High Speed Pneumatic Theory and Technology Volume II: Control System and Energy System 9811522014, 9789811522017

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Yaobao Yin

High Speed Pneumatic Theory and Technology Volume II Control System and Energy System

High Speed Pneumatic Theory and Technology Volume II

Yaobao Yin

High Speed Pneumatic Theory and Technology Volume II Control System and Energy System

123

Yaobao Yin School of Mechanical Engineering Tongji University Shanghai, China Translated by Jiangwei Wu Shanghai Maritime University Shanghai, China

ISBN 978-981-15-2201-7 ISBN 978-981-15-2202-4 https://doi.org/10.1007/978-981-15-2202-4

(eBook)

Jointly published with Shanghai Scientific and Technical Publishers, Shanghai, China The print edition is not for sale in China. Customers from China please order the print book from: Shanghai Scientific and Technical Publishers. © Springer Nature Singapore Pte Ltd. and Shanghai Scientific and Technical Publishers 2020 This work is subject to copyright. All rights are reserved by the Publishers, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publishers, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publishers nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publishers remain neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

Preface

Pneumatic servo control originated from the gas servo system of missile and rocket attitude control before and after World War II. In the past 60 years, in order to develop space in Europe and America, cold air or hot gas has been used as working medium for rocket attitude control and thrust vector control of aircraft. The attitude control of China’s Long March series launch vehicles uses cylinder gas source to drive pneumatic turbine and hydraulic pump to generate hydraulic energy. The thrust vector control of missiles and large launch vehicles uses integrated gas turbine pump electro-hydraulic integrated energy device. Because high-temperature, high-pressure, high-speed hot gas and ultra-high-pressure cold gas technology can be used in weapon systems, at present, countries have implemented strict control and blockade on aerospace high-speed pneumatic control theory and technology, and public reports are extremely rare. In 1960, J. L. Shearer, an American, co-authored Fluid Power Control, the first book on hydrodynamic control, based on pneumatic motor experiments. In 1963, the Japan Welding Association applied pneumatic system to automotive body spot welding machine, pneumatic solenoid valve and pneumatic proportional valve came out one after another. In 1965, Araki Kenji published Servo Mechanism, a representative work on pneumatic servo mechanism, which used chamber and spring compensation for pneumatic servo valves. In 1986, Chinese Qu Yiyi summed up the essence of foreign literature and compiled Pneumatic Servo System. For many years, high-temperature, high-pressure, high-speed, and high-precision pneumatic control theory and technology have been listed as the key research topic in various countries, but the public information and results are rare. In view of the lack of basic theory of high-speed pneumatic control in aerodynamics, the author systematically and timely summarizes the advanced basic theory and application technology of high-speed pneumatic control, especially the basic theory and key technologies applied to major projects formed in the process of research and development in aerospace, aviation, construction machinery, new energy vehicles, automated production lines, and other equipment, based on many years of practice in the development of major equipment and weapon systems including the pneumatic series research topics undertaken by the author founded by the National Defense Weapon System, the National High-tech Research and v

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Preface

Development Program (863 Program), the National Natural Science Foundation, the National Science and Technology Support Program, the Aviation Fund, the Shanghai Pujiang Talent Program, and the National Cooperation Program. This book is divided into 14 chapters. Chapter 1 is an introduction, focusing on the origin, types, and characteristics of pneumatic servo control, so that readers can understand the history, development process and typical flow characteristics of pneumatic control. Chapter 2 is pneumatic components foundation, which introduces the types, characteristics and basic characteristics of working medium, pneumatic control valve, and pneumatic servo valve. Chapters 3 and 4 are new principles of high-speed pneumatic servo valves including double-orifices symmetrical pneumatic servo valves, double-orifices asymmetrical pneumatic servo valves, asymmetrical hydraulic valves, symmetrical even underlaps pneumatic servo valves, symmetrical uneven underlaps pneumatic servo valves, zero-position flow state of pneumatic servo valves, asymmetrical pneumatic servo valve control pressure system. Chapter 5 describes the pneumatic servo system, involving the pneumatic servo system and its working point compensation method, valve-controlled pneumatic system mathematical model, examples. Chapters 6 and 7 introduce the pneumatic refrigeration mechanism, pneumatic heating mechanism, pneumatic temperature control principle, new structure, principle, and design method of ultra-high-pressure pneumatic pressure reducing valve, 35 and 70 MPa pneumatic pressure reducing valve. Chapter 8 introduces the characteristics of pneumatic actuators and pneumatic components in extreme environments, including the natural frequencies of cylinders and hydraulic cylinders, the characteristics of pneumatic motors, and the service characteristics of accumulators and cylinders in extreme temperatures. Chapters 9 and 10 describe the high-temperature and high-speed gas turbine pump electro-hydraulic energy system for aircraft, the aerodynamic principle of aircraft attitude control, involving the research achievements of electro-hydraulic servo control technology of aircraft gas turbine pump, gas generator, gas turbine, electro-hydraulic energy combination, gas turbine motor hydraulic pump electro-hydraulic energy system, gas steering gear, new pneumatic method and new principle of aircraft attitude control, etc. Chapters 11 and 12 introduce pneumatic DTH hammers and pneumatic hydraulic hammers, including the design theory, methods, and examples of large-diameter pneumatic DTH hammers and drills, high-speed pneumatic hydraulic composite hammers and analytical models of pile and soil. Chapters 13 and 14 are pneumatic frontier applications, including fuel cell vehicle hydrogen transmission system, pneumatic principle and mathematical model of the oscillating water column type wave power generation, and application example of oscillating water column wave power station. The purpose of this book is to provide useful frontier theoretical and practical materials for the professional and technical personnel in the research, design, manufacture, testing, and management of major equipment and weapons systems in China, and to promote the exploration of the unknown basic theories, technical approaches or solutions in the field of high-speed pneumatic control in aerodynamics.

Preface

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This book is based on the author’s research results and practical experience at home and abroad for many years, including the author’s research results in Tongji University, Shanghai Aerospace Control Technology Research Institute, Japanese National Saitama University. The book was mainly written by Prof. Yin Yaobao of Tongji University. Chapters 1, 3, 4, 6–10, 13, and 14 were written by Yin Yaobao. The materials of Chaps. 2 and 5 were provided by Qu Yiyi (Shanghai Jiao Tong University), and were written by Yin Yaobao. Chapters 11 and 12 were written by Guo Chuanxin (Beijing Institute of Building Mechanization) and Yin Yaobao. In the course of publishing, the book has been strongly supported and helped by Shanghai Scientific and Technical Publishers House, Shanghai Science and Technology Monographic Publishing Fund, and Tongji University’s teaching reform research and construction projects. Li Changming and Wang Yu, Ph.D. students, and Chen Hao, Master student in Prof. Yin Yaobao’s Research Department of Tongji University, and Master’s graduates from 2009 to 2013, assisted in data collection. I would like to express my thanks here. Shanghai, China

Yaobao Yin

Summary

The theory and application technology of high-speed pneumatic control are systematically discussed in this book. The main contents include pneumatic control components and actuators, new principles of high-speed pneumatic servo valves, pneumatic servo systems, pneumatic refrigeration and heating principles, ultra-high-pressure pneumatic control valves, characteristics of pneumatic components in extreme environments, electro-hydraulic energy and steering gear system of gas turbine pump for aircraft, aircraft attitude control pneumatic principles, pneumatic DTH hammer, pneumatic hydraulic pile hammer, fuel cell vehicle hydrogen transmission system, and marine wave power generation pneumatic principle and device. This book is full of illustrations and texts, in-depth and superficial, focusing on systematization, professionalism and frontier, and combines theory with practice closely. The application examples of major national projects are abundant and informative. This book can be read by scientists and technicians engaged in the research, design, manufacture, test, and management of advanced pneumatic control elements and devices for major equipment and weapon systems. It can also be used as a reference for teachers and students majoring in aviation, aerospace, naval vessels, machinery, energy, ocean, transportation, etc.

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Pneumatic Actuators, Driving Elements, and Accessories . . . . . . 8.1 Pneumatic Cylinder and Hydraulic Cylinder . . . . . . . . . . . . . 8.1.1 Classification of Pneumatic Cylinder and Hydraulic Cylinder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1.2 Natural Frequency of Pneumatic Cylinder . . . . . . . . 8.1.3 Natural Frequency of Hydraulic Cylinder . . . . . . . . . 8.1.4 Comparison of Pneumatic Cylinder System and Hydraulic Cylinder System . . . . . . . . . . . . . . . . 8.1.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 Structure and Characteristics of Actuators . . . . . . . . . . . . . . 8.2.1 Pneumatic Cylinder . . . . . . . . . . . . . . . . . . . . . . . . 8.2.2 Pneumatic Motor . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3 Aircraft Hydraulic Accumulator and Cylinder in Extreme Temperature Environment . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.1 Extreme Temperature Environment . . . . . . . . . . . . . 8.3.2 Van der Waals Equation for Real Gases . . . . . . . . . 8.3.3 Inflation Mass of High-Pressure Gas Cylinders . . . . 8.3.4 Gas Pressure Service Characteristics of High-Pressure Cylinders and Cavities . . . . . . . . . . . . . . . . . . . . . . 8.3.5 Service Characteristics of Accumulator . . . . . . . . . . 8.3.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . High-Temperature and High-Speed Gas Turbine Pump Electro-Hydraulic Energy System for Aircraft . . . . . . . . . . . 9.1 Electro-Hydraulic Servo Control Technology of Aircraft Gas Turbine Pump . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.1.1 Overview of Electro-Hydraulic Control Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.1.2 Elastic O-Ring Sealing Technology . . . . . . . . . .

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9.1.3

Technical Characteristics of Electric-Hydraulic Servo System for Aircraft . . . . . . . . . . . . . . . . . 9.1.4 Design Method of Air Defense Missile Control Execution System . . . . . . . . . . . . . . . . . . . . . . . 9.1.5 Auxiliary Energy for Air Defense Missiles . . . . . 9.1.6 Hydraulic Energy Application Technology of Gas Turbine Pump for Aircraft . . . . . . . . . . . 9.2 Power Matching Design of Steering System . . . . . . . . . . 9.2.1 Load Model of Steering System . . . . . . . . . . . . 9.2.2 Optimal Matching of Output Characteristics and Load Trajectories of Servo Mechanism . . . . 9.2.3 Energy Demand of Actual Steering System . . . . 9.2.4 Variation Factors of Working Pressure and Frequency Characteristics of System . . . . . . 9.3 Design Principle of Gas Generator . . . . . . . . . . . . . . . . . 9.3.1 Theoretic Derivation . . . . . . . . . . . . . . . . . . . . . 9.3.2 Application Discussion . . . . . . . . . . . . . . . . . . . 9.4 Design Principle of Small Gas Turbine for Missile . . . . . 9.4.1 Thermodynamic Process in Small Gas Turbine Nozzle for Missile . . . . . . . . . . . . . . . . . . . . . . 9.4.2 Efficiency of Small Gas Turbine in Missile Hydraulic System . . . . . . . . . . . . . . . . . . . . . . . 9.4.3 Graphical Analysis Method for Stress of Small Gas Turbine Disk for Missile . . . . . . . . . . . . . . 9.5 Starting Characteristics of Electronic and Hydraulic Power Unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.5.1 Description of EHPU Starting Characteristic . . . 9.5.2 EHPU Theoretical Modeling . . . . . . . . . . . . . . . 9.5.3 Starting Characteristics of Hydraulic System . . . 9.5.4 Starting Characteristics of Power Supply System Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Application of Aerodynamic Technology in Attitude Control of Aerocraft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.1 Aerodynamic Attitude Control Principle and Attitude Control Method of Aircraft . . . . . . . . . . . . . . . . . . . . . . 10.1.1 New Method and Principle of Attitude Control of Aircraft . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.1.2 Lateral Force Analysis of Attitude Control . . . . . 10.1.3 Experiments and Analysis . . . . . . . . . . . . . . . . . 10.1.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Contents

10.2 Laval Nozzle for Attitude Control of Aircraft . . . . . . . . . 10.2.1 Flow Field Analysis of Laval Nozzle . . . . . . . . . 10.2.2 Manufacturing Process Technology . . . . . . . . . . 10.3 Device for Changing Missile Motion Direction by Using Gas Generator and Transverse Force of Nozzle . . . . . . . 10.4 Process Technology of Gas Steering Engine . . . . . . . . . . 10.4.1 Structure and Working Principle . . . . . . . . . . . . 10.4.2 Redundancy Control . . . . . . . . . . . . . . . . . . . . . 10.4.3 Fit Clearance Control . . . . . . . . . . . . . . . . . . . . 10.4.4 Shell Assembly Quality . . . . . . . . . . . . . . . . . . 10.4.5 Technological Key Problem Test on Symmetry of Reaction Time . . . . . . . . . . . . . . . . . . . . . . . Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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11 Pneumatic Down-the-Hole Hammer . . . . . . . . . . . . . . . . . . . . . . 11.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Principle and Classification of Pneumatic DTH Hammer . . . . 11.2.1 Classification of Pneumatic DTH Hammer . . . . . . . . 11.2.2 Principle of Valve-Type Pneumatic DTH Hammer . . 11.2.3 Valveless Pneumatic DTH Hammer . . . . . . . . . . . . . 11.2.4 Large Diameter Pneumatic DTH Hammer . . . . . . . . 11.3 Principle and Parameter Design of Large Diameter Pneumatic DTH Hammer Impactor . . . . . . . . . . . . . . . . . . . 11.3.1 Design Requirements . . . . . . . . . . . . . . . . . . . . . . . 11.3.2 Overall Structure . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3.3 Selection of Working Parameters . . . . . . . . . . . . . . . 11.3.4 Calculation Method of Performance Parameters . . . . 11.3.5 Design of Key Parts . . . . . . . . . . . . . . . . . . . . . . . . 11.4 Dynamic Process and Theoretical Model of Large Diameter Pneumatic DTH Hammer . . . . . . . . . . . . . . . . . . . 11.4.1 Dynamic Process of Large Diameter Pneumatic DTH Hammer . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.4.2 Theoretical Model of Large Diameter Pneumatic DTH Hammer . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.4.3 Numerical Calculation of Large Diameter Pneumatic DTH Hammer . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.5 Design of Large Diameter DTH Hammer Bit and Spherical Tooth Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.5.1 Rock-Breaking Process by Impact . . . . . . . . . . . . . . 11.5.2 Mechanical Model of Side Tooth of Large Diameter Pneumatic DTH Hammer Bit . . . . . . . . . . 11.5.3 Layout Principle of Large Diameter Pneumatic DTH Hammer Bit . . . . . . . . . . . . . . . . . . . . . . . . .

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11.6 Typical Engineering Cases . . . . . . . . . . . . . . . . . 11.6.1 Project Site . . . . . . . . . . . . . . . . . . . . . . 11.6.2 Model and Parameters of Pneumatic DTH Hammer . . . . . . . . . . . . . . . . . . . . . . . . . 11.6.3 Construction Process . . . . . . . . . . . . . . . 11.6.4 Analysis of Bit Usage and Phenomenon . Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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12 Pneumatic–Hydraulic Pile Driving Hammer . . . . . . . . . . . . . . . . 12.1 Pneumatic–Hydraulic Composite Pile Driving Hammer . . . . . 12.1.1 Hydraulic System of Typical Hydraulic Pile Driving Hammer . . . . . . . . . . . . . . . . . . . . . . . . . . 12.1.2 Strike Frequency and Strike Energy . . . . . . . . . . . . . 12.1.3 Main Characteristics and Parameters . . . . . . . . . . . . 12.1.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.2 High-Speed Pneumatic–Hydraulic Composite Hammer . . . . . 12.2.1 Hydraulic System of Pneumatic–Hydraulic Pile Driving Hammer . . . . . . . . . . . . . . . . . . . . . . . . . . 12.2.2 Strike Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.2.3 Characteristics of Pneumatic–Hydraulic Pile Driving Hammer . . . . . . . . . . . . . . . . . . . . . . . . . . 12.2.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.3 Mathematical Model of High-Speed Pneumatic–Hydraulic Composite Hammer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.3.2 Mathematical Model . . . . . . . . . . . . . . . . . . . . . . . . 12.3.3 Characteristic and Example of Pneumatic–Hydraulic Composite Pile Driving Hammer . . . . . . . . . . . . . . . 12.3.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.4 Rapid Piling Process of High-Speed Pneumatic–Hydraulic Composite Hammer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.4.1 Principle of Rapid Piling . . . . . . . . . . . . . . . . . . . . 12.4.2 Mathematical Model for Descending Stage of Rapid Piling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.4.3 Influencing Factors of Rapid Piling . . . . . . . . . . . . . 12.4.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.5 Contact Model Pile and Soil . . . . . . . . . . . . . . . . . . . . . . . . 12.5.1 Finite Element Analysis Model of Pile and Soil . . . . 12.5.2 Finite Element Solution of Pile and Soil . . . . . . . . . 12.5.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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13 Application of Pneumatic Technology in Fuel Cell Vehicles . . 13.1 Pneumatic System and Fuel Cell Hydrogen Transmission System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.1.2 Space Hydrogen Energy Technology and Its Application . . . . . . . . . . . . . . . . . . . . . . . 13.1.3 Carbon Fiber Winding Cylinder for Fuel Cell Vehicle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.1.4 Fuel Cell Vehicle Hydrogen Transmission System 13.2 Hydrogen Transmission and Hydrogenation Characteristics of Vehicle-Borne High-Pressure Hydrogen Transmission System Cylinders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.2.1 Characteristics of Vehicle-Borne Hydrogen Transmission and Storage System . . . . . . . . . . . . 13.2.2 Hydrogen Transmission Pressure Characteristics of Vehicle-Borne Gas Cylinders . . . . . . . . . . . . . 13.2.3 Hydrogenation Pressure Characteristics of Vehicle-Borne Gas Cylinders . . . . . . . . . . . . . 13.2.4 Test Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.2.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Pneumatic Principle and Device of Oscillating Water Column Wave Power Generation . . . . . . . . . . . . . . . . . . . . . . 14.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.2 Basic Structure and Pneumatic Principle . . . . . . . . . . . . . . 14.3 Mathematical Model of Oscillating Water Column . . . . . . 14.3.1 Aerodynamic Model of Air Chamber . . . . . . . . . . 14.3.2 Frequency Response of Mighty Whale Energy Converter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.3.3 Examples of Numerical Calculation of Mighty Whale Energy Converter . . . . . . . . . . . . . . . . . . . 14.3.4 Characteristics of Floating Oscillating Water Column Wave Energy Converter . . . . . . . . . . . . . 14.4 Experimental Technique of Oscillatory Water Column Wave Energy Converter . . . . . . . . . . . . . . . . . . . . . . . . . 14.4.1 Test Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.4.2 Numerical Analysis . . . . . . . . . . . . . . . . . . . . . . 14.5 Application Examples of Oscillating Water Column Power Station . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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14.5.1 Examples of Oscillating Water Column Wave Power Generation in China . . . . . . . . . . . . . . 14.5.2 Examples of Oscillating Water Column Wave Power Generation in Foreign Countries . . . . . 14.6 Key Technologies of Oscillating Water Column Wave Power Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Chapter 8

Pneumatic Actuators, Driving Elements, and Accessories

Pneumatic cylinder and hydraulic cylinder are also called actuator or actuator cylinder. Their geometrical structure is basically the same. Single acting cylinder is an actuator driven by fluid force in one direction and by gravity or spring force of piston in the other direction. Single acting cylinder has the advantages of simple structure, easy production and manufacture, relatively low price, and space-saving in use. It is widely used in the executing agencies of various control systems, such as the single acting cylinder is widely used in force control of welding machine at present. There are few literature on force control and natural frequency of single acting cylinder and double acting cylinder. This chapter analyzes the natural frequency characteristics of single acting cylinder and double acting cylinder, introduces the structure and characteristics of cylinder and pneumatic motor, and analyzes the working performance of the air chamber of hydraulic system under extreme temperature environment.

8.1 8.1.1

Pneumatic Cylinder and Hydraulic Cylinder Classification of Pneumatic Cylinder and Hydraulic Cylinder

Pneumatic cylinders and hydraulic cylinders are devices that convert pressure energy of fluid into mechanical energy, and have been widely used in various control devices. From the point of view of movement form, it includes pneumatic cylinder or hydraulic cylinder (also known as cylinder), motor for rotary motion, swing cylinder for rotary motion, hydraulic cylinder, and other types. Pneumatic cylinder uses compressed air as the gas source, which converts the pressure energy of the gas into mechanical energy. According to the form of motion, cylinders or pneumatic actuators can be classified as follows: © Springer Nature Singapore Pte Ltd. and Shanghai Scientific and Technical Publishers 2020 Y. Yin, High Speed Pneumatic Theory and Technology Volume II, https://doi.org/10.1007/978-981-15-2202-4_8

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8 Pneumatic Actuators, Driving Elements and Accessories

Pneumatic cylinders or hydraulic cylinders Pneumatic cylinders or hydraulic cylinders

Motor

Single acting pneumatic cylinder or cylinder Double acting pneumatic cylinder or cylinder

Gear motor Vane motor Piston motor

Swing pneumatic cylinder or cylinder

Pneumatic cylinder or hydraulic cylinder can also be divided into single acting cylinder and double acting cylinder according to the following ways. (1) Single acting cylinder: Structurally, only one side of the piston is supplied with fluid with a certain pressure. The single acting cylinder relies on the fluid force in one direction to control the movement in that direction, and the return process relies on the action of external forces such as spring force or gravity. (2) Double acting cylinder: Structurally, both sides of the piston are supplied with a certain working pressure of fluid, under the action of fluid force on both sides, pneumatic cylinder or cylinder can move in the positive or negative direction. Generally, if the asymmetry of pneumatic cylinder or cylinder can be neglected, the initial position of piston is in the neutral position of cylinder, and both sides can be regarded as symmetrical structure, then it is called symmetrical cylinder or pneumatic cylinder. In fact, the cylinder or pneumatic cylinder moving in a straight line, and actuator of rotary motion are often asymmetrical, or the initial position works in a non-neutral position, which has strong nonlinear characteristics. Approximate calculation is often inadequate for similar structures or applications. Therefore, it is necessary to analyze the dynamic characteristics and control system design strictly. The high-performance and high-speed control performance of pneumatic or hydraulic systems are directly affected by the volumetric elastic coefficient of fluids. The natural frequencies of the fluid-controlled actuator with pressure depend on the parameters of the actuator, the load mass of the movable part, the effective area of the piston, the displacement, and the characteristics of the fluid. The natural frequencies play a dominant role in the performance of the fluid. This paper mainly analyzes the characteristics of pneumatic cylinder and hydraulic cylinder, including single acting cylinder and double acting cylinder.

8.1.2

Natural Frequency of Pneumatic Cylinder

8.1.2.1

Natural Frequency of Single Acting Cylinder

Figure 8.1 shows a typical load mass–spring system diagram, which shows the system composed of load mass M and spring K. The natural frequency of the system is

8.1 Pneumatic Cylinder and Hydraulic Cylinder

3

Fig. 8.1 Load mass–spring system

rffiffiffiffiffi K x¼ M

ð8:1Þ

In general, the natural frequency of pneumatic servo valve is much higher than that of pneumatic cylinder. Assuming that the cylinder chamber is in balance when it is closed, the natural frequency of pneumatic servo valve-controlled cylinder system varies with the state of a certain mass of gas in the chamber. Cylinder characteristics are derived from the volume of cylinder chamber, the change of air pressure in chamber, the change of volume, and the equation of motion of the movable part. Single acting or double acting cylinder system is equivalent to load-mass equivalent spring system. Figure 8.2 is a schematic diagram of a single acting pneumatic servo system. When gas is used as a working medium, the gas density of a certain mass in cylinder depends on pressure and temperature, and the

Fig. 8.2 Single acting pneumatic cylinder or hydraulic cylinder

4

8 Pneumatic Actuators, Driving Elements and Accessories

thermodynamic characteristics of gas need to be considered. As an ideal gas, the equation of state of the gas is pV n ¼ const

ð8:2Þ

where p Gas pressure; V Gas volume; n Variable index of gas state change. Finding derivation on both sides of the formula, it is obtained V n dp þ nV n1 pdV ¼ 0; that is, Vdp þ npdV ¼ 0 The definition of gas volumetric elastic modulus b0 in cylinder chamber is b0 ¼ V

dp ¼ np dV

ð8:3Þ

Here, gas is a compressible fluid, a function of pressure, which varies linearly with the pressure. Volumetric elastic modulus A of gas is not a constant, its value is related to gas pressure and variable index. For example, when the gas pressure is 5  105 Pa and 10  105 Pa, respectively, the volumetric modulus of elasticity of chamber is 7  105 Pa and 14  105 Pa, which is two times different in value. Assuming that the pneumatic cylinder system has a small disturbance near the equilibrium position, the pneumatic cylinder system is equivalent to the load mass– spring system. The equivalent spring stiffness acted by the pneumatic cylinder chamber is dF Adp A2 b0 ¼ ¼ dV dx V

ð8:4Þ

V ¼ V0 þ Ax

ð8:5Þ

Keq ¼ 

A

where V0 V x A

Cavity gas volume including pipeline (m3 ); Volume of Gas in Gas Chamber (m3 ); Displacement of piston from initial position (m); Effective area of cylinder piston (m2 ).

The natural frequency calculation method of pneumatic cylinder system is the same as that of load mass–spring system ðK ¼ 0Þ:

8.1 Pneumatic Cylinder and Hydraulic Cylinder

5

rffiffiffiffiffiffiffiffiffiffiffiffirffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Keq nA2 p nA2 p ¼ ¼ x¼ VM M ðV0 þ AxÞM

ð8:6Þ

When the piston is at the extreme position of the cylinder, that is, at the end of the piston ðx ¼ 0Þ, the natural frequency reaches the maximum. At this point, the natural frequency is xmax

sffiffiffiffiffiffiffiffiffiffi nA2 p ¼ V0 M

ð8:7Þ

As shown in Eq. (8.7), the smaller the volume of gas (V0 ) in the pipeline connected to the cylinder, that is, when the piston is at the end of the cylinder, the natural frequency of the cylinder system theoretically has the maximum value. Especially as shown in Eq. (8.6), the smaller the gas volume (V0 ) in the pipeline, such as V0 ¼ 0, when the piston is at the end of the cylinder, the theoretical natural frequency of the cylinder system has the maximum value. The theoretical relationship between the natural frequencies of a single acting cylinder system and the position of piston is shown in Fig. 8.3 and Table 8.1. From Fig. 8.3, it can be seen that the stiffness of equivalent gas spring in the chamber varies with the initial position of piston. When the piston of the single acting cylinder is at the end of the cylinder, the gas volume in the pipeline is the smallest (Piston in extreme position, near end cap x  0), the natural frequency of the pneumatic control system is the highest, and the equivalent spring stiffness of the gas in the air chamber reaches the maximum. For example, when the gas pressure is 5  105 Pa, the area of cylinder is 34:3 cm2 , and the volume of gas between cylinder and pipeline is 3:00 cm3 , the stiffness of air spring is keq ¼ 2:75  106 N=m.

Natural frequency

Fig. 8.3 Natural frequency characteristics of pneumatic single acting cylinder system ðK ¼ 0Þ

Initial position of piston

6

8 Pneumatic Actuators, Driving Elements and Accessories

Table 8.1 Natural frequency characteristics of pneumatic single acting cylinder system (V0 ¼ 0) x/s f%

0 ∞

0.1 316

0.2 224

0.3 183

0.4 158

0.5 142

0.6 129

0.7 120

0.8 112

0.9 106

1.0 100

Fig. 8.4 Structural sketch of double acting pneumatic cylinder and double acting hydraulic cylinder

8.1.2.2

Natural Frequency of Double Acting Cylinder

Figure 8.4 shows a schematic diagram of a double acting cylinder. It is defined that the piston stops steadily in the geometric intermediate position of the actuator as the reference state. The volume of gas is the volume in the pipeline and the volume in the actuator. The actuator system with different piston rod diameters on both sides of the actuator piston is equivalent to the equivalent mass–spring system composed of two equivalent gas springs, whose equivalent spring stiffness is A21 b1 V10 þ A1 x

ð8:8Þ

A22 b2 V20 þ A2 ðs  xÞ

ð8:9Þ

Keq1 ¼ Keq2 ¼ where V1 , V2 b1 ; b1 A1 ; A2

Fluid volume of two cavities of actuator, and V1 ¼ V10 þ A1 x, V2 ¼ V20 þ A2 ðs  xÞ; Volumetric elastic modulus of gas in two cavities of actuator, b1 ¼ np1 ; b2 ¼ np2 ; Effective area of two cavities of actuator (m2 );

8.1 Pneumatic Cylinder and Hydraulic Cylinder

7

V10 ; V20 Fluid volume between pipes and control valves on both sides (m3 ); p1 ; p2 Fluid Pressure in two cavities of actuator (Pa); s Maximum displacement of piston (m). The effective spring stiffness of two parallel equivalent mass–spring systems is K ¼ Keq1 þ Keq2 , that is, K¼

A21 b1 A22 b2 A21 np1 A22 np2 þ ¼ þ V10 þ A1 x V20 þ A2 ðs  xÞ V10 þ A1 x V20 þ A2 ðs  xÞ

ð8:10Þ

The natural frequency of the double acting cylinder is rffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi K A21 np1 A22 np2 x¼ ¼ þ M ðV10 þ A1 xÞM ½V20 þ A2 ðs  xÞM

ð8:11Þ

When the piston is in two extreme positions of the cylinder, there is, rffiffiffiffiffiffiffiffiffiffiffi Kmax1 M rffiffiffiffiffiffiffiffiffiffiffi Kmax2 ¼ M

When x ¼ 0; Kmax1 ¼

A21 np1 A22 np2 ; xmax1 ¼ þ V10 V20 þ A2 s

ð8:12Þ

When x ¼ s; Kmax2 ¼

A21 np1 A2 np2 þ 2 ; xmax2 V10 þ A1 s V20

ð8:13Þ

The following assumptions are made for the position control system with cylinder: (1) There is p1 A1 ¼ p2 A2 in the initial position equilibrium state of the cylinder. (2) The volume of gas in cylinder is much larger than that in pipeline, that is, the volume of gas in pipeline can be neglected, that is V10 ¼ V20 ¼ 0. By Eqs. (8.10) and (8.11), the equivalent gas spring stiffness and natural frequency of the cylinder system are, respectively,   nA1 p1 nA2 p2 1 1 þ þ ¼ nA1 p1 x sx x sx rffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  ffi K nA1 p1 1 1 þ  x0 ¼ ¼ M x sx M

K¼

ð8:14Þ

From the above equation, it can be seen that the natural frequency of the cylinder system varies with the initial position of the piston. The natural frequency characteristics of the double acting cylinder can be calculated by Eq. (8.14). The calculated results are shown in Fig. 8.5 and Table 8.2. According to Eq. (8.14), the condition for the minimum natural frequency is dK=dx ¼ 0, that is when x=s ¼ 0:5; K ¼ Kmin .

8 Pneumatic Actuators, Driving Elements and Accessories

atural frequency

8

0

Initial position of piston Fig. 8.5 Natural frequency characteristics of pneumatic double acting cylinder (A1 ¼ A2 or A1 6¼ A2 ) Table 8.2 Effect of initial pressure on natural frequency characteristics of dual acting cylinder (A1 ¼ A2 or A1 6¼ A2 ; V10 ¼ V20 ¼ 0) x/s f%

0 ∞

0.1 167

0.2 125

0.3 109

0.4 103

x ¼ xmin

0.5 100

0.6 103

0.7 109

0.8 125

0.9 167

1.0 ∞

rffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4nA1 p1 ¼ sM

It can be seen from the above equation that when the piston is in the central position of the cylinder, the natural frequency reaches the minimum, whether the double acting symmetrical cylinder or the double acting asymmetrical cylinder. The influence of piston initial position and cylinder initial pressure on frequency characteristics is shown in Fig. 8.6. The higher the initial value of cylinder gas pressure, the greater the natural frequency of cylinder.

8.1.3

Natural Frequency of Hydraulic Cylinder

The structure of hydraulic cylinder is similar to that of pneumatic cylinder. Hydraulic cylinder uses hydraulic oil as a working medium and cylinder uses compressed gas such as air as a working medium, but the basic characteristics of the two are quite different. The compressibility of hydraulic cylinders is generally shown in the dynamic characteristics of the cylinder system. The volume elasticity

8.1 Pneumatic Cylinder and Hydraulic Cylinder

9

atural frequency

Fig. 8.6 Effect of Initial pressure on natural frequency characteristics of double acting cylinder (A1 ¼ A2 or A1 6¼ A2 )

Initial position of piston

coefficient of hydraulic oil varies little with pressure and temperature, so it can be regarded as a hydraulic spring with larger spring stiffness. As shown in Fig. 8.4, the spring stiffness of the two equivalent springs of the double acting hydraulic cylinder system are respectively, Keq1 ¼

A21 b A22 b ; Keq2 ¼ V10 þ A1 x V20 þ A2 ðs  xÞ

The double acting hydraulic cylinder can be regarded as a mass–spring system consisting of two springs in parallel. The spring stiffness and natural frequency are, respectively, A21 b A22 b þ V10 þ A1 x V20 þ A2 ðs  xÞ rffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi K A21 b A22 b x¼ þ ¼ M ðV10 þ A1 xÞM ½V20 þ A2 ðs  xÞM

K¼

ð8:15Þ

When the natural frequency is minimized, and the piston position dK=dx ¼ 0, it is obtained that K ¼ Kmin ; x ¼ xmin pffiffiffiffiffi  pffiffiffiffiffi pffiffiffiffiffi A1 =A2 V20  A2 =A1 ÞV10 þ A1 s pffiffiffiffiffi pffiffiffiffiffi x0 ¼ A1 þ A2

ð8:16Þ

When the natural frequency is maximized, the piston is in two extreme positions at both ends of the hydraulic cylinder:

10

8 Pneumatic Actuators, Driving Elements and Accessories

A21 b A22 b þ V10 V20 þ A2 s A21 b A2 b þ 2 ¼ V10 þ A1 s V20

When x ¼ 0; Kmax1 ¼ When x ¼ s; Kmax2

When the volume of oil in pipeline is neglected and only the volume of oil in the cylinder is considered, the natural frequencies and their minimum values of the hydraulic cylinder system are, respectively, V10 ¼ V20 When, x0 ¼ xmin

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  ffi b A1 A2  þ ¼ 0; x ¼ M x sx

pffiffiffiffi ffi A1pffiffiffiffi s, the x0 ¼ pffiffiffi A1 þ A2 qffiffiffiffiffipffiffiffiffiffi pffiffiffiffiffi b A1 þ A2 : ¼ Ms

minimum

natural

ð8:17Þ frequency

is

By Eq. (8.17), the natural frequencies of double acting symmetrical hydraulic cylinders are shown in Fig. 8.7 and Table 8.3. When the piston is in two extreme positions of the hydraulic cylinder, the natural frequency reaches the maximum. When the piston is in the middle position of the hydraulic cylinder, the natural frequency reaches the minimum. qffiffiffiffiffiffi 2b When x0 ¼ 0:5s, the natural frequency reaches the minimum value x0 ¼ 2 AsM . When the effective area of the left and right piston rods of the hydraulic cylinder is not the same, the hydraulic cylinder is asymmetric. As shown in Eq. (8.17), for example, in the case of A1 ¼ 2A2 , the natural frequency characteristics of the cylinder are shown in Fig. 8.8 and Table 8.4. When the piston reaches the extreme position of the end caps on both sides of the cylinder, the natural frequency reaches

Natural frequency

Fig. 8.7 Natural frequency characteristics of double acting hydraulic cylinder (A1 ¼ A2 )

Initial position of piston

8.1 Pneumatic Cylinder and Hydraulic Cylinder

11

Table 8.3 Natural frequency characteristics of double acting hydraulic cylinder (A1 ¼ A2 ) x/s f%

0 ∞

0.1 167

0.2 125

0.3 109

0.4 103

0.5 100

0.6 103

0.7 109

0.8 125

0.9 167

1.0 ∞

Natural frequency

Fig. 8.8 Natural frequency characteristics of double acting asymmetric hydraulic cylinder (A1 ¼ 2A2 )

Initial position of piston Table 8.4 Natural frequency characteristics of double acting asymmetric hydraulic cylinder (A1 ¼ 2A2 ) x/s f%

0 ∞

0.1 190

0.2 139

0.3 118

0.4 107

0.5 102

0.6 100

0.7 103

0.8 114

0.9 145

1.0 ∞

the maximum value. But when the natural frequency is the minimum, the piston is not in the central position, but determined by the following equation: pffiffiffi  When x0 ¼ 2  2 s, the natural frequency reaches the minimum value ffi pffiffiffiqffiffiffiffiffi  2b . x0 ¼ 1 þ 2 AsM

8.1.4

Comparison of Pneumatic Cylinder System and Hydraulic Cylinder System

(1) Difference between incompressible and compressible fluids: Eqs. (8.11) and (8.15) show that the expressions of natural frequencies and dynamic characteristics of pneumatic cylinder system and hydraulic cylinder system are very similar. However, the volumetric elastic coefficients of fluids differ greatly. The volumetric elastic coefficient of hydraulic oil is very large and can be approximately considered as a noncompressible fluid. The compressibility of gases, such as air, must be taken into account.

12

8 Pneumatic Actuators, Driving Elements and Accessories

(2) Difference of Volumetric Elasticity Coefficient: Atmosphere b0 ¼ 7  105  14  105 ½Pa; Actuating Oil of Hydraulic System b ¼ 1:4  109  1:86  109 ½Pa; The difference is about 2000 times. (3) From the Eqs. (8.11) and (8.15), it can be seen that the natural frequencies of pffiffiffiffiffiffiffiffiffiffi cylinders and pneumatic cylinders are about 2000 times (45 times) different for actuators of the same size. (4) Difference of Piston Positions at the Minimum Natural Frequency: i. Pneumatic: The minimum natural frequencies of symmetrical and asymmetrical cylinders occur when the piston is in the middle of the cylinder. When analyzing the stability of the pneumatic system, only the piston in the neutral position of the cylinder needs to studied. ii. Hydraulic: The minimum natural frequency of a symmetrical cylinder occurs when the piston is in the middle of the cylinder. However, the minimum natural frequency of an asymmetric cylinder occurs somewhere in which the piston deviates from the middle of the cylinder. When analyzing the stability of hydraulic system, the symmetrical cylinder only needs to study that the piston is in the neutral position of the cylinder; the asymmetrical cylinder needs to study that the piston deviates from the neutral position of the cylinder. (5) The mechanical structure of hydraulic cylinder and cylinder is basically the same.

8.1.5

Conclusions

By analyzing the natural frequencies of pneumatic cylinder and hydraulic cylinder when the piston is in or off the central position of the actuator with asymmetric effective area on both sides, the following results can be obtained by comparing and analyzing them: (1) When the piston is in different positions, the natural frequencies of pneumatic cylinder or hydraulic cylinder are completely different. When the piston is in the position of both ends of the end cap of the actuator, the natural frequency reaches the maximum. (2) When the piston of pneumatic single acting cylinder is in the end position, the natural frequency reaches the maximum. When the piston is in the middle position, the natural frequency of the double acting cylinder reaches the minimum, whether the symmetrical cylinder A1 ¼ A2 or the asymmetrical cylinder A1 ¼ 2A2 . Symmetrical hydraulic cylinder, such as A1 ¼ A2 , when the piston is in the central position, the natural frequency reaches the minimum. For asymmetric cylinders, such as A1 ¼ 2A2 , the minimum natural frequency

8.1 Pneumatic Cylinder and Hydraulic Cylinder

13

occurs somewhere where the piston deviates from the center of the cylinder, pffiffiffi  such as x ¼ 2  2 s. (3) When the piston of the pneumatic cylinder or hydraulic cylinder is in the central position or somewhere away from the central position, the natural frequency is the smallest. At this time, the stability of the control system is the lowest, so it is necessary to analyze the stability of the system when the piston is in this position in detail. The maximum natural frequency occurs when the piston of the pneumatic cylinder or hydraulic cylinder is at both ends of the end cap, and the actuator system has good rapidity. The minimum and maximum natural frequencies are the key factors to be considered in the design and application of control systems. (4) The analysis method and results of linear motion actuator are also applicable to rotary motion swing actuator.

8.2 8.2.1

Structure and Characteristics of Actuators Pneumatic Cylinder

In pneumatic servo control system, the commonly used actuators are cylinder and pneumatic motor (vane motor and gear pneumatic motor). Figure 8.9 shows the typical structure of the pneumatic actuator cylinder. Although the structure of pneumatic servo control system is similar to that of hydraulic servo control system, the working conditions of actuators vary greatly because of different working media. For example, the lubrication condition of the actuator of pneumatic servo system is obviously not as good as that of the actuator of hydraulic servo system. It is difficult to analyze the problem by analytical method because of the nonlinear friction between the sealing filler of cylinder and the coupling parts with relative motion. For example, the difference between the characteristics of pneumatic servo mechanism obtained by linearization method and the actual characteristics is mainly caused by the nonlinear friction between the sealing filler and the moving parts. In order to better design and select a suitable pneumatic servo control system, it is meaningful to make some necessary analysis Fig. 8.9 Cylinder with buffer. 1—Piston rod; 2— back cylinder cap; 3— fastening stud; 4—cylinder body; 5—seals; 6—piston; 7—front cylinder cap (containing buffer oil circuit)

14

8 Pneumatic Actuators, Driving Elements and Accessories

Needle valve

(a)

(b)

Fig. 8.10 Structural sketch of double piston rod (a) and single piston rod (b) cylinder

for the executing elements of the system. This section focuses on the analysis of the reasons and characteristics of pneumatic cylinder widely used in servo control. The types of cylinders can be distinguished according to the mode of air supply, the formation of cylinder piston rod, the sealing method and whether there are buffers or not. Figure 8.10 shows the structure of the double piston rod and single piston rod cylinder. There is also a corrugated diaphragm (or film) cylinder in the cylinder series. Figure 8.11 shows the structure of this kind of cylinder. Obviously, the greatest advantage of this kind of corrugated diaphragm cylinder is that the friction between moving parts is almost imperceptible and there is no internal leakage. Of course, this kind of corrugated diaphragm cylinder is only suitable for small stroke control system. The working process with buffer groups can be referred to in Figs. 8.9 and 8.12. When the piston approaches the end of the cylinder quickly, before the piston stroke is over, in order to absorb the kinetic energy of the piston that the piston speed is reduced to prevent the piston from hitting the cylinder head, at the moment that the piston approaches the end of the cylinder head stroke, the sealing ring of the small piston of the buffer blocks the exhaust hole of the end cap and the passage of the cylinder capacity chamber. The gas enclosed at the end of the cylinder can only be throttled out to the outside of the cylinder through a needle valve. At this time, the piston compresses the gas enclosed at the end of the cylinder, which produces a cushioning and braking effect, so that the piston reduces speed and meets the requirement of preventing the piston from colliding with the end cap. After the cylinder completes the left stroke, the piston moves to the opposite direction (Fig. 8.12). The airflow enters the chamber at the end of the small piston of the buffer through the inlet hole. Except for part of the airflow enters the chamber

Fig. 8.11 Principle of corrugated diaphragm cylinder

Corrugated film Reset spring Piston rod

8.2 Structure and Characteristics of Actuators

15 Piston

Throttling needle valve

Piston rod

Inlet and exhaust holes One-way valve Buffer small piston

Fig. 8.12 Buffer schematic diagram

at the end of the cylinder through the throttling needle valve, most of the gas passes through the one-way valve to supply air in a non-damped way (or under the condition of very small damp) to drive the piston to complete the second stroke. In fact, whether in pneumatic transmission or pneumatic servo technology, in addition to the piston speed is very slow, usually a buffer cylinder is used.

8.2.1.1

Static Characteristics of Cylinders

The static characteristics of cylinder usually refer to the output thrust of cylinder and the amount of compressed gas consumed by cylinder in unit stroke. The following are described separately. (1) Cylinder Output Thrust Taking the single-side cylinder shown in Fig. 8.13 as an example, assuming that the effective area of both sides of the piston is A1 and A2 , respectively, and the gas supply and exhaust pressures are p1 and p2 , respectively, the theoretical thrust that the piston can output is as follows: Fth ¼ A1 p1  A2 p2

Fig. 8.13 Computation of cylinder thrust

ð8:18Þ

16

8 Pneumatic Actuators, Driving Elements and Accessories

In fact, the actual output thrust of the piston rod is smaller than the theoretical thrust Fth because of the mechanical friction between the inner wall of the cylinder and the piston seal ring and the inertia force of the cylinder moving parts. If factors such as friction force and inertia force are taken into account, the actual thrust output of the piston is as follows:     dv F ¼ Fth  Rf þ Uf ¼ A1 p1  A2 p2  Rf þ m dt

ð8:19Þ

or F ¼ A1 p1  A2 p2  Rf  m

dv dt

ð8:20Þ

where m v Rf

Mass of piston and parts moving with piston; Piston speed; The sum of all frictional forces in the cylinder device, including the frictional forces at the contact surface of the sealing filler and the sliding parts of the cylinder inner wall. The magnitude of these frictional forces is related to the type of sealing filler, working pressure, and processing conditions of cylinder inner wall. The frictional force is obtained by experiment and it is very difficult to calculate by mathematical analytic method.

(2) Gas consumption per stroke In the performance analysis or design calculation of the actuator of servo system, the important parameter is the geometric size of the actuator or the volume of the cylinder. Therefore, when calculating the amount of gas consumed in each stroke of the cylinder, the volume flow is usually converted from the weight of the gas consumed in each stroke to the volume flow of the gas under the standard atmospheric pressure. The purpose of this method is to select the standard cylinder conveniently because the volume is directly related to the size of the cylinder. If the single piston rod cylinder is discussed, as shown in Fig. 8.14, the amount of gas consumed by the cylinder during driving load and no-load return can be calculated, respectively. If the working volume of the cylinder is V1 and V2 , respectively, and the time required for each working stroke is t, according to the gas state equation, the relationship between the gas displacement per unit stroke and the pressure in the free state (standard atmospheric pressure) consumed by the round trip can be obtained as follows.

8.2 Structure and Characteristics of Actuators Fig. 8.14 Working sketch of cylinder

1. When loaded

17

Loaded

Load-free

pa Va1 ¼ ðp1 þ p2 ÞV1

ð8:21Þ

2. Load-free (i.e. no-load return) pa Va2 ¼ ðp1 þ p2 ÞV2

ð8:22Þ

3. Another expression is obtained by dividing Eqs. (8.21) and (8.22) by the time t required for working travel: pa Va1 ðp1 þ p2 Þ ¼ V1 t1 t1

ð8:21’Þ

pa Va2 ðp1 þ p2 Þ ¼ V2 t2 t2

ð8:22’Þ

4. Calculate the volume flow q1 and q2 of the gas required for each trip. Because the volumes on both sides of the piston are V1 ¼

pD2 L pðD2  d 2 ÞL and V2 ¼ 4 4

Under the standard condition, the gas volumetric displacement per unit stroke is, respectively, q1 ¼

Va1 Va2 and q2 ¼ t1 t2

If the unit conversion relation is introduced, the volume flow rate of gas required to complete a loaded working trip and a no-load return journey can be obtained.

18

8 Pneumatic Actuators, Driving Elements and Accessories

q1 ¼

60 pD2 L p1 þ p2 D 2 L p1 þ p2 ¼ 0:047 1000 4t1 t1 pa pa q2 ¼ 0:047

ðD2  d 2 ÞL p1 þ p2 t2 pa

ð8:23Þ ð8:24Þ

where Va1 Va2 pa V1 V1 p1 p2 D d L t1 ; t2

The amount of gas consumed by driving load stroke converted into standard gas volume under the standard condition; The amount of gas consumed during the no-load return journey is converted into the gas volume under the standard condition; Standard atmospheric pressure; The working volume of the side without piston rod; There is working volume on the side with piston rod. Inlet pressure; Exhaust pressure with load working stroke; Piston diameter; Piston rod diameter; Piston stroke; The time required for on-load working trip and no-load return trip.

Therefore, if the piston goes to and fro N times per minute, the theoretical value of the volume flow rate of the gas consumed under the standard atmospheric pressure is obtained as follows: Qth ¼ ðq1 t1 þ q2 t2 ÞN

ð8:25Þ

Generally, the leakage of gas in control elements (such as control valves and pipeline systems.) and other unexpected loss of gas flow account for 35*50% of the theoretical flow. Therefore, the actual gas required by the cylinder should be taken as 1.5 times of the theoretical gas consumption Qth .

