing to have free-moving valves.

Leakage Dimetral Valve Clearance

At 0.0025 At 0.0029

145 240

100 165

0.03 0.10 0.23 0.42

Under certain conditions, the ditches can be cast conveniently in the case. The conditions are: 1. The ditches should be at least 0.200 in wide and shallow in depth. The object here is to have sturdy and short core fingers so that the heat of solidification of aluminum may be rapidly carried away without core fingers getting too hot. If fingers get too thin, the life is short, and the time cycle of the die-casting machine is long. 2. In general, the valve body must be small in size with a small number of valves. Otherwise, in the space available, it becomes impossible to nest enough passages with the 0.200-in-wide passage requirement. 3. In general, the servo piston and struts must be oriented in a vertical position. Otherwise, the underface of the case has to be open in construction for the assembly of servo struts or servo multipliers.

Table 8.8.1.3.1 Effect of Clearance on Leakage Rating %

  120   360   870 1590

8.8.1.3.5 Separate Ditch Plate Versus Ditches Cast in Case

Assuming that, in general, we have six ports through which oil could leak and the line pressure is 100 psi, the rates of leakage shown in Table 8.8.1.3.2 could be expected.

cm3/min*

gpm

0.0015 0.002 0.0025 0.003

To elaborate on rate of oil leakage versus diametral clearance, refer to Figure 8.8.1.3.2, which shows three curves at 50, 100, and 200 psi for a 0.500 diameter valve with oil at 200°F. The leakage is for one port only. To obtain total leakage, the leakage rate must be multiplied by the number of ports involved. It is interesting to note that at 0.001 valve clearance, there is practically no leakage regardless of the three pressures shown.

Valve Clearance

cm3/min

*Oil leak at 100 psi at 200 F per one port for 0.500 diameter valve.

8.8.1.3.6 Valve Body Bolt Pattern A wisely chosen bolt pattern is of great help to manufacturing in that suction leaks at front pump and rear pump and pressure leaks across channels can be diminished. A poor bolt pattern generally imposes on manufacturing more demands on flatness and microfinish of mounting faces. Along with bolt pattern, the thin transfer plate must be supported in pressure areas to prevent the transfer plate from ballooning, which could cause a leak. 8.8.1.3.7 Valves 1. As mentioned earlier, valves with one diameter are most desirable to manufacturing, because a single-diameter valve can be continuously fed through the centerless grinder at a high production rate. Multiple-diameter valves are manually or automatically fixture-fed to the grinder at a much lower production rate. 2. Avoid valves having an L/D ratio approaching one. These valves are more difficult to orient for automatic feeding

Fig. 8.8.1.3.2  Leakage versus clearance (one 0.500 diameter value at 200°F).

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and more difficult to hold while grinding, contributing to a lower production rate. 3. Valves that are long for their small diameter are difficult to machine in the automatic screw machine because they bend under the force of the tool bit. As a general reference for 0.38 diameter valves and smaller, avoid a L/D ratio greater than five. 4. When considering valve diameters, keep in mind that the larger-diameter valves with their greater hydraulic force should be more able to overcome stickiness or a slight burr or dirt than a small-diameter valve.

It also appears that if the bore had a very rough finish, the valve would not wipe out any dirt that may have found itself in the path of the valve, as well as if the bore had a very smooth surface. So it can be said that a fine microfinish is desirable for a free-moving valve and good wiping action. The effect of microfinish on oil leakage at each port is insignificant when considering that even with 0.001 diametral clearance, the leakage around the valve is minute (Fig. 8.8.1.3.2). It is fortunate that the machining conditions necessary to produce a good and accurate bore are the same that will produce a fine microfinish—namely, high surface speed and light feed. Valve body flatness is obviously desirable to minimize distortion to valve bores by bolt tightening. The microfinish on the valve body face comes as a result of lapping. It is the flatness that is of primary concern and not the microfinish. Fortunately, here again, the degree of flatness appears to go hand-in-hand with microfinish.

8.8.1.3.8 Current Dimensioning Practice The highlights of Table 8.8.1.3.3 pertaining to the valve body are as follows: 1. In cast-iron, one port and land requires 0.30 in versus 0.25 in aluminum. 2. Casting draft angle is the same for both cast-iron and aluminum.

Note that manufacturer 4 with an aluminum valve body does not anodize his part. We do not have a satisfactory explanation for his success.

In aluminum, important passage locations can be held to −0.005 versus −0.010 for cast-iron.

The highlights in Table 8.8.1.3.4 pertaining to valves are: 1. The microfinish on valves varies among manufacturers from 15 to 30. Thirty microfinish can be attained quite easily, but 15 microfinish is a requirement for free valve movement. 2. Valve edge sharpness is required to produce a good wiping action if dirt is in the path of valve movement. Chamfered edges may wedge on dirt and therefore are undesirable. Everyone calls for a 0.003 break in valve edges, because a perfectly sharp edge would want to

The bore microfinish note on the drawings varied from 20 to 80 to none at all. It appears that, academically, if we had a perfectly bored hole and a perfect valve with no side loads, the valve would move very freely, regardless of what microfinish we had in the bore. But we do have distortion and runout in the bore, and there is some side load on the valve even though we design for minimum side load. The microfinish, therefore, need only be as fine as necessary to produce free valve movement. Table 8.8.1.3.3  Current Dimensioning Practice—Valve Body Material Wall Thickness at bore CL Passage width at CL Per port Draft angle at ports, deg Limits on important passage location Bore, microfinish Bore, total tolerance Bore, total ind. runout Face, flatness TIR Face, microfinish Finish stock Anodize

Mfr. 1

Mfr. 2

Mfr. 3

Mfr. 4

Mfr. 5

Mfr. 6

Aluminum

Aluminum

Aluminum

Aluminum

Cast-iron

Aluminum

0.12 0.012 0.24 1 max ±0.005

0.125 0.125 0.250 1 ±0.005

0.12 0.13 0.25 3/4 ±0.005

0.10 0.136 0.236 0.010/side ±0.010

0.15 0.15 0.30 1 max ±0.010

0.12 0.12 0.24 1 max ±0.005

0.001 0.0005 0.001

20 0.001 0.0005 0.001

45 0.001 0.0005

0.02 Yes

? Yes

80 0.001 0.0005 0.0003 32 ? Yes

0.001 0.0005 0.0005 30 0.06 No

0.001 0.0005 0.001 25 ? Yes

0.02 No

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Table 8.8.1.3.4  Current Dimensioning Practice—Valves Body Material Material: Steel Hardness Hardness, depth Diameters—total tolerance Diameters—TIR Microfinish—ground diameters Valve edge sharpness Designed diametral Clearance and valve

Mfr. 1

Mfr. 2

Mfr. 3

Mfr. 4

Mfr. 5

Mfr. 6

Aluminum

Aluminum

Aluminum

Aluminum

Cast-iron

Aluminum

1113 87 min 15 N 0.017/0.025 0.0005 0.0005

? ? ? 0.0005 0.0002 15

1112 89 min 15 N 0.005/0.015 0.0005 0.0003 20

1112 File hard 0.008/0.015 0.0005 0.0005 30

1112 File hard 0.008/0.020 0.0005 0.0005 30

1117 File hard 0.015/0.022 0.0005 0.0005 30

0.003 max 0.0005 0.0020

Sharp 0.0005 0.0020

0.003 0.0005 0.0020

0.003R max 0.0005 0.0020

0.003 0.0010 0.0025

0.003 0.001 0.0025

hang up and stick on the microfinish in the bore, and also a perfectly sharp edge would nick very easily in handling.

8.8.1.4  Conclusion

ance to produce free-moving valves and at the same time keep the oil leak equal to that in cast-iron. The tighter tolerance requires more expensive tools and a slower rate. Some people are more successful than others, but, in general, the aluminum valve body requires hand-deburring, while castiron has no hand-deburring. Aluminum requires anodizing followed by burnishing. Both aluminum and cast-iron have walnut shell blasting. It appears that the cast-iron valve body should cost less.

The following are rules for the proper construction of valve bodies:

8.8.2

Note that manufacturer 6, unlike the other aluminum users, has valve diametral clearances that are the same as in cast-iron.

1. Design the valve body as early as possible. Do not make it the last item.

Control Components—Sensors

Introduction In 1962, the SAE Design Practices: Passenger Car Automatic Transmissions book was introduced. Subsequent editions have been continually reviewed and revised by committees so that the AE series is truly a current resource for both new and experienced transmission engineers. The fourth edition, AE-29, has updated all chapters to include recently acquired knowledge, information, developments, and current manufacturing practices. As new technologies such as electronic controls have emerged, the reviewers and editors of the AE series have added new chapters and sections.

2. Have numerous discussions with the manufacturing group, and primarily with the process and tooling people, to come up with a valve body design that will be small, with single clamping and with no troublesome bores. All these features contribute to making a valve body troublefree and economical to build with a small capital investment. All of this can be done with no sacrifice to the desired function of the valve body. If designing for existing equipment, strive for small size for the indexing table machine with all bores from one direction and single clamping. For the transfer line, there will be bores from two directions at 180° with single clamping.

Control Components is one of the new sections in AE-29. Many of the design topics found in AE-29, Chapter 8, Section 8 reflect the cutting edge design thinking of worldwide automatic transmission engineers. Focus is also provided on the interdynamics that take place between the electronic systems of the engine and transmission. The material depth of knowledge will assist the senior as well as the new automatic transmission engineer. The topics “Hydraulic Control Systems” and “Design of Valve Body and Governor Systems” are included because they continue to perform important

If the equipment does not exist, strive to design for the indexing table machine because the capital investment is less with no sacrifice to production rate. As to using aluminum or cast-iron, there are strong opinions for each. For aluminum, the main advantage is weight. In aluminum, the valve bores must be held to a tighter toler8-95

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control functions. The remaining subsections are completely new additions to the control material presented in AE-18, the last publication.

er anticipation. The automatic transmission engineer must specify and select a wide variety of sensing devices ranging from SAW quartz elements to thin-film magnetic devices. Choosing the correct sensor for the automatic transmission application is the essence of Section 8.8.2.

The material in this section “Subchapter 8.8.2 Control Components—Sensors © 2005 Honeywell International Inc.” was assembled and written by Joe Gierut and John Titlow of Honeywell and is provided “Courtesy of Honeywell International Inc.”

Transmission sensors find applications in a wide variety of challenging locations and environmental conditions. Many sensors are found outside of the transmission case, submerged in the oil cavity area or nestled near the rotating members. The internal sensors are subject to the same conditions and specifications as the friction devices, transmission oil, and planetary gearsets.

8.8.2.1  General Design Overview More and more of the torque transfer that occurs during an upshift or downshift in today’s passenger car automatic transmission is electronically controlled. Sensors that can detect pressure, temperature, position, torque, and speed have seen a rapid deployment, both internal and external to the automatic transmission control logic. Electronic transmission control becomes a necessity as passenger car automatic transmissions migrate from three- and four-speed planetaries toward either five- to seven-speed gearsets or other new forms of efficient and compact gear trains.

The operating environment can have a thermal range of −40°C to 150°C simultaneously occurring with shock, vibration, electromagnetic compatibility (EMC), humidity, galvanic corrosion, and hostile fluids. These are all part of the design specification process. The Design Failure Mode and Effects Analysis (DFMEA), Process Failure Mode and Effects Analysis (PFMEA), and Design of Experiments (DOEs) for individual sensor designs will help produce a robust sensor.

Industry drivers for improving electronic transmission systems include fuel efficiency, shift quality, weight reduction, and aggressive emission standards. Sensors are used to help achieve these industry needs in the most efficient and effective manner possible.

8.8.2.2  Environmental and Test Conditions Some of the Design Validation Procedure and Report (DVP&R) testing should contain [4]:

Improving transmission performance is a high priority for all major vehicle OEMs. Replacement of hydromechanical control systems with sophisticated control algorithms and sensor technology has been taking place for some time. The emergence of Advanced Automatic Transmission Systems such as Continuously Variable Transmissions (CVTs), Automated Manual Transmissions (AMTs), Infinitely Variable Transmissions (IVTs), Double Clutch Transmissions (DCTs), and Hybrid Electric Vehicles (HEVs) all require significant sensor content for proper operation. Increased sensor usage is also expected to be driven by the regionally large transition of European vehicles from manual to automatic transmission systems.

A full electrical test on the initial lot of test samples and at the end of each individual environmental, electrical, and mechanical test A DOE to understand the relationship between design characteristics and sensor performance Thermal Shock testing Highly Accelerated Life Testing (HALT) Long-term reliability testing, equivalent to 250,000 km (155,343 miles) or b etter Drop, vibration, shock, connector push-pull, submersion testing Salt fog, humidity, long-term humidity, and chemical splash High-pressure water and/or steam washing Gravel, road stones, impact testing EMC, high voltage, short circuit, and current injection Sensor survival in hot contaminated transmission fluid Thermal cycling from −40°C to +150°C Pressure Sensors: Over pressure cycling at a minimum of three times the operating pressure

The sensors used in an automatic transmission and manufactured to standards of high reliability feed the critical signals in either analog or digital format into the Electronic Transmission Control Modules (ETCM). The ETCM and its associated actuation system supports additional planetary gearsets without the massive space and material constraints that the older hydraulic logic controls would require. In order for the ETCM to be effective, many transmission parameters must be measured in real time. These parameters include input/output rpm, vehicle speed, pressure, and driv-

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Pressure Sensors: Hydraulic pressure dithering testing to simulate an imperfect gear or vane pump with a marginal or defective tooth or vane

Magnetic gear tooth sensors register an output in response to the changing magnetic flux caused by the tooth / slot features of a moving ferrous target. Gear tooth sensors may use a magnetically biased Hall effect or magneto-resistive structure, often monolithically integrated with the signal conditioning electronic circuitry. This circuitry can provide such functions as voltage regulation, switch point control, power up recognition, directional processing, and output control. Along with the integrated circuit (IC) (see Fig. 8.8.2.1a), the sensor may include one or more voltage reference capacitors, a bias magnet, and filter/Electrical Static Discharge (ESD) discrete components all encased in a small, probe-type package (see Fig. 8.8.2.1b). The size and shape of the package make the gear-tooth sensor easy to mount or customize into final product configurations for almost any application (see Fig. 8.8.2.1c).

A key to a successful sensor design is knowing how the automatic transmission is constructed. There are three general assembly directions: drop in components from the pump or torque converter opening, install sensors along the outside of the case, or place sensors in the ECM (Electronic Control Module) valve body package via the oil pan. Where possible, the sensor design should not interfere or detract from the assembly pattern of an automatic transmission. A wide variety of engineering materials are available to the sensor designer. For the extreme thermal cycles and oil exposure, there are a variety of plastic resins available to protect and mechanically support the sensor. Sealing requirements can be met by a host of elastomeric compounds ranging from Buna-N to fluorocarbons. Where possible, a tapered pipe thread can provide both a mounting and a seal without the requirement for an additional part. Some material suggestions include:

 

Connectors: polyesters, polyphenyl sulfides, and nylons Seals: nitrile, fluorosilicones, fluorocarbons, and silicone Housings: plated steel, brass, stainless steel, and aluminum Mounting plates: plated steels

A

  B

C

Fig. 8.8.2.1  Integrated circuit package configurations. As the tooth of a ferrous metal target approaches the sensor face, it concentrates the magnetic flux from the bias magnet. The sensor detects this change in flux density, and when sufficient, changes the state of the output. The opposite occurs when a slot approaches the sensor face. This allows a sensor to detect a target’s teeth, or slots. Alternatively, some sensors are designed to reach peak signal from the transducer on tooth edges. The sensor output may be an open collector NPN transistor or a pulsed modulation of sensor supply current over the existing voltage supply connection. The latter configuration reduces the number of wires to the sensor from three or four (speed and direction) down to two. External circuitry or processors convert these output signals into rotational speed, position, frequency, and direction (see Fig. 8.8.2.2).

8.8.2.3  Speed Sensing The ability to measure speed is inferred by the electronic logic from the time intervals between a pulse counting sensor. There are a variety of magnetic sensors that provide rotational speed information based on the measurement of changing magnetic flux introduced by a multi-poled magnetic target or a ferrous target with a tooth slot pattern that perturbs a magnetically biased sensor. These sensors may be passive (coil based variable reluctance devices) or active (Hall effect or magneto-resistive thin-film devices produced by standard integrated circuit fabrication processes). Optical speed sensors are another option that is typically not practical due to the opaque contamination present in the automatic transmission area and the high operating temperatures. The best design of a speed sensor is one that can use a trigger wheel, gear, or plate that is already part of the automatic transmission. For example, a sensor could exploit as a target the gear teeth on the main pump of the automatic transmission. However, this would require a costly drilling and tapping step. Another option is to use the teeth on the engine starter ring gear. Rear or output speed sensing generally requires an additional component or can simply become part of the speedometer sensor.

  Fig. 8.8.2.2  Sensor package subassemblies. The performance of sensors containing a bias magnet is governed by a number of factors, such as target material, surface speed, tooth geometry, air gap, operational temperature range, and surrounding materials. Targets should be made of 8-97

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a material with high magnetic permeability and low residual induction. Cold rolled steels are ideal, but other soft magnetic materials may be used. The air gap distance between the sensor face and the target affects the magnitude of the magnetic signal used to drive the sensor output. Larger air gaps eventually reduce the differential magnetic signal to the point where output triggering becomes erratic and even nonexistent. (See Figs. 8.8.2.3 and 8.8.2.4.)

Inductive/variable reluctance sensors use Faraday’s Law as their operating principle. Fine-toothed gears produce more pulses per revolution, providing a near sinusoidal output. If there is run-out in the shaft that is measured, air gap dependence can greatly decrease the accuracy of the sensor. This type of sensor has been in the sensor market the longest, and is still commonly used for transmission speed sensors due to its low cost. As sensor complexity and functionality increases, developing cost-effective sensor solutions becomes an important factor for lowering overall system costs. Additionally, as the number of sensors used for improved vehicle performance and safety increases, the power available for proper sensor operation becomes more of an issue. To address this issue, many transmission designs are implementing two-wire active sensor technology. These sensors provide an excellent means of measuring linear and angular position, displacement, and direction. Compared to many mechanical and passive magnetic technologies, active magnetic sensors have advantages in sensitivity, response time, size, number of interface wires, and reliability. A fully integrated circuit in an active sensor helps to reduce system cost and to improve system reliability by combining differential Hall effect transducers or magnetoresistive elements with signal conditioning and output circuitry. With sensitivity to low magnetic fields, these sensors have large working distances, allowing the user to solve a variety of problems in custom applications.

Fig. 8.8.2.3  Final sensor.

Hall Sensor Technology:

Fig. 8.8.2.4  Target wheel application.

Hall sensors are solid-state devices. A typical Hall sensor has a smart IC that includes automatic gain control to improve gap sensitivity, vibration insensitivity, and temperature compensation for proper sensor operation. Hall effect sensors operate using the Lorentz force in a semiconducting chip. Given a rectangular thin plate of conductive material with an electric potential applied along the Y axis and a magnetic field applied perpendicular to the plate, the Lorentz force distorts the current flow toward one side of the conductive plate. This distorts the equipotential lines (the dotted lines in Fig. 8.8.2.5) and generates a Hall voltage.

As transmission designs become more sophisticated, active sensor technology is becoming more prevalent in new applications. Passive, variable reluctance sensing (VRS) is very simple, consisting of little more than a coil, magnet, and housing. Because of its simplicity, VRS is very cost effective and robust. The output signal generated by a VRS is directly proportional to the target RPM. This is an advantage at high RPMs because signal to noise is increased. However, this is a disadvantage for low-speed operation because the signal becomes too small to use. Passive VRS cannot be used for zero speed applications. The VRS sensor output requires signal conditioning in the control unit. Active sensing such as Hall and Anisotropic Magneto-Resistive (AMR) has a simpler interface with the control unit. However, these devices are inherently more complex than VRS and as such are typically more expensive. Active sensors have a variety of features that cannot be implemented by VRS: zero-speed operation, true power-on capability, consistently high output signal magnitude for better EMI performance, and diagnostic capability. In terms of package size, active sensors are much smaller than passive devices.

The Hall voltage is proportional to mB, where m is the mobility of the material and B is the magnitude of the magnetic field perpendicular to the Hall plate. Measurement points for the Hall signal (Vo1—Vo2) are usually located at the midpoint of the plate along the Y-axis. Most practical Hall elements are roughly square, and the angle of the current flow is proportional to the magnitude of the applied magnetic field.

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be seen since the last rising edge from the speed comparator. Additionally, an enabling circuit supplies a chip reset if three rising edges are seen in a row from the same comparator without seeing one from the other comparator.

Fig. 8.8.2.5  Hall sensor operation. Typical Characteristics of Two-wire Hall Effect Sensors (see Fig. 8.8.2.6): • Bipolar integrated differential Hall effect technology • 3.3 V to 20 V DC operation • 2-wire 7 mA / 14 mA standard current interface with direction pulse width modulated • 3.5 mm air gap capability • 1 Hz to 15 kHz operation • –40°C to 170°C operating temperature range • Integrated die level ESD protection structures

Fig. 8.8.2.7  Logic graph.

        Fig. 8.8.2.6  PWM differential Hall speed and direction sensor. Typical speed and direction sensor ICs use two differential Hall transducers with a standard automotive two-wire pulse width modulated interface to detect the speed and direction of a rotating ferrous target. The frequency of the digital supply current is proportional to the rotational speed of the target wheel, and the rotational direction is encoded by modulating the pulse width of the supply current.

Fig. 8.8.2.8  Sensor current versus time for clockwise and counter clockwise directions (2 pulses per tooth-slot).

Large air-gap capability that is insensitive to dynamic air-gap variation or rotational vibration is accomplished with dual peak detection and by digitally filtering out the first pulse after a direction reversal. Integrated bipolar differential Hall solutions provide a low-cost and high-reliability sensor that is ideal for the automotive environment.

Anisotropic Magneto-Resistive (AMR) Sensors: AMR sensors are solid-state devices that can be used in applications that require large air-gap capability (up to 10 mm for ring magnet sensing). Improved sensitivity and repeatability versus Hall effect technology are typical characteristics of this permalloy material. The output signal is insensitive to field strength variations and/or temperature-caused dimension variations when the magnetic signal is above the material saturation point of ~100 Gauss (see Fig. 8.8.2.9). After reaching the saturation point, the output for the AMR sensor will only vary with applied magnetic field direction.

Figures 8.8.2.7 and 8.8.2.8 show the direction decoding operation. The speed and direction comparators feed the decoding logic. The decoding logic block outputs speed and direction information to the one shot circuit. In order to eliminate rotational vibration pulses and jitter at a standstill condition, two conditions must be satisfied to achieve a speed trigger. First, the newly decoded direction must equal the old direction. Second, a rising edge from the direction comparator must

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Fig. 8.8.2.9  Output signal vs. field strength comparison. AMR sensors use a property found in thin films, such as an Fe-Ni permalloy, which changes resistance as a function of the orientation of the applied magnetic field. The material’s internal magnetic field and the current flowing through the permalloy make an angle θ with respect to each other, and this angle determines the resistance of the sensor (see Fig. 8.8.2.10). In the absence of a magnetic field, the material’s magnetization remains parallel to the current flow.

Fig. 8.8.2.10  AMR sensor operation. Typical Characteristics of AMR Permalloy Sensors (see Fig. 8.8.2.11): • Magnetically back biased for sensing ferrous targets; unbiased for sensing ring magnets. • Utilizes an adaptive algorithm to improve switch point accuracy. • Differential sensing (used for self compensation). • AMR sensitivity is ~500 times larger than Hall, resulting in exceptional repeatability performance. • One-chip sensor integration includes voltage regulator, signal conditioning, and protection circuitry. • High accuracy: over temperature speed, air gap, and mis-position.

Fig. 8.8.2.11  Anisotropic Magneto-Resistive (AMR) sensor IC.

The Giant Magneto-Resistive (GMR) sensor is called giant because its magnetic-field-dependent change in resistance is much greater (generates a larger output signal) than that of the AMR sensor. This permits wider air gap operation and/ or the use of a lower-cost magnet. As opposed to the macroscopic effect found in the AMR sensor, the GMR effect is quantum mechanical. It involves the coupling of microscopic electron spins between magnetic-moment layers. A layering of “soft” and “hard” magnets is created with cobalt and copper films to create a GMR transducer. 8.8.2.4  Position Sensors When selecting a sensor, engineers typically choose a technology based on a combination of cost, quality, and functional requirements. Most common technologies used are variable reluctance sensors, Hall effect sensors, magnetoresistive sensors (AMR and GMR), and potentiometric sensors. All of these technologies have robust qualities for automotive transmission applications, with varying degrees of accuracy and resolution. The oldest technologies include variable reluctance (VR) and potentiometric, which still remain players in the market due to their low costs. The newer technologies include Hall effect, anisotropic magnetoresistive, and giant magnetoresistive, all of which have higher resolutions and better noise margins than VRS or potentiometric systems. The transmission position sensor tends to take on characteristics of a multiple switch. Some Transmission Range Sensor (TRS) or Drive Mode units use discrete or continuous potentiometers to measure the shifter position and to inform the electronic transmission control unit (ETCU) of the driver’s desired gear. Alternatively, noncontact TRS sensors can be designed to incorporate multi-magnetic coded tracks for transmission position encoding by “Grey code” (see Figs. 8.8.2.12 and 8.8.2.13) signal capability, allowing for safe limp-home capability. Other possible TRS (Drive Mode) design configurations include “vane sensor” concepts, allowing for simplified magnetic components and low-cost sensor electronics.

Fig. 8.8.2.12  Transmission range sensor (TRS) linear position sensor. A sliding or rotating mechanical, electrical contact switch may also be used. Depending on the type of ETCU design, the 8-100

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Fig. 8.8.2.13  TRS linear position sensor output. transmission engineer can specify discrete points of contact or continuous, make-before-break contact designs.

bolt-on side package Hall effect TRS device can survive in the transmission area under the vehicle.

Both contact buttons and resistive slides require some type of permanent lubrication of the electrical contacts. This lubrication has to be capable of moving the particles of dust away from the contacts or wipers while maintaining uniform viscosity over a wide temperature range. Salt, petroleum products, and water can all bring the TRS device to a short life.

Hall effect devices have experienced constant improvements in performance since their first integration into sensors. Whereas −40°C has never been a tough problem for silicon devices to solve, the upper temperature range up to 135°C has been more challenging. Advances in Hall effect sensors from a variety of manufacturers allow for continuous operation in the 165°C range with temperature excursions up to 175°C.

The designer is also concerned with the location of the TRS device. In the passenger compartment it is relatively safe from the harsh environment of the vehicle undercarriage. However, the cost in additional wiring may offset the savings due to the robustness of the interior based design. The TRS device at the point of the main shift valve allows for a cost savings in wire but is offset to some degree by the cost of a more robust design to hold up to the more aggressive sensing location. Signal timing also places a constraint on the location of the TRS device.

Solid-state magnetic position sensors using Hall effect and magnetoresistive technologies provide an excellent means of measuring linear and angular position for gearshift and clutch position operation. Linear position sensors are also used for the identification and validation of gear position in automated manual transmissions.

In order to advance the TRS device beyond the performance of the multi-contact switch, one can consider the benefits of a multi-position Hall effect sensor. With proper signal conditioning, the Hall effect device can provide a highly repeatable indication of shift position. The main concern involves the high thermal effects that are present when the sensor is placed into the transmission fluid. A linear or rotational

Typical Characteristics of Linear Position Sensors (0 to 15 mm travel):

For applications that require moderate travel in the 0 to 15 mm range, a number of sensor products are available (see Figs. 8.8.2.14 and 8.8.2.15).

• Noncontacting programmable Hall effect design. • Programmable output enables sensing range of 2 mm to 15 mm anywhere inside the 15 mm range.

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• Programmable clamp voltages at end stops at desired range. • Designed for high temperature, high vibration, automotive under-hood environments. • Includes EMC components to meet automotive requirements. • Supply voltage = 4.5 V to 5.5 V. • Output ratiometric to supply. • Supply current = 10 mA max. • Operating temperature −40°C to +160°C. • Typical linearity 2% of full scale over all conditions. • Programmable output voltage characteristics. • Applications: gear position (automated manuals, DCTs, other… .).

acteristics of these sensor devices. This sensing approach can also be used for large-diameter rotational position sensing if the AMR sensors are configured in a circular pattern instead of a linear pattern, as shown in Fig. 8.8.2.17. The application-specific integrated circuit (ASIC) in this type of design tracks the magnetic target by multiplexing between pairs of adjacent AMR bridge ICs (labeled S1, Sx). The ASIC achieves highly accurate position determination by interpolating between the phase shifted signals from the pair of AMR ICs that are affected by the magnetic target (see Fig. 8.8.2.18a, 8.8.2.18b, 8.8.2.18c, and 8.8.2.18.d). The AMR sensors are always in saturation, so they only respond to the vector of the target’s magnetic field.

Fig. 8.8.2.14  Linear position sensor, 0 to 15 mm travel. Linear array modules can be developed for gear position applications requiring large linear movement (0 to 80 mm) with a high level of accuracy. See Fig. 8.8.2.16 for typical char-

Fig. 8.8.2.16  Linear array module (0 to 80 mm travel).

Fig. 8.8.2.17  Rotary array module. (0 to 360 degree).

Fig. 8.8.2.15  Linear position sensor output characteristics. 8-102

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Fig. 8.8.2.18a  Linear array module output—raw data. Fig. 8.8.2.18c  Linear array module output—sensor ratios.

Fig. 8.8.2.18b  Linear array module output— compensated data.

Fig. 8.8.2.18d  Linear array module output—straight line fit.

Typical Characteristics of Linear/Rotary Array Modules: • • • • • •

0 to 80 mm (linear) or 0 to 360 degrees (rotary) travel. Large air-gap capability (12.00 mm–15.00 mm). Insensitive to dynamic air-gap change. Less than 0.10 mm resolution. Fast response time. Movement of bias magnet generates sinusoidal signal response from each AMR bridge. • AMR bridge outputs are identical, but phase shifted by centerline-to-centerline spacing.

small size, and reliability are several advantages of magnetic position sensing (see Fig. 8.8.2.19, 8.8.2.20, and 8.8.2.21). Typical Characteristics of Rotary Position Sensors:

Similarly, rotary position sensors are used in applications requiring circular movement, providing transmission design engineers with greater flexibility for designing innovative transmission systems. Hall effect or magnetoresistive based sensors provide an excellent means of measuring both linear and angular position and displacement. High sensitivity,

• • • • •

Amplifying ASIC for AMR angular position sensor Low cost and easy to use Two-wire voltage output Large temperature range Absolute sensing angles up to 180 degrees or 360 degrees • Accuracy < ±1º possible

   Amplifying ASIC Fig. 8.8.2.19  Rotary position sensor components.

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Linear Variable Differential Transformer (LVDT) Sensors:

Fig. 8.8.2.20  Rotary position sensor construction. The rotary position sensor detects angular position of a diametrically magnetized magnet using magnetoresistive (AMR) technology. The voltage level of the two sinusoidal analog outputs is proportional to the angular position of the magnet. Position is determined from the two analog signals, which are 45 degrees out of phase. An amplifying ASIC integrated circuit enables minimum cost and highest reliability by combining the output circuitry and the signal conditioning on one IC. Two outputs from the completed sensor will be a Sine and Cosine wave, representative of the target position. The sensor output will be unique for 180 degrees (360 degrees of magnetic rotation is also possible). The AMR bridges are saturated at every point during the magnet rotation. Fields of 60 to 80 gauss over the entire area of the bridge provide sufficient field to saturate the AMR bridge.

Linear Variable Differential Transformer (LVDT) sensors involve three or more coils wrapped around a magnetically permeable core. The coil systems can consist of one primary coil, two secondary coils, and a movable core. Usually, designers attach the sensor’s core to a moving part that moves in unison with the target’s change in position. Potentiometric Sensors: Potentiometric angular position sensors often use multiple carbon-ink traces with separate contact assembly for electrical connection. This provides dual-potentiometer redundancy and facilitates diagnostic, self-monitoring functions. Input current is designed to match the contact/resistive track physical properties. If the input current is too low, contact fretting/erosion occurs; if it is too high, contact burnout occurs; and if designed correctly, long-life contact wetting is achieved. Potentiometric sensors feature ratiometric output, insensitivity to EMI, and insensitivity to temperature variations. Manufacturers prefer ratiometric output because it is easy to implement in circuits. 8.8.2.5  Pressure Sensing Pressure sensing is performed in several methods. Strain gage (resistive wire or ink), capacitance, piezoelectric, and silicon

Fig. 8.8.2.21  Rotary position sensor differential output. 8-104

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element. Each of these designs has cost vs. a design feature trade off. The sensor can be simple but the signal interpretation can be costly in some, while other designs simply cannot take the extreme heat or cold of an automatic transmission. Resistive Wire or Ink Strain Gage Designs: These sensors normally have a flexible metal diaphragm that separates the pressure media from the sensing element. Typically, a Wheatstone bridge design is used that is temperature compensating when connected to an ASIC conditioning device that may be complementary metal oxide semiconductor (CMOS), bipolar, or mixed signal. From concept to final product, pressure designs seek to isolate electronics from pressure media and the environment. A variety of pressure sensors are used in transmission applications. Pressure sensing products are typically designed and manufactured from a building block approach. They are then packaged into multiple final assembly configurations, resulting in improved efficiency throughout the supply chain (see Fig. 8.8.2.22). Innovative solutions such as combi-sensor (pressure/temperature/ valve) technology are also possible, working in partnership with vehicle OEM design requirements. In addition to improved hydraulic fluid control, pressure sensors are also under consideration for applications involving the improvement of transmission lubrication processes for gear longevity. This is especially important as transmission systems become more complex and longer warranty life is required.

Fig. 8.8.2.22  Pressure sensor. Typical Characteristics of Pressure Sensors: • • • • • • • • • • • •

Ratiometric analog output voltage Piezoresistive technology Electronic (ASIC) with wide application range Operating supply voltage: 5 V DC ± 0.5 Input current: < 10 mA Overvoltage protection: 18 V DC Reverse polarity protection: -16 V DC Response time: < 10 ms Radiated immunity: 100 V/m Output resolution: 10 Bit… 11 Bit Operating temperature range: –40°C to +135°C Storage temperature range: –40°C to +150°C

8.8.2.6  Temperature Sensing The Electronic Transmission Control Module (ETCM) needs to have a thermal input that can provide an inference of the automatic transmission overall operating temperature. Normally a thermocouple device is placed into the automatic transmission fluid. If the ETCM is submerged into the transmission fluid, then the internal thermocouple or diode of the control logic may infer the transmission temperature. The desired temperature measure point is the friction plate during engagement. This measurement is difficult, if not impossible to achieve within the cost constraint of today’s complex automatic transmission. The area most often used is the transmission fluid. Here the temperature of the fluid may lag several degrees from the actual friction element temperature. To compensate for this variance, the ETCM logic infers what the friction plate surface temperature might be from the sump fluid temperature. Temperature sensors in an automatic transmission environment need to be robust and accurate to properly produce a signal throughout a wide temperature range (–40°C to +150°C) and in a hostile chemical environment. When the ETCM has the correct temperature input, then the transmission fluid pressure can be lowered for cold weather to avoid many harsh shifts, and the pressure can be increased to prevent soft or slipping shifts on hot days. The temperature sensor is critical to the proper operation and customer satisfaction of the automatic transmission. Temperature sensors generally are of a thermocouple design where the thermocouple is protected from transmission assembly and metallic particles found in the transmission fluid of high-mileage vehicles. The protective enclosure can be of a metal or plastic, but thermal response time of the temperature sensor enclosure must always be considered first. 8.8.2.7  Barometric Absolute Pressure In the course of the early days of automatic transmission design, the vacuum modulator and governor valves served to identify driver intent to the hydraulic logic. As the vacuum decreased and the governor slowed, the hydraulic system was notified that the driver required more hydraulic pressure for anticipated downshifts. The same types of inputs are available to the ETCM from the engine control module. The manifold absolute pressure sensor along with the electronic vehicle speed signal provide the same inputs to the ETCM that the modulator and governor did to the hydraulic logic.

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However, knowing the altitude of the vehicle via a barometric absolute pressure (BAP) sensor assures that the ETCM will maintain the gear selection over longer periods of engine operation. The BAP can be included into the engine control logic or can be part of the ETCM. The important factor to remember is to allow the BAP sensor a path to atmosphere. If mounted internally within the transmission, then the sensor needs to be in a vented transmission case. If mounted externally then the sensor needs to be protected from the debris of the highway.

Numerous SAW Torque Applications Enabled by Flexible Mounting:

8.8.2.8  Torque Sensing

Electronic transmission control:

Surface Acoustic Wave (SAW) Torque Sensing is an emerging technology for automotive, transportation, rail, and other similar industries for use in powertrain and chassis applications. Significant research and development efforts have allowed for mass-production of SAW torque sensors at a cost-effective price (see Fig. 8.8.2.23). Certain engine, transmission, driveline, and chassis processes can often be controlled more precisely using SAW torque technology. Used in appropriate applications, complex control algorithm and system development, test, evaluation, and qualification time can often be significantly reduced with real-time torque sensor measurement that can provide feedback for closedloop control.

Improving engine, transmission, driveline, and chassis performance is a high priority for many major vehicle OEMs. Industry drivers for implementing torque into powertrain and driveline systems include: shift quality, fuel efficiency, weight reduction, emission standards, and vehicle safety. Indicative SAW Torque Sensor Applications and Potential Benefits:

• Input/output shaft torque and transmission component applications • Hybrid vehicle powertrain control: • Potential to improve shift smoothness, vehicle per­for­ mance, and fuel economy Electronic driveline control: • Torque management systems (4-wheel-drive and allwheel-drive vehicles)Potential to improve vehicle performance, stability. and safety Engine management: • Direct measurement of engine torque (crankshaft and powertrain component applications) • Potential to improve vehicle performance and fuel economy

SAW Torque Sensor Features: • • • • • • • • • • •

Batteryless, wireless operation Nominal resonant frequency, 433 MHz High measurement bandwidth up to 1 kHz Small, lightweight design Enhanced accuracy and resolution Immunity to electromagnetic interference High temperature operation up to 150°C Robust packaging, durable design Operates in many harsh environments Long-term stability Established manufacturing processes

Fig. 8.8.2.23  SAW torque sensor.

Surface Acoustic Wave (SAW) Technology: Surface Acoustic Wave (SAW) technology enables wireless, battery-less, noncontacting strain measurement often suitable for the measurement of torque, pressure, temperature, and other parameters. The SAW propagation mode is characterized by velocities typically five orders of magnitude below electromagnetic waves, with amplitudes in the order of nanometers and wavelengths in micrometers. Most energy is confined to within one wavelength of the surface. These characteristics have made SAW devices often ideal for the design of delay lines and filters widely used in radar, TV, and the mobile telecommunications industry. SAW devices are typically designed to operate within the frequency range 30 MHz to 3 GHz. However, unlike filters for telecoms, the SAW torque sensor technology presented here uses the influence of strain, mechanical and thermal, on the resonant frequency of a single-port SAW resonator—the first order effects being: i) a reduction in resonant frequency with increase in surface

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strain (distance the wave has to travel) and ii) a change in the wave propagation velocity. SAW torque sensor technology uses the principal tensile and compressive strains, which act at ± 45° to the axis, on the surface of a shaft in torsion for the measurement of torque (see Fig. 8.8.2.24). To RE coupler

SAW-Based Technology—How it Works: Piezoelectric SAW sensors use an oscillatory electric field to generate an acoustic wave that propagates on the substrate surface, then transforms back to an electric field for measurement. SAW sensors use piezoelectric material to generate and sense the acoustic wave (see Fig. 8.8.2.26).

Fig. 8.8.2.24  Single quartz die featuring a pair of nominal 433-MHz single-port SAW resonators. Typically, two SAW devices are used in one sensor, and differential measurement of resonant frequency is performed to achieve temperature compensation and eliminate sensitivity to shaft bending (see Fig. 8.8.2.25).

Fig. 8.8.2.26  SAW single-port resonator.

Fig. 8.8.2.25  Difference frequency measurements from two diametrically opposed sensor pairs. SAW devices operating at 433 MHz are bonded to metallic packages to enhance protection from surface contamination. However, again unlike filters in mobile phones, it is a requirement to couple the devices into the external strain field rather than to isolate them. As a result the bond-lines must be highly elastic with no micro-plasticity over the operational temperature range in order for the sensors not to exhibit unwanted creep or hysteresis. The development of this know-how has been an essential element in the development of successful sensors. The choice of piezoelectric material for SAW sensors is principally driven by performance, availability, and cost. Single-crystal quartz has been chosen because it is typically widely available in standard 4-in wafers, and can be processed routinely at low cost in high volume, using standard photo-lithographic techniques. Furthermore, quartz has a characteristic anisotropy, which can be often used by variations in cut angle and propagation direction to promote the maximization of sensitivity and provide first-order temperature compensation.

Each SAW resonator is interrogated by a short Radio Frequency (RF) burst transmitted through the rotary coupler to the sensing element. The transmit pulse lasts long enough such that its spectrum is narrow so that only one SAW device is efficiently excited at one time. A centrally placed Interdigital Transducer (IDT) converts the pulsed electrical input signal from the interrogator to a mechanical wave through the piezoelectric effect. These waves propagate from the resonator to the reflectors and back. This propagation continues to build energy until a resonance exists as a standing wave. The wavelength is roughly double the IDT spacing. SAW resonators typically continue to oscillate for a noticeable amount of time after the transmit pulse has been switched off. It is this decaying oscillation that is re-transmitted from the sensing element through the coupler and picked up by the transmit/receive electronics of the SAW interrogation board (see Fig. 8.8.2.27).

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tating SAW torque sensor and the stationary interrogation assembly. The SAW torque sensor is connected to the input terminals of the rotary coupler. The rotary coupler design is optimized for each individual application. Many coupler configurations are possible depending on torque measurement location and available space. A typical gap between the stator and the rotor rings of the coupler is 1 mm.   Fig. 8.8.2.27  SAW torque sensor electrical characteristics. The resonant frequency is a function of strain in the IDT in the direction of the resonator axis. Once the input signal stops, the IDT absorbs the acoustic energy and transmits the new frequency back to the receiver in the interrogation system. SAW sensor interrogation involves the measurement of frequency difference shifts between active and reference SAW devices to provide common mode rejection. In addition, coherent accumulation and averaging typically improves signal to noise ratio, while the measurement algorithm and monitoring of statistical variances promotes valid data. This system uses patent protected methodology for sensing and reading/interrogation. Wireless Operation through Rotary Coupler: SAW torque technology uses antennas and noncontacting rotary couplers to transmit RF power in and RF signals out of rotating items such as shafts and discs. RF signals are then typically transmitted via coaxial cables, or they may be locally interrogated and the results fed via CAN to a central display or to a system controller (see Fig. 8.8.2.28).

Fig. 8.8.2.28  SAW torque sensor assembly. The SAW torque sensor uses a rotary coupler design working in the 400-500 MHz frequency range. This design feature enables contact-less, battery-less operation between the ro-

Figure 8.8.2.28 illustrates a typical torque sensor assembly module. A key advantage of SAW torque sensors is “mounting flexibility,” allowing for numerous applications. SAW torque sensors can be mounted to virtually any component in a system that experiences torsional load. This key benefit of the technology allows design engineers many options when incorporating torque-sensing measurement into existing system applications. Overall, in its envisioned applications, SAW technology often offers the ability to provide high-bandwidth wireless measurement of torque in generic shaft and disc components, typical of the requirements of the automotive powertrain, over the full-specified operational temperature range. Enhanced resolution and accuracy, coupled with low hysteresis and drift, contribute to the constructor’s ability to derive high-quality signals suitable for closed-loop control of modern auto-transmission, driveline, and chassis systems. Automotive Powertrain Torque Sensing—System Control Optimization: Modern electronically controlled transmissions typically use “torque” as the basis for transmission shift control. Today’s systems often rely on empirically based look-up tables for torque measurement estimates. However, it is often difficult to accommodate all the potential factors that can affect the efficient operation of the powertrain system. New engine technologies such as cylinder de-activation and variable valve timing, sudden acceleration/deceleration, HVAC system on/ off usage, and various environmental effects all contribute to this issue, while service wear also affects both engine and transmission characteristics over time. Changes in acceleration during a power-up or downshift can often be significant. Power-off shifts are typically characterized by an audible noise in the driveline system. Achievement of both smoothness and durability in a transmission system design is typically expensive and space consuming. Powertrain torque control can often improve responsiveness and fuel efficiency without the “shift shock” and sluggish driving characteristics of many automatics. Significant fuel economy and performance gains are also expected benefits of moreefficient automatic transmission ratio changing. 8-108

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In addition to increased forward ratios, the emergence of advanced automatic transmission systems such as Continuously Variable Transmission (CVT), Infinitely Variable Transmission (IVT), Automated Manual Transmission (AMT), Double Clutch Transmission (DCT), and Hybrid Electric Vehicles (HEV) often require significant sensor content for proper operation. The addition of real-time torque measurement promotes the optimization of powertrain system management. As 4WD/AWD vehicle systems become more sophisticated and fully active systems become more prevalent, there is a pressing need for improved torque-sensing capability in driveline applications (including wheel corners). Increasingly accurate, active torque management can provide significant improvement over passive, electromechanical or hydraulic approaches. Torque management is expected to be a key factor regarding improved vehicle performance, stability, and safety. Real-time Torque Sensor: An attractive sensor for an automatic transmission would be a torque sensor that is capable of measuring real-time torque at a millisecond or better update rate. This sensor would be located at one or two essential points on the automatic transmission; i.e., at the input shaft or the output shaft or possibly both. Knowing the real-time torque, the transmission ECU would have the information necessary to continually update the transmission algorithms to promote smooth and/or fast shifts. All other material information can be typically derived from the engine sensors. With one or two torque sensors properly placed, the automatic transmission ECU would no longer need to infer shift timing from remote sensing points. The troublesome realtime delays that take place between the transmission ECU, the pressure sensors, and solenoid valves would no longer be a significant issue for the transmission designer. Existing torque sensors principally include resistance strain gauges (requiring slip rings for interrogation) and non-contacting sensors based on the principles of magnetostriction. However, as of this writing, torque sensors within the automotive world have been primarily used for the laboratory testing and evaluation of engine and transmission systems and their control algorithms. Over the past few years, research and development has been applied to the provision of an increasingly reliable and accurate, low-cost torque sensor technology for vehicle OEM applications. Surface Acoustic Wave “SAW” sensors provide wireless interrogation for applications such as transmission input shaft torque, transmission output shaft torque, and

driveline torque for four-wheel-drive (4WD) and all-wheeldrive (AWD) vehicles. Essentially, a torque sensor module can often be integrated within the powertrain, and torsional strain monitored, for proportional real-time torque measurement and corresponding system adjustments. Design Integration: Transmission sensors often find application in a variety of challenging locations and environmental conditions. With SAW torque technology, a compact package design typically provides ease of integration with existing system configurations. Various sensor mounting options are available, allowing engineers flexibility for system integration. Precise knowledge of the peak torques sustained by any element of an automotive powertrain will enable mechanical designs to be optimized in terms of the dimensions of shafts and disc components, thereby offering weight and real cost savings. Capability to Incorporate Speed Sensing (Torque ¥ Speed = “Power Modules”): The ability to measure speed is inferred by the electronic logic from the time intervals between a pulse-counting sensor. There are a variety of magnetic sensors that provide rotational speed information based on the measurement of changing magnetic flux introduced by a multi-poled magnetic target, or a ferrous target with a tooth slot pattern that perturbs a magnetically biased sensor. The target will typically have multiple points for signal generation along the circumference, i.e., multi-tooth gears, polarized ring-magnet with multiple North-South Poles. This allows for quicker signal pick-up at start-up and better overall accuracy. Powertrain (engine and transmission) and chassis (wheel speed) systems use speed sensors for system control. (Wheel corners use speed sensors for ABS systems.) A speed sensor product can be easily integrated into the torque sensor module stationary coupling. A target configuration can be easily incorporated into the rotating coupling or other system components as noted in the previous paragraph. Incorporation of speed and torque (power modules) allow for best total cost systems in these high-volume applications. 8.8.2.9  EMC Considerations Electromagnetic compatibility (EMC) and electromagnetic interference (EMI) are one of the more difficult design objectives to meet. Whether the request is to protect a sensor or an Electronic Control Module (ECM), the design tends to evolve more from experience as to what works and what does not than anything else. EMC protection comes in a wide

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variety of specifications, and essentially the sensor is either a transmitter or a receiver or both. The design engineer needs to become familiar with the terms of EMC, and an introductory class is highly recommended. The mechanics of solving EMC problems generally are solved using routine mechanical solutions. The conversion between the mechanical designer or sensor supplier and the EMC electrical engineer poses the difficulty. Mechanical EMC solutions might encompass a grounded gapless metal shield, metallic impregnated plastic resin, and a metal mounting or port to provide a true chassis ground for the electrical engineer. It is important to note that a sensor might not affect devices around the sensor as much as the devices would affect the sensor. The nearby electrical solenoids or actuators may generate an RF field high enough to trigger a false reading and thereby an undesirable shift. In EMC testing it is important for the design engineer to note the type of test antenna that is used during the test. A “Stripline” can be sensor directional and may provide a falsetrue reading that the sensor is not affected when indeed the sensor is vulnerable to EMC. Here it is important to ask the EMC test engineer if the sensor was rotated relative to the stripline and if several readings were taken. The more aggressive test antenna is the “Tri-Plate.” With this style of antenna, sensor position is not critical. If the sensor did not pass, then the sensor design needs to be reviewed as the signal is quite strong and overcomes any sensor test position. Most EMC tests do not call out a thermal environment but in an automatic transmission, especially if the device is submerged in the transmission fluid, a cold and hot environment should be part of a standard EMC-EMI test procedure. The EMC engineer may request that the powered sensor under test be submerged in transmission fluid to the nominal fluid level. External transmission sensors are subject to thermal conditions as well as EMI. Tests that include a “drive by” EMC requirement have to be considered. In the external sensor application, atmospheric humidity will most often tend to give a strong test over a controlled test cell environment. If the sensor is just passing the EMC-EMI test procedure, then an increase in humidity might be necessary to increase the robustness of the test. Vehicles that may operate in areas of continually high humidity will need to have the plastic components on the sensor conditioned with a long exposure to humidity prior to an EMC-EMI test. Conditioning may be for 250 hours at 85°C

/ 85% RH with a 24-hour dry off period to provide a suitable test device. 8.8.2.10  Acronyms and Definitions AC Coupled: The ability of a sensor to self adjust the reference bias level to compensate for changes in magnetic strength due to air gap, temperature, magnet material, or location. Air Gap: The distance between the top of a target tooth and the face of the gear-tooth sensor when the middle of a tooth is aligned with the centerline of the sensor. Air Gap Maximum Operating Limit: As a tone wheel rotates, a sensor is gradually moved away (air gap is gradually increased) until its output signal no longer exhibits a periodic switching waveform. The greatest distance at which the sensor’s switching waveform can be detected is called the air gap maximum operating limit (or maximum detectable air gap). Cycle-to-Cycle Repeatability/Accuracy: A measurement is made using a constant-speed servomotor driving a precision-machined tone wheel. The tone wheel includes an electronic marker that identifies a specific tooth. While the tone wheel is driven at constant speed, the sensor repeatedly measures a time history of the reference tooth’s passage. Cycle-to-cycle repeatability (angular scatter) is computed from a statistical scatter of the measured time variations, by using tone wheel geometry and speed to convert the time variations into angular scatter. DC Coupled: The switch point on the sensor is set at the time of assembly and does not vary with magnetic field changes. Differential Hall: An AC coupled sensor with two hall elements located on a single IC. The hall outputs are subtracted such that they equal to zero with no target present or when the sensor is centered on a tooth or on a slot. Peak signal from the differential Hall is obtained on tooth edges. Works well with small-featured targets. Duty Cycle: This is the time when the sensor is “On” divided by the total “On” and “Off ” time. Gauss: A unit of magnetic flux density. Hall Effect: The description given to the following phenomena: when a current-carrying conductor is placed into a magnetic field, a voltage will be generated perpendicular to both the current and the field. Hard Edge Offset: This is the angle (measured in degrees) from the target tooth edge to the sensor switch point. Magnetoresistive: A material that changes resistance with changing externally applied magnetic field. Commonly

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permalloy magnetoresistive elements are arranged in a Wheatstone bridge to convert applied magnetic field to a voltage. One Pulse per Pole Pair: A ring magnet sensor that gives one output pulse (a positive and negative transition) per magnet pole pair (north and south pole). Operate Point: The angle (measured in degrees) between the leading edge of the target tooth to the centerline of the sensor when the sensor switches states. This specification applies when the target is rotated in either direction (application specific). Operate Point Accuracy: Maximum change in operate point over all environmental conditions. Power Up: When power is applied to the sensor, the output will start in the correct state, sensing either a tooth or a slot. Reference Bias Level: The sensor’s internal reference level based on the magnetic flux density. This is used to set the operate and release point. Release Point: The angle (measured in degrees) between the trailing edge of the target tooth to the centerline of the sensor when the sensor switches states. This specification applies when the target is rotated in either direction (application specific). Repeatability: Operate point variation with constant temperature, RPM, supply voltage, and air gap. SAW: Surface Acoustic Wave. S/N Signal-to-Noise Ratio: Signal-to-noise ratio is a measure of the signal strength of the sensor relative to background noise. S/N values are generally listed as qualitative attributes, and are a measure of sensitivity (i.e., minimum detectable signal) of the sensor. Spur Gear: Broadly speaking, this is a straight-tooth target. The teeth can protrude straight up from the base of the wheel, or they can angle up from the base and level out. Straight-Tooth Gear: A target where the teeth run across the target width, perpendicular to the edge. Tangential Velocity: Surface speed of the spinning target determined by the following formula: (Target rpm ¥ gear diameter ¥ Pi)/60 Target Pitch: The arc length of a single tooth and slot. True Power-On Sensing: True power-on means that the correct output signal is measured and outputted immediately (typically within 200 ms) after power is applied to the sensor.

Two Pulse per Pole Pair: A ring magnet sensor which gives one output pulse (a positive and negative transition) per magnet pole (a north or south). Typical Gear: A rotary target with teeth protruding from the base—straight up. Zero Speed: After the sensor detects the first target edge, it will provide correct function down to zero speed. 8.8.2.11  References 1. Kilmartin, B., “Magnetoelastic Torque Sensor Utilizing a Thermal Sprayed Sense-Element for Automotive Transmission Applications,” SAE Paper 2003-01-0711, SAE International, Warrendale, PA, 2003. 2. Komatsu, H., “High-Performance, Flat Surface Resistive Element and its Application in Automotive Sensors,” SAE Paper 2002-01-1072, SAE International, Warrendale, PA, 2002. 3. Sparks, D., M. Chia, S. Zarabadi, “Reliability of Resonant Micromachined Sensors and Actuators.” SAE Paper 2001-01-0618, SAE International, Warrendale, PA, 2001. 4. Neuffer, K., K. Engelsdorf, and W. Brehm, “Electronic Transmission Control – From Stand Alone Components to Mechatronic Systems,” SAE Paper 960430, SAE International, Warrendale, PA, 1996. 5. Murdock, Joe, “Hall Effect Transducers, How to Apply Them as Sensors,” MICRO SWITCH a Honeywell Division, 1982. 6. Chilcote, Jason, Aaron Meyers, “2-Wire PWM AC-Coupled Differential Hall Speed & Direction Sensor,” Product Data Sheet, Honeywell Sensing & Control, January 2005. 7. Stolfus, Joel, Wayne Lamb, Ken Bechtold, and Curtis Johnson, “Linear Position Sensor, 0 to 15mm Travel,” Product Data Sheet, Honeywell Sensing & Control, April 2004. 8. Lamb, Wayne, “AMR Angular Position Sensor,” Product Data Sheet, Honeywell Sensing & Control, November 2003. 9. Ricks, Lamar, “Linear Array Module, 0 to 80 mm Travel,” Product Data Sheet, Honeywell Sensing & Control, January 2004. 10. Dr. Lohr, Ray (Transense Technologies), Joe Gierut (Honeywell Sensing & Control), “Automotive Powertrain and Chassis Torque Sensor Technology,” SAW Torque Technology Technical Manuscript, Honeywell Sensing & Control, February 2005. 11. Miller, Julia, Lisa Nayak, Roshelle Silverman, George Schoenbeck, and Emily Stiehl, “Linear & Rotary Position

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Sensors in the Automotive Transmission Segment,” The Technology & Management Program, University of Illinois at Urbana-Champaign (UIUC), Capstone Project, May 2004. 12. The authors wish to express a special thanks to Mr. Gary O’Brien, Technology Partner, Mr. Greg Furlong, Engineering Manager, Mr. Nick Busch, Principle Design Engineer, all from Honeywell International, Inc., for their dedicated input, and proofreading of this subsection of Chapter 8.

challenge. As electronic content in automatic transmission controls has become more complex, the system development tools have become more sophisticated. The development process and tools trends are driven by the desire to reduce vehicle prototypes, reduce development time, and perform development earlier in the process. Enablers of these trends are increases in computing power and increasingly standardized development tool systems provided by common outside OEM suppliers. Most of these standardized development tools facilitate engine and other vehicle systems development as well as transmission systems.

© 2005 Honeywell International Inc.

8.9.2 8.9 Development Technology Hussein Dourra, Ph.D. Technical Fellow, Advanced Powertrain Controls Chrysler Group LLC Ronald T. Cowan Specialist, Advanced Transmission Development Ford Motor Company Table of Contents—Development Technology 8.9.1  Overview 8.9.2  Development Tools 8.9.2.1 Fuel Economy Prediction Models 8.9.2.2 Dynamic Models 8.9.2.3 Software Tools 8.9.2.3.1  De-bugger 8.9.2.3.2  Open-Loop Bench 8.9.2.3.3  Closed-Loop Bench 8.9.2.3.4  Auto-code generation 8.9.3  Virtual Development Process 8.9.3.1 Benefits of the Virtual Environment Strategy 8.9.4 Application of the Design Strategy to Chrysler Six-Speed Transmission Program 8.9.4.1 Model-In-the-Loop Testing 8.9.4.2 Rapid Prototyping using the HIL (Bypass + HIL Testing) 8.9.4.3 Dynamometer Environment 8.9.4.4 In-Vehicle Testing 8.9.5  Final Results 8.9.6  Summary

8.9.1

Overview

Automakers face a variety of program development challenges during each new model year. New development processes are adapted regularly by the industry to manage this

Development Tools

Electronic automatic transmission control system development tools are listed below roughly in the order in which they are used as system development progresses: 8.9.2.1  Fuel Economy Prediction Models Powertrain simulation software provides estimates of fuel consumption during the EPA cycles and other driving cycles. Concepts affecting transmission efficiency and engine fuel scheduling are evaluated for their effect on fuel economy. These estimates assist in the transmission design selection and calibration process. The fuel economy simulation software itself is typically proprietary to the individual automotive companies. To provide improved accuracy for predicting fuel economy on a given driving cycle, the model needs to be accurate during steady-state operation and under transient conditions as well. A good method for doing this is to use both the engine controller and the transmission controller on a HIL stand with a simulated driving cycle. 8.9.2.2  Dynamic Models Transmission system and subsystem models are built using commercially available dynamic modeling software such as MATLAB®, EASY5®, DYMOLA®, dSPACE, as well as proprietary modeling software. These models provide valuable initial information, including efficiency estimates, for the fuel economy predictions discussed here, shift feel predictions, and controls requirements. These models also facilitate early strategy development and even initial calibrations. 8.9.2.3  Software Tools The initial powertrain control modules were programmed in Assembly Language and had their own set of development tools with limited capability. Today’s modules are programmed in C. Since C language is commercially supported, compilers, linkers, and system-build software are commer-

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cially available and have the ability to translate the C files into the machine language required for the target transmission or powertrain control processor. 8.9.2.3.1 De-bugger A de-bugger is basically a software model of the processor being programmed. The de-bugger helps the programmer check the software by providing the capability to set up input scripts and compare output data to expected reference data. Complex “breakpoints” can also be set up that halt the processor model between instructions, allowing the engineer to debug the problem at the highest detailed level. 8.9.2.3.2 Open-Loop Bench Open-Loop bench consists of a programmed controller, a load box to simulate the actuators being controlled by the processor, signal-generating equipment to simulate inputs to the controller, and equipment to evaluate the output. This bench is easily and quickly configured, but it lacks the sophistication of the closed-loop benches, described next. The operator can only set up the inputs and check that outputs are as expected.

8.9.3

Virtual Development Process

As mentioned above, recent improvements involve the use of virtual development methods to reduce dependencies on early prototype hardware and the hardware’s performance, to shorten the time required for new product development, and to improve the quality of the end product. The remaining portion of this chapter will cover the use of simulation in the development of the powertrain hardware. Chrysler Group’s powertrain development cycle that uses virtual methods is shown in Fig. 8.9.1. The first stage is called the “Initial Concept Model.” This phase gives an algorithm developer the chance to create algorithms in a non-restrictive environment. The tools that Chrysler Group uses in this phase are MATLAB, Simulink, and Stateflow. MATLAB is a numerical computation tool which uses a very simple scripting language known as mscript. Simulink and Stateflow are graphical modeling and simulation tools to use within MATLAB that allow for faster development and quick verification of concepts.

8.9.2.3.3 Closed-loop Bench Closed-Loop bench is also termed Hardware-In-the-Loop (HIL), Model-In-the-Loop (MIL), etc., depending upon their configuration. These benches are more capable development tools than a software bench because they provide a realistic dynamic relationship between the software’s output and its input. Closed-loop benches are configured differently depending upon which subsystem is under development. If a development item is a new sensor, a new actuator, or a new processor, and whether actual hardware is available or only a representative dynamic model, the closed-loop bench configuration would be different, accordingly. If actual hardware is used on a closed-loop bench, all dynamic models used on that bench must execute in real time. Limited computing power, in turn, limits the level of model detail that can be used here, and still meets this real-time requirement. 8.9.2.3.4 Auto-code generation Auto-code generation is quickly becoming reality. Autocoding will allow the control strategy, developed to control a model in MATLAB/Simulink/Stateflow®, to be translated directly into the C code required for the target control processor. Simulink and Stateflow are graphical modeling and simulation tools to use within MATLAB that allow for faster development and quick verification of concepts.

Fig. 8.9.1  Standard Chrysler Powertrain Development Cycle. The second phase is the “Rapid Prototyping Controller (RPC) Model” stage. This phase is where the initial algorithm concepts get life. The model is modified in Simulink with additional I/O blocks to enable the model to talk to hardware. Specifically, dSPACE Real-Time Interface (RTI) blocks are added to the Simulink model to make the connection between the ECU and the RPC Hardware (see Fig. 8.9.2). This allows Bypass Rapid Controller Prototyping for the purpose of validating assumptions of hardware, which includes the actuators and sensors used in the control system. In this phase, basically, the communication between the RPC and the ECU is defined and checked so that development can continue with confidence in the results. Additionally,

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this phase verifies initial algorithms; the engineer can make sure the system goes through all of the designed and required states. Software structure is checked and verified.

Fig. 8.9.2  Bypass Rapid Control Prototyping – RPC Phase. The third phase in the Powertrain Product Team Development Cycle is the “Implementation Model.” This stage is used to capture the limitations of algorithms and implementation in a production environment that reflects the additional restrictions of hardware response and fixed point processing. These restrictions can have a dramatic effect on the performance of an algorithm including the operating range of the algorithm and the reaction time during a transient event. This is the last phase of the development cycle prior to production coding of the algorithm. The performance of the model, therefore, must meet all the design requirements from the first phase through the third phase prior to being submitted to the production coding supplier. Also in this phase, dynamometer or vehicle testing is required as a final step before C coding. This step is needed to evaluate hardware inertias and vehicle dynamics effects on system control. The plant model shown in Fig. 8.9.3 is replaced by the actual hardware, and the same functional tests are executed and outputs are verified.

Fig. 8.9.3  Bypass Rapid Control Prototyping – Implementation Phase. The fourth “Coding” phase is done either by advanced convergence tools such as Target Link, Mathworks, etc. or by hand coding of the algorithms from the implementation model. The tools used in this phase are typical software development tools, editors, compilers, and debuggers, as discussed. The fifth phase is called “Unit Testing.” This phase is usually done by the production coding team to validate the delivery of production code which reflects the specification tested in the development phase. The current tools used for this validation are static system analysis simulators and HIL simulators. In these stage elements such as loop time, interrupts, and software structure are tested and evaluated.

The sixth phase, Sub-System Testing, is to integrate the production code and initiate functional testing; HIL can be used for the final validation prior to vehicle testing. This phase includes validation of functional and regulatory requirements. The HIL system must faithfully model the in-vehicle system if it is to be used at this level of validation: this includes evaluation of the expected range of hardware variability. This testing environment should also be automated to allow quick responses to last-minute issues. The final verification phase, Vehicle Testing, is the implementation of production code in the vehicle. Algorithm response with all of the vehicle dynamics present is evaluated in this stage. The vehicle must remain the final validation activity due to the assumptions that must be made about the dynamics of the vehicle to allow the virtual testing activity to be done. The complexity of the models that would be required to have the entire vehicle dynamics included, assuming that they could be characterized, would probably cause the realtime simulation to over-run the processor loop times, thereby losing the real-time effects. 8.9.3.1  Benefits of the Virtual Environment Strategy The benefits of the virtual environment strategy and technology are seen both directly and indirectly. The ability to develop and validate control algorithms without having either a control module or a physical plant to control allows a reduction in development time and cost. Additionally, the reduction of the number of prototypes will also reduce the cost of development. These are direct benefits of development cycles which use simulation techniques. Other benefits include the ability to have a robust control system so that hardware and other long-lead items can be developed without the difficulties that mal-performing control algorithms can cause. This fact has two paybacks, one being the reduction in the number of prototyped hardware units and the other being that you can reduce the number of prototype pieces at each level because the algorithm-induced failures should be reduced, if not eliminated. Additionally, certain hardware problems are more easily identified because the failure to provide a proper response becomes readily apparent during testing.

8.9.4 Application of Design Strategy to Chrysler Six-Speed Transmission This program introduced a new aspect to shift control at Chrysler; a double-swap shift (two elements are disengaged, and two different elements are engaged) is required to make full use of the downstream compounder configuration. The

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complete feasibility of this transmission and control strategy needed to be determined in a compressed time schedule to meet the product schedule. The control for this shift is very complex and required the development of totally new features. This process was successful and resulted in the completion of this program in the challenging time-line.

Application of the double-swap shifts, along with the tools used, is shown below:

8.9.4.1 Model-In-the-Loop Testing This phase is the first phase of simulations with the basic plant model and the controller algorithms running on the closed-loop, real-time platform. The algorithms in this phase could be in the floating-point format. The plant model used in this phase could be a somewhat simplified version that lacks fully representative performance.

Fig. 8.9.4  MIL Process. With the MIL process, many iterations to the logic can be made, as shown in Fig. 8.9.5.

Advantages of this step: • Controller and plant models can be executed in realtime • Easy and quick development • Comprehensive test strategies for the algorithms, which can be designed in this phase, are re-usable in future steps

Fig. 8.9.5  MIL Logic Development Process. Data collected in this phase are shown in Fig. 8.9.6.

Fig. 8.9.6  MIL Results: The signals above are divided into four categories: Solenoid; Accelerations – desired and measured; Output Torque with Friction Element Pressures; and Speeds—Engine, Turbine, Compounder, or Intermediate and Output.

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The information in Fig. 8.9.6 indicated that the concept was probably feasible. It shows the control parameters (solenoids) and system response (pressures and clutch torque). The output torque signal is used to evaluate shift control. A certain profile of output torque is required. Correlation to this profile is a measure to shift quality and to the torque transfer among the applying and releasing elements. During this phase, inputs from the control logic group to the hardware design can be made to facilitate the control strategy. In this program, a number of changes were made to hardware design based on the initial evaluations, e.g., orifice sizes in the hydraulic circuit, accumulator spring rates, and other items that affect response rates.

Fig. 8.9.7  HIL Development Process. With this system, verification was performed on the following: • • • • •

8.9.4.2 Rapid Prototyping using the HIL (Bypass + HIL Testing) In this phase the plant model (transmission model) is fairly complex and is implemented on the HIL. The new controller algorithms such as 2-3 double swap shift control, and new shift schedule are implemented in the model base environment. Special hooks are made in the original software so models can be run in the Rapid Prototyping Controller (RPC) system and connected with the carryover algorithms in the ECU. The controller algorithms are in fixed-point math. The ECU hardware is also used for managing the carryover IO functions. All the diagnostics are available in this phase. The dSPACE Plug-On-Device (POD) is used to bypass functions from the ECU to the RPC. The software environment allows easy access to all the controller software variables. Using dSPACE Real-Time Interface (RTI) and ControlDesk User Interface, users can easily interact with the algorithm and fine-tune it. Comparison between the results of the MIL versus the HIL can be analyzed.

The plant model still had the following limitations: • Clutch dynamics • Vehicle dynamics • Shift quality rating Data collected in this phase are shown in Fig. 8.9.8. 8.9.4.3  Dynamometer Environment After testing in the HIL environment, the control logic is tested in the dynamometer environment. In this phase the controller is now working with an actual plant. All the tests applied in earlier phases are carried out again. Advantages: • Less time required on the dynamometer for testing • Fewer or no break-downs of the plant due to controller errors • Tests schedules are re-used and comparisons are quick and easy • Logic and control equations are evaluated using actual hardware (clutch dynamics) • Adaptation study. This includes all learning parameters; convergence and sensitivity study of all learned parameters are evaluated for system control and stability.

Advantages: • The changes to the algorithms can be easily performed without any time consuming re-coding process. The changes to the algorithm are made in the Simulink environment and downloaded to the RPC system. This process is easy and efficient. • Plant model can be fairly complex. • Evaluate interaction with other ECUs; e.g., engine controller can be simulated. • Controller diagnostics and preliminary calibration can be achieved. • Simulations can be done long before the actual transmission hardware is available. • Minimize hardware failures due to errors in the transmission control logic or lw-level C-code implementation

C-Code low-level layer RPC bypass function verification Adaptation study Sensitivity study Feasibility study

Limitations: • Vehicle dynamics • Shift quality rating Data collected in this phase are shown in Fig. 8.9.9

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Fig. 8.9.8  HIL Results: The signals above are divided into five categories: Solenoid; Accelerations—desired and observed; Torques—Output and friction element; Pressures—friction element; and Speeds (Engine, Turbine, Compounder or intermediate, and Output speed).

Fig. 8.9.9  Dynamometer Results: The signals are divided into five categories: Solenoid; Accelerations – desired and observed; Output Torque; Friction Element Pressures; and Speeds—Engine, Turbine, Intermediate (Compounder), and Output. 8-117

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8.9.4.4  In-Vehicle Testing This is the final step in the development process. The controller logic used in the dynamometer was applied in the vehicle. Initially, the RPC system is mounted in the passenger compartment with the ECU mounted under-hood. The ECU, with the POD and RPC, is used to manage the control algorithms. All the factors that influence the controller behavior are in play. Later, the prototype controller would replace the RPC system. Advantages: • Correlation of results among HIL, dynamometer, and vehicle are evaluated. This check validates the performance of the control algorithms with full vehicle response and dynamics. • Final calibrations can be performed. • This is primarily a verification and final calibration phase and requires few if any changes to the algorithms. • Reduced chance of any failures due to algorithm or C coding errors. • Data collected in this phase are shown in Fig. 8.9.10.

8.9.5

Final Results of the Six-speed Feasibility Program

Two weeks after the transmission hardware was installed in the vehicle, the system was ready for an initial Executive Ride and Drive. Of course, the calibration was still in progress, but the control logic was in place, and the feasibility of this new system could be evaluated. In summary, this process was successful and proved to be very efficient. To have data from a vehicle with a workable control for such a complex system within a few hours after the transmission hardware installation was a significant achievement.

8.9.6

Summary

As programming languages continue to become more sophisticated, the software programmer will be further removed from the machine being programmed. Automatically generated code derived from system models will become reality, making modeling an even more important development tool than it is today. As computing power continues to increase, more-detailed models will be able to run in real time, supporting more-sophisticated closed-loop bench configurations. These modern tools will at least partially address the needs of future increasingly sophisticated automatic transmission controls, continued pressure toward up-front system and subsystem development, and the need for shorter development times using fewer vehicle prototypes.

Fig. 8.9.10  In-Vehicle Results: The signals are divided into four categories: Solenoid; Calculated accelerations; Pressures corresponding to solenoid activities/Output Torque; and Speeds—Engine, Turbine, Intermediate (Compounder), and Output. 8-118

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Chapter 9

Automatic Transmission Pump Design • Noise, vibration, and harshness (NVH) factors for all pumps • Survey of transmission pumps currently in use • What’s on the horizon

Introduction The goal of this chapter is to provide the reader with a single continuous source on automatic transmission pump design, instead of a compilation of papers from previous editions.

Again, this is an overview of basic hydraulic principles and provides a practical starting point for transmission pump design.

This chapter is an overview of basic hydraulic principles as they apply to pump systems in an automatic transmission. Discussion topics include:

Thanks to Nichols Portland’s product engineering department for its time and effort in writing this chapter and to the authors of the papers in the previous editions, which are referenced at the end of this chapter.

• Types of pumps • Types of pumping systems • Pump design guidelines • Common design factors – Determine the pump requirements – Determine pump theoretical displacement – Inlet design – Pump performance factors • Design factors for gerotor pumps • Design factors for crescent gear pumps • Design factors for external gear pumps • Design factors for variable displacement vane pumps

Special thanks to the SAE Auto Transmission Technical Standards Committee for the opportunity to participate in the rewriting of this chapter for this new edition. Glenn B. Mann Nichols Portland Division of Parker Hannifin T. Roeber, M. Goulet, P. Dion, and G. Mann Nichols Portland Division of Parker Hannifin

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9.1 Introduction

A design variation that fits between fixed and variable displacement is the binary pump, where two fixed displacement pumps are used in parallel. One pump is unloaded at higher speeds in order to save hydraulic power. Any of the fixed displacement pumps can be used to make a binary pump, with the displacement split based on the application. The external gear pump offers a unique option of using three gears to provide two different flow streams, but this design can result in only a 50/50 displacement split, which may not be optimum for the application. At higher speeds, a binary pump will have lower power consumption than a single fixed displacement pump. The cost will be between the single pump and a variable displacement vane pump.

The basic requirement for an automatic transmission or transaxle pump is to meet transmission flow demand quietly, efficiently, and cost effectively. The type of pump used depends on the design priorities of noise level, energy efficiency, and installed cost. In some areas, different pump types have inherent trade-offs, such as the cost for energy efficiency. In other areas, such as overall efficiency or noise, the differences among pumps may be due more to the quality and execution of the pump design than to the pump type. This chapter is an overview of basic hydraulic principles as they apply to pump systems in an automatic transmission. Discussion topics include the types of pumps used in automatic transmissions today, correct pump sizing, and design factors for each type of pump. Two pump systems used in transmissions—wet and dry sump—are also discussed. Last, a summary is included of which pumps are currently being used in vehicles available in North America.

9.3 Types of Pumping Systems Most automatic transmissions and transaxles use standard wet sump systems, where the oil gravity drains into the pan, and the pump takes it up directly. At least one transmission, however, uses a dry sump system. In the GM 4T80E transmission, the oil drains into a shallow pan. Two scavenge pumps drain the pan and transfer the oil to a separate tank that feeds the main pump. This tank helps to de-aerate the oil, improving oil quality. The disadvantage of this system is the added complexity, cost, and power draw. Advantages include more flexible packaging, a higher ground clearance because of the shallower pan, and improved oil quality.

9.2 Types of Pumps Figure 9.1 shows a family tree of the different pump types. Of the different variations, only four are currently used in automatic transmissions: • External gear pumps, a.k.a. spur gear pumps • Crescent gear pumps, a.k.a. internal-external or IX pumps • Tip sealing pumps, a.k.a. gerotor pumps • Sliding vane pumps

9.4 Pump Design Guidelines 9.4.1 Common Design Factors Step 1: Determine the pump requirements— “How much flow do you really need?” The critical first step in designing any pump is determining the flow requirements at key design points. Given the physics of pumps and the hydraulic system, the worst-case design point is usually hot idle. At this point, the specific demand of the transmission (flow per revolution) is at its highest, while the volumetric efficiency of the pump is at its lowest. This will be discussed in more detail in the next section. There are different methods for determining transmission flow requirements. Use as many methods as possible to provide a high level of confidence in the data. If a pump is undersized, it could fail to provide enough pressure to engage the clutches under extreme conditions. In addition, parts of the transmission may not be properly lubricated, leading to long-term wear problems. Conversely, if the pump is oversized, it will waste power, degrade fuel economy, and add to the heat load of the transmission. For new designs, many companies have developed analytical models that sum up

Fig. 9.1   Family tree of pump types. Of these, the first three are fixed displacement, while vane pumps are designed to vary their displacement. The intent of a variable displacement pump is to match pump output flow to system flow demand in order to save hydraulic power.

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the calculated flow requirements and leakages. Any theoretical model should be compared to existing transmissions of similar size and design parameters. Warranty data can also be analyzed to detect possible lubrication problems.

gine revolutions per minute. Nominally, a pump that runs at twice the engine speed should have half the displacement of one running at engine speed. However, with the improved volumetric efficiency, the size can be further reduced to save more power.

If a transmission is available for test, the flow requirements can be determined by using an external flow source. Disable the transmission pump and plumb in a variable flow pump and a flow meter. Then run the transmission to map out the system demand across the full range of speed, load, and temperature.

The formula for determining the theoretical pump displacement (assuming no leakage) is Theoretical pump displacement:

On a final note, it is a good idea to protect some real estate to allow for future design changes or adjustments to the pump requirements. For example, leaving space to increase the length of the pumping element by 10 to 20% can make future flow increases simple to incorporate.

Dtheo =

1000 × Q in cubic centimeters (9.1) N per revolution (cc/rev)

where Q = flow in liters per minute N = input speed in revolutions per minute

Step 2: Determine pump theoretical displacement— “How big is it?” Once the actual flow demand is known, the next step is to size the pump based on the expected volumetric efficiency. One reason pump size is determined at hot idle is that pump volumetric efficiency (Ev) is at its lowest level at this point. Figure 9.2 shows typical flow and volumetric efficiency versus speed curves for a fixed displacement transmission pump. From this, you can see that the pump internal leakage is independent of speed. Thus, the leakage is a larger proportion of the theoretical pump flow at low speeds, reaching a point where it “dead-heads” at a given pressure (output flow = leakage flow). This phenomenon is critical for pump sizing and becomes even more of an issue as engine idle speeds are reduced to improve fuel economy.

Accounting for pump leakage, the actual pump displacement will be Actual pump displacement:

Dactual =

Dtheo cc/rev EV

(9.2)

The volumetric efficiency assumed for this calculation should be based on a maximum clearance pump, using test data for similar pumps. Step 3: Inlet design—“If the oil can’t get into a pump, it can’t get out.” The second key to good pump design is the pump inlet. All pumps have an inherent cavitation speed, and this speed is determined by the shape and size of the intake, the rotational speed of the pumping element, and the vapor pressure of the fluid. Once a pump starts to cavitate, flow will level off (see Fig. 9.2), noise will increase dramatically, and physical damage to the pump components can occur. Also, when cavitation occurs, the dissolved air in the fluid is turned into air bubbles. These bubbles in the flow stream will make the fluid more compressible (reducing hydraulic response) and will decrease the load capability and heat transfer properties for the fluid. The only energy available to push oil into the pump is atmospheric pressure, so the primary focus should be to minimize pressure drops throughout the inlet circuit of the pump. There are two guidelines to follow when designing the suction side of a pump: flow velocity, and pressure drop. One rule of thumb is that the inlet flow velocity should never exceed 2 m/ sec, to ensure passage areas are adequate. However, this may be misleading if the inlet is long, has a high lift, or has many

Fig. 9. 2   Typical flow and efficiency curve for a gerotor transmission pump. The dependence of volumetric efficiency on idle speed may make the case for operating the pump at a multiple of en9-3

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sharp bends and area changes. A more accurate method is to calculate the total inlet pressure drop, keeping this drop to less than 30 kPa from the sump to the pump inlet port. The pressure drop calculation must include: • • • • • • •

inner gerotor while the shaft engages the gerotor and provides only the driving function. The outer gerotor is located in a close-fitting pocket in the pump housing that is eccentric to the shaft. The close fit between the gerotor and housing functions as a journal bearing to support the outer gerotor on a fluid film.

Total length of run Total amount of lift Number and severity of bends Cross-sectional area of tubes or passages Effective cross-sectional area of screens Surface finish of passages Viscosity of oil

Step 4: Pump performance factors—“What you can control and what you can’t.” The design goal for any pump is to meet the required flow using a minimum amount of input power. Because the pump does nothing to propel the vehicle, all power used by the pump is parasitic and must be minimized. There are two components of pump performance: volumetric, and mechanical. Both are influenced by the same factors: fluid viscosity, speed, outlet pressure, clearances, and pump design and materials. Of these factors, the first three are dictated by the application and are usually not negotiable. The fluid and temperatures determine fluid viscosity. Pump speed range may be varied only if the pump is belt, gear, or chain driven, but otherwise is determined by the engine and vehicle capabilities. Outlet pressure is a requirement of the application and must be met to ensure proper function of the transmission.

Fig. 9.3  Typical gerotor transmission pump—Ford 4R70W. The gerotor is an internal, tip-sealing gear set. The conjugate geometry of the set provides sealing between the N teeth on the inner gerotor and the N+1 lobes on the outer gerotor for the full rotation of the set. This requires close tolerances on the gerotor shape to provide adequate sealing between the high- and low-pressure sides of the pump. However, it eliminates the need for a separate sealing crescent in the pump housing, as in the case of a crescent pump.

The factors that can be controlled in the pump design are the sealing land design, the internal clearances, the porting design, and the materials used for the housing and cover. Of course, each of these must be weighed against other factors in the overall design. The length of the sealing lands in a pump must be weighed against packaging restrictions. Internal clearances are usually a trade-off among manufacturing capability, cost, and pump performance. The optimum material for a pump body may be cast iron, to better match thermal expansion of the gears and the housing; however, weight targets may push the design toward an aluminum housing.

Figure 9.3 shows a typical gerotor and its inlet and outlet ports. For each pumping chamber (there are N+1 chambers for a gerotor with N inner teeth), the chamber volume is smallest at maximum tooth engagement. As the inner gerotor rotates, this volume increases smoothly from a minimum at closed mesh to a maximum volume at the open mesh position. The minimum and maximum volumes occur along the line of the eccentricity. The increasing chamber volume creates a partial vacuum, and atmospheric pressure pushes fluid through the inlet circuit and into the pumping chamber. After the chamber reaches maximum volume, it decreases in volume for the remainder of the full rotation, returning to a minimum. As the chamber decreases, it squeezes the fluid into the outlet port, completing the transfer from the inlet to the outlet ports. To prevent the fluid from leaking back to the inlet port, the distance between the inlet and outlet ports must be at least as wide as the pumping chamber at those locations.

9.4.2 Design Factors for Gerotor Pumps Figure 9.3 shows a typical gerotor transmission pump. The basic components of the pump are the inner gerotor, outer gerotor, pump housing, and pump cover. The inner gerotor is usually supported by the driveshaft and driven by it. There are some applications, though, where the drive and support functions are separate. In such cases, a bearing supports the

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9.4.2.1 Flow

where

Factors that affect pump flow are pump displacement, speed, internal leakage, and cavitation flow loss (at higher speeds). Figure 9.2 shows a flow graph for a typical fixed displacement transmission pump and illustrates some of the effects of each of these factors:

QL = leakage flow in cubic millimeters per second H = height of the leak path (i.e., clearance) in millimeters Vo = relative velocity of the two surfaces in millimeters per second P = pressure drop across the leak path in megaPascal (N/ mm2) μ = absolute viscosity of the fluid in centipoise (N-s/ mm2) Z = length of the leak path in millimeters

• Theoretical pump flow is linear with speed. • Internal leakage is always present and is basically constant for given pressure, viscosity, and clearances. • Volumetric efficiency is the ratio of actual output flow to theoretical flow.