8.2.1.2

Dynamic Characteristics of Cylinder

In addition to the static characteristics of the cylinder as the output thrust and gas consumption of the cylinder piston discussed above, there are also the minimum starting pressure of the piston and the airtightness of the cylinder. Because of the inherent physical characteristics (such as compressibility) of gas itself, and the friction force at the inner wall of cylinder and the sealing filler of piston rod, the dynamic characteristics of cylinder are quite different from those of hydraulic cylinder. The dynamic characteristics of the cylinder include the starting characteristics of the cylinder, the motion characteristics of the piston, the natural

8.2 Structure and Characteristics of Actuators

19

frequencies of the cylinder, and the positioning characteristics of the piston. Several important dynamic characteristics are discussed below. (1) Load-free working characteristics The so-called load-free working characteristics mainly determine the lowest working pressure of the cylinder, that is to say, under this limit pressure, the cylinder does not crawl at low speed. The main factors affecting the minimum pressure are the processing accuracy and surface roughness of the sealing filler and the inner wall of the cylinder. The load-free working characteristic test methods are as follows (because it is not yet possible to accurately compute them by computational method): The cylinder running in and out after a period of time is placed horizontally without loading, then compressed gas is injected alternately at both ends of the piston to observe whether the piston moves smoothly and continuously, so as to determine the minimum working pressure. Practical experience shows that the lowest supply pressure (gauge pressure) used in general control system, that is, the lowest working pressure of cylinder is 0.02*0.05 MPa. Obviously, if the static friction between the piston and the cylinder wall is small, the minimum working pressure of the cylinder can be reduced. However, small friction force requires high accuracy of piston, and easily causes piston oscillation, which makes the cylinder work in an unstable state. (2) Frictional force of Cylinder Seals For one of the actuators used in pneumatic servo control system, an important principle is to minimize gas leakage (including external and internal leakage). However, due to the types of sealing parts at cylinder end cap and piston rod, the sealing form and sealing material of piston, air leakage is inevitable. Because the working medium of the system has little pollution to the environment, it is still allowed to leak to some extent. Frictional force of cylinder seals is directly related to piston starting, creeping, and delay. Therefore, the design of seals is particularly important. In order to obtain less leakage sealing device, it is bound to result in complex structure of sealing filler and increase friction force. Experience shows that the friction force at cylinder seals varies due to the different seal structure, lubrication state, piston residence time, and external load. The theoretical calculation between them is very difficult and can only be explained by the experimental results. In this paper, the experimental results of the typical seal structure shown in Fig. 8.15, which are influenced by the starting, running, and residence time of the cylinder, are presented as examples. The variation of pressure p1 , p2 , and piston stroke (expressed by displacement z) in the chambers on both sides of the piston in the cylinder can be approximately described by Fig. 8.16 during starting and running of the piston. As shown in the figure, if the gas pressure in the chambers on both sides of the piston is p1s and p2s when starting, and the pressure in the chambers on both sides of the piston is p1e

20

8 Pneumatic Actuators, Driving Elements and Accessories

Fig. 8.15 Cylinder piston seal construction

Pressure

1

2

Displacement z

Fig. 8.16 Pressure diagram inside cylinder

Time t and p2e when the piston speed is stable, the friction fs at starting and the friction fe at piston motion can be obtained, respectively, by the following: fs ¼ ðp1s  p2s ÞAf  W fe ¼ ðp1e  p2e ÞAf  W

 ð8:26Þ

where Af Effective area of cylinder piston; W Total weight including piston and piston rod. For the same lubrication condition of the cylinder coupling parts, the experimental results obtained by changing the residence time, i.e., the relationship between starting friction and residence time, are shown in Fig. 8.17. The variation of frictional force fv caused by different piston speeds is described in Fig. 8.18. From the above experimental results (Figs. 8.17 and 8.18), it can be seen that the length of piston residence time in cylinder and the difference of piston speed have little effect on the friction force. Therefore, in the analysis and design of pneumatic

8.2 Structure and Characteristics of Actuators

21

Frictional force f /N

Fig. 8.17 Effect of residence time

Good Lubrication General condition Poor l

Fig. 8.18 Effect of piston velocity

Frictional force f /N

Residence time/s

Piston speed /(m/s)

servo system, it is in line with or close to the actual situation to treat the friction resistance of the motion coupling parts in the cylinder as a constant. It must be pointed out that if there is a part of liquid lubrication between the sealing surfaces of cylinder piston, the friction force is usually expressed in the following: fce ðfriction forceÞ ¼ fc ðCoulomb friction forceÞ þ fe ðViscous friction forceÞ fce ¼ fc þ fe :

ð8:27Þ

or fce ¼ fc þ bv where b Viscous friction coefficient depending on the properties of lubricating fluids; v Piston speed.

22

8 Pneumatic Actuators, Driving Elements and Accessories

From the experimental results of Fig. 8.18, we can see that the piston speed has no effect on the friction force. Therefore, in this case, the change of friction resistance fce mainly depends on the change of nonlinear Coulomb friction force. So there is a big difference between the results obtained by the approximate linear method and the experimental results in the analysis and characteristic calculation of servo system.

8.2.1.3

Motion Characteristics of Piston

The purpose of discussing the motion characteristics of piston is to find out which factors are related to the variation of cylinder pressure, piston speed, and piston starting lag time during piston starting and running. The following will be through some actual piston motion curves to analyze the various factors affecting the piston motion characteristics. (1) Piston Motion Characteristics of No-load Ideal Cylinder When the cylinder is in the ideal state without load (i.e., without considering the influence of friction between coupling parts such as cylinder and piston and sealing packing), if the pressure in the chamber on both sides of the piston is p1 (inlet side) and p2 (exhaust side), and the piston speed is v and time is t, the variation of gas pressure p1 , p2 , and piston speed v with time t can be expressed by the curve in Fig. 8.19. The coordinates of pressure–time curve (or p=ps  t=Ta curve) and velocity–time curve (or v=v0  t=Ta curve) are expressed by a dimensionless quantity and p1 =ps , p2 =ps , v=v0 , t=Ta . Among them, ps is the supply pressure; v0 is the average velocity Fig. 8.19 Piston motion characteristics of no-load ideal cylinder

8.2 Structure and Characteristics of Actuators Fig. 8.20 Piston characteristic test circuit principle

23

Regulating valve

Solenoid reversing valve Gas supply pressure

To Atmosphere

of cylinder and piston in the isothermal process under the standard state; T0 is the time required for the piston to complete a stroke Zp with the average velocity v0 , that is, Ta ¼ zp =v0 . The piston motion characteristics of no-load ideal cylinder shown in Fig. 8.19 can be illustrated by the test circuit of cylinder piston characteristics shown in Fig. 8.20. As shown in Fig. 8.20, after the piston completes its last stroke, the solenoid reversing valve is switched on. At this time, the working chamber ① of the cylinder is connected to the gas source with the pressure of p0 , and a new working stroke is started. The compressed air enters the working chamber ① and causes the pressure p1 ¼ ps in chamber ①. Under the action of pressure difference p1  p2 ¼ Dp, the piston starts to move. With the acceleration of piston and the influence of load inertia, the gas entering the cylinder cannot be replenished, which causes the pressure p1 in chamber ① to decrease. At the same time, because the working chamber ② of the cylinder is connected with the atmosphere, the gas pressure p2 in chamber ② also decreases. Nevertheless, the pressure difference Dp ¼ p1  p2 remains positive (part A as shown in Fig. 8.19), so the piston continues to accelerate. When the piston speed ratio reaches v=v0 [ 1, the gas pressure p1 in the working chamber ① of the cylinder will be reduced to almost the same level as that in chamber ②, to less than p2 , i.e., p1  p2 \0 (part B as shown in Fig. 8.19), and the piston begins to decelerate. As the piston decelerates, the gas pressure p1 in the working chamber of the cylinder rises, and p1  p2 ¼ Dp is positive. The piston accelerates again, and the piston velocity curve shown in Fig. 8.19 shows that the piston velocity fluctuates several times near its average speed. (2) Piston Motion Characteristics of Actual Cylinder When discussing the motion characteristics of the piston in the ideal cylinder without load, many factors that affect the motion state of the piston are neglected. The piston motion characteristics of the actual cylinder are related to the mass of the moving parts of cylinder, the flow characteristics at the inlet and exhaust ports of

24

8 Pneumatic Actuators, Driving Elements and Accessories

cylinder, the initial position of the piston, and the change of the gas state in cylinder. In addition, the friction between the moving parts and the resistance at the sealing filler are also related. If these factors affecting piston motion characteristics at the same time are regarded as independent variables, the theoretical calculation results of piston motion characteristics under different conditions can be obtained. In order to investigate the influence of various factors on piston motion characteristics, the following dimensionless quantities and parameters are introduced. 1. B ¼ Cv1 =Cv2 represents the flow coefficient ratio of the inlet and exhaust passages of the cylinder. B value is large, indicating that the flow coefficient Cv1 of the inlet port is large, that is, the flow resistance of the inlet port is small, that is to say, the amount of gas entering the working chamber ① of the cylinder through the inlet port increases in unit time. A small B value indicates that the throttling loss at the outlet passage of the cylinder is large, and it becomes an outlet throttling  circuit.  2. I ¼ ðA1 ps =M Þ zp =v20 , when the action area A1 , the supply pressure ps , the piston working stroke zp , and the piston average velocity v0 are known, the dimensionless quantity is proportional to the reciprocal of the mass M of the cylinder moving parts. It shows that the smaller the I value, the greater the inertia of the cylinder moving parts. 3. S0 ¼ z0 =zp represents the ratio of the initial position of the piston before starting to the working stroke zp of the piston. The smaller the S0 value is, the closer the piston’s starting position is to the side of the inlet port, that is to say, the volume of cylinder working chamber ① is the smallest, while that of cylinder working chamber ② on the other side of the piston is the largest, and vice versa. 4. Ta ¼ zp =v0 represents the time required to complete a working stroke zp at the piston average velocity v0 . 5. Wt represents the total load acting on the piston (including frictional force). According to the dimensionless quantities p1 =ps , p2 =ps , v=v0 , t=Ta quoted previously and the newly defined dimensionless quantities B, I, S0 as well as the parameters Ta and load Wt , the gas state in the cylinder is calculated according to three different changing processes, that is, adiabatic process, variable process and isothermal process, and the calculated piston motion characteristics (i.e., the relationship between pressure p1 , p2 and piston velocity v and time t) and the experimental results are drawn together on the dimensionless coordinate diagram. Figures 8.21 and 8.22 are the theoretical curves and experimental results of the motion characteristics of cylinder and piston based on the above method (the dots in the figure represent the measured values). From Figs. 8.21 and 8.22, it can be seen that the theoretical calculation results are in good agreement with the measured results, if the gas state in cylinder is calculated according to the multivariate process (n ¼ 1:2). Therefore, in practical calculation, it is reasonable to regard the change of gas state in cylinder as a variable process (n ¼ 1:2).

8.2 Structure and Characteristics of Actuators

25

Fig. 8.21 Piston motion characteristics at different gas state change processes (I)

Fig. 8.22 Piston motion characteristics at different gas state change processes (II)

Other dimensionless variables and parameters remain unchanged, only changing the dimensionless B value. The theoretical and experimental results are shown in Figs. 8.23, 8.24, and 8.26. In the actual measurement process, different B values are obtained by changing the inlet flow coefficient Cv1 only and keeping the outlet flow coefficient Cv2 unchanged. From Figs. 8.23, 8.24, 8.25 and 8.26, it can be clearly seen that with the increase of B value, the amount of compressed gas entering the working chamber ① of the cylinder increases, while the p1 =ps value rises sharply, and the piston starts to move after reaching a certain value. At this time, if the B value is relatively small (as shown in Fig. 8.23, B ¼ 0:436), the piston with a certain speed will continuously increase the volume of cylinder chamber ①. If the gas supply is insufficient to keep up with the requirements of piston acceleration, the pressure p1 decreases faster than that of B value. For this reason, the piston velocity always

26

8 Pneumatic Actuators, Driving Elements and Accessories

Fig. 8.23 Piston motion characteristic curve (B ¼ 0:435)

Fig. 8.24 Piston motion characteristic curve (B ¼ 1:0)

fluctuates before it reaches its average velocity v0 , and then gradually approaches the average velocity u. If the B value is larger (as shown in Fig. 8.25, B ¼ 2:0), the piston gaining speed increases the volume of the cylinder chamber ① continuously, but because of the B value, the amount of gas entering chamber ① is sufficient, and the change of pressure p1 is not obvious, the piston is accelerated for a long time, and after exceeding the piston’s average speed, the piston will fluctuate slightly near its average velocity v0 and keep moving. If the value of B is large, such as B ¼ 6:8, the piston is accelerated for a long time in the case shown in Fig. 8.26. The velocity obtained is much faster than the average velocity v0 , and the value of the velocity is almost twice the average velocity. Obviously, increasing the B value can shorten the piston travel time. It can also be seen from the piston motion characteristic curve that with the increase of the volume of the cylinder chamber ① before the piston starts, the rising speed of the gas pressure p1 in chamber ① becomes slow, so the starting delay time of the piston increases. In practice, cylinders requiring frequent stopping and restarting at any position are similar to this situation.

8.2 Structure and Characteristics of Actuators

27

Fig. 8.25 Piston motion characteristic curve (B ¼ 2:0)

Fig. 8.26 Piston motion characteristic curve (B ¼ 6:8)

The motion characteristics of piston shown in Fig. 8.27 show that when inertia decreases, i.e., I value increases, the period of fluctuation of piston velocity decreases, i.e., the frequency of variation of velocity increases. And the piston velocity amplitude is larger than the other two cases (as shown in Figs. 8.24 and

28

8 Pneumatic Actuators, Driving Elements and Accessories

Fig. 8.27 Piston motion characteristic curve (I ¼ 269)

8.25). From Fig. 8.27, it can also be seen that the piston travel time is slightly shortened with the increase of I value. The change of load will also affect the motion characteristics of piston. With the increase of the load on the piston, the gas pressure required to drive the piston will increase, so the starting delay time will increase. In addition, when the piston starts, the change of the piston speed fluctuates up and down in a range smaller than the average speed v0 under heavy load. Comparing Figs. 8.24 and 8.27, it is found that the period of velocity variation in the initial stage is almost independent of the size of the load (Wt ), and they are almost equal. (3) Starting Delay Time of Cylinder Piston From Figs. 8.21, 8.22, 8.23, 8.24, 8.25, 8.26 and 8.27, it is clear that the piston does not act immediately when the controlling air flows into the actuator cylinder. It is only when the gas pressure in the working chamber of the cylinder reaches a certain value that the piston starts to move. Usually, the gas pressure at the moment when the piston starts to move is called the starting pressure pp . In this way, the preparation time from the airflow into the working chamber of the cylinder to the start of the action of the cylinder piston is defined as the starting delay time of the piston. The main factors affecting starting delay time are gas parameters (p; V), inertia and load of piston, and other moving parts. Because the motion parameters (velocity, acceleration, etc.) of the moving parts of the cylinder and the gas parameters entering the cylinder can be connected by the differential equation of motion, therefore, the gas parameter pp can be used to analytically correlate other factors affecting the delay time. In this way, it can be known in detail how these factors affect the delay time and provide a theoretical basis for the design of pneumatic servo mechanism and the selection of actuators. If the volume of the working chamber surrounded by the cylinder wall and piston is V (also known as initial volume) before starting of the cylinder piston, and the deformation of the cylinder wall is not considered when the piston is about to

8.2 Structure and Characteristics of Actuators

29

move, the volume V can be considered as the volume of the rigid pressure vessel. According to the relationship between the rate of change of gas weight entering the pressure chamber and the rate of pressure rise (the change of gas state is an isothermal process), it can be written that, dðDW Þ V0 dp ¼ dt RT dt

ð8:28Þ

If the change of gas in cylinder V0 is an adiabatic process, then dðDW Þ V0 dp ¼ dt kRT dt or G¼

V0 dp kRT dt

ð8:29Þ

where DW Mass of the gas entering cylinder; V0 When the piston is in the initial position (or when the piston is in a certain residence position), the volume surrounded by the inner diameter of cylinder and the piston. The value of V0 remains unchanged before the piston starts, which can be understood as the volume of the rigid chamber; k Gas state change index, for atmosphere k ¼ 1:4; R Gas constant; p In-cylinder gas pressure, the initial pressure is p0; T Absolute temperature of gas in cylinder; t Time. There may be two different situations for the flow into the working chamber V0 of the cylinder, i.e., sonic flow or subsonic flow. For the sound adiabatic flow p0 =ps  0:5283 (when k ¼ 1:4), the maximum weight flow into the cylinder is achieved. Gmax

ps ¼ c0 A0 pffiffiffiffiffi Ts

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  ðk þ 1Þ=ðk1Þ kg 2 R kþ1

ð8:30Þ

For subsonic adiabatic flow p0 =ps [ 0:5283, the gas mass flow into the cylinder is vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi "  1=k u  ðk1Þ=k # u 2kg ps p p t G ¼ c0 A0 pffiffiffiffiffi 1 ðk þ 1ÞR ps Ts ps

ð8:31Þ

30

8 Pneumatic Actuators, Driving Elements and Accessories

The change of gas temperature in the working chamber V0 of the cylinder is T ¼ T0

 ð1kÞ=k p0 p

ð8:32Þ

where ps Ts T0 A0 c0

Supply pressure; Absolute gas temperature; Initial temperature of gas in cylinder; Effective cross-section area of channel; Flow coefficient at intake passage.

With Eqs. (8.28)*(8.32), the relationship between piston starting delay time and various factors can be investigated according to two flow states. Knowing the factors affecting the starting delay time of piston is of great significance to the dynamic characteristics analysis of pneumatic servo system, which can guide us to consider the factors affecting the delay time from which aspects, so as to improve the dynamic characteristics of servo system to meet the requirements of use. Next, the starting delay time of piston will be investigated in the sonic (critical) and subsonic (noncritical) flow states. (1) Starting delay time of piston under critical flow condition. If the flow of air through the intake port of the cylinder into the working chamber of the cylinder is sonic adiabatic flow, and the process of gas state change in the cylinder is a polytropic process (according to the previous analysis, the polytropic process is closer to the actual situation), then according to Eqs. (8.29), (8.30), and (8.32), it can be obtained,

pffiffiffiffiffi ps T s c0 A 0 Ts

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  ðk þ 1Þ=ðk1Þ  ð1nÞ=n kg 2 V0 p dp ¼ R kþ1 dt nRT0 pa

So, pffiffiffiffiffi ps Ts c0 A0 Ts

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  ðk þ 1Þ=ðk1Þ  ð1nÞ=n kg 2 V0 p dt ¼ dp R kþ1 nRT0 pa

ð8:33Þ

or pð1nÞ=n dp ¼

nRT0 ð1nÞ=n p Gmax dt V0 0

ð8:34Þ

8.2 Structure and Characteristics of Actuators

31

where n Variation index, n  1:2 for compressed air. If the flow process of the air in the intake passage and the change of the gas state in the cylinder are all polytropic process, then there is pffiffiffiffiffi ps T s c0 A0 Ts

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  ðn þ 1Þ=ðn1Þ  ð1nÞ=n ng 2 V0 p dt ¼ dp R nþ1 nRT0 p0

ð8:33’Þ

or pð1nÞ=n dp ¼

nRT0 ð1nÞ=n p ðGmax Þn dt V0 0

ð8:34’Þ

The gas variation index n is constant. The pressure change in the working chamber of the cylinder can be obtained by integrating the above formula. Zp

pð1nÞ=n dp ¼

Zt

p0

0

nRT0 ð1nÞ=n p ðGmax Þn dt V0 0

Initial conditions: when t ¼ 0, the in-cylinder pressure p ¼ p0  pa (ambient atmospheric pressure). So it is obtained p1=n  p1=n a ¼

nRT0 ð1nÞ=n p ðGmax Þn t V0 a

ð8:35Þ

Because of the critical state of the maximum weight flow [Reference Eq. (8.30)] ps ðGmax Þn ¼ c0 A0 Ts R

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  ðn þ 1Þ=ðn1Þ 2 ngRTs nþ1

So the pressure change in the working chamber of cylinder is calculated by Eq. (8.35) as 2 RT0 ps p ¼ pa 4 c0 A0 V0 pa Ts R

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi3n  ðn þ 1Þ=ðn1Þ 2 5 ngRTs nþ1

ð8:36Þ

The above formula describes the variation of the pressure p on the piston (i.e., in the working chamber of the cylinder) with time t during the charging process. It shows that with the increase of intake time, the pressure in the working chamber of cylinder increases; when the p value reaches the starting pressure pa of the piston, the piston begins to move. The gas pressure p in the working chamber of cylinder

32

8 Pneumatic Actuators, Driving Elements and Accessories

starts at t ¼ 0 and gradually increases from p ¼ pa to the piston starting pressure p ¼ pp . The time t ¼ tp  0, i.e., the time interval tp between the piston’s stationary motion and the piston’s starting motion, is the starting delay time of the piston. If the airflow entering the cylinder through the intake passage of the cylinder is sonic, and the flow process and the state change of the gas in the cylinder are variable, the relationship between the starting delay time tp of the piston and the starting pressure pp of the piston can be obtained by the integral of Eq. (8.36). pZp

pð1nÞ=n dp ¼

p0 ¼pa

tZp

nRT0 ð1nÞ=n p ðGmax Þn dt V0 0 t¼0

ð8:37Þ

Thus, it is obtained 2

pp1=n

3 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  ðn þ 1Þ=ðn1Þ 2 4 RT0 c0 A0 ps ngRTs ¼ p1=n t p þ 15 a nþ1 V0 pa Ts R

After introducing the local sound speed asn ¼ supply flow, the result is as follows: 2 p1=n p

4 RT0 c0 A0 ps asn ¼ p1=n a V0 pa Ts R

ð8:38Þ

pffiffiffiffiffiffiffiffiffiffiffiffi ngRTs and p0 ¼ pa of the air

3 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  ðn þ 1Þ=ðn1Þ 2 1=n tp þ p0 5 nþ1

ð8:38’Þ

After finishing, the expression of starting delay time tp of piston is obtained. pa V0 Ts tp ¼ c0 A0 ps T0 asn K

"  # px 1=n 1 pa

ð8:39Þ

where sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  ðn þ 1Þ=ðn1Þ 2 K¼ nþ1 Obviously, the starting delay time of piston is related to the state parameters of working gas and the structural parameters of cylinder. For example, Eq. (8.39) shows that the starting delay time tp of piston will increase with the increase of initial volume V0 . Physically speaking, when the cross-section area of the intake passage of cylinder A0 is constant, the increase of the initial volume of the working chamber of cylinder V0 will undoubtedly increase the charging time, so the time to reach a certain starting pressure pp will increase, that is, the starting delay time of piston tp will increase. If the flow into the cylinder is not a changeable process, but an adiabatic flow state, and the change of the gas flow into the cylinder is not a

8.2 Structure and Characteristics of Actuators

33

changeable process, but an isothermal process, the expression of the starting delay time tp of the cylinder piston can be simplified as follows: tpk ¼

  p0 V0 Ts pp 1 c0 A0 ps T0 ask Kk p0

ð8:40Þ

tpk ¼

V0 Ts ð px  pa Þ c0 A0 ps T0 ask Kk

ð8:40’Þ

or,

where ask ¼ Kk =

pffiffiffiffiffiffiffiffiffiffiffiffi kgRTs ; rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 

k

Adiabatic index (For atmosphere k ¼ 1:4).

2 kþ1

ðk þ 1Þ=ðk1Þ

;

Obviously, the piston starting pressure pp has a certain relationship with the piston motion parameters (such as speed and acceleration), the sliding friction force between piston and cylinder wall and piston rod at the sealing filler. In general, these relationships can be expressed by the following differential equation of piston motion: m

d2 x  pp A þ P þ f ¼ 0 dt2

ð8:41Þ

where m x A P f

Converted mass of all moving parts on piston; Piston displacement; Piston effective area; Total load converted to the piston (including the force of back pressure on the piston); Total frictional force of piston and piston rod.

From the Eqs. (8.40)’ and (8.41), it can be seen that the delay time of piston starting is related to the workload of cylinder, the position of piston before starting or the initial volume of cylinder, friction force, and air source. Increasing friction force and load on piston will increase the starting delay time, and increasing supply pressure will help to shorten the delay time. For pneumatic servo system, in order to obtain a relatively small starting delay time tp , the supply pressure ps should be increased as much as possible. When the supply pressure of the pneumatic system is limited, the flow coefficient c of the intake passage can be increased. That is to say, tp should be shortened by increasing the section area of intake passage A appropriately and reducing the friction between

34

8 Pneumatic Actuators, Driving Elements and Accessories

cylinder wall and sealing packing. It must be pointed out that the starting delay time of piston is also related to the back pressure of piston, that is to say, to the exhaust process. Generally, the starting delay time tp of the piston of cylinder is between 0.038*0.042 s. (2) The starting delay time of piston in noncritical (subsonic) flow state. If the piston starting pressure pp is greater than the critical pressure of the gas flow, that is, pp [ 0:528; ps ¼ p , the flow in the cylinder passage is subsonic (noncritical). Then, Eq. (8.40)’ cannot be used to calculate piston starting delay time. Therefore, it is necessary to reestablish the analytical formula for calculating piston starting delay time under subsonic flow. The expression of the weight flow rate for subsonic flow of air through the intake passage into cylinder (if the gas state change in flow process is a changeable process) is as follows: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi "  #ffi u 2=n  ðn þ 1Þ=n ps u 2ng p p G ¼ c0 A0 pffiffiffiffiffiffiffiffi t  ps RTs n  1 ps

ð8:42Þ

The rate of pressure change (the rate of pressure change) in the working chamber V0 caused by the gas mass flow into the cylinder satisfies the following relationship (if the change of the gas state in chamber V0 is an isothermal process): G¼

V0 dp RT0 dt

ð8:43Þ

So, c0 A0 T0 V0

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ngR dp ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi dt ¼ r 2=n  ðn þ 1Þ=nffi ðn  1ÞTs p  pps ps

ð8:44Þ

Because the pressure acting on the piston rises from the initial pressure p0 to the piston starting pressure pp , and the piston is stationary before the starting pressure pp is reached, the time from the beginning of intake to the beginning of piston operation is t ¼ 0  t ¼ tp . The relationship between delay time tp and starting pressure pp can be obtained by integrating Eq. (8.44):

8.2 Structure and Characteristics of Actuators

Ztp 0

tpT

35

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Zpp 2ngR dp ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r dt ¼ 2=n  ðn þ 1Þ=nffi ðn  1ÞTs p p0  pps ps sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Zpp V0 ðn  1ÞTs dp ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi r ¼ 2=n  ðn þ 1Þ=n c0 A0 T0 2ngR p p p0  ps ps

c0 A0 T0 V0

ð8:45Þ

Similar to the sonic flow, the starting delay time tp of cylinder piston under subsonic flow is also affected by the gas flow parameters, the state parameters, and the motion parameters of the actuator (cylinder).

8.2.1.4

Cylinder Natural Frequency

The performance of the whole servo system will be affected by the performance of the actuator in the pneumatic servo system. In addition to the piston, starting delay time tp mentioned above is an important characteristic parameter of the cylinder, the natural frequency of the cylinder is also an important characteristic parameter. Referring to the method of calculating the undamped natural frequency of hydraulic cylinder by sliding valve in hydraulic servo system, the cylinder is regarded as a mass gas spring system. According to the definition of motion equation and volumetric elastic modulus B ¼ Dp=

DV V

Calculating undamped natural frequencies of cylinders xnk

sffiffiffiffiffiffiffiffiffiffiffiffi 2kA2 p ¼ V0 m

ð8:46Þ

The upper is the case in which the state change of gas in cylinder is the case of adiabatic process. If the change of gas state in cylinder is an isothermal process, the frequency formula given by Eq. (8.46) should be rewritten as follows: xnT

sffiffiffiffiffiffiffiffiffiffi 2A2 p ¼ V0 m

ð8:46’Þ

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8 Pneumatic Actuators, Driving Elements and Accessories

where A P V0 m

Effective section area of cylinder; Working pressure in cylinder, usually replaced by the supply pressure; Single-side volume of cylinder; Total mass of load and moving parts such as piston.

Generally speaking, the natural frequency of the cylinder is low and the range is 5*10 Hz. In addition to increasing the supply pressure can improve the natural frequency, it can also be used in the selection and design of cylinders to minimize the values of V and m, or try to increase the effective area of piston A.

8.2.1.5

Positioning Stop Accuracy of Piston

In the pneumatic servo control system, the stopping accuracy of piston at any position is a problem that has been widely valued, especially in the open-loop control system. For open-loop control system, the greatest obstacle to stop piston at any position according to the predetermined target and to meet the requirement of positioning accuracy is the error caused by the large compressibility of gas. For pneumatic servo system, although the feedback system can control the piston to stop at any position, due to the direct influence of gas compressibility, small static stiffness, and long delay time of repeated starting, the stability adjustment time of the system increases relatively, while the position accuracy becomes worse. If some compensation measures are added to the pneumatic servo system, such as using dynamic pressure feedback to improve the dynamic stiffness of the system, satisfactory position control accuracy can be obtained.

8.2.2

Pneumatic Motor

Usually, the actuator whose output is rotary motion is called pneumatic motor. If the movement of the output end of the actuator of the pneumatic servo system is required to be in the form of rotation, or the reciprocating motion with a long stroke, the pneumatic motor is mostly used. The long stroke output mechanism is realized by the combination of pneumatic motor and rack.

8.2.2.1

The Form and Characteristics of Pneumatic Motor

Unlike hydraulic motors, pneumatic motors have two types: expansion and non-expansion. Figure 8.28 shows a non-expansion pneumatic gear motor. This kind of gear pneumatic motor has the advantages of simple structure and can achieve positive and negative rotation; the disadvantage is that it cannot achieve full expansion, and the consumption of compressed air is slightly larger.

8.2 Structure and Characteristics of Actuators

37

Inlet hole (reversed as exhaust hole) Output Shaft valve

Gear

Exhaust hole (reversed as inlet hole)

Fig. 8.28 Pneumatic gear motor

Exhaust Rotor

Output Shaft

Inlet (positive turn)

Blade

Housing

Inlet (reverse turn)

Fig. 8.29 Operating principle of forward and reverse blade pneumatic motor

Figure 8.29 illustrates the working principle of a forward and reverse expansible gas vane motor. The expansion ratio of the expanded vane motor is 2:6 : 1. When gas (or compressed air) enters the motor from A or B inlet, the working state of counter-clockwise rotation or clockwise rotation can be obtained. If the rotation angle of the output shaft of the actuator is required to be 360° *720°, and the control load moment is not very large, and the rotation speed is relatively low, a spiral spline shaft swing pneumatic motor can be used. Figure 8.30 shows the basic structure of the swing pneumatic motor.

38

8 Pneumatic Actuators, Driving Elements and Accessories

Tube Piston

Seal up Output shaft

Spiral spline groove

Guide rod

Fig. 8.30 Pneumatic swing motor

8.2.2.2

Natural Frequency of Pneumatic Motor

The natural frequencies of pneumatic motors can be given directly by the following formulas: Natural frequencies of non-expansive pneumatic motors for adiabatic variation processes, xnn ¼ Dm

rffiffiffiffiffiffiffi 2kp VJ

ð8:47Þ

Natural frequencies of expansive pneumatic motors for adiabatic variation processes, rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2kp xnc ¼ Dmv Dmt VJ

ð8:48Þ

where p Dm Dmv Dmt V J k

Gas working pressure of pneumatic motor; Gas displacement of pneumatic motor; Volume flow rate of pneumatic motor; Torque displacement of pneumatic motor; Average working chamber volume of pneumatic motor; Sum of moment of inertia of rotating parts and load of pneumatic motor; Adiabatic index.

In general, if the size of the pneumatic motor is the same, the natural frequency of the non-expansion pneumatic motor is higher than that of the expansion pneumatic motor. That is to say, the stiffness of non-expansive pneumatic motor is large. Of course, when the same output power is achieved, the gas consumption of the

8.2 Structure and Characteristics of Actuators

39

Non-expansion Expansion

Fig. 8.31 p  V diagram of pneumatic motor

non-expansive pneumatic motor must be greater than that of the expansive pneumatic motor. The natural frequency of non-expansion pneumatic motor is higher than that of the same size expansion pneumatic motor. One obvious reason is that the working volume of non-expansion pneumatic motor is smaller than that of expansion pneumatic motor. That is to say, the expansion pneumatic motor increases its working chamber volume and reduces its natural frequency by further expanding to obtain energy for external work (Fig. 8.31). For those occasions where there are strict restrictions on the gas consumption of control system actuators (such as the actuator of gas pressure servo system used in space technology), most of them choose the expansion pneumatic motor. As shown in Fig. 8.29, the blade expansion gas motor is the actuator used in the thrust vector servo system of the ballistic missile control engine. Compared with the cylinder, the pneumatic motor can also use gear transmission to achieve a larger range of deceleration. Because of the large deceleration ratio, the effect of load factors on system characteristics can be significantly reduced. In addition, if the output of the system requires a larger working stroke, if the cylinder is used as the actuator, the working stroke of the cylinder will be too long, the initial volume of the cylinder V0 will be increased, the output stiffness will be reduced, and the natural frequency of the actuator will also be reduced, so the performance of the system will be significantly reduced. If the pneumatic rotary motor is used as the actuator of the servo system, with suitable rack or ball screw, the output device with a large reciprocating stroke can be formed, and the working requirements of the whole servo control system can be fulfilled. At this time, the working stroke of the system actuator is obviously longer, but it will not degrade the performance of the system as the control system composed of cylinders.

40

8.3

8 Pneumatic Actuators, Driving Elements and Accessories

Aircraft Hydraulic Accumulator and Cylinder in Extreme Temperature Environment

In the process of storage, transportation, and launch of aircraft, hydraulic components are often tested in extremely low-temperature and high-temperature environment. Storage conditions include extreme low temperature (40 C) and extreme high temperature ( þ 60 C). The characteristics of hydraulic accumulator and gas storage cylinder in large temperature range, especially the gas pressure and gas mass in the air chamber, and the working oil discharge and maximum oil filling characteristics of accumulator are very important to the design of aircraft hydraulic system.

8.3.1

Extreme Temperature Environment

Servo control originated from flying body attitude control of missile and rocket before and after World War II. Gas generator, pneumatic servo valve, and gas motor are used in gas servo system. Since 1950, in order to develop cosmic space, the United States, the Soviet Union, and Europe have used cold or hot gas driven pneumatic servo actuators or hydraulic actuators for servo control in thrust vector control and attitude control of space rockets and spacecraft. The actuator of attitude control system of China Long March series launch vehicle uses cylinder output gas source to drive pneumatic vane to drive hydraulic pump or motor pump to generate hydraulic energy. The storage and emission of gases, gas drive, and reliability of gas cylinder system in the extreme environment of aircraft have not been completely solved, and have been listed as an important issue. Hydraulic accumulator and gas booster tank are commonly used in aircraft hydraulic control system. Hydraulic accumulator uses the compressibility principle of sealed gas to work and realizes the function of oil absorption and drainage through the volume compression, expansion, and pressure change of the inflatable chamber. In order to ensure the normal operation of the hydraulic control system and improve the high altitude performance of the hydraulic system, the aircraft adopts a booster tank. The gas booster tanks of missiles and rocket vehicles and the booster tanks used by airplanes in high altitude flight are all under the action of pressurized gas to pressurize the sealed oil stored in the tank so as to increase the pressure on the oil surface of the tank in order to facilitate the oil suction of the hydraulic pump and prevent the oil suction of the hydraulic pump from producing cavitation. Hydraulic energy is often used in autopilot rudder control and seeker antenna servo mechanism of air defense missile. For example, American Hooker missile uses hydraulic steering engine to control rudder deflection. The Soviet S-300 missile initially used gas steering engine and then changed to hydraulic steering engine. The American Patriot Air Defense Missile adopts the electric variable pump

8.3 Aircraft Hydraulic Accumulator and Cylinder …

41

hydraulic steering gear. American Sparrow missiles use solid–gas generator to drive the hydraulic energy of gas–liquid accumulator-type seeker and nitrogen-driven gas–liquid accumulator-type driver. The British Sea Javelin Ship-to-Air Missile adopts gas motor driven hydraulic steering gear. Italian Aspider general air defense missile uses gas turbine pump and electro-hydraulic energy to drive the hydraulic steering gear and antenna hydraulic servo mechanism. The storage temperature range of aircraft is generally between 40 and þ 60 C. The hydraulic actuator or servo mechanism of missile or rocket mostly adopts small capacity, high-pressure closed hydraulic system, and the extreme working temperature of hydraulic oil reaches þ 160 C or higher. The hydraulic components of aircraft must work normally in a wide temperature range, but the performance problems under extreme low-temperature and extreme high-temperature conditions will become more complex. In the ground state, the accumulator chamber and booster tank cylinder are inflated, and the gas is filled to a certain pressure. During the stage of storage, transportation, launching, and flying of aircraft, the range of temperature variation is usually large. How to ensure the normal operation of the air chamber and its hydraulic accumulator in the whole temperature range is extremely important. At present, there are many studies on the performance of hydraulic accumulator under general environmental conditions, but there are few studies on the performance of hydraulic accumulator under extreme temperature conditions.

8.3.2

Van der Waals Equation for Real Gases

Aircraft often use hydraulic accumulator to absorb pressure impact or supply hydraulic energy, or pressurize the tank of closed hydraulic system by gas stored in cylinder. The gas pressure in a hydraulic accumulator or cylinder varies with the temperature of the storage environment, which usually varies in a wide range. For example, when the air chamber is inflated at the ambient temperature of :  40 C: in winter and used at þ 160 C in summer, the gas pressure in the hydraulic accumulator or cylinder rises greatly, and the pressure often exceeds the prescribed range of use. Therefore, in order to ensure that the pressure of the air chamber of the aircraft hydraulic system is within the normal range, when inflating the air chamber of an aircraft, the inflatable management is often carried out according to the actual operating conditions according to the two groups of operating conditions in autumn, winter and spring and summer. Real gas and ideal gas are very different under different conditions. Under the conditions of low density, low temperature (compared with room temperature), and low pressure (compared with atmospheric pressure), the real gas obeys the state equation of ideal gas. Under high pressure or low temperature, the state change of real gas is quite different from that of ideal gas. In the analysis and application of engineering technology, the gas characteristics

42

8 Pneumatic Actuators, Driving Elements and Accessories

under extreme high pressure or extreme low temperature are often corrected on the basis of ideal gas. The real gas takes into account the microscopic theory of material structure, such as the volume of gas molecule itself and the interaction force between gas molecules, which can better reflect the objective reality. The state equation for an ideal gas is pV ¼

m RT M

ð8:49Þ

where p V m M R T

Gas pressure ðPaÞ; Gas volume ðm3 Þ; Gas mass ðkgÞ; Gas molar mass ðkg=molÞ; Molar gas constant R ¼ 8:31J=ðmol KÞ; Gas thermodynamic temperature ðKÞ. The Van der Waals equation for real gases is 

 m2 a  m m p þ 2 2 V  b ¼ RT M M M V

ð8:50Þ

where



  a Proportional coefficient m6 Pa =mol2 ; b Gas constant ðm3 =molÞ. Among them, a and b are determined by measuring the pressure pk , volume Vk , and temperature Tk at the critical inflection point of gas, liquid, and solid three-phase isotherms. There are 9 Vk a ¼ 3Vk2 pk ¼ Vc RTc ; b ¼ 8 3 Vk ¼

3 RTk 8 pk

ð8:51Þ ð8:52Þ

For dry air, there is Tk ¼ 140:7 C; pk ¼ 3:72 MPa. The Van der Waals constants of several gases are shown in Table 8.5.

8.3.3

Inflation Mass of High-Pressure Gas Cylinders

For a certain volume of chamber, such as the chamber of hydraulic accumulator or the cylinder of gas booster tank, it is usually pre-inflated at a certain temperature on

8.3 Aircraft Hydraulic Accumulator and Cylinder … Table 8.5 Van der Waals constants of gases Gas

Molecular formula

Atmosphere Nitrogen Helium Argon

N2 He Ar

43

M/(g/mol)

  a= 101 m6 Pa=mol2

  b= 106 m3 =mol

28.97 28 4 40

1.36 1.41 0.034 1.357

36.51 39 24 32

the ground. The inflatable mass after reaching the pressure can be determined by Eq. (8.50). Doing deformation of Eq. (8.50), it is obtained, m3 

MV 2 M 2 V 2 pM 3 V 3 m þ ðRT þ pbÞm  ¼0 b ab ab

ð8:53Þ

Usually, according to the amount of oil needed by hydraulic accumulator in the hydraulic system, the minimum inflation pressure pmin and the maximum inflation pressure pmax of the hydraulic accumulator are determined. From the extreme low-temperature ambient temperature tmin and the lowest inflation pressure pmin , a group of inflation mass of gas in a certain volume chamber can be obtained by Eq. (8.53), that is, the inflation mass in autumn and winter. From the extreme high-temperature ambient temperature tmax and the maximum inflation pressure pmax , another group of inflation mass of gas can be obtained by Eq. (8.53), that is, the inflation mass in spring and summer. The inflation mass of these two groups of gases is determined by two inflation curves. For example, the normal working pressure of an aircraft hydraulic system is 21 MPa, and the permissible inflation pressure range of accumulator and small cylinder is 12.5*18.0 MPa in the temperature range of 40  þ 60 C. The inflation mass of the two inflation curves in spring and summer, and autumn and winter can be obtained by Eq. (8.53) under the conditions of autumn and winter 40 C; 12:5 MPa, and spring and summer þ 60 C; 18:0 MPa, respectively. Through two groups of inflation pressure curves, the storage pressure of hydraulic accumulator or cylinder can be ensured within the prescribed range of use.

8.3.4

Gas Pressure Service Characteristics of High-Pressure Cylinders and Cavities

For a certain volume accumulator chamber or gas booster tank, the pressure of a certain mass of gas in the chamber varies with the temperature of the storage, transportation, and launch environment of the aircraft after the completion of aeration on the ground. From Eq. (8.50), the state equation of real gas satisfies

44

8 Pneumatic Actuators, Driving Elements and Accessories

Fig. 8.32 Gas charging pressure characteristics of air or nitrogen cylinders

p¼

mR m2 a T 2 2 M ½V  ðm=M Þb M V

ð8:54Þ

Equation (8.54) reflects the variation of pressure of a certain mass gas with temperature. It can be seen that the gas pressure has a linear relationship with the absolute temperature of the gas, and also with the molar number of gas m=M, gas constant a, b. The smaller the molar number of gas m=M, the larger the gas constant b, the smaller the slope of pressure–temperature curve is shown in Eq. (8.54), and the more stable the pressure changes with temperature. Figure 8.32 shows the gas charging pressure characteristics of air or nitrogen. The air chamber volume of an aircraft is 490 cm3 , and the working pressure of its hydraulic system is 21 MPa. In the temperature range of 40  þ 60 C, in order to ensure the normal operation of the hydraulic accumulator, the gas charging pressure should be below 21 MPa, i.e., 12.5*18 MPa. Through two groups of temperature domains of −40*23°C (autumn, winter) and 13  þ 60 C (spring, summer), the air chamber of the hydraulic accumulator is inflated by one inflatable curve, respectively. Figure 8.33 shows the theoretical calculation results using the state equation of ideal gas and the real gas Van’s equation. The results show that under high pressure and extreme low-temperature conditions, the pressure characteristics calculated by ideal gas state equation are quite different from those calculated by real gas state equation, that is, Van der Waals equation, and the ideal gas state equation cannot accurately describe the pressure characteristics of gases. At this point, the Van der Waals equation of state of real gas must be used for calculation.

8.3 Aircraft Hydraulic Accumulator and Cylinder …

45

Equation of real gas Equation of ideal gas

Fig. 8.33 Comparisons of pressure characteristics between ideal gas state equation and real gas van’s equation

Air

Fig. 8.34 Comparisons of pressure characteristic curves of several different gases

Figure 8.34 shows a set of pressure characteristic curves of several different gases. The calculated results are based on the state equation of real gas, that is, Van der Waals equation. It can be seen from the figure that a gas filling curve in the temperature range of 40  þ 60 C from 12:5 to 18 MPa can be achieved by using

46

8 Pneumatic Actuators, Driving Elements and Accessories

Fig. 8.35 Three main working stages of hydraulic accumulator. a Inflation state; b maximum working pressure state; c minimum working pressure state

helium as a working medium. At present, however, the cost of helium production is relatively high.

8.3.5

Service Characteristics of Accumulator

Figure 8.35 is the three main working stages when using hydraulic accumulator. Figure 8.35a is the initial working state of the hydraulic accumulator; Fig. 8.35b is the maximum working pressure state of the hydraulic accumulator; Fig. 8.35c is the minimum working pressure state of the hydraulic accumulator. The working process of hydraulic accumulator is a short time oil filling and discharging process. The volume of the gas changes so rapidly that it is too late to exchange heat with the outside world. It can be considered that the state change process of the gas in the accumulator is an adiabatic process. For the gas in the accumulator chamber, there is, p1 V1n ¼ p2 V2n

ð8:55Þ

p2 V2n ¼ p3 V3n

ð8:56Þ

where n p1 ; V 1 p2 ; V 2 p3 ; V 3

Adiabatic index of gas compression and expansion during oil charging and discharging of accumulator; Pressure and volume of gas at the beginning of accumulator’s operation; Pressure and volume of gas under maximum pressure of accumulator; Pressure and volume of gas under minimum pressure of accumulator.

8.3 Aircraft Hydraulic Accumulator and Cylinder …

47

Fig. 8.36 Maximum oil filling and oil supply volume of accumulator in operation

In addition, V1  V2 is the maximum volume of accumulator when the maximum working pressure is applied, and V3  V2 is the working supply volume of accumulator. The maximum oil filling capacity of hydraulic accumulator can be obtained from Eqs. (8.55) and (8.56). "

 1n # p1 Va ¼ V1  V2 ¼ V1 1  p2

ð8:57Þ

The working oil supply volume of hydraulic accumulator is  1n " 1n # p1 p2 1 Vb ¼ V3  V2 ¼ V1 p2 p3

ð8:58Þ

In order to reduce the mass and volume of aircraft, the volume of fuel tank in hydraulic system can be designed as minimum as possible if it satisfies the change of oil volume during flight. The maximum volume of oil entering the hydraulic accumulator from the system, i.e., the maximum oil filling capacity of the accumulator, is an important index for the design of the hydraulic accumulator, booster tank, and closed hydraulic system of the aircraft, which must be fully considered. Formulas (8.57) and (8.58) reflect the maximum oil filling and oil supply volume of accumulator when working. The theoretical calculation results are shown in Fig. 8.36. It can be seen that when the accumulator is used to store energy, the

48

8 Pneumatic Actuators, Driving Elements and Accessories

inflatable pressure has a great influence on the maximum oil filling capacity and oil supply volume of the accumulator. In the process of analysis and design of closed hydraulic system for aircraft, the thermal expansion or shrinkage of hydraulic oil at the limit temperature should also be taken into account. The adjusting capacity of the air chamber of hydraulic accumulator and booster tank should be checked according to the actual working conditions, and the volume change caused by thermal expansion of hydraulic oil should be absorbed or supplemented.

8.3.6

Conclusions

The hydraulic control system of aircraft often undergoes large temperature range and storage process. In order to ensure the normal and reliable operation of the hydraulic accumulator and booster tank and meet the functional requirements of the hydraulic system in the range of storage temperature changes at extreme low temperature and extreme high temperature, it is necessary to reasonably manage the inflation of the air chamber of the hydraulic accumulator and the cylinder used in the booster tank. When the air chamber of the aircraft hydraulic system is inflated, the inflatable pressure management and the design of the hydraulic accumulator can be carried out according to the following methods. The conclusion can also be applied to the analysis of accumulator characteristics of ground hydraulic control system with a large variation of ambient temperature. (1) According to the requirement of working pressure and actual ambient temperature of the closed hydraulic system of aircraft, the charging mass of the gas in air chamber of the hydraulic accumulator or cylinder of the booster tank can be determined by Eq. (8.53). (2) The inflatable pressure and its variation law under different ambient temperatures are determined by Eq. (8.54). (3) The main performance of hydraulic accumulator, i.e., the working oil supply and the maximum oil filling, is calculated by Eqs. (8.57) and (8.58).

Bibliography 1. Yin Y, Qu Y, Yan J (1991) An investigation on hydraulic servo systems with asymmetric cylinder. In: Proceedings of the 1st international symposium on fluid power transmission and control (ISFP91). Beijing Institute of Technology Press, Beijing, China, pp 271–273 2. Yin Y (1994) Study on velocity gain characteristics of hydraulic control system. Autopilot Infrared Technol 73:23–29 3. Yin Y (1991) Research on flow matching control and precision of asymmetric hydraulic cylinder servo system. Master’s thesis of Shanghai Jiao Tong University 4. Yin Y (1993) The financial pressure characteristics of symmetric and unequal positive openings were studied. Hydraul Pneum Seals 50:22–26

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5. Yin Y, Akaki K, Ishino Y, Chen J (1997) Influence of piston position and area of cylinder on frequency. In: Proceedings of hydraulics and pneumatics conference, vol 5, Tokyo, pp 77–80 6. Yan J (1986) Hydraulic power control. Shanghai Jiao Tong University Press, Shanghai 7. Viersma TJ (1980) Analysis, synthesis and design of hydraulic servo systems and pipe lines. Delft University of Technology 8. Liu X, Araki K (1993) Frequncy characteristics of test banch with M-sequency signal. Hydraul Pneum 24(3):386–393 9. Yin Y (2012) Electro-hydraulic servo control theory and application technology in extreme environment. Shanghai Scientific & Technical Publishers, Shanghai 10. Yin Y, Yu C,Lu T et al (2006) Research on air chamber pressure characteristics of aircraft hydraulic control system. Autopilot Infrared Technol 2:8–12 11. Wu J, Yin Y (2007) Trend of hydraulic technology in Tongji University. Hydraul Pneum 46 (13):31–37 Japan Industry press 12. Yamaguchi A, Tanaka H (1986) Hydraulic and pneumatic engineering. Corona Corporation, Tokyo 13. Muto T (1992) Drive and control of actuator. Konora press 14. Japanese Society of Hydraulics and Pneumatics (1989) Handbook of Hydraulics and pneumatics. Ohm Corporation, Tokyo 15. Yin Y (1999) Research on asymmetric pneumatic servovalve and hardware compensation of high speed pneumatic force control system, vol 3. Saitama University 16. Yin Y (2011) Research on electro-hydraulic servo-valve characteristics of aircraft in extreme environment. Project conclusion report supported by the national natural science foundation of China (50775161), 20 Jan 2011 17. Yin Y (2008) Research on key basic theory of aircraft steering gear system. Shanghai pujiang talent plan (class A) summary report (06PJ14092), 30 Sept 2008 18. Qu Y (1986) Pneumatic servo system. Shanghai Jiao Tong University Press, Shanghai 19. Yin Y, Yu C, Lu T et al (2006) Research on the characteristics of hydraulic accumulator and cylinder in extreme temperature environment. Fluid Power Transm Control 5:10–13 20. Yin Y, Xiao Q, Yan S (2008) Analysis of the influence of temperature on electro-hydraulic servo valve. Fluid Power Transm Control 6:23–26 21. Yin Y, Yu C, Lu T et al (2006) Research on air chamber pressure characteristics of aircraft hydraulic control system. Autoplot Infrared Technol 2:8–12 22. Shu Z (1995) Discussion on auxiliary energy scheme of air defense missile. Autoplot Infrared Technol 1:25–36 23. Yin Y, Hu X, Li Y et al (2010) Mathematical modeling and analysis on hydraulic-pneumatic-compound hammers. Chin J Constr Mach 8(4):379–384 24. Yin Y, Huang W, Li L et al (2010) Analysis of the assembly stress of sleeve of electro-hydraulic servo valve based on FEM. Hydraul Pneum Seals 30(12):28–32 25. Yin Y, Xu J, Hu X et al (2010) Analysis of oil temperature of hydraulic systems of commercial aircraft. Chin Hydraul Pneum ISSN 9:55–58 26. Yin Y, Xu J, Hu X et al (2010) Analysis of oil temperature of hydraulic systems of commercial aircraft. In: Proceedings of the sixth national fluid transmission and control academic conference and the first conference on fluid power BBS in China and Japan, Lanzhou, 10–12 Aug 2010, pp 1–4 27. Cheng S (1978) General physics. People’s Education Press, Beijing 28. Yin Y (2009) Research on integrated design of ultra-high pressure pressure-reducing valve assembly in fuel cell vehicle. Shanghai magnolia technology talent fund summary report (2018B110), 28 May 2009 29. Yin Y (2010) Above 45 MPa research on hydrogen supercharging pressure control and regulation technology. Subject acceptance report of national high-tech research and development plan (National 863 Program) (2017AA05Z119), 30 June 2010

Chapter 9

High-Temperature and High-Speed Gas Turbine Pump Electro-Hydraulic Energy System for Aircraft

This chapter covers the electro-hydraulic servo control technology and its practical progress of aircraft gas turbine pump; the design theory and technology of the core components of gas power energy, such as steering gear system, gas generator, and gas turbine, etc.; starting characteristics of missile gas turbine motor pump with electro-hydraulic energy combination; basic characteristics and design technology of missile electro-hydraulic energy system; the power matching design method of steering gear system; and the design theory of electro-hydraulic energy system for high-temperature and high-speed gas turbine pump of aircraft is described in detail.