The most important factor is the height of the leak path H (a.k.a. the axial clearance). The maximum clearance is determined by the allowable leakage (H3 factor). This maximum clearance for an aluminum housing may be less than for a cast iron housing at assembly, because the difference in thermal expansion will increase the axial clearance at high temperature. Minimum axial clearance is determined by cold start transients. During a cold start, localized heating of the gear causes the gear to expand faster than the housing, creating interference if there is not enough clearance. A typical range for axial clearance in a gerotor pump is 20 to 60 microns (0.02 to 0.06 mm). To achieve the 20- to 60-micron clearances, most manufacturers use a selective fit process to match different gear thicknesses to the machined pocket.

Pump displacement for a gerotor pump is determined by the formula Gerotor pump displacement: where

D = 2 ¥ π ¥ P ¥ e ¥ W mm3/rev

(9.3)

D = displacement in cubic millimeters per revolution P = ID of the outer gerotor in millimeters e = eccentricity of the shaft to the pocket in millimeters W = width of the gerotor in millimeters Displacement is commonly expressed in cubic centimeters per revolution (cc/rev), and the conversion is 1000 mm3 per cc.

Tip leakage depends on the thickness of the gerotor (i.e., the width of the leak path) and the amount of tip clearance between the inner and outer rotors. This tip clearance is unaffected by temperature because the inner and outer gerotors are similar materials. The operating tip clearance, however, is affected by the dynamics of the outer rotor in its pocket. At low speed and high pressure, the minimum film thickness for the OD journal bearing decreases. This tends to reduce the operating tip clearance of the gerotor set by moving the outer rotor down relative to the inner rotor.

Internal leakage in a gerotor pump can take several paths: • Across the faces from the high-pressure port to the ID or OD • Across the face from the OD to the low-pressure port • Across the face from the high-pressure to the lowpressure ports • Through the tip clearance between the inner and outer gerotors

Cavitation occurs in all types of pumps. When the pump inlet pressure drops below the vapor pressure of the fluid, vapor and gas bubbles appear in the inlet port and displace fluid in part of each pumping chamber, reducing the output of the pump. This can occur due to restrictions in the pump inlet circuit and excessive operating speeds. In addition to reducing the output flow, cavitation causes high noise and pump damage. Damage occurs by erosion of the metal and can result in structural damage to the pump body and gerotor. Figure 9.2 shows flow versus speed for a pump mounted on a torque converter impeller hub and shows a cavitation flow loss at speeds above 3500 rpm. This flow loss may not affect transmission performance because the pump is producing more flow than needed at this speed; however, the increase in noise and damage to the pump may be unacceptable. Noise

The factors that affect the face leakage are axial clearance between the gerotor and housing, fluid viscosity, pressure difference, length and width of the leak paths, and relative velocities between the gerotor faces and the pump housing. The leakage can be characterized as Couette flow (laminar flow between flat plates), and the formula for this is

Couette flow: QL =

B × H × Vo B × H3 × P + 2 12 × µ × Z

(9.4)

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can be reduced by reducing the tip speed (tip diameter), increasing inlet flow areas, increasing the chamber fill time with extended porting, reducing the pump flow rate, or elevating the inlet pressure.

The second equation is for viscous drag between two flat plates rotating at a relative velocity. This simulates the drag on the gerotor faces, Face drag equation:

9.4.2.2 Power Consumption

PFACE =

The three components of power draw are hydraulic power, viscous losses, and mechanical losses. Hydraulic power is the pump output and is a result of the pressure times the flow rate. Because pressure is determined by the application, the only controllable factor is flow—either through the pump displacement or speed. The gerotor is a fixed displacement pump, so the power will always increase in proportion to speed. The flow referred to in this equation is the theoretical pump flow. Because internal leakage is pressure driven, all of the fluid must be pumped up to pressure before leaking back.



P×Q 60

PFACE = power loss per face in watts μ = absolute viscosity of the fluid in centipoise (N – s/mm2) N = rotational speed of the gerotor in revolutions per minute RO = outer radius of interest in millimeters RI = inner radius of interest in millimeters HF = clearance between the two plates in millimeters In both of these formulae, it is important to remember that the outer gerotor rotates N/(N + 1) times slower than the inner gerotor due to the gear teeth ratio. For face drag, the full face of the gerotor is not exposed to the housing. For the outer rotor, it is more accurate to assume the drag from the outside of the port to the rotor OD. For the inner rotor, use the ID to the inside of the port. Both of these formulae are useful for comparing options in the initial design stage, but in practice, they are estimates because the gerotor does not run centered in the pocket, either radially or axially.

(9.5)

where PIN = input power in watts P = pressure in kiloPascals Q = flow in liters per minute The viscous losses in a pump are due to the shearing of the fluid at the moving interfaces. There are two simple formulae for predicting viscous power loss. One is Petroff ’s equation for a lightly loaded bearing, which can be used to predict the losses at the OD of the gerotor,

Mechanical losses in a pump are minimal as long as proper clearances are used and there is no mechanical interference. The sliding contact of the inner to the outer gear is a minor contributor.

Petroff ’s equation:

POD

π 3 × µ × D3 × N 2 × W × (1 × 10−9 ) = (HR × 3600 × 1000)

(9.7)

where

Hydraulic power: PIN =

2 × π 3 × N 2 × µ × (R O4 − R I4 ) × (1 × 10−9 ) (HF × 3600 × 1000)

Another loss can occur when the distance between the ports is too wide, and the chamber starts to squeeze the fluid before it opens to the outlet port. This is referred to as “trapping” and causes a sharp rise in pressure in that pumping chamber, which translates into high torque and noise. This can be avoided by controlling the porting dimensions or adding a metering groove.

(9.6)

where POD = OD power loss in watts μ = absolute viscosity of the fluid in centipoise (N – s/mm2) D = OD of the outer gerotor in millimeters N = rotational speed of the gerotor in revolutions per minute W = width of the gerotor in millimeters HR = radial clearance between the gerotor OD and the pocket ID in millimeters

Other contributors to pump losses are seal drag and bearing drag. The interface between the gerotor OD and the pocket ID is critical. An error in this part of the design could result in an OD bearing failure at certain combinations of tolerance stack-up, low speed, high load, and high temperature. A minimum clearance is needed to avoid mechanical interference at the worst-case tolerance stack-up, which should include maximum material condition, maximum location errors, and 9-6

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maximum shaft deflection or other dynamic conditions. The maximum clearance must be small enough to perform as a hydrodynamic bearing. Because this is a journal bearing, the diameter must not be interrupted in the area of the highpressure fluid film, which is usually on the high-pressure side. There should also be no leaks present, which detract from the capacity of the OD bearing, such as oversized chamfers. For manufacturing reasons, there needs to be a chamfer on the gerotor OD to clear the machining radius in the bottom of the pocket or an undercut in the bottom of the pump housing. Either of these should be minimized to optimize bearing load capacity. For performance consistency and foolproof installation, an undercut is usually preferred.

9.4.3 Design Factors for Crescent Gear Pumps Figures 9.4 and 9.5 show a crescent gear transmission pump. The components include an inner gear, outer gear, pump housing, and pump cover. The crescent that forms a seal between the inner and outer gears is typically machined into the pump housing. The inner gear is usually located and driven by a driveshaft, although in some applications, the drive and support functions are separate. The outer gear is located in a close-fitting pocket in the pump housing. This close fit between the gear and the housing functions as a journal bearing to support the outer gear on a fluid film during operation. The pocket in the housing is offset from the shaft by the center distance of the gears.

Fig. 9.5  Standard involute crescent gear—GM 4L80E. At one time, gears with an involute profile prevailed (Fig. 9.5), but now several other gear types have become common, including shifted module involute gearing, trochoidal gearing (Trochocentric® and Gero-crescent™, see Fig. 9.4), and cycloidal gearing (dual cycloidal). Each of these gear shapes may have advantages, but the basic pump design parameters are the same for all. The principal of operation for a crescent gear pump is similar to that for other gear pumps. As the inner and outer gear teeth unmesh in the inlet port, the chamber between the teeth increases in size, creating a partial vacuum. This typically occurs in the first 15 to 20 degrees of rotation for a crescent gear pump. This causes atmospheric pressure to push fluid through the inlet circuit and into the pumping chamber. A crescent-shaped piece of housing material acts as a seal between the inlet and outlet ports (see Figs. 9.4 and 9.5), and on the outlet side, the fluid is squeezed out as the teeth mesh together again. 9.4.3.1 Flow Pump flow is determined by displacement, speed, internal leakage, and cavitation flow loss. Pump displacement for a crescent pump is determined by the swept area of the teeth, given in the formula

Fig. 9.4  Typical crescent gear transmission pump— Ford 5R55N.

Crescent pump [9.1]: D=

π 2 2 × W × ⎡ODINR − (PDOTR − (MDOTR − PDINR )) ⎤ mm3 /rev ⎣ ⎦ 4 (9.8)

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where

factor that works in favor of a crescent pump is that the relative motion between the gears and the crescent opposes the leakage flow.

ODINR = OD of the inner gear PDOTR = pitch diameter of the outer gear MDOTR = minor diameter of the outer gear PDINR = pitch diameter of the inner gear

The machine tool corner radius at the bottom of the crescent requires a clearance chamfer at the gear tips to avoid interference. These radii and chamfers should be minimized for best performance.

Note: Because PDOTR – PDINR equals twice the pump eccentricity (e), then

The length of the crescent also affects leakage because it determines how many teeth are sealing at a given time. Take care, though, that the crescent does not extend so far that the thin end sections become difficult to machine or subject to fatigue failure from pressure fluctuations.

(PDOTR – (MDOTR – PDINR)) = MDOTR – 2e W = gear width The leak paths for the fluid must be controlled to maximize pump efficiency, and these leak paths include:

9.4.3.2 Power Consumption

• Leakage across the face of the inner rotor to the ID • Leakage across the face of the outer rotor to the OD • Leakage between the inner gear teeth and the crescent ID • Leakage between the outer gear teeth and the crescent OD • Leakage across the face of the inner and outer gears between the outlet and inlet ports • Leakage past the radius at the base of the crescent and gear chamfers

Mechanical performance considerations for a crescent pump are hydraulic power (Eq. 9.5), OD viscous power loss (Eq. 9.6), face viscous power loss (Eq. 9.7), and mechanical losses.

9.4.4 Design Factors for External Gear Pumps Figures 9.6 and 9.7 show two pictures of external gear transmission pumps. Basic components of these pumps are the drive gear, the driven gear with idling shaft, housing, and cover. Again, the drive gear can be located and driven by the driveshaft, or the drive and support functions can be separated. One major difference between the external gear pump and the internal gear pumps (gerotor and crescent) is that the external gear pump primarily uses radial porting for the inlet and outlet. This can reduce the amount of axial length needed for a pump package. Secondary axial ports are typically needed to improve pump chamber filling and prevent trapping of fluid at the gear mesh.

The factors that affect these leakages are covered in the discussion for Eq. 9.4 on Couette flow. Axial clearance effects are similar to those for a gerotor pump. One minor difference is that the inner and outer gear pockets are machined in different steps, so care must be taken to match these pockets as closely as possible. This will avoid a leak path at the closed mesh crossover.

It is not necessary for the drive and driven gears to be the same size, as shown in Fig. 9.6. If the pitch diameter of the drive gear is increased to fit over a large shaft, the driven gear can be smaller, as long as the two gears have the same gear pitch. The theoretical displacement of the pump is determined by the size of the drive gear, and the displacement formula below takes this into account.

Leakage between the gear teeth and crescent is affected by several factors. The clearance from the tip of the inner gear to the crescent must accommodate several variables: shaftto-crescent location, shaft deflection and misalignment, gear ID-to-tip runout, and gear-to-shaft fit. The tip clearance in a crescent pump also can be greatly affected by thermal expansion. An aluminum housing expands more than a steel gear (wrought or sintered), and this increases the inner gear tip clearance at high temperature. This material combination is not recommended. The outer gear stack-up is similar, but it may have a tighter tip clearance because the pocket ID and crescent OD are machined in the same operation. For the inner gear, the shaft location is several steps removed from the machining of the crescent ID. The gear tooth design also affects tip leakage, because a narrow sealing land at the tooth tip is less effective than a wide land. Also, more teeth in contact with the sealing crescent gives better sealing. One

Figure 9.6 shows a typical automatic transmission external gear pump, while Fig. 9.7 shows a high-pressure pump for a continuously variable transmission (CVT). The design differences will be noted later in this section. 9.4.4.1 Flow Like other pumps, flow depends on displacement, speed, internal leakage, and cavitation flow losses. The displacement for an external gear pump is given by 9-8

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External gear pump: D=

The leak paths in an external gear pump are:

π × [OD12 − (PD1 − (OD2 − PD2 ))2] × W mm3/rev (9.9) 4

• Leakage around the tips of the drive and driven gears • Leakage across the faces from high pressure to low pressure • Leakage between the pump pocket radius and gear OD corner chamfer The axial clearances in an external gear pump are similar to those for gerotor and crescent gear pumps. Similar to a crescent pump, the two pocket depths must be closely matched to minimize the leak path at closed mesh. For automatic transmission pumps, the most common pump construction is shown in Fig. 9.6, with a machined pocket in an aluminum housing for the drive and driven gears. A disadvantage to this type of construction is the machining radius that will exist in the bottom corner of the pocket, and the gears must have a related chamfer for clearance. The leakage past this chamfer will increase pump leakage. Also, the tip clearance increases with temperature for an aluminum housing with sintered steel gears. For a higher-performance pump (Fig. 9.7), the separate center section can be made from cast iron to match the thermal expansion of the gears. This separate center section allows for closer control of axial clearance and has the added advantage that there is no machining radius at the bottom of the pocket, so the gears do not need chamfers on their tips. This can significantly improve the volumetric efficiency of the pump.

Fig. 9.6  External gear transmission pump—Honda MPXA.

For the drive gear, the radial clearance stack-up is similar to the inner crescent gear and must take into account the driveshaft location, pocket location, and gear runout. The driven gear can often have a tighter clearance because the idling pin can be located better than the driveshaft. Leakage past the tips is affected by operating tip clearance, the width of the tooth at the tip, and the number of teeth sealing at any one time. The operating tip clearance around both the drive and driven gears is determined by the design tip clearance, thermal expansion differences between the gears and housing, and housing wear.

Fig. 9.7  High-pressure external gear pump— Honda M4VA CVT.

External gear pumps can be limited in their use because of their inability to fill properly at high speeds. When a gerotor, crescent gear, or vane pump is filling, the elements are rotating in the same direction as the fluid flow, and the pump chambers are increasing at a relatively low rate of speed. However, when an external gear pump is filling, the gears are rotating in opposite directions, and they are separating at a relatively high rate of speed. Further, the direction in which the gears are travelling opposes that of the oil. This hinders the ability of the oil to enter the pumping chambers from a radial direction.

where OD1 = drive gear outside diameter PD1 = drive gear pitch diameter OD2 = driven gear outside diameter PD2 = driven gear pitch diameter W = gear width

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9.4.4.2 Power Consumption The mechanical performance considerations for an external gear pump are hydraulic power (Eq. 9.5), OD viscous power loss, idling pin bearing losses, face viscous power loss (Eq. 9.7), and mechanical losses. Because the OD of each gear is interrupted, Petroff ’s equation will not give an accurate prediction for OD power loss. Another power loss area to watch for is the porting at crossover, to ensure that there are no pressure traps that would increase the torque. 9.4.4.3 Tooth Forms Involute gearing is simple, forgiving, and efficient. Texts dealing with the topic are readily available, output and noise, vibration, and harshness (NVH) are not affected by pitchline runout, and mechanical efficiencies can approach 99%.

Fig. 9.8  Variable vane transmission pump—GM 4T65E. 9.4.5.1 Flow

That being said, one is not limited to the use of the involute tooth form. Many manufacturers of gears and pumps have developed tooth forms that can overcome certain limitations associated with involute gears. Some forms allow a gear to have a very small number of teeth without undercutting. Others have relatively tall teeth that offer more displacement from a given package size.

Vane pump flow depends on displacement, speed, internal leakage, and cavitation flow losses. Displacement for a vane pump is given by Vane pump [9.4]: D = 2eWN(2R ¥ sin(θ) – t ¥ cos(θ)] mm3/rev

(9.10)

where e = pump eccentricity (offset) W = rotor width N = number of vanes R = housing radius (slider, cam ring, etc.) θ = 180°/N t = vane thickness

9.4.5 Design Factors for Variable Displacement Vane Pumps Figure 9.8 shows a picture of a typical vane pump. Components include: • • • •

Rotor Vanes (7 to 11) Vane rings (quantity 2) Slider ring assembly (ring, face seals, pivot pin, and pivot seals) • Priming spring • Control piston assembly (optional)

Leak paths in a vane pump include: • Leakage across the face of the rotor from high pressure to low pressure • Leakage across the face of the vanes from high pressure to low pressure • Leakage across the face of the slider (seals are often used on the slider faces to minimize this) • Leakage between the vane and slot from high pressure to low pressure

In a sliding vane pump, the rotor is slotted to accept rectangular vanes that move radially in their slots. Rotor and vanes are enclosed in a slider, which is offset from the driveshaft. The amount of this offset can be controlled to vary the pump displacement. Slider offset is controlled by balancing control pressure on the slider against a priming spring on the opposite side of the slider while the slider pivots about a pin (GM pump [9.2]). Some designs use an intermediate control piston instead of having control pressure work directly on the slider (Nissan pump [9.3]).

9.4.5.2 Power Consumption Power consumption comes from hydraulic power (Eq. 9.5), viscous losses on the rotor faces (Eq. 9.7), friction of the vane tips on the slider ID (increases with pressure and speed), and friction of the vanes sliding in their slots (increases with pressure and speed). Because pump displacement can be varied, hydraulic power can be reduced at high speeds. Another loss 9-10

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9.5 Survey of Transmission Pumps Currently in Use

(not present in fixed displacement pumps) is the leakage flow needed to stabilize the control pressure. As in other pumps, the porting design must ensure there is no trapping of the fluid that would raise the input power, and this design must account for the full range of motion of the slider [9.5].

This information is based on data from the Mitchell repair manuals for vehicles available in North America [9.6, 9.7]. Those planning to design a transmission pump should familiarize themselves with current practices and the state of the art by reviewing current pumps from various transmission manufacturers to compare:

9.4.6 NVH Factors for All Pumps Many factors affect pump noise. There are two basic sources of noise and vibration: mechanical, and hydraulic. Mechanical noise comes from gear contact, shaft runouts, metal-tometal contacts, and so forth. Hydraulic noise comes from pressure ripple, which can excite vibration in the pump or somewhere downstream. Pressure ripple depends on the number of pumping chambers but is also affected by pump dynamics (shaft and gear runouts, form errors), cavitation, and system compliance.

• Physical size and packaging • Pump displacement • Materials and processing (casting walls, surface finishes, machining methods, etc.) • Porting schemes The trick in reviewing these pumps is to pay attention to the subtle features as well as the obvious, because the small details often make the difference.

Mechanical noise is best controlled with good design practices for bearing systems, locations, and runouts, and by using proper gear design and gear accuracy. Gear design is often a compromise, because a coarser pitch gear will give better packaging density (displacement per diameter) but will also tend to be noisier.

9.5.1 Who Uses What? The four types of pumps in use in automatic transmissions today are: • External gear pumps: used mostly by Honda/Acura, but also on the DaimlerChrysler 45RFE and GM 4T80E (scavenge pump only) • Crescent gear pumps, in different tooth shape variations: • Standard involute geometry: used by GM, Aisin, Ford, and DaimlerChrysler • Trochoidal geometry: used by Aisin, Toyota, Ford, and Nissan • Dual cycloidal geometry: used on the GM 4T80E • Shifted module involute geometry: used by ZF and some others • Gerotor pumps: used by Ford, DaimlerChrysler, and Mazda • Vane pumps: used by GM, Ford, Nissan, and Subaru

Hydraulic noise from pressure ripple is affected by the number of gear teeth (i.e., more teeth gives a lower-pressure ripple), shaft speed, pump porting, and the impedance of the downstream load. The number of gear teeth is often constrained by the packaging, so the most controllable part of the design is the porting. Each type of pump design has a basic porting design determined by the gear or vane geometry. Modifications to this basic design can include an extended inlet port, pre-compression, and metered porting. On a vane pump, the angular spacing of the vanes may be varied to break up the natural pumping frequency. Most pumps use some combination of these, and they are application specific. Noise is usually the most objectionable part of pump cavitation. Most pumps cavitate only at the highest end of their speed range. The duration of this high-speed operation varies by application and market, so concerns about cavitation damage must take these factors into account. Usually, pump noise increases gradually with speed and pressure, but there is a step increase when cavitation starts of as much as 10 dB(A). A good pump inlet design will help here, as well as optimizing the pump element proportions (small diameter helps, as well as limiting thickness). One design idea that can increase cavitation speed is to use the excess flow from the pump pressure regulating valve and route it back to the pump inlet, near the pump. This reduces the amount of oil that has to flow through the inlet line, and it provides some extra kinetic energy to enhance filling.

9.5.2 Operating Clearances The laws of physics determine the clearances within a pump. Because the fluids, temperatures, and operating pressures for transmissions are similar, the different pumps have similar clearances. Axial clearances are in the 20- to 50-micron range, with a few ranging up to 80 microns. For external and internal gear pumps, the radial clearance on the drive gear is usually larger than that for the driven gear. This is because the location of the driveshaft has more variables and is harder to locate as accurately as an idling pin to pocket or crescent to

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Design Practices: Passenger Car Automatic Transmissions

9.6 What Is Coming?

pocket. For a gerotor pump, the driveshaft location stack-up must be taken up in a combination of gerotor tip clearance and OD clearance. A summary of typical values follows:

It is always dangerous to predict the future, but some trends in the industry seem inevitable now, and these should be considered in new designs:

• External gear pumps (from Honda specifications): • Side clearance for drive gear: 0.210 to 0.264 mm • Side clearance for driven gear: 0.071 to 0.124 mm • Axial clearance for both gears: 0.025 to 0.050 mm • Internal gear pump (average of several manufacturers): • Inner gear to crescent clearance: 0.13 to 0.28 mm • Outer gear to crescent clearance: 0.10 to 0.15 mm • Outer gear to pocket clearance: 0.075 to 0.150 mm • Axial clearance for both gears: 0.02 to 0.05 mm • Gerotor pumps (average of several manufacturers): • Gerotor gears tip clearance: 0.09 to 0.19 mm • Outer gear to pocket clearance: 0.09 to 0.19 mm • Axial clearance: 0.02 to 0.05 mm • Vane pumps (information from Mazda, Nissan, and Subaru pumps—all the same): • Cam ring axial clearance: 0.010 to 0.023 mm • Rotor axial clearance: 0.030 to 0.043 mm • Vane axial clearance: 0.030 to 0.043 mm • Vane to rotor clearance: 0.030 to 0.043 mm

• Power savings as a driving force—binary pumps, better controls of variable pumps, and remote mounting of pumps. • 42-volt systems are making electrically driven pumps or auxiliary pumps possible. Cold start torque is a concern, but there are many advantages such as power savings, smart pumps, small size, packaging flexibility, noise, and so forth. For instance, an electrically driven pump can be smaller in diameter than the torque tube that drives many pump gears now. At the same time, it can just match transmission flow demand by varying the electric motor speed based on the required pressure. With a smaller speed range for the pump, it can be further optimized for minimum power draw and noise generation.

9.7 References 1. Froslie, L. E., “Internal-External Gears and InternalExternal Rotor Pumps for Transmissions”, from AE-18, Design Practices: Passenger Car Automatic Transmissions,” Third Edition, Society of Automotive Engineers, Warrendale, PA, 1994. 2. Koivunen, E. A., P. A. LeBar, Jr., and R. J. Green, “Variable Capacity Pumps,” from AE-18, Design Practices: Passenger Car Automatic Transmissions, Third Edition, Society of Automotive Engineers, Warrendale, PA, 1994. 3. Murota, K., “Analysis of Stability and Response of a Variable Displacement Vane-Pump,” Society of Automotive Engineers of Japan, 1989; available as SAE Paper No. 4-11-2-25, Society of Automotive Engineers, Warrendale, PA. 4. Stapleton, R. W., “Variable Capacity Transmission Pump,” from AE-5, Design Practices: Passenger Car Automatic Transmissions, Second Edition, Society of Automotive Engineers, Warrendale, PA, 1973. 5. Singh, T., “Design of Vane Pump Suction Porting to Reduce Cavitation at High Operating Speeds,” SAE Paper No. 911937, Society of Automotive Engineers, Warrendale, PA, 1991. 6. “Transmission Service and Repair, 1997–98 Domestic Vehicles,” Mitchell Repair Information Company, San Diego, CA, 1999. 7. “Transmission Service and Repair, 1997–98 Imported Vehicles,” Mitchell Repair Information Company, San Diego, CA, 1999.

9.5.3 Pump Displacements The repair manuals do not contain displacement information. However, this can be calculated for most pumps using basic measurements of the pump housings and gears. These formulae are included in each section for pump types and typically are accurate to within a few percent.

9.5.4 Construction Materials The three basic components to each of the pump types are the housing, cover, and pumping elements. The housing and cover can be either cast iron or aluminum. For the housing, the performance trade-off between these two materials is weight versus volumetric performance. Aluminum is lighter than cast iron, but the coefficient of thermal expansion is higher, which results in more leakage at high temperatures. Different material combinations are used in all the different types of pumps. Aluminum also has a lower modulus of elasticity than cast iron, which may give more deflection and thus more leakage if this is not taken into account. The external and internal gears, gerotors, and the rotors and cam rings for the vane pumps are usually made from various grades of sintered steel. Some are subjected to steam oxide treatment or conventional hardening. Vanes for the vane pumps are machined from heat-treated steel.

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Chapter 10

Seals and Gaskets

SAE J1002 “Evaluation of Elastohydrodynamic Seals” SAE J110 “Testing of Radial Lip Seal”

Introduction Transmission Seals A multitude of sealing components are deemed essential to the function of the automatic transmission. Nonetheless, all transmission seals can be categorized largely as either internal or external in terms of their function. This chapter provides a fundamental discourse of gaskets and shaft seals which comprise a majority of the external sealing components used on automatic transmissions today.

Gaskets Gaskets create a static seal around the perimeter of a joint that is formed between two mating structures of a transmission, such as two case halves or a case and pan. Most gaskets today are made from highly engineered polymers designed to handle the temperature extremes of the application and remain impervious to oil degradation. Section 10.1 covers the important considerations of gasket design when looking to seal static joints in an automatic transmission. A list of references at the end of this chapter provides additional resources on the subject of gasket design for automotive transmissions.

Radial Shaft Seals A radial shaft seal maintains a seal between a rotating shaft and generally static bore of the transmission case, allowing power to be transmitted into and out of the unit while retaining the lubricating fluid and excluding contamination. This chapter provides an overview of transmission radial shaft seals and important aspects of their design such as application parameters, materials, installation, testing, and failure analysis. Additional information for radial shaft seals can be obtained from:

Sealing technology is co-evolving with automatic transmission design and will continue to do so as powertrain engineers are challenged with increasing performance demands from their customers. This chapter provides a comprehensive overview of seal and gasket design considerations for use in current state-of-the-art automatic transmissions.

SAE J111 “Terminology of Radial Lip Seals” SAE J946 “Application Guide to Radial Lip Seals”

Andrew F. Joseph Jeff Nelson Freudenberg NOK Sealing Technologies

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10.1  An Overview of Automatic Transmission Gaskets

materials found in nature such as rubber, pulp-based paper, cork, and asbestos, and were relatively simple in their construction. The need for gaskets to seal at higher temperatures and against more chemically aggressive lubricants resulted in the use of engineered materials such as synthetic rubber and composites in automotive transmission sealing applications. In addition to material science advancements, gasket technology has also benefited from improvements in manufacturing. Automation has significantly reduced piece-to-piece variation, while in-process quality checks such as electronic vision systems and in some cases, leak check stations, have minimized pass-through defects. Transmission gasket design will continue to advance as powertrain packaging constraints and greater environmental awareness exert additional performance demands in the realm of automotive transmission sealing.

Andrew F. Joseph Jeff Nelson Lane Noble Freudenberg NOK Sealing Technologies

10.1.1  Abstract The evolution of transmission gasket technology over the last century has been commensurate with the rise in consumer expectations of automotive powertrain cost and reliability. Today, transmission gaskets are expected to seal over the life of the vehicle, which is likely to exceed 150,000 miles. The continuous improvement of gasket design and manufacturing methods has made the fulfillment of that expectation possible. Powertrain engineers have a number of gasket materials and designs from which to choose in order to find optimal sealing solutions for their applications. This section provides an overview of transmission gasket technology with particular emphasis on those application parameters that require careful consideration when designing a sealed joint.

10.1.3  Design Considerations The assembly of transmission components results in structural and non-structural joints that are typically sealed with gaskets. A structural joint is one where both halves of the assembly are load bearing members and are subject to external forces. An example of a transmission structural joint is the rear adapter housing and main case interface on a fourwheel-drive application. In this case, both components are attached to the vehicle’s sub-frame, as well as each other, and are subjected to independent loads and moments (Fig 10.1.1a). A transmission’s case and bottom oil pan assembly is an example of a non-structural joint, as the pan is fastened only to the case and no other components. For structural joints, the gasket must be capable of transferring loads across the joint, over many cycles while performing its sealing function. The term “static sealing,” as applied to gaskets, is somewhat of a misnomer given that transmission structural joints operate within a dynamic environment [7]. Transmission joints are subjected to constant motion as a result of vibration and thermal expansion. Therefore, the gasket must be resistant to abrasion and have minimal compressive stress relaxation (CSR) if it is to seal over the life of the transmission.

10.1.2  Introduction A gasket’s primary function is to prevent the passing of fluid through a joined structure to the environment while also excluding contaminants. An assembled structure can be hermetically sealed without the aid of a gasket if the mating surfaces of its adjoining components are perfectly flat, free of defects, and fastened with at least equal precision. Achieving such ideal assembly conditions would be impractical and cost prohibitive in the mass-production environment of automotive powertrain manufacturing. A more pragmatic solution is to use a gasket as a sealing mechanism between two mating components of “less-than-perfect” surface finish at the joint interface. A gasket therefore must also serve as a compensatory, load-bearing boundary layer between two mating components. The challenge facing the powertrain engineer is to design a joint with the least overall system cost by balancing gasket complexity with the surface finish quality of the mating components. As a general guideline, the gasket should be as thin as possible while maintaining conformability along the mating flange surfaces. Thinner gaskets result in less exposure to the fluid being sealed and have less compression set than a thicker gasket made from the same material.



(a) structural joint

(b) non-structural joint

Fig. 10.1.1  Schematic of gasketed joint types.

Advancement in gasket design has been largely the result of material development. Early gaskets were made from raw

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When designing a sealed joint, whether structural or nonstructural, the powertrain engineer must consider the following application parameters [1]: Temperature Pressure External Environment Fluid Type Flange Material Flange Stiffness Sealing Land Width Bolt Material

different interpretations of a surface finish when taken alone. Therefore, it is recommended to use all three evaluation parameters to obtain the best indication of surface roughness with respect to sealing.

Bolt Load Bolt Span Flange Surface Finish Pressure Flange Flatness Flange Porosity Motion (for structural joints)

Waviness depth, or total waviness (Wt), is the highest peakto-valley vertical distance of the waviness profile measured within the assessment length. Waviness may result from machine vibration during processing or from distortion as a result of heat treatment. Figure 10.1.2 illustrates the relationship between roughness and waviness.

Design for assembly (DFA) and serviceability may also be evaluated when designing a gasket for an application. Additionally, a tolerance stack-up (arithmetic, RMS) should be performed to ensure that the gasket will be properly located under all tolerance cases for all the components in the assembly. Surface finish comprises several measurable characteristics, each of which affects the gasket’s ability to form an effective seal at the interface of the flange. These surface finish attributes include roughness, waviness, lay, and flaws such as porosity. Roughness is the normally inherent surface texture that results from a production process such as casting or machining. This random variation in texture can be measured easily using a stylus probe to create a profile trace of the surface. The resultant data can then be quantified in several ways. Average Roughness, Ra, is the average amplitude (height) of the surface variance from its mean profile over the evaluation length. Total Roughness, Rt, simply measures the difference in height between the highest and lowest points captured within the evaluation length. Rz-DIN and Rz-ISO are calculated values for Mean Roughness Depth. Rz-DIN is the average of five differential maximum and minimum heights measured within five separate sample lengths, which added together equal the evaluation length used in Ra and Rt and can be expressed as

Fig. 10.1.2  Profile trace showing roughness (R) and waviness (W). (Courtesy of the Mahr Corporation) Lay describes the visible pattern observed on the surface, which is typically the result of the machining process used to generate the surface, and is usually described as being linear, cross-hatch, circular, radial, or random [3]. Flaws are unintentional interruptions of the surface texture and may be the result of mishandling, tool marks, material inclusions, or porosity.

10.1.4  Transmission Gasket Materials 10.1.4.1  Paper Cellulose fiber reinforced composite material (typically referred to as paper) is one of the earliest gasket materials to be used in automotive powertrain sealing applications with its usage dating back to the early part of the 20th Century. Paper gasket usage by OEMs declined steadily through the 1990s in favor of gaskets made from elastomeric materials. Nonetheless, characteristics such as relatively low cost and adaptability to a wide range of surface finishes have continued to make paper an attractive sealing material. Early paper gaskets were essentially of low quality, ranged in thickness from 0.076 to 2.286 mm, and were made from conventional paper mill processes [4]. Paper gasket technology has advanced over time to meet increasing demands in powertrain sealing performance, and consequently, so has its manufacturing process.

R z-DIN = 1/5 (R z1 + R z2 + R z3 + R z4 + R z5)

Rz-ISO is the sum of the averaged five highest and averaged five lowest points, relative to the mean, identified within a sampling trace and is given by the following formula [2]. 5

5

i =1

i =1

R zISO = 1/ 5∑ ypi + 1/ 5∑ ypi Like the three blind men who each touch a different part of the elephant and then surmise three different animals, these three types of roughness measurements may present very

Today, transmission paper gaskets are made from engineered materials designed to meet specific sealing requirements for powertrain applications. Typical paper gasket construction is 10-3

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comprised of three main elements: fiber, filler, and a binder. Fibers account for the structural integrity of the paper and may be either natural organic (vegetable or wood cellulose), synthetic organic (aramid, nylon, polyester, or acrylic) or synthetic inorganic (glass or mineral) [5]. Filler materials such as clay, mica, talc, and graphite are added to the paper to increase its density and lower creep relaxation. Lastly, the fiber and filler materials are bonded together with a binder such as an SBR, ABR, or NBR latex compound to improve the paper’s fluid resistance [5]. The heat resistance of paper gaskets will vary from 107°C to 260°C, depending on the combination of filler and binder materials used.

Cork is a highly compressible material, which enables it to conform to flanges with less than ideal surface conditions. Pure cork gaskets were limited to applications with operating temperatures of 120°C or less, and had high compression set and poor dimensional stability. Cork/rubber composite gaskets, also introduced by Armstrong, replaced pure cork gaskets in the 1970s and had improved high-temperature capability, oil resistance, and slightly more resilience. By the 1980s, however, elastomeric gasket technology had reached the point where it was a superior alternative to cork/rubber gaskets in automatic transmissions.

One of the reasons, aside from low cost, that makes paper an attractive gasket material to powertrain designers is its forgiving surface finish requirements for mating components. The recommended average roughness (Ra) for good sealability of paper is on the order of 1.5 to 3.2 μm. The allowable peak-to-valley (Rz) roughness range for paper is generally accepted to be 10.5 to 17 μm. Additionally, paper gaskets require minimal sealing land and can seal against flange widths as narrow as 4 mm.

10.1.4.3  Rubber Coated Metal Although more commonly used in engine sealing applications, Rubber Coated Metal (RCM) is an effective sealing material for transmission joints as well. RCM is ideally suited to applications where higher sealing pressure capability and minimal flange distortion is required. As its name implies, RCM gaskets consist of a thin metal substrate with a rubber coating that is chemically bonded with the aid of an adhesive. The rubber coating may be applied after the gasket substrate is blanked; however, the coil stock is usually coated with rubber prior to stamping. Depending on the pressure and corrosive nature of the fluid media, the metal substrate may be low-carbon steel, aluminum, or stainless steel and range in thickness from 0.15 mm to 0.3 mm. The following rubber compounds with maximum temperature ratings are commonly used coating materials: NBR (100°C), HNBR (200°C), and FKM (250°C) for the most severe sealing environments. The rubber coating is available in varying thicknesses from 0.025 mm to 0.13 mm, per side. An expansion agent can be added to the rubber compound to produce a coating with more foam-like characteristics, which in turn provides better conformability against surface finish imperfections.

The sealing performance of paper gaskets can be enhanced through the use of a rubber encapsulate. The rubber coating, typically nitrile, SBR, or Neoprene™ (chloroprene), is applied to the entire surface of the gasket by either dipping or rolling. This coating feature improves the gasket’s ability to conform to surface imperfections and, more importantly, reduces its permeability by sealing the cut edge of the gasket. A PTFE or clay-based release coating may be added to the rubber-coated gasket to minimize sticking to the flange when removing it from the joint. A nitrile or silicone sealing bead may be applied to the gasket in virtually any pattern desired. The rubber bead improves the gasket’s ability to handle flange warpage and improves its sealability by increasing the contact pressure at the joint along the printed line. A rubber bead may also improve sealability in applications where the sealing land is minimal. Silicone cures at a taller bead profile than nitrile but has poorer longterm durability in automatic transmission fluid (ATF) and is generally not recommended for automatic transmission applications. Both compounds are typically screen printed onto the gasket but may also be applied by liquid injection using an automated dispenser.

The RCM gasket is manufactured through conventional stamping technology. The gasket design may also include embossment features around orifices to improve sealing performance in specific areas. The two most common embossment shapes are half- and full-width beads (Figs. 10.1.3a and 10.1.3b). The primary function of the embossment is to concentrate the bolt load at its point of contact along the bead line. For RCM gaskets with a stainless steel substrate, the embossment feature also limits the creep relaxation by acting like a spring, maintaining bolt load even after exposure to many thermal cycles. RCM gaskets can also withstand a very high compression load; however, they require relatively tight surface finish controls on mating components (Ra ≤ 2.5 μm, Rz = 10 μm max.). If flange surface finish conditions can be maintained, and the bolt load is above the load-to-seal, RCM gaskets can provide a very durable, low-cost sealing solution.

10.1.4.2  Cork and Cork/Rubber Developed during the Industrial Revolution, pure cork gaskets have been used in automotive powertrain applications since 1912, when they were first introduced by the Armstrong Cork Company [4]. Cork is a natural resource found in the bark of the cork oak tree, a species that is indigenous to the Mediterranean regions of Europe and North Africa. 10-4

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provides a relative comparison of base rubber compounds commonly used in powertrain sealing applications. The majority of molded elastomeric transmission gaskets are made from Ethylene Acrylic (AEM), also known by its Dupont trademarked name, VAMAC®. Early versions of this compound required post-curing after molding to obtain the desired materials properties. The first non-post-cure VAMAC gasket was introduced in an OEM transmission application in 1990.

(a) half-width

AEM’s good tear strength, resistance to compression set at moderate temperatures, and relatively low cost make it an attractive material for use in automotive powertrain gaskets. AEM may exhibit swell in some automatic transmission fluids. Fluoroelastomers such as FKM and FVMQ are capable of withstanding higher temperatures than AEM but at a substantially higher cost. FKM, however, generally has relatively poor low-temperature flexibility unless it is specially blended for low-temperature performance. FKM is recommended in applications where low compression set after prolonged hightemperature exposure to petroleum oils is required.

(b) full-width Fig. 10.1.3  RCM gasket embossment types.

Polyacrylate (ACM) is an acrylic based compound, comparable in cost to AEM, but with relatively inferior lowtemperature flexibility. ACM has good performance in lubricants where sulfur is present; however, its use should be avoided in applications where exposure to water may be a likely occurrence.

10.1.4.4  Elastomers Elastomers are a desirable gasket material because they can be molded to shape and bonded to other materials, giving the engineer greater versatility in the design. Elastomers can also be blended with filler materials to obtain varying degrees of hardness. The application of synthetic rubber gaskets in automotive transmissions has risen steadily over the past two decades, and their usage will continue to rise as compounds are continuously improved by rubber manufacturers, making them more attractive to powertrain engineers. The trend in recent years for OEMs has been marked by a need for premium elastomers that are capable of withstanding higher temperatures and more aggressive lubricants. Table 10.1.1

Silicone (VMQ) is an inorganic rubber compound invented in 1944 and is one of the earliest synthetic elastomeric materials to be used in powertrain applications. Silicone has greater high- and low-temperature performance characteristics than most materials but has relatively poor hydrocarbon permeability resistance. Silicone was gradually replaced by ACM, AEM, and FKM in molded gasket applications as ATFs with higher concentrations of EP additives became more

Table 10.1.1  Comparison of Elastomeric Polymers Max. Tensile Strength (MPa) Durometer Range (Shore A) Abrasion Resistance Compression Set Resistance *Temperature Resistance (°C) ATF Compatibility Relative Base Polymer Cost to NBR

NBR

AEM

ACM

VMQ

FKM

HNBR

20.7 20–95 Excellent Good –40 to +125 Excellent 100

17.2 40–90 Good Fair-Good –30 to +175 Fair-Good 150

17.2 40–90 Fair Good –20 to +150 Good-Ex 150

10.3 5–90 Poor Good-Ex –60 to +225 Poor 150–200

13.2 60–90 Good Good-Ex –25 to +225 Good-Ex 500

41 45–95 Excellent Good-Ex –25 to +150 Good 300

*The useful operating temperature range may vary by specific polymer blend and product application. See Section 10.1.11 for compound acronym designations.

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prevalent. Silicone is generally not recommended for use in automatic transmissions.

difference between the carrier thickness and the bead height at free-state. For most elastomeric materials, a 15–25% gasket bead compression is desired (at LMC) for all components in the assembly stack. This amount of compression results in about 1 MPa of contact pressure between the gasket and flanges at initial assembly. The contact pressure will decrease significantly over time, as compression set is inherent in all elastomeric materials to varying degrees. Loss of sealing performance due to compression set is offset by the rubber’s tendency to adhere to the metal joint and conform to the microscopic irregularities at the surface of the flange. Because of the considerable contact area between the carrier and flanges with edge-bonded gaskets, there is little concern for plastic deformation around the bolt holes. As a general rule of thumb, the minimum flange width of the carrier should be 2.5 times greater than its thickness to prevent excessive die roll during the stamping operation. The minimum flange width is a function of the gasket’s construction, which impacts the width of the gasket and the required tolerance stack of the gasket and the mating surfaces.

10.1.5  Elastomeric Gasket Design Elastomeric gaskets are engineered components, consisting of three or more materials in some cases, and consequently their design warrants considerable treatment as a topic here. Elastomeric gaskets may be of rigid or non-rigid construction. Rigid gaskets have a steel, aluminum, or plastic carrier that provides support to the rubber gasket and are easier to assemble into the transmission. Non-rigid gaskets, which cost less to manufacture, consist entirely of the molded elastomer and must rely on a retaining feature in the joint, such as a groove, in order to position the gasket and hold its shape. Aluminum edge bond, over-molded steel, and void-volume carrier gaskets are the three predominant carrier designs in use today. 10.1.5.1  Aluminum Edge-Bonded Gasket

10.1.5.2  Over-Molded Steel Gasket

Aluminum edge bond, as its name implies, is an elastomeric gasket bonded to the inner edge of a heat-treated aluminum carrier, typically 3003 H14. The aluminum carrier, which is treated with a heat-reactive adhesive to improve bonding, may range in thickness from 1 to 3 mm. Aluminum is an expensive carrier material relative to steel but does offer the advantages of lower weight and less susceptibility to corrosion. The carrier performs three essential functions for the gasket assembly by: 1) properly positioning the gasket in the joint prior to assembly, 2) acting as a load bearing member, and 3) serving as an assembly aid. The gasket may incorporate one or two sealing beads (Fig. 10.1.4).

Over-molded gaskets incorporate a steel carrier that is molded over its entire surface with an elastomeric rubber. Compression limiters, made from steel or powder metal, are molded or pressed into the assembly. Figure 10.1.5 shows a cross-sectional view of an over-molded steel gasket with a compression limiter. Over-molded steel gaskets typically have continuous double-bead on both sides that diverge and converge around each limiter. The stamped steel backbone is often constructed from 0.5 mm AISI C1008-C1010 steel. This type of gasket is highly tolerant of waviness variation and is therefore well suited to applications with stamped steel pans as one of the mating members. Over-molded gaskets also work well in joints where the sealing land area has a high amount of shift or horizontal tolerance stack-up.

(a) Single bead

Fig 10.1.5  Cross section of steel over-molded gasket with limiter.

(b) Double bead Fig. 10.1.4  Cross sections of aluminum edge-bonded gasket designs.

The size of the compression limiter is an important consideration in the design of the over-molded steel gasket. The inside diameter of the compression limiter must be sized such that it allows for sufficient clearance of the fastener’s major diameter and compensates for variances in true position of the tapped hole as well as its own inside diameter tolerance

The aluminum edge-bonded gasket is self-limiting in that the aluminum backbone acts as a compression stop for the assembled joint. As a result, the compressed height of the gasket can be carefully controlled by design and is limited to the

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and true position. The outside diameter of the limiter must provide for a sufficient load-bearing surface as to prevent coining of either the case or cover flange when fully loaded. Coining negates the function of the limiter by embedding or “sinking” it into the flange and allowing the gasket to become over-compressed, resulting in a degradation of the gasket’s sealability due to strain-induced failure.

is reduced (i.e., volume must remain constant). The gasket designer typically targets an 85% to 90% gasket volume-tovoid ratio at MMC, taking into account material expansion due to heat and chemical effects. As with edge-bonded and over-molded designs, an initial contact pressure of 1 MPa at the bead and flange interface is considered desirable. This type of design offers two advantages in that it requires slightly less land width than other carrier types to seal and can directly incorporate features, such as wire retaining clips or assembly aids, into the molded plastic carrier. However, the tooling costs associated with the plastic injection molded carrier may make it prohibitively expensive in some low volume applications.

Similar to edge-bonded gaskets, over-molded gaskets are designed so that the bead will have sufficient contact with the land over all horizontal stack conditions. Variables to consider in this stack analysis are [6]: Bolt diameter and size tolerance Pan hole size, size tolerance, and true position Gasket hole size, size tolerance, and true position Profile of cover-pan sealing land Profile of case sealing land Case size, size tolerance, and true position Gasket profile

10.1.5.4  Press-in-Place Gaskets Press-in-place gaskets are similar to void-volume carrier gaskets in that they seal the joint by “filling” a void as they are displaced under load. In this case, however, the void, such as a groove, is present in one of the mating components. The advantage with this design is a lower gasket cost, as it does not require a carrier or limiters. However, the difference in overall system sealing cost may vary, as the groove must be cast, machined, or molded in one of the mating components. Press-in-place gaskets have no backbone and are therefore more difficult to handle and assemble into the transmission. The gasket’s width, at several locations along its perimeter, is greater than the width of the groove and acts as a retention feature (not shown in Fig. 10.1.7a example) that aids installation of the gasket into the groove.

10.1.5.3  Void-Volume Carrier Gasket Void-volume carrier gaskets typically have a glass-filled nylon thermoplastic carrier to which the elastomeric gasket is molded. Bonding of the elastomer is achieved through the use of an adhesive or mechanical bond locks molded into the carrier. The difference with void-volume versus edgebonded or over-molded designs is that an appropriately sized groove must be molded into the carrier that will allow for displacement of the rubber bead as the joint is tightened. The cross-sectional views of a void-volume gasket in Fig. 10.1.6 illustrate a typical design for this type of gasket.

     

(a) gasket

(b) groove

Fig. 10.1.6  Cross section of void-volume carrier gasket.

Fig. 10.1.7  Cross-section of press-in-place gasket and mating groove.

As with over-molded steel gaskets, compression limiters should be used to limit the clamping force exerted on the gasket. Because rubber is an incompressible material, the gasket bead must be allowed to increase in width as its height

The groove should be chamfered and tapered slightly to aid with installation and prevent damage to the gasket that could arise from sharp edges or burrs.

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Press-in-place gaskets should have an 80 to 85% void-tovolume ratio to allow for thermal expansion of the rubber and swelling due to oil. The minimum amount of gasket compression when assembled should be 15% for optimal sealing performance. Similar to other elastomeric gasket designs, the contact pressure at LMC should be at least 1 MPa to allow for adequate sealability after CSR has occurred.

ples that have been tensile tested to failure. The judgment criterion for the principle strain results in the model is based on the average measured break strain of the material, controlled for temperature. Figure 10.1.8 shows the FEA principle strain results of an assembled press-in-place gasket at LMC. The maximum strain of 24.6% is well below the material’s strain limit. The contact pressure is of greater concern at LMC, and at 1.46 MPa, meets the minimum requirement for long-term sealability, as shown in Fig. 10.1.9. Figure 10.1.10 shows that the principle strain at MMC is still well below the material’s break strain and also shows that there is sufficient volume remaining within the cavity to allow for thermal expansion. Contact pressure at MMC is 3.24 MPa (Fig. 10.1.11).

In general, elastomeric gaskets require tighter surface finish controls than paper gaskets but are less sensitive to surface finish irregularities than RCM gaskets. Softer rubber compounds are more compliant than harder ones and therefore require less stringent surface finish controls on mating flanges. However, compounds that are more pliable provide lower contact loads for the same void-volume ratio. Table 10.1.2 provides general surface finish guidelines for elastomeric gaskets in the hardness range of 65 to 75 Shore A.

For a better understanding of the complete sealing system, a three-dimensional FEA can also be used to model variation in gasket strain/stress as well as flange deflection that can result from changes in fastener spacing and boss design.

10.1.6  Finite Element Analysis of Elastomeric Gaskets Gasket design may be optimized through the use of Finite Element Analysis (FEA). FEA may also be used to shorten the development of a design and reduce system costs. One of the challenges facing a gasket designer is determining the proper amount of gasket compression in a joint. If there is not enough compression, then the gasket may leak due to insufficient sealing load. Conversely, if there is too much compressive stress, then the gasket may leak as a result of strain-induced failure. To complicate matters, elastomers have nonlinear stress-strain curves that change with temperature. Therefore, predicting a gasket’s response under load in an application such as a transmission, where temperature may vary considerably, is a mathematically complex problem best modeled using FEA. Figures 10.1.8 through 10.1.11 show a press-in-place gasket design aided by FEA technique. The designer of this FKM press-in-place gasket needed to ensure that it would maintain sufficient contact pressure for sealing at LMC but would not exhibit excess strain if assembled into a joint under MMC conditions. The stress-strain curve for the material modeled in the application is generated from an average of three sam-

Fig. 10.1.8  FEA of press-in-place gasket cross-section at LMC showing principle strain. (Courtesy of FNGP Gaskets Division, Manchester, NH)

Table 10.1.2  Recommended Flatness and Surface Finish Values for Mating Surfaces Sealed with Elastomeric Gaskets Gasket/Groove Type Edge-Bonded and Overmolded Void Volume Press-in-Place/Machined Al Press-in-Place/As Cast Al Press-in-Place/Composite

Flatness

Ra max

Rz ISO max

Rt max

Wt max

(mm/mm)

(μm)

(μm)

(μm)

(μm)

1.8

11.0

14.0

4.8 3.2

30.0 20.0

40.0 25.0

0.075/50 0.15/50

14.0

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Fig. 10.1.11  FEA of press-in-place gasket cross-section at MMC showing contact pressure. (Courtesy of FNGP Gaskets Division, Manchester, NH)

Fig. 10.1.9  FEA of press-in-place gasket cross-section at LMC showing contact pressure. (Courtesy of FNGP Gaskets Division, Manchester, NH)

10.1.7  RTV, Cure-in-Place, and Liquid Injection Sealing 10.1.7.1  RTV Room Temperature Vulcanizing (RTV) is a type of formin-place-gasket that consists of a liquid silicone compound that is applied directly as a continuous bead to one surface of a set of mating flanges. The joint is assembled shortly after application of the RTV while the bead is still fluid. The bead flows over the land area when compressed, resulting in a very thin layer of gasket material that seals by filling in the voids between the flanges and adhering to them. RTV silicones cure by absorbing moisture from the air. Rate of cure is a function of the ambient humidity, flange width, and material thickness. RTV gaskets have negligible thickness and are not factored into the assembly tolerance stack-up [7]. RTV sealed joints are considered to be completely rigid and have very good torque retention as flange motion is minimal. Unlike compression gaskets, however, RTV gaskets are susceptible to shear failure. Even though flange surface finish requirements are less stringent with RTV, the waviness should be minimized to reduce the film thickness and limit the RTV’s shear stress and exposure to fluid. The use of positioning dowels also minimizes shear loads at the joint. Joints made with dissimilar materials must also be carefully considered, as RTV may not adequately compensate for differential rates

Fig. 10.1.10  FEA of press-in-place gasket cross-section at MMC showing principle strain. (Courtesy of FNGP Gaskets Division, Manchester, NH)

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of thermal expansion. The relative unit cost of an RTV gasket is very low and, unlike compression gaskets, does not require tooling (molds, die cutters, etc.) or manual assembly; however, automotive OEM capital investment is considerably higher for automated dispensing systems. There are several concerns with respect to manufacturing that must be considered when using RTV. Since RTV gaskets seal by bonding to the mating flanges, it is important that the joint surfaces be free of contamination (oils, dust, metal chips, etc.) to ensure adequate rubber-to-metal adhesion. As mentioned previously, the amount of moisture in the air will affect how quickly the RTV cures after being dispensed. Humidity may vary appreciably with seasonal changes, depending on the manufacturing location, and therefore special environmental controls within the plant may be required to ensure consistent quality. The amount and manner in which the RTV material is applied are also key process control parameters. Too much material may result in sump contamination and too little material may insufficiently seal. Additionally, RTV must be applied in a continuous and even bead around the perimeter of the flange, as interruptions could result in a potential leak path. For these reasons, it is recommended that the RTV gasket be applied with an automated dispenser with metered flow to minimize manufacturing defects. Once the RTV is applied, any line stoppages can result in its skinning over and preventing appropriate flow and adhesion during joint assembly. Work in process material will need to be cleaned off-line and re-introduced into the value stream. Lastly, risks and costs posed by in-plant and after-sale serviceability of RTV gaskets should be noted. Because RTV gaskets seal by creating a bonded assembly at the joint, the mating flanges must be carefully cleaned of all residual gasket material prior to re-application and re-assembly. Cleaning is labor intensive and presents a contamination risk. These concerns must be weighed against the benefits of low per-unit cost and manufacturing versatility of RTV. 10.1.7.2  Cure-in-Place Gaskets Cure-in-place gasket (CIPG) technology involves dispensing a rubber bead on one of the mating components and allowing the rubber to fully cure before assembling the joint. This sealing method differs from RTV in that the rubber bead is only bonded to one of the flange surfaces and requires compression loading to form a seal at the other interface, similar to a molded type elastomeric gasket. Depending on the design, CIPGs may require a groove in the mating flange to accommodate the bead’s displacement. Unlike molded press-in-place or void-volume carrier gaskets, the groove’s height-to-width ratio for a CIPG must be less than one, and there is relatively low control over bead shape when dispens-

ing. A CIPG will affect assembly stack-up and therefore its height, and corresponding tolerance must be factored into the overall joint design. Damage due to handling and assembly is still a risk with CIPGs as the gasket now becomes part of a subassembly that must be mated to another component. The traditional material choices for CIPGs have been silicone and polyurethane; however, recent advancements in material technology have allowed higher-performance elastomers such as AEM and FKM to be dispensed in liquid form and then cured with ultraviolet light [8]. 10.1.7.3  Liquid Injection Sealing Liquid injection sealing, as its name suggests, is a means by which liquid silicone is injected into a preassembled joint that is specifically designed with an injection port and groove (runner) to allow for rubber material flow. The liquid silicone completely fills the groove, pushing out the entrapped air through the mating flanges. Both the injection pressure and volume of rubber shot are metered to ensure that the groove is completely filled [9]. A vulcanizing catalyst can be added to the rubber compound to shorten the cure time. Unlike void volume and press-in-place molded gasket designs that target a void-to-volume ratio of 80–90%, liquid injection sealing completely fills the groove with rubber. The gasket does not bond to the substrate after curing and remains in an unloaded state. Gasket loading occurs after the silicone rubber comes in contact with oil and begins to swell within the confined space, thereby exerting a sealing load onto the groove’s walls. The advantage of this process is that the gasket component is never exposed to handling or assembly operations where it may be nicked or cut [9]. The disadvantage of this sealing method is that it requires automotive OEMs to incorporate an injection molding process into their assembly operations, adding manufacturing cost and complexity. For automatic transmission applications, this technology is currently limited to rubbers that swell in contact with ATF. Lastly, servicing remains a problem with liquid injection sealing, as authorized service centers will not have the equipment to replace in kind.

10.1.8  Testing and Design Validation of Gaskets Automotive gasket manufacturers perform extensive testing on their products to ensure that they will perform as intended over their expected life. Gasket testing occurs at all phases of the product development cycle and involves material testing, bench testing, dynamometer testing, and in some cases in-vehicle validation testing. A comprehensive treatment of gasket testing is beyond the scope of this paper; however, a brief discussion of the most common gasket tests is provided.

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10.1.8.1  ASTM Test Standards for Gasket Materials As mentioned earlier, material science plays a significant role in gasket technology and not surprisingly, a number of ASTM tests have been developed specifically to measure the performance of gasket materials. Table 10.1.3 lists some of the more commonly applied standards for gasket material testing. Rubber materials that are used in automotive applications, as well as other industrial applications, are treated as a separate materials category by the ASTM. Table 10.1.4 lists some of the more frequently used ASTM test standards for rubber materials that are used in the fabrication of automotive powertrain gaskets as well as other products [7]. The key material properties of any gasket are conformability, heat resistance, fluid resistance, and dynamic recovery. Each of these material properties will affect the gasket’s ability to seal.

Table 10.1.4  Commonly Used ASTM Test Standards for Rubber Products Used in Automotive Applications ASTM Designation D 395 D 412 D 429 D 471 D 573 D 624

10.1.8.2  Sealability Testing Sealability testing is the most direct measure of a material’s ability to seal a joint. This test typically involves placing a ring-shaped test specimen between two steel cylinders with a predetermined surface finish and applying a controlled clamp load to the assembled fixture. Figure 10.1.12 shows a photograph of a static pressure test fixture used to test gasket material sealability. Static fluid pressure, in the form of nitrogen gas or automatic transmission fluid, is introduced through the wall of one of the cylinders. A flowmeter measures the leakage rate (in mL/h) of fluid that passes either through or around the gasket to atmosphere. The clamp load and surface finish can be varied to better understand the test material’s sensitivity to changes in these parameters. A gasket design can also be tested for sealability by using a leak test fixture that simulates the intended application. This type of

D 2240

ASTM Title Test Methods for Rubber Property— Compression Set Test Methods for Vulcanized Rubber and Thermoplastic Rubbers and Thermoplastic Elastomers—Tension Test Methods for Rubber Property—Adhesion to Rigid Substrates Test Method for Rubber Property—Effect of Liquids Test Method for Rubber—Deterioration in an Air Oven Test Method for Tear Strength of Conventional Vulcanized Rubber and Thermoplastic Elastomers Test Method for Rubber Property—Durometer Hardness

bench test not only tests the gasket material’s ability to seal but also evaluates the gasket’s geometric design and how well it functions in the application.

Table 10.1.3  Commonly Used ASTM Test Standards for Gasket Materials ASTM Designation F 36-93 F 37-89 F 38-93 F 146-93a F 152-87 (1993)є1 F 363-89 F 1087-88

ASTM Title Test Method for Compressibility and Recovery of Gasket Materials Test Methods for Sealability of Gasket Materials Test Methods for Creep Relaxation of a Gasket Material Test Methods for Fluid Resistance of Gasket Materials Test Methods for Tension Testing of Nonmetallic Gasket Materials Test Method for Corrosion Testing of Gaskets Test Method for Linear Dimensional Stability of a Gasket Material to Moisture

Fig. 10.1.12  Test fixture for gasket material sealability test. 10.1.8.3  Fuji Pressure Measurement Gasket sealability can also be measured indirectly through the use of Fuji Prescale Film™, a thin, pressure-sensitive membrane that produces a reddish imprint when compressed between two mating surfaces, such as a gasket and a flange. The resultant image shows the extent of contact (presence of color) between the gasket and flange as well as the amount of pressure (intensity of color) exerted at any point of contact between the two components. Figure 10.1.13 shows a 10-11

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Fuji Film™ impression of an RCM gasket that has been compressed in a joint. Notice that the areas around the bolt holes and embossment ring are darker in color, signifying higher contact stresses at those features. The film, which can only be used one time, is available in different levels of sensitivity, ranging from “Ultra Super Low” (0.2 to 0.59 MPa ) to “High” (49.03 to 127.49 MPa), as the application requires. A more detailed analysis of the results can be obtained by scanning the image into a computer with optical imaging software that quantifies the pressure distribution with a color-keyed scale. This analysis tool is useful for optimizing bolt spacing and identifying potential leak paths due to insufficient loading. It should be noted, however, that Fuji Film™ only captures the initial load condition of a joint. Contact stresses at the joint will decay over time as a result of gasket stress-relaxation.

erally –40° to +150°C) at a specified frequency and duration. The gasket design should be tested at both the minimum and maximum assembly bolt torques to capture the lowest and highest case initial loading conditions. The gasket fixture is filled with oil and may be pressurized, depending on the application. The gasket joint is then monitored closely throughout the test for any signs of leaking. Phosphorous dye, which appears as a fluorescent green color under a black light, may be added to the oil to aid in the detection of very small leaks or seepage. Upon disassembly of the test fixture, the gasket is visually inspected for evidence of bead crush and chemical degradation. Thermal cycle testing does not exactly replicate the long-term application of a gasket, as it usually does not account for other stress factors such as NVH and fluid impingement. Nonetheless, thermal cycle testing is probably the best indicator of gasket longevity short of dynamometer or vehicle testing.

10.1.9  Conclusion

Fig. 10.1.13  Fuji Prescale™ pressure image of an RCM gasket. 10.1.8.4  Thermal Cycle Testing Gasket failure as a result of thermal degradation is of particular concern to powertrain engineers. The mechanical properties of gaskets are known to change in a time-dependant temperature environment and may adversely affect the gasket’s ability to seal a joint. “For gaskets in elevated-temperature service, mechanical stability, creep and relaxation resistance, and weight loss of gasket materials are considered mechanical key properties that should be monitored with time to determine whether a gasket will maintain a safe long-term tightness performance of a joint” [10]. Therefore, a gasket design should be vigorously tested in an environment that simulates, as close as possible, the working conditions of the application with respect to flange geometry, rigidity, bolt spacing, loading, fluid type, internal pressure, and thermal effects [10]. A typical thermal cycle test involves placing a gasket test fixture into a programmable, laboratory oven that is capable of cycling between high and low setpoint temperatures (gen-

Present day automatic transmission gasket technology is the result of continuous improvements that have been made over the last century, largely in response to the auto manufacturers’ increased expectations of sealing performance. In fact, “the trend toward increasing product development and warranty cost sharing responsibilities between [powertrain] manufacturers and sealing system suppliers is pushing the need for improved knowledge of actual sealing system life” [1]. As a result of the collaborative efforts made between sealing manufacturers and passenger vehicle OEMs, today’s powertrain engineers have an array of gasket solutions that they can consider for their applications. Advancements in material science, coupled with improvements in manufacturing efficiency, have been the driving force behind gasket technology, and this impetus will continue as long as automatic transmissions are used in automobiles.

10.1.10  Acknowledgments The authors wish to thank James A. Hazel and David R. Heim of FNGP’s Manchester, NH Division, for their valued contributions to the elastomeric gaskets section of this paper.

10.1.11  Acronyms and Definitions Acronyms and trade names for commonly used elastomers in powertrain applications: ACM—Polyacrylate AEM—Ethylene Acrylic

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FKM—Fluorocarbon FVMQ—Fluorosilicone HNBR—Hydrogenated Nitrile Butadiene Rubber NBR—Nitrile Butadiene Rubber or Buna-N SBR—Styrene Butadiene Rubber VMQ—Silicone PTFE—Polytetrafluoroethylene General engineering acronyms and terms used within the industry:

8. Dobel, Theresa M. and Christian Ruepping, “New CuredIn Place Gasket Technology Using UV-Cured High Performance Elastomers,” SAE Paper No. 2004-01-1038, SAE International, Warrendale, PA, 2004. 9. Jacobs, Thomas G., “Liquid Injection Sealing: New and Novel Approach to Meet Gasketing Needs,” SAE Paper No. 2003-01-0943, SAE International, Warrendale, PA, 2003. 10. Derenne, M., J. R. Payne, L. Marchand, and A. Bazergui, Chapter 4 in Gaskets—Design, Selection, and Testing, by D. E. Czernik, McGraw-Hill, New York, 1996, pp. 133–134.

CSR—Compressive Stress Relaxation—A measure of the residual force, expressed in percentage remaining, a loaded gasket exerts against a mating surface after exposure to fluids and temperature over a given period of time. DFA—Design for Assembly—An approach to designing products with the objective of reducing component complexity and quantity in order to optimize the assembly process and lower overall cost. RTV—Room Temperature Vulcanization—An acronym used to describe a fluid, silicone-based rubber that cures at room temperature, either by reacting with moisture in the air or by means of a curing agent. FEA—Finite Element Analysis—A numerical analysis technique, performed with the aid of a computer, that models the stress and displacement behaviors of a deformable body under load.

10.2  An Overview of Transmission Radial Shaft Seals Susan M. Bothe Jeff Dieterle Jeff Nelson Freudenberg NOK Sealing Technologies

10.2.1  Abstract

10.1.12  References 1. Widder, Edward, “Advances Toward Life Estimation in Static Sealing,” SAE Paper No. 2003-01-0477, SAE International, Warrendale, PA, 2003. 2. Mahr Corporation, “Surface Texture Seminar,” Cincinnati, OH. 3. Widder, Edward and Donald Bajner, “Surface WavinessSealing’s Hidden Enemy,” SAE Paper No. 980578, SAE International, Warrendale, PA, 1998. 4. Brown, Delwyn S. and Alexander L. Gordon, “Past, Present and Future of the Automotive Gasket Industry,” SAE Paper No. 800268, SAE International, Warrendale, PA, 1980. 5. Elsesser, Paul H., “Manufacturing Lexide® Gaskets,” Boise Cascade Corporation, Beaver Falls, NY, 1985. 6. Freudenberg-NOK General Partnership, “Overmolded Steel Carriers/Limiters,” Manchester, NH. 7. Czernik, Daniel E., “Gaskets Design, Selection, and Testing,” McGraw-Hill, New York, NY, 1996.

This section provides an overview of transmission radial shaft seals and typical considerations regarding design, material selection, installation, testing, and failure analysis. Designs may vary depending on the seal manufacturer, as well as the application, which includes the seal environment, shaft conditions, and bore conditions. There are also many design features available to improve performance, including but not limited to outside diameter (O.D.) designs, contamination exclusion features, and hydrodynamic aids. Additional resources for radial shaft seals can be obtained from: SAE J111 “Terminology of Radial Lip Seals” SAE J946 “Application Guide to Radial Lip Seals” SAE J1002 “Evaluation of Elastohydrodynamic Seals” SAE J110 “Testing of Radial Lip Seal”

10.2.2  Introduction A radial shaft seal is used to seal a rotating shaft against the predominantly stationary housing of the unit. The most important functioning area of the radial shaft seal is the sealing edge which contacts the surface area of a rotating shaft; see Fig. 10.2.1 for the seal nomenclature. The sealing mechanism in the sealing lip is critically important when it comes to the sealing function. It is dependent on: • The layout of the sealing lip • The properties of the elastomeric material • The finish of the shaft surface

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  1  Seal Width   2  Metal Case (Outer)   3  Housing   4  Inner Case   5  Outside Face   6  Inside Face   7  Radial Wall   8  Seal Outer Diameter   9 Housing Bore Diameter 10 Spring Position (R-Value) 11  Spring Groove 12  Garter Spring 13  Heel Section

14  Flex Section 15  Spring Retainer Lip 16  Inside Lip Angle 17  Toe Face 18  Auxiliary (Dust) Lip 19  Rib (Helix) 20  Contact Point 21  Inside Lip Surface 22  Spring Set Lip Diameter 23 Free Lip (Unsprung) Diameter 24  Contact Line Height 25  Lip Height 26  Lip Angle

Fig. 10.2.1  Seal nomenclature. A good knowledge base in seal design and function is required prior to establishing and interpreting characteristic dimensions. Dimensions are set by each manufacturer depending on the material properties, size, and lip geometry. Dimensions Hd, Sm, and hF are shown in Fig. 10.2.2 and are calculated based on the shaft diameter and the operating conditions. The dimension for the length of the lip is the measurement Hd, the cross-section of the lip is Sm, and the characteristic dimension for the distance from the center of the spring to the sealing edge is the R-value, hF. The coordination of both Hd and Sm dimensions affect the flexibility of the lip. Long and flexible sealing lips are utilized for high tolerances of offset (static eccentricity) and concentricity; however, a short profile and a stable profile for the shaft can be utilized for a pressurized application. The angle of the sealing lip influences the sealing mechanism by affecting conditions for contact pressure: • Oiled side: steep angle 35–60 degrees • Air side: shallow angle 12–30 degrees

Fig. 10.2.2  Location of dimensions Hd, Sm, hF, and the sealing lip angles.

The characteristic dimension for the distance from the center of the spring to the sealing edge is the spring plane (R-Value). An R-Value dimension that is too small can result in the toppling over of the seal, especially with any radial shaft deflection. If hF is too large, it can force the profile to tilt, which causes a wide contact area on the shaft. This results in a wide wear track. The most important functional area of the radial shaft seal is the sealing edge which contacts the surface area of a rotating shaft. The sealing mechanism in the sealing lip contact area has the greatest impact on the performance of the seal and its function. This is dependent on the layout of the sealing lip, the properties of the elastomeric material, and the shaft surface finish. The sealing lip inner diameter in a free state is always smaller than the shaft diameter. The covering (also pre-tension) is the difference between these two measurements. The radial force of the sealing lip, in combination with the geometry of the sealing lip angle and spring plane distance, produces an asymmetric footprint representing the pressure contact points; see Fig. 10.2.3 for the location of the radial force.

Fig. 10.2.3  Location of radial force. This is of significant importance as it relates to sealing function. The contact pressure distribution by the asymmetric footprint, and the power generated by the rotating shaft, lead to a predictable characteristic deformation of the sealing lip. This predictable performance requires a good elastomeric material which provides a clear structure of the sealing lip’s distortion features. This “distortion” occurs during the running-in phase of the seal. Therefore, this run-in phase is critical to the performance of the seal. It creates a helix-effect, and in combination with the shaft rotation, a pumping action directed at the oil side of the unit due to the predictable lip deformation; see Fig. 10.2.4. Even when stationary, the medium and lubrication used in sealing penetrates the lip by capillary action on the uneven areas of the shaft. However, there is still direct contact of sealing lip with the shaft. See Fig. 10.2.5 for a cross section of the seal contact area. Should the complex relationships between the sealing lip and contact area be disrupted by the following items, the seal will not perform properly and will be prone to leak: 10-14

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• improper shaft surface finish • scratches, pores, and other imperfections on the shaft and seal • contamination or corrosive products in the medium • hardening and cracks on the sealing edge

choosing the seal material; this will be discussed further in the section, “Material Selection.” In general, the system temperature increases as the shaft speed increases. Design features can also assist with temperature reduction at the lip contact area, such as hydrodynamic aids, which will be discussed within the design features section. Using a lubricant that promotes seal durability can significantly increase seal life. In general, using a fluid that has good lubricity is desired. Additive packages that prevent oil breakdown at higher temperatures can attack a seal material, and should be reviewed with the seal manufacturer. With the proper choice of fluid, seal design, and materials, seals can often exhibit long life in clean environments. Even in dirty environments, long life can be achieved if appropriate exclusion devices are applied.

Fig. 10.2.4  Diagram of the pumping action.

10.2.3.2  Shaft

Fig. 10.2.5  Cross section of the seal contact area.

10.2.3  Design Considerations Developing the design for a radial shaft seal not only involves the seal design itself, but also knowledge of the surrounding components and environment. Most applications include the environmental conditions, a rotating shaft, a stationary bore, and other packaging area limitations. Many of these components and environmental conditions emulate those of non-transmission applications; however, these findings focus on transmission specific considerations.

The structure of the shaft as it relates to the surface area at point of contact with the sealing lip directly impacts the function of the seal and the durability of the sealing system. See Fig. 10.2.6 for the shaft nomenclature. The condition of the shaft is as important as the condition of the seal if proper sealing and long life are to be achieved. Care must be taken to specify the proper design and process parameters for production of the shaft. Also, adequate care in handling and protection of the sealing surface must be followed, as handling damage to the running surface is one of the most frequent causes of seal leakage. Scratches, pressure sites, rust, and other damage on the seal’s running surface ultimately lead to leakage problems. Great care in protecting the shaft during production and through to final assembly is recommended. This can be accomplished by using protective sleeves and special transporting devices.

10.2.3.1  Environment The primary factors influencing the durability of a seal are the temperature, fluid, and seal material. A seal will generate heat in excess of the oil sump temperature. To determine the maximum temperature limitations of any particular material, you must look carefully at the operating conditions. First, determine the excess lip temperature generated in the application. Then, add to that the oil sump temperature. This is the upper temperature limit requirement to consider when

Fig. 10.2.6  Shaft nomenclature relative to the seal and bore.

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Seal and shaft compatibility is dependent on four conditions: shaft tolerance, lead-in chamfer, finish, and hardness. Proper consideration of these conditions will assist in providing optimal seal performance. The shaft tolerance recommendations for general applications are listed in Table 10.2.1. The tolerance range should be decreased for high-speed or -pressure applications. A shaft lead-in chamfer is suggested to assist in the installation process. Without a proper chamfer, the seal lip may be damaged or distorted. This may result in a leak path through the sealing lip or a dislodged garter spring. Table 10.2.2 provides recommended shaft chamfer values. Shaft surface finish is very important as this greatly influences the amount of lip wear. When the depth of roughness is too shallow (especially with higher surface speed), the potential for problems exists due to the inability of the lubricant to effectively reach the sealing edge. This can result in premature hardening and the formation of cracks and possibly signs of combustion on the sealing edge. When the height of roughness is too high, the potential for problems exists with excessive premature wear and possible leakage within the sealing system. The method of achieving this finish should not be overlooked. The recommended roughness is as follows: • Rotating 10 to 20 μ inch Ra (.25 μm to .50 μm Ra): Rmax = 31–126 μ inch (0.8–3.2 μm) • Reciprocating 5 to 10 μ inch Ra (.13 μm to .25 μm Ra)

Shaft hardness is an important factor to prevent excessive wear, deformation, scratches, or nicks, and to allow for easy machining for proper roughness. Under normal conditions, the seal contact area of the shaft should be Rockwell hardness HRC 45 minimum. Other Recommended Shaft Conditions: • No machine lead permitted (plunge grinding recommended) • Seal contact area to have no scratches, nicks, or defects and be free of contamination • When installing seal over a spline, a protective cover or bullet should be used • Seal diameter < Bearing journal diameter • Seal diameter > Spline diameter As discussed, the method of achieving these conditions should not be overlooked. Typically, plunge grind process is recommended to ensure the desired non-oriented state of the shaft. The advantages of this process include: • Short to medium grind marks—good for lip lubrication • Lay is perpendicular to the shaft axis which results in no lead angle 10.2.3.3  Bore The bore material and design impacts the retention of the seal, and the outside diameter (O.D.) sealing function. Steel and cast iron provide good surfaces for both rubber-covered and metal O.D. seals. For soft alloy (aluminum) bores,

Table 10.2.1  Recommended Shaft Diameter Tolerance Shaft Diameter (inch)

Tolerance (inch)

Shaft Diameter (mm)

Tolerance (mm)

±0.003 ±0.004 ±0.005

Up to 100 100.10 to 150.00 150.10 to 250.0

±0.08 ±0.10 ±0.13

Up to 4.000 4.001 to 6.000 6.001 to 10.000

Table 10.2.2  Recommended Shaft Chamfer Inches Shaft Diameter Up to 1.000 1.001 to 2.000 2.001 to 3.000 3.001 to 4.000 4.001 to 5.000 5.001 to 6.000 6.001 to 7.000

Millimeters Chamfer Diameter

Shaft Diameter

Chamfer Diameter

S.D.-0.094 S.D.-0.140 S.D.-0.166 S.D.-0.196 S.D.-0.220 S.D.-0.260 S.D.-0.276

Up to 25.00 25.01 to 50.00 50.01 to 75.00 75.01 to 100.00 100.01 to 125.00 125.01 to 150.00 150.01 to 175.00

S.D.-2.4 S.D.-3.6 S.D.-4.2 S.D.-5.0 S.D.-5.6 S.D.-6.6 S.D.-7.0

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rubber-covered O.D. seals provide better sealing capability. In aluminum or other soft alloy bores, metal O.D. seals occasionally back out of the bore due to thermal expansion of the soft alloy. Rubber, having a higher coefficient of thermal expansion than carbon steel, will tighten in the bores as temperature rises. Metal O.D. seals are not recommended for use in plastic or nylon housings. These materials typically expand at a high rate, causing leakage around the seal O.D. Rubbercovered O.D. seals should be used in these situations. A bore chamfer is necessary to assist with installation of the seal. Proper chamfer angle and depth minimizes cocking or lack of squareness of the seal to the shaft, distortion of the seal cases, and assembly force. See Fig. 10.2.7 for the recommended bore chamfer design. Fig. 10.2.8  Diagram of eccentricity.

10.2.4  Design Features Although the most important functional area of the radial shaft seal is the sealing edge, additional design features are commonly utilized in transmission applications to provide a more robust design. These features include O.D. design, contamination exclusion designs, and hydrodynamic aids.

Fig. 10.2.7  Recommended bore chamfer. Excessively rough bore finishes may allow paths for fluid to leak between seal O.D. and bore. The rubber O.D. seal is capable of functioning with a rougher finish. A minimum bore roughness is recommended for rubber O.D. seals to improve retention. Table 10.2.3 presents the recommended bore surface finishes.

10.2.4.1  O.D. Design There are several reasons to consider the design of the seal O.D. The first one is to prevent leakage at the outside diameter, as shown in Fig. 10.2.9. The O.D. design must also ensure that the seal will be retained in the bore without installation complications.

Table 10.2.3  Recommended Bore Surface Roughness Maximum Roughness

Minimum Roughness

Metal O.D.

Rubber O.D.

100 μinch Ra 2.50 μm Ra 492 μinch Rmax 12.5 μm Rmax

150 μinch Ra 3.75 μm Ra

Metal O.D.

Rubber O.D.

None None

60 μinch Ra 1.5 μm Ra

Eccentricity is determined by measuring the shaft runout, TIR, and shaft-to-bore misalignment. Combine the two results for the total eccentricity the seal lip must follow to function effectively. See Fig. 10.2.8 for a diagram of eccentricity. As eccentricity increases and/or shaft speed increases, it becomes more difficult for the lip to follow the shaft.

Fig. 10.2.9  Outside diameter leak path. Many custom shapes and configurations are available; however, general examples are listed in Table 10.2.4. The previous bore section discusses more details regarding application differences between metal and rubber O.D. designs.

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Table 10.2.4  General Examples of O.D. Designs Type

O.D. Cross-Section

Rubber

Standard

Ribbed

Lead-In Gasket

Outside Edge Gasket

Standard with & without Latex Coating

With Flange and Sealant Bead

Rubber & Metal Combined With Flange

Metal

10.2.4.2  Contamination Exclusion Features The seal must be capable of stopping any outside contamination from damaging and/or grooving the seal’s main lip and ingesting into the oil. Added exclusion features should not generate excessive heat in high-speed applications. Within a transmission, these features are generally used for output seal applications because the “air side” of the seal is external to the transmission assembly. All other transmission radial shaft seals do not typically require contamination exclusion features because the “air side” is internal to the transmission assembly, and not exposed to dust, dirt, mud, and other debris (see Fig. 10.2.10).

Many special designs can be provided to fit the specific application, but Fig. 10.2.11 shows some general examples that are in common use. 10.2.4.3  Hydrodynamic Aids As mentioned previously, the main sealing lip used in a transmission will run on a microscopic layer of fluid (see Fig. 10.2.5). To help reduce temperatures under the main lip, hydrodynamic aids are molded onto the air side angle of the main lip (see item 19 in Fig. 10.2.1). These aids will pump lubrication back into the housing as the shaft continues to spin. Due to the constant flow of lubrication, the under-lip temperature will be less affected by the frictional heat generated from the dynamics of the shaft. Also, the addition of hydrodynamic aids can improve the seal performance during the break in period. With the addition of the hydrodynamic aids, the seal will be able to compensate for small imperfections in the interface. Over the course of time as the seal wears, the aids will eventually lose their ability to pump and the seal will function as a plain lip seal.

Fig. 10.2.10  Diagram of contamination location.

Seal manufacturers have different options for types of hydrodynamic aids to use in a design. The hydrodynamic aids can 10-18

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Double Dirt Lip

Excessive End Play

Radial Contacting “Slinger”

Axial Contacting “Slinger”

Single Dirt Lip

Non Contacting “Slinger”

Fig. 10.2.11  Examples of contamination exclusion features. either be uni-directional or bi-directional, but it depends on the application as to which type will be optimal. If the shaft will only spin in one direction, the uni-directional option is recommended. This type of hydrodynamic aid will provide the best pumping ability for the seal and keep the under-lip temperatures to a minimum. Figure 10.2.12 shows a few examples of typical hydrodynamic aids used in seal design.

of the material. Typically, for the most robust design Fluoroelastomer (FKM) material will provide the most heat and wear resistance. However, Polyacrylate (ACM) and Ethylene Acrylic (AEM) are also common for transmission shaft seals. Hydrogenated Nitrile (HNBR) is suitable for transmission applications, but it is not common. Nitrile (NBR) is no longer used for transmission shaft seals due to the technological advances with FKM, ACM, AEM, and HNBR. Table 10.2.5 shows the standard temperature ranges and advantages/disadvantages for the common types of elastomers used in radial shaft seal applications.

10.2.6  Installation The subject of installation represents an area commonly overlooked when selecting an oil seal for an application. Studies have shown this area to be one of the major causes of premature seal failure.

Fig. 10.2.12  “On-Shaft” contact patterns of some elastohydrodynamic aids [1].

10.2.5  Material Selection Many different options are available to consider when selecting the right elastomer for the application. The type of elastomer will depend on the operating temperatures, compatibility with the lubricants being sealed, and physical properties

To assist the installation, the seal inner diameter should be prelubricated with grease or oil to reduce sliding friction of contact surfaces. This will also help protect the seal lips during initial run-in. Also, for seals with a rubber outer diameter, prelubrication can help prevent any kind of tearing that may occur during installation. An installation tool should always be used when installing an oil seal. The use of a tool improves ease of installation and reduces the possibility of seal cocking (nonperpendicular to shaft). A hydraulic or pneumatic press is advised to supply necessary force to install the seal. Figure 10.2.13 shows several examples of both improper and recommended installation methods.