9.1 9.1.1

Electro-Hydraulic Servo Control Technology of Aircraft Gas Turbine Pump Overview of Electro-Hydraulic Control Technology

From the development process of electro-hydraulic control technology, we can see the basis of current technology level and the future development prospects, that is, the development trend of high power, high voltage, high temperature, high speed, high reliability, and information management. The history of hydraulic control technology can be traced back to 240 B.C., when an ancient Egyptian invented the first hydraulic servo mechanism in human history, the water clock. Since then, hydraulic control technology has been stuck in a long historical process, until the eighteenth century European Industrial Revolution period. The Industrial revolution has injected considerable vitality into hydraulic control technology. Many practical inventions have emerged. The emergence of a variety of hydraulic mechanical devices, especially hydraulic valves, has greatly increased the influence of hydraulic technology. At the end of the eighteenth century, hydraulic components such as pumps, hydraulic presses, © Springer Nature Singapore Pte Ltd. and Shanghai Scientific and Technical Publishers 2020 Y. Yin, High Speed Pneumatic Theory and Technology Volume II, https://doi.org/10.1007/978-981-15-2202-4_9

51

52

9 High-Temperature and High-Speed Gas Turbine Pump …

and hydraulic cylinders appeared. In the early nineteenth century, hydraulic technology made some significant progress, including the use of oil as a working medium and the use of electricity to drive direction control valves. In the 1940s and 1950s, the development of electro-hydraulic control technology was accelerated. Two-stage electro-hydraulic servo valve, nozzle baffle element, and feedback device are all products of this period. In the 1950s and 1960s, the development of electro-hydraulic components and technology was at their peak. Electro-hydraulic servo control technology played an important role in military applications, especially in aviation and aerospace applications. These applications include radar drive, guidance platform drive, and missile launcher control at first, and then extend to missile flight control, radar antenna positioning, aircraft flight control system stability, dynamic adjustment of radar magnetron chamber, and thrust vector control of aircraft. Electro-hydraulic servo actuator is used for navigation and control of space launch vehicle. The application of electro-hydraulic control technology in nonmilitary industry is more and more, mainly used in the machine tool industry. The electro-hydraulic system is used in the positioning servo device of numerically controlled machine tool, and the hydraulic servo motor is used instead of manual operation. Secondly, it is used in construction machinery. In the following decades, the industrial application of electro-hydraulic control technology has been further extended to industrial robotic control, plastic processing, geological and mineral exploration, gas or steam turbine control, and automation of mobile equipment. The application of electro-hydraulic servo control in the field of experiment is the direct result of the influence of military application on nonmilitary application. There are many achievements in the development of electro-hydraulic servo control devices, such as servo valves with pressure feedback, redundant servo valves, three-stage servo valves, and servo actuators. Electro-hydraulic proportional control technology and proportional valve appeared in the late 1960s and early 1970s. Proportional valves are designed to reduce costs, usually the cost of proportional valves is only a fraction of that of servo valves. The performance of proportional valve is inferior to that of the servo valve, but advanced control technology and electronic device makes up for the inherent deficiencies of proportional valve, and makes its performance and efficiency close to that of servo valve. The rapid development of electronic technology and devices has promoted the evolution of electro-hydraulic control technology. In the 1970s, the advent of integrated circuits and the birth of microprocessors endowed machines with mathematical computing and processing capabilities. The electronic (microelectronic) devices and devices consisting of integrated circuits are small in size but have high output power, strong signal processing capability, excellent reproducibility and stability, and low in price. With the support of such electronic (microelectronic) control devices, electro-hydraulic control technology is moving to a new height.

9.1 Electro-Hydraulic Servo Control Technology of Aircraft Gas Turbine Pump

9.1.1.1

53

Development Status of Airborne Electro-Hydraulic Control Technology

Up to now, the level of electro-hydraulic control technology can be roughly reflected by the following details: Many electro-hydraulic control valves are equipped with electronic devices, so-called “on-borne” electronic devices. This combined installation method, which directly installs the driver and signal regulating circuit on the valve body, has the advantage of reducing the number of connections between the valve and the central control system. Because according to the traditional layout, the valve is always adjacent to the actuator and the central control device is often located in the electric control platform far from the actuator. Many long cables and electrical connectors are needed to connect the two systems, and they are the least reliable part of the electro-hydraulic control system. The combination installation of embedded chips improves the reliability significantly by simplifying and omitting cable connections and connectors. A single electro-hydraulic device can have many functions, thus saving many devices and simplifying the system and operation. The only thing to do is to send the right signals to them. For example, it can control speed, position, acceleration, force or pressure as long as the corresponding sensors, feedback devices, and control logic/processing devices are provided for the servo valve. In addition to improving reliability, the on-borne electronic circuits of valves and pumps can also form a coexistence mode of distributed control and centralized control. For industrial applications, the preferred equipment configuration is a programmable logic controller (PLC), which can send instructions to several valves and pumps. A variety of on-borne functional components, especially those suitable for open-loop control, have emerged as the times require. Some components can provide adjustable switching-on and disconnection of slope change, i.e., flexible transformation, so that acceleration and deceleration can be controlled, thereby mitigating the system impact caused by on–off valve control. These devices are generally integrated and can be adjusted online. When used in motion control with a high requirement, an industrial motion control device is usually used to realize simultaneous control of acceleration, speed, and position. This device can be either a controller for independent application or a plug-in for the extended bus of PLC. Because of the implementation of serial communication bus standard, a large number of electro-hydraulic devices such as valves, pumps, and solenoids can be controlled by only one pair of wires.

9.1.1.2

Development Trend

(1) Development and restrictive factors of ultrahigh pressure Hydraulic technology is famous for its high output force and power density. The key is to use high pressure. It is a trend to continue to develop toward ultrahigh pressure. However, the increase in working pressure of hydraulic

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9 High-Temperature and High-Speed Gas Turbine Pump …

system is restricted by many factors. Excessive pressure means taking risks. Corrosion and dirt will cause serious wear and tear in the flow path under high pressure. In order to adapt to the extremely high working pressure, the strength and wall thickness of components will increase greatly, resulting in the increase of volume and weight or the decrease of working area and displacement. In the case of a given load, the reduction of displacement and working area caused by high working pressure will make the resonance frequency of hydraulic machinery lower and bring difficulties to control. Therefore, it can be foreseen that a series of key basic theories need to be solved in order to greatly increase work pressure. (2) Energy-saving and efficiency-enhancing Efficiency has always been one of the most concerned issues. Hydraulic drive can easily provide enough power for the load to move, especially in a straight line, which is its obvious advantage over electric drive. However, due to throttling loss and volume loss, its energy consumption is large and its efficiency is not very high. Although hydraulic drive has its own unique advantages compared with traditional mechanical drive, it should be noted that the electric drive industry is progressing rapidly and is developing toward the direction of small size and high power. The wires used are getting thinner and the working current is getting bigger and bigger. The development and application of room temperature superconducting materials is a great impetus to the application of electric drive. It means energy-saving, which is the future direction of development. If the hydraulic system does not develop in the direction of energy-saving and efficiency-increasing, the electric drive will probably encroach on the exclusive application fields of hydraulic drive, especially those applications requiring large force, high speed, and linear motion. (3) Integrated sensitive element/sensor Sensitive elements or sensors help to monitor, control, and adjust the parameters of the electro-hydraulic system. They also play an important role in the combination of hydraulic technology and microelectronic control. Integrative sensor structure is the direction of development, because it helps to improve the dynamic response and reliability of the system. The electro-hydraulic device provides matching sensitive elements or sensors. The sensors used in the electro-hydraulic system have the ability to store and correct data. The microelectronic control device downloads the data and interprets and translates it. The development of multipurpose interface devices enables users to select any kind of sensitive elements; the host computer will identify the types of sensitive elements used, such as digital or analog, serial or parallel, and translate their output. Modern control theory, such as state variable feedback control, can effectively improve the response of electro-hydraulic system. On the basis of the dynamic characteristics of valves and other components, this technology requires not only measurement and feedback of controlled output, but also some key variables in the system, such as internal pressure. These state

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variables are sensed and fed back by sensitive elements. In some systems, the optimal reduced-order state variable feedback can shorten the stability time of the loop. (4) The role of software Software is very important for the development of electro-hydraulic control technology in the future. Hydraulic components or devices with sensors and two-way communication interfaces can communicate with all other components or devices and the host computer by means of software. The key parameters of hydraulic components can be stored in a self-contained memory that can be directly used by computers. Computer simulations and other calculations are performed to determine whether components are compatible with each other. The host computer can use the inquiry software to inquire about its setting parameters to the peripheral equipment equipped with a two-way data transmission line, and then use these parameters to complete the communication protocol, so that users can easily set up new peripheral equipment. Once all the hydraulic components such as pumps, motors, valves, and cylinders are equipped with sensors and two-way data transmission lines, the computer can not only control and monitor the hydraulic machinery through them, but also give the machine complete self-diagnosis ability. The basic performance and qualified performance data of hydraulic components are stored in a huge database in the control/monitoring computer. The computer measures the current performance of all components at a predetermined time interval and compares it with the basic performance. If the performance is outside the qualified window, the computer will give a warning and shut down the machine when the situation is critical. Full automatic diagnostic ability, i.e., health diagnosis, is necessary for future machines, because the complexity of machines is getting higher and higher, and it is impossible to check and troubleshoot machine failures by general means. (5) Control and eliminate leakage Leakage is a unique and long-term problem of the hydrodynamic system. Internal leakage of hydraulic system will lead to waste of energy, reduction of volume efficiency and mechanical efficiency, and affect the dynamic and static performance of the system, while external leakage is more concerned, because it may pollute the environment. Objectively speaking, the scope of leakage is often extremely limited, which will not bring significant harm to the environment. However, the leakage is an embarrassing thing, which damages the image of hydraulic technology. Over the years, leakage has been regarded as a topic related to environmental pollution, and the public’s demand for environmental cleanliness is increasing. This requires that effective measures be taken to further reduce or eliminate leakage or eliminate the potential hazards of leakage fluid within the professional disciplines. These measures include improving sealing and leak-proof technology, selecting appropriate hydraulic system pipelines, receiving professional technical training in the maintenance of hydraulic equipment, developing and using environmentally friendly fluids

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instead of petroleum-based fluids as working media, such as pure water or biodegradable fluids. Eliminating leakage is one of the most important challenges that hydraulic technology faces at present. When the hydraulic system is no longer troubled by leakage, the competitiveness of hydraulic technology will increase significantly. (6) Application of computer-aided engineering The rise of Computer-Aided Engineering (CAE) in the 1980s has brought hydraulic technology to a new stage. By means of computer simulation, the designer of hydraulic system circuit and component can quickly and economically inspect his ideas and schemes, which save a lot of time and obtains the best intuitive results. Computer-aided design (CAD) was used as a simple method to draw hydraulic circuit diagram and hydraulic component diagram in the early years. Today, their function is much more than that. Now it is moving toward performance prediction. The entity modeling method can not only draw the entity diagram, but also evaluate the performance data such as strength, weight, center of gravity, and moment of inertia. The designer of hydraulic components will be able to predict the hydrodynamic properties of components by deliberating the hydrodynamic relationship and carrying out virtual experiments, i.e., simulation tests. This evaluation technology prior to the prototype has been widely used. The computer-aided design of hydraulic system needs an effective CAD program group. Each component in the system has its own independent mathematical model. The program contains a large capacity component model library. Building component models requires a lot of parameter data. These data are usually not available to manufacturers. Therefore, although there are many hydraulic system CAD programs in the world, they have not been widely used. Software vendors’ models are usually not perfect enough, but self-made models require specialized skills. Moreover, it is not easy to transition from mathematical expressions to real hardware features and eliminate the differences between models and real hardware. These models must include not only the steady-state results, but also the differential equations that form the basis of the dynamic response. Dynamic performance evaluation is a necessary work to simulate a system. Failure to perform dynamic performance evaluation will result in imperfect simulation results. Before the design of hydraulic circuit, a high level of engineering analysis is needed, that is, required by the original equipment manufacturer and the users of hydraulic equipment. Without meaningful data specially used to establish mathematical models, it is difficult to establish mathematical models. Servo valves are examples with suitable mathematical models. The establishment of mathematical model of hydraulic components depends on laboratory tests, otherwise it is difficult to achieve. Mathematical models of pumps and hydraulic motors require manufacturers to provide leakage and friction coefficients. Other key modeling data, such as the continuous equation required for the measurement curve, the leakage coefficient varying with temperature and pressure, and even the transfer function or nonlinear differential equation,

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should also be provided by the manufacturer to the user. Once these ideas and requirements are universally recognized and responded to by manufacturers and implemented, the mathematical model of hydraulic components will become as common as assembly drawings. This is also a great contribution to simulation or simulation technology.

9.1.1.3

Material—An Important Contributing Factor to the Evolution of Electro-Hydraulic Technology

The emergence and application of new materials further promote the evolutionary changes of electro-hydraulic technology. As far as the steel materials used most in the hydraulic system are concerned, if they have higher strength without increasing the cost and reducing the machinability, the hydraulic machinery will be more powerful and reliable. The use of ceramic materials in hydraulic systems has been tried and achieved some success. The improvement of the properties of magnetic materials (magnets) is more effective in promoting the development of electro-hydraulic technology. If the magnetic saturation current of the magnetic material can be increased, the coil or solenoid with the same turn number can produce greater electromagnetic force. As the electrical–mechanical interface of the electro-hydraulic valve, solenoid generates greater force, which means that the direct valve with a larger flow can be manufactured at almost no additional cost. High-performance magnets have high saturation current and high flux density, allowing a large current to be overdriven, resulting in greater electromagnetic force. This force can be effectively used to accelerate the spool valve, resulting in greater dynamic bandwidth or higher frequency response. When the solenoid which can give greater force is used as the electrical–mechanical interface of the electro-hydraulic valve, the pilot stage will not be used. This creates conditions for the development of large flow, fast action, and low-cost electro-hydraulic valves.

9.1.1.4

Electrorheological Technology

Electrorheological fluids (ER fluids) are suspended fluids that can flow freely in a free state. Once it is under the action of electric field, it will solidify rapidly and show viscous, cementitious, or hard properties according to the intensity of electric field. This characteristic makes it ideal for valves, dampers, and power transmission devices of hydraulic and mechanical systems. ER fluid responds very quickly to electrical signals, and can change the state of liquid–solid or solid–liquid in less than 1 ms. The solidification degree is proportional to the field strength. This makes it suitable for direct control by fast electronic devices, such as microcomputers. This is its most important advantage. The possibility of ER fluid technology application is mainly based on its two characteristics: low input power and high response speed. Although the working voltage is as high as several thousand volts, the current

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density is very low, usually below 10 mA=cm2 . It can be processed by ordinary solid-state electronic devices. Because the working current is very small (no more than 2 mA), the input power is very low. The small-signal response of ER fluid is approximate to the first-order link, and its angular frequency is about 1 kHz. This value is one order of magnitude higher than the rotation frequency of most electromagnetic devices, including electro-hydraulic servo valves, and avoids the unique electromagnetic effect of magnetic coils. ER fluid is suitable for pulse width modulation control, which can reduce energy consumption, simplify design, save moving parts, reduce wear, and prolong life. However, ER fluids also have some practical problems. Firstly, the curing strength is not high enough. Usually, the shear strength is below 5 kPa=mm, so the transfer of moment is limited. Further improvement of curing strength requires higher electric field strength (e.g., from 2 to 4 kV) or higher free viscosity of fluids. However, high electric field strength corresponds to large consumption current, and there are some problems both in terms of safety and economy. If the free viscosity of the fluid is too large, the surface abrasion of the device will be aggravated, and particle deposition will occur easily. Therefore, the increase of field strength and free viscosity is limited, and there is no more room to improve the curing strength of fluids. Secondly, the temperature stability of ER fluid (especially water-bearing ER fluid) is poor, so the working temperature is usually limited to a narrow range of 0*80 °C. Although these defects have limited the application of ER fluid technology, the technology has made significant progress in the past 20 years, and anhydrous ER fluid is close to practical use. Electrorheological fluid technology has tremendous application potential and may represent the future of hydraulic technology. Today’s hydrodynamic technology is an automation technology including drive, control, and detection. The process of electro-hydraulic integration that hydraulic technology combined with microelectronics technology is accelerating. With the development of electro-hydraulic control technology, it is still possible to make some evolutionary changes and developments. The most significant progress may be made in electronic equipment, control strategy, software, and materials.

9.1.2

Elastic O-Ring Sealing Technology

Elastic O-ring has been used for sealing fluid to prevent leakage for more than 70 years. The key technology of this type of sealing ring is discussed, and the selection, design, protection, and development of sealing technology are emphatically analyzed. The application of fluid transmission and control mostly needs to solve the leakage problem. The leakage of fluid system not only wastes energy, reduces volumetric efficiency and mechanical efficiency, but also affects the static and dynamic performance of the system. Fluid leakage can cause environmental pollution, which is considered as a public hazard in today’s increasing environmental

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awareness. Leakage is an unsafe or dangerous hidden danger, which can lead to accidents and even disasters. Two major accidents that shocked the world in the mid-1980s, the nuclear leakage caused by the failure of valve seal at Chernobyl Nuclear Power Station in the Soviet Union and the explosion accident of the American space shuttle, were caused by the leakage, causing huge losses and impact. From another point of view, many sophisticated products and equipment in an unclean environment may be damaged by the infiltration of dust-laden fluid into the interior. Therefore, the prevention of leakage is an important issue. Leakage has always been prevented by sealing. There are many kinds of seals, such as gap seals, elastomer compression deformation seals, mechanical seals, and ferromagnetic fluid seals. Compression deformation of elastomer is the most commonly used sealing form, and O-ring is the most common configuration. Elastic O-ring (hereinafter referred to as O-ring) has been a patent for more than 70 years since it first became a patent in 1939. In the early 1940s and 1950s, O-rings were mainly used in military fields such as aircraft hydraulic systems, and since then, they have rapidly expanded to other industrial fields. Today the O-ring covers almost all parts of the world and almost all industries, from clocks and watches to jewelry to space shuttles. Sealing technology has been developing continuously for more than 70 years, but the basic configuration of O-ring has remained unchanged, which shows its strong vitality.

9.1.2.1

Configuration and Sealing Principle of O-Ring

O-ring is a kind of elastic ring with a standard circular cross section. It relies on the elastic deformation caused by compression to form a pressure fit on the surface of the sealed component to prevent fluid from passing through to achieve sealing, as shown in Fig. 9.1. d is the clearance value between holes and shafts, p is the pressure of hydraulic oil, and d is the diameter of sealing ring section. The key factor of sealing, i.e., the compression amount or compression rate of O-ring in the embedded state, must be coordinated with component size, application type, fluid pressure, and material property of O-ring itself. Otherwise, effective sealing can not be achieved and O-ring will be damaged. In addition to the elastic deformation seal under direct compression, O-ring can also be used as an elastic energizing element of U-ring. The O-ring is embedded in the U-groove of the cross section of the polymer U-ring, forcing the lip of the

Fig. 9.1 O-ring radial seal

9 High-Temperature and High-Speed Gas Turbine Pump …

60 Fig. 9.2 O-ring radial combined seal

U-ring to stretch and close to the sealed surface to achieve sealing, as shown in Fig. 9.2. The elastic force of O-ring in the sealing structure acts on the inner lip of U-ring to provide low-pressure sealing force. High-pressure sealing pressure is provided by fluid. Figure 9.3 is the schematic diagram of O-ring seal.

9.1.2.2

Characteristics of O-Ring Seal

(1) It has a simple structure and good reliability. (2) Low price, economical and practical, and mass production can ensure mass supply. (3) It can compensate the radial runout within the allowable range. (4) It can be sealed in all directions (radial, axial, or along any angle). (5) Wide applicability. Suitable for all types of sealing applications (face seal, radial seal, static seal, and dynamic seal). (6) It can be used repeatedly in the limit working range (pressure, temperature, speed, and cycle). (7) No protective coating is required. (8) Material can be selected according to application. (9) Easy to install, usually without special tools. (10) No tightening is required.

9.1.2.3

O-Ring Material

O-rings are usually made of elastic natural rubber or synthetic rubber. Synthetic rubber is cured by a combination of chemical ingredients. Ingredients are generally classified as follows: polymer (elastomer); inert filler (carbon black or mineral filler); reinforcing agent; catalyst, activator, retarder, and curing agent; anti-degradation agent; plasticizer; process aids for accelerating molding; special additives (pigments, flame retardants, etc.). Synthetic rubber materials suitable for engineering application can be made by selecting specific ingredient combinations and proportions. At present, there are more than ten kinds of rubber materials widely used, and each material can have different formulations and proportions, so the characteristics of the material are different. The properties and characteristics of these rubber materials are summarized below.

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(a)

O-ring

Designed O-ring groove

When not under pressure

(b)

pressure When not under pressure

Leakage arrest status

(c)

Excessive pressure Leakage arrest status (d)

(e)

Squeeze out

Pressure

When retaining ring is used Fig. 9.3 Seal principle of O-ring

(1) Extensibility: Natural rubber is the best. (2) Resilience: The best is still natural rubber. (3) Tensile strength: Natural rubber, urethane, and polychlorinated rubber have high tensile strength. The tensile strength of styrene–butadiene, polypropylene rubber ester and fluorosilicone rubber is slightly worse.

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(4) Tear resistance: Natural rubber, urethane, and polyurethane are preferred. The tear resistance of silicone rubber and fluorosilicone rubber is poor. (5) Compressive permanent deformation: Urethane polyurethane, silicone, fluorosilicone, and fluorocarbon rubber are the best. Polyacrylate and chloroprene rubber are slightly worse. (6) Corrosion resistance: Natural rubber, styrene–butadiene, propylene–ethylene, chloroprene, nitrile, urethane, and polyurethane rubber all have excellent abrasion resistance, while silicone rubber and fluorosilicone rubber are less corrosion resistant. (7) Cold and heat resistance: The best are propylene–ethylene, silicon–copper, and fluorosilicone rubber. Polyacrylate and fluorocarbon rubber are heat-resistant but not cold-resistant; natural rubber, styrene–butadiene, urethane, and polyurethane rubber have good cold-resistant but slightly poor heat-resistant. (8) Weather aging resistance: natural rubber is the worst. Butadiene–styrene and nitrile rubber are in general. The rest are mostly good. (9) Fire resistance: fluorocarbon rubber is the best, followed by chloroprene, fluorosilicone, and silicone rubber. Most of the rest are not fire-resistant. (10) Water and steam resistance: propylene vinyl rubber is the best. Urethane and natural rubber, styrene-butadiene, nitrile, and fluorocarbon rubber took the second place. Polyacrylate and polyurethane rubber have poor water and steam resistance. (11) Acid resistance: Fluorocarbon rubber is the best. The acid resistance of polyacrylate, urethane, and polyurethane rubber is poor. (12) Oil resistance: polyacrylate, nitrile, urethane, and fluorocarbon rubber have excellent oil resistance; natural rubber, styrene-butadiene and propylene vinyl rubber are not oil-resistant. (13) Ozone resistance: Except natural rubber, styrene-butadiene, nitrile, and urethane rubber, most of them have excellent ozone resistance.

9.1.2.4

Selection and Design of O-Ring

The sealing of O-ring and its application seem simple, but in fact, it is not easy to achieve a good sealing effect, which requires proper selection and correct design. The selection and design of O-rings must be based on the specific application environment to ensure that O-rings are compatible with the application environment factors such as the size of sealing components, sealing type, fluid medium, fluid pressure, and ambient temperature. To this end, the following principles must be followed: (1) The specifications and dimensions of O-rings must be coordinated with the sealed components to ensure proper compression of O-rings so as to achieve effective sealing and good system performance. The maximum diameter

9.1 Electro-Hydraulic Servo Control Technology of Aircraft Gas Turbine Pump Fig. 9.4 Maximum diameter clearance (2 g) of O-rings without retaining rings

63

pressure

clearance (2 g) of O-ring without retaining ring should be controlled as shown in Fig. 9.4. (2) The specifications, dimensions, and materials of O-ring must be suitable for application types, such as larger compression ratio for face seal and smaller compression ratio for radial seal, larger compression ratio for static seal and smaller compression ratio for dynamic seal, larger compression ratio for reciprocating dynamic seal and smaller compression ratio for rotary dynamic seal. (3) O-ring material must be compatible with fluid pressure. Figure 9.5 shows the failure process of O-ring under high-pressure fluid extrusion under a radial seal. Figure 9.6 shows the characteristic curves of the relationship between the fluid pressure and the allowable radial clearance of three O-rings with different Shore

Fig. 9.6 Curve of relationship between fluid pressure and allowable radial clearance of materials with different hardness

Fluid pressure/mPa

Fig. 9.5 Failure process of O-ring under high-pressure fluid extrusion under radial sealing

Extrusion zone

(Shore hardness) Non-extrusion zone

Radial clearance/mm

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64 Fig. 9.7 Protection ring to prevent O-ring from squeezing into radial clearance

hardness (Hs70, Hs80, and Hs90). These curves are actually the extrusion limits of O-rings. When high hardness material cannot be used, plastic protective rings with a low friction coefficient can be used to prevent O-rings from being squeezed into the gap, as shown in Fig. 9.7. (4) The material of O-ring must be adapted to the applied temperature, that is, the temperature limit or allowable temperature range of the material must cover the applied temperature range. (5) O-ring material must be compatible with fluid. Choosing O-ring material should ensure that there is no obvious change in performance under the action of the applied fluid medium.

9.1.2.5

Protection and Fault Prevention of O-Ring

Sound O-ring can ensure a good sealing effect. Therefore, O-ring must be protected. Following the above principles, seal failure caused by improper selection and design and permanent compression deformation, wear, extrusion damage, aging, oxidation, and elasticity loss of O-ring can be avoided. In addition, other aspects must be taken to protect O-ring from damage: (1) O-ring rubber should be fully vulcanized to improve resilience to enhance the ability to resist permanent compression deformation. (2) Too rough surface of metal components, sharp edges, and improper assembly methods can easily cause O-ring damage. (3) Improve the concentricity of components, reduce the irregularity of radial clearance caused by eccentricity, and relieve the extrusion of O-ring. (4) Abrasive impurities entrained in the fluid must be filtered with a filter or wear-resistant O-ring materials such as nitrile carbide and urethane must be used. (5) The O-ring can cause many tiny cracks perpendicular to the stress direction due to ozone erosion. This requires the use of ozone-resistant materials.

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9.1.3

65

Technical Characteristics of Electric-Hydraulic Servo System for Aircraft

Electro-hydraulic servo technology has developed rapidly since the mid-1960s, and matured gradually in the early twenty-first century. It has been widely used in various industrial fields. Aeronautics and astronautics have a high demand for electro-hydraulic servo technology, which generally reflects the professional level of electro-hydraulic servo control technology. The development of electro-hydraulic servo technology involves many aspects, such as system and component design, material, testing, and manufacturing technology. In general, high power, high voltage, high temperature, high speed, high reliability, and mechanical–electrical integration have become a main line throughout the development process, and have achieved historic results. The development requirements of aeronautics and astronautics electro-hydraulic servo technology and the technical characteristics of civil industry applications are analyzed as follows.

9.1.3.1

High Power

Aerospace vehicle and modern production equipment have remarkable characteristics of large capacity, high efficiency, and high reliability. The electro-hydraulic servo system, as a transmission and control device, is developing toward high power accordingly. Take American Civil Aviation DC Series Aircraft (Douglas, then merged into McDonald Douglas), for example, such as DC-6 (1950), DC-7 (1955), DC-8 (1960), DC-10 (1971, 300 seat class), the power of its hydraulic system is 19; 24; 67; 340 kW, which has increased 17 times in 20 years. In the field of aerospace, the power of hydraulic system is increasing rapidly. For example, the power of V-2 Saturn rocket (1940) hydraulic system is 0:42 kW, while the power of Saturn-V rocket (1969) first-stage hydraulic system is 462 kW. Table 9.1 lists some examples of the application of high-power levels in hydraulic system.

Table 9.1 Examples of high-power application of hydraulic systems System

Power/kW

Substage hydraulic system of Saturn-V rocket in USA Swing hydraulic system of spacecraft main engine Hydraulic system of B-1B bomber Hydraulic system of space shuttle takeoff-separation overload simulator Hydraulic system of 30,000-ton steel tube mill

462 447 746 1,749 746

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Table 9.2 Renewal of main technical indicators of American DC series passenger aircraft hydraulic pumps Passenger Aircraft

Pump Power/kW

Weight/power/ (kg/kW)

Overhaul/ h

Percentage of cost per kilowatt/%

DC-6 DC-7 DC-8 DC-10

19 24 67 340

0.43 0.26 – 0.29

1500 1500 1600 8000

100 70 – 50

During the development of hydraulic power to large capacity, a series of technical problems have been solved as follows: (1) Weight Reduction Limit the weight of the structure and increase the power–weight ratio of the system, so that the system can obtain excellent technical performance and economic results. Therefore, reasonable design (such as integration of components and oil circuits, optimization of structural parameters) is required. High-strength light alloys (such as aluminum alloy and titanium alloy) and magnetic materials with high magnetic energy levels (such as rare earth magnets) are used. Table 9.2 shows the update of the main technical specifications of DC series hydraulic pumps for passenger aircraft in the United States. Large rocket (such as Saturn-V stage 1) high-power hydraulic system, whose hydraulic pump (4
350 L=min) drains from the engine propellant (RP-1 kerosene) delivery system, uses working pressure of 13:7 MPa, working medium of RP-1 kerosene, simplifies the system structure, and reduces weight. This is an earlier hydraulic system using the kerosene medium. (2) Saving Energy Consumption Hydraulic energy supply can automatically adjust the flow rate of hydraulic pump to adapt to the change of load in order to achieve power matching, minimize energy loss, reduce system calorific value, and prolong working life. Variable hydraulic pumps are used to replace the quantitative pumps when the hydraulic power of civil aviation passenger aircraft reaches above 60 kW. In the civil industry, the regulation type and characteristics of hydraulic pumps are studied, and various types of energy-saving pumps are developed. In the field of heavy industrial hydraulic pressure, the flow rate of variable displacement pump is controlled by computer, and its input is load, that is, the working spectrum of corresponding pressure and flow rate. At the same time, multi-pressure hydraulic system has been developed. For example, the working pressure of the hydraulic system of American DC-80 passenger aircraft is 20:6=10:3 MPa, and its low-pressure block is used for aircraft cruising. A.O. Smith’s 30,000-ton press has three pressure modes in its hydraulic system, i.e., 20:6=24=44 MPa. Low pressure and large flow are used for fast no-load travel, while high pressure and small flow are used for heavy load and slow speed travel.

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(3) Hydraulic Components Develop large capacity hydraulic components, such as three-stage electro-hydraulic servo valve. The three-stage electro-hydraulic servo valve for Saturn-V rocket has a spool diameter of 25:4 mm, a stroke of 2:79 mm, and a flow rate of 510 ðL=minÞ. A dynamic pressure feedback electro-hydraulic servo valve was developed and applied for swing nozzle of high-power rocket engine (its mass is 4000*8000 kg). It can realize dynamic damping to control the movement of a large inertia load, restrain the resonance of the system, and ensure a wider passband. (4) Manufacturing Technology The processing requirements of large parts in high-power system are high, and technologies such as centrifugal casting, heat treatment, precision processing of inner holes, surface treatment, static pressure strength, and sealing test should be solved. Actuator barrels (16 pairs) of hydraulic load-bearing platform of giant rocket erecting transporter have a maximum size of 680
534
2540 ðmmÞ (inner diameter
outer diameter
length). The static load of the actuator barrel (single piece) loading test is 22701 t, and the pressure of the oil chamber does not decrease within 24 h, and the position of the piston does not drift. 9.1.3.2

High Pressure and High Temperature

(1) High Pressure From the 1940s to the present, the common working pressure of hydraulic system has increased from 5 to 27:4 MPa. In the 1980s, the United States developed a 55 MPa working pressure hydraulic system for F-14 fighter aircraft and replaced the original 20:6 MPa working pressure. The whole-system ground simulation test and single-channel flight test were completed. The prototype operated for 520 h. When the working pressure of the system is increased, the weight and volume of the system are reduced by 30 and 40%, as shown in Table 9.3. The study of working pressure in foreign aviation industry shows that the optimum working pressure of aircraft hydraulic system is 27:4 MPa, which is Table 9.3 Weight of hydraulic components of American J-14 fighter after high pressure Project

Weight/kg Pressure 20.6 MPa

Pressure 55 MPa

Hydraulic pump and hydraulic motor Actuators Oil tank Pipe Pipe joint Support seat Other

66.7 399.7 71.3 185 16.3 40.4 124.3

41.7 332 42.2 90.7 10.8 26.3 89

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Table 9.4 Working pressure of typical hydraulic systems Name

Working pressure

F-14 fighter B-1 bomber Saturn-V rocket erection transporter Space shuttle takeoff-separation overload simulator 25-ton hydraulic excavator Hydraulic platform of marine mining vessel Hydraulic roof pillar in mine

55 27.4 34*35.8 27.4 34 34 41*69

Table 9.5 Distribution ratio of working pressure of hydraulic pump and electro-hydraulic servo valve Working pressure

Hydraulic piston pump

Electro-hydraulic servo valve

34

25 46.8 28.2

31.4 60 8.6

not much higher than the standard pressure of 20:6 MPa. The so-called optimal working pressure is still a controversial issue. In order to reduce structure size and system weight/power ratio, high-pressure hydraulic systems have been developed for military aircraft and ground equipment. Some examples are listed in Table 9.4. Table 9.5 shows the distribution of hydraulic pumps and electro-hydraulic servo valves in the European and American hydraulic industry according to working pressure in 1988. (2) High Temperature High-temperature working environment (e.g., engine compartment, metallurgical equipment) and high speed, heavy load, long-term operation of hydraulic system heating temperature rise, due to structural weight and space position constraints, it is difficult to maintain the normal working temperature of the ground solely by forced cooling or adiabatic, in recent years, the development of high-temperature hydraulic system has become a reality. The oil temperature of the Trident missile hydraulic system is 204*260 °C. The working temperature range of the hydraulic system of the American SR-71 high altitude reconnaissance aircraft is 54  þ 315  C. Hydraulic components installed in engine compartment (no less than 538  C) are coated with a heat shield (7:6 mm thick) made of chromium–nickel–iron alloy foil, which is used to limit the oil temperature of hydraulic oil to below 315  C. (3) Problems and Key Technologies Caused by High Pressure and High Temperature 1. Sealing material. Under high pressure, rubber sealing rings will accelerate tensile aging, extrusion damage, and reliability and service life are reduced. At high temperature, rubber sealing materials will accelerate aging, reduce

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toughness, and cause small pieces of erosion. For this reason, the O-ring of metal thin tube has been developed, which is made of stainless steel and nickel–chromium–iron alloy. Another way is to develop heat-resistant materials with high-dimensional stability and low friction coefficient, such as fluoroplastics with glass fibers and molybdenum disulfide (working temperature allowed 315  C). The U.S. Space Shuttle Hydraulic System (204  C) uses Vitin E60C synthetic rubber seals. 2. Hydraulic oil. Hydraulic oil has lower shear stability, lower viscosity, worse lubricity, and accelerated wear of parts under high pressure and high temperature, which affects the damping characteristics of oil circuit. In order to improve the shear stability, thermal stability, and fire resistance of hydraulic oil, MIL-H-83282 synthetic hydrocarbon hydraulic oil was developed in the United States and applied to the hydraulic systems of F-14 and space shuttles. Usually, the hydraulic system using MIL-H-5606 hydraulic oil is compatible with this new oil. Table 9.6 lists the main indicators of these two types of hydraulic oils. 3. Leakage loss and service life. Increasing the working pressure and temperature will inevitably increase the leakage loss of hydraulic system and reduce the volume efficiency. In order to limit the leakage loss, it is necessary to reduce the fitting clearance of the parts and improve the manufacturing accuracy, but it is necessary to take into account the stress and thermal deformation of the parts so as not to clamp the precise movable couple. At high temperature, the worsening lubricity of hydraulic oil or annealing effect on hardened surface of parts leads to accelerated wear of movable parts. In order to increase the working temperature of oil from 135 to 204  C, the structure and material of parts have been changed in USA. Using high-temperature wear-resistant coating, the weight of the test prototype increased by 10%, while the working life was only 1/5 of the original. 4. Structure mechanical properties. The structure is easy to deform under high temperature and high pressure. High-temperature creep of materials and high-temperature relaxation of elastic components occur. Friction accelerates material wear at high temperatures.

Table 9.6 Main indicators of Mil-H-5606 hydraulic oil and MIL-H-83282 synthetic hydrocarbon hydraulic oil Main Indicators

MIL-H-5606

MIL-H-83282

Flash point temperature Spontaneous combustion temperature Viscosity Temperature of maximum viscosity Shear stability and viscosity change rate

93.3 243.3 10 −53.9 −14.28

210 371 10.28 −40 −0.69

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9.1.3.3

High Speed

When the output flow of the hydraulic pump is constant per minute, increasing the rotational speed can reduce the displacement per revolution, thus reducing the geometric size of the hydraulic pump and achieving the purpose of reducing weight. On the other hand, the development of prime mover to high speed also puts forward high-speed requirements for hydraulic pumps. The typical power transmission form of rocket electro-hydraulic servo system is the output shaft reducer hydraulic pump of turbopump (propellant transport in power system). In order to reduce the volume, weight, and efficiency, it is necessary to remove the reducer, so as to improve the speed of the hydraulic pump to match it. While increasing the speed of the hydraulic pump, it is necessary to keep the working life of the pump unchanged. It is necessary to solve the problem of overheating and wear resistance of the parts, such as developing heat-resistant, wear-resistant sealing materials, and metal coatings, and adopting high-speed precision bearings. In order to ensure that the hydraulic pump sucks oil adequately at high speed, it is necessary to increase the suction pressure of the pump. And it is necessary to pressurize the tank or increase the pre-pressurization of the first-stage pre-pump, which can work at a lower speed. Table 9.7 lists the application examples of hydraulic pumps with different rotational speeds, from which the advantages of using high rotational speeds to reduce weight can be seen.

9.1.3.4

High Reliability

In extreme environments, electro-hydraulic servo systems may have various failure modes, such as servo valve (nozzle, throttle hole) blocking, slide valve clamping, input circuit breaking, and feedback disconnection. First of all, measures must be taken to improve reliability in design to ensure absolute safety.

Table 9.7 Weight and application examples of hydraulic pumps with different rotational speeds for aircraft

Missile hydraulic system Rocket hydraulic system Aircraft hydraulic system Aircraft hydraulic system

Turbine speed/ (r/min)

Hydraulic pump Speed/(r/min) Pressure/MPa

Flow/(L/min)

Weight/kg

90,000

13,000

24

12.5

0.75

10,000

5,000

20.7

38

9.5

-

11,200

20.7

14.4

1.5

-

10,000

20.7

36.1

2.17

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(1) Component Integration Hydraulic integration blocks have been widely used, reducing or even eliminating conduits and connectors. The maintainability is improved by using cartridge components, and the integral combination simplifies the installation and improves the adaptability to vibration and impact environment. (2) Replacing Electrical Feedback with Mechanical Feedback The position feedback of electro-hydraulic servo actuators used by American militias, Saturn-V rockets, space shuttles, and Apollo lunar simulators is mechanical feedback. This device has the ability of “failure ! return to zero” and “failure ! safety”. Compared with the feedback of potentiometer and differential transformer, this device can save a considerable number of connecting cables, wiring solder joints, and corresponding electronic circuits, and improve the reliability, but its structure requires higher manufacturing accuracy. (3) Redundancy Design for Key Parts In general, redundancy design is used in hydraulic energy, electro-hydraulic servo valve, and actuator. 1. Parallel hydraulic system. Parallel hydraulic system is used in large aircraft and space shuttle without exception. The American space shuttle orbiter has four independent hydraulic sources, which supply oil to every single unit of the control system through a central hydraulic combination to form the whole system. Each hydraulic power source has 50% (whole hydraulic power source) working capacity. If one hydraulic energy source fails, the whole system can still work normally. When the second hydraulic energy source fails, it can ensure a safe return, that is, it has fault working/fault safety capability. 2. Dual series structure. The dual series structure is used for the electro-hydraulic servo actuator of the rudder and landing gear of the American space shuttle orbiter. The rudder surface is driven by four actuators (in double series layout). Each actuator provides 50% of the required control force for the rudder surface. When two of the actuators fail, the rudder still has 100% driving force. 3. Detection and correction (error correction) structure. The redundant damped servo actuator of F-111 fighter bomber is this type of structure. The information of its three channels, i.e., working, standby, and benchmark, is compared in pairs to detect the mismatch between channels (e.g., setting zero drift, gain, working limit, etc.). When the difference exceeds the set value, the system switches from working (fault) channel to standby channel. This kind of structure is complex, and its comparison and monitoring components should have high reliability. It is simpler and more reliable to replace the reference channel and comparator (hardware) with a single board computer and its software. 4. Redundant electro-hydraulic servo valve. The electro-hydraulic servo system of American space shuttle adopts four redundant electro-hydraulic servo valves, three sublevel Saturn-V rocket electro-hydraulic servo systems, and three redundant electro-hydraulic servo valves, all produced by MOOG Company. It

72

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consists of three (or four) electro-hydraulic servo valves to control a power stage slide valve. The output of each servo valve is algebraically added on the slide valve to synthesize the displacement of the spool. As long as the gain and feedback gain of the servo valve are high enough, when the fault output (interference displacement) occurs in one channel, the output can be offset by other normal working channels through feedback, and the effect of the fault can be corrected. This form is compact in structure and hardly increases system weight and power consumption. According to the polarity and magnitude of input signal, the hydraulic servo system of missile and spacecraft controls the deflection angle of rocket engine, rudder, movable nozzle or spoiler of missile, and runner in a proportional or relay manner, and generates a certain control force or moment to control the movement and attitude of missile and spacecraft. Early missile hydraulic servo mechanism was relatively simple, such as V-1 and V-2 missile hydraulic servo mechanism developed in Germany in World War II, which was driven by a DC motor to drive gear pump as energy source, control signal was input to the wet torque motor, driving a balance lever, two needle valves were hung at both ends of the lever to control highand low-pressure hydraulic oil, input to the two cavities of actuator. The actuator outputs a certain moment to drive the load. Dry torque motor and double nozzle servo valve appeared in the early 1950s, and the electro-hydraulic servo system became more and more perfect in the 1960s. With the development of aerospace and missile technology, the requirement for the reliability of launch vehicle is getting higher and higher. At present, the overall reliability of the advanced launch vehicle in the world is 0.99, which requires that the reliability of the control system approaches 0.999. As a key component of the control system, the reliability of the servo mechanism is above 0.999. Such a level of reliability cannot be achieved by the conventional hydraulic servo mechanism. Therefore, the reliability of servo mechanism must be improved essentially. In the early 1960s, when the United States launched Hercules I missile, the position sensor cable was broken, which made the servo system in an open-loop state, resulting in the missile out of control, and ultimately caused the launch failure. In order to improve the reliability of missile and vehicle servo system afterward, the servo actuator was changed from electrical feedback to mechanical feedback. The electro-hydraulic servo mechanism of the space shuttle and the launch vehicle adopts full technology and a redundant hydraulic servo mechanism. It has been used in Saturn-V S-IVB, Hercules III-M, and the space shuttle in USA. Figure 9.8 shows the schematic diagram of the four redundant servo mechanisms of the booster of the US space shuttle. Compared with the conventional servo mechanism, the characteristics of the four redundant servo mechanisms of the space shuttle booster shown in Fig. 9.8 are as follows: (1) The high-power mechanical parts of the hydraulic servo mechanism have high reliability, while the low-power electrical and hydraulic amplifiers have low reliability. The servo amplifiers and servo valves have four redundancies, and

9.1 Electro-Hydraulic Servo Control Technology of Aircraft Gas Turbine Pump

Mechanical Feedback Spring Frame Component

Servo Valve D

73

Power stage spool sleeve assembly Servo Valve B

Servo Valve C Dynamic pressure feedback damping piston

Mechanical Feedback Linkage Device

Solenoid isolation valve

Servo Valve A

Strain gauge piston displacement sensor

Feedback cone Actuator main piston Shear piston displacement feedback mechanism

Fig. 9.8 Schematic diagram of four redundant servo mechanisms of US space shuttle booster

the actuators have no redundancy. Reasonable layout is needed to reduce weight and volume. (2) The position signal is fed back to the torque motor of four servo valves by mechanical feedback, which forms a closed loop. (3) The sliding valve of each servo valve is provided with a dynamic pressure feedback channel to reduce the pressure gain of the servo valve. A differential pressure sensor is installed at the output end of each servo valve, and the output signal is fed back to the input end of the servo amplifier to reduce the force between the redundant channels, improve the dynamic performance of the servo mechanism, and ensure the normal management of the redundancy based on differential pressure. (4) The energy of redundant servo mechanism is dual redundancy, and one servo actuator is automatically selected from the two energy sources by a reversing valve. If any energy fails, the whole servo mechanism can still work normally.

9.1.3.5

Digitization and Informatization

Traditional hydraulic technology has introduced modern microelectronics technology and computer technology into the stage of modernization. Computer has been widely used in hydraulic equipment.

74

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(1) Computer Control Compared with an analog servo system, digital electro-hydraulic servo system has higher control precision, stronger anti-interference ability, wider and more flexible functions. Taking the coordinated loading system for structural fatigue test of American space shuttle as an example, there are 374 electro-hydraulic servo loading actuators, 209 servo loops, and more than 5000 sensors in the system. An Xcrox 530 computer and inferior computer of each channel controls the loading program to load each channel in coordination according to various load spectra (simulating 40 load conditions). It has the functions of working mode selection, real-time data processing and monitoring, and protection. The 100-channel hydraulic loading system controlled by computer was successfully developed by China Aviation Industry Department in 1988. (2) Computer-Aided Testing and Fault Diagnosis The test automation of the electro-hydraulic servo valve debugging system of MOOG Company has been greatly improved after the computer was used. The flow characteristics, pressure characteristics, zero leakage characteristics, and pressure– flow characteristics of the valve are tested automatically. The characteristic curves and data (such as flow gain, pressure gain, linearity, symmetry, resolution, hysteresis and dynamic response) are given. Online monitoring of the operation of hydraulic system is realized. For example, the cavitation diagnosis of hydraulic pumps has been carried out at home and abroad. The pressure fluctuation spectra of hydraulic pumps and the vibration power spectra of shell have been analyzed by computer. According to the low-frequency component of pressure spectrum, the occurrence of cavitation is judged, and the relationship between the frequency component of vibration power spectrum, vibration energy of each frequency, and cavitation is studied. (3) Computer-Aided Design and Analysis In recent years, China has introduced or developed a relatively complete hydraulic CAD software system, simulation analysis and design software from abroad, which can be applied to hydraulic components and system design calculation, dynamic simulation, identification, and performance optimization of hydraulic systems. (4) Digital Control Hydraulic Components Digital hydraulic control components (such as pulse width modulated solenoid valves) can receive computer information directly (if necessary, add amplifiers) to achieve action. It simplifies the interface, but has low-frequency response, and is used in occasions where control requirements are not high. The digital control flow valve and pressure valve developed by the author in Tokyo Meter can directly set and measure the flow and pressure through the button on the valve body and the embedded chip. In addition, “stepping motor–reducer–screw/nut sleeve–hydraulic slide valve” combination, whose input is pulse sequence and output is linear

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displacement of slide valve, has the advantages of strong antipollution ability, low cost, but long lag time, low resolution, and poor dynamic performance. The electro-hydraulic servo system is closely combined with electronic technology and computer technology to form a highly reliable, efficient, and digital hydraulic servo mechanism. In 1980 and 1987, the US Air Force Aeronautical Thrust Laboratory and the US Air Force Artificial Navigation Laboratory published “Digital Electro-hydraulic Servo Mechanism for Advanced Missiles”. It consists of a controller, a servo valve, a power vector motor, and a drive mechanism. Its maximum output torque is 28 kgf m, its maximum no-load speed is 250 =s, and its rudder deflection angle is up to 35 . It is used for airborne multipurpose high-performance missiles. The working principle of digital electro-hydraulic servo mechanism is shown in Fig. 9.9. The power vector motor is a small inertia

Logic Controller

Pulse Input

Primary Valve

Electro-hydraulic servo valve

Electro-hydraulic servo valve

Oil return

Electro-hydraulic servo valve

Slide valve

Winding Nozzle baffle

Oil supply Rotor trajectory

Output shaft Housing

Actuators

Blade

Reaction pin

Fig. 9.9 Schematic diagram of digital electro-hydraulic servo mechanism

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high-speed motor without rotating blades. Four servo valves receive digital electrical signals from the controller and control eight working chambers of the power vector motor. They can swing positively and negatively and drive the rudder surface through the transmission mechanism. No feedback device, direct use of computer for guidance and control, zero drift of ambient temperature is small.