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Table 10.2.5  Material Designations and Descriptions Material Designation

Material

Temperature Range (°C)

Advantages

Disadvantages

NBR

Nitrile

–40 to +100

Good wear and oil resistance

Poor high-temp capability

HNBR

Hydrogenated Nitrile

–40 to +130

Improved wear resistance over NBR

ACM

Polyacrylate

–30 to +150

Similar oil resistance to NBR Good high-temp capability

Poor resistance to polar solvents Cold flexibility limited when compared to comparable NBR grade Poor compression set

Good oil resistance

Poor resistance to hot water (steam)

AEM

Ethylene Acrylic

–40 to +150

Good temp range

Can crack at low temperatures Tendency for high swell

FKM

Fluoroelastomer

–40 to +200

Fair wear resistance Resistant to high-temp

Poor dry running Poor low-temp capability

Excellent chemical and wear   resistance

Poor amine resistance

In each recommended method, installation load is absorbed by either the housing or the bottom plate to prevent seal damage and to assist in locating the seal properly within the bore. Additionally, listed below is the recommended procedure for proper seal installation:

4. Use a hydraulic press or other suitable method to ensure that proper force and speed are applied. 5. Use proper tools. 6. Install the seal, contaminant and damage free. 7. Open only 1 package of seals at a time. 8. Installation area must be kept clean. 9. Tools, protective sleeves, and bullets must be kept clean and periodically inspected for damage.

1. Prepare proper housing bore diameter and chamfer. 2. Prepare proper shaft diameter and chamfer. 3. Ensure appropriate prelubrication (usually the lubricant being sealed).

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Improper:

Recommended:

Fig. 10.2.13  Improper and recommended installation methods. 10-21

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Shaft Installation:

10.2.7  Testing

The advisable sequence of installation is to install the seal over the shaft and then into the housing bore. Care should be exercised not to damage or deform the seal lip. The proper chamfer angle will minimize this problem. When installing over a keyway or spine, a sleeve or bullet should be employed to protect the seal lip from cuts, as shown in Fig. 10.2.14. Where the shaft must be installed through the seal, centering guides for the shaft will prevent lip deformation and dislodging of the spring. When possible, the shaft should be rotated as it passes through the seal to reduce sliding friction.

“When the mechanical properties of the candidate lip seals have been established, it is sometimes desirable to conduct dynamic tests on the seals under controlled environmental testing conditions. The time spent in conducting laboratory seal tests is invaluable in determining their performance in the actual application.” [2] SAE J110 lists several common tests, including but not limited to: the test procedures, equipment recommended, dynamic functional test parameters, and low-temperature test parameters. Additionally, environmental exclusion testing is recommended for seals that are required to exclude contaminates, such as transmission output radial shaft seals. Details of this type of test procedure are located within the Rubber Manufacturers Association’s (RMA) technical bulletin, “Environmental Exclusion Test Procedures For Radial Shaft Seals,” OS-18.

10.2.8  Failure Analysis

Fig. 10.2.14  Shaft installation with a sleeve or bullet.

After detection of leakage, the user must first determine the origin or specific location of the leakage source. Then the entire sealing system must be analyzed to determine the root cause of the failure to prevent reoccurrence. Fig-

Fig. 10.2.15  Fishbone diagram for sealing system leakage.

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ure 10.2.15 shows a fishbone diagram to visually assist with items that must be considered within the sealing system analysis. Specific details of how to analyze the sealing system leakage, both for laboratory test conditions and in the field, are located within the Rubber Manufacturers Association’s (RMA) technical bulletin, “Sealing System Leakage Analysis Guide,” OS-17.

items for a radial shaft seal application are the material, shaft diameter, bore size, and the external geometry surrounding the seal. Within the radial shaft seal industry, there are many design features that can be utilized; however, they can only be properly used if the application is fully defined.

10.2.9  Conclusions

1. Society of Automotive Engineers Radial Lip Seal ­Committee, April 1994, “Seals—Evaluation of Elastohydrodynamic—SAE J1002,” SAE International, Warrendale, PA. 2. “SAE Fluid Sealing Handbook Radial Lip Seals—SAE HS-1417,” pg. 14, 1996, SAE International, Warrendale, PA.

Throughout the radial shaft seal industry there are many design features that exist to ensure a robust design. During the radial shaft seal design process, it is important to ensure that all the application information is defined from the start of the program. If any product changes are necessary, it is critical to understand their impact on the sealing functionality. The key

10.2.10  References

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Chapter 11

Transmission Temperature Control and Lubrication Table of Contents

transmitting power; this energy can generate temperatures that lead to distress in friction materials, clutch components, bushings, seals, and especially certain properties of the automatic transmission fluid (ATF), thus, the use of “Cooling” in the previous title. The major contributor of this energy, if so equipped, is generally the torque converter. And typically, transmissions take the hot ATF from the torque converter and route it to the cooler and then on to the lubrication system. As noted in 11.6, this provides the coolest oil available to the lubrication system, which gives greater capacity to bushings, thrustwashers, etc. Some transmissions have deviated from this oil routing because the filtered ATF for lubrication passes through the torque converter first, where it is exposed to possible dirt contamination from the clutch or material not adequately removed during torque converter assembly.

11.1 Introduction—Discussion on the new and updated portions of this chapter as well as a review of the significance of some system features. 11.2 Transmission Cooling Systems: Oil-to-Water Type— AE-18 discussion which has been reviewed and approved for current use. 11.3 Transmission Cooling Systems: Air Cooling—AE-18 discussion which has been reviewed and approved for current use. 11.4 Temperature Effects on Transmission Operation— AE-18 discussion which has been reviewed and approved for current use. 11.5 Temperature Control and Fuel Consumption— Discussion of effects of temperature on fuel economy and some features which can be used to control temperature and reduce fuel consumption. 11.6 Design and Validation of Automatic Transmission Lubrication Circuits—Discussion of the many aspects of lubrication system design and testing.

Control of the torque converter clutch is a significant consideration that will have a major influence on transmission temperature. Recent control developments include such features as continuous controlled converter slip, clutch energy/ temperature calculations, clutch use from 1st gear through top gear, change in clutch use strategy with ATF temperature and vehicle operating condition, and use of engine management under severe conditions. These features give the transmission engineer a new set of tools to use in controlling transmission temperature. They allow the engineer to provide greater smoothness under normal conditions and still avoid

11.1 Introduction The chapter name was modified from using “Cooling” to “Temperature Control” to recognize the efforts being directed toward more complete control of temperature. The major role of any transmission temperature control system, of course, is to remove the excessive energy added by the inefficiencies of 11-1

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temperature-related distress by restricting operations with high heat dissipation at high ATF temperatures.

temperature control system must be verified in customercorrelated testing in the actual vehicle environment, because the interactions between the numerous vehicle systems involved can substantially affect results.

In order to meet the extended life requirements, manufacturers are focusing on the ATF temperature profile during the full life of the transmission and not just at the highest temperatures. Some warranty and temperature-histogram data have shown a correlation between mean operation temperature and transmission warranty. With engine operating temperatures increasing, engine coolant use to cool the ATF becomes a critical consideration. The use of an oil-to-air (OTA) cooler provides a colder source for dissipating ATF heat than does the oil-to-water (OTW) cooler. OTW systems for trailer tow, etc., typically use an OTA auxiliary cooler.

It is intended that the following papers provide some basic engineering information to aid in the design and development of transmission temperature control and lubrication systems. Section 11.2 covers OTW coolers; 11.3 covers OTA cooling, and 11.4 addresses the effects of temperature. These sections present a somewhat-dated, traditional view of transmission cooling. Section 11.5 presents cold-flow bypass, which is just one of the new features being developed to improve temperature control. Other new developments have recently appeared, and others are likely to be introduced in the next few years. Section 11.6 presents information on the design, modeling, and testing of lubrication circuits. The effects of lubrication on transmission parasitic losses are also being studied. Too much flow to the clutch plates, for example, can cause higher drag. Some plates are being designed to minimize drag with moderate flow, but lube flow should be designed to be just adequate for durability for certain clutches.

As government-mandated fuel economy standards become more stringent, the need to achieve normal operating transmission temperatures quickly to minimize thermally-induced parasitic losses is another serious consideration. Here the OTW cooler helps because the engine coolant warms the ATF for some time after start-up. Several features are, or have been, developed to improve the ATF warm-up rate. Some of these improvements work by trapping the heat normally generated by transmission inefficiencies and preventing any ATF flow to the coolers until a desired operating temperature is achieved.

11.2 Transmission Cooling Systems: Oil-to-Water Type

One unusual problem, also noted in 11.6, is that, in some systems with OTA coolers, the ATF temperature can be so cold that flow through the coolant system at very low ambient temperatures is essentially zero. This low flow may have some very negative effects that need to be addressed.

E. F. Farrell Borg and Beck Div., Borg-Warner Corp. Revised and Updated October 1971 by: T. M. Wang Borg and Beck Div., Borg-Warner Corp.

The use of on-board electronic control components (i.e., electronics in the ATF environment) is an added critical factor. High temperatures, even for brief periods, can have a destructive effect on the electronic controls. Development is increasing the critical temperature that is tolerable, but margin for error remains small.

The advent of automatic transmissions with hydrodynamic drive members brings with it a cooling problem that is not inherent in hand-shifted, mechanical types. This does not imply that hydrodynamic drive elements and hydraulic servomechanisms are inherent power wasters, but rather that their allowable operating temperature range is rather limited. Therefore, the heat generated in these devices must be promptly transferred to our universal heat sink, namely the atmosphere. Ultimately, the distinction between air- and water-cooling ceases to exist, and the fact remains that watercooling employs a more circuitous path to the atmosphere.

Over the years, the vehicle stylist has placed greater demands on the vehicle/engine/transmission cooling system due to the space limitations of aerodynamic design. This initially led to the use of OTW cooling of transmission fluid as the primary design direction. However, the added considerations, discussed above, have resulted in the manufacturers choosing different and more complex approaches to transmission temperature control with features that are new to the industry. Temperature control needs to be addressed early in the design of the automatic transmission and the relevant portions of the planned vehicle platforms to ensure that all requirements can be achieved. Although simulation of the systems involved in transmission temperature is being used to reduce the required vehicle testing, the adequacy of the

The more circuitous path of the water-cooling systems does, however, increase the thermal capacity by virtue of the water contained therein. In this respect, the water-cooling system is better able to handle transient heat pulses, thus more closely approaching the conventional dry clutch. This is accomplished in the water-cooling system by the high specific heat and heat of vaporization of the water, while the dry clutch

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tolerates relatively high temperatures. However, to exploit this advantage fully, a relatively high oil flow rate must be maintained in the cooling circuit to transfer heat rapidly, from where it is generated to where it is absorbed, without permitting the source temperature to rise rapidly under transient conditions. Unfortunately, high oil flow rates mean large oil passages (which are difficult to provide through the maze of shafts, sleeves, and collector rings) which the oil must traverse in the hydraulic circuit of an automatic transmission. However, the writer’s experience indicates that more generous oil passages in an automatic transmission could sharply reduce the number of shift quality problems associated with this device. Since this latter consideration deals with thermal transients of much shorter duration than those that presently concern us, it will be left for consideration in some future paper. The real distinction between these two problems is one of degree rather than kind, since both refer to the rate of temperature rise of the source. The present problem can be treated with the aid of ordinary differential equations, using time as the independent variable, while the shift quality problem requires the use of partial differential equations involving both spatial and temporal variables.

to obtain performance is deplorable, since such practice reflects large thermal transients into the transmission, along with other disadvantages to be enumerated later. Due consideration of the various items listed above implies quantitative information relating to certain elements in the cooling system, aimed at imparting a so-called “feeling” for the cooling problem.

11.2.1 Permissible Oil Temperatures Generally speaking, a maximum oil temperature of 300°F is conceded; however, it is more desirable to hold this temperature between 260° and 280°F. A desirable lower limit of operating oil temperature ranges from 190° to 210°F, although 165°F is encountered more frequently under ordinary driving conditions in the Midwest. Good coupling range performance is obtained when the oil temperature in the torque converter is 200°F because the viscosity is quite low, while most of the soluble air and water vapor have been stripped off at this temperature. It is also desirable to attain the above operating temperature rapidly in the interest of good fuel economy at road load. The watercooled system is advantageous in this regard, because engine cooling systems are generally designed for rapid warm-up. Thus, it is possible to reflect heat into the transmission via its cooler in cold weather.

In view of the above considerations, it is apparent that time spent in taking a comprehensive view of the cooling circuit will permit one to best exploit its potentialities. As an aid toward this end, certain broad generalizations can be made: 1. Low-pressure drop (large passages and few turns) is desirable in the fluid flow circuits. 2. Large thermal capacity is desirable to increase running time under transient conditions. 3. Counterflow heat transfer circuits best exploit the available temperature differences. 4. Fluids from sections of the circuit where temperature differences are greatest should be used; this applies to direct air-cooled systems also. 5. The system should be designed for minimum vulnerability, which is, by far, the most important factor because continuity of service, even at a reduced level, is imperative. 6. The capacity of the heat exchanger should be adequate to handle the steady-state heat generation of the transmission. 7. The heat generation rate of a transmission in a given vehicle is more closely allied with the weight and size of the vehicle, as well as the type of service expected of it, than with the horsepower of its engine. 8. A torque converter badly matched to a vehicle’s engine can largely obviate the conclusion drawn in item 7. The tendency to use high stall speeds with flexible engines

11.2.2 Required Heat Rejection Rates Since the cooling load largely depends on the size and weight of the vehicle in which a given transmission is used, typical examples will be cited here. 1. A small car with a shipping weight listed at 2720 lb, when operated at a test weight of 3800 lb, shows a peak transmission heat generating rate of 700 Btu/min during a WOT start to 30 mph. The average heat generation rate during this interval is 260 Btu/min, while at 30 mph road load it is 90 Btu/min. (More details are available in Refs. 1 and 2.) The car was equipped with a direct air-cooled system having a heat rejection rate of 190 Btu/min at a temperature differential over ambient of 180°F. The car’s cooling capacity was based upon the requirement that it exert a drawbar pull of 400 lb at 20 mph on a level road. This requirement correlates quite well with road tests in which the car towed a trailer up a hill. 2. A larger car in the 5200 lb test weight class, with an engine twice as powerful as the one in the vehicle described in example 1, uses a 300 Btu/min oil cooler (water-type located in the radiator bottom tank) rated at 2.2 gpm

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with an entering oil temperature of 300°F and a water temperature of 180°F. A maximum oil side pressure drop of 15 psi at 2.2 gpm is specified for this cooler. The transmission cooling system is so coordinated with the engine cooling system of this car that acceptable oil temperatures can be maintained while exerting a drawbar pull of 520 lb at 30 mph on a level road. A critical examination of items 1 and 2 reveals that the transmission ratio, axle ratio, and tire size were not specified in either case. This was an intentional omission to emphasize the overall picture. There is no simple rule for sizing a transmission oil cooler, but some statements can be made in regard to vehicle service factors used to determine acceptable cooling levels. Thus, if one wishes to become skilled in the art of transmission cooling, one should first acquire knowledge of vehicle propulsion dynamics. In so doing, one is bound to become inquisitive about transmission and driveline losses that contribute to cooling load. This inquisitiveness could lead one to make reductions in the losses, thus solving the cooling problem in the best possible manner. However, since reductions in driveline losses are long-range projects at best, data on oil cooler performance will be presented in the next section as an aid to solving immediate problems. Fig. 11.2.1  Oil cooler performance.

11.2.3 Performance and Design Features of Commercial Oil-to-Water Coolers Performance curves on typical oil-to-water coolers are shown in Fig. 11.2.1; typical coolers are shown in Fig. 11.2.2. The heat rejection curves (Fig. 11.2.1) are based on an initial temperature difference of 100°F between oil and water, with an entering oil temperature of 240°F. The tests were conducted with transmission Type A oil. Curve D, as contrasted to curve C, illustrates the pressure drop and capacity penalty that must be paid for compactness with the use of minimal heat transfer surface. The coolers are mounted externally to both the radiator and transmission, each having its own outer casing that defines the water circuit. Cooler C is used in the hose connecting the bottom tank of the radiator to the water pump suction, while cooler D is mounted by a bracket bolted to the transmission case and is supplied with a partial flow of water in a manner similar to a car heater. More information regarding these coolers may be found in Ref. 3. Curves A and B represent tubular oil coolers designed for mounting in the radiator bottom tank, both having an O.D. of 1 in and a length of 10 in. The oil coolers differ, however, in the orientation of heat transfer surface on the oil side. In cooler A. the extended oil side surface is oriented with its broad elements transverse to the direction of oil flow, while those of cooler B are oriented in the longitudinal direction.

Fig. 11.2.2  Representative oil cooler. It is quite evident from the curves that the A type of cooler achieves its added heat rejection rate at the expense of pressure drop and pumping power. Thus, a 17% increase in heat rejection is attended by an 89% increase in pressure drop, with an oil flow of 2.2 gpm. In the event that such a large increase in pressure drop cannot be tolerated, the heat rejection of cooler type B can be increased by 17% with only a 9% increase in pressure drop by increasing its length from 10 to 12 in. This latter move is possible because the oil-fitting pressure drop is a major part of the total pressure drop in the case of the type B cooler. A typical tubular oil cooler mounted in a radiator tank is shown in Fig. 11.2.3. The plate type of the cooler shown in Fig. 11.2.4 may also be similarly mounted with equal facility. Some constructional details of both the tubular and plate oil

11-4

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coolers are shown in Fig. 11.2.4. The contrast between the longitudinal and transverse extended oil side heat transfer surface is shown in a close-up view (Fig. 11.2.5). One of the compact cars uses a tubular oil cooler without an extended surface on the oil side, since its cooling requirements are modest. For clarity, “extended heat transfer surface” is usually referred to as the “turbulizer.”

In the case of the torque converter, resistance data are available. Curves are presented for an 11-in machine in Fig. 11.2.6, while Fig. 11.2.7 shows the basic geometry of the fluid circuit used to obtain the test data. A comparison of Fig. 11.2.6A and 11.2.6B shows immediately that the dynamic and static resistance of the subject system is not the same and that the dynamic resistance varies with the speed ratio.

Fig. 11.2.3  Tubular oil cooler mounted in radiator bottom tank.

Fig. 11.2.4  Close-up of oil coolers.

Fig. 11.2.6  Converter charging oil flow resistance.

Fig. 11.2.5  Magnified view of turbulizers.

11.2.4 Flow Resistance of Transmission Hydraulic Circuits The resistance of the transmission proper is so varied and intimately connected with the pressure control system that it is impossible to make definite statements with regard to this item. However, many transmissions maintain a line pressure of about 80 psi in forward gear and 125+ psi in reverse, while circulating oil through the cooling system.

Fig. 11.2.7  Schematic of converter charging circuit. 11-5

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The impeller is a remarkable pump. It is actually in series with the charging pump and thus acts as a negative resistance to the external circuit. However, the full head of the impeller is not available for this function. Instead, the counterhead of the space between items 1a and 2 in Fig. 11.2.7 must be accounted for, because it is also rotating. The curves in Fig. 11.2.6B are lines of constant pressure drop from inlet to outlet. Thus, if the 30-psi curve at 4.5 gpm and 0.53 speed ratio is compared with a static resistance of 47 psi at this flow, a 17-psi contribution of the impeller is obtained. The impeller head contribution varies with both input speed and speed ratio, the input speed being 1500 rpm for the curves in Fig. 11.2.6B. Thus, it is possible to derive an equation that determines the relationship of the speed and speed ratio to the effective head of the impeller. This has been done, and the development of this equation is given in Appendix A.

2. Thermal capacity of system:   System A—water-cooling (20 units for radiator water)   System B—air-cooling

WC = 26 Btu/°F

Cooler Ratings System A—water-cooling hAS = 3.0 Btu/min/°F ITD System B—air-cooling hAS = 1.0 Btu/min/°F ITD (ITD = inlet temperature difference) Initial Oil Temperature Uo = 180°F (systems A and B) Sink Temperatures System A—water temperature 180°F = Um System B—air temperature   70°F = Um Transient Heat Transfer Equation (Appendix B)

11.2.5 Thermal Transients and Their Effect on Oil Cooler Sizing

where: β = hAS A = (βUm + H) Ψ = WC

In the early days, when hydrodynamic torque converters were first being considered for automatic transmissions, many engineers were quite apprehensive about keeping the oil temperature under control. Although some good all-mechanical automatic transmissions were available in test cars, the friction members were difficult to keep under control. However, the concern regarding the potential cooling problem associated with hydrodynamic drives led to great lengths to save the mechanical system. The control system that resulted from these efforts became so manifold that the hydraulic systems of present-day automatics resemble the plumbing of a wash basin by comparison. Eventually, an endeavor was made to resolve the potential cooling problems posed by the inclusion of a hydrodynamic drive member, including the author’s assignment to design torque converter vanes and oil coolers to compensate for their deficiencies.

U=

⎞ A ⎛A − ⎜ − Uo ⎟ e −βt Ψ ⎠ β ⎝β

(11.2.1)

System A: β = 3.0 Btu/min/°F A = (3 × 180 + 600) = 1140 Ψ = 46 Btu/°F therefore: 1,140 ⎛ 1,140 ⎞ U= −⎜ − 180⎟ e −3.0t 46 ⎠ 3.0 ⎝ 3.0 U = 381 – 201e–0.0653t °F t = ∞ U∞ = 381° equilibrium oil temperature

Initially, we envisioned the possibility of a driver applying the brake while simultaneously depressing the throttle. Immediate concern was therefore given to the matter of the heat that would be generated during such a simultaneous action. Upon further consideration and research, however, we concluded that the thermal capacity of the system would offset any possible difficulties, provided the brake were applied and the throttle depressed for only a short period of time. The theoretical development of the transient heat transfer concept is given in Appendix B; a typical example is given next for orientation purposes. Assumed Constants of System 1. Rate of heat generation:

WC = 46 Btu/°F

System B: β = 1.0 Btu/min/°F A = (1 × 70 + 600) = 670 Ψ = 26 Btu/°F therefore: ⎛ 670 ⎞ U = 670 − ⎜ − 180⎟ e −1.0t 26 ⎝ 1.0 ⎠ U = 670 – 490e–0.0385t °F t = ∞ U∞ = 670° equilibrium oil temperature

H = 600 Btu/min 11-6

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Table 11.2.1  Transient Oil Temperatures of Two Systems*

The transient oil temperatures of the two systems A and B (water-cooled and air-cooled, respectively) are shown in Table 11.2.1 and plotted in Fig. 11.2.8. An examination of the data and corresponding curves indicates that the water-cooled system holds the oil temperature down longer. However, the design constants used in this example may be a little optimistic for the water-cooled system, since a large share of the radiator’s thermal capacity was allocated to it. This was done to illustrate a point made earlier, namely, that high oil flows would enhance the cooler capacity and could exploit the thermal capacity of the system water. The radiator and engine cooling water in a car would have a thermal capacity of about 35 Btu/°F. A typical torque converter and transmission has an effective thermal capacity of 26 Btu/°F for the present-day aluminum-cased variety. In referring to the large difference in unit heat transfer capacity of the water-cooled versus air-cooled systems used in the previous example, it should be borne in mind that the one refers to radiator water and the other to ambient air. Therefore, initial temperature differences are considerably different in both cases; they are much larger for the air-cooled system. It should not be intimated, however, that the air-cooled system furnishes marginal cooling, because a direct comparison of the two systems cited would not be valid.

Oil Temperature, F Time t, min

System A Water-Cooled

System B Air-Cooled

 0  1  2  4  8 10

180 193 205 226 262 276

180 198 224 247 302 327

*See Fig. 8 for graphic presentation of data.

If the objective is to obtain a maximum oil temperature of 280°F, calculations have shown a safe running time of 6.3 min for the air-cooled system and 10.3 min for the water-cooled system. Since the heat rejection rate of 600 Btu/min used in this example represents very severe vehicle usage, it is difficult to conceive of an automobile being subjected to this rate for extended periods. However, this conclusion should not be extended to commercial vehicles, even taxicabs, because their design constants and usage factors are not comparable to the family car. A word is in order concerning road and dynamometer tests, as they are influenced by system thermal capacity. First of all, comparisons between two cooling systems should not be made on the basis of short runs only, or upon final steadystate temperatures. Instead, safe running time of reasonable duration should be sought. The effective thermal capacity of the typical transmission and converter mentioned above was determined from dynamometer tests on an air-cooled system, with the dynamometer adjusted to maintain equal inlet and outlet oil temperatures, although both increased simultaneously with time. Since the input and output power was being measured and a suitable correction made for converter windage, the heat generation rate could be determined. Similarly, in view of the equal oil temperatures, the system was dissipating all the heat generated except that being stored. Therefore, by careful plotting of the temperature versus time curves, and then comparing these with the theoretical calculations

Fig. 11.2.8  Transient temperature rise of transmission oil. for various combinations of parameters, it was possible to determine the effective thermal capacity of the system. The value obtained applied to several modifications of the converter cooling fan and air inlet and outlet configurations. Thus, it is thought to be reasonably close to fact. One should not attempt to evaluate this factor by simply weighing all the parts of the system and multiplying them by their respective specific heats, since all parts of the system do not have the same intimacy of contact with the hot oil. Also, in a car one might expect to find heat being transferred from the bell housing to the engine or vice versa. It is possible that the taxicab problem could be related to a flow of heat from the 11-7

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Design Practices: Passenger Car Automatic Transmissions

engine during idling immediately after coping with rushhour traffic. A similar situation might occur after extensive high-speed driving followed by idling at the curb. In this event, the thermal capacity of the engine block would act as an unaccounted-for source of stored heat which seeks to escape by the most convenient route.

it to rotate at the mean speed of items 1 and 2. Because this mean speed is always less than the impeller speed, the head developed in the space between items 2 and 1a is always less than the impeller head. Part of the impeller head is available for overcoming the fluid resistance of the inlet and outlet passages, thus aiding the external charging pump. The maximum influence of the impeller head on charging oil flow occurs at stall, because the angular velocity in the space between items 2 and 1a is then minimum. The following mathematical analysis is a quantitative explanation of the above:

11.2.6 Conclusion This paper is aimed at the younger members of the profession in the hope that an exposure to the history of the subject and its overall relationship to the vehicle might encourage them to look at the broad aspects of problems. The deplorable tendency toward specialization that is prevalent today can only lead to monstrous combinations of parts ill-suited to functioning as a unified mechanism, in spite of the fact that each is a highly perfected device in its own right.

Ne =

where:

Ni + No 2

(11.2.A-1)

Ni = impeller speed, rpm (item 1) No = turbine speed, rpm (item 2) Ne = mean fluid speed between items 2 and 1a The impeller head P1 varies as the square of its speed and diameter, as well as the mass density of the fluid if we desire to express it in pressure units. Impeller head varies also with the impeller vane geometry, being greater for forward leaning vanes and less for backward leaning ones.

11.2.7 References 1. Farrell, E. F., “Propulsion Dynamics of Motor Vehicles,” Paper 1 presented at SAE Annual Meeting, Detroit, MI, January 1957. 2. Sicklesteel, D. T., “Torque Converter Cooling,” SAE Quarterly Transactions, Vol. 6 (1952), pp. 151–153, SAE International, Warrendale, PA. 3. McDonough, R. P., “The Development and Application of Oil Coolers for Torque Converters,” Paper 530141 presented at SAE National Tractor Meeting, Milwaukee, WI, September 1953. 4. Kelley, O. K., “The Polyphase Torque Converter,” Discussion by E. F. Farrell, Proceedings of National Conference on Industrial Hydraulics, Vol. II, Fourth Meeting, October 1948.

Therefore: P1 = ρD12K1N12 = C1N12



(11.2.A-2)

Since a similar relation exists for the space b between items 2 and 1a: 2

⎛ N + No ⎞ Pb = c 2N 2b = C 2 ⎜ i ⎟ ⎝ 2 ⎠



(11.2.A-3)

For a radial impeller, C1 and C2 are essentially equal. Thus, the net available head to assist the charging pump is: 2 ⎡ ⎛ N + No ⎞ ⎤ ΔP = P1 − Pb = C1 ⎢ Ni2 − ⎜ i ⎟ ⎥ ⎝ 2 ⎠ ⎦ ⎣

11.2.8 Appendix A

(11.2.A-4)

Eq. 11.2.A-4 can be written as:

11.2.8.1 Effect of Impeller Head on Charging Flow Through Torque Converters Referring to Fig. 11.2.7, it is noted that the charging oil flows into the I.D. of the impeller (item 1) and then proceeds radially outward while being acted on by the impeller vanes. It is obvious that a centrifugal head is imparted to the oil in its transit through the impeller, this head being proportional to the square of the impeller speed.

⎡

1 1 No 1 ⎛ No ⎞ − − 4 2 Ni 4 ⎜⎝ Ni ⎟⎠

ΔP =

C1N12 ⎢1 −

ΔP =

2 ⎡ 1 N ⎛N ⎞ ⎤ C1Ni2 ⎢3 − 2 o − ⎜ o ⎟ ⎥ Ni ⎝ Ni ⎠ ⎥⎦ 4 ⎢⎣

⎢⎣

2

⎤ ⎥ ⎥⎦

(11.2.A-6)

2 2 No ⎛ No ⎞ ⎤ ⎛ Ni ⎞ ⎡ ΔP = C o ⎜ 3 − 2 − ⎥ ⎢ ⎝ 1,000 ⎟⎠ ⎢ Ni ⎜⎝ Ni ⎟⎠ ⎥⎦ ⎣

The charging oil then escapes by flowing over the O.D. of the turbine (item 2), which rotates at output speed into the space between the cover (1a) and the turbine (2). In this space, the fluid is driven by boundary-layer friction, which causes

11-8

(11.2.A-5)

(11.2.A-7)

Transmission Temperature Control and Lubrication

Co =



1 × 106 C1 4

edly give better correlation between theory and experiment. Furthermore, at high speed ratios, the wide variation in exit velocity across the impeller exit fluid channel between vanes will introduce an additional loss, reducing the net impeller head. Since quantitative information relative to velocity distribution in converter-vaned channels is proprietary knowhow useful in designing such machines, it is not propitious to disclose this information here. However, the static resistance approximates the dynamic so closely above 0.90 speed ratio that it may be used for all practical purposes in designing a cooling system.

(11.2.A-8)

Since Co is intimately connected with the converter geometry and fluid properties in a rather complex manner, the analytical approach will not be labored here. However, the writer has obtained a solution for this problem and uses it for other purposes as well as for computing turbine thrust. When concerned with a converter for which hardware already exists, Co can readily be determined by test. In referring to Fig. 11.2.6B, we note that, at a pressure drop of 30 psi and an oil rate of 4.5 gpm, the speed ratio is 0.53, while the static resistance of the system is 47 psi at 4.5 gpm (Fig. 11.2.6A). Because the impeller speed was 1500 rpm for this particular test, it is possible to evaluate Co from the equation for ΔP. Thus: ΔP = 47 – 30 = 17 psi (experimental value) Co =

2

17

⎛ 1,500 ⎞ 2 ⎟ ( 3.00 − 2 × 0.53 − 0.53 ) ⎜⎝ 1,000 ⎠

11.2.9 Appendix B 11.2.9.1 Transient Temperatures in Transmissions Given a container (source) in which heat is being generated at a constant rate of H thermal units per unit time, whose thermal capacity is Ψ units. Further, let heat be conducted away from the container at the rate of β thermal units per unit time, per unit difference in temperature between it and the sink receiving the heat. How does the internal temperature of the system (source) vary with time?

(11.2.A-9)

= 4.55 (11.2.A-10)



Let:

2 2 ⎛ No ⎞ ⎛ No ⎞ ⎤ ⎛ Ni ⎞ ⎡ ΔP = 4.55 ⎜ 3.00 − 2 − ⎢ ⎜⎝ N ⎟⎠ ⎜⎝ N ⎟⎠ ⎥ (11.2.A-11) ⎝ 1,000 ⎟⎠ ⎢ i i ⎥⎦ ⎣

Wn = weight of any element of system Cn = specific heat of element of system Ψ = WC = ∑Wn Cn heat capacity of entire system As = external heat transfer surface of system h = coefficient of heat transfer from surface to surrounding medium H = rate at which heat is being generated in system t = time U = instantaneous temperature of system Um = temperature of surrounding medium

Evaluating Eq. 11.2.A-11 at various speed ratios and assuming a constant dynamic pressure drop of 30 psi, the comparative data shown in Table 11.2.A-1, exhibited graphically by the dash-dot curve in Fig. 11.2.6B, are obtained. An examination of Table 11.2.A-1 and the graphical data in Fig. 11.2.6B indicate that the calculated and experimental values are in good agreement up to 0.70 speed ratio. The differences at higher speed ratios could reflect lack of resolving power of the experimental setup, because we are using the small difference of two relatively large pressures. A more refined setup using a U-tube mercury manometer to measure the pressure difference directly would undoubt-

Then it follows that: Let:

Table 11.2.A-1  Pressure Drop Constant at 30 psi Calculated

WC

dU + hAS ( U − U m ) = H dt

WC = Y  and  h AS = b

Test

Speed Ratio, No/Ni

ΔP, psi

Q, gpm

DP, psi

Q, gpm

0.00 0.20 0.40 0.53 0.70 0.90

30.75 26.2 20.9 17.0 11.4 4.0

5.17 4.95 4.68 4.50 4.17 3.78

32.5 27.5 22.0 17.0 10.0   1.0

5.25 5.00 4.72 4.50 4.13 3.55

Therefore:

dU βU (βU m + H ) + − =0 Ψ Ψ dt

Let:

WC = Y  and  h AS = b

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Design Practices: Passenger Car Automatic Transmissions

11.3 Transmission Cooling Systems: Air Cooling

Therefore:



1 t = − log e k ( A − βU ) β Ψ

M. G. Gabriel Transmission and Chassis Div., Ford Motor Co.

Transient Heat Transfer Equation Let:

(β Um + H) = A

(11.2.B-1)



dU βU A + − =0 Ψ Ψ dt

(11.2.B-2)



dU 1 = ( A − βU ) Ψ dt

(11.2.B-3)

dU dt = Ψ ( A − βU )

(11.2.B-4)

1 t = − log e k ( A − βU ) β Ψ

(11.2.B-5)

Then:

Therefore:

(k = integration constant)



e −βt Ψ A − βU At t = 0, U = Uo , e −βt Ψ = 1 1 k= A − βUo







k=

A − βU = ( A − βUo )e −βt Ψ

Thus:

U=

⎞ A ⎛A − ⎜ − Uo ⎟ e −βt Ψ ⎠ β ⎝β

(11.2.B-6) (11.2.B-7) (11.2.B-8)

Air-cooling has been utilized in some degree ever since the automatic transmission was introduced to the motoring public. At first, the flow of air normally passing over its outer surface was sufficient to cool the transmission. However, forced air-cooling was used in a 1939 installation comprised of a fluid coupling in combination with a conventional three-speed gearbox and disconnect clutch (Fig. 11.3.1). Cooling fins on the coupling supplied sufficient heat rejection for all normal driving conditions, provided a heavy load was not towed, which might result in excessive coupling slip. As vehicle power-to-weight ratios increased and torque converter transmissions became available, the normal surface cooling was supplemented with forced air or watercooling. In 1950, two torque converter transmission designs were introduced which incorporated forced air-cooling. One unit, employing the converter in all three gears, featured an aluminum die-cast impeller with integral cooling fins. The other transmission, which provided a lockup clutch in direct drive, used an all-steel fabricated converter with a special cooling shroud. Since then, air-cooling has been used continuously in a variety of arrangements, alone or in combination with water-cooling.

(11.2.B-9)

(11.2.B-10)

The physical significance of the term A/β is interesting insofar as it represents the temperature the system would attain in an infinite time if the initial assumptions continue to be valid. The above analysis is applicable to torque converter temperature rise problems, provided that judgment is used in selecting the constants. If no cooler is used, then the constant β = zero, and:

dU H = Ψ dt H U = Uo + t Ψ

(11.2.B-11)

Fig. 11.3.1  Fluid coupling with air-cooling.

(11.2.B-12) 11-10

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11.3.1 Nomenclature

11.3.2 Transmission Cooling Objectives

A = surface area of converter (excluding fins) b = fin thickness cp = specific heat at constant pressure d = diameter D = converter circuit diameter, ft Dp = characteristic diameter of air circuit passage Ff = fin frequency noise °F = degree Fahrenheit g = acceleration of gravity h = film heat transfer coefficient H = total heat flow Hf = head produced by cooling fins k = thermal conductivity L = length of fin (along airpath) Lp = characteristic length of air passage n = number of fins N = impeller rotational speed, rpm P = nominal pitch or fin spacing Pr = Prandtl number Q = quantity of airflow r = radius ro, ri = tin outlet and inlet radius, respectively roso, risi = exit and inlet “whirl,” respectively Re = Reynolds number s = tangential component of absolute air velocity; also fluid stress t = transmission temperature ta = ambient air temperature Δtm = n  ominal temperature difference between lubricant and air U = overall coefficient of heat transfer V = velocity w = width or height of fin, ft W = weight Δx = thickness of shell τ = time, heat sink factor μ = dynamic viscosity, lb/(ft-h) ρ = density, lb/ft3 φ = coefficient (dependent on transmission configuration) ∼ = proportional

The objective of a transmission cooling system is threefold: 1. To provide adequate cooling in conditions of extreme vehicle operation and high ambient temperatures. 2. To permit the oil to rise to a satisfactory operating temperature level in the shortest period of time from vehicle starting, particularly in cold-weather conditions. 3. To maintain near-optimum oil temperatures during normal vehicle operation. To meet these qualifications, various factors must be taken into account in considering air-cooling for a transmission vehicle application. Transmission arrangement and characteristics greatly determine the type of cooling system most practical. Air-cooling is ideal for installations with a hydrodynamic member having a relatively large cooling surface, particularly where converter oil circulation is limited. On the other hand, designs using small fluid couplings with low cooling surface areas provide limited air-cooling. The vehicle package, as well as the transmission arrangement, may indicate the type of cooling system to be used (Fig. 11.3.2). For example, an air-cooling system is the most logical for a transaxle when combined with an air-cooled engine. Vehicle power-to-weight ratio, as well as vehicle usage, affect the amount of heat generated within a particular transmission. Increasing the engine size in a given vehicle results in greater power input to the transmission under accelerating conditions, with correspondingly higher average oil temperature level. With regard to usage, towing a three-ton trailer with a compact car, for example, would require an extensive transmission cooling system, to say the least. On the subject of optimum transmission operating temperature, many factors are involved. All transmissions do not necessarily have the same optimum temperature, but it is generally in the band from 150° to 250°F.

Fig. 11.3.2  Converter air-cooling in transaxle installation. 11-11

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Table 11.3.1 summarizes the factors affecting optimum temperatures. Table 11.3.1  Factors Affecting Optimum Temperatures Item

Effect of Increased Temperature

Lubricant

Lower viscosity; increased specific heat; increased tendency for additive breakdown Increased efficiency corresponding to reduced viscosity Increased overall efficiency; decreased capacity, particularly at low speeds Increased leakage Reduction in operating life; increased leakage Change in coefficients of friction affecting shift calibration

Torque converter or fluid coupling Pumps Valve body Seals Friction members

11.3.3 Designing for Air-Cooling The conventional way in which forced air-cooling is provided uses the torque converter directly (Fig. 11.3.3). Appropriate fins are positioned on the outside of the impeller. These act as a centrifugal fan, which pumps or impels ambient air around the hot outer surface of the torque converter. The heated air is then discharged tangentially near the bottom of the converter housing.

Fig. 11.3.3 Conventional air-cooling. Housing Design—The converter housing defines the passageways and porting in an air-cooled system. It should take three considerations into account: 1. Airflow requirements 2. Minimum air noise 3. Screening Package limitations and practical experience greatly influence the converter housing design for cooling. However, some direction can be obtained from the projection heat transfer and corresponding airflow requirements.

It is desirable to make the air inlet and outlet ports as large as possible. In addition, they should be located away from any vehicle restrictions, such as exhaust pipes or frame members, to develop maximum airflow. In keeping with the centrifugal fan action of the fins, the inlet ports are usually positioned as close to the centerline as possible, with the outer periphery of the gearbox as the practical limitation. When the inlet is not near the center, a shroud is generally used to help guide the air toward the center or eye of the cooling fins and then around the converter. Another aspect of the housing design involves stress studies which must be conducted to avoid sections of high-stress concentration at the air inlet ports, particularly when die-cast aluminum construction is used instead of cast-iron. Suitable stiffening ribs can be incorporated to provide the necessary structural strength. Depending on the design configuration, air friction losses in the housing are proportional to the square of the air velocity. To minimize these losses, 70 ft/s is a practicable limit of air velocity. Also, sharp bends in the air passageways are to be avoided. The formula for this factor is:



loss ~

L pρ ⎛ V 2 ⎞ 1 D p ⎜⎝ 2g ⎟⎠ (Re)0.25



(11.3.1)

Symbols used in the formula are identified in the Nomenclature, Section 11.3.1. At high impeller speeds and airflows, attention must be given to elimination of air noise. Between the rotating cooling fins and transmission housing, high relative velocities exist, and these can result in a whistling noise. Also, air resonance can develop from pressure pulsations at any local pockets or air inlet openings. To keep these objectionable noises to a minimum, it is necessary to avoid close cooling fin clearances, local housing protrusions, and pockets or holes, particularly in the area of the cooling fins. What little noise remains blends with the engine and general vehicle background noise. Effective air inlet screening should be provided to minimize the induction of dirt particles as well as foreign matter that may cause actual physical damage. Air inlet ports can be located at the top of the transmission housing, farthest from the surface of the road, to reduce the tendency to draw in road particles. However, allowances must be made for higher air temperatures that exist at this location and for low tunnel clearances that may restrict airflow. At the outlet port no screening is usually necessary because of the natural pressure barrier developed by the discharging air.