9.1.4

Design Method of Air Defense Missile Control Execution System

Air defense missile control actuation system (CAS) refers to the execution system of missile control system, which mainly consists of steering gear and its energy, control mechanism, and control surface, also known as steering gear control system. Its working principle is shown in Fig. 9.10. The command control signal generated by the formation device of the intermediate and terminal guidance commands of the air defense missile control execution system is superimposed with the automatic stabilization signal feedback from acceleration, damping, and rolling loops, and is used as the input signal of the rudder system. Compared with the feedback signal of the rudder system itself, the error signal is formed. Then it is amplified synthetically by the integrated amplifier and transmitted to the steering gear. Under the input power of the energy on the missile, the steering gear provides the control moment, drives by the control mechanism and overcomes the load moment, deflects the control surface according to the polarity and amplitude of the control command, and makes the missile fly according to the predetermined control trajectory until it hits the target.

Control Actuation System

Energy

Control signal Integrated amplifier

Stable signal

Steering engine Feedback potentiometer

Manipulator

Feedback mechanism

Control surface

Rudder Energy system

Fig. 9.10 Working principle diagram of air defense missile control actuation system

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As the unity of control and structure and the joint of signal flow and power flow, the control execution system is not only the execution system of control system, but also the component of missile structure. As the main hardware equipment of missile control system, the control system requires high specific performance and specific power. Because its performance not only affects the frequency characteristics of missile control system, but also affects the frequency coupling between auxiliary energy and control mechanism, as well as the dynamic flutter and static divergence of aeroelasticity of control surface, its design plays an important role in the whole missile design. The objective of missile control execution system design is to optimize the comprehensive performance, and it is feasible. To achieve this goal, it mainly depends on two aspects: on the one hand, it depends on the rationality of the indicators required by the overall implementation system and the feasibility of scheme selection; on the other hand, it depends on the technological advancement and the effectiveness of the design method adopted by the execution system. Next, the design idea and method of air defense missile control actuation system are summarized from the overall point of view. The key points are to clarify the comprehensive requirements, to clarify the restrictive conditions and extreme environmental conditions, to conduct demonstration and analysis, to determine the main criteria, and to verify performance indicators. 9.1.4.1

Comprehensive Requirements

(1) The basic design requirements are shown in Table 9.8. (2) The additional design conditions are shown in Table 9.9. 9.1.4.2

Demonstration Process

Before the missile control system, launch control system and telemetry system put forward the design requirements for the control actuation system, it needs to go through the necessity demonstration. Before accepting the task of development, the control actuation system must make feasibility analysis. The important issues of demonstration and analysis are as follows: (1) The series of the execution system depends on whether the series of the missile adopts gas rudder for vertical launch control (e.g., American sparrow is a single-stage missile, but adopts vertical launch control, so it is still two-stage). The number of actuating systems depends on the setting of rudder and aileron (There are rudders and ailerons separated, such as the French rattlesnake, Sam 6 of the Soviet Union; there are also rudders and ailerons integrated, such as Sea Sparrows, Aspide, Italy), and the differential mode of rudder and aileron (Mechanical differential, such as Sam 2 of the Soviet Union; Electrical differential, such as Sea Sparrows). The installation space of the execution

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Table 9.8 Basic requirements for the design of air defense missile control execution system Serial number

Parameter

Explain

1

Stall moment

2 3

Hinge moment Counter-maneuvering moment Control surface velocity Inertia of control surface Control surface load

Maximum braking moment of actuator when control surface velocity approaches zero Control surface pneumatic hinge moment Moment of control surface in counter manipulation Deflection angular velocity of control surface at no-load and full-load Inertia of control surface actuator around control surface rotating axis Rating and maximum of aerodynamic load on control surface Control surface comprehensive deviation angle

4 5 6 7

16

Control plane deflection Steering gear type Steering system bandwidth Stepped response of rudder system Static stiffness of rudder system Dynamic stiffness of rudder system Dead zone of rudder system Invalid stroke of rudder system Positioning accuracy of rudder system Working hours

17

Service life

18 19

Environment condition Reliability

20

Maintainability

21 22 23

Effective size Effective weight Manufacturing cost

8 9 10 11 12 13 14 15

Types of energy used by steering gear In the frequency domain, the frequency range when the rudder system drops to 3 dB Response characteristics of rudder system to step signals in time domain Static torsional stiffness of control surface deflection in rudder system Dynamic torsional stiffness of control surface deflection in rudder system Insensitive zone of rudder system Driving clearance of rudder system Driving accuracy of rudder system The longest duration of the execution system in flight Total life of the execution system during its service life Environmental conditions of execution system during storage, operation, and flight Average trouble-free running time of execution system during service life Limitation of service processing for inspection and maintenance of execution system Effective structure size of execution system Effective structural weight of execution system Development and production funds of executive system

Remarks

9.1 Electro-Hydraulic Servo Control Technology of Aircraft Gas Turbine Pump

(2)

(3)

(4)

(5)

79

system depends on the arrangement of the missile position, the aerodynamic layout and the structure of the solid rocket motor nozzle. Whether the rudder system adopts angular position feedback or angular velocity feedback or hinge moment feedback mainly depends on missile type, control mode, rudder type, and quality requirements. Most common air defense missiles use angular feedback (such as Sparrow and Sam 2), which is characterized by high positioning accuracy and good control rigidity. Hinge moment feedback is often used in small missiles and is combined with gas actuators (e.g., American Chaparral) to simplify the missile-borne control system. The type of rudder depends on the control response and load power of the rudder system, and to a large extent, it is related to the comprehensive utilization of missile-borne auxiliary energy, whether there is counter manipulation during flight and the structure space of the rudder cabin, etc. Usually, hydraulic actuators are the preferred type to provide high response and high power, which are used by American Patriots, Hookers, and Sea Sparrows. If the comprehensive utilization of missile-borne auxiliary energy can be considered, the weight of missile can be effectively reduced. In addition, flight test practice has proved that if air-conditioned actuator is used, the phenomenon of control surface counter control should be avoided absolutely. Whether the actuator, servo valve, and feedback potentiometer in the rudder torsion structure adopt the whole structure or the bulk structure generally depends on the shape and size of the structure space provided by the rudder cabin. The type of control mechanism is the same as the type of steering gear structure, which mainly depends on the structure space provided by the rudder cabin. Usually, the linear feedback structure of the integral steering gear is matched with the push–pull linkage mechanism and installed in the larger cylindrical structure space (such as Sam 2, Sam 3) in the hollow. The angular feedback structure of the decentralized steering gear is matched with the push– push lever mechanism, and is installed in a small cylindrical structure space (e.g., Sea Sparrows, Aspide) in the hollow. The solid (long nozzle of engine) annular cylindrical structure space, according to tradition and need, has integrated actuator push–pull actuator (such as British Sea Javelin) and decentralized actuator push–pull actuator (such as Patriot). Likewise, due to the limitation of effective space, the installation of pitch and yaw two-way control mechanism is often asymmetrical to the integral steering gear. In this way, if the two control systems are completely symmetrical, the polarity of the steering gear (or the polarity of the guidance command) must be changed in order to coordinate the polarity of the two control surfaces. Whether the rudder system adopts mechanical differential or electric differential, it can be cross-matched with integral or decentralized rudder. Is the actuator energy of the control execution system co-source or sub-source with the seeker antenna energy? Is it integrated with other missile-borne auxiliary energy or provided independently? From the point of view of reducing weight, reducing volume and making design more economical and reasonable, generally speaking, as long as conditions permit, common source

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Table 9.9 Additional conditions for the design of air defense missile control execution system Distinguish Control trajectory

Serial Number 1

2

3 4 Frequency coupling

5

6

Launch and control system Telemetry system

Parameter

Explain

Variation law of control surface deflection angle Law of moment change on control surface Law of change of locking moment Energy level conversion time Controlling the bending -torsion frequency ratio of actuator Natural vibration and energy characteristic frequency ratio of mechanisms

Control surface deflection change of typical control trajectory Moment change of control surface of typical control trajectory Change of locking moment of typical control trajectory Interstage conversion time of energy level I and II Natural vibration frequency ratio of bending and torsion of control surface actuator

7

Energy start time

8

Output signal of rudder system integrated amplifier Control surface torque

9

10

Control plane deflection

11

Energy characteristic parameters

Remarks

Controlling surface actuator torsional vibration frequency and energy characteristic frequency ratio Time from energy start to pressure establishment Using corresponding telemetry additives Using corresponding telemetry sensor and amplifier Using corresponding telemetry sensors or additives For example, the pressure, flow rate, temperature and vibration of gas and liquid energy sources; or current, voltage, frequency of power supply, etc.

scheme and comprehensive utilization of missile-borne auxiliary energy should be adopted as far as possible without affecting the performance of energy user subsystems. Of course, this is not always the case because of special requirements and conditions. (6) The eccentric speed of the control surface depends on the instantaneous change rate of the control command and the stable signal and the speed load characteristics of the steering gear. The former is related to the design

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condition of control trajectory, while the latter is the inherent characteristic of the selected steering gear. The deflection speed of control surface is usually related to missile aerodynamic configuration. The duck rudder (e.g., French rattlesnake) is lower, the normal rudder (e.g., Sam 2) and the tail rudder (e.g., patriots and standards) are moderate, and the full-motion wing (e.g., sparrows and Aspide) is higher. In fact, for the linearized missile control body, the first thing is to limit the rolling angle of the missile, requiring the aileron steering gear of the rolling loop to have a higher speed. In order to ensure the change rate of missile maneuvering overload, the steering gear of pitch and yaw loop should also have proper speed. In general, yaw speed is lower than pitch speed. If the independent aileron rudder with the electric differential scheme is adopted, the yaw speed can also be satisfied when the pitching speed of the rudder is guaranteed. The problem is that the load speed should be allowed to drop more than the no-load speed, even if the patriot’s steering gear, its load speed is only about one-seventh of the no-load speed. Of course, for those with special requirements, the rudder deflection speed cannot be arbitrarily reduced. (7) The load moment of the control surface (including rudder and aileron) depends on the maximum velocity pressure on the control trajectory, the aerodynamic configuration of the missile, the maximum angle of attack, and the maximum comprehensive deflection angle of the control surface. The maximum flying velocity pressure is determined by the maximum Mach number and the minimum flying altitude of the missile. The aerodynamic layout of missile directly determines the equivalent area of the control surface and the position of the spindle (i.e., the force arm between the aerodynamic pressure center and the spindle). The maximum angle of attack and rudder deflection are determined by the maximum allowable overload of the missile. In order to reduce the hinge moment of the control surface, the full-motion wing is not used as far as possible, but the combined duck rudder, such as the French Rattlesnake, is preferred. Or, as Patriots do, allow greater anti-manipulation. The combined duck rudder not only has a small equivalent area, but also the aerodynamic pressure center varies very little with the missile’s flight speed. Therefore, the hinge moment on the rudder surface is very small, and the hydraulic and electric rudders with strong counter-maneuverability are allowed to have larger counter-maneuvering moment. That is to change the polarity and size of the acting arm and minimize the maximum positive control moment. In the case of patriots, the ratio of positive and negative control torques is about 5:4, as shown in Fig. 9.11. (8) The comprehensive deflection angle of control surface (including rudder and aileron) depends on the maximum allowable rudder deflection angle and the equivalent maximum aileron deflection angle. The former is limited by the maximum allowable overload of controlled trajectory, and the latter is determined by the maximum allowable interference of rolling circuit. Whether using mechanical or electrical differential, whether using push–pull or push– push steering engine, the comprehensive deflection angle of the control surface cannot be too large, generally in the range of 20  30 , especially the

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Steering gear angular velocity/(° ) Rudder deflection angle

Counter-manipulation (Increasing Moment)

Aerodynamic moment/( N•m) Positive Manipulation (Resistance Moment)

Fig. 9.11 Angular velocity curve of steering engine with aerodynamic moment

maximum comprehensive deflection angle of the full-motion wing is not more than 22 , and other aerodynamic configurations rarely exceed 35 . Otherwise, it will easily make the missile out of control, increase the aerodynamic resistance, increase the nonlinearity and asymmetry of the control mechanism, and make the arrangement of the mechanism more difficult. (9) The quality, volume, reliability, and cost of the control execution system have a great influence on the overall performance of the air defense missile control system. Therefore, in the overall design of the control execution system, the above indicators must be fully demonstrated, comprehensively analyzed, and comprehensively compared. Figure 9.12 shows the weight optimization work band of the control execution system with time as abscissa, weight as ordinate, power as reference index, and load cycle percentage as condition. Similarly, the optimal work band for volume, reliability, and cost can be obtained. The basic types of the optimal or suboptimal control execution system can be determined by calculating the intersection of the above indicators with overlapping method, considering the counter-maneuverability, the comprehensive utilization of missile-borne auxiliary energy. and other special factors. (10) There are six relative criteria for comprehensive evaluation of control execution system, including complexity, reliability, maintainability, cost, performance, and development potential. Usually, the most important concern is relative performance. Systems with good technical performance tend to be more complex, less reliable, and more expensive, but the impact on weight and volume is not obvious. This is because the weight and volume depend mainly on the system structure, design technology, structural materials, and manufacturing process. Reliability and cost are not sensitive to volume or even weight. They are functions of complexity and number of parts, and are related to maintainability. Therefore, comprehensive consideration should be given to the comprehensive evaluation of the control execution system.

83

System Mass/kg

Output power(×0.735kw)

9.1 Electro-Hydraulic Servo Control Technology of Aircraft Gas Turbine Pump

Working hours T/s Fig. 9.12 Control actuation system weight optimum work band (1/3 load cycle). A-Gas execution system (solid–gas generator size according to 100% load cycle) and cold gas execution system; B-Gas and cold gas pressurized discharge hydraulic actuating system; C-Gas turbine pump cyclic hydraulic execution system; D-Battery motor pump cyclic hydraulic execution system; E-Gas motor pump cyclic hydraulic execution system (energy comprehensive utilization)

9.1.4.3

Main Criterion

(1) Rudder System 1. The frequency bandwidth of rudder system. The rudder system is essentially a low-pass filter. In order to ensure a certain frequency bandwidth of the rudder system, it is not necessary to increase the gain of the integrated amplifier, the speed of the rudder, and the transmission ratio of the control mechanism as much as possible. Because this will make the system work unstable, the energy power becomes very large, and the equivalent force arm becomes too small. The method of introducing inertial feedback network can be considered to solve this problem. 2. Electrical differential synchronization. The rudder aileron system will inevitably cause additional effects, i.e., additional aileron effect or rudder effect, because the two rudder systems are not synchronized. Generally speaking, this kind of additional effect is small, and there is a certain margin of control surface comprehensive deflection angle, rudder circuit will not be blocked, so the problem is not serious. In order to improve the asynchronism of the two rudder systems caused by electric differential, technical measures such as characteristic selection, slope adjustment and sum–difference cross-feedback can be adopted in the design of rudder system when the additional effect is large and the comprehensive deflection margin is small. 3. Electric zero lock. The rudder system using zero return signal as control surface locking has the following conditions: the rudder system is in normal working condition, stalling moment must be greater than maximum locking

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moment, positioning accuracy is fairly high, and ineffective travel is small enough. In this way, the control surface can be locked in zero position reliably and accurately. 4. Resistance to counter manipulation. In order to reduce the aerodynamic moment of the control surface, modern air defense missiles will work in the counter-maneuvering state, so the rudder system must have the counter-maneuvering ability. The key here is to select the right type of steering gear, in which the hydraulic steering gear will be optimized. Flight tests show that the control surface of an air defense missile with “compensated” or “overcompensated” aerodynamic configuration is in an countermaneuvering control state in the subsonic and transonic flight phases, and the rudder system of the air-cooled rudder is out of control and divergent, while the rudder system of the hydraulic rudder can still work normally. (2) Steering Engine 1. Steering engine bandwidth. It is decided by the frequency bandwidth distribution of the rudder system that it should be compressed as much as possible. The research and development practice has proved that over-wide bandwidth necessarily requires an increase in the speed gain of the steering gear, thus significantly increasing the power of steering gear and its energy. Over-wide bandwidth is susceptible to electronic noise and other interference. Under some incentives, the control surface will even produce self-excited oscillation, which will cause system instability. 2. Steering speed. It mainly depends on the frequency bandwidth of the steering gear and the equivalent force arm of the mechanism. In addition to the special cases such as counter- maneuvering of control surface and static instability control of missile, the steering gear is required to have a larger load speed, and the steering and damping loops of control surface are respectively provided with deep negative feedback. Normally, the speed of the steering gear should not be too high to ensure the stability of the system, reduce the energy power, and obtain the appropriate equivalent force arm of the mechanism. 3. Steering engine moment. It should be able to overcome the comprehensive load moment such as hinge moment, inertia moment, damping moment, and friction moment of the control surface, and provide a certain speed of the control surface under the rated load moment. Even under the action of the maximum hinge moment, for reliable operation, the rudder should maintain the minimum control surface speed. 4. Load characteristic analysis. Figure 9.13 shows the load characteristic curve of the control surface of a typical aerodynamic layout air defense missile with full-motion wing. Its main characteristic is the elastic load. The trajectory of the velocity–moment characteristic curve is a rotating dislocation ellipse with a slightly inclined axis and slightly distorted. The arrow direction indicates the main characteristics of the load. For most air defense missiles controlled by air rudder, stiffness (i.e., hinge moment) plays a

9.1 Electro-Hydraulic Servo Control Technology of Aircraft Gas Turbine Pump Load speed/(°

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) N Load power(0.735kW) Isovelocity curve N Power curve

Load moment M/(N•m)

Fig. 9.13 Load characteristic (velocity, power) curve

dominant role. The arrow direction is clockwise. For very few air defense missiles using thrust vector control (TVC), the inertia (i.e., moment of inertia) plays a leading role, and the arrow direction is counterclockwise. The corresponding power curve cross rotates in 1 shape in four quadrants. 5. Steering engine output characteristics. No matter what type of steering engine, its output characteristic curve must contain the load characteristic. Taking the hydraulic steering engine as an example, the matching situation is shown in Fig. 9.14 according to the principle of maximum power point. It is obvious from the figure that the steering gear curve just contains the load curve, and the two are tangent at the maximum power point. Both positive and counter control (resistance and assistant moment) have good matching relationship. (3) Manipulating mechanism 1. Dynamic characteristics of manipulating mechanism. Approximate to the oscillation link, it is essentially a quasi-elastic system with a certain stiffness, inertia, damping, friction, and active clearance. Its typical frequency characteristics are shown in Fig. 9.15. The control surface manipulating mechanism should have appropriate natural frequency and structural damping, smaller friction, and clearance. It not only satisfies the frequency bandwidth of the rudder system, but also prevents the flutter of the control surface. The research and development practice proves that the low natural frequency of the manipulating mechanism will destroy the frequency characteristic test of the rudder system due to the structural resonance and the excessive amplitude. 2. Static characteristics of manipulating mechanism. In order to satisfy the symmetry of the straightness of the rudder system and the aileron differential, the linear transmission relationship between the control surface deflection and the rudder stroke is required. It is mainly guaranteed by

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Rudder shaft speed (° Steering engine characteristic curve (maximum control current)

)

Load characteristic curve Maximum power point Manipulating moment Load moment Fig. 9.14 Matching of output characteristics and load characteristics of steering engine

(a) Rudder deflection angle Required value

(b) Amplitude gain

Actual value

Steering gear stroke

Frequency

Phase lag Fig. 9.15 Characteristic of steering gear manipulating mechanism. a Static characteristics; b dynamic characteristics

design. The transmission ratio is the characteristic parameter of the manipulating mechanism, which depends on the equivalent force arm of the mechanism. Equivalent force arm can adjust the transmission ratio of manipulating mechanism and change the distribution relationship between moment and speed. Once the equivalent force arm is determined, the steering stroke and the deviation angle of the control surface, the steering thrust and the steering moment of the control surface, and the transmission

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and conversion relationship between the steering speed and the speed of the control surface also depend on it. Therefore, it is an extremely important parameter of the manipulating mechanism. Only by careful design can the optimal transmission ratio be obtained. 3. Frequency specification for manipulating mechanism. Manipulating mechanism has dual functions of motion conversion and power transfer. Besides strength and stiffness specifications, its design should mainly be carried out according to frequency specifications to meet the dynamic characteristics of the control surface manipulating mechanism, ensure the frequency bandwidth of the rudder system, prevent the resonance damage of the rudder control structure, and avoid the aeroelastic problems that may arise in rudder control, such as the rudder control torsional stiffness is insufficient, which causes static divergence under counter-manipulating conditions; the coupling of the rudder control torsional bending frequency causes dynamic flutter under the condition of aerodynamic and energy interconnection. 4. Installation adjustment and clearance of feedback mechanism. Feedback mechanism is only used for decentralized steering gear. Gear mechanism or connecting rod mechanism is often used to transfer the control surface deflection to the steering gear feedback potentiometer with a certain magnification factor, so that the steering system loop is closed. The feedback mechanism is required to be installed with correct polarity, sufficient straightness, and symmetry to facilitate precise adjustment (e.g., stepless adjustment of center distance of gear pair, rod length of connecting rod mechanism, potentiometer shaft, etc.), inspection, and reliable locking. In connection with mechanism and installation of potentiometer, the overall dynamic stiffness and anti-vibration strength of the combination should be paid special attention. Various technical measures (such as doubleleaf gear with ring torsion spring, gear with hairspring, and compensating spherical hinge.) are adopted to eliminate the clearance of the mechanism and ensure the stability of the rudder system. 5. Setting and type of locking mechanism. Locking mechanism is used to reliably lock the control surface which is not working for a certain time, such as the storage and transportation of missile until launching, or before starting control, or before the separation of the first and second stages of two-stage missile, and to reliably unlock it when needed. Generally, when the precision of the electric lock on the return-to-zero line of the rudder system is limited by the zero error of the rudder system and the moving gap or the working state of the energy source, the special control surface locking mechanism must be adopted. The locking mechanism of the control surface of the second-stage missile must ensure that it is still locked reliably under the maximum hinge moment in the first-stage flight. When separating, the lock must be reliably unlocked under the corresponding hinge moment. If the locking moment is insufficient, the control surface will be unlocked in advance, which will eventually lead to the air disintegration of the missile.

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(4) Control Surface 1. Moment of inertia of control surface. In order to ensure that the steering system has sufficient frequency bandwidth and prevent the structural resonance damage caused by the low natural frequency of the steering mechanism, the method of increasing the stiffness of the steering mechanism is used, and the weight of the steering mechanism is also increased. A simple and effective method is to reduce the inertia of the control plane and increase the natural frequency of the rudder control mechanism by changing the material or the specific structure of the profile without affecting the aerodynamic shape of the control surface. 2. “Balance” or “Overbalance” in the control surface. In order to prevent the dynamic flutter of rudder control mechanism, besides changing the geometrical shape of control plane or profile, structural materials, and mass distribution, the main commonly used method is to install a proper counterweight before the control surface spindle, which is used to adjust the relative position between the center of mass and the spindle so that it can be on or in front of the spindle in order to achieve “balance” or “overbalance”, such is the case with Sea Sparrows and Aspide. 3. “Compensation” or “Overcompensation” of the control plane is listed in the above section. (5) Energy There is energy source dedicated to the control executing system, also shared with seeker antennas, and even power the whole missile power grid at the same time. It covers a wide range of issues, which are complex and need to be explored. The summary is as follows: 1. Ballistic function of energy design. Different from ground energy, the power and total power of missile-borne energy are limited, so the rated power of missile-borne energy (taking control execution system as an example) is not determined by the product of the maximum hinge moment and the maximum rudder deviation velocity that may occur in all control trajectories, and the total power is not the product of the power and the longest flight time. According to the control trajectory function, the power spectrum and total work–time curve which may appear in practice are obtained, and the rated power and total work of energy are determined accordingly. 2. Study on the working condition of control trajectory. For the control execution system, the variation law of control plane deflection angle and the curve of control plane angular velocity and hinge moment varying with flight time are mainly studied. For seeker antenna, the variation law of antenna deflection angle and the curve of antenna swing angular velocity and inertia moment with flight time are studied. For the full-missile power grid, the current consumption, voltage, and frequency curves of all power supply subsystems with time-of-flight are mainly studied. Three groups of power spectrum and total power–time curves are obtained as the basis for energy

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design of steering gear, antenna, and missile power grid. If the auxiliary energy of the whole missile is utilized comprehensively, the three groups of curves need to be fitted again to form the total power spectrum and total work. In order to study the authenticity of typical working conditions of missiles and the adaptability of control execution system, foreign countries specialize in launching control execution system test vehicle (CTV). 3. Choice of Constant Power Energy and Variable Power Energy. The energy of the control execution system must match the control trajectory condition. The meaning of “matching” usually refers to “tolerance”, and “coincidence” as a special case is “adaptation”. Corresponding to inclusiveness and overlap are “constant power energy” and “variable power energy”. Usually, for small missiles, constant power energy is mostly used, such as gas execution system of Chaparral, Sam 7, which is simple, applicable, and low cost. For large missiles, priority should be given to variable power energy sources adapted to the variation of ballistic conditions, such as Patriot Battery Electric Variable Pump Hydraulic Execution System, Javelin Gas Motor Variable Pump Hydraulic Execution System, and Sea Sparrow Nitrogen Booster Accumulator Hydraulic Execution System. But in fact, many large projectiles still use constant power energy, such as Sam 2, 6 series air-conditioning execution system and Aspide gas turbine quantitative pump hydraulic execution system. The reason is closely related to historical inheritance and design style, besides considering ballistic conditions and load cycle percentage. 4. Consideration of Excretory Energy and Recycling Energy. As far as we know, the gas energy, the cold energy, and the power supply used by electric steering engines (such as Chaparral, Sam 7), air-conditioned steering engines (such as Sam 2, 6), and electric steering engines (such as French Rattlesnake, American Tail Thorn) are all excretory, and the working medium is not recycled after used. Hydraulic energy used in hydraulic steering gear can be divided into noncyclic (discharge) and cyclic. The former is basically a gas (gas or cold) turbocharged accumulator, while the latter is of different types with different primary energy sources, such as gas turbine quantitative pump with solid propellant, gas motor variable pump with liquid unit agent (flow controllable), and motor variable pump with chemical battery. Their applicability is related to preferred working belts as shown in Fig. 9.12. 5. Isolation of energy interconnection between common source and comprehensive utilization. In common source and comprehensive utilization, effective technical measures must be taken to restrict “isolation” of “intersection”. Aspide is a typical example of the integrated utilization of common source and missile-borne energy (Fig. 9.16). In order to prevent the “intersection” of antenna hydraulic energy when the hydraulic control execution system works with large flow, a current limiting valve is set at the source junction to control and isolate the flow into the control execution system, so as to ensure that the antenna energy of the seeker has sufficient

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Electro-hydraulic Power supply to full missile energy combination

Current Limiting Valve

Oil filtration

Loading Valve

Unidirectional valve

Hydraulic pump

Alternator

Reducer

Turbine

Solid propellant gas generator

To steering gear

Hydraulic relief valve

Hydraulic safety valve

Self-pressurized oil tank

Gas pressure regulating valve Exhaust

To wireless energy

Total oil return

Fig. 9.16 Block diagram of comprehensive utilization of hydraulic common source and missile-borne electro-hydraulic energy

flow. In order to prevent the no-load of the hydraulic system from interacting with the turbogenerator, a loading valve (or repression valve) is set at the outlet of the hydraulic pump to regulate and isolate the flow into the hydraulic system, to load the pump, to prevent the no-load of the turbine from overturning, and to ensure that the speed, frequency, and voltage of the generator do not exceed the limit. Of course, damper disks, such as sparrow gas turbogenerator, and regulators, such as Sam 6 cold gas turbogenerator, can also be used to regulate the speed of turbogenerator. 6. Instantaneous method of providing peak trajectory power. After choosing the motor with less rated power, how to get more transient power? For the circulating hydraulic system, the method of gas pressurized accumulator can be used. In the case of instantaneous large rudder deflection speed, a certain rate of pressure change is converted to the supplementary flow of accumulator, which together with the hydraulic pump provides the instantaneous peak flow of missile trajectory. For example, Patriot Hydraulic Execution System (Figure 9.17), when the missile suddenly maneuvers, the load flow of the system increases sharply, the pressure drops sharply, and the pressure feedback makes the variable displacement pump swash plate to the maximum position to provide the maximum flow, while the helium pressurized hydraulic accumulator rapidly provides the instantaneous supplementary flow. For the electric steering system of clutch-controlled driving motor, because of the existence of high-power clutch and decelerating gear system, its flywheel effect can be used to convert the instantaneous stall moment into the supplementary flywheel moment with a certain rate of speed change, and together with the motor, the instantaneous peak moment of missile trajectory can be provided, such as the standard missile electric actuating system.

9.1 Electro-Hydraulic Servo Control Technology of Aircraft Gas Turbine Pump

Battery

Motor

Variable pump

To steering gear

Electric Explosion Valve

Nitrogen cylinder

Pneumatic booster tank

Gas-liquid accumulator

Pneumatic booster unit

Unidirectional pump

Hydraulic safety valve

Electric Pump Unit

Oil filtration

91

Self-steering gear

Fig. 9.17 Block diagram of battery motor variable pump with gas–liquid accumulator

9.1.4.4

Performance Test

During the development of the control execution system, many ground tests are needed, and finally the flight test is checked and passed. Taking the comprehensive utilization of gas turbine energy for the two-stage missile as an example, as shown in Fig. 9.18, the main performance test items are shown in Fig. 9.19. Here is a brief overview of the representative feature test items. (1) Frequency characteristic test and structural resonance test When the rudder system is working, the sinusoidal excitation of the rudder is used. If the signal before the integrated amplifier is used as input and the remote sensor for rudder deflection is used as output, the amplitude and phase–frequency characteristics of the rudder system can be obtained. For the push–pull linkage mechanism of the integral steering gear, the feedback potentiometer is used as the input signal and the rudder deflection telemetry sensor is used as the output signal to obtain the amplitude and phase–frequency characteristics of the manipulating mechanism. If the resonance of the manipulating mechanism is maintained at the natural vibration point for a certain time, this is the anti-structural resonance test of the manipulating mechanism. The mechanism and steering arm should be kept intact after vibration. (2) Simulated Load Test and System Anti-Counter Manipulation Test Under the working condition of the rudder system, the rudder is stimulated by sinusoidal excitation of a certain frequency and amplitude, and a load simulator is used to impose a linear or constant load on the rudder surface. It is required that the

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Stage II

Stage I Full-missile power grid

Power Electro-hydraulic combination servo valve

Secondary hydraulic energy

Electro-hydrHydraulic aulic servo relay valve

Flow limit valve

Adjustable pressure gas generator

Turbine reducer

Electro-hydraulic servo valve

Electromagnetic hydraulic switch

Primary hydraulic energy

Power source energy combination

Gas rudder servo system Hydraulic rudder lock

Seeker antenna Ground launch Air rudder and control servo system servo system system

Inter-stage separation joint

Hydraulic loading valve Alternator

Hydraulic Self-pressurized piston pump oil tank

Fig. 9.18 Schematic diagram of comprehensive utilization of gas turbine pump energy for two-stage missile

rudder deviation motion be smooth without blocking, the waveform be not distorted, and the phase shift be within a certain range. At the same time, the polarity of loading can be changed, the assistant moment can be generated to simulate the counter-maneuvering state, and the anti-counter maneuvering ability of rudder system can be tested by using the parameters of ballistic characteristic points at subsonic and transonic speeds. It should satisfy all the requirements of the loop characteristics of control system. (3) Vibration Modal Characteristic Test of Control Execution System The rudder control system and the missile-borne hydraulic energy are in the working state. The steering surface is clamped at zero position by the input return-to-zero signal of the integrated amplifier. The wideband electromagnetic exciter is used to excite the rudder surface. The displacement or velocity of each characteristic point on the rudder surface is measured by a precise sensor. The natural frequencies and modes of the rudder surface are obtained, and the torsion-bending frequency ratio is determined, which provides a basis for the analysis of rudder control flutter. At the same time, the frequency response characteristics of high-speed rotating components of missile-borne energy, such as turbines, generators, and hydraulic pumps, can be measured by vibration spectrum analysis.

9.1 Electro-Hydraulic Servo Control Technology of Aircraft Gas Turbine Pump

Structural resonance test test Frequency characteristic test

Energy module test

Control components test

Rudder system test

Simulated Load Test

Relevant characteristic test of auxiliary components Working characteristic test of hydraulic energy Power characteristic test of primary energy

Strength test

Mechanisms components test

Characteristic test of integrated amplifier Characteristic test of feedback potentiometer

Strength test

Characteristic test of electro-hydraulic servo valve

Control characteristic test of guidance mechanism Characteristic test of feedback mechanism Characteristic test of manipulating mechanism gth test

Working life test

Frequency characteristic test Transient characteristic test Modal characterristic test

93

Strength test Sealing test Failure test Performance test Climate environment test Mechanical environmental test Working life test

Long-term storage test

Unit testing of control system Power interconnection test Electromagnetic compatibility (EMC) test

Joint test of guidance and control system Missile launch control docking test

Unit test of guidance system Unit test of power supply system Unit testing of electrical system

Thermal separation simulated flight test Open loop state Closed loop State

Independent loop

Missile flight test

Guidance loop status Closed loop

Fuze-warhead coordination status

Fig. 9.19 Main project block diagram of the performance test of the control execution system (excluding the telemetry part of the execution system)

(4) Working life test Working life usually refers to the total time of no-load test, which should meet the requirements of the test cycle of guidance and control system. At this time, the rudder system is in working state, and the missile-borne energy is in ground test state. (5) Energy Interconnection Test and EMC Test The guidance and control systems are in the joint test state. Energy Interconnection Isolation Test: For missile-borne integrated energy, the transient no-load low pressure of hydraulic system is simulated, the control and isolation function of hydraulic loading valve is checked, the transient no-load large flow of steering gear is simulated, and the control and isolation function of hydraulic limiting valve is checked. When the transient interference is removed, both valves should be removed isolation in a short time.

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EMC test between execution system and missile-borne electronic equipment: When the missile-borne equipment is fully online, the electrical products of the execution system, such as the explosive tube, electric igniter, turbogenerator, electromagnetic spring lock, pressure relay, electromagnetic hydraulic switch, electro-hydraulic servo valve, linear potentiometer, and integrated amplifier, are required to work normally without the influence of radio frequency interference of the missile-borne electronic equipment. Similarly, the work of electrical products of this system should not affect the normal operation of missile-borne electronic equipment, especially computers, strapdown inertial navigation units, seekers, and electric fuzes. (6) Flight test The flight test related to the control execution system is the missile flight test in the independent loop state and the closed-loop state. Independent open loop means that the damp loop and the acceleration loop are disconnected. Because of the non-damped stability and acceleration feedback, the trajectory changes dramatically. For the control execution system, both hinge moment and rudder deflection speed are the most serious conditions. Because of the stability of damping and the feedback of acceleration, the trajectory of the independent closed loop changes smoothly and the trajectory condition changes slightly. Closed loop refers to the missile guidance loop in a closed state, and the closest state to the actual combat is the combat telemetry state, aiming at fuze-warhead coordination research of missiles. The independent circuit mainly examines the signal response characteristics, power drive characteristics, anti-counter maneuvering ability, and the adaptability of the corresponding energy trajectory conditions of the execution system. At the same time, the correctness of launch control and flight control timing is further verified. The closed loop mainly examines the EMC capability, energy interconnection and isolation capability of the system, and the reliability of the control and execution system in the real climate and mechanical environment, in the complex flight and electronic environment.

9.1.4.5

Summary

(1) Control Actuation System The control actuation system has been combined with digital autopilot and strapdown inertial navigation system (both controlled by missile-borne computer). The rudder system is still based on position control servo system and is developing in the direction of digital control. Most of the rudder systems can work under the control surface counter-maneuvering state, and the speed requirement of the rudder is also reduced appropriately. The types of steering gear are still diverse and traditional. Hydraulic steering gear is the most common type of large missiles, followed by air-conditioned steering gear, while gas steering gear and electric steering gear are used simultaneously for small missiles. Electric steering gear, because of

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its convenient use, no leakage, and conforming to the requirements of missile-borne energy unit, has developed from small missile to large missile, especially ship-borne air defense missile. The control surface differential schemes are mostly electric differential schemes, and mechanical differential schemes are seldom used. Hydraulic steering gear is mostly used in the United States, air-conditioned steering gear in the Soviet Union and electric steering gear in France. One is to provide separate energy for the control execution system, and the other is to make comprehensive use of the auxiliary energy of the whole missile. (2) Control Trajectory Working Condition In order to design the execution system and its energy economically and rationally, it is necessary to study the working conditions of the system comprehensively from two aspects: control signal flow and energy power flow. Its main contents include the control surface deflection motion law and the corresponding load moment change law; the execution system dynamic characteristics and aerodynamic elasticity; the law of seeker antenna angle change and corresponding load moment change; the law of missile-borne power grid load current, frequency, voltage change with ballistic. These parameters are all functions of trajectory control. Therefore, comprehensive research involves general, guidance, control, aerodynamics, load, aeroelasticity and structure, and other related specialties. Only by vigorous coordination and close cooperation can it work. The numerical calculation can be used in the study of working conditions, and it can be combined with missile flight test if necessary. (3) General Argumentation and Systematic Analysis The necessity demonstration of missile overall scheme is an important prerequisite for the technical feasibility analysis of the execution system, and the technical feasibility analysis of the execution system is a reliable guarantee for the implementation of the overall technical requirements of the missile. They should work together and participate crosswise. It allows the system to put forward “counter-requirements” and “counter-suggestions” to the overall scheme, and also allows the overall scheme to modify the overall requirements and propose technical issues to the system. Only by organic combination and feedback control design method can the best and most applicable system scheme be obtained.

9.1.5

Auxiliary Energy for Air Defense Missiles

Combining with the design method of air defense missile control actuation system, the classification forms of missile-borne auxiliary energy and primary energy of air defense missile are discussed, and typical examples are analyzed. This section elaborates on a series of important issues of missile energy, such as unit and diversity, separate and comprehensive utilization, source and common source, constant and variable power, quantitative and variable pumps, discharge and

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circulation, and primary energy types, and obtains the key points of scheme selection and the prediction of missile-borne auxiliary energy. With the development of air defense missiles, the requirement of miniaturization and portability of missile-borne equipment is getting higher and higher. As far as missile-borne electronic equipment is concerned, the problem is relatively easy to solve because of the small control power required by electronic components. For missile-borne auxiliary energy, the corresponding heating, strength, materials, and other issues are relatively difficult to solve because of the large driving power required by the gas-hydraulic electromechanical equipment. The way is to strengthen the study of ballistic conditions and put forward practical energy requirements. The key point lies in how to rationally allocate and comprehensively utilize the missile-borne auxiliary energy so as to make the scheme have the best characteristics as far as possible. The missile-borne energy of air defense missile should be broadly divided into two parts: main energy (power plant propellant) and auxiliary energy (full-missile power supply, guidance and control system energy, and supercharging energy for propellant transport system of power plant). The configuration and comprehensive utilization of missile-borne auxiliary energy are discussed below.

9.1.5.1

Classification of Energy Program

(1) Comprehensive Utilization of Energy in Propellant Conveying system of Power Plant and Execution System 1. Cold air source. It is used not only in the propellant tank of turbocharged liquid rocket engine, but also in the cold air actuator of control execution system. For example, as shown in Fig. 9.20, the Russian SA-2 ground-to-air missile series. 2. Gas source. After decompression of the gas produced by decomposition of liquid unit agent (such as I.P.N isopropyl nitrate), the flexible rubber bag of the fuel tank of the turbocharged ramjet is pressurized, at the same time, the gas motor hydraulic pump is driven to supply oil to the hydraulic steering gear. For example, as shown in Fig. 9.21, the British Javelin ship-to-air missile. 3. Stamping air source. The high-speed ramjet air from the ramjet inlet drives the fuel delivery pump and the hydraulic pump at the same time through the ramjet turbine, which respectively supplies fuel to the ramjet and hydraulic oil to the hydraulic steering gear. They are often used for coastal or anti-aircraft missiles powered by certain ramjet engines, as shown in Fig. 9.22. (2) Comprehensive Utilization of Power Supply and Execution System Energy 1. DC power supply. Batteries on missiles supply power not only to electrical equipment, but also to electric steering gear. As shown in Fig. 9.23, such as

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American Tail Spine, Standard, French Rattlesnake, and other air defense missiles. 2. AC power supply. The turbogenerator on missile can be divided into the following types according to its working fluid and driving object: (a) Gas turbines drive both alternators and hydraulic pumps. As shown in Fig. 9.24, the general anti-aircraft missile Aspide is used in the Italian army. (b) The air-conditioned turbine drives the alternator, and the air-conditioned air feeds the steering gear. As shown in Fig. 9.25, the ground-to-air missiles of Russia SA-3 and SA-6 are used. (c) The ramjet air turbine not only drives the fuel delivery pump, but also drives the alternator and the hydraulic pump after increasing the speed. They are commonly used in coastal defense missiles or air defense missiles powered by some ramjet engines, as shown in Fig. 9.22. (3) Configuration of Missile-borne Auxiliary Energy There are two basic configurations of missile energy: common source and separate source. Common sources are usually closely related to comprehensive utilization, and separate sources have their own specific constraints. They are described according to different energy types. 1. Hydraulic source. The seeker antenna and the autopilot steering gear of Aspide are co-source, as shown in Fig. 9.24. The American Sparrow series missiles are separated sources. The seeker antenna is powered by a piston hydraulic accumulator pressurized by solid charge gas, while the pilot steering gear is powered by a capsule hydraulic accumulator with a gas decompressor pressurized by high-pressure nitrogen, and is shown in Fig. 9.26. 2. Gas source. The gas of gas turbine generator driving the American Chaparral ground-to-air missile and the gas supplied to gas steering gear are

Liquid rocket engine Gas turbine Liquid gas generator Liquid unit agent tank

Cold air steering gear

Propellant pump Propellant tank

Pressure Reducer II

Pressure Reducer III Pressure Reducer I

High pressure cold air cylinder

Fig. 9.20 Configuration chart of cooling and gas sources for Russian SA-2 ground-to-air missile series

9 High-Temperature and High-Speed Gas Turbine Pump …

98 Fuel tank

Hydraulic steering gear Gas motor variable displacement pump

Decompressor Pressure feedback

Liquid gas generator Flow regulating valve

Differential piston tank

Liquid Unit Agent Tank

Fig. 9.21 Common source configuration chart of British Javelin ship-to-air missile gas source

Ramjet Fuel pump Fuel tank

Electrical equipment Ram turbine

Speed Increaser

Alternator

Hydraulic steering gear Hydraulic pump Hydraulic oil tank

High Speed Air Inlet

Fig. 9.22 Common source configuration chart of ramjet air source for a missile

Electrical equipment

Electric steering gear Filtering equipment

Battery on Missile Fig. 9.23 Full-missile DC power supply (American Tail Spine, Standard, French Rattlesnake)

common sources, as shown in Fig. 9.27. The gas used for turbogenerator driving Sparrow series is separated from the gas used for hydraulic power boosting of seeker antenna, as shown in Fig. 9.26. 3. Cold air source. The cooling turbogenerator used by Sam 3 (SA-3) and Sam 6 (SA-6) is co-source with the cold air steering gear, as shown in Fig. 9.25, while the separate cold air source is very rare in air defense missiles. 4. Electric source. The French rattlesnake is a common source. The battery on the missile provides unified power supply to the electrical equipment of the whole missile, including the electric steering gear, as shown in Fig. 9.23. The American Patriot, on the other hand, operates separately from the electric variable displacement pump by dedicated batteries, as shown in Fig. 9.28.

9.1 Electro-Hydraulic Servo Control Technology of Aircraft Gas Turbine Pump Hydraulic steering gear

Electrical equipment Power Converter

Gas pressure regulating valve Solid Gas Generator

Seeker antenna

Current Limiting Valve

Hydraulic pump

Gas turbine

Alternator

99

Selfpressurized tank

Loading Valve

Pressure relief valve

Fig. 9.24 Gas turbine driven alternator and hydraulic pump (Aspide, Italy)

Cold air steering gear

Electrical equipment Alternator

Cold air turbine

Decompressor II Decompressor I

High pressure cold air cylinder Fig. 9.25 Cooled-air turbine driven alternator and pneumatic steering gear (SA-3 and SA-6, Russia)

5. Unit agent. Gas for melting pressure of fuel tank of Sea Javelin ramjet and gas for driving gas motor hydraulic pump in execution system are common source, which are all unit agent I.P.N, as shown in Fig. 9.21. The gas generated by Sam 2 (i.e., SA-2) unit agent I.P.N. is specifically used to drive the propellant pump of liquid rocket engine, not to pressurize the propellant tank before pump, as shown in Fig. 9.20. (4) Classification of Missile-borne Auxiliary Energy and Its Primary Energy 1. Classified according to the working substance elements of auxiliary energy. (a) Diversified auxiliary energy sources. For example, the Patriot is three-source including electricity, gas and liquid, separate sources system; the Aspide is three-source including fuel, electricity and liquid, common source system; the Chaparral is a fuel-electricity binary, common source type; the Sam 3 (SA-3), Sam 6 (SA-6) is a gas-electricity binary, common source type. (b) Unitized auxiliary energy. For example, the French Rattlesnake, the American Standard is unitary and co-source.

9 High-Temperature and High-Speed Gas Turbine Pump …

100

Electrical equipment

Seeker antenna

Pilot steering gear Capsule gas-liquid accumulator

Alternator Gas turbine

Decompressor

Solid Gas Generator

High pressure nitrogen cylinder

Piston type gas-liquid accumulator

Solid Gas Generator

Fig. 9.26 Energy source separation system on missile (American Sparrow)

Gas steering gear

Electrical equipment Alternator

Gas turbine

Regulating valve Solid Gas Generator

Fig. 9.27 Common source energy system on missile (American Chaparral)

2. Classified according to the primary energy working medium used by electro-hydraulic energy. (a) Gas generated by solid–gas generator is used as a primary energy source. Such as Sparrow series gas turbine generator, gas turbocharged accumulator; such as Aspide gas turbine driven generator hydraulic pump. (b) Gas generated by liquid gas generator is used as a primary energy source. For example, SA-2 series gas turbine propellant delivery pump, Sea Javelin gas motor hydraulic pump. (c) High-pressure cold air is used as a primary energy source. For example, Sam 3 (SA-3), Sam 6 (SA-6) cold air turbogenerator, Sparrow series of high-pressure nitrogen pressurized accumulator. (d) Ram air is used as a primary energy source, such as some types of impact turbine driven alternator fuel transfer pump. (e) Batteries are used as primary energy sources, such as Patriot DC motor driven pressure compensation variable hydraulic pumps.