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Torque Converter Design—The general design of the torque converter greatly dictates the configuration of the cooling fins and corresponding shroud (Fig. 11.3.4). One of the original air-cooled transmissions utilizes an aluminum die-cast impeller member in the torque converter: 68 cooling fins were cast integrally as straight radial protrusions on the outside of the impeller housing. Excellent heat transfer was thus combined with structural strength. In the arrangement shown in Fig. 11.3.5, the aluminum impeller is located at the front of the torque converter. Although a somewhat different airflow circuit is employed, the cooling principle is the same: 50 cooling fins are cast integrally with the impeller, and the converter drive plate acts as a mating shroud. This is a good air-cooled design incorporating large fins to provide maximum surface area and effective airflow.

Fig. 11.3.5  Air-cooled converter with front-oriented impeller.

For maximum strength and high-volume production, steel impeller construction is generally preferred (Fig. 11.3.6). A one-piece stamping combining the cooling fins and the shroud is fabricated to match the impeller outer contour and is spot-welded in place. This shroud develops the head required to circulate the air effectively from the inside outward around the impeller. For maximum airflow, it is desirable to use a shroud with a large exit radius and small inlet radius. The optimum dimensions generally require verification by means of heat rejection tests. If it is integral with the impeller, a shroud is not required in the torque converter housing. In comparison with steel construction, the aluminum converter provides the better cooling capacity as a result of the high rate of heat transfer through the integral fins.

Fig. 11.3.6  Steel converter with shroud. Cooling Fin Design—In aluminum die-cast impellers, the cooling fins are generally straight and radial. However, in fabricated steel units, fin curvature may be provided to increase airflow, with subsequent gain in rejected heat (Fig. 11.3.7). Decreasing the exit angle toward a forward bend tends to increase airflow. Flow will also go up somewhat if the fin inlet is tilted toward the direction of rotation. In addition, inlet air shock losses and air noise level will be reduced. The head produced by the cooling fins is dependent on fin geometry, as defined by Eq. 11.3.2.



Hf ~

N (roso − ri si ) g

(11.3.2)

Figure 11.3.8 illustrates the air velocity vectors involved at the inlet and outlet of the cooling fins. Fig. 11.3.4  Air-cooled aluminum converter.

The number of fins may be increased to raise airflow and improve cooling. However, experimentation is generally necessary to determine the optimum number required. The 11-13

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point of diminishing returns is soon reached when the gains are offset by the added air restriction and air friction losses. Although the addition of fins reduces sound intensity slightly, it does raise the frequency, and because there is a lower human tolerance to higher frequency, sometimes fewer fins are used. The design factor for fin frequency noise is: Ff ~



Nn 60

(11.3.3)

Acceptable blading spacing, reflecting current practice, may be estimated from the following relation for pitch in aluminum impellers: P = 0.01



(ro − ri ) D 2w



Fig. 11.3.7  Steel converter with shroud and integral fins.

(11.3.4)

(Use 0.17 instead of 0.01 for steel impellers.) Air-cooling has been used in installations with engine displacements from 140 to 340 in3 or more. To transmit the torque of the greater output engines, a torque converter of larger diameter is generally required. As a result, the cooling capacity is increased, since the air discharge rate varies approximately as the third power of the fin radius. For this reason, the radial location of the fins is also an effective way of modifying the cooling for a given installation. Q ∼ N, r3



(11.3.5)

Cooling capacity varies with impeller speed, a disadvantage of an air-cooling system.

Fig. 11.3.8  Vector diagram of air velocities at cooling fins.

Figure 11.3.9 depicts a typical airflow chart plotted with respect to impeller rpm. It is based on a dynamometer test of a 10.25-in-diameter steel converter, incorporating 12 fins formed integrally with the attached cooling shroud. Oil temperature is maintained at 200°F. Although of relatively low magnitude, the pumping power requirements of the cooling fins increase as the cube of the impeller speed for a given design. Figure 11.3.10 illustrates the requirements, plotted on a log-log chart for two converter sizes. The data are taken from actual dynamometer tests conducted with fins, and with fins removed from the impeller. In summary, air-cooling capacity for a given transmission design may be modified by changing the following: 1. Effective airflow area around impeller and through passageways 2. Area of inlet and outlet ports 3. Position and shape of ports 4. Radial location and configuration of cooling fins

Fig. 11.3.9  Airflow versus RPM.

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The foregoing design considerations and procedures have intentionally been discussed on a broad, general basis. Differences in design, the complexity of the heat transfer problem, and the variety of operating conditions preclude a single design approach to cooling.

Fig. 11.3.11  Power loss and efficiency versus mph.

Fig. 11.3.10  Cooling fin power requirements versus RPM. Procedure—A general five-step procedure to develop an air-cooled system is as follows: 1. Determine the transmission heat load. Figure 11.3.11 illustrates a typical power loss curve for a two-speed converter transmission. It shows the relationship between full-throttle transmission efficiency and the corresponding maximum heat input to the transmission. The steady-state road-load heat input is also given. Losses under grade-load, in addition to road-load, can also be determined: they are not illustrated in this chart. 2. Calculate the film coefficients of heat transfer. Based on the relationships given in the Appendix, the approximate film coefficients can be calculated for various vehicle operating conditions. 3. Determine equilibrium, temperature, and heat rejection rate. Oil temperature may be determined for a given condition by equating the total rejected heat to the transmission net power loss (heat input). 4. Make design adjustments in cooling capacity. By adjusting one or more of the controlling variables, the maximum transmission operating temperatures may usually be held within design objectives. 5. Perform dynamometer and vehicle qualification tests. Some compromises must be made in every installation, and the test results should indicate these. After completion of the initial tests, minor cooling system changes may be made, followed by a final system checkout.

11.3.4 Qualification Vehicle Tests—To qualify a transmission as properly cooled, a variety of tests may be conducted within the vehicle and on the dynamometer. Although these tests are not standardized throughout the industry, they are all designed to check cooling against the objectives outlined earlier in this paper. The most important vehicle tests are made to ensure that a transmission will not overheat to the point of malfunction or damage under conditions of extreme vehicle operation. These tests, conducted at high ambient temperature, are of three basic types and are self-explanatory: 1. Heavy-traffic, stop-and-go, city driving 2. High-speed, turnpike driving 3. Grade and high-altitude operation A test, which is often used as a criterion (type 3), is to negotiate the 10-mile-long grade, averaging 4.8%, leading from Davis Dam, Arizona. The vehicle is weighted with the equivalent of four passengers. It tows a load that may be as great as 5000 lb curb weight, depending on the horsepower and operational requirements of the vehicle under test. At the start of the test, the transmission oil temperature, usually measured at the front pump, is established at 200°F, and the ambient temperature is at approximately 100°F. If at the summit the temperature has not exceeded the maximum design operating temperature, the cooling is considered adequate.

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Should this test so indicate, additional air-cooling capacity is incorporated by means of design modifications. If the aircooling system is still inadequate, a small oil-to-water transmission cooler may be installed in the engine radiator. Tests such as the one described are simulated conveniently and quickly, using a fully instrumented chassis dynamometer. Even though heat radiation and air density influences do not duplicate the actual road conditions, the effect of individual cooling design changes may be determined and comparisons of the relative cooling of competitive vehicles can be readily made. Figure 11.3.12 illustrates one type of data obtained that represents the results of chassis dynamometer cooling tests for comparing three vehicles. Temperature versus operating time is plotted: it does not quite stabilize at the end of the top gear, and therefore a downshift is indicated. The test conditions for all vehicles are the same: 100°F ambient air, 30 mph apparent vehicle speed, 4.8% grade, and approximately 26 hp at the rear wheels, simulating a 1500-lb towed load. An automatic transmission reaches its normal temperature after a certain distance and time, depending on the type of vehicle operation. Figure 11.3.13 depicts transmission oil warm-up versus distance for an air-cooled installation under suburban driving conditions. The vehicle was stabilized at about 60°F ambient temperature prior to the start of the test. Engine radiator water outlet temperature is shown to illustrate the potential for faster warm-up and better overall temperature stabilization when a transmission oil-to-water cooler is added in the radiator.

Fig. 11.3.13  Warm-up temperature versus distance. Dynamometer Tests—In addition to vehicle tests, doubledynamometer tests of the transmission may be conducted to determine cooling characteristics (Fig. 11.3.14). The transmission is enclosed in a special plenum chamber. Air, preheated to 100°F, is routed through the chamber and the converter. A micromanometer is used in combination with a supplementary blower to simulate vehicle conditions. By using extensive thermoelectric instrumentation, the airflow, equilibrium temperatures, and heat rejection rates are determined at various loads and speeds. Figure 11.3.15 illustrates an example curve developed from these dynamometer tests. It is a plot of torque converter heat dissipation for a series of equilibrium oil temperatures employing an 11.75-in-diameter converter with an aluminum impeller.

Fig. 11.3.14  Dynamometer cooling test installation.

Fig. 11.3.12  Temperature versus running time at 30 mph and at high load. 11-16

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Transmission Temperature Control and Lubrication

namic member. However, a separate oil-air heat exchanger may be installed in place of, or as a supplement to, the conventional air or transmission water-cooling. The unit illustrated in Fig. 11.3.16 was used in one production installation mounted in front of the radiator, as shown. This particular cooler is about 8-in square with 16 oil passes, and dissipates about 1.5 Btu/min/°F differential at 30 mph. Because of its relatively high cost, it is selected only when needed for difficult cooling installations. Heat transfer of a separate oil-air cooler is defined by the rate of oil flow, the effective surface area, and the mean temperature difference between the oil and air. The design problem is similar to that of an oil-to-water heat exchanger.

Fig. 11.3.15  Converter heat rejection characteristics. Heat Capacity—In brief periods of extreme loads, the transmission can safely absorb more heat than it rejects. This capacity can be stated in terms of a heat sink factor. Assuming optimum oil circulation, the heat sink factor improves with greater transmission weight, higher component specific heats, and greater heat rejection. Because of the relatively high specific heat property of oil, transmission sump oil capacity is of significant influence. The heat-sink factor, T, provides a conservative indication of the length of time required for a given temperature rise under high load. It is easier to calculate, although not so accurate, in comparison with the more exact exponential equation included in the Appendix for reference.



100∑ Wc p Hi − ∑ HL



11.3.6 Summary Air-cooling is an economical, practical, and effective method of cooling automatic transmission fluid. It may be used exclusive of other cooling, or in combination with water cooling for additional flexibility as well as capacity. A design procedure is presented to define more adequately an organized approach to transmission cooling problems. Heat transfer relationships formulated in the Appendix indicate the relative importance of various factors concerned with cooling.

For a transient operating condition, the heat sink factor is: τ=

Fig. 11.3.16  Oil-to-air cooler installation.

(11.3.6)

where:

The design of a cooling system for a new transmission should be considered as the new unit progresses. Sufficient cooling for the extreme loads must be provided. If, beyond this requirement, effort has been directed toward maintaining optimum oil temperatures at most operating conditions and ambient temperatures, the cooling system will be certain to carry out its important role.

Hi = heat input = 42.4 (trans. input hp) (1-trans. eff.), Btu/min ∑HL = summation of transmission heat transfer due to convection, conduction, and radiation, Btu/min ∑Wcp = summation of products of weight and specific heat of transmission components, Btu/°F

11.3.5 Separate Oil-Air Cooler

11.3.7 Acknowledgment

All the previous discussion has been limited to a conventional transmission air-cooling system, integral with the hydrody-

The author wishes to express his appreciation particularly to E. W. Konrad and P. G. Roberts for their valued sugges-

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tions, and to the others who contributed to the preparation of this paper.

The overall coefficient of heat transfer U is defined by the relation: 1 1 Δx = + U h k

(11.3.A-2)

11.3.8 References



1. Chapman, C. S. and R. J. Gorsky, “The New Buick Special Automatic Transmission,” Paper 610404 presented at SAE International Automotive Engineering Congress, Detroit, MI, January 1961. 2. Winchell, F. J., “The Chevrolet Corvair (Transaxle),” Paper l40C presented at SAE Annual Meeting, Detroit, January 1960. 3. Eckert, E. R. G., “Heat and Mass Transfer,” New York: McGraw-Hill Book Co. Inc., 1959. 4. Heldt, P. M., “Modern Automatic Transmission,” Philadelphia: Chilton Co., 1950. 5. Madison, Richard D., “Fan Engineering,” Buffalo: Buffalo Forge Co., 1948. 6. Keenan, J. H. and J. Kay, “Thermodynamic Properties of Air, “New York: John Wiley & Sons, Inc., 1945. 7. Jakob, Max and George A. Hawkins, “Elements of Heat Transfer and Insulation,” New York: John Wiley & Sons, Inc., 1942.

The relationship for the airfilm coefficient of heat transfer is developed as an extension of the Prandtl equation:

11.3.9 Appendix Air-cooling of automatic transmissions is subject to the laws governing heat transfer in conduction, convection, and radiation. However, because of the transient operating conditions and involved conduction and convection heat flows, calculation of the transmission heat rejection is difficult and can be only approximated. Cooling due to radiation is relatively insignificant and is neglected in this analysis. For an air-cooled transmission, most of the heat is rejected by a combination of conduction and forced convection at: 1. The torque converter outer surface 2. The transmission outer surface Heat Rejected by Torque Converter—To compute the heat rejected per unit time by the torque converter (units are based on the lb-ft-h system):

H = UA Δ tm + n 2L2 bkh   approx. (11.3.A-1)

where the second term represents the heat lost by the cooling fins.

h=

sc p  for flow for turbulent turbulent flow V [1 + 0.8(Pr − 1)]

(11.3.A-3)

This assumes that the laminar sublayer air velocity equals 0.8 of the air velocity in the mainstream. Since for turbulent flow: s=

0.0395ρV 2 (from Blasius)  (from Blasius) (Re)0.25

(11.3.A-4)

h=

0.0395ρVc p (Re) [1 + 0.8(Pr − 1)]

(11.3.A-5)

by substitution:

0.25



Equation 11.3.A-5 may be simplified by substitution of quantities that remain fairly constant in the range encountered. For air: Pr = 0.70 cp = 0.24 Btu/lb-°F μ = 0.0475 lb/(ft-h) As an approximation: d = 2w (based on hydraulic radius analogy) V = 188 DN air velocity, ft/h (neglecting the effect of fin and housing configuration) Therefore:

h=

0.248(DNρ)0.75 Btu/h-ft 2 -°F (11.3.A-6) w 0.25

Because the film coefficient on the inside oil surface is not very influential, it is neglected for simplification. Heat Transfer from Transmission Outer Surface—To calculate the heat transfer from the case wall to the surrounding air, it is necessary to know the temperature gradient with respect to distance from the wall. It has been demonstrated that this slope is very steep for turbulent flow and can be approximated in terms of heat flow and fluid friction. Because of the difficult nature of the problem of expressing heat transfer from a transmission within a moving vehicle, this relationship can serve only as a guide.

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Transmission Temperature Control and Lubrication

Airfilm coefficient: h=φ



0.08 ρc pV (Re)0.25

(11.3.A-7)

dt



n = 12   L = 2.5 in   b = 0.032 in The second term of Eq. 11.3.A-1 becomes:

Transient temperature rise:

∑ Wc dτ = hA( t − ta ) + Hi

Heat Rejected by Steel Fins Given dimensions:



H = n 2L2 bkh

(11.3.A-8)

Integrating and substituting for the constant of integration: Hi − UA ( t − t a ) = e −UAτ ΣWc Hi − UAΔtm



(11.3.A-9)



H = UAΔtm + n 2L2 bkh

t = temperature at time τ Δtm = temperature differential with respect to air at zero time

Δtm = 100°F ρ = 0.069 lb/ft3 for air N = 2000 rpm A = 2 ft2 k = 19 Btu/h-ft-°F for steel D = 10.25 in w = 0.4 in k = 101 Btu/h-ft-°F for aluminum Δx = 0.16 in To determine airfilm coefficient (refer to Eq. 11.3.A-6):

0.248(0.854 × 2,000 × 0.069)0.75 h= (0.0333)0.25

H=

Sample Calculations Given data:

0.248(DNρ)0.75 w 0.25

(11.3.A-10)

1 1 Δx = + k U h

1 1 = + 0.0007 = 0.0482 U 21

(11.3A-14)

= 69 Btu/min approx. rejected by converter

φ = 0.54 Δx = 0.18 in average A = 6 ft2 effective Δtm = 100°F V = 30 mph cp = 0.24 for air 0.25 (Re) = 22 (calculated) and, referring to Eq. 11.3.A-7: h=φ

0.08 ρc pV (Re)0.25

⎛ 0.08 ⎞ (0.069)(0.24)(44 × 3,600) h = 0.54 ⎜ ⎝ 22 ⎟⎠

The second term of Eq. 11.3.A-2 becomes:

2 × 100 ⎛ 1 ⎞ ⎜ ⎟ +0 0.0482 ⎝ 60 ⎠

Heat Rejected by Outside of Transmission Given conditions:

= 21 Btu/h-ft 2-°F

0.16 Δx = = 0.0007 19 × 12 k

= 4 Btu/h approx. (negligible, for 12 steel fins)

Therefore (see Eq. 11.3.A-1):

where:

h=

(11.3.A-13)

2

⎛ 2.5 ⎞ ⎛ 0.032 ⎞ (19)(21) = 12 2 ⎜ ⎝ 12 ⎟⎠ ⎜⎝ 12 ⎟⎠

(11.3.A-11)

   = 5.15



(11.3.A-15)

and, referring to Eq. 11.3.A-2: 1 1 Δx = + k U h

(11.3.A-16) 1 0.18 1 = + = 0.194 (neglecting (neglectingoil oilfilm film coefficient) U 5.15 101 × 12  coefficient)

(11.3.A-12)

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11.4.1 Transmission Cooling Circuits

H = UAΔtm =

6 × 100 ⎛ 1 ⎞ Btu/min approx. approx ⎜ ⎟ = 51 Btu/min 0.194 ⎝ 60 ⎠

(11.3.A-17)

(It is assumed that the entire transmission wall is at 100°F differential with respect to air.) Heat Sink Factor Given conditions: Input = 10 hp (net) Weight of steel components = 100 lb Weight of aluminum components = 30 lb Weight of oil = 11 lb cp = 0.12 Btu/lb-°F for steel cp = 0.22 Btu/lb-°F for aluminum cp = 0.5 Btu/lb-°F for oil then:

∑ Wc p = 100 × 0.12 + 30 × 0.22 + 11 × 0.5 = 24.1 τ= =

100∑ Wc p Hi − ∑ HL



(11.3.A-18)

(Refer to Eq. 11.3.A-6)

100 × 24.1 10 × 42.4 − (69 + 51)

(11.3.A-19)

= 8 min (approx.) for 100°F rise

11.4 Temperature Effects on Transmission Operation T. J. Griffen Cadillac Motor Car Div., General Motors Corp. The reliability of today’s planetary gears, clutch materials, thrust washers, and in general all mechanical components of the transmission has extended transmission life to the point that time and temperature have become the limiting factors. What are the problems associated with heat in transmissions and what can be done about it? What are the temperatures encountered in today’s automatics? This paper has been prepared in an attempt to answer these questions.

Before we appraise some of the effects of heat on materials, let us review some of the basic cooling circuits in today’s transmissions. The two basic systems most commonly employed today are represented schematically in Figs. 11.4.1 and 11.4.2. These systems are used with an external heat exchanger. The basic difference between the two circuits is that oil is fed directly from the pump to the cooler for Fig. 11.4.1, and in Fig. 11.4.2, the oil is routed through the fluid member before entering the cooler. The system in Fig. 11.4.1 has the advantage of providing lower-temperature oil to the fluid member, thus obtaining the highest possible coupling efficiency. Figure 11.4.1 has a further advantage over Fig. 11.4.2 in simplifying the lubrication circuit. The extra complication of lubrication for Fig. 11.4.2 may be worthwhile, because lower-temperature oil can be provided to cool clutches and bearings. One might expect the most efficient cooling from Fig. 11.4.2, because the greatest oil temperature differential will be presented to the heat exchanger. This same advantage is obtained when using air-cooling directly on the fluid member; however, here it is not necessary to route the oil externally. Therefore, the simplified lubrication system of Fig. 11.4.1 can be retained. It should be noted that in both systems, the oil to the cooler is first routed through the regulator valve in such a manner that, if pressures drop below regulation, the flow to the cooler is cut off. There is a very good reason for this in that an all-out effort is made to protect the clutches and bands. At very low speeds and higher temperatures, pumps are not able to maintain regulated pressures; therefore, to minimize the demand on the pump, the flow to the cooler is cut off. Momentary loss of flow to the cooler and lubrication system is not serious at lower speeds because loads are light. On the other hand, loss of pressure to a clutch or band can be very serious if it permits slip. In Fig. 11.4.1, a compromise has been provided in the use of a bypass orifice to the cooler. If conditions are such that the pump does not provide regulated pressure and the main flow to the cooler is shut off, the bypass will still maintain a small amount of flow to the cooler and lubrication system. One must be very careful in the selection of this orifice size so as not to impair the operation of the controls and clutches; however, its advantage is in cooling for city traffic operation. It cannot be said that there is any one system best for all transmissions. Each is intended to do a specific job for the particular type of transmission being considered, and all factors must be weighed in the design stages.

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and the inner seals of a piston are usually hotter than the outer. This may not be true for a piston seal during a clutch shift under heavy load. No temperature is shown for the fluid member, since this is a function of the load imposed and the type of cooling circuit employed.

Fig. 11.4.1  Oil from pump to cooler system. Fig. 11.4.3  Temperature variation throughout transmission.

11.4.3 Cooling Tests Cooling tests should reflect, with sufficient margin of safety, the type of service to which the vehicle will be subjected. With the mobility of today’s passenger cars, a cooling system must be capable of handling many different driving situations. Owners living in a northern climate should experience no cooling difficulties in their area; however, they may spend their winters in Florida or their summers in the West, hauling a four-bedroom house trailer up the mountains.

A very important and often overlooked step in determining the cooling requirements of a transmission is the selection of locations where temperatures are to be measured. An error here may be very misleading to the design engineer in the selection of materials, and may also be misleading in retests where changes are being evaluated for their effect on cooling. In working with a new design, it is customary to explore the entire transmission with thermocouples to find unusual hot spots and also to locate one position that will represent the highest temperature of the major portion of the transmission. This location should be free of rapid fluctuations and is important for fluid life tests.

Pikes Peak Tests—One of the best-known sites for transmission cooling tests is the Pikes Peak toll road at Colorado Springs, Colorado. The popularity of this testing ground is understandable, since the performance of many items on a vehicle can be evaluated at this one location. With daytime ambient temperatures possible from 85°F at Colorado Springs to below freezing at the summit, one can check both heater and air-conditioning operation in the same day. The extremely dusty road up the Peak provides quite a challenge for body sealing and engine filters. The effect of altitude on engine performance can be determined on the way up and brake performance can be checked on the way down. Although it is true that the drive up Pikes Peak does not represent the average customer’s daily driving habits, it does present a severe requirement for engine and transmission cooling. Engineers consider that adequate cooling has been provided if temperatures can be limited to 275°F.

To illustrate some of the temperature variables throughout a transmission, Fig. 11.4.3 shows that with a 250°F sump temperature, the front generally runs hotter than the rear,

Testing techniques may vary somewhat on the Peak, but experience has shown that in normal driving conditions, the highest temperatures are encountered with slow drivers.

Fig. 11.4.2  Oil from fluid member to cooler system.

11.4.2 Temperature Measurements

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Although test specifications outline a specific choice of speeds and gears for average use, road conditions and tourist congestion will automatically limit the test speeds. In contrast, oil flow and airflow are generally in abundance for operation on the Peak, since one is forced to increase engine speeds to negotiate the switchback roads. The addition of cooling area in the transmission heat exchanger, or the addition of cooling fins on the fluid member for air-cooling, is very effective in improving cooling at Pikes Peak.

mary cause of failure heat. This rebuilder was well aware of temperature in transmissions; in fact, he has devised his own test route for checking out transmission cooling.

City Driving—Transmission cooling in city traffic is the extreme opposite of that required for Pikes Peak and presents one of the most difficult cooling problems. Engine speeds are low and much of the time is spent at idle. It is here that the size and efficiency of pump and the amount of internal leakage play a very important part in maintaining oil flow to the cooler. As the temperature rises in a transmission, it becomes increasingly difficult for the pump to maintain regulated pressures at lower speeds. In Fig. 11.4.4, the volumetric efficiency is decreasing with rising temperature; at higher temperatures, the flow to the cooler is represented in Fig. 11.4.5. Studies of operation in city traffic indicate that pump speeds rarely exceed 1800 rpm, and the majority of the time is spent below 1000 rpm. It can be seen that very little oil flow to the cooler is available for this type of service. It is here that the bypass orifice (Fig. 11.4.1) offers improved cooling. The effect of the bypass orifice is shown in Fig. 11.4.5 by the difference between the low-speed dotted curve and that shown with triangles. During stop-and-go driving, the bypass will provide oil flow to the cooler even at idle. The dashed line in Fig. 11.4.5 shows what happens to the normal cooler flow as the temperature rises and/or internal leaks are increasing. This is characteristic of what happens in all transmissions at extremely high temperatures and might be termed progressive failure of the cooling system. If a temperature is reached at which stabilization has not been achieved with a given rate of heat input, the pump becomes less able to carry this heat away through its cooler flow, and temperatures will go out of control. At this point, increasing the size of the cooler will be of little help, because the heat is just not getting out of the transmission. The most effective way of improving city traffic cooling is to increase pump size and reduce leakages. New York City is a severe test on transmission cooling. This is primarily due to the extremely congested traffic conditions and the narrowness of streets restricting air cooling. A large rebuilder in New York estimated the average automatic transmission life in his area to be 30,000 miles, with the pri-

Fig. 11.4.4  Effect of temperature on pump volumetric efficiency.

Fig. 11.4.5  Loss of oil flow to cooler by leaking seal ring. Turnpike Driving—With the efficiency of today’s transmissions, expressway driving does not present a serious problem in transmission cooling. If satisfactory cooling has been provided for city traffic and Pikes Peak operation, overheating should not occur on turnpikes. However, we must be watchful of this situation, because these road improvements encourage owners to hitch up their ranch home on wheels. Laboratory Hot Tunnel Cooling Tests—To omit the variable of ambient and to be able to test year round, it is desirable to bring cooling tests into the laboratory. Facilities are available for controlling air temperature, air speed, car speed, and/ or load for almost any driving situation. However, it must be stressed that one should never depend on the hot tunnel for the complete solution to transmission cooling problems. It is a wonderful tool for making comparisons of different proposals, but correlation with actual driving conditions should be made.

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11.4.4 Temperature Effect on Rubber Parts With complete test data on the operating temperatures of a transmission, designers may determine whether the materials they have chosen will give good service life. Unfortunately, most materials with a greater ability to resist deterioration from heat also have a higher price tag. This forces cost-conscious designers to be careful in their selection of materials. The relationship between cost and temperature resistance is shown in Fig. 11.4.6.

alarming loss of tensile strength at 250°F. Immersion heating tests will show silicone to swell up to 30%. Technicians will insist that this material just will not work in a transmission. Apparently, the transmission will not listen to the laboratory. BA-12, on the other hand, seems to behave very well for tensile, tear, and swell properties, but it is not nearly as good as silicone for resistance to heat. Materials for seals must never be selected for their heat resistance alone. The entire environment must be considered.

Although compounding materials will vary between seal suppliers, and some differences will be found in the heat resistance of a particular type of seal, there are only four basic classifications used in transmissions today: 1. 2. 3. 4.

Buna N Polyacrylate (PA-21) Butylacrylate (BA-12) Silicone

These materials are presented in graphic form in Fig. 11.4.7, with a temperature rating based on the type of environment to which they are subjected. Because temperatures will vary throughout a transmission, it may be possible to use some of the less expensive materials with complete success. Buna N, for instance, performs better when completely immersed in oil rather than when partially exposed to air. This compound has been used successfully for static O-ring gaskets, liners for rubber oil hoses, and in some cases for the transmission rear seal. Failure in Buna N is characterized by hardening and cracking. These cracks will start in the thin sections of a lip seal and may be so minute that the seal must be flexed to make them visible. On the other hand, advanced cases may show complete separation of the seal. Buna N has been used in the past for clutch piston seals, but with the introduction of the polyacrylates, this is rapidly becoming a thing of the past. PA-21 (Fig. 11.4.7) will give good service up to 300°F, and appears to be compatible with most of the current transmission fluids. This material does not harden with age, but does appear to become “lazy” or lose some of its liveliness after a time. This probably accounts for its not being completely accepted in the rotating shaft seal field. In using this material, one must be careful of surface irregularities and carefully pilot the piston in its bore. Rotating shaft seals are predominately made from the BA-12 and silicone compounds. In Fig. 11.4.7, there are two temperature ratings for silicone. In spite of excellent success by most of today’s transmission manufacturers in using silicone for front pump seals, laboratory tests show a remarkable and

Fig. 11.4.6  Cost for higher-temperature rubber.

Fig. 11.4.7  Temperature resistance of rubber.

11.4.5 Transmission Fluid Life The effect of heat on transmission fluid has received a great deal of engineering attention in past years. Simultaneous with use of the first automatic, it was recognized that this fluid would be called upon to do some unusual things. The petroleum industry has done a remarkable job of improving resistance to heat and oxidation in transmission fluids. A testimonial to this fact is the recent confidence shown by a

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few manufacturers in the elimination of their recommendation for drain intervals. Those manufacturers who do specify drain intervals do so on the basis of miles the vehicle has been driven (Fig. 11.4.8). The variation in drain recommendations probably reflects the conservatism of some manufacturers rather than the differences in fluid life. While one manufacturer may base the recommendation on the worst type of driving the vehicle could be subjected to, another may be specifying for the average driver. In either case, using mileage as a yardstick for fluid life is far from accurate. Inspection of the fluid in the first stages of failure will show a dark brown appearance. It is difficult for an owner to catch this point of failure because the time or mileage difference between this slight change in color and heavy sludge is very short. Chemical analysis of the fluid, although impractical for field use, appears to be the only method available today to determine the condition of the fluid prior to failure. With the extensive use of red dye in transmission fluids, owners would be grateful for a color change to yellow or green prior to fluid failure; however, for the moment, mileage must be the measure for refill recommendations. Transmission fluid fails as the result of being exposed to temperature and aeration for prolonged periods of time. As seen in Fig. 11.4.9, it takes little temperature rise to accelerate rapidly the rate of fluid deterioration. Although the shape of this curve will not change for any given situation, the life scale will be affected by the quality of fluid and the type of transmission being considered. The fluid life of any transmission is usually arrived at through a series of laboratory tests, vehicle tests, and the evaluation

of field service information. For a new design, this last item will not be available.

Fig. 11.4.9  Fluid deterioration rate doubles for every 17°F rise in temperature. Bench Testing Fluid Life—Today there are as many oxidation tests for transmission fluid as there are different transmissions on the market. This is rightly so, since each design will affect the life of its fluid. This is why full-scale transmissions are used in bench tests, driven by either an electric motor or gasoline engine and accurately controlled for cycles, speed, and temperature. Heating is accomplished by either creating inefficiency within the unit (such as by a reversed stator), shifting clutches, or placing strip heaters on the bottom pan. The objective in any fluid life test is to determine the number of hours at a given temperature that a fluid will remain usable in a particular transmission. The fluid can be considered as having failed when sludge and varnish have formed to the point at which these deposits will not be removed by draining. The fluid must be considered as having failed when transmission operation has been so

Fig. 11.4.8  Manufacturers’ recommended oil changes. 11-24

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severely impaired that a refill will not correct the malady. Chemical analysis of the fluid, mentioned earlier, is used extensively in charting the progress of a laboratory fluid oxidation test. Figure 11.4.10 shows that the fluid base number will go to zero when failure occurs. At this point, the acid number will rise sharply (Fig. 11.4.11). With the base number at zero, protection against oxidation is depleted, and rapid formation of sludge and varnish begins. Figures 11.4.10 and 11.4.11 also show how this rate of deterioration doubles when the temperature is increased by 17°F. When a complete set of acid and base curves for the entire range of operating temperatures has been established, any transmission can be analyzed for its fluid life expectancy.

Again, we must employ our chemical analysis technique and apply it to fluid samples from high-mileage vehicle tests that represent owner service. Usually, time will not permit running the fluid to failure in a vehicle, and therefore it may be necessary to gain a thorough understanding of the average operating temperature throughout the test. By using the bench tests for comparison of acid and base numbers, and applying the doubling factor for every 17°F rise in temperature, the miles to failure may be extrapolated. To gain further insight into the factors that affect fluid life, and to simplify our discussion, let us refer to the acid and base numbers as simply percent additive protection against oxidation. As a baseline, Fig. 11.4.12 shows that for a vehicle operating at 275°F and achieving 15,000 miles before fluid failure, its mileage would be approximately doubled at 260°F operating temperature. When varnish and sludge deposits are allowed to accumulate in a transmission and are not thoroughly cleaned out, the life of the refill will be reduced, as indicated in Fig. 11.4.13. Fluid life is reduced approximately 60% when the total sump capacity is reduced only 30% (Fig. 11.4.14). These data point up the necessity of running consistent fluid levels and taking a minimum number of samples when testing. Earlier in this paper, credit was given to the petroleum industry for these improvements in transmission fluid. This improvement is shown in Fig. 11.4.15, which compares a good Type A fluid to a good Suffix A fluid. Manufacturers using one of the top grades of Suffix A fluid for factory fill may find that their owners use the minimum-grade Suffix A for refill and are not obtaining the mileage recommended. This again points up the desirability of a simple test in the field for determining the need for changing fluid. Mileage is certainly no accurate yardstick of fluid life in a transmission, but it is all we have.

Fig. 11.4.10  Effect of higher temperature on transmission fluid base number.

Fig. 11.4.11  Effect of higher temperature on transmission fluid total acid number. Vehicle Oxidation Tests—Bench tests alone cannot be used as a means of determining refill recommendations. Vehicle operation represents an accumulation of a number of different temperatures for varying lengths of time, whereas bench tests reflect one temperature for a specific length of time. The problem is therefore to convert bench test hours into vehicle test miles.

Fig. 11.4.12  Effect of 17°F temperature rise on transmission fluid life.

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satisfactorily at this temperature, at subzero temperatures it may not have enough fluid. Figure 11.4.16 shows the effect of temperature on fluid level in a transmission. Although, in this particular case, a shallower pan has the advantage of reducing the level rise at higher temperatures, the level sensitivity is increased at lower temperatures because the pan is more completely filled with controls. Transmissions are checked for level more frequently in the 100° to 200°F range, where more error in level will be introduced.

Fig. 11.4.13  Effect of sludge and varnish deposits on refill life.

Fig. 11.4.16  Variation of fluid level with temperature.

Fig. 11.4.14  Effect of reduced volume on fluid life.

11.4.6 Temperature Effect on Transmission Operation Up to this point, deleterious effects of temperature on various components throughout the transmission have been discussed. Although designers will strive to make their unit perform consistently throughout the entire temperature range, usually a compromise must be made.

Fig. 11.4.15  Type A versus Suffix A fluids, 275°F. Temperature Effect on Fluid Level and Foam—With the compacting of today’s transmissions and operating temperatures ranging from subzero to 300°F, the fluid level in transmissions has become very critical. In past years, manufacturers have allowed as much as a 1-qt variation in level. Today, however, many transmissions require levels accurate to 1 pt for optimum performance. Fluid levels change so drastically with temperature that, in some cases, it is necessary to specify the temperature at which the level should be checked. In some cases, even if a transmission is only 1 qt low at 160° to 200°F and is operating

Most noticeable to any operator is the effect of temperature on the unit’s shift feel. Many factors—such as the type of valve body material, leakage in the clutch unit, the type of friction material, and the type of fluid—play an important part in the effects of temperature on shift feel. It may be necessary to make adjustments in these, as well as to consider other factors that make possible a combination least affected by temperature. Figures 11.4.17 and 11.4.18 represent the effect of temperature on clutch and fluid friction. Here we see a completely opposite trend. Both curves use the same type of friction material, yet with one type of oil, the friction decreases as the temperature rises, whereas with another type the friction rises. With rising temperatures, one would expect shifts in Fig. 11.4.17 to become softer and longer in duration, and this can be compensated for by adjusting the size of the feed orifice to the clutch. The orifice will appear larger at higher temperatures, giving a faster apply to the clutch. The opposite condition will be experienced if the fluid in Fig. 11.4.18 is 11-26

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used, and controls must be provided to handle this change of friction with temperature.

11.5 Temperature Control and Fuel Consumption

The effect of temperature on shifting a fluid coupling is similar to that shown in Fig. 11.4.18, except that the rate of fill rather than friction is affected. At low temperatures, the feed must be as large as possible to avoid delay in the shift. However, as the temperature increases, the feed must be restricted to avoid abrupt shifts. This is accomplished by employing a bimetallic strip to close off one of two feed holes as temperatures rise. Thermostatic elements have also been used successfully in problems of delayed shifts at low temperatures with conventional clutches. By using the spring tension of a bimetallic strip directly on the throttle valve, in opposition to the force generating throttle valve pressure, an earlier shift schedule can be obtained at low temperatures.

The goal for continuous fuel economy improvement has focused on, among other things, methods to reduce parasitic losses within the vehicle powertrain. As is commonly known, the transmission viscous drag from friction elements and other rotating components can be improved with a reduction in transmission fluid viscosity. Since fluid viscosity is reduced as transmission temperature increases, a rapid warm-up in transmission oil temperature is a key objective. The following section describes a modified transmission cooling system that provides a more-rapid and complete warm-up for the transmission. This section is mainly adapted from SAE 200101-1760 and explains the fuel economy benefits that result with the use of a cooler bypass system that restricts flow from ambient to a desired operating temperature (approximately 80°–90°C).

Every design will have its own peculiarity as to temperature effects on operation. There are many simple devices that can be employed to handle problems created by temperature. With a knowledge of the few basic devices and a thorough understanding of the materials used in a particular design, engineers should have no trouble coping with the temperature problems in transmissions.

Fig. 11.4.17  Temperature effect on clutch friction.

It has become crucial for vehicle manufacturers to find ways to increase vehicle fuel economy because of the stringent, mandated fuel economy standards. The transmission plays a key role in the overall efficiency of the vehicle’s powertrain. Because the peak efficiency of an automatic transmission typically occurs at its targeted operating temperature, the more quickly a transmission achieves that temperature, the better its average efficiency for any given trip will be. With improved efficiency, the transmission allows the engine to consume less fuel, yet deliver the same or better vehicle performance. A transmission cooling strategy using a thermostatic coldflow bypass to divert fluid around an oil-to-air heat exchanger showed, in tests conducted, an improvement in warm-up rate over a baseline system that had an in-tank cooler plus an auxiliary oil-to-air system. The baseline system included an auxiliary cooler because one is typically required for any use greater than strictly light-duty service. The proposed system was based on a fully oil-to-air cooler because they generally perform better under grade conditions and provide lower mean life ATF temperatures. The thermostatic bypass can be used with an OTW, in-tank cooler or with an OTA, oil-to-air cooler. Its use with an intank cooler, however, will show less benefit due to the warming of the ATF that already occurs from warm-up of the engine coolant. The difference in warm-up rates is drivingand-route-dependent because the engine coolant temperature will rise more slowly on a low-power-demand route and the heat from transmission inefficiency will vary substantially depending on speed and torque delivered. Figure 11.5.1 illustrates the baseline transmission cooling system which includes an oil-to-air auxiliary cooler. With this system, the oil has access to the transmission cooling

Fig. 11.4.18  Temperature effect on clutch friction. 11-27

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Fig. 11.5.1  Baseline transmission cooling system. circuit under all operating and ambient temperature conditions, whether or not cooling is required. The temperature of the oil is dependent on the temperature of the engine cooling system. Figure 11.5.2 illustrates the proposed system with a standalone OTA transmission cooling system and a thermostatic cold-flow bypass. The bypass valve senses the oil temperature and determines whether the oil requires cooling. With this system, the temperature of the oil is independent of the engine cooling system temperature. Figure 11.5.3 shows the operating characteristics of the coldflow thermostatic bypass valve. The flow through the transmission oil cooler is zero until a predetermined temperature

Tb is achieved. When temperature Tb is achieved, a portion of the flow is allowed through the transmission oil cooler. Once the oil temperature has reached the predetermined temperature Tc, 100% of the oil flow is directed through the transmission oil cooler. Test Plan—Testing was conducted at the Imperial Oil All Weather Chassis Dynamometer (AWCD) wind tunnel located in Sarnia, Ontario, Canada. This facility was chosen for its ability to control ambient temperatures, vary loads, and measure vehicle fuel consumption. A special fuel cart was designed to accurately measure the mass of the fuel consumed by the vehicle during testing. The fuel cart was connected directly to the engine fuel rail system to allow

Fig. 11.5.2  Standalone OTA transmission cooling system with bypass. 11-28

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temperature. Continue blowing 100 km/h air over vehicle until all fluid temperatures reach desired ambient temperature. 5. Run 100 km/h road-load condition for 30 minutes. Results The key parameters used for fuel consumption analysis were fuel mass flow rate, transmission system temperature, engine speed, and distance traveled. Fuel flow was monitored as a mass flow rate to give a better understanding of the amount of fuel consumed by the vehicle.