9.1 Electro-Hydraulic Servo Control Technology of Aircraft Gas Turbine Pump Electrical equipment Pressure Compensation Variable Pump nt

Hydraulic steering gear Pressure Compensation Variable Pump nt

Motor Filter device Missile-on Battery

101

Special Battery

Pressure Compensation Variable Pump Oil tank

Decompressor

Accumulator

High pressure nitrogen cylinder

Fig. 9.28 Energy source separation system on missile (American Patriot)

9.1.5.2

Application Examples

(1) Fundamental Principles 1. Between the missile-borne auxiliary energy and the main energy (propellant of power plant), the interior of the missile-borne auxiliary energy must be considered comprehensively on the premise of meeting the overall performance index of missile, which is the premise of determining the type of missile-borne auxiliary energy. 2. From the point of view of reducing weight, reducing volume, compressing energy types, convenient operation and use, making the design more economical and reasonable, generally speaking, as long as conditions permit, comprehensive utilization of missile-borne auxiliary energy and common source mode should be adopted as far as possible without affecting the performance of relevant subsystems (energy users), which is the basis for the selection of missile-borne auxiliary energy schemes. 3. When there are correlative cross-linkages in the related subsystems (energy users), the missile-borne auxiliary energy must take effective technical measures to remove cross-linkages or improve the cross-linkage situation, so as to create conditions for comprehensive utilization and Realization of common sources. 4. If there are special requirements and restrictions (including nontechnical factors), the missile-borne auxiliary energy can only be allocated separately, using a separate source scheme. (2) Looking at the Technology Development of Missile-borne Auxiliary Energy through the Evolution from Sparrow Series to Aspide In Sparrow series missile-borne auxiliary energy sources, the power source (gas turbine generator), the seeker antenna hydraulic energy source (gas turbocharged piston accumulator), and the pilot steering gear hydraulic source (nitrogen turbocharged capsule accumulator) are separated and self-sufficient, as shown in Fig. 9.26. The advantages of this kind of self-contained energy are each energy source is completely independent and does not interfere with each other. There is no problem of “interconnection” between energy sources. The

102

9 High-Temperature and High-Speed Gas Turbine Pump …

power matches the working condition best, the preinstallation detection is convenient, the pipeline loss is very small, the energy comes with itself, and the reliability is guaranteed by the components. The disadvantage of this method is that the self-contained energy of components causes repeated settings, and the weight, volume, and cost are uneconomical. The power of each subsystem cannot be adjusted mutually, and the structure layout is not reasonable. In Aspide missile-borne auxiliary energy sources, the primary energy source of the missile-borne auxiliary energy source (gas turbine generator and loading valve), the pilot steering gear hydraulic power source (gas turbine hydraulic pump and limiting valve), and the seeker antenna hydraulic power source (gas turbine pump and reducing valve) are solid propellant gas turbines, three sources are integrated and are comprehensively utilized, as shown in Fig. 9.24. The advantages of this kind of combined energy are the weight, volume, and cost are more economical, the power among the subsystems can be adjusted to a certain extent, and the structure layout is more reasonable. The disadvantage is that the subsystem energy is not independent because of the primary common source, the energy is easy to interfere with each other, and there is a “cross-link” problem. Isolation measures must be adopted, and that makes the system more complex and to some extent affects the reliability. In addition, it is not easy to achieve the best matching between power and working conditions, inconvenient to detect before installation, and has a large loss of pipeline. The main reasons why Aspide missile-borne auxiliary energy system does not follow the old system of independent separate source excretion of its prototype Sparrow series, but adopts the new system of integrated common source circulation are as follows: 1. Needs of task. It mainly refers to the increase of flight time. Compared with the Sparrow series, the thrust of the Aspide solid rocket motor increases with the increase of its length. Considering the initial velocity of the aircraft, the longest working time of the missile is 60 s. From the optimum working band diagram of missile-borne energy, it is more reasonable to adopt pump hydraulic circulation system than extrusion hydraulic circulation system. 2. Possibility at reality. Aspide energy systems designer firmly grasps the two aspects of comprehensive utilization of missile-borne auxiliary energy and miniaturization of missile-borne equipment. Based on the technology of Sparrow series gas generator, gas turbine, alternator, and gas turbocharged accumulator, combining combustion, electricity, liquid, and machine, a centralized and unified miniaturized electro-hydraulic energy combination, together with other small and exquisite hydraulic accessories, is developed, which can not only be loaded in space, but also has lighter weight than the independent and dispersed ones. 3. Performance assurance. It is mainly to take some isolation measures to improve the “interconnection” among the three subsystems and ensure their respective performance. These measures are as follows:

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(a) In order to prevent the influence of no-load of hydraulic pump on the “cross-connection” of generator overrunning, a loading valve (or repression valve) is set at the outlet of hydraulic pump to regulate and isolate. By using pressure feedback from pump outlet, the opening of loading valve is reduced, the flow into hydraulic system is blocked, and the pump is loaded by throttling and boosting to avoid no-load turbine running, so as to ensure that the speed, frequency, and voltage of the generator do not exceed the limit. In order to prevent the influence of the hydraulic servo system of the seeker antenna on the “intersection” of the servo speed when the pilot hydraulic steering gear operates at a large flow rate, a current limiting valve is set at the intersection of the hydraulic system and the branch to regulate and isolate. Negative feedback of pressure difference is used to reduce the opening of current limiting valve, to limit the flow into the rudder, and to ensure the follow-up speed of the seeker antenna so as to search or track the target instantaneously and quickly. (3) Liquid Unit Agent SA-2 and Application in Sea Javelin SA-2 series liquid unit agents (isopropyl nitrate), as a special auxiliary energy for liquid rocket engine propellant delivery system (requiring low pressure and large flow), provide propellant from the storage tank to the combustion chamber of liquid rocket engine by turbine, which is driven by gas generated by decomposition of liquid gas generator, coaxial driven oxidizer pump and burner pump. Turbine is started by gunpowder starter, which is a small, short-term solid charge gas generator. The gas generated by the decomposition of liquid unit agent (IPN) of Sea Javelin is used as primary energy for both systems, as shown in Fig. 9.21. One way goes to the hydraulic steering system of the autopilot, and another way goes to boost the ramjet fuel tank through the decompressor. Its main supplier is the former. The gas motor hydraulic pump in the figure supplies oil to the hydraulic steering gear (requiring high pressure and small flow rate). The linear reciprocating motor pump is essentially a gas pressurized hydraulic accumulator with stroke as cycle, controlled by gas-hydraulic linkage distribution valve, gas pressure compensation, continuous operation, and variable flow output. It has a series of advantages, such as high efficiency, fast response (small inertia, good acceleration), reliability (no rotating parts), and short starting time. In addition, the differential piston type oil reservoir is used not only as boosting oil supply before pump of gas motor hydraulic pump to prevent cavitation erosion, but also as volume compensation and temperature compensation for system leakage. In essence, it is a self-boosting oil tank with double compensation ability. The auxiliary energy system adopts the common source system which is common for the control actuation system and the power transmission system. Its main characteristics are

104

9 High-Temperature and High-Speed Gas Turbine Pump …

1. Variable energy variable flow output varies with ballistic conditions. Mainly through gas pressure feedback, the flow of liquid unit agent (I.P.N) is automatically adjusted by flow control valve to match the change of ballistic conditions. 2. The whole system needs less total work, less oil, and lower temperature rise. Because of the variable flow output matching primary energy and ballistic conditions, there is no heating temperature rise of oil caused by the overflow of constant flow output through relief valve bypass. The actual oil volume is only about 355 ml, and the maximum dynamic range is up to 80 km. 3. The complex primary energy plant, inconvenient filling, and high toxicity of unit agent are the drawbacks of this system. In the specific selection, the conditions of working conditions, ballistic control measures and comprehensive utilization of energy, and other related issues must be fully considered, after balancing the pros and cons to determine. (4) Control Method of Missile-borne Turbogenerator The advantages of using turbogenerator as a power source are large power– weight ratio, convenient test and inspection, and easy to realize the comprehensive utilization of missile-borne auxiliary energy, and common source scheme. In order to ensure the stable output frequency and voltage of the alternator, it is necessary to limit the speed of the turbine. There are many ways to regulate the speed of turbogenerator. Here are some examples. 1. Hydraulic loading valves (or repressor valves) are installed in the coaxial drive hydraulic pump system with the generator to prevent the crosslinking effect of no-load hydraulic pump on generator overturn, such as the Italian Aspide gas turbine generator described earlier. 2. The eddy current damper disk is installed in the generator, and the principle that the eddy current damper is proportional to the rotational speed is used to stabilize the rotational speed, such as the American Sea Sparrow gas turbine generator. 3. Centrifugal governor is installed in the generator, and the relationship between centrifugal throttling and rotational speed is used to control the air intake to stabilize the rotational speed, such as Russian Sam 3 and 6 cold air turbogenerator. (5) Key Points for Selection of Missile-borne Auxiliary Energy Scheme 1. Single energy source and multiple energy sources. The rigidity of cold air energy is poor, the size of cylinder structure is large, and the effect of ambient temperature is great. Hydraulic energy has many advantages, such as good rigidity, high power, and hard control characteristics, but it has complex devices, multiple energy sources, and inconvenient use and maintenance. Considering the tactical use, maintenance, and reliability, it is better to use unitized missile-borne auxiliary energy.

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2. Individual setting and comprehensive utilization. The precondition is the scheme and combination form of missile power stacking, control execution, and power supply. 3. The gains and losses of comprehensive utilization. Taking the gas turbine electro-hydraulic energy scheme as an example, these possible negative effects are as follows: (a) The performance of power supply and hydraulic circuit and common source hydraulic circuit is “interlinked” and the complex improvement measures are taken to this end affect their relative reliability to a certain extent. (b) The “contradiction” between power supply and hydraulic circuit, common source hydraulic circuit, and the improvement of each circuit separately and its test maintenance, as well as the cross-coordination for this purpose, often make the universality compromise mediocre. (c) The influence of gas turbine exhaust back pressure varying with missile flight altitude and angle of attack will result in a considerable change range of energy output power and generator frequency, which limits the applicability to a certain extent. 4. Source division and common source. Source separation refers to the subsystem self-sufficient energy source, as set separately. It can design the best power matching according to its own working conditions, without energy cross-talk interference, equipment installation, performance improvement, test, and maintenance have greater flexibility. Common sources are usually closely related to comprehensive utilization, and need to have certain conditions, such as “energy compatibility” between subsystems, the possibility of structural installation, etc. 5. Constant power and variable power. This is for the control execution system energy, and matching with the missile control trajectory condition is the basic criterion for its design and selection. 6. Quantitative pump and variable displacement pump. Both of them are used in circulating hydraulic system and correspond to constant power and variable power, respectively. They are the key hydraulic components of the two systems. 7. Excretory and circulatory. They all refer to the hydraulic source. From the “weight, power, and time” optimum working zone of the control execution system and its energy sources, the hydraulic energy source applicability schemes are as follows: (a) Short range is gas or cold gas pressurized accumulator discharge hydraulic energy; (b) Medium and short range are the circulating hydraulic energy of gas turbine quantitative pump. (c) Medium and long range are the circulating hydraulic energy of battery electric variable displacement pump.

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(d) Medium and long-range ramjet is the circulating hydraulic energy for variable displacement pump driven by gas motor. 8. Primary energy (a) Gas pressurization and cold gas pressurization. The boosting mode of propellant delivery system of liquid rocket engine or ramjet engine mainly depends on the traditional design idea. For example, the helium of Patriot Driver pressurizes the hydraulic accumulator and the hydraulic tank at the same time. In terms of safety and reliability, the sequence of gas chemical stability is helium, nitrogen, and air in turn. (b) Gas drive and cold air drive. For the turbopump of propellant delivery system, gas is usually used to drive, and for the turbogenerator, there are two driving modes. The former has higher power and higher efficiency than the latter. (c) Solid Charge Gas and Liquid Unit Gas. According to the requirement of control execution system, the former is suitable for constant power output energy with high percentage of load cycle, not too long working time and unadjustable gas flow, such as Aspide. The latter is suitable for variable power output energy, such as Sea Javelin, which has low load cycle percentage, long working time, and adjustable gas flow. (d) Gas turbine and gas motor. Two kinds of gas driving devices of hydraulic circulating system, which are matched with solid–gas constant power system and liquid–gas variable power system, respectively, are the main driving components of this system. (e) Power Supply. Compared with early chemical batteries, gas turbine generators have the main advantages of high specific power in terms of weight and size, and do not require large converters. (f) Stamping air. It is only suitable for ramjet-powered missiles and should be used comprehensively. Typical examples of missile-borne auxiliary energy schemes for air defense missiles are shown in Table 9.10.

9.1.5.3

Summary

The development of missile-borne auxiliary energy of air defense missile depends on the development trend of air defense missile and its related subsystems. The main development trends of modern air defense missiles are power solidification, guidance dual-mode (radar, infrared), seeker initiation (active radar), fuze laser, control dual (aerodynamic and thrust vectors), transmission digitization, implementation of electrodynamics, power battery (a large number of thermal batteries and converters), and launch simplification (inclined to adopt box vertical launching or nonmanagement launch mode after launching).

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(1) With the solidification of air defense missile engine, the use of method of obtaining auxiliary energy from missile main propulsion system is less and less when ramjet engine is seldom used and liquid rocket engine is seldom used. (2) For medium-range air defense missiles, Aspide, which uses solid gas generator and turbine as the primary energy combination, power supply to the whole missile, and hydraulic source to be shared by pilot and seeker, is a successful example of comprehensive utilization of missile-borne auxiliary energy and common source with hydraulic. (3) For small field air defense missiles and larger ship-to-air missiles, with the emergence of high-efficiency thermal batteries and advanced electric steering gear, in order to facilitate operational use and improve operational reliability, most of them adopt a single power supply scheme to realize the modularization of missile-borne auxiliary energy. (4) For medium and long-range air defense missiles, the circulating hydraulic energy still occupies the traditional advantage. With the development of related technology, the accumulator system of battery motor hydraulic variable displacement pump (such as American Patriot) has replaced the fixed pressure valve system of solid–gas generator turbo-hydraulic quantitative pump (such as British Thunderbird) and the self-pressurizing tank system of liquid gas generator motor hydraulic variable displacement pump (such as British Sea Javelin). (5) Solid gas energy gas actuator and gas control still have considerable potential for thrust vector control or vertical launching of small and medium-sized air defense missiles. (6) The influence of tradition is deeply rooted. For a considerable period of time, for small and medium-sized air defense missiles, the main types of missile-borne auxiliary energy of their respective improved models and successor models in Russia are cold air source, cold air turbogenerator, excretory or circulatory hydraulic power source in the United States and Britain, as well as thermal batteries and power unit in France. (7) Missile-borne auxiliary energy is an important project in the development of air defense missiles, which deserves great effort and careful study. The proper selection of its scheme will directly affect the success or failure of the missile-related subsystems and the whole missile, so it must be taken seriously. Weight and space are the basic problems of scheme selection. As far as auxiliary energy is concerned, it can be achieved by improving mechanical efficiency and reducing energy loss.

Tailstock

Chaparral

Sparrow

5

6

Sam-6

3

4

Sam-3

2

U.S.A

Sam-2

1

Russia

Model

Serial number

Country

Mid-low altitude

Low altitude

Ultralow altitude portable

Mid-low altitude

Mid-low altitude

Middle and high altitude

Type

Solid rocket engine

Solid rocket engine

Solid rocket engine Solid impact engine Solid rocket engine

Liquid rocket engine

Main power

Hydraulic

Gas

Electric

Cold air

Cold air

Cold air

Steering engine

Power supply: solid charge generator, driving gas turbine generator;

Gas Source: Solid Charge Generator, Driving Gas Turbine Generator; Supply Gas to Steering Engine

Power Supply: Thermal Battery, Power Supply to Full Bomb Electrical Equipment (Including Electric Actuator)

Ditto

Power supply: chemical battery; Gas source: hydraulic unit agent, driving gas turbine pump to transport propellant; Cold air source: compressed air, booster propellant tank; air supply to steering gear I and II Cold air source: compressed air, driving air turbogenerator; air supply to steering gear I, II

Auxiliary/primary energy

Table 9.10 Typical examples of missile-borne auxiliary energy schemes for air defense missiles

(continued)

Single source, Comprehensive Utilization, Common Source, Variable Power, Excretory Multisource, Comprehensive Utilization, Common Source, Constant Power, Excretory Type Multisource, individual settings, source division,

Ditto

Ditto

Multisource, Comprehensive Utilization, Constant Power, Excretory Type

Characteristic

108 9 High-Temperature and High-Speed Gas Turbine Pump …

10

11

France

Italy

Patriot

8

Aspide

Rattlesnake

Sea Javelin

Standard

7

9

Model

Serial number

Britain

Country

Table 9.10 (continued)

Mid-low altitude, General purpose of the Army

Low altitude

Medium-range ship-to-air

Medium and Long Range

Medium-range ship-to-air

Type

Solid rocket engine

Solid rocket engine

Ramjet

Solid rocket engine Solid rocket engine

Main power

Hydraulic

Electric

Hydraulic

Hydraulic

Electric

Steering engine

Gas Source: Solid Charge Generator, which supplies gas to turbine and drives generator and hydraulic pump at the same time. Power supply to the whole missile and oil supply to the hydraulic steering gear and seeker, respectively

Power supply: One battery supplies power to the generator, drives the variable displacement pump to supply oil to the steering gear, and the other battery supplies power to other electrical equipment on the missile. Cold air source: helium, pressurize the tank before pump, inflate the gas–liquid accumulator Power supply: thermal battery; Gas Source: Liquid Unit Agent, Gas Supercharged Fuel Tank; Drive Gas Motor Variable Pump, Supply Oil to Steering Engine I, II Power supply: Battery, power supply to all-missile electrical equipment (including electric steering gear)

variable power, excretory type

Gas source: solid charge generator, gas supercharged accumulator, guide antenna for fuel supply; Cold air source: nitrogen, booster accumulator, oil supply to steering gear Same as Tailstock

Single source, comprehensive utilization, common source, variable power, excretory Multisource, individual settings, source division, constant power, cyclic

Multisource, comprehensive utilization, common source, variable power, cyclic

Multisource, individual settings, source division, variable power, cyclic

Same as Tailstock

Characteristic

Auxiliary/primary energy

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9 High-Temperature and High-Speed Gas Turbine Pump …

110

9.1.6

Hydraulic Energy Application Technology of Gas Turbine Pump for Aircraft

9.1.6.1

Application of Gas Primary Energy

Gas technology is widely used in missile control actuation system. In addition to gas servo mechanism and its energy, it is mainly used as primary energy of missile hydraulic system, directly pressurizing hydraulic tank or indirectly driving hydraulic oil pump through turbine and motor. The former belongs to extrusion hydraulic system, while the latter belongs to circulation hydraulic system. As a primary energy source, gas is used in the circulating hydraulic system of tactical air defense missile, which can be divided into two categories: one is the common gas turbine quantitative pump (Fig. 9.29); the other is the rare gas motor variable pump (Fig. 9.30). Gas turbopump usually uses solid charge gas generator, and hydraulic plunger pump is a quantitative pump. Its advantages are simple composition and easy to use. It is suitable for hydraulic servo mechanism with complex trajectory conditions, high load cycle percentage, high average power, and not too long working time. The disadvantage is constant power output, gas parameters cannot be adjusted. Gas motor pumps usually use liquid unit gas generators. Gas motor pump is a variable displacement pump. This gas driven linear (reciprocating) motor pump is essentially a gas turbocharged accumulator with cycle travel and continuous Gas Turbine Pump Set Solid Charge Gas Generator

Retarder

Turbine

Piston pump

Connected to Hydraulic System

Fig. 9.29 Block diagram of gas turbine pump

Gas Motor Pump Set

Gas Motor Pump Set

Gas Distribution Motor pump Valve

Oil Distribution Valve

Pressure feedback Flow regulating valve

Liquid Unit Agent Tank

Fig. 9.30 Block diagram of gas motor pump

Connected to Hydraulic System

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operation. It has the advantages of high efficiency, fast response (small inertia, good acceleration), reliability (no high-speed rotating parts), and short starting time. When working, the gas produced by the decomposition of liquid unit agent drives motor pump feeding oil to the hydraulic system. The flow rate of liquid unit agent is automatically adjusted by the flow control valve through gas pressure feedback. Its advantages are variable power output, output power matching load power. It is suitable for hydraulic servo mechanism with smooth trajectory, low load cycle percentage and average power, and long working time. The disadvantages are complex composition, inconvenient use, toxicity of liquid unit agent, and high cost of single use. It should be pointed out that the gas motor pump scheme is rare even in foreign countries, because the application of this scheme is conditional. These conditions include: 1. long working time; 2. smooth trajectory, minimum load cycle percentage, and average power; 3. gas generated by liquid unit agent can be comprehensively utilized in the auxiliary energy of the whole missile; 4. mature technology and experience.

9.1.6.2

Application of Gas Turbine Pump

Gas turbine pump has the advantages of simple composition, convenient use, and high reliability, and has been widely used at home and abroad. The gas turbine pumps of tactical air defense missiles can be divided into two categories: one is with accumulator and gas booster tank, and the gas part does not have gas relief valve (Fig. 9.31). The other is with gas relief valve, hydraulic loading valve, flow-limiting valve, and self-pressurized tank (Fig. 9.32). Figure 9.31 shows a gas turbine pump system with a gas nozzle and a gas booster tank. Its advantage is a simple composition. The pressure of the hydraulic system is constant after the accumulator is introduced. It can absorb the hydraulic impact of the system and stabilize the pressure fluctuation of the pump, and also provide a larger instantaneous supplementary flow to the system. When launching, the electric explosion valve is used to control the pressurization of small cylinders to the tank, which solves the problem of gas and oil leakage in the tank under long-term storage conditions. Its disadvantage is that it is inconvenient to use and needs to supply gas to accumulator and small cylinder. Before launching in high-temperature environment, it is necessary to install a suitable vent nozzle to relieve the overflow pressure of the gas generator, so as to increase the content and time of service operation. Because there is no gas relief valve and hydraulic loading valve, when the servo valve is not loaded, the turbopump may have a short time overturn. The system is suitable for hydraulic system with a high requirement of constant pressure, high requirement of instantaneous rudder deflection speed, air source equipment in technical position, good service condition, and certain overturning ability of turbopump. A vertical launch flight tester in China adopts a gas turbine pump with accumulator.

9 High-Temperature and High-Speed Gas Turbine Pump …

112

Turbo pump set Solid Charge Gas Generator

UnidirectiTurbine Retarder Pump Oil filter onal valve

Exhaust Small cylinder

Electric Explosion Valve

Gasliquid accumu lator

Servo valve

Relief valve

High temperature ventilator Gas booster tank

Fig. 9.31 Block diagram of gas turbine pump with gas nozzle and gas booster tank

Power Supply to Full Missile Current Limiting Valve

Oil filter

Loading Valve

Pump r

Alternator

Retarder

Connecting to hydraulic energy of seeker antenna

Servo valve

Relief valve

Safety valve

Self-pressurized tank

Gas relief valve

Turbine

Solid Charge Gas Generator

Unidirectional valve

Electro-hydraulic Energy Unit

Exhaust

Fig. 9.32 Block diagram of gas turbine pump system with gas relief valve and self-pressurized tank

Figure 9.32 shows a gas turbine pump system with a gas relief valve, a hydraulic loading valve, and a self-pressurized tank. Its advantage is that the pressure control of gas generator is stable and the service handling is simple. When the servo valve is idle, the turbine will not overturn. Turbine coaxial drive generators and hydraulic pumps provide power and hydraulic energy for the whole missile, so that the auxiliary energy on the missile can be comprehensively utilized. Its disadvantage is that without accumulator, the pressure is not constant enough to provide a larger instantaneous supplementary flow. The system is suitable for hydraulic systems with constant pressure and low instantaneous rudder deviation speed, no air source equipment in technical position, poor service conditions, and no overturning capability of turbopump. The Aspide air defense missile, which is commonly used by the Italian armed forces, belongs to the gas turbine pump scheme with gas relief valve and self-pressurized fuel tank. It is noteworthy that the circulating hydraulic system without accumulator is rare at home and abroad. In addition to British arrows and Italian Aspide, they have basically accumulators, and even the hydraulic system of American Patriot electric variable pump has a large gas-hydraulic accumulator. There are conditions without

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accumulator: 1. The working pressure of the electro-hydraulic servo valve can fluctuate in a certain range; 2. The control system does not require the rudder’s deviation speed and basically does not require the system to provide instantaneous supplementary flow; 3. High-pressure feedback self-boosting tank can play a role of accumulator; 4. Require the hydraulic system designer to carry out the comprehensive optimal design, determine the working condition parameters reasonably, and put forward constructive counter-requirements for trajectory selection and control system design.

9.1.6.3

Working Area of Gas Turbine Pump Hydraulic System

Gas turbine pump has the characteristics of quick start, high specific power, convenient use, good reliability, and easy to realize the comprehensive utilization of auxiliary energy on missile. It is suitable for tactical air defense missiles with high load cycle percentage and medium working time, and has been widely used at home and abroad. However, it is not the only ideal solution. From the hydraulic system working belt (Fig. 9.33), there are three alternatives, including short-term use of gas pressurized storage tank, long-term use of battery motor variable displacement pump (Fig. 9.34). The working area of hydraulic system is a graph composed of a series of equal power curves with the working time as the abscissa and the system mass as the ordinate. It is mainly for the analysis and reference of the whole and system in the demonstration of the scheme. Figure 9.33 shows the mass work belt, which can also list the volume, cost, and reliability of the work belt. It should be noted that in the illustration of various schemes, the comprehensive utilization of auxiliary energy on missile is considered only for the unit agent gas motor pump. From Fig. 9.33, it can be seen that the optimum selection schemes for different tactical air defense missile hydraulic systems are as follows: (1) (2) (3) (4)

Gas booster accumulator in short range; Gas turbine quantitative pump in short and medium range; Battery electric variable displacement pump in medium and long distance; The medium and long-distance ramjet is a variable displacement pump of gas motor.

Figure 9.34 shows the battery electric variable pump hydraulic system of the American Patriot air defense missile. The battery uses silver–zinc battery with high current density and high voltage, and the motor adopts a special designed DC complex-excitation fully enclosed explosion-proof motor with radio frequency interference filter. Variable displacement pump adopts axial piston pressure compensating variable displacement pump; special helium cylinder is used to pressurize gas–liquid accumulator and gas booster tank, which is controlled by electric detonation valve before launching; and hydraulic safety valve is used to stabilize system pressure safety overflow.

9 High-Temperature and High-Speed Gas Turbine Pump …

System mass/kg

Output power ( 0.735kW)

114

Working hours /s Fig. 9.33 Working area of hydraulic system. A—Gas turbocharged accumulator; B—Gas turbine quantitative pump; C—Battery motor variable pump; D—Gas motor variable pump

Electric Pump Unit Battery

Electric machinery

Variable pump

Oil filter

Unidirectional valve Servo valve

Gas-liquid accumulator

Safety valve

Gas booster tank

Electric Explosion Valve Helium cylinder Fig. 9.34 Hydraulic system block diagram of battery electric variable displacement pump for American patriot air defense missile

The greatest characteristic of electric variable displacement pump is that it can realize the automatic matching of energy and ballistic conditions. The greatest disadvantage is that it still needs too much power supply and battery mass. As for working time is a controversial issue, some foreign experts believe that it is not generally suitable for tactical missiles with short working time. The key is that with the solution of miniaturization, high-performance chemical batteries or thermal batteries, missiles for short working time are entirely possible.

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The application prospects of gas turbopump depend on the level of solid charge and turbine development, and on whether the overall and system designers can understand the ballistic conditions and improve the ballistic conditions. Gas turbopump hydraulic system and electric system have their own characteristics. From the point of view of easy maintenance, reliability, and simplification of auxiliary energy on missile, electric steering gear is suitable, especially for small field air defense missiles and ship-borne defense missiles.

9.2

Power Matching Design of Steering System

9.2.1

Load Model of Steering System

There are several kinds of loads to be overcome in the hydraulic steering system. First, the moment generated by the aerodynamic force on the rudder surface, namely the hinge moment, is related to the flight altitude, Mach number, angle of attack, rudder deflection angle, and rudder surface angular velocity of the missile. It is a variable parameter in the flight process. The second is the inertia moment of rudder surface and transmission mechanism, which is related to the inertia of rudder surface, rudder shaft, piston, and transmission mechanism. The third is the friction moment produced by the transmission mechanism, including the dry friction moment. In addition, there are viscous damping moments, i.e., aerodynamic damping moments, which are related to the angular velocity and mass of rudder surface. The stiffness of the connector also has some influence. When hydraulic steering gear system works normally, it not only needs to overcome the above load force, but also needs to achieve a certain load speed. The relationship between load force and load speed is called load characteristics. Here the typical load forms are inertia load and the overlapping load of inertia load and elastic load, ignoring the damping force and friction force.

9.2.1.1

Load Trajectory

The load that hydraulic actuator needs to overcome is F ¼ mY€ þ KY

ð9:1Þ

where m m1 þ m2 , m1 is piston mass, m2 is equivalent mass of rudder surface and transmission mechanism (kg); K Comprehensive elastic coefficient (N=m); Y Piston displacement (m).

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The dynamic index of the system is often given in the form of frequency, so the displacement of the piston is assumed to be Y ¼ R sin xt

ð9:2Þ

Y_ ¼ Rx cos xt ¼ Y_ max cos xt

ð9:3Þ

Y€ ¼ Rx2 sin xt

ð9:4Þ

Then, there is

where R Piston motion amplitude, i.e., maximum displacement (m); x System bandwidth (rad=s). Substituting Eqs. (9.2) and (9.4) into Eq. (9.1), it is obtained,
 F ¼ mRx2 þ KR sin xt ¼ Fmax sin xt

ð9:5Þ

Figure 9.35 shows the load speed and load force–time history curves obtained by Eqs. (9.3) and (9.5). Simultaneous Eqs. (9.3) and (9.5), it can be written as 

F mRx2 þ KR

2



Y_ þ Rx

2 ¼1

ð9:6Þ

As shown in Fig. 9.36, the load trajectory corresponding to the above equation is a positive ellipse. When the friction moment of rudder and transmission mechanism is considered, the load trajectory is shown in Fig. 9.37. When the viscous damping moment is considered, the load trajectory is distorted, as shown in Fig. 9.38. Reference can be made to the relevant literature.

Fig. 9.35 Time-dependence curve of load force and load velocity

9.2 Power Matching Design of Steering System Fig. 9.36 Typical load trajectory

Fig. 9.37 Load trajectory diagram considering friction moment of rudder and transmission mechanism

Fig. 9.38 Load trajectory diagram considering viscous damping torque

9.2.1.2

Load Maximum Power Point

Load output power can be written as  1
N ¼ F Y_ ¼ Rx mRx2 þ KR sin 2xt 2

117

118

9 High-Temperature and High-Speed Gas Turbine Pump …

There is dN=dt ¼ 0 at the maximum output power point, and tan xt ¼ 1 is pffiffiffi obtained. At this time, sin xt ¼ cos xt ¼ 1= 2, then pffiffiffi Y_ ¼ Y_ max = 2

ð9:7Þ

 1
Nmax ¼ Rx mRx2 þ KR ¼ Fmax Y_ max =2 2

9.2.1.3

Load Trajectory Characteristics

(1) From Fig. 9.35, it can be seen that the load speed and load force are sinusoidal curves with the same frequency and 90 phase difference. The maximum load force and maximum load speed do not occur at the same time, but differ by a quarter of the motion cycle. (2) As shown in Fig. 9.39, the load trajectory composed of typical load force and load speed is in the form of positive ellipse, the maximum load speed Y_ max ¼ Rx and the maximum load force Fmax ¼ KR  mRx2 . (3) The maximum power point of the load trajectory appears at 1/4 of the system bandwidth. The maximum load power is Nmax ¼ Fmax Y_ max =2, the load speed pffiffiffi Y_ N ¼ Y_ max = 2 at the maximum power point, and the load force pffiffiffi FN ¼ Fmax = 2. (4) As long as the maximum no-load speed and the maximum output moment of the rudder surface are known, the load characteristics of the rudder system under typical load conditions have been basically determined. Figure 9.40 shows the actual load characteristics of a steering system with maximum output load power at point N.

Fig. 9.39 Load trajectory diagram composed of typical load force and load speed

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119

Load speed/(

Fig. 9.40 Actual load characteristics of a steering system

9.2.2

Optimal Matching of Output Characteristics and Load Trajectories of Servo Mechanism

(1) Energy Work Pressure Usually the installation space of hydraulic steering system is very limited. Therefore, higher working pressure should be chosen as far as possible. Because the higher the pressure, the smaller the piston area when overcoming the same load force, the smaller the flow required by the servo valve at this time, so the volume and weight of hydraulic energy and power mechanism will be greatly reduced. However, with the increase of pressure, the strength requirement of hydraulic components increases, and in turn, the volume and weight of components increase. On the other hand, the increase in pressure will increase leakage and flow noise, and oil temperature will also increase. At present, the commonly used working pressure specifications are 32, 21, 14 and 7 MPa. The working pressure of hydraulic steering system can be determined according to the requirements of volume, weight, noise, and other comprehensive factors. (2) Optimal Power Matching Design According to the load trajectory and the pressure of the hydraulic energy system, the no-load flow of the servo valve and the effective area of the actuator piston under the optimal matching design conditions can be obtained. The output characteristics of power control elements are compatible with the load trajectory characteristics to achieve load matching. On the one hand, the output characteristics of power control elements fully envelop the load characteristics to meet the requirements of fully dragging load. On the other hand, it means that the output characteristics and load characteristics of power control elements match each other at the maximum power position, that is, to achieve the optimal power matching design, improve power utilization, reduce energy

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Load trajectory characteristic curve Output characteristic curve of servo valve

Fig. 9.41 Optimum power matching diagram of steering gear system

consumption, and reduce the volume and mass of the system structure and components as much as possible. The electro-hydraulic servo valve is set as zero-opening four-way servo valve and the actuator is symmetrical, neglecting leakage and fluid compression. The output characteristic curve of the servo valve is shown in Fig. 9.41. The maximum power position point N has Load Flow

pffiffiffi QL ¼ Q0 = 3

Load pressure is

2 PL ¼ Ps 3

ð9:8Þ ð9:9Þ

where Q0 No-load flow of servo valve, i.e., the flow at PL ¼ 0 (m3 =s); Ps Working pressure at servo valve inlet (Pa). When the maximum output power point N1 of the servo valve coincides with the maximum power point N of the load trajectory, the optimal power matching is achieved and the hydraulic energy consumption is minimum. From Eqs. (9.6)*(9.9), the following can be obtained: pffiffiffi pffiffiffi QL ¼ Q0 = 3 ¼ a= 2 pffiffiffi 2 PL ¼ Ps ¼ b= 2 3 where a b

Maximum load flow (m3 =s); Maximum load pressure (Pa).

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121

a ¼ AY_ max ¼ ARd_ max b ¼ Fmax =A ¼ Mmax =ðRAÞ

d_ max No-load angular velocity of rudder surface; Mmax Rudder stall hinge moment. 3 Fmax A ¼ pffiffiffi 2 2 Ps

ð9:10Þ

So, Q0 ¼

rffiffiffi 3 _ AYmax 2

ð9:11Þ

Equations (9.10) and (9.11) are the design and calculation formulas of the effective area of the actuator piston A and the no-load flow Q0 of the servo valve under the optimum power matching conditions. In engineering practice, it is often necessary to round the calculation results or select suitable specifications of actuators or servo valves according to existing product samples before checking them.

9.2.3

Energy Demand of Actual Steering System

Hydraulic steering gear system of ground-to-air missile and air-to-air missile mostly uses four rudder surfaces to share one hydraulic energy source. In the whole flight trajectory of the missile, its energy consumption level is uneven. In most working hours, the power consumption level of energy is low, and only at some point in the initial stage and close to the target can there be relatively large power demand. On the other hand, the four rudder surfaces generally do not work at the same time, and the probability of four rudder surfaces simultaneously requiring maximum power is extremely small. Based on the above two reasons, combined with the telemetry flight results and design experience of the model products, energy power is recommended to be designed as 67*75% of the maximum power. In this way, it not only meets the requirements of actual working conditions, but also greatly reduces the size, volume, and mass of steering gear system and parts, and facilitates the miniaturization and integration of system design.

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9.2.4

Variation Factors of Working Pressure and Frequency Characteristics of System

(1) Influence Factors of Working Pressure Steering gear system design is generally based on constant working pressure and optimal conditions, which is rarely seen. Therefore, it is of great significance to analyze the working conditions of the system under changing pressures. The electro-hydraulic servo valve is the key component of the hydraulic servo system. Its technical performance has a great influence on the whole system. The transfer function of the servo valve is an approximate linear analytical expression of the dynamic characteristics of the servo valve. The actual dynamic characteristics of servo valves are related to many factors, such as input signal amplitude, oil supply pressure, oil temperature, environment temperature, load conditions, and so on. Valve coefficients are usually obtained under the assumption of constant supply pressure. The actual working process of aircraft steering system is a complex and changeable process. The unstable factors of servo valve inlet pressure are as follows. 1. Changes in ballistic conditions and external loads; 2. Interaction between multiple parallel loops or subsystems; 3. The primary energy work is unstable, including power supply characteristics, high temperature of gas energy, low-temperature performance differences, variable characteristics of hydraulic pumps, and the decline of volume efficiency in the working process; 4. The difference between the actual working point of relief valve and the adjustment working point is the deviation of working point. (2) Simulation results of amplitude–phase–frequency characteristics Taking the fluctuation of working pressure as an example, the frequency characteristics of the steering system are analyzed. Combining with the dynamic technical indicators of frequency bandwidth under different working pressures given in a servo valve sample, the three coefficients of the electro-hydraulic servo valve are fitted in the range of working pressure changing according to the actual operating conditions. Figure 9.42 shows the simulation results of amplitude–phase–frequency characteristics of a steering system under varying pressure. The coefficient of servo valve changes when the working pressure of the system decreases, which results in the decrease of the amplitude of the output frequency response. In the design of hydraulic steering system, the output frequency characteristics should be guaranteed to meet the practical requirements within the minimum allowable working pressure range.

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Fig. 9.42 Amplitude and phase–frequency characteristics chart of closed loop of hydraulic steering system

9.3

Design Principle of Gas Generator

The analytic relationship between gas power, thrust, and solid charge gas generator, and the analytic relationship between gas pressure and characteristic parameters of charge grain and working nozzle are deduced. The unique analytic relationship between combustion pressure change rate and relative change rate of characteristic diameter of charge and nozzle is deduced emphatically. Examples are given to illustrate relevant engineering applications, and the main parameters affecting gas pressure and its deviation are discussed. The calculation formula of gas pressure comprehensive deviation is put forward. To master the key technology of gas design, the above calculation formula and results are very important. Gas-powered energy and gas generator design technology have been widely used in modern tactical ground-to-air missiles because of its advanced and economic characteristics. For gas turbines, such as the American Chaparral missile and Sparrow missile, they are used to drive generators, such as the Italian Aspide

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missile to drive generators and hydraulic pumps, to provide power for missiles or at the same time to provide liquid energy. In the aspect of gas control, for example, Russian Dole missile uses air rudder to control the flight attitude of missile during vertical launching at low altitude. All these applications are inseparable from solid charge gas generator and working nozzle (turbine nozzle or control nozzle), which provide power for missile energy and thrust for missile control. Among the design elements that determine the missile energy power or missile control thrust, the gas pressure before the nozzle is the most important. If the pipeline pressure drop is ignored, it is the pressure of the combustion chamber of the gas generator. Therefore, the key of this kind of gas design technology lies in the discussion of the functional relationship between gas pressure and characteristic parameters of grain and nozzle, and the quantitative analysis of gas pressure changes caused by the change of characteristic parameters, which are of great significance to the development and practice of model.

9.3.1

Theoretic Derivation

9.3.1.1

Hypothesis

(1) The gas generator is a solid charge, a cylindrical retarded propellant, and a smoke-burning end. (2) Turbine nozzles or control nozzles are Laval-shaped expansion nozzles with circular throats. (3) The retarded propellant has been selected, and the physical and chemical properties and thermodynamic properties of the propellant have been determined. The pressure index is 0.5. (4) Nozzle outlet pressure p0 ¼ 0:1 MPa. (5) External atmospheric pressure pa  pe . (6) Constant ambient temperature.

9.3.1.2

Correlation Analysis

Under the above assumptions, the following correlation analysis is made: (1) Gas power and gas pressure: The output power of gas turbine nozzle depends on the inlet pressure of the nozzle and the pressure ratio between the inlet and outlet. (2) Gas thrust and gas pressure: The output thrust of gas-controlled nozzle depends on the ratio of inlet pressure to inlet pressure. (3) Gas pressure and characteristic area: Gas pressure at nozzle entrance depends on the ratio of grain area to nozzle throat area, or the ratio of characteristic area.

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125

(4) Gas pressure and characteristic diameter: The gas pressure at the nozzle inlet depends on the ratio of grain diameter to nozzle throat diameter, or the ratio of characteristic diameter. (5) Change rate of burning pressure and relative change rate of characteristic diameter: The change rate of gas pressure at nozzle inlet depends on the ratio of grain diameter to relative change rate of nozzle diameter, or the ratio of relative change rate of characteristic diameter.

9.3.1.3

Derivation of Equations

(1) Functional Relationship between Gas Power and Gas Pressure 

 m  pe N ¼E 1 pc pc

ð9:12Þ

where N pc pe m

E

Gas output power (kW); Gas pressure in front of nozzle (MPa); Gas pressure at nozzle outlet (MPa); Coefficient, m ¼ c1 c ; Specific heat ratio of grain; þ1 pffiffiffiffiffiffiffiffiffiffiffiffi 2cðc1 Þ Coefficient, E ¼ m1 RTc cg c þ2 1 A0 ;

R Tc g A0

Gas constant of grain, R ¼ J=ðkg  KÞ; Gas temperature in front of nozzle (K); Gravity acceleration, g ¼ 9:81 m=s2 ; Area of nozzle throat (cm2 ).

c

Simplify

h m i If pe pc , 1  ppec ! 1, Eq. (9.12) can be simplified to N  Epc

ð9:13Þ

Deduction _ in the equation, the single adiabatic work L is Because the gas power N ¼ Lx,   m  RTc pe L¼ 1 pc m pc

ð9:14Þ

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The weight flow rate is x_ ¼ A1 A0 pc

ð9:15Þ

In Eq. (9.15), gas flow coefficient is  cþ1 rffiffiffiffiffiffiffiffi 2ðc1Þ cg 2 At ¼ RTc c þ 1

ð9:16Þ

From the above equations, after sorting out, it can be obtained, 

 m  pe N ¼E 1 pc pc

ð9:17Þ

(2) Functional Relationship between Gas Thrust and Gas Pressure Equation 

 m 12 pe F ¼H 1 pc pc

ð9:18Þ

where F Gas output thrust (N); ffi rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi þ1 cc1 H 2 2 Coefficient, H ¼ c c1 c þ 1 A0 . Simplify

h m i12 If pe pc , 1  ppec ! 1, Eq. (9.18) can be simplified to F  Hpc

ð9:19Þ

x_ v g

ð9:20Þ

Deduction Because the gas thrust is F¼ In Eq. (9.20), the weight flow rate is "rffiffiffiffiffiffiffiffi þ1 # 2cðc1 Þ cg 2 x_ ¼ A0 pc RTc c þ 1

ð9:21Þ

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127

The gas outlet velocity is sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi   m  2gr pe RT 1  v¼ r1 pc

ð9:22Þ

From the above equations, after sorting out, it can be obtained, 

 m 12 pe F ¼H 1 pc pc

ð9:23Þ

(3) Functional Relationship between Gas Pressure and Characteristic Area Equation  pc ¼ k 2

Ab A0

2 ð9:24Þ

where A0 K d at

Area of nozzle throat (cm2 ); Coefficient, K ¼ d aA1t ; Grains weight (g=cm3 ); Burning rate temperature coefficient ½mm=ðs  MPaÞ ; a 1 ¼ a 0 ½ 1 þ a T ð T  T0 Þ

a0 Temperature coefficient of burning rate ½mm=ðs  MPaÞ ; aT Temperature sensitivity coefficient (1=K); T Environmental temperature (K); T0 Room temperature, T0 ¼ 293 K.

at

ð9:25Þ

room

temperature

Deduction Because the nozzle weight flow rate is x_ 0 ¼ A1 A0 pc

ð9:26Þ

The weight flow rate of the grain is x_ d ¼ dAb r

ð9:27Þ

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where Ab Area of grain (cm2 ). In Eq. (9.27), the burning rate of grain is ð9:28Þ

r ¼ at pnc

According to the principle of gas flow continuity, the weight flow through the nozzle should be equal to the weight flow out of the grain. After sorting out, it can be obtained,  1 a1 Ab 1n pc ¼ d At A0

ð9:29Þ

Set n ¼ 0:5, substituting K ¼ d aA1t , it is obtained  pc ¼ k 2

Ab A0

2 ð9:30Þ

(4) Functional relationship between gas pressure and characteristic diameter From the simplification of the above equation, it is obtained pc ¼ k 2

 4 db d0

ð9:31Þ

where db Grain diameter (cm); d0 Nozzle throat diameter (cm). (5) Functional relationship between gas pressure change rate and relative change rate of characteristic diameter Equation a¼

b 1  Dd db 0 1  Dd d0

where a Gas pressure change rate; Ddb Variation of grain diameter (cm); Dd0 Variation of nozzle diameter (cm).

!4 1

ð9:32Þ

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129

Deduction The gas pressure corresponding to the changed grain diameter db and nozzle diameter d0 is p0c

 0 4 db ¼k d00 2

ð9:33Þ

The burning pressure change rate is a¼

p0c  pc p0c ¼ 1¼ pc pc

 0 0 4 db =d0 1 db =d0

ð9:34Þ

Set db0 ¼ db  Ddb , d00 ¼ d0  Dd0 , after sorting out, the above equation can be written as,  a¼

 1  ðDdb =db Þ 4 1 1 þ ðDd0 =d0 Þ

9.3.2

Application Discussion

9.3.2.1

Applied Range

ð9:35Þ

(1) Setting the gas pressure, calculating or checking the output power of the turbine nozzle. (2) Setting the gas pressure, calculating or checking the output thrust of the control nozzle. (3) Setting the characteristic parameter ratio of grain to nozzle (area ratio or diameter square ratio), calculating or checking gas pressure. (4) Setting the relative manufacturing accuracy of grain and nozzle diameter, calculating or checking whether the change rate of gas pressure meets the expected requirements, and adjusting the manufacturing tolerance range accordingly. (5) Setting the relative ablation rate or deformation rate of nozzle material, calculating or checking whether the change rate of gas pressure exceeds the expected requirement, and finally selecting the nozzle material. (6) The above items can also be assumed to be opposite, and the appropriate gas pressure, the best characteristic parameter ratio, the optimized relative manufacturing accuracy, the relative ablation rate, and the relative deformation rate can be calculated or checked.

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9.3.2.2

Case Analysis

Example 1 Checking Gas Pressure pc It is known that: grain parameters pressure index n ¼ 0:5, unit weight d ¼ 1:52 g=cm3 ), ambient temperature T ¼ 40  C, low-temperature burning rate coefficient at ¼ 0:88151 g mm/s MPa , gas temperature T ¼ 1605:6 K, gas flow coefficient A1 ¼ 7:7888
103 =s, grain diameter db ¼ 7:7 cm, nozzle diameter d0 ¼ 0:23 cm. Solution pc ¼ 3:57 MPa can be obtained by directly substituting known conditions into formula (9.31) and k. Compared with the expected design requirement of ½pc ¼ 3:5 MPa, the error is þ 2%. Example 2 Checking Gas Pressure Change Rate a 0 ¼ 7:700:01 cm, nozzle diameter It is known that grain diameter tolerance dDd b

tolerance d0þ Dd0 ¼ 0:230þ 0:003 cm.

Solution a ¼ 5:528% can be obtained by directly substituting known conditions into formula (9.35). It satisfies the experience value ½a ¼ 8% which is usually allowed in design. Explanation: 1. Burning pressure change rate depends on the tolerance of characteristic diameter, i.e., manufacturing accuracy, especially nozzle diameter tolerance. Because of its small absolute value, it is more important than grain diameter tolerance. In engineering, Ddb is guaranteed by the manufacturing accuracy of grain mold and the shrinkage rate of grain, Dd0 is guaranteed by the manufacturing accuracy of nozzle machinery and the high-temperature performance of nozzle material. 2. Because the gas nozzle works above 1300  C, in order to ensure that the nozzle aperture is not eroded or corroded by high-temperature gas, the special alloy with high-temperature coal gas erosion and ablation resistance and corrosion resistance, no deformation or low deformation must be selected. Engineering practice has proved that Copper–Titanium alloy TZM is the preferred material and its performance is superior to that of stainless steel 1Cr18NiTiA and heat-resistant alloy GH36.

9.3.2.3

Related Discussion

(1) Effect of ambient temperature The characteristics of gas generator are affected by ambient temperature, which can be adjusted by setting a gas regulating valve. It is assumed that the ambient temperature of the grain is constant in the preceding text. In fact, the ambient temperature of tactical surface-to-air missiles varies greatly, usually from

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131

40  þ 60  C. When the physical and chemical properties of the grain and the related structural parameters are determined, the gas output power or pressure of the slow-burning charge of solid–gas generator is the inherent state function of the initial ambient temperature of grain. In the above temperature range, the corresponding output power and pressure vary greatly, reaching 2.5 times and 2.2 times, respectively. In order to ensure that the output power or pressure varies in a small range in the whole temperature range, gas regulating valves are usually installed in the gas system. The valve is essentially a gas overflow constant pressure valve. With the increase of ambient temperature, it overflows part of the gas, and tries to keep the gas pressure unchanged to control the pressure range of the combustion chamber of the gas generator in front of the nozzle. (2) Effect of grain pressure index The influence of grain pressure index leads to the appearance of zero pressure index grain. The assumed grain pressure index n ¼ 0:5 is actually variable and has a great influence on combustion pressure. 1 Set h ¼ 1n , substituting into equation (9.29), it is obtained,    h a1 Ab pc ¼ d A1 A0

ð9:36Þ

The corresponding relationship between h and n is shown in Table 9.11. Thus it can be seen: 1. The pressure index n has an exponential relationship with burning pressure pc . The smaller n is, the smaller h is, and the smaller pc is. When n ¼ 0; h ¼ 1, there is a linear relationship between the pressure index n and burning pressure pc . 2. The pressure index n varies 3.33 times in the scope of engineering use, and the corresponding influence index h varies 2.4 times in the scope of engineering use. Unless the special needs of high combustion pressure are met, the smaller pressure index is usually used to minimize the formulation accuracy and manufacturing accuracy of the related performance structural parameters on the premise of meeting the comprehensive physical and chemical properties of the grain. (3) Effect of Temperature Sensitivity Coefficient of Grain The influence of temperature-sensitive coefficient of grain leads to the demand of temperature-insensitive grain. It is assumed that the temperature sensitivity

Table 9.11 Pressure index of retarded propellant and its influence coefficient n Pressure index ө influence index Explain

0 1

0.2 0.25 0.33 1.25 1.33 1.5 Scope of engineering use

0.5 2

0.66 3

1 1

9 High-Temperature and High-Speed Gas Turbine Pump …

132 Fig. 9.43 Temperature function diagram of burning rate temperature coefficient

Fig. 9.44 Temperature function curves of burning rate temperature coefficient

coefficient of the grain is unchanged, but actually changes. It directly affects the burning rate and flow rate of the grain, and then affects the gas pressure. From the above equations, it can be seen that burning rate r and burning pressure pc are functions of burning rate temperature coefficient at . From the above equations, it can be seen that when the ambient temperature T and the ambient burning rate temperature coefficient at are constant, at depends only on the temperature sensitivity coefficient aT . At present, the range of temperature sensitivity coefficient aT of retarded charge used in engineering is usually 0:0025  0:0045, and the difference between maximum and minimum values is 1.8 times. According to the above equations, the temperature function figure of the burning rate temperature coefficient can be drawn, as shown in Fig. 9.43. The family of curves at different times is drawn, as shown in Fig. 9.44. From Fig. 9.43, it can be seen that the temperature sensitivity coefficient is the slope of the above linear equation. From Fig. 9.44, it can be seen that different temperature sensitivity coefficients are the slopes of the different linear families (intersect at point). The physical meaning of slope is to represent the gradient of growth with change. In order to reduce the range of burning rate and burning pressure at high and low temperatures, the requirement of developing temperatureinsensitive grain is put forward in engineering practice.

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133

(4) Effect of deviation between pressure index and temperature sensitivity coefficient of grain The influence of the deviation between the pressure index and the temperature-sensitive coefficient of the grain requires that the physical and chemical properties of the grain be relatively stable. 1. The influence of pressure index deviation on combustion pressure deviation. For example, if the pressure index and its allowable deviation of a retarded charge are n  Dn ¼ 0:28ð1  11%Þ  0:28  0:03, i.e., change in the range of 0:25  0:31, the corresponding combustion pressure will change in the range of 3:637  4:069 MPa at low temperature 40  C, with deviation of 6% from the nominal value. 2. The influence of temperature sensitivity coefficient deviation on combustion pressure deviation. For example, if the temperature sensitivity coefficient and its allowable difference of a retarded charge are aT  DaT ¼ 0:00282ð1  6%Þ  ð0:00282  0:00017Þ=K, i.e., the range of 0:00265  0:00299, the corresponding combustion pressure deviation at low temperature 40  C is 2:5% of the nominal value. Countermeasure: In order to reduce the influence of the deviation of physical and chemical performance parameters such as pressure index and temperature sensitivity coefficient on gas pressure and gas power, strict quality control must be carried out on the raw material formulation and manufacturing process of the grain to ensure the relative stability of physical, chemical, and thermodynamic properties of the bulk production grain. (5) Effect of the tolerances of main parameters on the comprehensive deviation of combustion pressure Considering the influence of the main parameters tolerance of retarded propellant on the comprehensive deviation of combustion pressure, it is necessary to reasonably distribute and calculate the tolerance. 1. Allocation of tolerances for main parameters Allocation criteria: Adjustment and control are made according to the process accessibility and degree of difficulty of combustion pressure tolerance to the related main influencing parameter tolerances. As mentioned above, the main parameter deviations affecting the combustion pressure deviation are sorted as follows according to the magnitude of their effects: (a) The relative deviation 11% of the grain pressure index affects the combustion pressure deviation d2 ¼ 6%. (b) The relative manufacturing accuracy of nozzle diameter and grain diameter are þ 1:3% and 0:13%, respectively, which affect the combustion pressure deviation d1 ¼ 5:5%. (c) The relative deviation 6% of the grain temperature sensitivity coefficient affects the combustion pressure deviation d3 ¼ 2:5%.