Fig. 11.5.3  Operational characteristics for the cold-flow thermostatic bypass valve.

for an accurate monitoring of the fuel flow. A total of 21 parameters were monitored during testing at a sample rate of once every ten seconds. In addition, 13 of the 21 parameters were concurrently sampled at a rate of twice per second. This was done to capture any slight fluctuations that may have occurred while the vehicle was operating. The data that was sampled twice per second included the fuel mass flow rate and transmission system temperature. The vehicle was tested at both road-load and grade-load, trailer tow conditions; but an analysis indicates that the benefit could only be measured at road-load conditions so only those results are included here. The road-load condition assumed a gross vehicle weight (GVW) of 3250 kg. For a given ambient temperature, the vehicle was first tested with the standalone OTA transmission cooling system with bypass, and then testing was repeated with the baseline transmission cooling system. A total of four different ambient air temperatures were tested: 25°C, 10°C, 0°C and –20°C. Test Conditions (steady-state, road-load conditions) 50 km/h road-load at 3250 kg GVW 100 km/h road-load at 3250 kg GVW For all test conditions, the heat was turned off in the vehicle. Although not typical driver usage, this was done to provide consistency across all ambient conditions. Also, leaving the heat off would be a benefit to the conventional system because this would cause the thermostat to open earlier. Test Procedure—Road-Load and Trailer-Tow 1. Soak vehicle at desired ambient air temperature for a minimum of 8 hours. 2. Run 50 km/h road-load condition for 30 minutes. 3. Set test cell temperature to 20 degrees below desired ambient and blow 100 km/h air over vehicle. 4. When the transmission oil temperature reaches the desired temperature, return test cell to desired ambient

Statistical analysis was applied to the data collected. Fuel mass flow was measured twice per second. A sixty-datapoint sliding average was applied to the fuel mass flow rate to dampen the pulse width fluctuations of the fuel injectors. The remaining parameters monitored were reported in their absolute values. Calculated numbers include the volume of fuel consumed and vehicle fuel economy. Vehicle fuel economy was calculated from the mass of fuel consumed during the test. The specific gravity of the wintergrade fuel used was 0.724. This fuel was used for all ambient test conditions to allow for consistency. Once the volume of fuel consumed was calculated, this value was combined with the actual vehicle distance traveled to calculate the overall vehicle fuel economy for the test conditions. The combined average fuel economy over all four temperature ranges for the 50 km/h road-load condition showed a fuel economy of 17.01 mi/gal for the transmission with cooler bypass system and 16.32 mi/gal for the baseline cooling system. This equates to a 4.2% fuel economy improvement at this light-load condition. The combined average fuel economy for the 100 km/h roadload condition showed a fuel economy of 14.97 mi/gal for the transmission with cooler bypass system and 14.60 mi/gal for the conventional cooling system. This equates to a 2.5% fuel economy improvement.

11.5.1 Conclusions The fuel economy under the conditions tested shows a significant improvement for an OTA cooler with a cold-flow thermostatic bypass valve over a baseline OTW system with an auxiliary OTA cooler. The fuel economy improvement on the EPA cycles, however, would be less because the percentage measured only applies to the fuel used during steadystate cruise operations. The EPA cycles involve periods with higher-load accelerations occurring, and the improvement in parasitic loads is much less significant than during the steady-state cruises.

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A proper transmission thermal management system will benefit the transmission operation, as well as provide an improvement in fuel economy. The addition of the thermostatic, cold-flow bypass valve represents a significant improvement in the overall thermal management of an automatic transmission.

11.5.2 References 1. Semel, R. R., “Fuel Economy Improvements Through Improved Automatic Transmission Warmup—Stand Alone Oil to Air (OTA) Transmission Cooling Strategy with Thermostatic Cold Flow Bypass Valve,” Paper No. 200101-1760, SAE International, Warrendale, PA, 2001. 2. Semel, R. R., “Improved Automatic Transmission Warmup—Stand Alone Oil to Air (OTA) Transmission Cooling Strategy with Thermostatic Bypass Valve,” Paper No. 2000-01-0963, SAE International, Warrendale, PA, 2000. 3. Semel, R. R, “Stand Alone Oil to Air (OTA) Transmission Cooling Strategy.” 1999 Vehicle Thermal Management Systems (VTMS4) Conference Proceedings, Paper No. C543/088/99. 4. Soldner, J., “A New Compact Cooling Module for the Heat Management of Passenger Cars,” 1999 Vehicle Thermal Management Systems (VTMS4) Conference Proceedings, Paper No. C543/036/99. 5. Willermet, P. A., “ATF Bulk Oxidative Degradation and Its Effects on LVFA Friction and the Performance of a Modulated Torque Converter Clutch,” Paper No. SAE982668, SAE International, Warrendale, PA, 1998. 6. Deen, H. E., “Automatic Transmission Fluids—Properties and Performance,” Paper No. SAE-841214, SAE International, Warrendale, PA, 1984.

11.6 Design and Validation of Automatic Transmission Lubrication Circuits James T. Gooden Automatic Transmission Engineering Operations, Ford Motor Co. Automatic transmissions are made up of numerous parts that slide, rub, and heat up during operation. These parts would fail quickly without some mechanism to remove this heat and reduce friction. The general purpose of a transmission’s lubrication circuit is to extend the life of these components by supplying enough oil to ensure adequate cooling and minimal wear.

to make after a cross-section freeze. This paper will describe the planning steps involved in designing a lubrication circuit for a new transmission program.

11.6.1 Nomenclature A = Area B = (Regression Coefficient) c = radial clearance cd = discharge coefficient d = diameter Dh = hydraulic diameter Dm = mean diameter ρ = density e = eccentricity l = length of passage M = (Regression Coefficient) N = (Regression Coefficient for Eq. 11.6.9 only) N = rotational speed (rpm) ΔP = pressure drop Pc = centrifugal pressure Q = volumetric flow rate ri = inner radius ro = outer radius R = fluid resistance S = wetted perimeter μ = dynamic viscosity ω = angular rotational speed (rad/sec)

11.6.2 Identify Parts Requiring Lubrication Before a lubrication circuit can be designed, the parts requiring lubricating oil must be identified. Most parts require lubricating oil for localized cooling or for producing an oil film. Additionally, some transmissions have parts that use oil from the lubrication circuit for special needs, such as to fill a clutch balance dam to offset centrifugal forces of an adjacent clutch piston or to fill a mechanical diode to dampen motion of its internal struts. Typical parts that require lubrication flow: • • • • •

One of the greatest challenges with establishing a robust lubrication system is that significant changes are very difficult

Radial Needle Bearings Thrust Needle Bearings Bushings Thrust Washers One Way Clutches

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• • • • • •

11.6.4 Establish Oil Delivery Strategy

Mechanical Diodes Bands Clutches Balance Dams Planetary Gearsets Rotating Seals

The first steps towards designing the lubrication distribution system are: • Partition the transmission into zones • Establish sources of oil flow • Establish oil distribution circuit

11.6.3 Establish Lubrication Flow Targets to Each Component

These steps are highly iterative and simultaneous.

This step serves two important purposes. The more obvious purpose is to help establish distribution targets; the less obvious purpose is to help establish the capacity of the pump. If the flow targets are too conservative, the capacity of the pump will be over-designed, leading to reduced fuel economy, higher costs, and larger package space requirements. If the flow targets are inadequate, the capacity of the pump can be under-designed, potentially leading to compromises in component durability. It is important to recognize that once the pump capacity is established, it is very difficult to make changes to it later.

11.6.4.1  Partition the Transmission into Lube Zones

The process of quantifying oil flow requirements of each component will not be covered in the scope of this paper. The following comments, however, are provided to help develop robust requirements: • The lubrication flow rate targets should be established as a function of operating load and speed. Most components will need less oil at low input speeds when pump capacity is lowest and need more oil at high input speeds when pump capacity is highest. • Some components may only require oil in certain gears. For example, planetary carriers, one way clutches, balance dams, rotating seals, bearings, bushings, and washers do not need any oil flow at all in gears where there is no relative motion. • Whenever possible, tests should be run to verify what the oil flow requirements to critical components actually are. • In general, under moderate speeds and loads, needle bearings, bushings, washers, and rotating seals are viewed as requiring minimal oil flow (under 0.1 L/min). • One-way clutches and mechanical diodes tend to need slightly more (at or around 0.1 L/min). • Friction clutches and planetary gearsets will tend to need the most oil (between 0.1 L/min and 1 L/min). These target flow rates can vary significantly from one application to the next; however, they do tend to fall within the range described.

Lube zones are created to simplify the efforts to distribute oil to the required parts in the transmission. For example, many rear-wheel-drive transmissions partition their lube circuits to have a “front zone” and a “rear zone.” The front zone delivers oil to components near the front of the transmission; the rear zone delivers oil to components near the rear of the transmission. Other rear-wheel-drive transmissions may only have one lube zone, where oil is introduced into the lube circuit at one end of the transmission and is expected to deliver the target oil flow to every component in the transmission. For front-wheel-drive transmissions, the transmission usually will have two zones for the front and rear of the barrel plus another for a differential unit. Distribution efforts can be simplified significantly by partitioning the transmission into two or more zones. More zones means that each zone delivers oil to fewer components. Different zones can be designed to have different pressure or flow scheduling to compensate for changing delivery requirements. 11.6.4.2  Establish Lube Sources Each zone will need a source of lube flow controlled in a way to ensure adequate distribution. Cooler return is a common source of oil for lube circuit zones, but sometimes other sources are used. One pitfall to avoid when establishing the sources of lube is to make sure that rotational effects will not impede efforts to distribute oil as intended. For example, if a lube source is a controlled pressure that feeds into a spinning shaft, the shaft will produce a centrifugal head that will impede oil flow into it. There is a risk that the flow rate can be reduced significantly at high rotational speed. Similarly, if two zones are fed oil by that same controlled pressure source and one zone tends to have decreasing back pressure at high speeds and the other increases at high speeds, the first may get all of the oil at high speeds. If that does not match the intended distribution targets, the risk of lube starvation problems increases.

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To prevent such zone distribution problems, different sources should be used to deliver oil to zones that have different back pressure characteristics as a function of rotational speed. Some typical sources include cooler return, line pressure, and a dedicated valve. Cooler Return as a Source Most automatic transmissions in the automotive industry use cooler return as the source of oil flow for their lube circuits. This is the coolest oil in the transmission, which leads to better component cooling and thicker oil films. Another advantage is that it is in series with another hydraulic system (the cooler and usually the converter), which reduces the pump capacity requirement. The primary disadvantage is that the pressure/flow rate schedule is not always aligned with the requirements of the lube circuit. For example, many torque converters have pressure limit valves to minimize the effects of converter ballooning, which might compromise the desired lubrication circuit flow rates at high speeds. One pitfall that is easily overlooked is that the main control system in many transmissions is designed with some form of priority schedule. This means that pump output is first used to support line pressure and other main control functions, while the cooler circuit gets whatever is left. If the pump is not sized appropriately, cooler flow (and lube flow) can be compromised. A common operating condition that produces this problem is hot weather trailer towing in city traffic, where line pressure is high, the oil is very hot, and pump speeds are low. With the high temperature and line pressure, leaks in the controls will increase, so higher flow rates are needed to support line pressure. For similar reasons, pump output decreases. Both will compromise the flow rate of oil available to the cooling and lubrication circuit. Taking this concern into account when establishing the size of the pump minimizes this problem. Another pitfall to avoid is any compromise to lube flow from extremely cold weather. Oil will not flow well in the cooler or cooler line when at temperatures below freezing. To prevent frozen cooling systems from limiting oil flow to the lube circuit, a cooler bypass circuit must be designed to allow oil flow to the lube circuit during transmission and cooling system warm-up. Line Pressure as a Source As with using cooler return as a source of lube for portions of the transmission, many transmissions will use line pressure (or some related pressure signal that is proportional to line pressure) as a source of lube for one or more lube zones. Line pressure is normally much higher than needed

to deliver the flow rate needed in the lube circuit, so simple orifices are used to step the pressure down and deliver the appropriate flow rate to that lube circuit zone. One advantage with using line pressure is that in general, it increases (leading to more oil flow) under conditions where more lube is needed. For example, many transmissions are designed to schedule line pressure to increase at high speeds and high torque conditions to ensure appropriate clutch capacity. At the same time, higher speeds and loads will lead to higher component lube requirements to maintain necessary cooling rates and oil films. Dedicated Lube Flow Valves Special lube flow control valves can be designed to deliver a specific flow rate or pressure schedule to the lubrication system to better parallel the required flow of the lubrication circuit than the other two options described previously. Few transmissions in the industry use this approach because the benefit does not usually justify the added cost, weight, and package space requirements. 11.6.4.3  Initial Lube Routing After all parts requiring oil are identified, the decisions of how oil can be delivered to them are made. There are four primary methods for delivering lubricating oil to each component, and in order of preference, they are: • • • •

Use the lube circuit to route oil through the part Use the lube circuit to direct oil at the part Direct “barrel splash” at the part Rely upon leaks from clutch circuits

Using the lube circuit to route oil directly through a part is the most preferred method because it is the most predictable method on the list. Unfortunately, most of the parts requiring the highest flow rates, such as planetary carriers and friction clutches, are in locations that are not easy to include within the pressurized portion of the lube circuit. For those parts, the lube circuit is used to direct oil at the parts, where oil splashes from a lube hole or thrust bearing toward the part of interest. Directing “barrel splash” is not a preferred way to deliver oil, but this method can be used effectively for parts that do not produce much heat or friction, such as thrust washers and some thrust bearings, so only a small amount of oil is needed. In many of these cases, these parts are in locations that are likely to receive oil splashing in the barrel, such as against a front or center support or side of the case.

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Relying upon seal leakage from a clutch circuit is not a preferred way to deliver oil to a component and should be avoided if possible. One obvious pitfall with this method is that “calibrated” seal leaks are difficult to design and wide variation can be expected. If implemented carefully, however, the use of seal leaks can be an efficient, low-cost method to deliver lubricating oil to a part. Significant effort should be placed upon ensuring that adequate lube will be delivered to each part in a manner that is easy to control. Ideally, every part requiring lube should have some path leading to it that has a feature that can be changed easily and inexpensively as the distribution is optimized. Ideally, the overall circuit architecture should be designed so that changes to the flow rates delivered to any given path will not significantly affect the distribution of oil to other paths. The ideal way to control the distribution of oil in a given lube zone is to create what some people call a “pressurized manifold” system. In this system, nearly all lube oil is delivered into an axial hole in a shaft and distributed using several radial holes drilled in that shaft near the components of interest. This strategy works very well because the distribution can be tuned easily by either changing the diameter of the radial oil holes, or by changing the number of radial holes drilled in a particular location. Factors that are difficult to control, such as end clearances, will not tend to affect the distribution. Some transmission manufacturers use this lube circuit layout in all of their transmissions. However, many other transmissions do not use this layout, primarily because of the drawback of requiring larger-diameter shafts to offset the stress concentration of the radial holes, which can significantly increase the size of surrounding parts for an undesirably large barrel diameter. Another drawback is that high pressure can be required to deliver the required lube flow rate at high rotational speeds to overcome the centrifugal heads developed. This problem can be avoided by feeding oil into the shaft at one end of it, but that requires axial space that is not normally available. Within the various branches of the circuit, routing a lube path against a centrifugal head should be avoided; i.e., branches of the flow path should flow away from the transmission centerline rather than toward it. Under high speeds, the lube circuit may not have adequate static pressure available to flow against the centrifugal head developed and, as a result, the oil will flow down alternate paths. Avoid routing oil axially past thrust bearings and other areas where end clearances can be expected. There will be a significant quantity of oil leakage under the operating conditions that form an end clearance in that location.

To use oil efficiently, arrange the flow paths so that parts are fed lube oil in series rather than in parallel. This can reduce the amount of lube oil required for a circuit, but it is important to recognize that the oil may heat up after passing through the first part and be less effective at cooling the parts downstream. Usually, a higher flow rate will compensate for the rise in oil temperature. Lube Path for Planetary Carriers The lube path to pinion bearings should be designed to use lubrication oil as efficiently as possible. It is preferred to use a lube catcher to route oil directly through the pinion shafts and into the pinion bearings so that all or nearly all oil directed to the carrier is used to cool the bearings and not merely splashing around them. Because most of the oil is directed into the pinion bearings when a catcher is used, less oil is needed for the carrier overall than for a carrier without a catcher. There is a cost penalty and some axial space needed for a catcher, so catchers can be omitted for lower-speed carriers. One pitfall with lube catchers is that they are not very effective with transmission applications that have stationary carriers that carry relatively high speeds and loads. Lube oil will tend to settle at the bottom of the catcher and only feed those pinions oriented at the bottom. Instead of a lube catcher, the carrier should be designed to deliver pressurized lube to the pinion bearings; for example, by drilling holes into the carrier housing that intersect pinion shaft oil holes directly. The carrier must be designed to allow the oil entering the pinion bearing to exhaust easily. A poor exhaust path will impede oil flow. Many transmissions will cut a radial slot next to the pinion washers to do this. Some planetary designs have incorporated special pinion washer designs that attempt to “pump” oil out of the pinion bearings as they spin. Lube Path for Clutches Most clutches are fed oil by having oil “splash directed” toward a clutch hub, and distributed between each plate pair through oil holes in the hub. The clutch hub should have a dam to help ensure that oil directed to the hub will be routed through the oil holes rather than spilling over the side of the hub. An example is shown in Fig. 11.6.1. Clutch hubs that are produced by a stamping process should have oil holes located in different spline teeth to ensure that oil is distributed evenly. If more than one oil hole is located within a given spline tooth, distribution between the holes can be unpredictable.

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Fig. 11.6.1  Typical clutch hub lube dam. Oil holes in the clutch hub should be sized and spaced so that oil fed to the hub will be directed toward all friction surfaces. One strategy is to place one or more relatively small holes (approximately φ2 mm) at the axial location of each friction surface. Another strategy is to place large holes (approximately φ6 mm) or long slots (approximately 6 × 2 mm) in axial locations that overlap several friction surfaces. An advantage of the larger holes is that the machining is easier and holes will be drilled on fewer planes. An advantage of the smaller holes is that oil is more directly controlled to each friction surface. Distribution Calibration Features A technique that will help control the distribution of oil more efficiently is to try to have every branch of the lube circuit controlled by at least one feature that can be adjusted easily if a change to the distribution is necessary. These features should be from a process that can be changed easily, inexpensively, and without changing the integrity of the transmission. Drilled holes are common calibration features for a lubrication circuit. To adjust the oil flow through the hole is usually as simple as changing a drill bit for a new diameter hole without adding cost or reducing strength of the part. Formed holes, such as cast holes, are desirable because there is little or no cost associated with them other than to put the features in the dies. One drawback is that formed holes will usually have a draft angle to them, which may give different results than a drilled hole. Another is that dimensional variation can be unacceptably large. Depending upon the process, there might be a limit to how small the hole diameter can be. As long as these concerns are investigated, a formed hole can be a good choice. Bushing grooves are moderately effective in tuning in lube distribution. In general, the number of grooves, groove angle,

and the groove shape can be adjusted to tune oil flow distribution. The number of grooves is limited by the diameter of the bushing and is usually less than four for most light-duty transmission applications. The groove angle is usually a standard 30° or 45° angle which can be oriented to "pump" oil in either direction (left to right or right to left) and in some cases, grooves can be placed in both directions if the bushing spins in different directions from one gear to the next. Common groove shapes include triangular, semi-circular, and trapezoidal. These shapes are somewhat standard in size, so basically, a change in shape changes the flow area. For the lowest flow rates, a triangular groove is used (smallest area) and for the maximum flow rates, trapezoidal is used (largest area). Usually, the depth of the grooves is not adjusted, in part because of process limitations. The primary drawback of placing bushings in the flow path of other parts is that the flow area of the groove is quite small, which limits oil flow. Thrust bearings will be within many flow paths in the lube circuit, but are the least desirable feature to use to adjust the flow distribution of oil. One reason is that design changes are expensive and time consuming to make. Spline tooth clearances are also undesirable features to use for adjusting lube distribution. Dimensional variation will add far too much variability to any leak across a spline joint.

11.6.5 Create a Math Model of the Lubrication Circuit Many software tools are available to analyze fluid flow. Computational Fluid Dynamic (CFD) software is the most sophisticated, but not practical for analyzing a transmission lubrication circuit. A one-dimensional lumped sum approach is usually sufficient for modeling the distribution of oil in a lubrication circuit. Many commercial software packages are available that can model lubrication circuits in that manner; however, rotating passages are rarely included in their component libraries and will need to be added manually. Some custom codes and commercial software packages might use a concept known as “electrical analogy” to analyze their hydraulic systems. This concept involves relating hydraulic pressure to electrical voltage and hydraulic flow rate to electrical current to simplify the hydraulic systems analysis by using the concepts used for electrical circuits. One relationship that is used in the electrical analogy concept is fluid resistance, which is the hydraulic equivalent to Ohm’s Law:

ΔP = QR

(11.6.1)

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The fluid resistance for a laminar round line can be determined by rearranging the Hagen-Poiseuille equation to get the relationship:

R=

128µl πd 4

(11.6.2)

Nearly any equation that relates laminar flow rate to pressure drop can be rearranged to indicate a fluid resistance; however, when considering turbulent flow, rotating effects, or other nonlinear losses, the electrical analogy concept is more difficult to apply. Fluid resistance tends to be a common term used to describe the relationship between pressure drop and flow rate even when using software that does not claim to use the electrical analogy concept. The following paragraphs will describe how to interpret what passages in the transmission lubrication circuit should be in the model and what modeling component should be used to represent typical passages. The lube model should include any passage that affects the distribution of oil within the pressurized portion of the lube circuit. Features that might help direct “splash oil” toward other parts should not be included. The boundaries of the lube model can be simplified to start where the oil enters the barrel and end where the pressure is assumed to drop to atmospheric. Oil delivery can be represented by either a controlled pressure or flow source unless there is a desire to include the features in the control circuit that controls the delivery of oil to the lubrication circuit. Drilled holes are represented as simple, round passages that are usually included within the component libraries of most analytical tools. Some tools will automatically include minor losses, such as entry and exhaust losses; however, an orifice of an equivalent flow area can be a reasonable estimate if the component library has no other way to represent minor losses. If the drilled hole is in a part that spins, a rotational head will usually need to be included in the simulation. A limitation of many commercial hydraulic system analysis tools is that they do not have component libraries that account for effects of rotation. If that is the case, user-defined components will need to be added. For spinning radial holes, the following equation can be used: 1 Pc = ρω 2 (ro2 − ri2 ) (11.6.3) 2 If this pressure opposes flow through the spinning hole (flow direction is from the outer to inner radius), this pressure

will be a loss in addition to any viscous or inertia losses. As rotational speed increases, this centrifugal pressure will eventually exceed the inlet pressure available, which will result in shutting off oil flow. If the centrifugal pressure assists oil flow, this pressure will be subtracted from any viscous or inertia losses. It is important to note that as rotational speed is increased, the inlet pressure will eventually be drawn below atmospheric pressure, producing a negative pressure at the inlet of the passage. It is important to limit rotational effects so that unrealistic pumping will not occur. There is a limit to how far the inlet pressure can be drawn negative before the pumping head will effectively “shut off,” and the model must reflect that. Above that rotational speed, the pressure drop across the passage is nearly zero. This characteristic is similar to that of rotating thrust bearings described later and shown in Fig. 11.6.6. For spinning axial holes, rotational effects do not impede or assist oil flow and can usually be ignored. Most annular passages will have negligible pressure drops and can be ignored unless their clearance is small (under 1 mm radial). Usually, any relative motion between the journal and shaft can be ignored as well without compromising the results. It is important, however, to include eccentricity in the model. Equation 11.6.4 shows a common form of the equation that calculates pressure drop of an annular passage. For a given flow rate, the difference in pressure drop between a perfectly concentric annulus and a fully eccentric annulus is 2.5, which is quite significant. −1



2 12µl ⎡ 3⎛ e⎞ ⎤ ΔP = 1 + ⎜ ⎟ ⎢ ⎥ Q πDmc 3 ⎣ 2⎝ c⎠ ⎦

(11.6.4)

Bushings without angled grooves can be represented as an annular passage. Few software packages are available to model the pumping effects of angled bushing grooves. In the absence of a reliable bushing component model, a simple bushing test can be run to characterize the effects of pumping, and a user-defined model can be created to represent those results. As with bushings, thrust bearing component models are not normally available in most commercial software packages. Experimentation has shown that Eq. 11.6.5 works well.

ΔP = R * Q – B * N2

(11.6.5)

The first term represents viscous effects and basically matches the fluid resistance defined in the electrical analogy concept described previously. The second term represents rotational effects.

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The first term can be represented by any laminar passage that uses dimensions calculated to give the same fluid resistance as indicated by a characterization test. Typically, a round line as shown in Eq. 11.6.6 or a pair of parallel discs as shown in Eq. 11.6.7 is used to represent a thrust bearing’s viscous effects. ΔP 128µl R= = Q Q πd 4



R=



ΔP 6µln(ro /ri ) = Q πc 3

(11.6.6) (11.6.7)

Rotational effects are a function of rotating speed squared, but Eq. 11.6.3 cannot be used to determine coefficient “B” because there are two rotational speeds involved instead of one. Merely substituting the average speed or differential speed into Eq. 11.6.3 does not predict “B” reliably. Without a reliable method for calculating this coefficient, test data is needed to determine the value of “B” for each gear state of each thrust bearing. As with spinning radial holes, the rotating effects of thrust bearings must be limited so that the inlet pressure is not drawn farther negative than indicated in the characterization tests. These tests are described later, and this characteristic is indicated in Fig. 11.6.6. Non-round passages can usually be represented by the hydraulic diameter concept without a significant compromise in accuracy. The clearance between teeth in a spline joint is a common application of the hydraulic diameter concept. Figure 11.6.2 shows an end view of a typical spline joint. To calculate hydraulic diameter for this example or any other passage, calculate the wetted perimeter and cross-sectional area of the passage and use Eq. 11.6.8.

Dh =



4A S

(11.6.8)

Many textbooks discourage the use of the hydraulic diameter concept to represent laminar flow in non-round passages; however, the error involved might be acceptable for the intent of many lubrication system analyses. Another approach to represent non-round passages in a lube system model is to run a simple CFD model for that passage to characterize its pressure drop over the expected flow rate range of the application. If the results are linear, the passage can be represented by a simple laminar round hole with a diameter and length selected to give the same resistance as indicated by the CFD results. If the flow is not linear, the passage can usually be represented by an orifice in series with a laminar round hole. A regression analysis of the CFD results can be used to help approximate the appropriate dimensions for the orifice and laminar line component.

11.6.6 Validation of the Lubrication Circuit There are four basic types of tests that are run for lubrication circuits. A lubrication distribution test is a rather expensive, lengthy test that measures the flow rate distribution of the lubrication circuit. A lube zone characterization test is a somewhat basic test that helps to quantify flow rate delivery to each lube zone and characterize the backpressure on the control system. Component characterization tests are intended to quantify viscous losses, inertia losses, and pumping effects of spinning parts. Flow visualization tests use radiation to “see” through the transmission case to watch oil flow distribution in real time. Not all of these tests are necessary to conduct to design a robust lubrication circuit, but each has its own unique purposes. 11.6.6.1 Lubrication Distribution Test A lubrication distribution test determines the flow rate distribution of a transmission’s lubrication circuit for a given input flow rate, transmission input speed, transmission gear state, and supply oil temperature. The results from this type of test include the following purposes: • Confirmation that the lube distribution matches established targets • Assessment of the impact of a transmission design change on the lube system • Confirmation that the analytical lubrication system model results are correct The Test Fixture

Fig. 11.6.2 

End view of spline tooth clearance.

The test fixture is a transmission assembly that has an internal network of seals to isolate lube paths of interest that direct

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oil to drain tubes along the bottom of the transmission for measurement. The input shaft is spun so that rotational effects are monitored and all gears are simulated.

the overall oil flow into each zone. Simply adjusting the flow rate to each zone to represent each temperature is sufficient for most transmission applications.

Internally, the test fixture is designed to include only the transmission components that impact the distribution of lube flow and the components needed to maintain the proper rotational speeds. Usually the transmission components are used unchanged in the areas where lubrication is under pressure. In areas where lube is not pressurized, i.e.,”splashing around,” the parts can be changed as needed to incorporate features that help isolate various lube flow paths for measurement and to incorporate features that allow a mechanical control of gear states. The use of the transmission controls and clutch system to control gear state is discouraged because of the limitations they place on the ability to isolate lube paths for measurement and to avoid inaccuracy from unintended leaks from the clutch circuits.

Input shaft speed should be run from 0 to the maximum speed of the transmission for each gear, preferably in increments of 500 rpm to catch any unusual changes in flow distribution that might occur.

Isolating specific lube paths for measurement requires the use of a network of seals to route the oil from the exhaust location in the lube circuit to the drain tube at the bottom of the case. Many of these seals are large in diameter, which can result in very high surface speeds. Because of the high speeds, care should be taken to ensure that the seal will not overheat and disintegrate during testing. The flow rates from each drain tube are typically measured manually by holding a beaker under a drain tube for a set amount of time (using a stop watch) so that a volumetric flow rate can be calculated. This process is very slow, but the “beaker and stopwatch” method is fairly accurate. Test Parameters Typical test parameters for a lubrication distribution test include: • • • •

Oil flow rate to each lube circuit zone Supply oil temperature Input shaft speed Gear state

Oil flow rates to each lube circuit zone should be set to represent at least a minimum, nominal, and maximum expected flow rate for each operating condition. These flow rates can be obtained from the results of either a hydraulic system model or a lube mapping test. Supply oil temperature can be investigated; however, the distribution of oil does not tend to vary significantly with changes of oil temperature. The most significant impact of varying oil temperature is that the oil viscosity will change and, depending upon the type of controls in place, may affect

Ideally, every gear state should be run. Reverse should be run, but in cases where the test fixture design can be significantly simplified by leaving out reverse, it may be acceptable to leave reverse out if there is a high level of confidence in the analytical results. There is little value in running Neutral unless there is a known problem to monitor. Recorded Data The following data should be recorded: • Flow rates from each drain tube • Inlet pressure Sources of Variation Some common sources of variation between runs and to the model results include end clearance variation, dimensional variation, and miscellaneous fixture issues End clearance variation is a potentially significant contributor to lube distribution variation. Any change in the end clearance will lead to a change in the restriction of the many end clearance gaps adjacent to thrust bearings that are not under load, which changes the flow distribution of the lube circuit. The total end clearance for a given stack path of the transmission is also distributed among several locations. A simple measurement of the total end clearance can help clarify differences between test results of different builds and can be used to update the lube model for comparison purposes. Unfortunately, how this total end clearance is distributed between each clearance location (such as thrust bearings not under load) is completely random and unpredictable. Dimensional variation is somewhat easier to address. Before assembling the test fixture, the dimensions that affect lube distribution, such as hole diameters, should be measured to assist in updating the model to better represent test results. Several issues associated with the test fixture can compromise test repeatability and accuracy. Seal leaks within the fixture can compromise accuracy and can be difficult to detect depending upon the type of seal selected. Inadequate fixture drainage/venting can also compromise accuracy and is very difficult to detect unless the case is modified to have transparent windows to visually monitor internal drainage.

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Data Presentation Each drain tube represents oil flow of a given branch of the circuit. Plotting these results versus input speed for each gear will work well for model validation. To validate that the design meets its objectives, the results will need to be adjusted to represent flow rates to each part requiring lube. For most parts, the flow rates delivered to them will be the flow rates measured from a specific drain tube. Other parts might require adding the flow rates from two or more drain tubes. 11.6.6.2 Lube Zone Characterization Test This type of test is used to determine the flow rate delivered to the lube circuit as a function of various operating conditions of the transmission and also quantifies the backpressure that the lubrication system puts on the hydraulic controls. The results of this test would normally be used to determine the correct flow settings for a lubrication distribution test and lube model and/or confirms that the hydraulic system supplies the quantity of oil to the lubrication system that was established by the hydraulic system model. Test Parameters Typical test parameters that are adjusted include: • • • • •

Input shaft rpm Line pressure Converter state Sump oil temperature Gear state

Each transmission application may require a slightly different list of parameters to control, depending upon the design of the main control assembly. Input rpm has one of the largest impacts on lube flow. Pump output will usually increase with input rpm, increasing flow available to the lube circuit. Line pressure can affect lubrication flow in one of two ways. If a lube circuit zone is supplied oil by line pressure directly or by some other pressure signal that is proportional to line pressure, flow to that lube circuit zone will be proportional to line pressure. If a lube circuit zone is supplied oil from cooler return, flow to that lube circuit can be inversely proportional to line pressure when the control circuit delivers lube under a priority schedule and pump capacity is marginal.

circuit is different for each converter state. In these conditions of higher flow restriction, downstream lube zone flow rates will be reduced. Higher sump oil temperature will lead to reduced pump volumetric efficiency and higher-flow-rate demands in the main control, which can lead to reduced flow rates to lube circuit zones subject to a priority system. Ideally, gear state should not affect the flow rate of oil to the lubrication circuit. Unfortunately, this is not always the case. In each gear state, different clutch elements are on and off. Each of those clutch circuits will have different leakage characteristics, which will introduce some variability in the amount of oil left for the lube circuit. Recorded Data The following data should be recorded: • • • •

Flow rates to each lube zone Cooler flow rate Inlet pressure at each zone Other relevant pressures and flow rates

Lube circuit flow rates are normally measured by routing oil out of the transmission to an external flow meter, and then back into the transmission. This is difficult to do without compromising the data. Care should be taken to ensure that the modifications to the transmissions would not induce restrictions that will compromise the data. Lube zone inlet pressures are also of value to measure for model correlation and for insight into correcting design shortcomings. In general, as many pressures should be measured in the hydraulic system as possible without compromising the data so that relationships between different hydraulic circuits and the lube system can be determined. This information is also of value for model correlation and insight into correcting design shortcomings. Data Presentation Some useful plots include: • • • • •

Converter state can change the flow rate delivered to a lube circuit zone. Usually, the flow restriction through a converter

Restrictions of each lube circuit Restrictions of the cooler circuit Restrictions of the converter circuit Lube circuit flow as a function of cooler flow Cooler flow as a function of pump flow

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Restrictions to each lube circuit, cooler, and converter circuit can be used to help update a system model. This will involve plotting pressure drop versus flow and running a regression analysis. The regression analysis should use Eq. 11.6.9.

ΔP = MQ2 + NQ

(11.6.9)

The first term represents inertia losses. The second represents viscous losses.



Solving for length:

The equation for a round laminar line is:





128µl Q πd 4



(11.6.11)





128µl ρ Q + 2 2 Q2 πd 4 2c d A

(11.6.12)

This implies that the regression coefficients, N and M, can be represented as:

128µl N= πd 4

(11.6.13)

Fig. 11.6.3 

l=

8ρ π 2c d2 M



N ρ M 16πc d2µ

(11.6.15)

(11.6.16)

Knowing that the oil properties at this temperature are:

Placing the orifice in series with the laminar line: ΔP =

d= 4

An example cooler restriction plot is shown with a regression line in Fig. 11.6.3.

Using an orifice equation to represent minor losses: 2 Q = cd A ρ ΔP

(11.6.14)

At this point, this restriction can be entered into a lube model as a laminar line in series with an orifice.

(11.6.10)



ρ 2c d2 A 2

By declaring cd an arbitrary number, such as 0.611, and assuming that the orifice is round with the same diameter as the round laminar line:

The model can be updated easily by representing the inertia term by a representative orifice and the viscous term by a representative round line. One approach to this is the following.

ΔP =

M=



ρ = 0.82 gm/cm3

(11.6.17)



μ = 6.915 cP

(11.6.18)

It can be shown that this cooler can be represented by an orifice with a diameter of 5.07 mm in series with a laminar line of the same diameter and a length of 433 mm. Flow to lube circuit zones (fed by cooler return) as a function of cooler flow can be useful plots. Figure 11.6.4 shows an example lube circuit zone flow as a function of cooler flow. This

Example cooler restriction. 11-39

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Fig. 11.6.4 

Example lube zone flow vs. cooler flow.

example only required a linear fit, which basically implies that this lube circuit receives 26.77% of the cooler flow regardless of cooler flow rate, gear state, input speed, etc. Flow to the cooler circuit as a function of pump flow at different line pressures for each converter state can be useful to

see what conditions are most critical to each variable. Figure 11.6.5 shows an example of cooler flow (which is the source of oil for several lube circuit zones) as a function of pump flow and a specific solenoid current (VFS) that controls line pressure for a locked converter. This plot shows that under low pump output speeds (under 20 L/min) the higher line

Fig. 11.6.5  Cooler flow rate as a function of pump delivery at various line pressures (VFS currents). 11-40

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pressures (lower VFS1 signals) produce lower cooler flow rates than the lower line pressures. For example, at a pump output of 10 L/min, max line/0 VFS1 produces a cooler flow rate of 2 L/min, where min line/1000 VFS1 produces a cooler flow rate of around 6.5 L/min. Above a pump output of 20 L/min, cooler flow is proportional to line pressure (higher flows under higher line pressure). This suggests that there is the potential of a pump capacity issue under the pump speeds that produce a flow rate of 20 L/min. 11.6.6.3  Component Characterization Test Many lube paths cannot be represented in an analytical model by a straightforward textbook equation. When the flow paths are not of a simple geometry, especially if the path is rotating within the transmission, a test may be needed to determine how to represent that passage in a lubrication system model. Some examples of what could be run in a component lube test include thrust bearings, thrust washers, radial needle bearings, and bushings. The following describes how a characterization test could be run for a thrust bearing. Test Parameters Typical test parameters include: • • • •

Flow rate Oil temperature Rotational speed Gear state

Flow rate should be controlled instead of inlet pressure to better represent the environment of the transmission. A controlled oil flow rate will limit the pumping effects because at some critical speed, the inlet pressure will be drawn below atmospheric pressure to a point where pumping effects will cease at higher speeds. If the inlet pressure were controlled instead, the flow rate would “run away” at high speeds until the pump capacity of the test stand is compromised and no longer able to sustain inlet pressure.

effects. If the flow is behaving in a laminar manner, pressure drop versus temperature should change inversely proportional to the viscosity of the oil (which can be determined from the temperature). If the flow is behaving in a turbulent manner, there might be very little difference in pressure drop between one temperature and another. For the purposes of improving the lube model, the temperatures tested should be within the normal operating range of the transmission. Rotational speed and gear state are extremely important to include. It is important to understand that a test like this should be run where the kinematics of the part are accurately simulated. For example, the right and left races of a thrust bearing should spin as they would spin in the transmission application and not merely simulate the same “differential speed” or “average speed” between the two races. The effects of rotation are not a simple function of “differential speed” or “average speed.” Rotational speed should be run at as many speeds as considered reasonable so that the location of the transition region can be understood. The ideal method of adjusting speed is to run a “slow sweep,” which is to slowly ramp the speed from static to a maximum speed condition and take data points along the way. If a slow sweep is not feasible for some reason, running in step sizes of 500 rpm would likely capture any critical speed points of interest; however, finer steps would be even better. A hysteresis trend is typical, showing a much smaller pumping effect for decreasing speed than increasing speed. This can be important to incorporate in a lube model so that the design can protect for operation in both cases. Figure 11.6.6 shows a typical pressure drop vs. rotating speed for a thrust bearing with a fixed flow rate.

At least three flows should be run in the test to help determine whether the flow will behave linearly (suggesting laminar flow) or nonlinearly (suggesting turbulent flow) with pressure to help establish the regression equation. It is recommended that at a minimum, the expected minimum, nominal, and maximum flow rates are run in this test so that extrapolation will not be required when these results are incorporated into the lube model. Supply oil temperature is another common signal to vary. At least three temperatures should be run to verify temperature

Fig. 11.6.6 

Example pressure vs. rpm characteristic of a thrust bearing.

As shown, the pressure drop across the bearing decreases as a function of rotational speed. It can be shown that the

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decreasing trend is a function of rotational speed squared. A rather large negative pressure will develop when the speed is increased until the pressure drops to a significant vacuum, where the pressure drop becomes a value just above atmospheric. When speed is decreased, the pressure does not drop below atmospheric and eventually follows the same path as previously at lower speeds. Recorded Data Typically, pressure drop is the only data that is recorded. Data Presentation The data can be presented in many ways to help understand the pressure drop versus each signal parameter. Some useful plots include: • Pressure drop versus input rpm (for a specific gear state, temperature, and flow) • Pressure drop versus flow rate at 0 rpm Plots of pressure drop versus rpm will help show if there is a similar trend as previously shown in Fig. 11.6.6, which will help set up the regression analysis by identifying each flow region. Plots of pressure drop versus flow rate will show whether the flow rate is laminar and whether there is any interaction between flow rate and rotational speed. Basically, if there is a linear relationship between flow and pressure drop (for 0 rpm), the regression equation can be set up assuming that the flow is laminar. If that slope is similar for higher speeds, then there is no interaction between flow rate and input rpm when determining pressure drop.

inside that test specimen in real time. Basically, the neutron beam will pass through parts with low hydrogen content, including aluminum. The beam will not pass through parts with high hydrogen content, such as organic materials including oil, seals, and friction material. Steel parts have a moderate amount of hydrogen in them, so the beam will only pass through relatively thin steel parts. Generally, when viewing oil flow, neutron radioscopy and most other visualization techniques will indicate the presence of oil, but will not quantify the flow rate of the oil. In other words, these techniques can indicate “no oil,” “some oil,” and “lots of oil” by how dark or thick the oil appears in the image, but will not usually provide more detailed results than that. For most problems of interest, this is enough information to help solve them. Typical Applications The most common transmission application is visualization of oil flow through a pinion bearing. These techniques can help determine if oil flow directed at a pinion gear is flowing through the bearing or merely splashing around the gear. Occasionally, parasitic loss and clutch cooling problems can occur when oil flow between each clutch plate is uneven. For example, in the extreme cases, nearly all the oil directed to a six-plate clutch may go between only one pair of clutch plates, leading to poor cooling between the other plate pairs. The lube distribution test fixture will not be able to address this problem, but neutron radioscopy can be used to visualize the oil flow between the clutch plates and determine the relative distribution of oil between each plate pair by how equally spaced the clutch plates are.

Past results for thrust bearings have suggested that Eq. 11.6.5 will fit the data well.

In general, a heat problem with any part cooled by “splash lube” rather than a pressurized source could be a good application for a flow visualization technique.

11.6.6.4 Flow Visualization Test

Limitations

There will be times where lubrication problems may occur in a transmission, where the testing techniques described previously are not able to identify them. These problems could be issues where a part overheats and the distribution test and/ or model suggests that there is adequate flow. In these cases, there is reason to suspect that maybe something was missed in the distribution test fixture design and/or the lube model. Neutron radioscopy is one of several flow visualization techniques that are available to evaluate lubrication problems.

Each flow visualization technique has a unique set of limitations that must be carefully considered before attempting to proceed further. The resolution of the image is not as good as a photograph, so there is a limit to how small the flow passage of interest can be and still be visible in the image. Other parts made of a material that blocks the radiation beam may block the view of the passage of interest. For example, thick steel will block the view of oil flow when using the neutron radioscopy technique, so when attempting to view oil flow in a pinion bearing, the ring gear must be removed or replaced with an equivalent aluminum part.