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Obviously, the influence of two items (a) and (c) is too great, and necessary adjustments are needed, otherwise the deviation of combustion pressure will certainly exceed the allowable deviation. If n  Dn ¼ 0:28ð1  4%Þ is used, the corresponding deviation of combustion pressure is 1:5%. If aT  DaT ¼ 0:00282ð1  3%Þ is used, the corresponding deviation of combustion pressure is 1:3%. After adjustment, the order of main parameter deviation and its influence on combustion pressure deviation is as follows: (a) The relative manufacturing accuracy of nozzle diameter and grain diameter are still þ 1:3% and 0:13%, respectively, which still affects the combustion pressure deviation d1 ¼ 5:5%. (b) The relative deviation 4% of the grain pressure index affects the combustion pressure deviation d2 ¼ 1:5%. (c) The relative deviation 3% of the grain temperature sensitivity coefficient affects the combustion pressure deviation d3 ¼ 1:3%. The deviations of main parameters are eventually allocated and determined by working nozzle design drawings and retarded grain development task book. (2) Computation of Combustion Pressure Comprehensive Deviation Calculating criteria: It mainly depends on the combined effects of the combustion pressure deviation d1 caused by the relative manufacturing accuracy of nozzle diameter and grain diameter, the combustion pressure deviation d2 caused by the relative deviation of grain pressure index, and the combustion pressure deviation d3 caused by the relative deviation of grain temperature sensitivity coefficient. Calculating method: In engineering practice, it should not only be considered that the maximum of each deviation is unlikely to occur at the same time, and that the three deviations are unlikely to overlap without compensation, but also take into account the actual situation of small batch production and production instability in the development process. Therefore, the three deviations should be added up by statistics and multiplied by a certain coefficient as the comprehensive deviation of combustion pressure. The computational equation is k ¼ 1:2

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r21 þ r22 þ r22

ð9:37Þ

where k Combustion pressure comprehensive deviation; d1 Combustion pressure deviation caused by relative manufacturing accuracy of nozzle and grain diameter;

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135

d2 Combustion pressure deviation caused by relative deviation of grain pressure index; d3 Combustion pressure deviation caused by relative deviation of grain temperature sensitivity coefficient. When the adjusted relative deviation of combustion pressure is substituted into Eq. (9.37), k ¼ 7% is obtained, which meets the experience value ½d ¼ 8% which is usually allowed in design.

9.4

Design Principle of Small Gas Turbine for Missile

9.4.1

Thermodynamic Process in Small Gas Turbine Nozzle for Missile

The missile uses the hot gas generated by retarded propellant combustion as the power source, drives the gas turbine, drives the hydraulic pump and generator, and provides the hydraulic energy and power for the whole missile. The process of converting heat energy of gas into mechanical energy in gas turbine is completed in one time in the nozzle. In this section, the thermodynamic process of gas passing through the nozzle is analyzed, and the practical nozzle flow formula is deduced by using the first law of thermodynamics. Small gas turbines for missiles are generally single-stage pure impulse turbines. The process of converting heat energy of gas into mechanical energy is completed at one time in the nozzle. Therefore, the analysis of the thermodynamic process in the nozzle is of great significance to the thermodynamic calculation of the turbine and the study of its variable working condition characteristics. The working process of working fluid in thermal power machinery can be basically divided into the following situations: (1) (2) (3) (4) (5)

Constant pressure process; Constant volume process; Isothermal process; Isentropic adiabatic process; Variable process.

The nozzle is relatively short, and the friction loss in the nozzle can be generally neglected. Considering the high speed of the airflow, the heat exchange between the nozzle and the outside can also be neglected. The flow process of gas in the nozzle can be regarded as isentropic and adiabatic process. This simplification is also significant for studying the variable working condition characteristics of the nozzle and making qualitative analysis.

9 High-Temperature and High-Speed Gas Turbine Pump …

136

According to the first law of thermodynamics, the first analytic equation is dq ¼ dU þ pdV where q U p V

Heat of working process; Internal energy of working fluid; Pressure of working fluid; Specific volume of working fluids.

Because of the high temperature of gas, its state is far from saturation, the distance between molecules is large, and the potential energy between molecules can be neglected, so it can be treated as ideal gas. The internal energy of ideal gas is only a single value function of temperature. The above equation can be expressed as dq ¼ CV dT þ pdV where CV Specific heat of gas at constant volume. Assuming that the flow process is adiabatic, dq ¼ 0, that is, CV dT þ pdV ¼ 0

ð9:38Þ

For ideal gases, its state equation is pV ¼ RT, then there is T ¼ pV=R

ð9:39Þ

where R Gas Constant. Substituting Eq. (9.39) into Eq. (9.38), there is CV dðpV=RÞ þ pdV ¼ 0 ðCV þ RÞpdV þ CV Vdp ¼ 0 where Cp Specific heat of gas at constant pressure, CV þ R ¼ Cp . That is Cp pdV þ CV Vdp ¼ 0, set Cp =CV ¼ k, there is kpdV þ Vdp ¼ 0. Finally integral, there is, pV k ¼ constant value

ð9:40Þ

9.4 Design Principle of Small Gas Turbine for Missile

137

Fig. 9.45 Enthalpy–entropy conversion diagram of gas at nozzle

The above equation is the flow process equation of adiabatic process. By using the equation of state pV ¼ RT of ideal gas, it can be derived from the above equation ðp2 =p1 Þðk1Þ=k ¼ T2 =T1 T2 =T1 ¼ ðV2 =V1 Þðk1Þ where k Adiabatic index, k ¼ Cp =CV . In this way, the state parameters of the gas at the nozzle exit can be derived from the two state parameters at the nozzle inlet. However, due to various mechanical losses in the actual process of airflow, it is obviously inaccurate to make engineering calculations according to the abovementioned equations. Therefore, mechanical losses such as friction must be considered. Gas expands and accelerates to obtain kinetic energy in the nozzle, but at the same time, it loses some kinetic energy due to mechanical losses such as friction and so on. This part of the loss is bound to heat the gas, making its enthalpy higher than the isentropic adiabatic process. The process is represented on the enthalpy–entropy coordinate graph as shown in Fig. 9.45.

9 High-Temperature and High-Speed Gas Turbine Pump …

138

In figure, S is entropy, P1 and P2 are isobaric curves. It can be seen from the figure that the enthalpy of point 20 is higher than that of the end point 2 of adiabatic process, and the entropy is also increased. The process is no longer an isentropic process. In thermodynamics, it is called a variable process. Next, the flow process equation of the variable process is derived. If the inner surface of the nozzle is uniformly machined and the roughness is the same, it can be assumed that the micro heat generated by friction is proportional to the decrease of enthalpy. There is dq ¼ ndh

ð9:41Þ

where n Nozzle loss coefficient. From the second analytic expression of the first law of thermodynamics, it can be obtained dq ¼ dqm ¼ dh  Vdp That is ndh ¼ dh  Vdp ð1 þ nÞdh  Vdp ¼ 0

ð9:42Þ

dh ¼ Cp dT ¼ kdðpV Þ=ðk  1Þ

ð9:43Þ

Because of

Substituting (9.43) into (9.42), it can be obtained ð1 þ nÞ  k ðpdV þ VdpÞ=ðk  1Þ  Vdp ¼ 0 After sorting, there is mdV=V þ dp=p ¼ 0

ð9:44Þ

m ¼ k ð1 þ nÞ=ðkn þ 1Þ Integral Eq. (9.44), it can be obtained pV m ¼ constant value

ð9:45Þ

9.4 Design Principle of Small Gas Turbine for Missile

139

Using the equation of state pV ¼ RT of ideal gas, after derivation of equation, there is T2 =T1 ¼ ðV2 =V1 Þðm1Þ T2 =T1 ¼ ðp2 =p1 Þðm1Þ=m

ð9:46Þ

where m Variability index. When two state parameters (e.g., p1 , V1 ) of nozzle inlet are known, the state parameters of nozzle outlet can be calculated. According to the equation of energy conservation, there is C12 C 02 þ h1 ¼ 1 þ h02 2 2 where h1 Enthalpy of nozzle inlet; C1 Nozzle inlet velocity; 0 H2 Actual enthalpy of nozzle outlet; 0

0

C2 Actual velocity of nozzle outlet, C2 ¼

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi h
 C2 i 0 2 h1  h2 þ 21 .

Generally, when the gas enters the nozzle from the gas generator, its velocity is very small, which can be neglected compared with the outlet velocity, so the above equation can be converted into C102

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi h iffi
ffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi m1 k 0 RT1 1  ðp2 =p1 Þ m ð9:47Þ ¼ 2 h1  h2 ¼ 2Cp ðT1  T2 Þ ¼ 2 k1

So the formula for calculating gas flow rate is f2 C 02 p1 f2 G ¼ 01 ¼ pffiffiffiffiffiffiffiffi V2 RT1

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi h iffi 2 m1 2k m m ðp2 =p1 Þ 1  ðp2 =p1 Þ k1

where G f2 V2 T1

Flow; Nozzle outlet area; Nozzle outlet specific volume; Gas initial temperature (absolute standard temperature).

ð9:48Þ

140

9.4.2

9 High-Temperature and High-Speed Gas Turbine Pump …

Efficiency of Small Gas Turbine in Missile Hydraulic System

Small gas turbines of aircraft use gas of solid retardant propellant as working fluid. Generally speaking, they are pure impulse turbines. Because this kind of gas turbine uses high enthalpy working fluid, its weight and size are small, its specific power is high, and its starting speed is fast. Because of its simple structure, there are no parts for reciprocating motion. It is not easy to get stuck at high temperature and has high reliability. It is widely used in the hydraulic system of medium and short-range tactical air defense missiles at home and abroad. Therefore, it is necessary to discuss and optimize many factors affecting turbine performance, so that gas turbine will be more viable in the competition with other primary energy sources of various hydraulic systems. Here, only the efficiency of this gas turbine is discussed preliminarily. Generally speaking, efficiency is a very important index for a prime motor. The gas turbines discussed here are used in extremely compact spaces and in situations where weight restrictions are quite stringent. Therefore, the pursuit of efficiency must take into account the size and weight, or even the pursuit of efficiency is mainly to reduce the size and weight, followed by the economy. In fact, for this particular occasion, the working time of the whole power plant is not long, the total power is very small, and the economic loss caused by low efficiency is small. This is quite different from the general power plant. Moreover, in order to improve efficiency, the corresponding economic cost must be paid. It is necessary to find a way to improve efficiency significantly at a low cost. In this kind of small gas turbine, there are several kinds of losses when working fluid works: 1 nozzle loss; 2 blade loss; 3 excess speed kinetic energy loss; 4 leakage loss; 5 wheel disk friction blast loss; 6 part intake loss; 7 kinds of mechanical losses (gear, bearing, coupling, etc.). From the calculation and analysis of the following examples, it can be seen that various losses account for the proportion of total turbine input power. The known parameters are as follows: Gas initial pressure p0 ¼ 4:98 MPa, gas initial temperature T0 ¼ 1500 K, gas constant R ¼ 437:6 J=ðkg KÞ, gas adiabatic index K ¼ 1:27, nozzle throat diameter dkp ¼ 2:5 mm, nozzle outlet angle ar ¼ 22 , turbine calculated diameter DCD ¼ 290 mm, design speed n ¼ 6000 r=min. Table 9.12 shows the value and percentage of wheel circumferential work, effective work and losses per kilogram of gas turbine at design speed 6000 r=min. From the comparison of various losses, it can be seen that the largest part of the loss is the residual kinetic energy loss, accounting for 26.80% of the total input energy. Obviously, this loss must be reduced first. From the velocity triangle, it can be seen that the simpler and more effective way to reduce the turbine outlet speed is to increase the speed of revolution, and with the increase of the speed of revolution, a minimum outlet speed can be obtained, and

9.4 Design Principle of Small Gas Turbine for Missile

141

Table 9.12 Wheel circumferential work, effective work, and losses of working fluid per kg at turbine rotational speed 6000 r/min (J/kg)

Percentage of total input work (%)

Remarks

VPUN = 169190.4 VY = 325493.7 VYU = 389806.1 VLOU = 28440.17 VLT = 6328.681 VLQ = 172423.3 VLM = 21696.66 LE = 339914.4

11.63288 22.37969 26.80157 1.955436 0.4351357 11.85516 1.491779 23.3712

Nozzle work loss Blade work loss Residual kinetic energy work loss Leakage work loss Wheel disk friction blast work loss Partial intake work loss Mechanical work loss Effective work, percentage, effective efficiency turbine input total work Turbine design speed Turbine output power

N = 60,000 r/min Ne ¼ 4:970 128 kw

the residual kinetic energy loss corresponding to the minimum outlet speed can also be minimized. If only the loss of nozzle, blade, and residual kinetic energy is deducted, the wheel circumferential work of the turbine can be obtained, which corresponds to the wheel circumferential efficiency. The formula for calculating the wheel circumference efficiency is as follows:     u u cos b2 gu ¼ 2u cos a1  1þ/ c1 c2 cos b1 2

ð9:49Þ

where u U a1 b1 ; b2 c1 c2 u

Nozzle velocity loss coefficient; Velocity loss coefficient of blade; Nozzle outlet angle; Moving blade air inlet angle; Nozzle outlet velocity (Fig. 9.46); Absolute velocity at moving blade outlet; Circumferential speed of Cascade wheel (Blade high-middle line).

In the above equation let u=c1 ¼ k, which is the so-called characteristic ratio, and derive it:   @gu cos b2 ¼ au2 1 þ / ðcos a1  2kÞ ¼ 0 @k cos b1 The optimum characteristic ratio can be found as kopt ¼ cos a1 =2. In this case, a1 ¼ 22 , then k ¼ 0:464. However, this is only the best point of wheel circumferential efficiency. For practical effective efficiency, its best

9 High-Temperature and High-Speed Gas Turbine Pump …

142

Fig. 9.46 Triangular vector distribution of airflow velocity at rotational speed 6000 r/min

characteristic is lower than k ¼ u=c1 . This is because when the residual kinetic energy loss decreases with the increase of rotational speed, other losses such as disk friction blast loss and partial intake loss increase sharply with the increase of rotational speed, partially offsetting the gains from reducing the residual kinetic energy loss. The best working point can be easily obtained by computer (Table 9.13, Fig. 9.47). In this case, at N ¼ 97000 r=min, the efficiency of the turbine is the highest. The losses at design point ge ¼ 27:7%, Ne ¼ 5:88 kW are shown in Table 9.14. Comparing Table 9.14 with Table 9.12, it can be seen that the residual kinetic energy loss decreased from 389806:1 to 255932 J per kilogram of gas. The friction blast loss increased from 6328:7 to 27226:0 J, and the partial intake loss increased from 172423:0 to 278751 J. These two losses increased sharply with the increase of rotational speed. But overall, the efficiency increased from 23:4% to

Table 9.13 Variation of power with rotational speed of gas turbine in initial and final state of working medium N N N N N N N N N N N N

= = = = = = = = = = = =

40000 45000 50000 55000 60000 65000 70000 75000 80000 85000 90000 95000

Ne Ne Ne Ne Ne Ne Ne Ne Ne Ne Ne Ne

= = = = = = = = = = = =

3.767295 4.112336 4.428102 4.714175 4.970128 5.195523 5.38991 5.552823 5.683781 5.782289 5.847825 5.879851

N N N N N N N N N N N

= = = = = = = = = = =

100000 105000 110000 115000 120000 125000 130000 135000 140000 145000 150000

Ne Ne Ne Ne Ne Ne Ne Ne Ne Ne Ne

= = = = = = = = = = =

5.877799 5.841069 5.769031 5.661011 5.516279 5.33405 5.113459 4.858552 4.553248 4.211325 3.826358

9.4 Design Principle of Small Gas Turbine for Missile

143

Turbine input power/kw

Fig. 9.47 Turbine output power varies with rotational speed at a given input power

Turbine rotational speed/(r/min) Table 9.14 Wheel circumferential work, effective work, and losses of working fluid per kg at turbine rotational speed 97000 r/min (J/kg)

Percentage of total input work (%)

Remarks

VPUN = 169190.4 VY = 255488.4 VYU = 255932 VLOU = 38632.47 VLT = 27225.96 VLQ = 278751 VLM = 25682.38 LE = 402357.3

11.63288 17.56296 17.5969 2.656219 1.871952 19.16584 1.765821 27.66453

Nozzle work loss Blade work loss Residual kinetic energy work loss Leakage work loss Wheel disk friction blast work loss Partial intake work loss Mechanical work loss Effective work, percentage, effective efficiency turbine input total work Turbine design speed Turbine output power

N = 97,000 r/min Ne ¼ 5:883 149 kW

27:7%. With the input power unchanged, the output power increases from 4:97 kW at 6000 r=min to 5:88 kW. Of course, the increase of rotational speed is limited by the strength and other factors, so the strength of the turbine disk, the critical speed of the rotating shaft, the bearing capacity, and accuracy of the bearing must be considered comprehensively. It can be seen from the characteristic ratio k ¼ u=c1 that in addition to increasing the rotational speed and increasing the circumferential velocity u accordingly to achieve the optimal characteristic ratio, reducing c1 can also be adopted, i.e., reducing

9 High-Temperature and High-Speed Gas Turbine Pump …

144

the nozzle outlet speed, so as to achieve the optimal characteristic ratio and achieve high efficiency. But in doing so, it is necessary to use working fluids with low enthalpy, such as compressed air. For the same working time and the same power output, the weight and size of the whole device will increase a lot, so it is not advisable. Another way to reduce the loss of residual kinetic energy is to adopt a double-ring wheel structure in turbines. At this time, the exhaust of the first row of moving blades passes through the steering blades and then enters the second row of blades to work, so the residual kinetic energy can be fully recovered. If a preliminary estimate is made for this example, the effective power of 2:7 kW h can be obtained from the second row of blades. Its speed is still 6000 r=min, and the total power can reach 7:7 kW. It seems to be more profitable than increasing the speed, but the complex structure of the double-ring wheel makes it more difficult to process the impeller and more demanding to install it. Moreover, it is obvious that the weight of the rotor must be almost doubled and the axial size of the plate doubled, which is unfavorable to the axial bearing capacity of the cantilever rotor. When the rotor is balanced, it is possible to make double-sided balancing (dynamic balancing). In addition, the structure of the shell is more complex, the corresponding weight and size are increased, so the cost is not small.

9.4.3

Graphical Analysis Method for Stress of Small Gas Turbine Disk for Missile

The gas turbine of missile uses the gas produced by retarded propellant as the working medium. Because of the high temperature and pressure (p0 ¼ 4:0  5:0 MPa; t0  1200  C), the gas has a high enthalpy value, i.e., the available work of working medium per unit weight. In order to make the turbine work at the optimum efficiency point, it is necessary to adopt a high rotational speed of the disk. Obviously, it is necessary to estimate the stress of the disk in the preliminary design. Firstly, the simple impeller with equal thickness is analyzed and the force equilibrium equation is established. For small gas turbine disks for missiles, the axial thickness is relatively thin, so they can be treated as plane stress. A unit body is arbitrarily intercepted from an equal thickness plate (Fig. 9.48). Its range is surrounded by dr, d/, and unit length dz ¼ 1. Obviously, the centrifugal force produced by its own mass is as follows rx2 dm ¼ rx2 qrd/dr ¼ qx2 r 2 d/dr where q Material density; x Disk angular velocity.

9.4 Design Principle of Small Gas Turbine for Missile

145

Fig. 9.48 Force analysis diagram of small gas turbine blade for missile

The force equilibrium equation of the unit body is   @rr dr ðr þ dr Þd/ þ qx2 r 2 drd/  rr rd/  r1 drd/ ¼ 0 rr þ @r The higher order terms are omitted from the above formula, and it is noted that the variables are only single-valued functions of r, it can be obtained after sorting out rr þ r

drr  r1 þ qx2 r 2 ¼ 0 dr

ð9:50Þ

In order to solve rr and r1 , the relationship between stress and strain is needed. In the radial direction, the total radial deformation at r is u. The total radial deformation at r þ dr is u þ ddur dr, so the radial strain is er ¼

u þ ddur dr  u du ¼ dr dr

ð9:51Þ

9 High-Temperature and High-Speed Gas Turbine Pump …

146

e1  2pr ¼ 2pu can be easily obtained in tangential direction, that is er ¼ u=r

ð9:52Þ

The deformation of impeller is in the elastic deformation range, so the stress and strain should conform to Hooke’s law. For plane stress, there are er ¼ E1 ðrr  ur1 Þ e1 ¼ E1 ðr1  urr Þ

 ð9:53Þ

where E Modulus of Elasticity; l Poisson’s ratio. Substituting Eqs. (9.51) and (9.52) into Eq. (9.53), it is obtained,

9 E du þ u u = rr ¼ 1u 2 r dr

E u du ; r1 ¼ 1u þ u 2 r dr

ð9:54Þ

Substituting Eq. (9.54) into Eq. (9.50), there is d2 u 1 du u 1  u2 2  qx r ¼ 0 þ þ dr 2 r dr r 2 E Set

1u2 E

qx2 ¼ K, there is   d 1 dður Þ þ Kr ¼ 0 dr r dr

After integrating twice, there is u ¼ K

r3 r 1 þ C1 þ C2 2 r 8

ð9:55Þ

Substituting Eq. (9.55) into Eq. (9.54), it is obtained rr ¼  3 þ8 u qx2 r 2 þ 2 2 rt ¼  13u 8 qx r þ

E 2ð1uÞ C1 E 2ð1uÞ C1

 1 þE u r12 C2 þ 1 þE u r12 C2

) ð9:56Þ

The integral constants C1 and C2 can be obtained by known boundary conditions. Usually, the radial stress rra around the wheel and the radial stress rri at the center hole of the wheel are known values, but the following drawing process can avoid the tedious solution of C1 and C2 .

9.4 Design Principle of Small Gas Turbine for Missile

147

Set the following equations for Eq. (9.56) 3þu 2 qx 8 1  3u 2 qx Kt ¼ 8 E C1 a¼ 2ð 1  uÞ E C2 b¼ 1þu

Kr ¼

All these four terms are known constants. Let x ¼ 1=r 2 , and substituting into Eq. (9.56), there is Kr x Kt rt ¼ a þ bx  x

rr ¼ a  bx 

It can be found from the above equation that the stress is composed of straight-line a  bx or a þ bx and inverse ratio curve Kr =x or Kt =x. Firstly, the radial stress rr is solved in the second quadrant, and the x-axis is pointed to the right (Fig. 9.49). Curves Kt =x can undoubtedly be drawn, but there are unknown integral constants C1 and C2 in a and b. The vertical line intersects Kr =x at point e from xr , and then extends the vertical line to point f so that ef ¼ eri . The vertical line intersects the Kr =x curve at point h from xa and extends the vertical line to point g to connect hg ¼ rra . Obviously, this line is a  bx. Then the tangential stress rt is solved in the first quadrant. First, make line Kt =x, then extend fg to point j and l. Thus, the shaded part of Fig. 9.49 is the radial and tangential stresses of the disk at different radii. The ultimate goal is to solve the stress distribution of unequal thickness disks, such as those with Fig. 9.50 (Fig. 9.51). For this reason, the disk is divided into many rings of equal thickness. Generally, it is enough to divide the disk into 8–12 segments. Each ring can be solved according to the steps described above. At the junction of the rings (Fig. 9.51), the radial stress has the following relationship: That is to say, the radial stress in the inner ring of n þ 1 section multiplied by the width of n þ 1 section should be equal to the radial stress in the outer ring of n section multiplied by the width of n section. That is   rr;n þ 1 bn ¼ rr;n ðnÞ bn þ 1

ð9:58Þ

9 High-Temperature and High-Speed Gas Turbine Pump …

148

plane plane

Fig. 9.49 Radial stress solution diagram

Fig. 9.50 Nonuniform thickness disk

The tangential strain at the junction of two rings in tangential direction should be equal: ðnÞ X t

That is,

¼

ðnÞ 1
ðnÞ 1
rt;n þ 1  lrr;n þ 1 ¼ rt;n  lrr;n E E

9.4 Design Principle of Small Gas Turbine for Missile

149

Fig. 9.51 Stress of cross-section wheel disc




rt;n þ 1  rt;n

ðnÞ


ðnÞ ¼ l rr;n þ 1  rr;n

ðrt ÞðnÞ ¼ uðDrr ÞðnÞ

ð9:59Þ

The labeling ðnÞ in the above equations indicates the calculation in the outer ring junction surface of n-segment. It is now possible to plot the solution in this way, using known boundary conditions, such as the radial stress of the outer ring of n þ 1 in Fig. 9.51, the ð n þ 1Þ rr;n þ 1 has been obtained, so point O can be obtained in Fig. 9.52. Making line MN ðnÞ

ðnÞ

crosses point O at any slope, then MM 00 ¼ rr;n þ 1 and NN 00 ¼ rt;n þ 1 . From Eqs. (9.58) and (9.59), there are 00 rðnÞ r;n ¼ MM ðnÞ

rt

bn þ 1 ¼ M 0 M 00 bn

¼ MM 0 l ¼ NN 0

In this way, the M 0 N 0 connection specifies the solution of stress in n-segment.

150

9 High-Temperature and High-Speed Gas Turbine Pump …

Fig. 9.52 Outer ring radial stress diagram

In the same way, the stress of the whole wheel disk can be plotted one by one. For example, a ring and a ring are drawn from the outside to the inside of the wheel disk. The loads on the periphery caused by centrifugal force of blade mass are known boundary conditions. A group of r0ri , r0ta are the radial stress on the inner hole ring and the tangential stress on the periphery. However, r0ri does not agree with the real boundary condition rri in this set of solutions. This is because the slope in the above drawing process is arbitrary. r0ri ¼ rri occurs only by coincidence. Therefore, it is necessary to take a new slope as MN line and repeat the above drawing process. Finally, a set of r00ri ¼ r00ta is obtained. In order to obtain real rta , linear interpolation can be carried out graphically (Fig. 9.53). In Fig. 9.53, rri is the real boundary condition, and rta is the corresponding real solution. In this way, the correct MN line can be obtained by using boundary conditions rri and rta which is just obtained. Repeat the above drawing process, and the stress of the whole turbine disk can be solved.

Fig. 9.53 Linear interpolation graphic method

One soluƟon

Two soluƟon

9.5 Starting Characteristics of Electronic and Hydraulic Power Unit

9.5

151

Starting Characteristics of Electronic and Hydraulic Power Unit

This section analyzes the dynamic characteristics of the electronic and hydraulic power unit (EHPU), i.e., starting characteristics, establishes a theoretical model describing the starting characteristics of EHPU, analyzes the main parameters affecting the starting characteristics, and combines simulation and experiment to describe effective measures to improve the starting characteristics of EHPU, so as to achieve the reliable launching and performance indicators of the whole missile. EHPU is an important core component of missile electro-hydraulic energy system. It provides hydraulic power for missile-mounted hydraulic system and power for all kinds of electrical equipment of missile. EHPU is mainly composed of gas generator, gas pressure regulating valve, gas turbine, generator, hydraulic pump, and so on. When EHPU works, the electric ignition tube of gas generator ignites under the action of DC voltage, ignites ignition components, delay grain, and main grain, produces high-temperature and high-pressure gas with a certain peak pressure, promotes gas turbine to rotate at a high speed, drives generator and hydraulic pump to start rapidly after deceleration, and quickly builds hydraulic pressure in a short time and makes motor frequency meet the starting requirements. After a certain delay time, the gas regulator valve is connected, and the pressure of the gas generator is adjusted by the gas regulator valve to the set working pressure. The gas generator works steadily under this pressure and drives the gas turbine to run. After the gearbox decelerates, it drives the generator and the hydraulic pump to work, and outputs the power supply and the hydraulic source.

9.5.1

Description of EHPU Starting Characteristic

EHPU should meet the requirements of steady-state performance indicators, that is, to output a certain amount of pressure, flow, and voltage, and also to meet the requirements of starting characteristics. The starting characteristics of EHPU required by the whole missile are as follows: (1) Establishment time of hydraulic pressure tp 0:5 s; (2) Start-up time of power supply tp 0:75 s. The starting characteristics of electronic and hydraulic power unit, i.e., the relationship between gas pressure and power frequency and starting time, are shown in Fig. 9.54. Starting characteristic index is determined by the control condition of the whole missile. It is related to whether the whole missile can be launched normally, and it is also an important criterion to test whether the whole missile system and its parameters are normal. In the development of EHPU, starting characteristics have always been an important part of EHPU research. In order to meet the requirements

9 High-Temperature and High-Speed Gas Turbine Pump …

152 Fig. 9.54 Starting characteristics of electronic and hydraulic power unit (gas pressure and power frequency versus starting time)

of starting characteristics, it is necessary to consider the influence of various factors in the system design, and have corresponding special requirements for each component of EHPU. There are many difficulties involved. The theoretical modeling and parameter matching of the system are difficult to some extent. In the process of tackling this difficult problem, tackling key problems and phased experiments have been experienced many times in order to finally meet the requirements of starting characteristics.

9.5.2

EHPU Theoretical Modeling

EHPU gas generator, as a primary energy source, drives the turbine to rotate and drives the generator and hydraulic pump to work. The gas flow through the nozzle of the gas generator can be expressed as follows vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi " 2   2 #ffi u u k pa k pa k þ 1 pb Ub Gq ¼ Cd F t2g  k1 pb pb where Gq pb Cd pa F Ub g k

Gas flow rate; Import pressure; Flow coefficient; Export pressure; Flow area of gas generator nozzle; Specific gravity of imported gas; Gravity acceleration; Adiabatic index.

ð9:60Þ

9.5 Starting Characteristics of Electronic and Hydraulic Power Unit

153

The output power of gas turbine is N ¼ gGq Lmg

ð9:61Þ

where N Turbine output power; g Turbine efficiency; Lmg Gas adiabatic work. Steady output power of the turbine can be obtained by Eqs. (9.60) and (9.61), which are proportional to the gas pressure. The output power of gas turbine is consumed on generator and hydraulic pump. The output power of generator is Nn ¼

pffiffiffi 3ðI1 V1 þ I2 V2 Þ cos /

ð9:62Þ

where I1 ; I2 Winding current (A); V1 ; V2 Winding voltage (V). The power consumed by the generator accounts for a small proportion of the total output power of the EHPU. The output power of the hydraulic pump is NP ¼ PQ=612

ð9:63Þ

where P Pump output pressure (kgf=cm2 ); Q Pump output flow (L=min). The output power of hydraulic pump is consumed in relief valve and steering system, which accounts for the majority of the total output power of EHPU. When the gas generator drives EHPU to run, it accelerates gradually from static state to running state. In this process, inertia load of turbine disk, gear, generator, and hydraulic pump should be overcome, and load moment should also be overcome. Therefore, in the process of starting, the starting power of gas generator must be increased to produce peak power, that is, starting driving power. N0 ¼ NA þ N where N0 Start drive power; NA Additional power; N Steady-state power.

ð9:64Þ

9 High-Temperature and High-Speed Gas Turbine Pump …

154 Fig. 9.55 Starting power curve of gas generator


 N0 ¼ N0 pg ; tp ; tr ¼ KN

ð9:65Þ

where K Additional power coefficient; pg Gas peak pressure; N Steady-state power. Starting power curve of gas generator, i.e., the relationship between output gas power and starting time during starting process of gas generator, is shown in Fig. 9.55. Assuming the fitting model of starting power curve is N00 ¼ k 0 ekt þ M

ð9:66Þ

where k0 Fitting coefficient; M Adjustment of parameters. The starting power curve fitting model of Eq. (9.66) can be used to simulate the corresponding parameters through the measured curve. Then starting power and related starting characteristic parameters are determined by Eq. (9.65).

9.5.3

Starting Characteristics of Hydraulic System

Hydraulic pressure setup time tp of EHPU starting characteristic is an important index for normal operation of hydraulic system of missile control system. By

9.5 Starting Characteristics of Electronic and Hydraulic Power Unit

155

detecting the time of hydraulic pressure setup as a return signal, this important criterion is one of missile launch and control conditions. The establishment of hydraulic pressure cannot be achieved by only improving the starting power of gas generator. Hydraulic pressure is ultimately determined by the load, so the rapid establishment of hydraulic pressure is to take measures on the hydraulic load. A loading valve is used in EHPU system, which is directly connected to the outlet of hydraulic pump. The function of loading valve is mainly embodied in the starting section of EHPU. When EHPU starts, the oil is fed into the oil inlet end of loading valve. When the oil inlet pressure is lower than the set spring force, the guide rod cannot drive the large valve core to move to the right. At this time, the oil inlet and return routes are not fully connected. Oil enters the return routes through the valve sleeve and the large spool, through the orifice throttling of the small spool, and through the flow groove between the valve sleeve and the shell. Therefore, when starting, the oil resistance is very large, which makes the valve inlet pressure established quickly. When the pressure at the inlet end rises, the small spool is attached to the left cap under the action of pressure, and the guide rod assembly drives the large spool to move to the right under the action of pressure difference at both ends. When the big spool moves to a certain distance, the valve opens, the intake and return oil routes are fully connected, the resistance of the oil routes decreases, the flow rate increases, the loading valve reaches a certain pressure at this time, and the flow rate reaches the rated value. The characteristic curve of the loading valve is shown in Fig. 9.56. Curve p1 is pressure–flow characteristic curve p1  Q before loading valve, curve p2 is pressure–flow characteristic curve after loading valve, curve p3 is flow characteristic curve of pressure difference ðp1  p2 Þ, and Q before and after loading valve. The working characteristic of the loading valve in the system is the differential pressure–flow characteristic shown in curve p3 . From the curve, when EHPU starts, the pressure difference before and after loading valve is larger, the pressure before loading valve is larger than that after loading valve, and the corresponding flow rate

Fig. 9.56 Characteristic curve of loading valve

156

9 High-Temperature and High-Speed Gas Turbine Pump …

is smaller. After the system pressure is established, the pressure difference before and after the loading valve decreases gradually, the flow rate increases rapidly, and the resistance decreases. At this time, the pressure building process of the starting section is completed.

9.5.4

Starting Characteristics of Power Supply System

The starting time tr of power supply system is based on the time when the motor frequency reaches a certain value, and the motor frequency can also be regarded as the EHPU rotation speed, that is to say, to improve the starting speed of the starting section, so that the system can accelerate the starting and achieve a higher speed in a short time. Therefore, the performance index of the starting section of gas generator is particularly important, which is related to the starting power and directly affects the starting characteristics of the system.

9.5.4.1

Effect of Gas Peak Pressure on Starting Characteristics

The speed of EHPU starting section is related to inertia J and load Z of EHPU itself, as well as peak pressure of gas generator starting section. It can be described as nðtÞ ¼ f ðpmax ; J; Z Þ

ð9:67Þ

As shown in Fig. 9.57, increasing peak pressure of gas generator, i.e., increasing starting power, gas pressure at different peak pressures of 1, 2, 3, 4, and starting characteristic relationship between motor frequency and time change process are shown in Fig. 9.57. From the figure, it can be seen that increasing peak gas pressure is effective for accelerating the start of the system, and the effect is remarkable, which has been verified in many key experiments. However, in the EHPU system, the peak gas pressure cannot be raised too high. On the one hand, it is limited by the structural strength, and on the other hand, the frequency of the motor is also limited to a certain extent, the voltage cannot be too high, otherwise the power supply system is unstable. Therefore, the selection of peak gas pressure should be within an appropriate range.

9.5.4.2

Effect of Pressure Impulse on Starting Characteristics

Starting characteristic requirement of power supply system refers to a certain frequency and voltage requirement within a certain period of time, that is, the starting and accelerating accumulative time of EHPU. For the pressure of gas generator, it is the accumulation of pressure impulse, as shown in Fig. 9.58.

9.5 Starting Characteristics of Electronic and Hydraulic Power Unit

157

Fig. 9.57 Characteristic relationship between peak gas pressure, motor frequency, and starting time

Fig. 9.58 Relationship between pressure impulse and starting time

t1 Z

F ¼ pdt

ð9:68Þ

t2

where F p

Pressure impulse (Pa  s); Gas pressure (Pa).

As shown in Fig. 9.59, the influence of different pressure impulses F1 , F2 , F3 , F4 on starting characteristics is discussed. As can be seen from the graph, in the case of comparing the pressure impulse, the pressure impulse is large, the starting time is fast, the pressure impulse is small, and the starting time is long. At this time, the peak pressure is not the main factor, but an adjustment factor. A delay tube is installed on the generator to maintain a certain pressure time and accumulate pressure impulse through the isolated combustion of the delay grain, so as to achieve the purpose of fast starting.

9 High-Temperature and High-Speed Gas Turbine Pump …

158 Fig. 9.59 Effect of different pressure impulse on starting characteristics

9.5.4.3

Effect of High and Low-Temperature Performance on Starting Characteristics

Usually, EHPU is required to work normally at high temperature ( þ 62  C) and low temperature (40  C). That is to say, the starting characteristics under high and low temperature conditions should also meet the requirements. The influence of high and low temperature on starting characteristics is mainly reflected in the gas generator and hydraulic oil. The ignition components and main grain of the gas generator are affected by temperature, and the burning rate changes greatly, which makes the gas pressure change greatly. See the following: a ¼ a0 erp ðTT0 Þ

ð9:69Þ

where a a0 T0 rp

Burning rate; Standard burning rate; Standard temperature; Temperature sensitivity coefficient.

At low temperature, the viscosity and resistance of hydraulic oil increase, which aggravates the starting load and affects the starting characteristics. The starting characteristics of EHPU under high and low temperatures are shown in Fig. 9.60. It can be seen that the starting characteristics of EHPU under high and low temperatures are quite different. Curve 1 starts slowest at low temperature, so the system design considerations must meet the severe operating conditions under low temperature.

9.5 Starting Characteristics of Electronic and Hydraulic Power Unit

159

Fig. 9.60 Starting characteristics of EHPU at high and low temperatures. 1—Low temperature; 2—high temperature

9.5.4.4

Main Ways to Improve Starting Characteristic of Power Supply System

According to the above analysis and test verification, the main way to improve the starting characteristics of power supply system is to match reasonably the pressure characteristics of the starting section of the gas generator. The gas pressure in the starting section of the gas generator consists of the following parts: pq ¼ py þ ps þ pz

ð9:70Þ

where pq py ps pz

Start-up pressure; Ignition component pressure; Delay pipe pressure; Main grain pressure.

When the pressure choosing and matching designing of the three parts of the starting section of gas generator, the factors such as burning rate change, pressure matching and delay time under high and low temperature conditions should be taken into account so as to make the comprehensive gas pressure of the three parts meet the requirements of starting characteristics.

Bibliography 1. Lai Y (1989) Several problems in the development of electro-hydraulic servo technology. Autoplot Infrared Technol 4:1–7 2. Shu Z (1992) Overview of design method of air defense missile control execution system. Autoplot Infrared Technol 4:1–13

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3. Yin Y,Chen Z (1995) Power matching design of hydraulic steering gear system. Autoplot Infrared Technol 80:37–41 4. Shu Z (1995) Discussion on auxiliary energy scheme of air defense missile. Autoplot Infrared Technol 1:25–36 5. Zhu M (1992) Review and prospect of electro-hydraulic control technology. Autoplot Infrared Technol 2:37–41 6. Zhu M (2000) Overview of elastic o-ring sealing technology. Autoplot Infrared Technol 4:35–40 7. Shu Z (1991) Application analysis of gas turbo pump hydraulic energy in tactical air defense missile. Autoplot Infrared Technol 1:18–22 8. Yin Y,Yu C,Lu T, Others (2006) Research on air chamber pressure characteristics of aerocraft hydraulic control system. Autoplot Infrared Technol 2:8–12 9. Yin Y,Zhang L,Fu J (2011) The utility model relates to a high pressure pneumatic pressure reducing valve, 201110011195, 11 May 2011 10. Yin Y (1996) Study on the influence of overflow valve working point on the frequency characteristics of missile electro-hydraulic energy system. Autoplot Infrared Technol 82: 38–43 11. Yin Y (1995) Mechanism and characteristic analysis of single - stage overflow valve with balanced piston. Shanghai Aerosp 12(3):14–17 12. Yin Y,Zhao Y (2009) Overflow valve with liquid resistance and liquid capacity feedback, 200910121621.4, 12 June 2009 13. Kirillov MN (1982) Principle of turbine machinery. China Machine Press, Beijing 14. Shen W,Zhen P (1983) Engineering mechanics. Higher Education Press, Beijing 15. Traupel W (1985) Thermal turbine. Water Resources and Electric Power Press, Beijing 16. Thomas HJ (1984) Thermische kraf tanlagen. Springer-Verlager, Berlin 17. Xujier DK (1973) Liquid propellant rocket engine design. National Defense Industry Press, Beijing 18. Kirilov HH (1959) Gas turbine and gas turbine installations. China Machine Press, Beijing 19. Wu H (1982) Structure and strength calculation of turbine parts. China Machine Press, Beijing 20. Song J (1991) Exploration on improving the efficiency of small gas turbine used in missile hydraulic system. Autoplot Infrared Technol 1:23–36 21. Shu Z (1996) Discussion on the relationship between gas pressure and nozzle characteristic parameter function—technical analysis and application of gas design. Autoplot Infrared Technol 3:39–46 22. Gao Z, Song J (1993) Analysis of gas-turbine driven electro-hydraulic energy combination system. Shanghai Aerosp 1:5–8 23. Gan K (1998) EHPU starting characteristic analysis and experimental research. Autoplot Infrared Technol 4:3–27 24. Gao Z (1992) Starting characteristic analysis of hydraulic pump energy combination of gas turbine motor. Autoplot Infrared Technol 2:21–24 25. Yin Y (2012) Electro-hydraulic servo control theory and application technology in extreme environment. Shanghai science and technology press, Shanghai 26. Yin Y (2008) Research on key basic theory of aerocraft steering gear system. Shanghai pujiang talent plan (class A) summary report (06PJ14092), 30 Sept 2008 27. Yin Y (2009) Research on integrated design of ultra-high pressure pressure-reducing valve assembly in fuel cell vehicle. Shanghai magnolia technology talent fund summary report (2018B110), 28 May 2009 28. Li J, Yin Y (2009) Research on temperature control and pulsation technology of hydraulic system—research on temperature control technology. Technical summary report of tongji university large passenger aerocraft project (Develop) (No.TJME-09-290), 22 Dec 2009 29. Yin Y (2010) Above 45 MPa research on hydrogen supercharging pressure control and regulation technology. Subject acceptance report of national high-tech research and development plan (National 863 Program) (2017AA05Z119), 30 June 2010

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30. Yin Y, Hu D, Chen Z (1993) Project missile hydraulic energy system project demonstration report. Shanghai space administration 803 research institute, 3 31. Song J (1994) Thermodynamic processes in small gas turbine nozzles used in missiles. Autoplot Infrared Technol 1:20–22 32. Song J (1994) The influence of the change of back pressure caused by flight altitude on the exit velocity and angle of the nozzle of the gas turbine used in the projectile. Autoplot Infrared Technol 4:20–22

Chapter 10

Application of Aerodynamic Technology in Attitude Control of Aerocraft

Since the emergence of aircraft attitude control technology in 1952, it has been common to use jet reaction force for attitude control of airplane or satellite, but it is rare to use jet reaction force for missile aircraft. Attitude control of missile vehicle includes attitude stabilization and attitude maneuver, which can realize pitch, yaw, and roll of missile vehicle. The former is to maintain the existing attitude, while the latter is to redirect the missile from one attitude to another. At present, the attitude control of aircraft mostly adopts aerodynamic control and thrust vector control. The former is based on the principle of relativity of motion and the basic law of gas flow, using rudder surface and air resistance to control flight direction. Its control is related to flight speed, flight altitude, and the shape of the aircraft. The flight altitude of the aircraft is limited in the atmosphere, and it is difficult to satisfy the attitude control under the condition of low speed and low dynamic pressure. The latter controls the flight of aircraft by deflecting the nozzle, changing the direction of exhaust gas from engine, and realizes the attitude control by utilizing thrust generated by engine. However, the design of this type of attitude control structure is complex, and the sealing requirements for the rotating or swinging parts of the nozzle are high. In this chapter, the attitude control method of aircraft using jet lateral force is introduced, including the structure of aerodynamic system, control method, aircraft direction control scheme, and key technology. The thermodynamic and dynamic models of Laval nozzle are emphatically established, and the distributions of velocity field, pressure field, and temperature field inside Laval nozzle are analyzed, which can be used as theoretical basis for nozzle structure design and process design.

© Springer Nature Singapore Pte Ltd. and Shanghai Scientific and Technical Publishers 2020 Y. Yin, High Speed Pneumatic Theory and Technology Volume II, https://doi.org/10.1007/978-981-15-2202-4_10

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164

10.1

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Application of Aerodynamic Technology in Attitude Control …

Aerodynamic Attitude Control Principle and Attitude Control Method of Aircraft

Aiming at the complex and difficult structure of hydraulic, electric, and gas steering gears for conventional attitude control of aircraft, a new attitude control method using jet reaction force of aircraft is proposed. The flight control device based on this method is portable, basically not limited by flight altitude, and its structure is simple and easy to realize. Nitrogen is stored at high pressure and injected at supersonic speed through Laval nozzle after decompression. The reaction force between nitrogen and ambient atmosphere is formed to control the attitude of the aircraft. When eight nozzles are arranged circumferentially, different combinations of forces are formed when different nozzles are opened, and 64 possible lateral forces of control attitude can be obtained. A series of experiments and comparative analysis are carried out for the lateral force of attitude control. The theoretical results are basically consistent with the experimental results, and the validity of the method is verified. With the same nozzle and gas source, the lateral force provided by each nozzle is the same, which can be extended to nozzles with different parameters, and the lateral force provided by each nozzle is different. The proposed analysis method and results can be used as a reference for the demonstration of aircraft attitude control.

10.1.1 New Method and Principle of Attitude Control of Aircraft Figure 10.1a is the schematic diagram of attitude control method for single jet reaction force, and Fig. 10.1b, c are the schematic diagram of two parallel jet reaction force control devices. Eight nozzle reaction force control devices are connected in parallel on the same high-pressure cylinder. Each nozzle can work intermittently according to the need. The solenoid valve controls the nozzle switch and obtains different combinations of nozzle reaction force to realize the pitch, yaw, and roll attitude control of the aircraft. As shown in Fig. 10.1b, the attitude control device of the aircraft consists of eight parallel devices, which distribute circumferentially on the missile body of the aircraft. The reaction force provided acts on the radial direction of the aircraft and can directly control the pitch and yaw of the aircraft. When the distribution of nozzles deviates from a certain radial angle, as shown in Fig. 10.1c, the reaction force provided generates a torque on the centroid of the aircraft. When multiple nozzles work together, the roll of the aircraft can be controlled. As shown in Fig. 10.1a, the working principle of a single jet reaction force control device is as follows: The high-pressure gas is stored in the cylinder. Under the action of given current, the explosive tube explodes, the valve of the

10.1

Aerodynamic Attitude Control Principle and Attitude …

165

(a)

Laval nozzle

(b)

Out

(c)

Fig. 10.1 Schematic diagram of aircraft attitude control method using jet reaction force. a Pneumatic system diagram of single nozzle lateral force generator; b nozzle layout diagram of pitch and yaw aircraft; c nozzle layout diagram of rolling aircraft. 1—High-pressure cylinder; 2—electric explosion tube; 3—solenoid valve; 4—pressure relief valve; 5—Laval nozzle; 6* 13—parallel jet reaction attitude control device

explosive tube opens, the gas is supplied by the cylinder controlled by the solenoid valve, and the high-pressure gas is decompressed by the decompression valve and transported to the Laval nozzle, which accelerates the gas from subsonic velocity to supersonic velocity, thus forming a huge reaction force. The resultant force is the force needed for attitude control. Because the lateral force is directly controlled by the solenoid valve, the actual use of such systems is not limited by the flight height of the aircraft.

166

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Application of Aerodynamic Technology in Attitude Control …

10.1.2 Lateral Force Analysis of Attitude Control Eight jet reaction force control devices are distributed radially in parallel on missile aircraft. When different nozzles are opened, the magnitude and direction of the resultant force are different. Combining with Fig. 10.1b, the direction of nozzle No. 6 is taken as 0
direction, and the number and direction of nozzles opened by solenoid valve are different, and different lateral forces will be obtained. As shown in Fig. 10.2, for the thrust synthesis diagram of each nozzle, the direction of nozzle No. 6 is defined as x direction and that of nozzle No. 8 is defined as y direction. The lateral force of each nozzle is decomposed into x and y directions, and the resultant force in x direction is Fx and in y direction is Fy : Fx ¼ n10 F10 þ n9 F9 cos 45
þ n11 F11 cos 45
 n6 F6  n7 F7 cos 45
 n13 F13 cos 45
Fy ¼ n12 F12 þ n11 F11 cos 45
þ n13 F13 cos 45
 n8 F8  n7 F7 cos 45
 n9 F9 cos 45
where F6  F13 Lateral force provided by each single nozzle when nozzle 6*nozzle 13 is opened; n6  n13 Switching coefficients of lateral forces provided by individual nozzles of nozzle 6*nozzle 13. The value is 1 when opening and 0 when closing. With the same nozzle and gas source, the lateral force provided by each nozzle is the same, and the magnitude of force from F6 to F13 is F. It can be extended to

Fig. 10.2 Schematic diagram of thrust synthesis of nozzles

10.1

Aerodynamic Attitude Control Principle and Attitude …

167

nozzles with different parameters, and the lateral force provided by each nozzle is different. Then the magnitude and direction of resultant force FR are, respectively, FR ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Fx2 þ Fy2

h ¼ arctan

Fy Fx

ð10:1Þ ð10:2Þ

where h Angle direction of resultant force FR . According to the flight requirements of the aircraft, different solenoid valves are opened in different time periods, and different lateral force combinations are obtained to realize the pitch and yaw attitude control of the aircraft. Table 10.1 lists 64 kinds of lateral force conditions for attitude control when eight nozzles are arranged circumferentially, and the lateral force provided by each nozzle is the same. When a nozzle is opened, there are eight lateral forces of the same size but different directions (Fig. 10.3). When two adjacent nozzles are opened at the same time, there are eight lateral forces of the same size but different directions. If nozzles 6 and 7 are opened at the same time, the lateral force of pffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffi 157:5
direction and resultant force of 2 þ 2F will be obtained, as shown in Fig. 10.4a. When two nozzles spaced by one nozzle are opened at the same time, there are eight lateral forces of the same magnitude but different directions. If nozzles 6 and 8 are opened at the same time, the lateral forces of 135
direction pffiffiffi and 2F resultant force will be obtained, as shown in Fig. 10.5a. When two nozzles with two spacing nozzles are opened at the same time, there are eight lateral forces of the same magnitude but different directions. If nozzles 6 and 9 are opened at the same time, the lateral forces of 112:5
direction and resultant force of pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffi 2  2F will be obtained, as shown in Fig. 10.6a. When two nozzles with three spacing nozzles are opened, such as nozzles 6 and 10, the lateral forces produced by the two nozzles cancel each other, and the resultant force is 0. Therefore, when two nozzles are opened, there are 24 different lateral forces. Similarly, when three nozzles are opened simultaneously, there are 24 different lateral forces (Figs. 10.7, 10.8, and 10.9). When four nozzles are opened at the same time, there are eight different lateral forces (Fig. 10.10). There are 64 possible lateral force conditions for attitude control. According to the flight requirements of the aircraft, different solenoid valves are opened in different time periods, and different lateral force combinations are obtained to realize the pitch and yaw attitude control of the aircraft.

168

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Application of Aerodynamic Technology in Attitude Control …

Table 10.1 64 kinds of possible lateral forces for attitude control Number of working nozzles

Lateral force magnitude

Lateral force direction

Serial number of nozzles opened

Figure

1

F

2

pffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffi 2 þ 2F

180° −135° −90° −45° 0° 45° 90° 135° −157.5° −112.5° −67.5° −22.5° 22.5° 67.5° 112.5° 157.5° −135° −90° −45° 0° 45° 90° 135° 180° −112.5° −67.5° −22.5° 22.5° 67.5° 112.5° 157.5° −157.5°

6 7 8 9 10 11 12 13 6, 7 7, 8 8, 9 9, 10 10, 11 11, 12 12, 13 13, 6 6, 8 7, 9 8, 10 9, 11 10, 12 11, 13 12, 6 13, 7 6, 9 7, 10 8, 11 9, 12 10, 13 11, 6 12, 7 13, 8

Fig. 10.3a Fig. 10.3b Fig. 10.3c Fig. 10.3d Fig. 10.3e Fig. 10.3f Fig. 10.3g Fig. 10.3h Fig. 10.4a Fig. 10.4b Fig. 10.4c Fig. 10.4d Fig. 10.4e Fig. 10.4f Fig. 10.4g Fig. 10.4h Fig. 10.5a Fig. 10.5b Fig. 10.5c Fig. 10.5d Fig. 10.5e Fig. 10.5f Fig. 10.5g Fig. 10.5h Fig. 10.6a Fig. 10.6b Fig. 10.6c Fig. 10.6d Fig. 10.6e Fig. 10.6f Fig. 10.6g Fig. 10.6h (continued)

pffiffiffi 2F

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffi 2  2F

10.1

Aerodynamic Attitude Control Principle and Attitude …

169

Table 10.1 (continued) Number of working nozzles 3

Lateral force magnitude pffiffiffi ð1 þ 2Þ F

pffiffiffi 3F

pffiffiffi 3F

4

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffi 4 þ 2 2F

Lateral force direction

Serial number of nozzles opened

Figure

−135° −90° −45° 0° 45° 90° 135° 180° −125.3° −80.3° 35.3° 9.7° 54.7° 99.7° 144.7° −170.3° −99.7° −54.7° −9.7° 35.3° 80.3° 125.3° 170.3° −144.7° −122.5° −67.5° −22.5° 22.5° 67.5° 122.5° 157.5° −157.5°

6, 7, 8 7, 8, 9 8, 9, 10 9, 10, 11 10, 11, 12 11, 12, 13 12, 13, 6 13, 6, 7 6, 7, 9 7, 8, 10 8, 9, 11 9, 10, 12 10, 11, 13 11, 12, 6 12, 13, 7 13, 6, 8 6, 8, 9 7, 9, 10 8, 10, 11 9, 11, 12 10, 12, 13 11, 13, 6 12, 6, 7 13, 6, 7 6, 7, 8, 9 7, 8, 9, 10 8, 9, 10, 11 9, 10, 11, 12 10, 11, 12, 13 11, 12, 13, 6 12, 13, 6, 7 13, 6, 7, 8

Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig.

10.7a 10.7b 10.7c 10.7d 10.7e 10.7f 10.7g 10.7h 10.8a 10.8b 10.8c 10.8d 10.8e 10.8f 10.8g 10.8h 10.9a 10.9b 10.9c 10.9d 10.9e 10.9f 10.9g 10.9h 10.10a 10.10b 10.10c 10.10d 10.10e 10.10f 10.10g 10.10h

10.1.3 Experiments and Analysis 10.1.3.1

Design Scheme

Aiming at the overall requirement of lateral force control device proposed by whole system for the control cabin, the current control cabin adopts the gas scheme. After ignition by the gas generator, the lateral thrust is generated by the high-temperature

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Application of Aerodynamic Technology in Attitude Control …

Fig. 10.3 Schematic diagram of lateral force operation I (opening one nozzle)

Fig. 10.4 Schematic diagram of lateral force operation II (opening two nozzles; resultant force pffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffi magnitude 2 þ 2F)

and high-pressure gas injection produced by high-energy propellant. However, the high temperature of gas, large gas particles and impurities are the shortcomings, which can easily affect the operation of the steering gear, and the high temperature generated by gas may affect the work of other components in the control cabin. In view of the shortcomings of the gas scheme of the lateral power plant, considering the high cleanliness of the high-pressure cold air and the ability to detect the performance before and after installation and adjustment, the high-pressure cold air cylinder is used to replace the gas generator, which is installed in the control cabin

10.1

Aerodynamic Attitude Control Principle and Attitude …

171

Fig. 10.5 Schematic diagram of lateral force operation III (opening two nozzles; resultant force pffiffiffi magnitude 2F)

Fig. 10.6 Schematic diagram of lateral force operation IV (opening two nozzles; resultant force pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffi magnitude 2  2F)

where the gas generator is installed. High-pressure cold gas injection method is used to generate lateral force. The lateral force control device of a certain type of aircraft requires thrust F ¼ 5  8 N, working time t ¼ 0:5 s, using straight tube injection (non-Laval tube). Figure 10.11 shows the principle of thrust experiment. The high-pressure air source passes through the pressure reducing valve and enters the experimental chamber to eject the cold air. The air source is supplied by the ground cylinder. The experimental cabin is connected with the ground cylinder by connecting pipes, adapters,

172

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Application of Aerodynamic Technology in Attitude Control …

Fig. 10.7 Schematic diagram of lateral force operation V (opening three nozzles; resultant force pffiffiffi  magnitude 1 þ 2 F)

Fig. 10.8 Schematic diagram of lateral force operation VI (opening three nozzles; resultant force pffiffiffi magnitude 3F)

pressure relief valves, and so on. The throttle orifice plate is installed in the connecting joint of the experimental cabin. High-pressure cold air enters the reversing valve through the pipeline, transfer tooling, and intake pipe, and sprays the cold air through the outlet pipe. The experimental cabin is installed on the horizontal slide platform and connected with the thrust sensor through the tooling. The thrust generated by the ejected cooling gas is transmitted to the thrust sensor through the reaction force. The signal amplifier amplifies the signal of the thrust sensor and outputs it to the data acquisition computer for acquisition and monitoring.

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Aerodynamic Attitude Control Principle and Attitude …

173

Fig. 10.9 Schematic diagram of lateral force operation VII (opening three nozzles; resultant force pffiffiffi magnitude 3F)

Fig. 10.10 Schematic diagram of lateral force operation VIII (opening four nozzles; resultant pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffi force magnitude 4 þ 2 2F)

10.1.3.2

Experimental Results and Analysis of Thrust

(1) Thrust Experiment Without Orifice The high-pressure gas source is directly ejected through the relief valve and nozzle, and the thrust fluctuates greatly. The change of air pressure or load flow in the relief valve will make the displacement of the relief valve core change dynamically, which will cause the output pressure of the relief valve to change dynamically and

174

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Application of Aerodynamic Technology in Attitude Control …

Pressure gauge 1 Pressure gauge 2 Pressure relief High pressure valve gas source Experimental cabin Thrust Sensor Signal amplifier Data Acquisition Computer Fig. 10.11 Schematic diagram of thrust experimental

fluctuate. Moreover, because no throttling measures are taken and the gas consumption is large, the pressure relief valve will be in an overshoot state and cannot regulate the pressure normally. Therefore, throttling measures should be taken to stabilize the working pressure. (2) Thrust Experiment With Orifice According to the thrust requirement of the lateral force device of the aircraft, the ventilation pressure is about 6:5 MPa and the size of the throttle orifice is /1:15  /1:2 mm. The thrust experimental data are shown in Table 10.2. The results show that when the throttle orifice is /1:15  /1:2 mm and the working pressure is not less than 6:5 MPa, the thrust generated meets the thrust requirements of the lateral force device. Comparing the measured value with the theoretical value, see Table 10.3. The thrust measured by experiment is less than that by theoretical calculation, which is caused by pressure loss, flow loss, and velocity loss in pipeline. It shows that the experimental results are in good agreement with the theoretical analysis. Table 10.2 Thrust experimental data of different throttle orifices Throttle orifice size/mm

Working pressure/MPa

Thrust data/N

Throttle orifice size/mm

Working pressure/MPa

Thrust data/N

/1:1 /1:15

6.6 6.6

4.5 4.8

/1:2 /1:25

6.6 6.4

5 5.6

Table 10.3 Comparison of measured and theoretical values Throttle orifice size/mm

Working pressure/ MPa

Computational thrust/N

Experimental thrust/N

/1:15

6.6

6.94

4.8

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Aerodynamic Attitude Control Principle and Attitude …

175

10.1.4 Conclusions A new attitude control method based on jet reaction force is presented. The lateral force is generated by eight circumferentially distributed nozzles. The main conclusions are as follows: (1) The attitude control method of the aircraft is composed of eight parallel devices, which distribute circumferentially on the missile body of the aircraft and provide the reaction force acting on the radial direction of the aircraft. When the distribution of Laval nozzles deviates from the radial direction and two or more Laval nozzles cooperate, the roll of the aircraft can be controlled. (2) Eight nozzle jet reaction force control devices are connected in parallel on the same high-pressure cylinder. Each nozzle can work intermittently according to the need, and the solenoid valve controls the nozzle switch to obtain different reaction force combinations, so as to realize the pitch, yaw, and roll attitude control of the aircraft. Since the lateral force is directly controlled by solenoid valves, the actual use of such systems is not limited by the flight altitude of aircraft. (3) The calculation method of resultant force when different nozzles are opened is analyzed, and 64 possible lateral forces of attitude control are obtained. With the same nozzle and gas source, the lateral force provided by each nozzle is the same, which can be extended to nozzles with different parameters, and the lateral force provided by each nozzle is different.

10.2

Laval Nozzle for Attitude Control of Aircraft

Aiming at the complex and difficult structure of conventional hydraulic steering engine, electric steering engine, and gas steering engine of aircraft, the thermodynamic and dynamic model of Laval nozzle is established on the basis of a new attitude control method using jet reaction force. The distributions of velocity field, pressure field, and temperature field inside Laval nozzle are analyzed to provide theoretical basis for nozzle structure design and process design. The results show that the velocity of airflow in throat and initial expansion section changes rapidly, and the gas scours seriously on the wall. Anti-scour protective materials and technological treatment measures can be adopted in this part. The pressure on the wall of the nozzle in the contraction section is high, and the pressure on the throat and the wall of the initial expansion section varies sharply. The protective material with higher strength can be used. During the process of airflow passing through Laval nozzle, the temperature decreases continuously, but the wall temperature changes little. The temperature at the nozzle throat decreases rapidly and changes unevenly. It can be seen that the convergence section and throat of the nozzle pay

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attention to ablation protection treatment. The theoretical results in this part are in agreement with the experimental results. The results can be used as a theoretical basis for the structure and process design of Laval nozzle.

10.2.1 Flow Field Analysis of Laval Nozzle 10.2.1.1

Physical Model

Because the Laval nozzle is a circular section pipe, its three-dimensional flow can be simplified to two-dimensional axisymmetric flow. The double arc method is used to design the profile of axisymmetric nozzle. The design dimensions include the angle a between the straight line and the vertical line of the contraction section, the radius R1 of the small arc at the throat, the radius R2 of the large arc at the expansion section, the angle b between the common tangent of the large arc and the small arc and the horizontal line, the radius ri of the entrance section, the radius r  of the throat section, the radius re of the exit section, and the total length l of the nozzle.

10.2.1.2

Boundary Conditions for Throttle Ports

The gas flow through Laval nozzle accelerates from subsonic to supersonic, and the velocity increases gradually, while the pressure, temperature, and density decrease gradually. It is a compressible flow. The entrance boundary condition is set to the entrance pressure, and the total pressure and other scalar values of the entrance boundary are given at the entrance boundary. The pressure entrance boundary is suitable for compressible flow. The outlet boundary condition is set to the pressure outlet, and the static pressure of the flow outlet is specified. The density coupling algorithm for compressible flow is adopted, and the velocity component and density are taken as basic variables. The S-A one-equation turbulence model is chosen to simulate the flow with wall confinement.

10.2.1.3

Basic Equation of Fluid

Fluid flow obeys the laws of mass conservation, momentum conservation, and energy conservation. The flow of nozzle gas is in turbulent state, and the governing equation includes turbulent equation. (1) Mass Conservation Equation The increase of mass in a fluid element per unit time is equivalent to the net mass flowing into the element at the same time interval. The equation of mass conservation is

10.2

Laval Nozzle for Attitude Control of Aircraft

177

@q þ r  ðqvÞ ¼ 0 @t

ð10:3Þ

where q t v ∇

Gas density; Time; Velocity vector; Hamiltonian operator.

(2) Momentum Conservation Equation The change rate of fluid momentum to time in a microelement is equal to the sum of forces acting on the microelement by the outside, that is @ ðqvÞ þ r  ðqvvÞ ¼ r  p þ r  s þ qg þ F @t

ð10:4Þ

where p Static pressure on fluid microelement; g and F Gravitational volume force acting on the microelement and other external volume forces (such as magnetic force); s Viscous stress tensor acting on the surface of microelement due to molecular viscous action.

(3) Energy Conservation Equation The increment rate of the energy of the microelement is equal to the net heat flux into the microelement plus the work done by the volume force and the surface force on the microelement, that is @ ðqE Þ þ r  ½vðqE þ pÞ ¼ r  @t

keff rT 

X

! hj Jj þ seff v þ Sh

ð10:5Þ

j

where E keff hj Jj Sh

Unit control volume total energy, that is, the sum of internal energy and kinetic energy; Effective thermal conductivity; The enthalpy of component j; Diffusion flux of component j; Exothermic and endothermic caused by chemical reactions.

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The first three terms on the right side of Eq. (10.5) are energy transfer due to heat conduction, component diffusion, and viscous diffusion, respectively. For Laval nozzles, there are no chemical components and reactions. There is X

hj Jj ¼ 0; Sh ¼ 0

j

Equation (10.5) can be simplified as @ ðqEÞ þ r  ½vðqE þ pÞ ¼ r  ðkeff rT þ seff vÞ @t

ð10:6Þ

(4) Turbulence Control Equation During turbulent motion, the particles of fluid mix randomly with each other, and their velocity and pressure fluctuate randomly in space and time. The S-A one-equation turbulence model with wall restriction is used for the flow in Laval nozzle. Compared with the two-equation model, the model has less computation and better stability. The intermediate variable ~m is introduced to obtain the turbulent motion viscosity coefficient by solving the transport equation of the intermediate variable. "  2 # @ ðq~tÞ @ ðq~tui Þ 1 @ @~t @~t þ ¼ Gt þ ðu þ q~tÞ þ Cb2 q  Yt þ S~t ð10:7Þ @t @xi r~t @xj @xj @xj where ~m Turbulent motion viscosity; Gm Turbulence viscosity increase term; Ym Decrease of turbulent viscosity caused by wall barrier and viscous damping occurs in the near wall region; S~m User-defined source items. In the governing equation of fluid flow, the density and volume of compressible medium must take into account the effects of temperature and pressure, as well as the effects of medium viscosity on the flow. The equation of state of ideal gas is used to calculate the relationship among pressure, density, and temperature of gas. p ¼ RT q where p q T R

Absolute pressure of gas; Gas density; Thermodynamic temperature of gas; Gas constant.

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Laval Nozzle for Attitude Control of Aircraft

179

Gas temperature T represents the kinetic energy of molecular thermal motion. The viscous coefficient of a gas depends only on the temperature of the gas and has nothing to do with the pressure. The change relationship can be expressed in Sutherland’s form, i.e., l ¼ l0

 1:5   T T0 þ Ts T0 T þ Ts

where l l0 T0 Ts

Viscosity at temperature T ½kg=ðm  sÞ; Reference viscosity at reference temperature T0 ½kg=ðm  sÞ; Reference temperature, T0 ¼ 288:15 K; Sutherland constant, Ts ¼ 110:4 K.

10.2.1.4

Distribution Law of Flow Field

The density-based coupling algorithm is used to solve the problem. The residual of each calculation is set to 105 . The iteration is carried out in FLUENT. When the residual converges, the iteration is completed and the results are output. Suppose the inlet pressure of Laval nozzle is 11 MPa and the inlet velocity is 150 m=s. The physical dimensions of Laval nozzle are a ¼ 65
; R1 ¼ 4 mm; R2 ¼ 180 mm; b ¼ 17
; ri ¼ 6 mm; r  ¼ 4 mm; re ¼ 9:37 mm; l ¼ 28:1 mm: According to the above parameters and flow control equation, the pressure field, velocity field, and temperature field of the airflow in Laval nozzle can be calculated by CFD software. (1) Distribution of Velocity Field Figure 10.12 shows the velocity field distribution nephogram in Laval nozzle. Figure 10.13 shows the Mach number distribution in Laval nozzle. The two charts show that the velocity of the gas flow in the Laval nozzle varies continuously. Laval nozzle divides gas flow into three parts: convergence, throat, and expansion. The results of Mach number distribution show that the gas flow velocity at the entrance is small and the Mach number at the convergence stage is low, which is subsonic flow (M < 1). The Mach number of gas in the throat is about 1, which is a transonic flow. When the gas enters the expansion section, it will continue to accelerate due to the decrease of pressure and expansion of the gas. In the expansion section, the gas will flow at supersonic speed, M > 1. In Fig. 10.13, the Mach number contours of airflow in throat and initial expansion section are densely distributed, which indicates that the airflow velocity varies rapidly and the wall erosion is serious, so the protective materials should be selected carefully. In the boundary layer near the wall, due to the influence of viscous drag, the velocity of gas flow is very small, the velocity gradient of the boundary layer far from the wall is large, and the velocity varies sharply, and along the flow direction,

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Fig. 10.12 Distribution of velocity field inside Laval nozzle (m/s)

Fig. 10.13 Distribution of Mach number inside Laval nozzle (Mach number)

the boundary layer becomes thicker. Because of the gas viscosity, a layer of gas close to the wall is appressed to the wall, and its velocity is 0. Because of the friction between the gas layers, the slightly outer gas layer is restrained by the gas layer close to the wall with the velocity of 0. The velocity decreases to nearly 0, but there is still a velocity. The effect of friction and mutual restraint between gases is spreading out layer by layer. The closer the gas is to the wall, the greater the pulling effect is, the farther away it is from the wall, and the smaller the pulling effect is.

10.2

Laval Nozzle for Attitude Control of Aircraft

181

The essence of friction between layers of gases is caused by the irregular thermal motion of gaseous molecules, which causes the mass exchange of gases in different flow layers. The molecular momentum of two adjacent layers of gas varies with the different velocities of airflow in each layer. Mass exchange between adjacent layers brings momentum exchange. The thickness of the boundary layer is generally defined as the vertical distance from the mainstream velocity of 99% in the boundary layer to the wall. Because the main flow velocity in Laval nozzle is increasing, the boundary layer of Laval nozzle is getting thicker and thicker. (2) Distribution of Pressure Field Figure 10.14 shows the pressure field distribution nephogram in Laval nozzle. The pressure in Laval nozzle varies continuously with the flow of gas. In the whole nozzle, the pressure of gas decreases continuously. Like the velocity distribution, the Laval nozzle divides the gas flow into three parts: convergence, throat, and expansion. The average pressure at the inlet is set at 11 MPa, and the average pressure at the outlet decreases to 0:15 MPa when the air passes through the Laval nozzle. Figure 10.15 shows the pressure distribution on the wall of Laval nozzle along the axis direction. The gas in Laval nozzle passes through the contraction section and throat and enters the expansion section. Combining with Fig. 10.14, the pressure of the gas in the throat and the initial expansion section varies dramatically, i.e., at 3  7 mm in Fig. 10.15, the pressure in the expansion section varies relatively gently. The pressure of nozzle in contraction section is high, and the pressure in throat and initial expansion section varies sharply. The protective material with higher strength should be selected.

Fig. 10.14 Pressure distribution inside Laval nozzle

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Fig. 10.15 Wall pressure distribution of Laval nozzle along the axis

When the pressure at the exit section of the nozzle is exactly equal to the external backpressure, the gas expands completely in the nozzle, the nozzle is in the optimum expansion state, the nozzle throat reaches the critical state, and the outlet flow is supersonic. When the fluid flows out of the nozzle, it neither expands nor compresses, and it is a parallel jet. The flow velocity in the nozzle is supersonic. When there is a small disturbance in the external environment, the propagation velocity of the disturbance (sound velocity) is less than the flow velocity, and the disturbance cannot enter the nozzle. When the inlet pressure of nozzle is increased on the basis of the optimum expansion state, the outlet pressure of nozzle is also increased, which makes the outlet pressure stronger than the external backpressure. At this time, the gas is not fully expanded in the nozzle and its energy is not fully utilized. After the gas flows out of the nozzle, it will continue to expand until the pressure equals the external backpressure. At this time, the disturbance outside the nozzle cannot be conversely transmitted to the nozzle. Contrary to under expansion state, when the inlet pressure of nozzle is reduced on the basis of the optimal expansion state, the outlet pressure of nozzle decreases, which makes the outlet pressure less than the external backpressure. At this time, the excessive expansion of gas in the nozzle will produce shock wave at the nozzle outlet, which may affect the flow in the nozzle. In order to make the flow in nozzle free from external interference, pe  pa must be satisfied, which is the mechanical condition of nozzle design. As shown in Fig. 10.16, the pressure variation at nozzle axis under different inlet pressures is illustrated. The inlet pressure of 1 is 9:8 MPa, and the pressure decreases continuously in the nozzle and decreases to 0:13 MPa at the outlet. The inlet pressure of 2 is 6:1 MPa. At x ¼ 25:5 lm, the pressure decreases to 0:1 MPa. From here on, the flow in the nozzle will be disturbed by the external pressure. When the external pressure is 0, the pressure at the outlet of the nozzle can be reduced to 0:07 MPa. The inlet pressure of 3 is 2:8 MPa, and the pressure decreases to 0:1 MPa at x ¼ 23 lm. From here on, the flow in the nozzle will be disturbed by external pressure, and then the pressure in the nozzle will continue to decrease to zero.

Laval Nozzle for Attitude Control of Aircraft

183

Pressure p /MPa

10.2

Position x /mm Fig. 10.16 Pressure distribution at the nozzle center along the axis. 1—Inlet pressure 9:8 MPa; 2—inlet pressure 6:1 MPa; 3—inlet pressure 2:8 MPa

(3) Distribution of Temperature Field Figure 10.17 shows the temperature distribution in the Laval nozzle. The temperature of gas in Laval nozzle changes continuously when it flows, and the temperature of gas decreases continuously throughout the nozzle. The average temperature at the entrance is set to 600 K. The airflow passes through the Laval nozzle, and the average temperature at the exit decreases to 210 K. Figure 10.18 shows the temperature variation of Laval nozzle wall. The temperature at the entrance wall is 610 K. As the gas passes through the Laval nozzle,

Fig. 10.17 Temperature distribution map inside Laval nozzle (K)

Fig. 10.18 Temperature distribution map of Laval nozzle wall along axis

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Temperature T/K

184

Position x/mm

the temperature decreases. When it reaches the exit wall, its temperature is 558 K, and the temperature of the whole nozzle wall changes little. In the nozzle throat, the temperature drops rapidly and local uneven changes occur. When choosing nozzle material, the ablation protection of the convergence section of nozzle and throat should be considered emphatically.

10.2.2 Manufacturing Process Technology Based on a new attitude control method using jet reaction force, the Laval nozzle flow field distribution law is obtained when the inlet pressure is 11 MPa, the inlet velocity is 150 m=s and the inlet temperature is 600 K. (1) Laval nozzle divides gas flow into three parts, namely convergence, throat, and expansion. The gas flow in Laval nozzle is continuous and accelerates gradually, and the pressure and temperature decrease gradually. (2) The velocity field distribution in Laval nozzle designed by double arc method is reasonable. It can achieve continuous acceleration from 150 m/s at the inlet to 907 m/s at the outlet, and the velocity distribution at the outlet is uniform, with Mach number reaching 3.0. In the throat and initial expansion section, the airflow velocity changes rapidly and the wall erosion is serious. Therefore, attention should be paid to the selection of anti-erosion protective materials. (3) The pressure of nozzle wall in contraction section is high, and the pressure changes sharply in throat and initial expansion section. The protective material with higher strength should be selected. When the inlet pressure is lowered, the pressure of the gas in the nozzle decreases to the same or even smaller than the external pressure when it does not reach the outlet. At this time, the external pressure will interfere with the flow of the gas in the nozzle. (4) The airflow through the Laval nozzle decreases continuously, but the wall temperature changes little. At the throat of the nozzle, the temperature drops rapidly and local nonuniform changes appear. When choosing nozzle material, emphasis should be laid on the ablation protection of nozzle convergence section and throat.

10.3

10.3

Device for Changing Missile Motion Direction …

185

Device for Changing Missile Motion Direction by Using Gas Generator and Transverse Force of Nozzle

The main advantage of using gas generator and nozzle to generate transverse force is that the magnitude of transverse force is less dependent on the flight speed of missile. There are many types of transverse force generating devices. The system consists of the following main components: gas generator, gas nozzle, ball valve, and solenoid control elements. The position of the nozzle is located near the front end of the missile and distributed uniformly along the circumference. The number of nozzles is generally three to four or more. Figure 10.19 shows the first structure of the transverse force generator. The gas generated by the gas generator 5 in the figure pass through the ball valve 8 and is discharged by the nozzle 7, thus generating the transverse force. Here, three nozzles are evenly distributed around the circumference. Component 9 is a star-shaped linkage plate. It should have three arms relative to the number of nozzles. The center of the star-shaped linkage plate is supported on a spherical or hemispherical support, so it can tilt in all directions. Component 6 is the control cable, whose direction is consistent with the missile’s longitudinal axis. One end is connected with the corresponding arm of the star-shaped linkage plate, and the other end is fixed on the restrictor 1 of the anchor plate 3. If the solenoid 4 is not activated, the gas power acting on the three ball valves tightens the three control cables through the stem 10 and the star linkage plate 9. At this time, the amount of gas discharged from the three nozzles is equal, and the three forces produced offset each other. Now if a lateral force is needed in the direction of a nozzle, the electromagnets of the other two valves are activated simultaneously, attracting the anchor plate 3 and pulling two corresponding control cables. The control cable pulls the corresponding arm of the star-shaped linkage plate, thus jacking the corresponding stem 10,

Fig. 10.19 Transverse force generating device of the first structural form. 1—Restrictor; 2—shaft; 3—anchor plate; 4, 13—electromagnet; 5, 12—gas generator; 6—control cable; 7, 11—nozzle; 8—ball valve; 9—star linkage plate; 10—stem

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closing the two valves. At the same time, because the anchor plate 3 itself can rotate around the shaft 2, the control cable of the valve to be opened is loosened, and the ball valve is opened, exceeding the original opening level. The nozzle discharges more gas, which generates transverse force in the required direction. Obviously, this transverse force is obtained by two effects: on the one hand, the nozzle flow of the valve increases and increases the force, on the other hand, because the valve closes in the opposite direction, there is no flow of gas, and no force, which cancels the original force. If the other two electromagnets are cut off, the gas force forces the star linkage plate to return to the balanced tension state of the three control cables. The valve openings in all directions are the same, and the flow rate is the same. Therefore, the forces in all aspects offset and the balance is restored. Another example of the structure is shown in Fig. 10.20. The same thing as the previous structure is that it also has a star linkage plate. The gas generated by the gas generator is introduced from the conduit 1 to the nozzle 2. Its flow rate is controlled by piston valve 3 and stem 4 is driven by star linkage plate. In the structural example of Fig. 10.20, the star-shaped linkage plate has two arms, which are connected with two valve stems and drive two pistons. The star-shaped linkage plate 6 is supported in its center. It can deflect on the supporting bearing 8 and bear the load of spring 7. Component 5 is an electromagnet, and rod 9 is coupled with electromagnet. When the electromagnet is excited, the rod will move axially. In this way, the star linkage plate rotates and tilts around the bearing 8. Thus, the valve of the nozzle can be opened or closed, and the gas flow rate can be changed. Compared with the rudder system, the transverse force generated by this structure is less dependent on the missile speed. However, because the missile

Fig. 10.20 Transverse force generating device of the second structural form. 1, 13—Conduit; 2, 12 —nozzle; 3, 11—piston valve; 4—stem; 5, 10—electromagnet; 6—star linkage plate; 7—spring; 8 —bearing; 9—rod

10.3

Device for Changing Missile Motion Direction …

187

speed will affect the back pressure of the gas nozzle, the change of back pressure will affect the gas velocity and flow rate at the nozzle outlet, thus affecting the magnitude of the force. Flight altitude also affects the back pressure of the nozzle, so it also affects the magnitude of transverse force. The same gas valve opening at different flight altitudes, the gas flow rate and speed, and the magnitude of the force generated are different. The ambient temperature will affect the pressure and combustion speed of the gas generator, and the pressure of the gas generator will increase when the ambient temperature is high, which will increase the gas velocity and flow rate at the outlet of the gas nozzle at the same valve opening, thus affecting the magnitude of transverse force. The aforementioned factors must be taken into account when designing the whole system and corresponding measures should be taken. Otherwise, the impact will be great.

10.4

Process Technology of Gas Steering Engine

In the production of a gas steering engine in many batches, there have been some major faults such as valve core stopping, piston jamming, and unqualified performance. After many years of process technological research, the causes of failure were found: the influence of redundancy, the out-of-control gap between the valve sleeve and the spool, the low quality of the key components, the unreasonable debugging technical requirements, and so on. After adopting a series of process technological measures, the performance and reliability of the gas steering engine are guaranteed.

10.4.1 Structure and Working Principle Gas steering engine is the actuator of a certain missile control system, which is mainly composed of noumenon, shell, coil, piston, spool, bushing, valve piece, and so on (Fig. 10.21). When working, the positive and negative half-cycles of the width-modulated square-wave pulse signal with a certain frequency from the autopilot are input into the two coils of the steering gear, respectively, which alternately generates electromagnetic attractive force in opposite directions to the valve core assembly. Under the action of electromagnetic attractive force, the valve core assembly moves reciprocally, and the working medium is directed to both ends of the piston to promote the reciprocating motion of the piston. The piston drives the rudder surface to make corresponding deflection through the transmission mechanism. When a

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Fig. 10.21 Schematic diagram of gas steering engine structural. 1—Noumenon; 2—piston; 3— shell; 4—coil; 5—valve spool; 6—left external valve plate; 7—left valve plate; 8—medium valve plate; 9—right valve plate; 10—right external valve plate; 11—bushing; 12—rudder surface

missile is flying, the deflection of the rudder surface and the rotating missile body form a control force to control the missile flight. Previously, the main quality problems of the gas steering engine were poor reliability, and there were some major faults such as valve core stopping, piston jamming, and unqualified performance. Many times, the pilot fire test failed because of the quality problems of the gas steering engine (Table 10.4). Only after batch repairs, the pilot fire test passed. In combination with production practice, the relevant personnel have carried out many years of process technological research and ignition tests, and finally found out the causes of the failure, and took effective measures to ensure the reliability and performance requirements of the gas steering engine.

10.4.2 Redundancy Control In gas steering engine, the fit clearance between valve sleeve and valve core, body and piston is very small. In the work, the spool, piston, and bushing are in the reciprocating linear motion state, especially with flowing gas. These characteristics make the redundancy a great threat to the reliability and performance of gas steering

10.4

Process Technology of Gas Steering Engine

189

Table 10.4 Faults of gas steering engine in pilot fire test Serial number

Number

State

Fault phenomena

Causes of failure

Solutions

1

01

Low temperature

Valve core stopping

Strengthen quality control of heat treatment process and check metallographic structure of valve plate

2

02

High temperature

Valve core stopping

3

03

High temperature

Valve core stopping

Valve plate runs out of control during heat treatment, contains excessive Austenite, and the hole of valve sleeve shrinks during ignition Wear of measuring head results in smaller mating clearance between valve sleeve and spool Valve spool is burred

4

04

Lifetime

Disqualification of reaction time symmetry

The opening of the slide valve is not symmetrical

Improve the measurement method and control the fit clearance Strengthen the control of redundancy Control the symmetry of slide valve opening

engine. On the other hand, the gas actuator has dozens of ventilation slots. The structure shape is irregular, and the assembly and grinding must be carried out crosswise. Cylinder is an open structure, which makes it more difficult to control the redundancy. One of the important reasons for valve core stopping and piston stuck is that there is redundancy in the steering gear. Through continuous improvement, the following measures have been taken to effectively control the redundancy: Improve the design, make the structural dimension tolerance coordinated and reasonable, and avoid redundancy due to supplementary processing in the assembly process. For example, after the original rudder axle is pressed and installed, the inner hole shrinks. In order to load the steel ball, it is necessary to supplement the reaming bore, which inevitably causes redundancy. After adjusting the tolerance, the original drawbacks were eliminated. When processing valve core, piston, and bushing, the burr should be strictly checked and controlled by microscope according to assembly requirements. The valve sleeve hole on the shell assembly is composed of several parts which are combined and ground. The control of grinding sand is an important link in controlling surplus. The original process is difficult to completely remove the grinding sand deep inside the valve sleeve hole. If slightly neglected, over a long period of time, the grinding sand will be solidified inside the valve sleeve and cannot be cleaned, resulting in batch scrap. After improvement, the grinding sand will not enter the inner depth of the valve sleeve hole. The grinding sand on the

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grinding surface is easy to flow out of the valve sleeve hole. After decomposition and inspection of several sets of samples, no abrasive sand was found inside the valve sleeve, which shows that this method is reliable and effective. A variety of methods (such as demagnetization, vibration, bubble scrubbing, ultrasonic scrubbing, washing, and high-pressure air blowing) are used comprehensively to remove the redundant parts repeatedly when assembling. When assembling, the spool, bushing, piston, valve sleeve hole, and cylinder hole are inspected by a special person with a microscope. Inspectors also need to review and try their best to ensure that the assembled parts are free of redundancy. The steering gear is assembled on the super clean worktable, and the production site is kept regular, clean, and civilized. The steering gear is testing installed first. Avoid the problem of screw coating falling off in formal assembly. After testing installation, the electricity and ventilation running-in test of the steering gear under different frequencies and atmospheric pressures is carried out. Then decomposition, cleaning reviews the appearance of components, and then formal assembly. It is conducive to eliminating the possible residue or the excess produced in the trial run.

10.4.3 Fit Clearance Control The fit clearance between valve sleeve and valve core is an important characteristic parameter in gas steering engine. Increasing the mating clearance will increase the leakage of working medium, reduce the output torque, and increase the reaction time, and the smaller the mating clearance, the more inflexible the movement of the valve core will be, even stuck. There are many factors affecting the fit clearance, so corresponding control methods should be adopted. The working medium for ground test of gas steering engine is compressed air at room temperature, and the working medium for pilot fire or flight test is gas. Although the gas is filtered, a large amount of carbon particles will be entrained into the matching place, which makes the matching clearance relatively smaller and is unfavorable to the movement of the valve core. The heat capacity of the body assembly is much larger than that of the valve core; and the valve sleeve, shell, and body are heated through the ventilation channel, while the valve core is almost surrounded by gas; the radial expansion of the valve sleeve is restricted by the shell and the body, but the valve core has no such restriction. Because of these conditions, under the action of gas, the radial expansion of the valve sleeve hole is less than the radial expansion of the valve core in a certain period of time. This also makes the fit clearance smaller. This is the reason why the gas steering gear with small clearance works normally in ground test and will break down under the action of gas. The design specifies the mating clearance between the valve sleeve and the spool. Later, according to a large number of ignition test data, the clearance was adjusted during assembly. It is difficult to accurately measure the dimension of

10.4

Process Technology of Gas Steering Engine

191

valve sleeve hole to ensure the requirement of fit clearance. There are many grooves on the surface of the hole. Previously, it was difficult to measure the minimum aperture and the wear of the measuring head by using the small-hole gauge. It was easy to produce the error that the measured value was larger than the actual value, resulting in the composite clearance between the valve sleeve and the valve core less than the required value, which caused the valve core to stop swinging when the gas steering engine was ignited. Later, the measurement method was improved by using the small-hole scale combined with the grouping plug rod. At the same time, changing the original method of measuring and matching only by assembly workers, first by specialized personnel to measure and match, then by assembly workers to self-test, inspectors to reexamine, find problems and coordinate treatment in time, improve the reliability of measurement, ensure the fit clearance. The metallographic structure of each valve plate that makes up the valve sleeve has an important influence on the mating clearance between the valve sleeve and the spool. A batch of products had been faulted during ignition because of excessive retained Austenite in the metallographic structure of valve plates. Later, monitoring was strengthened during heat treatment of valve plates. After heat treatment, the inspection requirement of metallographic structure was increased to ensure the stability of the hole size and clearance of valve sleeve under gas working condition.

10.4.4 Shell Assembly Quality The shell assembly consists of a combination valve sleeve and a shell. Shell assembly is the key component of gas steering engine, which has a key characteristic and an important characteristic. The quality of shell assembly has an important influence on the reliability and performance of gas steering engine. Due to the high precision requirement, many processing and assembly procedures, and complex influencing factors of shell components, the qualified rate of shell components in a long period of time is only about 60%. After tackling key technical problems, these problems have been solved. (1) Major Quality Problems The coaxiality of 2 /3:5 mm hole to /2:5 mm hole exceeds the design requirement. The qualified rate is 60  70%. /2:5 mm hole cylinder exceeds the design requirements. After vacuum quenching treatment, the /3:5 mm orifices of left and right external valve plates shrink to form an inverted cone. The uneven distribution of oxide skin on the surface of the hole affects the flexible and reliable movement of the bushing. (2) Improvement Measures Improve the accuracy and quality of the valve plate. Improve the verticality of /2:5 mm hole on the valve plate to the end surface, and ensure the coaxiality

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Application of Aerodynamic Technology in Attitude Control …

requirement of /3:5 mm hole on the left and right outer valve plates to /2:5 mm hole. Leave a little margin when /3:5 mm hole on the left and right outer valve plates is machined. After quenching, the oxide scales on the surface and root of /3:5 mm holes were removed with natural tar. The shape of the hole is slightly modified. After vacuum quenching, the /2:5 mm holes of the left and right valve plates are grinded, which makes the /2:5 mm holes of the left and right valve plates slightly larger than the /2:5 mm holes of the left and right external valve plates in order to improve the combination accuracy. Improve the accuracy of the combination, strictly select the valve plate, and measure the actual value of /2:5 mm hole of valve plates with the grouping plug rod before the combination. Then select groups to ensure that the /2:5 mm hole of the left and right valve plates in each group is slightly larger than that of the left and right external valve plates. Control the deformation of the mandrel and improve the combination process. Originally, each valve plate was put on the mandrel and fastened with nuts and washers, and then the combination was completed. Later, the coaxiality requirement of /0:015 mm for the two central holes of the combined mandrel was added. The self-aligning washer (conical washer and spherical washer) is used instead of the original flat washer to reduce the deformation of the mandrel and improve the combination quality. Measures have also been taken to improve the grinding quality of /2:5 mm holes and ensure the cylindricity of holes in shell assemblies, so that the qualified rate of shell assemblies can reach more than 95%.

10.4.5 Technological Key Problem Test on Symmetry of Reaction Time For the gas steering engine in the steering engine cabin, the redundant materials are controlled, the clearance between the valve sleeve and the valve core is controlled, the quality of the shell components is improved, and the qualified steering engine is debugged completely according to the static debugging index. In the first pilot fire test, the problem of over-symmetry of reaction time occurred. This is a major quality problem of unqualified test. Relevant personnel carried out technical research again. Firstly, many ignition tests were carried out on the steering gear, eliminating various possibilities of over-symmetry of reaction time. Secondly, the friction marks of the sliding valve opening observed on the valve core of the steering gear are seriously asymmetric. Two experiments of different symmetry of the sliding valve opening are carried out with the process steering gear. In the first test, the parameters of the process steering gear simulated the original steering gear were debugged (the opening of the sliding valve was seriously asymmetric), and then the ignition test was carried out. In the second test, the sliding valve opening of the process steering gear was adjusted symmetrically, and then the ignition test was carried out. The following results are obtained from the test data: the symmetry of

10.4

Process Technology of Gas Steering Engine

193

reaction time of the first test rudder is over-symmetry, and the fault of the test rudder is reproduced; the reaction time of the second ignition test is symmetrical and meets the technical requirements. Later, ignition tests were carried out on the other three sets of steering gear with the opening of the sliding valve adjusted more symmetrically. The symmetry of reaction time is well controlled and meets the requirements of technical conditions. (1) Analysis of Original Static Debugging Technical Indicators By analyzing the original static debugging technical indicators, it can be found that: it is the unreasonable requirement of these debugging technical indicators that results in the serious asymmetry of the sliding valve opening of the test steering gear. The original static debugging technical index has the requirement of symmetry of no-load flow. The factors affecting the symmetry of no-load flow are not only the symmetry of the sliding valve opening, but also the structural symmetry of the two channels. For example, working edge roundness, shape, dimension and surface roughness of ventilation channel, the connection of the air passages between the parts, the size and shape tolerance of the spool, bush, piston, and cylinder bore of the slide valve are different. When debugging, the flow asymmetry caused by the structural asymmetry of the two channels can be achieved by adjusting the opening of the slide valve. Although the static technical specifications and reaction time can be qualified in the test through compressed air, the symmetrical change of reaction time will be caused by the change of sliding valve opening under the working condition of gas. (2) Controlling the Symmetry of Slide Valve Opening and Adjusting the Technical Indicators of Commissioning According to the above test results and the analysis of the original static debugging technical indicators, in order to ensure the symmetry of reaction time under gas working condition, the symmetry of sliding valve opening must be guaranteed. The measurement of sliding valve opening is based on the position of the spool in zero alignment. In order to improve the measurement accuracy of sliding valve opening, the requirement of zero position for the difference of the middle pressure should also be raised. Later, the debugging practice of two batches of gas steering engines reflects the debugging requirements after adjustment, which is quite difficult for batch production. After replacing parts and repeatedly assembling and adjusting, about 10% of the steering engines still cannot meet the requirements of flow symmetry. In the face of this situation, it is necessary to find out the influence of flow symmetry on reaction time symmetry through experiments, and then consider whether it is allowed to relax the flow symmetry index. For this reason, three sets of steering engines whose flow symmetry exceeds the standard and other adjustment indexes meet the requirements are tested for ignition. The results show that the symmetry of reaction time of the three sets of steering engines is still good when they are ignited.

194

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Application of Aerodynamic Technology in Attitude Control …

According to the test results, in order to ensure quality, facilitate production, and improve efficiency, the flow symmetry index of steering gear is improved. (3) Conclusion After taking the above improvement measures, the production of gas steering engine is relatively smooth, the previous faults do not recur, the routine ignition test passes once, and the quality of product is no longer affected by the unreliable quality of gas steering engine. Practice shows that these improvement measures are effective.

Bibliography 1. Yin Y, Zhang L, Gao Z et al (2012) Analysis of attitude control method of flight machine based on gas-jet side force. In: Proceedings of the 2011 international conference on advances in construction machinery and vehicle engineering, Chinese construction machinery society, Shanghai Scientific & Technical Publishers, pp 413–418 2. Yin Y (2012) Electro-hydraulic servo control theory and application technology in extreme environment. Shanghai science and technology press, Shanghai 3. Zhang L (2012) Research on attitude control system of aerocraft based on jet reaction force (0920030068). Tongji university master’s thesis 4. Song J (1996) Use gas generator and nozzle to generate lateral force to change the direction of the missile. Autoplot Infrared Technol 3:47–48 5. Qu X (1996) Technology of gas rudder and steering gear. Autoplot Infrared Technol 3:51–55 6. Wu H (1982) Structure and strength calculation of turbine parts. China machine press, Beijing 7. Robeson RE (1980) Space vehicle attitude control technology for 20 years. Foreign Space Technol 2:48–57 8. Deng Y, Tian J, Wang Y et al (2006) Overview of aerocraft attitude control methods. Tactical Missile Control Technol 02:7–13 9. Wang X-R, Zhou C-S, Ju Y-T, Jiang G-Z (2008) Counter design for length-shorted nozzle of solid rocket engine. J Ballist 20(4):77–80 10. Chen W-M, Huang S-B, He Y-J (2009) Study on reaction-jet controller of air-to-air missile. Aero Weapon 2:43–46 11. Kurtenbach FJ (1981) Flight evaluation of a simplified gross thrust calculation technique using an F100 turbofan engine in an F-15 airplane. NASA Technical Paper 1782 12. Kurtenbach FJ (1979) Evaluation of a simplified gross thrust calculation technique using two prototype F100 turbofan engines in an altitude facility. NASA TP 1482 13. Hughes DL (1981) Comparison of three thrust calculation methods using in-flight thrust data. NASA Technical Memorandum 81360 14. Biesradny Thomas J, Lee D, Rodriguez Jose R (1978) Airflow and thrust calibration of an F100 engine S/N P68005 at selected flight condition. NASA TP 21069 15. Chen Z (2004) Engineering fluid mechanics. Higher Education Press, Beijing

Chapter 11

Pneumatic Down-the-Hole Hammer

Pneumatic down-the-hole (DTH) hammer is a pneumatic drilling tool using compressed air as a power source. It is suitable for drilling in pebble, gravel, and hard rock strata. It is often used in building pile foundation construction, bridge, mining, geological exploration, hydrological wells, and other fields. Pneumatic DTH hammer is more suitable for complex strata, especially for rock strata and loose strata than conventional rotary drilling rigs and long screw drilling rigs. This chapter introduces the application of large diameter pneumatic DTH hammer, the development, classification and working principle of pneumatic DTH hammer. It focuses on the analysis of the principle and design method of large diameter pneumatic DTH hammer impactor, dynamic model, drilling bit design method and examples, typical engineering cases.