Neutron radioscopy is a technique that involves passing a beam of neutrons through a test specimen to visualize oil flow

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Transmission Temperature Control and Lubrication

11.6.7 References 1. Merritt, Herbert E., Hydraulic Control Systems, John Wiley & Sons, New York, 1967. 2. Lindsay, John T. and C. W. Kauffman, “Real Time Neutron Radiography Applications in Gas Turbine and In-

ternal Combustion Engine Technology,” ASME Paper No. 88-GT-214, The American Society of Mechanical Engineers, New York, NY 1988.

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Chapter 12

ATF and Driveline Fluids Craig Tipton Lubrizol Corporation

is included on how to evaluate used driveline oils, describing common test methods and some comments on interpreting the test results. Finally the future direction of driveline fluid development is discussed. A glossary of terms is included at the end. The chapter is divided into the following sections:

Tze-Chi Jao Afton Chemical Corporation Timothy Newcomb BorgWarner

• • • • • • • • • • •

Introduction This chapter is intended to provide an overview of driveline fluids, in particular automatic transmission fluids (ATFs), and is intended to be a general reference for those working with such fluids. Included are an introduction to driveline fluids, highlighting what sets them apart from other lubricants, a history of ATF development, a description of key physical ATF properties, and a comparison of ATF fluid specifications. Also featured are descriptions of the chemical composition of such fluids and the commonly used basestocks. A section

Introduction History of ATF development Key physical properties Basestocks and their impact on performance Chemical composition Driveline fluid specifications Evaluating the condition of used driveline oils Future directions Acknowledgments Glossary of terms Key references

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12.1 Introduction

the engine starting system, and maintenance of flow to the hydraulic pump and its ability to supply oil pressure.

Driveline fluids, apart from hypoid gear oils, are a specialized group of lubricants used in transmission and hydraulic applications in motor vehicles. There are many different types of transmission fluids, including automatic transmission fluids (ATFs), push-belt and chain-type continuously variable transmission (CVT) fluids, manual transmission fluids, dual clutch transmission (DCT) fluids, farm tractor hydraulic fluids, off-highway heavy-duty equipment fluids, torque fluids, and traction drive fluids. These fluids are formulated to meet stringent requirements for clutch friction durability, low-temperature fluidity, anti-wear, and high resistance to oxidation. Functionally, the ATF fulfills four major requirements [12.1, 12.2]:

Flash Point and Volatility: These properties are important and are specified due to concerns over changes in properties due to evaporation of low-molecular-weight components and safety of the fluids during handling or in the factory. Flash and fire points are important in case the fluid is ejected under the hood of the vehicle. Miscibility and Compatibility: The fluid needs to be miscible and compatible both with other ATFs and with itself. The fluids cannot produce precipitates, gel, or show other nonhomogeneities, such as separating out components. These are all detrimental to fluid function and may clog filters and any narrow openings in the fluid system.

1. A torque transfer medium in the torque converter and in clutch interfaces 2. A hydraulic control medium for actuation of valve body and clutch systems 3. Lubrication and protection of gears, bushings, bearings, and seals 4. A heat transfer medium for the removal of excess heat generated, for example, in the torque converter and in clutch engagements

Foam: Foam control is important to retard unwanted fluid volume growth and fluid ejection from the transmission and loss of incompressibility of the fluid for hydraulic function. Corrosion: Corrosion protection is required for ferrous metal rusting when moisture inevitably enters the transmission and for copper and other alloys used in bushings, thrust washers, and electrical control contacts and wires. Organic Materials Compatibility: Compatibility with polymeric-based materials used in the transmission, such as seals, wire insulation, and plastic thrust washers, gears, and filter screens, requires extensive testing for factory fill, but compatibility with elastomeric seal materials are usually the only tests required in service-fill specifications.

Automatic transmission fluid is a large part of the market and is often the most widely available driveline fluid. It finds use not only in automatic transmissions but also as a hydraulic fluid and power steering fluid. The properties of an ATF are very important and enable modern transmission and hydraulic systems to provide good customer perception of shift quality over the life of the vehicle; good fluidity in extremely cold climates for proper hydraulic system response; durability of bushings, bearings, and gears; and the maintenance of physical properties under conditions of oxidative, thermal, and mechanical stress.

Anti-Wear: Anti-wear is an important requirement, and specifications, dependent on the manufacturer, may concentrate on hydraulic pump wear, gear wear, and/or pitting. Resistance to Oxidative and Thermal Breakdown: It does not matter whether a transmission fluid is formulated from a mineral oil or a synthetic base fluid; it is still subject to oxidation during use. Any hydrocarbon-based fluid has the ability to react with oxygen in the air. Thermal breakdown can occur when the conditions of the environment facilitate oxidation and other detrimental chemical reactions. These reactions are deleterious to the fluid properties and in extreme cases can cause complete gelling and solidification of a transmission fluid. Modern ATF specifications universally call for tests to measure thermo-oxidative stability, although the specific tests differ from manufacturer to manufacturer.

To meet the requirements of these functions in a wide range of operating conditions, ranging from –40°C in cold climates to temperatures of 180°C or even higher in extreme conditions of mountain trailer towing or idling in traffic when ambient temperatures are high, a large number of properties, both physical and performance, often appear in specifications for specific reasons: Viscosity: Most specifications, globally, call for similar properties of viscosity at high and low temperature, but they may differ as to viscosity retention during use. This is because some fluids lose viscosity due to mechanical shear of high-molecular-weight chemical thickeners during use. Low-temperature fluidity is important because of the effect on hydraulic system pressure rise times, viscous drag on

Friction and Friction Retention: Precise requirements for friction and friction stability are properties that distinguish ATF from most other fluids. Most automatic transmission manufacturers design the function and control of the transmission around the characteristics of the fluid and friction materials that are employed. Design and control philosophies, 12-2

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ATF and Driveline Fluids

12.2 History of ATF Development

as well as the ratio of power throughput to transmission size requirements, dictate the selection of both the friction material and the fluid properties. Fluids and clutches must have sufficient holding capacity when engaged. When the clutch is engaging, the level of dynamic friction, as well as how the coefficient of friction varies with temperature and speed, affects both durability and the perception of shift quality. The coefficient of friction is a characteristic of the entire clutch system, and the observed friction depends on the nature of the composite friction material, the steel reaction member, and the characteristics of the fluid at various speeds and temperatures. Extended durability testing in clutch friction machines, bench test devices, and actual transmission dynamometers are used to measure the retention of friction to ensure performance over the life of the vehicle. Newer transmissions employing lock-up clutches or controlledslip torque converter clutches have additional requirements of maintaining a positive slope of the speed versus friction coefficient curve to avoid the development of torque oscillations known as shudder.

When automatic transmissions were first introduced in the late 1930s, they were often lubricated with engine oil. Transmissions, however, had different performance requirements than engines, and the use of engine oils for this application was soon found to be inadequate. Some specialized fluids were used in automatic transmissions during the period from the late 30s to 1949 when the first specification to standardize the requirements for a mineral oil automatic transmission fluid was introduced by General Motors and was designated as “Type A.” Importantly, the Type A specification also provided a process for qualification of service-fill ATF through a trademark and licensing procedure. Further advances in this specification occurred because it was found that some Type A qualified ATFs showed deficiencies in oxidation resistance, leading to the introduction of the Type A, Suffix A (or TASA) specification in 1957. During this period, many manufacturers used Type A or Type A, Suffix A fluids for their automatic transmission-equipped vehicles. Ford’s factory-fill fluids met specification M2C33-A-B that describes a fluid with the Type A, Suffix A characteristics. In this time period, transmission fluid service life was fairly short, and frequent transmission oil changes were called for.

Frictionally, the different types of fluids can vary widely. Some fluids have a high static relative to the dynamic friction, while others may have a very low static relative to the dynamic friction. CVT fluids are very similar to ATF, except that they have met special requirements for metal-on-metal friction and wear durability. Off-highway fluids may come in heavier viscosities and have high static friction. Traction fluids may be physically similar to ATF but use special synthetic base fluids that become highly viscous under very high contact pressure. Automotive hypoid gear oils are a completely different class of fluid but can also be categorized frictionally. Table 12.1 shows fluid friction characteristics in very general terms.

Ford introduced the M2C33-D specification in 1961 after it was approved for service fluid use in 1960 model year vehicles. This change was driven by the need for better oxidation control that was measured by the new Merc-O-Matic oxidation test. Also, anti-wear performance and higher static capacity were included. In 1967, both General Motors and Ford again introduced upgraded specifications for their ATFs. Ford’s specification was written with the objective of a “fill-for-life” fluid with improved anti-oxidation, wear, and friction performance. This new fluid was described by the M2C33-F specification and was conventionally called “Type F” [12.3]. It was also a service-fill specification, and Ford granted approvals under the specification, along with qualification numbers. This specification was similar to M2C-33D. Differences included a six-pack clutch friction test that required a high static coefficient of friction. It was felt at Ford that an ATF with a friction curve similar to base oil would undergo less frictional change with time than a fluid that incorporated a chemical friction modifier. The rationale was that the friction modifier could degrade, and the friction characteristics would revert to those of the base oil. Another driving force was to reduce the number of plates in the clutch pack to get a more consistent shift characteristic. Oxidation resistance was increased through raising the temperature of the MercO-Matic oxidation test from 300° to 325°F.

Table 12.1  General Frictional Properties of Driveline Fluid Types Fluid Type Automatic Transmission Type F Automatic Transmission Farm Tractor Hydraulic Push-Belt and Chain CVT Off-Highway Transmission Automotive Traction Manual Transmission Dual Clutch Transmission Automotive Gear Oil Limited Slip Automotive Gear Oil

Dynamic Friction

Static Friction

High High

Low to Moderate High

High High High High High High Moderate Moderate

Very Low High High Low to Moderate Low to Very Low Low to Very Low Moderate Low to Very Low

Also in 1967, General Motors introduced the DEXRON® specification [12.4]. The primary issues addressed by this 12-3

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Design Practices: Passenger Car Automatic Transmissions

new specification included improved shift-time retention and clutch plate durability. Also addressed were improvements in low-temperature viscosity, foaming characteristics, oxidation resistance, and seal and nylon compatibility with the fluid. DEXRON® also became a registered trademark and included qualification procedures and testing protocols to ensure the quality of service-fill DEXRON® fluids in the marketplace.

introduced, which called for a narrow band of acceptability in the ratio of static to dynamic friction in the M2C138-CJ fluids. This specification was followed by the M2C166-H [12.7] specification for factory-fill fluids requiring improved friction characteristics in lock-up torque converters for factory-fill fluids. In this specification, Ford introduced the BJ10-4 bench oxidation test, later referred to as the aluminum beaker oxidation test (ABOT), to replace the oxidation test conducted in a motored transmission. Ford then introduced the MERCON® specification in January 1987 [12.8], a trademarked fluid, for service fill with procedures for qualification and licensing of fluids to ensure quality in the marketplace.

Chrysler upgraded its requirements for ATF during this time, with a new specification for factory fill, MS4228, replacing the older MS-3256 that had described a Type A, Suffix A-type fluid [12.5]. Particular attention was given to lowtemperature viscosity in this specification, to provide for adequate time to start and time to shift at low temperatures. New oxidation resistance requirements were included in the new specification and evaluated using a special Chrysler bench oxidation test.

From this point forward, General Motors, Ford, and Chrysler in North America all came forth with a progression of upgrades to these basic specifications. Again, the basic themes of low-temperature fluidity, further improvements in frictional durability, anti-wear, and oxidation resistance were evident as requirements in these areas became ever more demanding. Table 12.3 gives a progression of the ATF specifications from the major North American manufacturers during this time. Table 12.3 shows how viscosity performance, particularly low-temperature fluidity, has also evolved.

Ford deviated from the Type F concept of a high-static-friction fluid with the introduction of the M2C138-CJ specification in 1974 [12.6], which called for a friction-modified fluid. This type of fluid was introduced to alleviate the difficult engineering task of reducing gear engagement noise with fluids designed for high static friction. A new friction test was Table 12.2  History of ATF Specifications Specification Type A Type A, Suffix A Type F MS-3256 MS-4228 DEXRON® DEXRON®-II* M2C138-CJ DEXRON®-II MS-7176D M2C166-H MERCON® DEXRON®-IIE DEXRON®-IIE Rev. DEXRON®-III MERCON® V DEXRON®-IV DEXRON®-IIIG** DEXRON®-III*** MS-9602, Change C DEXRON®-IIIH

Number

6137M 6137M

6137-M 6137-M 6297-M M2C185-A 6301-M 6417-M 6418-M

Year

Company

1949 1957 1959 1964 1966 1967 1973 1974 1978, July 1980, May 1981, June 1987, January 1990, October 1992, August 1993, April 1996, July 1997, April 1997, April 1997, April 1999, August 2003, April

GM GM Ford Chrysler Chrysler GM GM Ford GM Chrysler Ford Ford GM GM GM Ford GM GM GM DaimlerChrysler GM

* DEXRON®-II was originally released using “C” qualification numbers. In 1975, after suppliers rolled over approvals due to GM mandating a fix for the cooler corrosion problem, the qualification numbers were preceded by a “D.” This led to referring to the fluids as DEXRON®-II “C” or “D.” ** Upgrade for ECCC vehicle test and sprag clutch wear. *** Upgrade for factory fill.

12-4

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ATF and Driveline Fluids

Table 12.3  ASTM Procedures for Some Lubricant Physical Properties Specification

Kinematic Viscosity (ASTM D 445 @ 100°C)

General Motors Type A

49 SUS min. @ 210°F

Type A, Suffix A

49 SUS min. @ 210°F

DEXRON®

7.0 cSt @ 210°C

DEXRON®-II*

None specified

5.5 cSt @ 210°F during and at end of specified tests

DEXRON®-IIE

None specified

DEXRON®-III

None specified

DEXRON®-IIIH

None specified

>5.5 cSt @ 100°C used fluid from oxidation test; >5.0 cSt @ 100°C used fluid from cycling test >5.5 cSt @ 100°C used fluid from oxidation test; >5.0 cSt @ 100°C used fluid from cycling test >5.5 cSt @ 100°C used fluid from oxidation test; >5.0 cSt @ 100°C used fluid from cycling test

Ford Type F

Minimum Viscosity 46.5 SUS @ 210°F during and after cycling and performance tests 46.5 SUS @ 210°F during and after cycling and performance tests 5.5 cSt @ 210°F during and at end of specified tests

M2C138-CJ M2C166-H MERCON®

49 SUS min. (7.0 cSt) @ 210°F 7.0 cSt min. @ 98.9°C 6.8 cSt min. @ 100°C 6.8 cSt min. @ 100°C

46.5 SUS (6.2 cSt) min. after 8000-cycle WOT test 6.2 cSt min. after FTLM BJ 12-4 6.0 cSt min. after FTLM BJ 12-4 5.0 cSt min. in GM cycling test

MERCON® V

6.8 cSt min. @ 100°C

6.8 cSt min. @ 100°C after 40 passes in FISST (ASTM D 5275)

Chrysler/DaimlerChrysler MS-3256 49 SUS min. @ 210°F MS-4228

49 SUS min. @ 210°F

MS-7176D

7.25 cSt min. @ 100°C

MS-9602, Change C

7.0 to 7.5 cSt min. @ 100°C

48 SUS min. @ 210°F after Chrysler shear 461C-112 48 SUS min. @ 210°F after Chrysler shear 461C-112 5.8 cSt min. after 30 passes in ASTM D 3945B 6.5 cSt min. after 20-hr KRL shear

Low-Temperature Viscosity 7000 SUS max. (extrapolated from 210°F and 100°F values) 4500 cP max. @ –10°F 64,000 cP max. @ –40°F 4000 cP max. @ –10°F 55,000 cP max. @ –40°F in Brookfield viscometer 4000 cP max. @ –10°F (–23.3°C) 55,000 cP max. @ –40°F in Brookfield viscometer 1500 cP max. at –20°C 5000 cP max. at –30°C 20,000 cP max. at –40°C 1500 cP max. at –20°C 5000 cP max. at –30°C 20,000 cP max. at –40°C 1500 cP max. at –20°C 5000 cP max. at –30°C 20,000 cP max. at –40°C 1400 cP max. @ –40°F in Ford test method BJ 3-2 1700 cP max. @ –18°C 1700 cP max. @ –18°C 1500 cP max. @ –20°C 20,000 cP max. @ –40°C 1500 cP max. @ –20°C 9000 + 4000 cP max. @ –40°C 7000 cP max. at –20°F in Chrysler method 461C-114 2300 cP max. at –20°F in Chrysler method 461C-114 4500 cP max. @ –28.9°C 20,000 cP max. @ –40°C 3000 cP max. @ –28.9°C 10,000 cP max. @ –40°Cs

* Viscosity of ATF originally was specified in Saybolt Universal Seconds at Fahrenheit temperatures until the specifications underwent metrification and were modernized. ** Generally, low-temperature viscosity is measured and ASTM D 2983 Brookfield procedure unless otherwise stated. Temperatures are stated in either Fahrenheit or Celsius, depending on the time period of the specification.

12.3 Key Physical Properties

these physical properties can be found in papers written by Kemp and Linden [12.9], Klaus and Tewksbury [12.10], Caines and Haycock [12.11], and Fien [12.12]. Measurements of these physical properties are usually performed according to ASTM methods, and several are identified in Table 12.4.

To achieve the optimal performance of the automatic transmission, design engineers need to know the physical properties of ATF that are responsible for the various functions in automatic transmissions. Excellent sources of information concerning 12-5

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Design Practices: Passenger Car Automatic Transmissions

Table 12.4  History of the Specification of ATF Viscosity in North America ASTM Method D 445 D 2983 D 341 D 2270 D 4683 D 1298 D 2717 D 2887 D 97 D 2500 D 92 D 971 D 2780

The second way to express the viscosity is by kinematic viscosity. This viscosity is commonly measured through a capillary method through πPr 4 ν= t (12.4) 8LV

Property Viscosity—40°C and 100°C (Kinematic—cSt) Viscosity—low temperature (Brookfield—cP) Standard viscosity temperature charts Viscosity index Shear resistance Density; specific gravity Thermal conductivity Boiling range distribution Pour point Cloud point Flash point/fire point Surface tension Air solubility

where P, t, and V are the pressure drop across the capillary, time of flow, and volume of fluid flowing through the capillary, respectively, while r and L are the radius and length of the capillary, respectively. The kinematic viscosity is commonly expressed in stokes (St) or centistokes (cSt). One stoke is 10–4 m2/sec in SI units or 1 cm2/sec, and one centistoke is 10–6 m2/sec or 1 mm2/sec. Kinematic viscosity is related to dynamic viscosity by Kinematic viscosity =

Viscosity: Viscosity is the measure of the internal friction or the resistance to flow of a liquid under shear. It is one of the most important physical properties of a lubricant. There are two ways to express viscosity. One is expressed as dynamic viscosity through

Effect of Temperature on Viscosity: Viscosity depends strongly on the temperature and decreases as the temperature increases. Figure 12.1 illustrates this relationship for a typical driveline fluid. The dependency of lubricant viscosity on temperature follows the MacCoull–Walther equation over a considerable temperature range

(12.1)

The SI unit for dynamic viscosity is milliPascal second (mPa-s); however, instead of this unit, centipoise (cP) is commonly used. One mPa-s equals 1 cP. Dynamic viscosity is also known as absolute viscosity. Two types of rotational viscometers are often used to measure dynamic viscosity. One type employs two concentric cylinders with their annulus containing the fluid for viscosity measurement. The viscosity is related to the physical parameters measured and viscometer geometry through η=



(12.2) where τ, a, and ω are the torque measured, the depth of fluid in the annulus space, and the angular velocity, respectively, while r1 and r2 are the radii of the outer and inner cylinders, respectively. A typical Brookfield viscometer is built based on this principle. The second type employs a circular cone and a circular plate with a thin film of fluid placed between the two. Either the cone or the plate rotates. The viscosity is related to the torque measured and viscometer geometry through

3τθ 2ωπr 3

(12.6)

(12.3)

where τ, θ, ω, and r are the torque, the angle between the cone and plate, the angular velocity, and the maximum radius of the cone, respectively.

AE-29_Ch12.indd 6

log log(ν + 0.7) = A – B log T

where ν is the kinematic viscosity in mm2/sec, T is the temperature in Kelvin, and A and B are constants. The value of 0.7 is valid for viscosities ranging from 2 × 107 to 2 cSt (below 2 cSt, a minor adjustment is made) [12.12, 12.13]. This method is not valid at temperatures above the first boiling fraction of the lubricant or below the cloud point [12.13].

τ ( r12 − r22 ) 4πaωr12r22

η=

(12.5)

As a common practice, the viscosity at low temperatures is measured by a Brookfield viscometer and reported as absolute viscosity, whereas the viscosity at high temperatures is measured by capillary viscometers and reported as kinematic viscosity. The temperatures of interest for a typical ATF range between –40°C and +150°C.

Each physical property is briefly described in this section.

Dynamic viscosity = force/sheared area shear stress = velocity/film thickness shear rate

dynamic viscosity density of liquid

12-6

Fig. 12.1  The effect of temperature on lubricant viscosity for a typical driveline fluid. The inset is log(viscosity) versus temperature plot.

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ATF and Driveline Fluids

Another commonly used expression to describe the temperature dependence of viscosity is the viscosity index (VI). This is an arbitrary scale and is calculated based on two reference oils according to

VI =

L−U L−H

three ATFs; Fluids A and B are formulated with a non-shear stable viscosity index improver, while Fluid C is formulated with a shear stable viscosity index improver [12.14]. These three ATFs were sheared using a Gaulin homogenizer; one pass and six passes of shearing are representatives of 12,000 and 32,000 kilometers of operation in a vehicle transmission, respectively [12.14].

(12.7)

where U is the 40°C viscosity of the unknown oil, L is the 40°C viscosity of a reference oil of 0 VI with the same 100°C viscosity as U, and H is the 40°C viscosity of another reference oil of 100 VI with the same 100°C viscosity as U. The higher the viscosity index, the smaller the relative change in viscosity with temperature. Note that comparison of viscosity index among fluids is valid only when the fluids possess similar 100°C viscosities. Effect of Pressure on Viscosity: Pressure increases viscosity, and above 10 MPa, this increase is significant for mineral oils. The pressure dependency can be calculated from the Barus equation as

ηt,P = ηt,0 exp(αP)

Fig. 12. 2  Effect of mechanical shear on kinematic viscosity.

(12.8)

where ηt,P equals the dynamic viscosity at temperature t and gage pressure P, ηt,o equals the dynamic viscosity at temperature t and atmospheric pressure, P equals the gage pressure, and α is the viscosity-pressure coefficient. Roeland’s equation [12.12] represents a further refinement of viscosity change with pressure ηt,P + 1.200 = (log ηt,0 + 1.200) * (1 + P/C)Z

(12.9)

where C is a constant dependent on the units of pressure, and Z is a constant characteristic of the lubricant under pressure. For mineral oils, Z can be estimated from the dynamic viscosities at 40°C and 100°C as Z = 7.81*[H40,0 – H100,0]1.5 * [0.885 – 0.864*Ht,0]

Fig. 12.3  Effect of temporary viscosity loss on ATF 100°C viscosity.

(12.10)

Specific Gravity and Density: Specific gravity is defined as the dimensionless ratio of weight of a given volume of product to the weight of an equal volume of water at 15.6°C. Density is defined as the mass of unit volume of a product generally expressed as 1 g/cm3. Lubricant suppliers will provide density data in terms of API (American Petroleum Institute) gravity. This is an expression of density measured with a hydrometer and possesses an inverse relationship to specific gravity. The API gravity can be calculated from specific gravity by the relationship

where Ht,0 = log[ log(ηt,0) +1.200] at temperature t°C. Effect of Shear on Viscosity: The viscosity of base oil, either mineral or synthetic, is not expected to change significantly when it is subjected to shear. However, high-molecular-weight viscosity index improvers are often added to the ATF formulation to alter the viscometrics, and these are affected by shear. The introduction of relatively high-molecular-weight viscosity index improvers to ATF can introduce either permanent viscosity loss or temporary viscosity loss. Permanent viscosity loss occurs when the high-molecular-weight polymer breaks down as a result of shearing. Temporary viscosity loss occurs when a fluid is under high shear rate and the viscosity is reduced reversibly, meaning the viscosity will be restored as soon as shearing returns to the low shear rate. Figures 12.2 and 12.3 show the comparison of permanent viscosity losses and temporary viscosity loss, respectively, for

API gravity = –141.5/(specific gravity) – 131.5

(12.11)

Oil density decreases approximately linearly as temperature increases. Figure 12.4 shows the temperature dependence of density for a commercial ATF. This is a fundamental property of the base lubricant chemistry, and the dependence of 12-7

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Design Practices: Passenger Car Automatic Transmissions

density on temperature is similar for similar base oil types [12.9, 12.12]. Mineral base oils typically possess densities between 0.86 and 0.98 g/cm3; however, a value of 0.87 g/cm3 is typical of driveline fluids.

Bulk modulus increases with increasing pressure and decreases with increasing temperature. Dissolved gases will decrease the bulk modulus of mineral oils. Gas Solubility in Oils: A mineral lubricant can contain significant amounts of dissolved gases, generally air. These dissolved gases are invisible but can seriously impact key lubricant properties such as viscosity, foaming, bulk modulus, cavitation, heat transfer, oxidation, and boundary lubrication. A fluid can contain up to 10% dissolved gases at room temperature. The volume of gas dissolved in a unit volume of fluid is referred to as the Bunsen coefficient. As with other liquid media, increased temperature and pressure increase the dissolution of gases into oils. During the operation of a transmission, the fluid undergoes variations in both temperature and pressure. When the amount of gas in the oil exceeds its saturation point, for example, when the transmission shifts from a heavy-duty cycle to a light-duty cycle, the fluid will become hazy as bubbles form. This is referred to as entrained gases, typically entrained air.

Fig. 12.4  Typical temperature variation of driveline fluid density. Volumetric Thermal Expansion: The thermal expansion volume is expressed as the coefficient of thermal expansion (α) and is defined as

α=

1 ⎛ dv ⎞ ⎜ ⎟ V0 ⎝ dt ⎠

It is noteworthy that air entrainment is in the form of extremely small bubbles dispersed throughout the bulk of the oil. It is quite different from foam, which is a dispersion of a gas in a liquid in which the individual gas bubbles are separated by thin liquid films called lamellae. Entrained air can also be introduced into the oil through mechanical action from the free air [12.15].

(12.12)

where V0, dV, and dT are the initial volume, the differential volume change, and the differential temperature change, respectively. The coefficient of thermal expansion for mineral oil lubricants varies almost linearly with fluid density [12.12].

12.4 Basestocks and Their Impact on Performance

Bulk Modulus: Bulk modulus is the resistance of a fluid to a decrease in volume when under compression. Compressibility is the reciprocal of the bulk modulus or the fluids’ inclination to be compressed. There are two accepted methods of expressing bulk modulus. One is the isothermal secant bulk modulus, and the other is the isothermal tangent bulk modulus. The secant bulk modulus is defined by

BM S =

(P − P 0 )V0 V0 − V

Basestocks used to formulate driveline fluids are normally mineral oils or synthetic oils. Mineral oils are refined from crude oil, preferably a paraffinic crude, whereas a synthetic oil is made by chemically reacting compounds of specific chemical composition. The manufacturing process for mineral basestocks has greatly improved over the last two decades. Conventional solvent refining and solvent de-waxing processes have given way to the use of hydrocracking and hydrotreating processes, followed by various catalyst-based de-waxing processes [12.16–12.18]. The typical conventional solvent refining process uses solvent extraction to remove unwanted fractions, such as aromatics and wax. In contrast, hydrocracking and hydrotreating processes involve various degrees of hydrogenation, which removes sulfur, nitrogen, and colored contaminants. Improvements in the de-waxing process allow the manufacture of basestocks with improved low-temperature fluidity.

(12.13)

where BMS, P, P0, V, and V0 are secant modulus in milliPascals, pressure of measurement, atmospheric pressure, the relative volume at P, and the relative volume at P0, respectively. The tangent bulk modulus is defined by

⎡ dP ⎤ BM t = −V ⎢ ⎣ dV ⎥⎦ t

(12.14)

where BMt, V, dP, and dV are tangent bulk modulus in milliPascals, relative volume at P, differential pressure change, and differential volume change, respectively. The tangent bulk modulus is always greater than the secant bulk modulus.

Mineral basestocks are described by their viscosity index. Table 12.5 compares several different high viscosity index mineral stocks. 12-8

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Table 12.5  Typical Properties of Hydrofinished High Viscosity Index Stocks

Stock 90 Neutral 100 Neutral 200 Neutral 350 Neutral 650 Neutral 150 Bright Stock

Kinematic Viscosity (cSt)

Specific Gravity (15.6°C)

Sulfur (wt%)

VI

40°C

100°C

Pour Point (°C)

Flash Point (°C)

0.860 0.860 0.872 0.877 0.882 0.895

0.005 0.065 0.096 0.126 0.155 0.263

  92 101   99   97   96   95

17.40 20.39 40.74 65.59 117.9 438.0

  3.68   4.11   6.23   8.39 12.43 29.46

–15 –13 –20 –18 –18 –18

190 192 226 252 272 302

(Courtesy of Lubrizol Ready Reference Internet Site; used with permission)

As the result of manufacturing process changes, commercial basestocks cover a range of physical and chemical properties. The API has classified basestocks into five groups, as shown in Table 12.6. Mineral oil-derived basestocks fall into three groups: Group I, Group II, and Group III, according to the content of sulfur, saturates, and viscosity index. Synthetic basestocks fall into two groups: Group IV, which is reserved for polyalphaolefins (PAOs), and Group V, which includes all other synthetic oils.

although hydroprocessed mineral stocks had replaced the synthetic stock in this fluid. Now, many lubricants marketed as synthetic are, in fact, of mineral stock origin.

Table 12.6  API Classification of Basestocks Base Oil Group

Sulfur (%)

I II III IV V

>0.03 120 All polyalphaolefins (PAOs). All other basestocks not included in Groups I, II, III, or IV.

Fig. 12.5  Continuum of paraffinic base oil quality. (Adapted with permission from PetroTrends’ Internet site.)

Group II+: Recently, the designation “Group II+” has emerged to describe base oils that possess significantly higher viscosity indexes than the 100 that is typical for most Group II stocks. Group II+ is not an official API grade but is useful for distinguishing the performance advantages these basestocks offer over other Group II basestocks. This illustrates that although basestocks are classified into groups, there actually exists a continuum of fluids. This is best illustrated in Fig. 12.5.

The changes in physical and chemical properties of the basestocks have been very beneficial to ATF formulation because they significantly increase the ability of the ATFs to meet the OEMs’ higher lubricant performance requirements. At the same time, the changes also have a negative impact on the ability of the base oil to perform in some areas. The following discussion will address the impact of basestock changes on formulation strategy and performance.

Mineral Stocks Marketed as Synthetics: Group III basestocks possess similar characteristics to PAOs but at about half the price. This has led to the replacement of PAOs in many synthetic formulations. In 1999, the National Advertising Division of the Council of Better Business Bureaus ruled that Castrol Syntec motor oil could be marketed as a synthetic,

Impact on ATF Low-Temperature Properties: Viscosity index (VI) is a measure of the viscosity variation of the basestock with temperature. The higher the viscosity index value, the lower the Brookfield viscosity at –40°C. This directly impacts the low-temperature fluidity of the fully formulated 12-9

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Design Practices: Passenger Car Automatic Transmissions

oil. The introduction of higher viscosity index basestocks enabled OEMs to set more stringent lower-temperature viscosity requirements. When DEXRON®-II was introduced in the early 1970s, ATFs could be readily formulated with conventional solvent-refined Group I basestocks because the Brookfield viscosity at –40°C required then was 50,000 cP. When DEXRON®IIE and MERCON® specifications were introduced in 1989 and 1992, respectively, the required Brookfield viscosity at –40°C was reduced to 20,000 cP. This radical change in lowtemperature viscosity requirements made it difficult to formulate ATF with the conventional Group I solvent neutral base oils [12.19, 12.20]. When MERCON® V was introduced in 1996, a blend of Group II and Group IV was needed to meet the Brookfield viscosity at –40°C of 13,000 cP [12.21, 12.22]. When DaimlerChrysler MS-9602 was introduced in 1998, Group III or higher viscosity-grade basestock was required to meet the specification of 10,000 cP [12.23]. A Group IV basestock was used to satisfy General Motors Allison Division’s TES-295 specification, which stipulates the Brookfield viscosity at –40°C to be equal to or less than 8700 cP [12.24]. When higher viscosity index basestocks are used, less highmolecular-weight polymer (viscosity index improver) is needed to maintain the lubricant viscosity at high temperature. The direct benefit is improved shear stability. Fluid shear stability is determined by the molecular weight and treat rate of the polymeric viscosity modifier contained in the fluid. Higher treat rates of high-molecular-weight polymers produce shear unstable fluids. Fluids not containing polymeric viscosity modifiers produce shear stable fluids and are Newtonian fluids [12.20]. Impact on ATF Oxidation Stability: Along with OEMs’ increasing stringent requirements in low-temperature fluidity of ATFs is their demand for better oxidation stability. Good oxidation stability is essential to achieve longer extended drain intervals or fill-for-life performance. Aromatic components and unsaturated hydrocarbons tend to have poor oxidation stability when compared with saturated hydrocarbons. It has been observed that although additive chemistry can make significant contributions to controlling the oxidation process, it cannot indefinitely protect chemical structures in the basestock prone to free radical oxidation. There is a point, beyond which, no amount of conventional antioxidants can stave off catastrophic oxidation of the basestock. From there, the ability to lengthen the service life of ATF must come from the basestock itself. The DEXRON®-III specification requires fluids to exhibit less than a 3.25 increase in TAN (total acid number) after the GM 4L60 Oxidation Test. It has been predicted that to improve the oxidation performance in

this test, such that the after test ΔTAN of the fluid is less than 1.0, would require the use of a Group III basestock [12.20]. Impact on Seal Compatibility: Various elastomeric materials such as polyacrylate, nitrile, fluoroelastomers, and silicone (polysiloxane derivatives) are used in automatic transmissions to prevent both internal and external leakage of fluid. Transmission leaks can occur when the seal materials shrink or harden or become too soft. The basestock has a major influence on the seal swell properties of various elastomers. Naphthenic (cycloparaffin) and aromatic basestocks are good seal swell media for silicone, viton, and nitrile elastomers. Highly paraffinic hydrocracked basestocks or PAOs tend to shrink some seal materials unless blended with appropriate seal swell agents such as esters, aromatic compounds, or sulfones to counter this behavior. This is the main disadvantage of synthetic basestocks and unconventional basestocks. The dosage for seal swell agents can vary from zero to several percent by weight, depending on the basestock.

12.5 Chemical Composition Driveline fluids consist of three essential components: the basestock, which comprises up to 90% of the fluid; the additive package, which comprises up to 10% of the fluid; and, if required, viscosity index improvers. How these various components find their way into the fluid depends on the application and the geographical location of the fluid supplier. In North America, the additive companies are responsible for developing the chemical constituents of the performance package to meet the performance specifications of the OEM. This package is purchased by oil companies, who in turn blend the additive package with a basestock and, if required, a viscosity index improver. Sometimes, the oil company will top-treat the fluid (i.e., add additional additives to the fluid) to alter the performance. The oil company then supplies the lubricant to the OEM. In Asia and Europe, the situation is usually different. The oil company is responsible for developing the chemical construction of the performance package. The oil company will purchase a complete or partial additive package and use this to develop the final chemical construction. In such cases, the additive companies may not fully understand the requirements of the application. The nature of the basestock was discussed in the previous section. The remainder of this section will discuss viscosity index improvers and additive packages [12.25]. Viscosity Index Improvers (VIIs): These are polymers added to mineral oils to maintain viscosity at high temperatures. At low temperatures, these polymers curl upon themselves 12-10

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and occupy a small volume; consequently, they interact little with the bulk oil. This results in little addition to the viscosity of the bulk oil. As the temperature is increased, the polymer uncurls and interacts to a greater extent with the bulk oil, effectively increasing the viscosity of the fluid. Common types of viscosity index improvers are olefin copolymers (OCPs), polymethacrylates (PMAs), hydrogenated styrenediene (STD), and styrene-polyester (STPE) polymers. The poor low-temperature characteristics of OCPs have resulted in PMAs being preferred for ATF applications [12.25]. Breakdown of viscosity index improvers through mechanical action (shear) and oxidation causes a loss of viscosity at higher temperature. Shear stable viscosity index improvers, such as star polymers, have been developed to counter this effect. The performance or additive package consists of essentially two groups: those that interact in the bulk oil, and those that are surface active. Additives that function by adsorbing onto surfaces include rust inhibitors, friction modifiers, anti-wear agents, extreme pressure agents, and detergents. Many of the surface-active additives are composed of roughly linear molecules that have a polar head group (i.e., the surface active portion that contains oxygen, nitrogen, sulfur, or phosphorus atoms) and a non-polar tail (an oil-loving hydrocarbon chain). Additives that function in the bulk oil include antioxidants, demulsifiers and anti-foam agents, dispersants, and seal swell agents. Here we describe each type of additive component, its typical chemistry, and its function. Note that components are grouped by their most recognized function. Many additives will perform multiple functions. For example, zinc dithiophosphates are considered primarily anti-wear agents; however, they also improve antioxidant performance. The additives that make up the performance package often interfere with each other. This is particularly true of the surface-active components. For example, a particular anti-wear agent may enable the fluid to meet gear protection targets by adsorbing onto surfaces under high load conditions. However, this same anti-wear agent may also adsorb so strongly under normal load conditions that the modifiers necessary for friction control are excluded from the surface, resulting in rough shifts and shudder in the vehicle. To design a driveline fluid requires a high degree of expertise. Successful driveline lubricants balance different additive chemistries to achieve the required performance. This balance can be disturbed by the addition of top-treatments (i.e., additives added to the fully formulated lubricant). Top-treatments may enhance one attribute of the fluid (as advertised) but likely at the expense of another attribute. Top-treatments are never recommended. Modifications to fluids should always be done with the assistance or direction of the manufacturers of the additive package.

Friction Modifiers: These additives are necessary for controlling the transfer of torque in the friction clutches. Friction modifiers are long-chain molecules with a polar head group and a non-polar hydrocarbon chain. The polar head group is designed to form a physical bond with both metal and composite surfaces, and the length of the hydrocarbon chain increases the strength of the lubricant film. These additives include amines, fatty acids, alcohols, esters, and amides. These modifiers are active over a range of temperatures typically above 60°C. Rust and Corrosion Inhibitors: These protect metal surfaces from oxidation due to entrained air and acidic products in the oil. The presence of water accelerates the oxidation process. There are two types of inhibitors. Inhibitors of the first type neutralize the acids formed in the oils. Inhibitors of the second type form protective layers on metal surfaces by either physical or chemical bonds. The film formers are similar in construction to the friction modifiers, consisting of a polar head group with a non-polar hydrocarbon tail. However, the nature of the head group and the length of the tail are very different. Rust inhibitors can contain acidic head groups (i.e., the rust preventative is itself an acid), whereas corrosion inhibitors are mainly sulfur-containing compounds designed to react with non-ferrous or yellow metals. These additives are active at lower temperatures and may interfere with the performance of friction modifiers at lower temperatures. Anti-Wear and Extreme Pressure Agents: Unlike friction modifiers and film-forming rust inhibitors, these additives chemically react with metal surfaces to form a protective film. These additives are important at elevated loads and reduced speeds where the viscosity of the oil is insufficient to maintain hydrodynamic lubrication. Under these conditions of mixed and boundary contact, the interface temperatures rise and, if the temperature rise is sufficient, the anti-wear and/or extreme pressure additives are thermally activated (decomposed) and react with the metal surfaces. Anti-wear components generally contain phosphorous compounds and are activated (decomposed) at contact temperatures below 200°C. Extreme-pressure components generally contain sulfur compounds and are activated (decomposed) at contact temperatures above 200°C. Whereas this affords good protection for metal parts, the activation (decomposition) of these additives in the clutch interface can lead to a loss of torque transfer quality through the deposition of thermal degradation products on the clutch plate. These additives typically contain indicator elements such as Zn, P, S, B, or Cl and so their presence, or that of their reactive products, is readily detectable. These additives can also interfere with the performance of the friction modifiers at elevated temperatures through competition for surface adsorption sites.

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Design Practices: Passenger Car Automatic Transmissions

Detergents: These additives are metal salts of organic acids (a soap) made by neutralizing the acid with a metal oxide or metal hydroxide. Detergents can contain more oxide or hydroxide than necessary to neutralize the acid, and the excess is referred to as the “overbase.” This overbase is available to neutralize acids that may form through oxidation of the oil. Once in the transmission the soap portion of the detergent helps disperse fluid degradation products preventing the deposition of these materials within the transmission. Dispersants: These additives suspend oil-insoluble degradation products, small particulates, and water, thereby reducing the deposition of these materials on surfaces within the transmission. Like friction modifiers, rust inhibitors, and detergents, dispersants also consist of polar head-groups combined with non-polar tails. The polar groups surround the degradation products (which are also polar in nature) while the non-polar tails keep the entire assembly soluble in the oil and prevent particulate agglomeration. These additives are generally of higher molecular weight than detergents, but not as large as the polymers typically used as viscosity index improvers. Antioxidants: These additives act to disrupt the reaction of oxygen with the base oil. Lubricants are hydrocarbons and will react with oxygen at sufficiently high temperatures. The temperature where this becomes significant depends on the nature of the base oil. Chemically, this is a free radical reaction, and the oxidation inhibitors (antioxidants) are molecules that either scavenge free radicals or decompose hydroperoxides. Foam Inhibitors: These are generally silicones and work by altering the surface tension of the oil, thereby facilitating the separation of air bubbles from the fluid. These additives are present in very small concentrations. (Typically,