11.1

Overview

In 1813, Richard Trivetick, an Englishman, first invented a percussive rock drill powered by steam. The percussion action really became a continuous action. In 1844, a British named Blonton invented a rock drill powered by compressed air. In 1855, Feuentinimolu developed a pneumatic rock drill and obtained the first invention patent of rock drill in the world. Subsequently, Italian engineers Bartlett and Jeman Samet improved the previous rock drill, and the experiment was successful in 1857, which was the beginning of modern percussion drilling technology. In the same year, the Montcenis Tunnel, which connects France and Italy, officially used the integrated rock drill powered by compressed air. Later, 1857 was regarded as the first year of the birth of pneumatic rock drill. Hammer impact equipment with modern characteristics appeared in 1896. The rock drill made by George Lenner, an American, has an impact frequency of 30 Hz. It also has a ratchet-claw screw rod rotary drilling mechanism and a wet powder discharging device. Its structure is not much different from the rock drill widely © Springer Nature Singapore Pte Ltd. and Shanghai Scientific and Technical Publishers 2020 Y. Yin, High Speed Pneumatic Theory and Technology Volume II, https://doi.org/10.1007/978-981-15-2202-4_11

195

196

11

Pneumatic Down-the-Hole Hammer

used in modern times. People call George Lena’s rock drill a major breakthrough in the history of rock drill development. In 1938, the German-manufactured air leg and tungsten carbide bits. The expandable air leg was used to exert thrust on the bits to support the body weight of the rock drill, thus greatly reducing the physical consumption of workers. The tungsten carbide bit greatly reduces the number of grinding, and the drilling depth increases from 0:6
0:9 to 9
12 m after one grinding. The application of tungsten carbide opens a way for deep hole rock drilling. Ingersoll-Rand Company of the United States noticed that the impact energy of the deep hole connecting rod drill lost in the drill rod was larger, and proposed the idea of putting the drill into the bottom of the hole, which was patented in 1932. However, due to various constraints, it was not until the late 1940s that open-pit mines began to be tried out. In 1951, Belgian Engineer Andrei Stannuiko designed and manufactured a DTH impactor similar to the modern DTH impactor (At that time, it was called a down-the-hole drill.). The DTH impactor not only makes full use of the impact energy of the equipment, but also greatly reduces the noise, improves the working environment and reduces the heavy manual labor of the workers. Because the efficiency of open-pit drilling is 2
3 times higher than that of steel rope percussive drilling rig, it has been recognized as economical and effective drilling equipment for drilling hard ore. Subsequently, the down-hole equipment was continuously improved, and the large aperture of open-pit mine was extended to the small aperture of underground mine. Compressed air pressure used in foreign countries increased from 0:5
0:6 MPa in the initial stage, 0:7
0:88 MPa in the 1960s and 1:4
1:75 MPa in the early 1970s to 2:1
2:6 MPa in the late 1970s. In the 1980s, pneumatic DTH hammer has been applied to the field of geological core exploration abroad, and the depth of the blasting hole in DTH hammer construction has been extended from several meters to tens of meters to hundreds of meters of exploration boreholes. Developing DTH hammer blasting hole from without core-taking into core-taking sampling drilling, and the development from ordinary positive circulation drilling to central sampling drilling, namely, CSR (center sample recovery) drilling method. With the application of DTH hammer in exploration, foreign drilling technicians began to study penetrating DTH hammer and reverse circulation drilling technology. The College of Construction Engineering of Jilin University (formerly Changchun University of Science and Technology) has studied pneumatic DTH hammer for more than 30 years. Penetrating pneumatic DTH hammer, reverse circulation penetrating DTH hammer, single large diameter wet reverse circulation penetrating DTH hammer and combined diameter DTH hammer have been developed. The diameter of the borehole reaches 600
1200 mm. The rock entry equipment currently used in China is basically percussive drilling, which has poor drilling ability, low efficiency, easy collapse, and serious mud pollution. DTH hammer drilling technology is one of the most efficient drilling methods in hard rock at present. With the enlargement of drilling diameter and the increase of

11.1

Overview

197

drilling depth, the air consumption of DTH hammer increases, the cost of DTH hammer drilling increases exponentially, and the drilling efficiency is low. By using double power head DTH hammer drilling machine, i.e., long screw drilling machine and pneumatic DTH hammer, rapid drilling can be realized in various soft and hard loose strata, gravel strata, pebble strata and rock strata under complex geological conditions, forming rock-socketed piles with large bearing capacity and anti-slide piles for preventing geological hazards. Its adaptability is strong and construction efficiency is high, which is 3–10 times higher than that of conventional percussive rotary drilling. The pore-forming quality is good and there is no mud pollution. This equipment is the most advanced construction equipment for drilling pile holes in rock entry and loose strata and has been serialized. Large diameter DTH hammer with double power head is a drilling technology combined with double power head drill and large diameter DTH hammer. As shown in Fig. 11.1, it combines DTH hammer high-energy percussive rotary rock fragmentation drilling and DTH hammer high-frequency rotary percussive drilling. It has the characteristics of high drilling efficiency, good drilling quality, and strong adaptability to complex conditions. Figure 11.2 shows an example of the application of pneumatic DTH hammer in a copper mine disaster in Chile. The underground

Fig. 11.1 Dual power head pneumatic DTH hammer

198

11

Pneumatic Down-the-Hole Hammer

Fig. 11.2 Application of pneumatic DTH hammer in copper mine disaster in Chile

collapse event was from August 5, 2010 to October 14, 2010. During the 69 days, 33 miners were trapped in 700 m underground. Pneumatic DTH is used to hammer into rock drilling, and finally the trapped miners are rescued from the underground through the hole.

11.2

Principle and Classification of Pneumatic DTH Hammer

11.2.1 Classification of Pneumatic DTH Hammer Pneumatic DTH hammer is a pneumatic impact tool with foam agent as well as flushing medium. The impact energy produced by it is transmitted directly to the drill bit at a certain impact frequency, and then driven by the drill rig and the drill pipe by rotation, resulting in the pulsating breakage of rock. At the same time, the compressed air discharged by the impactor is used to cool the drill bit, and the broken rock particles are discharged so as to realize the impact, rotation, and drilling at the bottom of the hole. (1) Pneumatic DTH hammer can be divided into valve-type and valveless type according to the valve distribution mode and structure of impactor. As shown in Fig. 11.3, the valve-type pneumatic DTH hammer makes the compressed air enter the front and rear chambers alternately through various forms of control valves, which promotes the reciprocating motion of the piston to produce impact effect. The piston moves to the front and back dead points of the cylinder block, which generates pressure signals to push the control switch and cause the piston to change impact direction. The valve-type DTH hammer cylinder has a simple valve distribution process, and the compressed air only undergoes two-valve distribution processes: intake and exhaust. Figure 11.4 shows that the valveless pneumatic DTH hammer has no valve. The valve

11.2

Principle and Classification of Pneumatic DTH Hammer

199

Fig. 11.3 Structural schematic diagram of valve-type pneumatic DTH hammer (1—Upper connector, 2—Check valve; 3—Adjusting washer; 4—Valve plate; 5—Valve seat; 6—Piston; 7—Outer cylinder; 8—Inner cylinder; 9—Bushing; 10—Brazing jacket; 11—Round key; 12—Drilling bit)

Fig. 11.4 Structure schematic diagram of valveless pneumatic DTH hammer (1—Joint; 2—Check valve; 3—Valve seat; 4—Inner cylinder; 5—Piston; 6—Outer cylinder; 7—Bushing; 8—Card key; 9—Spline sleeve; 10—Drilling bit)

distribution system which controls the reciprocating motion of the piston is arranged on the cylinder wall, and the valve distribution is automatically supplied when the piston moves. (2) According to the rated working pressure of DTH hammer, pneumatic DTH hammer can be divided into low wind pressure DTH hammer and medium and high wind pressure DTH hammer. Low wind pressure DTH hammer generally refers to its rated working pressure ranging from 0.5 to 0.7 MPa, such as CIR series produced by Yihua Ingersoll-Rand Mine Construction Machinery Co., Ltd., WC and DJ series produced by Wuxi Prospecting Machinery Factory. Medium and high wind pressure DTH hammer refers to DTH hammer with working pressure above 0.7 MPa, such as DH and DHD high wind pressure series produced by Yihua Ingersoll-Rand Mine Construction Machinery Co., Ltd., CJ2, GQ and CJ series produced by Wuxi Prospecting Machinery Factory, JW and JG series produced by Jiaxing Metallurgical Machinery Factory. In general, the DTH hammer with working pressure of 0:7
1:2 MPa is called medium wind pressure DTH hammer, and the DTH hammer with working pressure above 1:2 MPa is called high wind pressure DTH hammer. (3) According to the drilling diameter of DTH hammer, it can be divided into small diameter DTH hammer and large diameter DTH hammer. The hole diameter below 200 mm is called small diameter DTH hammer, such as CIR90, CIR110, CIR150, CIR170, J-80, J-80B, J-100, J-100B, and J150 series. The hole diameter larger than 200 mm is called large diameter DTH hammers, such as DH, DHD, CJZ, JW-200, J-200B, J-250, and FGC-15 series.

200

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Pneumatic Down-the-Hole Hammer

(4) According to the central through hole of DTH hammer, it can be divided into ordinary DTH hammer and through DTH hammer. For example, FGC-150 is a through DTH hammer, the rest are ordinary DTH hammers. The through DTH hammer can drill in hard rock and sandy pebble with large diameter, and carry out continuous reverse circulation sampling. It has high drilling efficiency, low requirements for matching equipment (compressor air volume and air volume), and improves drilling depth.

11.2.2 Principle of Valve-Type Pneumatic DTH Hammer Figure 11.3 shows that when the valve-type pneumatic DTH hammer is working, high-pressure gas enters the cylinder body from the upper connector 1 and opens the check valve 2. A part of the gas enters the bottom of the hole through the central hole passage of valve seat 5, piston 6 and the exhaust hole of drilling bit 12, and directly blows and washes the bottom of the hole. Other compressed air enters the valve train with valve plate 4, and relies on piston 6 and valve rod (integrated with seat 5), bore on inner cylinder 8 and groove on bushing 9 to cooperate, so that the valve plate rises and falls, realizes the conversion of inlet and exhaust of front and rear air chambers, and promotes reciprocating motion of piston. Pneumatic DTH hammer with valve consumes a lot of air and the valve is easy to be damaged.

11.2.3 Valveless Pneumatic DTH Hammer Figure 11.4 shows the schematic structure of valveless pneumatic DTH hammer. The working principle is that the compressor discharges compressed air, enters the DTH hammer upper joint 1 through the pipeline system, pushes open the check valve 2, and reaches the annular space at the upper end of the valve seat 3. At this time, compressed air is divided into two ways: one way from the radial hole on the check valve to the central passage between the check valve and the valve seat; the other way into the space between the outer cylinder 6 and the inner cylinder 4. When one of the compressed air enters the valve seat, it is continuously discharged through the central small hole of the valve seat, and through the piston 5 central hole, the central hole and the exhaust hole of the drill bit to the outside of the bit, cooling the bit, carrying bottom hole cuttings, and returning to the surface through the annular hole between the drill string and the borehole wall. The airflow in this way is strong jet flow. It does not enter the DTH hammer chamber and does not participate in the work. It only plays the role of strong blow hole bottom, cooling drill bit and removing cuttings. The adjusting gaskets in the valve seat are designed as a group. The central holes of different sizes are designed on the gaskets to adjust the velocity of strong jet flow. According to the requirement of air source

11.2

Principle and Classification of Pneumatic DTH Hammer

201

and drilling chip removal, the non-hole gasket can also be placed, that is, the strong jet air can be canceled, so that the compressed air can be used to drive the DTH hammer to work, and the consumption of compressed air can be saved. When another compressed air enters the ring groove of the inner and outer cylinders, it enters the front chamber (the space surrounded by the piston 5, bushing 7 and inner cylinder 4) of the DTH hammer through the radial hole of the inner cylinder and acts on the piston. Because the piston has an annular area difference, the piston goes up and starts to return. When the middle ring of the piston runs to the lower end of the inner cylinder, the intake passage of the front chamber is closed, and the front chamber is in a closed state. The piston stroke in this section is the intake stroke of the front chamber (Lfi). Thereafter, the compressed air in the front chamber works by expanding itself, pushing the piston upward until the lower end of the piston moves to the radial hole in the middle of the bushing, and the expanding work stroke ends, which is the working stroke of the front chamber expansion (Lfe). Since then, the piston continues to move upward due to inertia, and its lower end surface passes through the radial hole in the middle of the bushing. The gas in the front chamber is discharged through the axial hole in the upper end surface of the bushing, the radial hole in the middle, the central hole in the drill bit, and the exhaust hole. The piston runs upward until the upper dead point, which is the exhaust stroke of the front chamber (Lfo). Corresponding to the intake, expansion, and exhaust of the front chamber, the rear chamber (the space enclosed by valve seat, inner cylinder and piston) undergoes three-valve distribution processes. The piston moves upward from the lower dead point until the upper end of the piston contacts the lower end of the valve seat. In this process, the gas in the rear chamber is discharged through the piston center hole, the drill center hole and the exhaust hole, which is the exhaust stroke of the rear chamber (Lbo). After the exhaust stroke is terminated, the piston continues to move upward until the lower end of the piston’s upper ring contacts the lower edge of the inner cylinder ring groove. This stroke is the compression stroke of the rear chamber (Lbc). The piston continues to ascend, the lower ring surface of the upper end surface exceeds the lower edge of the inner cylinder ring groove, and compressed air enters the rear chamber through the annular clearance of the inner cylinder ring groove, which gradually increases the gas pressure in the rear chamber and decelerates the piston until it finally forces the piston to stop moving, i.e., the piston moves to the upper dead point. This stage is the rear chamber intake stroke (Lbi). After the piston returns to the upper dead point, the piston reverses into the stroke stage because the high-pressure air continuously enters the rear chamber and acts on the upper end face of the piston to push the piston downward. The same motion as the piston return stroke, in the stroke motion the front chamber undergoes exhaust stroke (Lfo), compression stroke (Lfc) and intake stroke (Lfi) in turn, while the rear chamber experiences intake stroke (Lbi), expansion stroke (Lbe) and exhaust stroke (Lbo). The piston return stroke completes one cycle at a time, realizing one impact. According to the working principle, when DTH hammer works, the valve distribution process is completed by the reciprocating motion of the piston itself.

202

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Pneumatic Down-the-Hole Hammer

The piston is not only the working element that generates mechanical impact energy, but also the control element of reciprocating motion, and the only moving part. Therefore, the failure rate of DTH hammer is low and its life is long. The piston completes an impact, and the front and rear chambers each experience an expansion stroke. Because the stroke does not need air supply, the air consumption is greatly reduced. Valveless pneumatic DTH hammer has the following characteristics: (1) Simple air distribution system, direct pressure blowing, short air path, low gas pressure loss, and the elimination of complex air distribution machine. (2) By using compressed gas expansion to work, the gas consumption of DTH hammer is greatly reduced. (3) The service life of DTH hammer parts is approximately the same, and the maintenance work of DTH hammer has been improved. (4) Valveless DTH hammer requires high processing accuracy, and it is difficult to design its structure and size.

11.2.4 Large Diameter Pneumatic DTH Hammer Large diameter pneumatic DTH hammer is important equipment for rock drilling. During the construction of large-scale projects, such as high-rise buildings, important factory buildings, ports, wharfs, highways, railways, bridges, water conservancy, and Hydropower junctions, drilling construction of large-diameter hard rock and gravel is involved. In recent years, large diameter (  400 mm) pneumatic DTH hammers have been developed in the United States, Japan, South Korea, and other countries for the construction of rock entry pile foundations and anti-slide piles. At present, domestic large diameter drilling equipment over 400 mm mainly depends on imports. Drilling diameter of DTH hammer in China is less than 400 mm, which is called medium and small diameter DTH hammer. Figure 11.5 shows the picture of 800 mm large diameter pneumatic DTH hammer and matching drill bit imported by Shanghai Zhenzhong Machinery Manufacturing Co., Ltd. in 2011 by Japan Construction and Adjustment Corporation. American Ingersoll-Rand Company first produced pneumatic DTH hammers with single-head and Cluster Drills series, a total of 40 models, which are used for drilling and grouting construction of large-caliber projects. Single-head DTH hammer is suitable for 90
762 mm aperture range; cluster DTH hammer is composed of 16 single hammers at most, and suitable for 610
1980 mm aperture range. At present, Ingersoll-Rand large diameter pneumatic DTH hammer has been widely used in the construction of foundation pile holes, diaphragm wall and hard rock drilling in deep water wells, and has achieved high drilling efficiency. For large diameter pile holes and engineering holes, cluster DTH hammer is used to form holes at one time. In order to adapt to the construction of “multi-aperture”

11.2

Principle and Classification of Pneumatic DTH Hammer

203

Fig. 11.5 800 mm large diameter pneumatic DTH hammer and matching bits imported from Japan

Table 11.1 Parameters table of Ingersoll-Rand large diameter pneumatic DTH hammer Model

DHD112W

Air consumption (m3 =min)@wind pressure (kg/cm2 ) Low wind pressure

Medium wind pressure

High wind pressure

[email protected]

[email protected]

[email protected]

External diameter (mm)

Length (mm)

Weight (kg)

Aperture (mm)

276

1933

598

302*455

DHD112WS

[email protected]

[email protected]

[email protected]

276

1933

674

302*455

DH12

[email protected]

52.4@14

[email protected]

276

1933

583

302*455

DH11

[email protected]

52.4@14

[email protected]

254

1933

561

297*445

DH12S

[email protected]

52.4@14

[email protected]

276

1933

660

508*559

PPD112 L

23.4@7

–

–

276

3200

904

302*445

PPD112 LS

23.4@7

–

–

276

3300

987

508*559

QL200

[email protected]

[email protected]

[email protected]

396.2

1671

816

660*762

or “plum blossom spots”, single-head large-caliber DTH hammer is used. Tables 11.1 and 11.2 are the product parameter tables of single-head large diameter pneumatic DTH hammer and CD series cluster DTH hammer of Ingersoll-Rand Company, respectively. South Korea Dongyu Machinery Company has been producing small DTH and deep DTH hammer drills for groundwater and hot spring development since 1990, and has successively introduced large-caliber DTH hammers. Its large diameter pneumatic DTH hammer products include D. W410, D. W750 and CD series of cluster DTH hammer. The product parameters of D. W410 and D. W750 DTH hammers are shown in Table 11.3. Each type of DTH hammer has three kinds of air supply pressure: low, medium, and high. Among them, the low wind pressure of D. W410 pneumatic DTH hammer is 10:5 kgf=cm2 , the consumption of air is

204

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Pneumatic Down-the-Hole Hammer

Table 11.2 Technical parameters table of Ingersoll-Rand cluster pneumatic DTH hammer Model

Air consumption (m3 =min)@wind pressure (kg/cm2 ) Low wind Medium wind High wind pressure pressure pressure

External diameter (mm)

Length (mm)

Aperture (mm)

CD30 CD36 CD42 CD48 CD50

[email protected] [email protected] [email protected] [email protected] [email protected]

724 876 1029 1181 1486

2078 2078 2078 2078 2078

762 914 1067 1219 1524

[email protected] [email protected] [email protected] [email protected] [email protected]

[email protected] [email protected] [email protected] [email protected] [email protected]

Table 11.3 Product parameters table of D.W410 and D.W750 large diameter pneumatic DTH hammers of Korea Dongyu Machinery Model

Aperture (mm)

Drill hammer diameter (mm)

Cylinder diameter (mm)

Piston stroke (mm)

Piston weight (mm)

Length (mm)

Weight (mm)

D.W410 D.W750

457*650 800*1 200

406 740

310 500

150 100

265 785

1998 2560

1570 5700

40:5 m3 =min; the medium pressure is 14:0 kgf=cm2 , the consumption of air is 60 m3 =min; the high wind pressure is 17:6 kgf=cm2 , the consumption of air is 85 m3 =min. Figure 11.6 is the schematic diagram of structure of D. W410 DTH hammer. The axial hole of the rigid valve is the intake passage of gas. The gas enters the front and rear air chambers through the cavity between the cylinder block and the inner sleeve. The axial groove on the piston is the intake passage of the front chamber, the pedal valve is the exhaust passage of the front chamber, the groove on

Fig. 11.6 Structural sketch of D.W410 large diameter pneumatic DTH hammer of Korea Dongyu Machinery (1—Front connector; 2, 18—Gasket; 3—O-ring; 4—Check valve; 5—Spring; 6— Washer (shock absorber); 7—Shock absorber; 8—Rigid valve; 9—O-ring; 10—Sleeve; 11—Inner jacket; 12—Piston; 13—Pedal valve; 14—Stop ring; 15, 16—Buckling ring; 17—Pin; 19—Rear connector; 20—Drilling bit)

11.2

Principle and Classification of Pneumatic DTH Hammer

205

Table 11.4 Pneumatic DTH hammer parameters table of top drill, Korea Model

Borehole diameter (mm)

Connection mode

External diameter (mm)

Length (mm)

Weight (kg)

ACE120 ACE380

311*451 445*559

286 376

1889 1715

608 1140

TD320 TD350 TD450

355*475 445*508 460*610

320 357 400

1818 1866 1807

890 1080 1338

TD450S

460*610

424

1881

1492

TD550

610*850

525

1875

2308

TD700

710*975

650

1867

4300

TD800

870*1 200

758

1884

6000

TDU350

445*508

Pin connection Pin, hexagonal connection Pin connection Pin connection Pin, hexagonal connection Pin, hexagonal connection Pin, hexagonal connection Hexagonal connection Hexagonal connection Pin connection

350

1499

936

the inner wall of the inner sleeve is the intake passage of the back chamber, and the central hole of the piston is the exhaust passage of the back chamber. Top Drill Company of Korea began to produce DTH hammers in 1999. Selection of special steel and high precision machining, the production of DTH hammer can be equipped with different shock absorbers, according to the specific application of the choice of positive or reverse circulation drilling, change the opening pressure of the check valve. The drilling range is from small diameter 70 mm to large diameter 1200 mm. The product parameters of large diameter DTH hammer with drilling diameter over 400 mm are shown in Table 11.4. It can be seen from the table that the connection mode between DTH hammer and drill pipe includes pin connection or hexagonal connection. The main technical difficulties of large diameter pneumatic DTH hammer are as follows: (1) Drilling efficiency is low. Large diameter foundation pile hole has large diameter, complex drilling stratum, high requirement of drilling verticality, good quality of grouting, and the hole position cannot be moved. These characteristics and requirements bring some difficulties to large diameter drilling construction. Usually, the upper part of the borehole is a loose layer or soft layer, and the lower part is moderate weathering or even fresh bedrock; or the soft layer or loose layer is intercalated with large boulders and drift stones. Hard rock or big solitary rock drilling workload only accounts for about 10% of the total footage in drilling, but the drilling efficiency is very low, and the drilling time accounts for more than 50% of the total drilling time. How to solve

206

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Pneumatic Down-the-Hole Hammer

the drilling efficiency of large diameter pneumatic DTH hammer is one of the key problems. (2) Air compressors are not easy to match. Because of the large borehole diameter and the large amount of air needed for slag discharge, the need for both large air volume and high air pressure will increase the investment of air compressor equipment and the energy consumption of air compressor. Conventional medium and low air pressure air compressors will not be able to be used together, which directly affects the popularization and application of this technology. (3) It is difficult to manufacture and assemble. Large diameter drilling requires large-size DTH hammer impactor. Large-size equipment is difficult to manufacture and assemble. (4) The mechanism and process of pneumatic DTH hammer impactor are complex. At present, there are few studies on the pneumatic mechanism of impactor at home and abroad. The pneumatic principle, thermodynamic mechanism, critical sonic flow process and aerodynamic matching parameter relationship involved in the impact process need to be studied in depth, and the design method of the impactor system is urgently needed.

11.3

Principle and Parameter Design of Large Diameter Pneumatic DTH Hammer Impactor

Referring to the design methods and ideas of foreign products, the principle and design method of large diameter pneumatic DTH hammer impactor are introduced, including selecting the structure type of DTH hammer, putting forward the appropriate calculation method of performance parameters, designing the parameters of key parts, and drawing parts and overall assembly drawings.

11.3.1 Design Requirements Referring to the large diameter pneumatic DTH hammer of Korea Dongyu Machinery Co., Ltd., the design method of 600 mm large diameter pneumatic DTH hammer impactor is analyzed. The impactor is the power tool to produce impact power and frequency, and is the most important component of DTH hammer. The quality of impactor directly affects the efficiency, quality, cost, and safety of drilling. In order to obtain a reasonable and advanced design scheme, it is necessary to conduct a comprehensive and in-depth analysis of various requirements. According to the design objectives of DTH hammer impactor, the primary and secondary requirements should be distinguished and coordinated, so as to centralize and unify the requirements of all aspects as far as possible.

11.3

Principle and Parameter Design of Large Diameter …

207

The main tasks of the overall design of large diameter DTH hammer impactor include: (1) Determine the parameters of DTH hammer impactor according to the selected type and use requirements. (2) Drawing the general assembly drawing of DTH hammer (including drill bit). The overall design basis of DTH hammer impactor is as follows: (1) Stratigraphic conditions: complex geology such as filling layer, clay layer, pebble layer, and weathered sand layer. (2) Drilling method and technology: Rotary force and axial thrust are provided by double power DTH hammer drilling machine (combined construction of double power head long screw drilling machine and pneumatic DTH hammer), high-pressure gas is provided by air compressor, and percussive rotary compaction drilling is carried out. (3) Conditions and requirements: Drilling without water and meet certain drilling speed requirements.

11.3.2 Overall Structure (1) Valveless DTH impactor Large diameter pneumatic DTH hammer is designed for the construction of pile foundation in complex geology such as filling layer, pebble layer, and sand layer. Therefore, DTH hammer with low frequency and high impact energy is selected, and its drilling effect is more remarkable. According to the requirements of pneumatic impact compaction equipment and DTH hammer at home and abroad, valveless valve distribution mechanism is adopted. Figure 11.7 shows that the valveless DTH impactor adopts a double cylinder structure, with grooves and holes in the cylinder block for air intake and grooves in the piston. The reciprocating motion of the piston can be realized by opening or closing the corresponding air

Fig. 11.7 Structure schematic diagram of valveless central exhaust DTH hammer (1—Upper connector; 2—Check valve; 3—Adjust gasket; 4—Intake seat; 5—Inner cylinder; 6—Outer cylinder; 7—Nozzle; 8—Piston; 9—Sleeve; 10—Guide sleeve; 11—Round keys; 12—Lower connector; 13—Drilling bit)

208

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Pneumatic Down-the-Hole Hammer

passages depending on the motion of the piston itself. Finally, the exhaust is carried out through the central exhaust passage. Valveless DTH hammer has only piston as a moving part, and its overall structure is simple. (2) Central exhaust DTH impactor Large diameter pneumatic DTH hammer impactor adopts central exhaust structure, as shown in Fig. 11.7. The central exhaust impactor refers to the working exhaust gas of the impactor and a part of compressed air, which directly enters the bottom of the hole from the hollow passage of the piston and the drill bit. The exhaust gas and some compressed air from the side exhaust impactor are discharged from the special holes on the impactor cylinder body to the hole wall and then to the bottom of the hole.

11.3.3 Selection of Working Parameters The drilling parameters of DTH hammer mainly include drilling diameter, drilling depth, drilling direction, and rock firmness coefficient. They are all determined by the construction technology. These parameters are the original parameters for designing large diameter pneumatic DTH hammer impactor. According to these original parameters, the main working parameters of impact equipment, namely working gas pressure, impact energy, impact frequency, and output power, can be determined. (1) Working gas pressure p of DTH hammer To select and determine the design pressure of DTH hammer, it is necessary to consider the use of DTH hammer and its operation mode, as well as the ability to manufacture compressed air equipment at present, such as whether high-pressure air compressor can be manufactured or not. The international standard ISO5941-1979 has stipulated the design pressures to be used in priority, as detailed in Table 11.5. At present, 0:49 MPað0:5 MPaÞ is widely used as the design pressure of Table 11.5 Priority design pressure for pneumatic tools and pneumatic machinery Priority design pressure (MPa)

Examples of application occasions

0.4 0.63

Rock drills and other equipment for coal mines General rock drilling machinery, road construction and construction equipment, machine shop, sheet metal industry, shipyard engineering tools, etc. Sandblasting equipment for mass production; DTH impactor equipment Heavy-duty DTH impactor Pressure to be used later

1 1.6 2.5

11.3

Principle and Parameter Design of Large Diameter …

209

pneumatic impact equipment in China. The large diameter pneumatic DTH hammer designed in this case is used for rapid drilling in various complex geological conditions, such as filling stratum, clay stratum, pebble stratum, and weathered sand stratum, to form large bearing capacity rock entry pile and anti-slide pile to prevent geological hazards. Drilling diameter  600 mm requires high-pressure impact equipment to form large bearing capacity. Combined with ISO5941-1979, the tentative design pressure is 1:6 MPa. (2) Estimation of impact energy e For the DTH impactor used for drilling large holes, its design impact energy fluctuates widely, generally more than 100 J. This is related to the use of high-pressure air handling equipment in DTH impactor. The design impact energy can be pre-calculated according to the following empirical formulas: e ¼ 21K

p 0:152D e pp

ð11:1Þ

where p Supply pressure of DTH hammer (Pa); pp Standard design pressure, pp ¼ 5  105 Pa; K Amplitude modulation coefficient, K value fluctuates in the range of 1
1:17, when the supply pressure of pneumatic circuit is 5  105 Pa, K ¼ 1; D Drilling diameter (cm).

(3) Impact frequency Choosing the impact frequency is an important work in the design of large diameter pneumatic DTH hammer impactor. The output power of DTH hammer can be directly increased by increasing the impact frequency when the impact energy e is selected. In terms of the structure of impactor, to increase the impact frequency, the piston stroke must be reduced, which will reduce the impact energy of a single impact. When the impact energy of a single impact decreases to a certain extent, no matter how to increase the impact frequency, there will be no good drilling effect. On the contrary, increasing piston stroke can improve the single impact energy and reduce the impact frequency. Therefore, the selection of impact frequency is restricted by impact energy. The design frequency of pneumatic DTH hammer is generally lower than that of other percussive drilling machines. Usually, when the design pressure is 0:5 MPa, it is not more than 16:6 Hz. However, the design pressure of large diameter pneumatic DTH hammer used in complex geology such as fill, pebble, and sand layers is far more than 0:5 MPa, so the impact frequency fluctuation range of its equipment is

210

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Pneumatic Down-the-Hole Hammer

large. The impact frequency of DTH hammer equipment can be estimated according to the following empirical formulas: f ¼ 10:4 þ 7:6p

ð11:2Þ

In the formula, the unit of frequency f is Hz and the unit of design pressure p of DTH hammer is MPa. (4) Output Power After choosing the impact energy and frequency, the output power of the equipment can be obtained by taking the product of the impact energy and the impact frequency, whose unit is kW.

11.3.4 Calculation Method of Performance Parameters When DTH hammer impactor works, its internal dynamic process is very complex. It is assumed that the pressure of the air chamber and the atmosphere in the exhaust stage of the impactor is one atmosphere in a working cycle. When the air chamber is connected with the compressor pipeline, the pressure is the supply pressure. When the air chamber is disconnected from the atmosphere and the compressed gas pipeline, the process of an adiabatic expansion or adiabatic compression should be considered.

11.3.4.1

Calculation Method for General Design of Performance Parameters

A modified coefficient is used to generalize the effects of mechanics and thermodynamics, which is called the total coefficient method. The basic idea of calculating the total coefficient is the gas pressure in the piston is nonconstant, and the actual stroke of the piston is less than the structural stroke. The weight of the moving parts, the mechanical friction resistance, and the rebound force after collision have a great influence on the performance parameters. (1) Calculation of impact energy The work done by the piston of the impactor to the drill bit can be expressed as the product of the force P and the distance s experienced, i.e., e ¼ Ps ¼ pw Ak s

ð11:3Þ

11.3

Principle and Parameter Design of Large Diameter …

211

where pw Gas pressure in loop; Ak Forced area of piston rear chamber; s Piston stroke under the action of force P. Considering various losses and efficiencies, the above equation can be modified to e ¼ K a pw A k s

ð11:4Þ

where Ka Conversion coefficient of impact energy. Only the exact Ka is given can the above equation be calculated. The actual Ka value of the impactor can be obtained by experiment and inversion. The conversion coefficient Ka of the relevant DTH hammer impactor can be found in Table 11.6. (2) Impact frequency When the cycle time of the impactor is T, the impact frequency is f ¼ 1=T ¼ 1=ðat1 Þ

ð11:5Þ

where t1 Stroke time. The impact cycle time is expressed by the stroke time t1 multiplied by a proportional coefficient a which is at least greater than 2. Assuming that the initial velocity of piston motion is zero in stroke stage, the piston moves with uniform acceleration. In stroke s, the motion time of piston is as follows:
t1 ¼

2sGk pw A k g

1=2 ð11:6Þ

where Gk Piston weight; g Gravity acceleration. The impact frequency is f ¼


 1 pw Ak g 1=2 a 2sGk

ð11:7Þ

0.5 0.7 1.05 1.38 Valve distribution type

Air pressure (MPa)

150

0.42 0.40 – – – – – – Plate valve

100

J series

0.37 – – –

170 0.38 – – –

200 0.46 – – – Valveless

W-210

Table 11.6 Conversion coefficient Ka of impact energy of impactor

325

– – 0.38 0.42 – – – – Butterfly valve

275

DHD series

– 0.40 – –

400 – 0.40 – –

500

– 0.38 – –

AM4

– 0.37 – –

AM5

AM series

– 0.38 – –

AM6

– – 0.38 – – 0.35 – – Plate valve

Mach 6 series 590 670

212 11 Pneumatic Down-the-Hole Hammer

11.3

Principle and Parameter Design of Large Diameter …

213

After using the correction coefficient k, there is f ¼k


 1 pw Ak g 1=2 a 2sGk

ð11:8Þ

If factor k=a is represented by a total coefficient b, then there is
 pw Ak g 1=2 f ¼b 2sGk

ð11:9Þ

In the equation, b can be obtained by looking up Table 11.7. (3) Output Power Output power refers to the total work done by the impactor in every second, expressed in N: N ¼ ef

ð11:10Þ

By substituting the values of e and f into the above equation, there is N ¼ Ka bð2Gk Þ0:5 ðpw Ak Þ1:5 ðsgÞ0:5

ð11:11Þ

The above equation shows that both the output power and the supply pressure are proportional to the power of 1.5 power of the working area of the cylinder. The foreign high-pressure impactor is designed based on this basic principle.

11.3.4.2

Piecewise Calculation Method for Calculating Performance Parameters

Valveless impactor valve distribution state is divided into three stages: intake, expansion and inertial sliding. Its performance parameters can be calculated by stages. The stroke stage diagram is shown in Fig. 11.8. (1) Calculation of impact energy According to the work-energy principle, the impact energy of the impactor is the difference between the pressure power of the back chamber of the cylinder and the resistance power of the front chamber in the stroke stage, that is, Z Z e ¼ pA dVA  pq dVq ¼ e1 þ e2 þ e3  e4  e5  e6 ð11:12Þ

0.5 0.7 1.76 Valve distribution type

Air pressure (MPa)

0.62 0.62 – – – – Plate valve

J Series 100 150

0.56 – –

170 0.69 – –

200 0.54 – – Valveless

W-210

Table 11.7 Conversion factor b of impact frequency of impactor 500 – 0.40 –

400

– – – 0.38 0.40 0.39 – – – Butterfly valve

DHD Series 275 325 – 0.52 –

24

– 0.49 –

15

– 0.52 –

15

– 0.53 –

16 – 0.52 0.35 Valveless

DHD-260

214 11 Pneumatic Down-the-Hole Hammer

Principle and Parameter Design of Large Diameter …

11.3

215

P Air absolute pressure/MPa Rear chamber

Front chamber

Inlet Exhaust

Expand Compress

Exhaust

Piston displacement/m

Inlet

Fig. 11.8 Diagram of DTH hammer impactor

where pA ; pq VA ; Vq e1 ; e2 ; e3 e4 ; e5 ; e6

Air pressure of rear chamber and front chamber of cylinder; Working volume of rear chamber and front chamber of cylinder; Intake, compression and exhaust power of rear chamber in stroke stage; Exhaust power, compression power and intake power of front chamber in stroke stage.

The intake power e1 of the rear chamber in stroke is e1 ¼ p1 Vjk ¼ p1 Ak sjk

ð11:13Þ

where p1 Vjk Ak sjk

Gas pressure (absolute pressure); Back chamber intake gas volume in stroke stage; Working area of piston rear chamber; Inlet length of rear chamber in stroke stage.

The expansion work e2 of the rear chamber in stroke stage is calculated in adiabatic state. Then " " #
K1 #
K1 p1 V1 V1 p1 V 1 p2 K 1 1 e2 ¼ or e2 ¼ K1 V2 K 1 p1

ð11:14Þ

where p1 ; p2 V1 ; V2

Rear chamber pressure (absolute pressure) at the beginning and end of expansion stage; Volume of rear chamber at the beginning and end of expansion stage.

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11

Pneumatic Down-the-Hole Hammer

The exhaust power e3 of the rear chamber in stroke stage is e3 ¼ pqk Ah sqh ¼

p þ p  2 3 Ah sqh 2

ð11:15Þ

where pqk Average pressure of rear chamber in sliding stage; sqh Inertial sliding length of piston in stroke stage. The exhaust resistance work of the front chamber in stroke stage is e4 ¼ p4 Aq sbq

ð11:16Þ

where p4 Exhaust residual pressure of front chamber in stroke stage; Aq Working area of piston front end; sbq Inertial sliding length of piston in stroke stage. In stroke stage, the compression power e5 of the front chamber is calculated according to the adiabatic state, and the specific calculation method is the same as e2 . The intake power e6 of the front chamber in stroke stage is
e6 ¼

 p06 þ p6 Aq sjq 2

ð11:17Þ

where p6 , p06 Loop pressure, p6 ¼ p1 ; sjq Length of front chamber. According to the same method, the pressure work of the front chamber and the resistance work of the rear chamber can be calculated. After calculating the impact energy of the impactor, the final impact velocity of the piston can be calculated from the kinetic energy formula, that is
v¼ where Gk Piston weight; g Gravity acceleration; e Piston impact energy.

2eg Gk

1=2 ð11:18Þ

11.3

Principle and Parameter Design of Large Diameter …

217

(2) Impact frequency According to the force condition of each stage of piston stroke and return stroke, the piston stroke time t1 and return time t2 can be calculated by kinematics and dynamics equation, and the formula for calculating impact frequency is obtained as follows. f ¼

1 t1 þ t2

ð11:19Þ

Because the pressure acting on the piston by stroke and return stroke varies with time and the law of change is different in different stages of motion, the average pressure and its acceleration, velocity and time in each stage of motion should be calculated first, and then the impact frequency should be calculated. In order to simplify the calculation, the variable acceleration motion of piston under variable force can be replaced by the uniform acceleration motion under equivalent pressure according to the principle of equivalent force. The average equivalent pressure is e Ak Ds

ð11:20Þ


 pp Ak g 1=2 1 1 þ s 2DsGk

ð11:21Þ

pp ¼ where, Ds Actual piston stroke. The impact frequency is f ¼ where

s Return stroke time coefficient of piston, generally s ¼ 1:15
1:5.

11.3.4.3

Performance Parameter Linear Equation Method

This method was first proposed by Soviet scholar, because it was found that the pressure of the back chamber changed linearly when the piston in stroke stage in the dynamic diagram of the gas pick obtained from the study. On this basis, the performance parameters of the impactor are calculated, that is the linear equation method of performance parameters, which is not introduced here. From the above methods, it can be seen that the traditional methods for analyzing the dynamic process of impact equipment do not take into account the influence of gas thermodynamics, or modify the influence of gas thermodynamic

218

11

Pneumatic Down-the-Hole Hammer

change by modifying the coefficient, so the results may be closer to the actual results. In order to obtain a more accurate internal dynamic process of DTH hammer, it is necessary to consider the influence of gas heat transfer in the front and rear chamber of impactor. For this reason, the mathematical model of piston motion in cylinder block and the change of gas state in front and rear chamber are established.

11.3.5 Design of Key Parts 11.3.5.1

Design of Cylinder

The main structural parameters of DTH hammer include cylinder diameter, piston structural stroke and piston size. Cylinder block is the guiding device of piston movement, and also the frame of the whole impactor. From the point of view of valve distribution, the cylinder block is also used to transport working media. Increasing the diameter of the cylinder can increase the impact energy and frequency of the impactor. Therefore, the diameter of the cylinder should be enlarged as much as possible when the size of the structure is allowed. Generally, the difference between the outside diameter and the hole diameter of DTH hammer should not be less than 15
20 mm, while the outer sleeve and cylinder of DTH hammer should not be too thin. Therefore, the ratio of cylinder diameter to borehole diameter of DTH hammer is more than 0.5. The working diameter D and structural stroke s of the cylinder are calculated according to the following equations:
D¼

e 0:785apk

s¼

e aAh p

13

ð11:22Þ ð11:23Þ

where e a p Ah k

Impact energy of impactor; Impact energy conversion coefficient; Working gas pressure (Pa); Effective working area of piston; Proportional coefficient between piston structure stroke and cylinder diameter, which can be determined by comparing the same type of equipment.

11.3

Principle and Parameter Design of Large Diameter …

219

Fig. 11.9 Outer cylinder model. a Sectional drawing of outer cylinder; b outer cylinder shape

The unit of diameter D in Eq. (11.22) is m. Considering that DTH hammer impactor is limited by mining technology and borehole size, cylinder diameter, and stroke can be selected according to the following equation: D ¼ kDK ¼ ð0:57
0:68ÞDK

ð11:24Þ

where DK Drilling diameter. Normally, the valve rod size of the central exhaust impactor is estimated by the following equation: d ¼ ð0:32
0:42ÞD

ð11:25Þ

The model of the outer cylinder of large diameter pneumatic DTH hammer is shown in Fig. 11.9, and the sectional drawing of the outer cylinder is shown in Fig. 11.9a.

11.3.5.2

Piston Design

Piston is the main moving part of DTH hammer impactor. Viewed from the function of piston in valve distribution and the load it bears in operation, the piston should have high dimensional accuracy and surface roughness, so that it can adapt to high-frequency up-down reciprocating motion and good airtightness. In the pneumatic DTH hammer, the piston large diameter matches with the outer cylinder and the small diameter matches with the inner cylinder. After the inner and outer cylinder dimensions are determined, the piston large and small diameters are also determined. The piston weight is estimated by the following equation: Gk ¼ 0:0205D2:84

ð11:26Þ

The upper equation is obtained when the diameter unit of cylinder block is cm, in which the Gk unit is kg. The piston model of large diameter pneumatic DTH hammer is shown in Fig. 11.10.

220

11

Pneumatic Down-the-Hole Hammer

Fig. 11.10 Piston model

11.3.5.3

Design of Valve Distribution Path

(1) Valve distribution area Valve distribution area refers to the area of working air flowing through each passage. The ratio of air pavement area to cylinder working area is called the ratio of valve distribution area. If the ratio of valve distribution area is expressed by K, then there is K¼

A or A ¼ KAh Ah

ð11:27Þ

where A Required valve distribution area; Ah Corresponding piston working area. The velocity of gas flow can be calculated according to the following equation: v¼

Qc0 60Acp

ð11:28Þ

where Q c0 cp A

Air consumption of impactor equipment; Air gravity at an absolute atmospheric pressure, c0 ¼ 12:25 N=m3 ; Air gravity of working gas (absolute pressure); Valve distribution area.

The reasonable flow velocity of gas in the pipeline is generally 30
70 m=s, the clearance flow velocity in the valve is not more than 60
70 m=s, the airflow

11.3

Principle and Parameter Design of Large Diameter …

221

velocity in the valve passage in the cylinder block is not more than 40
50 m=s, and the airflow velocity in the exhaust passage should not exceed the sound speed, and should be limited to 100
150 m=s as far as possible. (2) Valve distribution length Valveless pneumatic DTH hammer relies on the reciprocating motion of the piston itself to form different intake and exhaust channels to realize the valve distribution. The valve distribution is arranged on the piston and its size is determined according to the piston stroke. The valve distribution length ratio is expressed by the following equation: ki ¼ ai =s ði ¼ 1
7Þ

ð11:29Þ

where ki ai s a1 a2 a3 a4 a5 a6 a7

Corresponding valve distribution length ratio; Corresponding valve distribution length (m); Structural stroke of piston (m); Exhaust length of front chamber (m); Expansion length of front chamber (m); Inlet length of front chamber (m); Inlet length of rear chamber (m); Expansion length of rear chamber (m); Exhaust length of rear chamber (m); Rear air cushion length.

Soviet scholar A. T. Kajura has carried out experiments on various valveless valve distribution mechanisms and worked out the optimal valve distribution relationship between valve distribution length ai and piston structure stroke s, as shown in Table 11.8. Considering the change of thermodynamic state in the gas chamber, the data in the table above can be revised as follows, as shown in Table 11.9.

Table 11.8 Optimal value of parameter ratio ki of ai to piston actual stroke ss Length ratio

k1

k2

k3

k4

k5

k6

k7

k

Expression Numerical value

a1 =s 0.364

a2 =s 0.455

a3 =s 0.91

a4 =s 0.728

a5 =s 0.091

a6 =s 0.181

a7 =s 0.135

ss =s 0.865

Table 11.9 Recommended value of parameter ratio ki of ai to piston actual stroke ss Length ratio

k1

k2

k3

k4

k5

k6

k7

k

Expression Numerical value

a1 =s 0.4

a2 =s 0.266

a3 =s 0.866

a4 =s 0.6

a5 =s 0.166

a6 =s 0.233

a7 =s 0.13

ss =s 0.9

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Pneumatic Down-the-Hole Hammer

Fig. 11.11 Valve distribution mechanism model. a Inner cylinder; b valve seat

As shown in Fig. 11.11, the valve distribution of large diameter pneumatic DTH hammer includes inner cylinder and valve seat, radial hole of valve seat, cutting plane and radial hole of outer surface of inner cylinder, and axial groove of inner wall. (3) Fit clearance The structural design also includes the fit clearance of the moving parts of the impactor. The fit clearance directly affects the power and pressure and air consumption of the impactor. The test data show that the pressure and air consumption and equipment power can fluctuate by 30*40% with different clearances. In addition, the life of moving parts of pneumatic tools depends to a considerable extent on the maximum allowable clearance. Generally speaking, if the fit clearance is too small, the moving resistance of the moving parts will be large, the mechanical efficiency will be low, and even the phenomenon of sticky cylinder, stagnation, and sticky parts will occur; if the gap is too large, gas channeling will easily occur between the working chamber and non-working chamber. A large amount of compressed air leaks, which reduces the pressure of the working chamber, increases the consumption of compressed air and reduces the performance of the product. For impactor, the amount of compressed air leaking through the clearance between cylinder and piston can be calculated by the following equation: Q¼

pDd2 Dp 12lL

ð11:30Þ

where D d Dp l L

Cylinder diameter; Fit clearance between piston and cylinder block (unilateral value); Pressure difference on both sides of piston; Hydrodynamic viscous coefficient; Length of airtight surface.

It can be seen that the air leakage is proportional to the cubic of the clearance. Choice of clearance between cylinder and piston of impactor: DTH hammer is between 0.06 mm and 0.09 mm. Ensure that the maximum leakage is not more than 15*20% of the total gas consumption. Referring to various design manuals and standards, the cylinder, piston, and gas path can be designed in detail. The design parameters of a large diameter pneumatic DTH hammer are shown in Table 11.10.

11.4

Dynamic Process and Theoretical Model of Large Diameter …

223

Table 11.10 Technical parameters of a large diameter pneumatic DTH hammer Bore diameter (mm)

Cylinder diameter (mm)

Supply pressure (MPa)

Piston stroke (mm)

Piston mass (kg)

Valve-type

Exhaust mode

600

370

1.6

170

230

Valveless

Central exhaust

11.4

Dynamic Process and Theoretical Model of Large Diameter Pneumatic DTH Hammer

11.4.1 Dynamic Process of Large Diameter Pneumatic DTH Hammer Figure 11.12 shows the structure of large diameter pneumatic DTH hammer. Figure 11.13 shows the main components of large diameter pneumatic DTH hammer. The space surrounded by valve seat 3, inner cylinder 4, and piston 6 is the rear chamber of DTH hammer impactor, while the space surrounded by outer cylinder 5, piston 6, bushing 8, and drilling bit 9 is the front chamber of DTH hammer impactor. The DTH hammer needs to go through one return stroke and one stroke in an impact cycle. According to the different states of the front and rear chambers, it can be divided into 10 stages. The front and rear chambers can be divided into four different states, namely, intake, closed compression, exhaust, and closed expansion. The working principle is as follows: high-pressure gas passes through the central through hole of the upper joint 1, and top opening check valve 2 enters the inner part of DTH hammer. Then it passes through the axial hole on the valve seat 3, the passage between the inner cylinder 4 and the outer cylinder 5, and the axial groove on the piston 6, and enters the front chamber. The rear chamber is exhausted by the central through hole of the piston 6, and the piston 6 accelerates upward under the action of the upper and lower pressure. This process is the first

Fig. 11.12 Structural schematic diagram of large diameter pneumatic DTH hammer (1—Upper joint; 2—Check valve; 3—Valve seat; 4—Inner cylinder; 5—Outer cylinder; 6—Piston; 7— Exhaust valve; 8—Bushing; 9—Drilling bit)

224

11 Upper joint

Pneumatic Down-the-Hole Hammer

Clamp Shim spring Spiral casing

Check valve Spring

Harfur block Valve seat

Lower joint Inner cylinder Piston

Outer cylinder

Exhaust valve

Bushing

Shim

Drilling bit

Fig. 11.13 Major components of pneumatic DTH hammer

stage. When the upper end face of piston 6 passes through the lower end face of valve seat 3, the back chamber is closed and compressed, the front chamber is intake, and the piston 6 accelerates upward. This process is the second stage. When piston 6 moves to the intake passage of front chamber are blocked, the front and back chambers are closed, but the pressure of the front chamber is greater than that of the back chamber, and the piston still accelerates upward, which is the third stage. The piston 6 continues to move upward, opening the inlet passage of the rear chamber, and the gas enters the rear chamber. At this time, the pressure of the rear chamber exceeds the pressure of the front chamber. The piston moves from upward acceleration to upward deceleration, but the speed does not decrease to zero. This process is the fourth stage. When the lower end of piston passes over the upper end of exhaust valve 7, the lower chamber exhausts and the upper chamber still intakes. The piston continues to decelerate until the speed decreases to zero. This process is the fifth stage. These five stages constitute the return motion of the piston 6, after which the piston 6 will move downward. The sequence of five stages is the same as the ascending process, but the sequence is opposite. Finally, piston 6 impacts drilling bit 9 to produce impact energy. Figure 11.14 shows five cycle diagrams of single cycle return of pneumatic DTH hammer. Figure 11.15 shows the valve distribution status of the front and rear chamber of DTH hammer. The origin of the coordinates is the upper end of the piston impact drill. The X-axis is the axis of the cylinder block. X ðtÞ represents the displacement of the piston with time. The piston first makes a return motion, during which the front chamber experiences intake stroke (L4 ), expansion stroke (L2  L4 ) and exhaust stroke (Lmax  L2 ). The rear

11.4

Dynamic Process and Theoretical Model of Large Diameter …

Rear chamber

225

Compress

Front chamber Stage 2: Front-chamber intake and rear-chamber compression

Stage 1: Front-chamber intake and rear-chamber exhaust

Rear air chamber intake Front chamber expansion

Front chamber exhaust

Stage 3: Stage 4: Stage 5: Front chamber expansion and Front chamber expansion and Exhaust from front chamber rear chamber compression rear chamber intake and inlet from rear chamber Fig. 11.14 Return stroke five cycles of DTH hammer single cycle

chamber has experienced exhaust stroke (L5 ), compression stroke (L3  L5 ) and intake stroke (L1  L3 ), in which Lmax is the maximum return displacement of piston actual motion and L1 is the structural stroke. In stroke motion, the front chamber experiences exhaust stroke (Lmax  L2 ), compression stroke (L2  L4 ) and intake stroke (L4 ), and the rear chamber experiences intake stroke (L1  L3 ), expansion stroke (L3  L5 ) and exhaust stroke (L5 ). Table 11.11 lists the gas distribution process of the front and rear chambers. The single cycle of DTH hammer

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Intake

Exhaust

Compression (expansion)

Stroke stage

Return stage

Expansion (Compression)

Exhaust

Piston

Intake

Rear chamber

Front chamber

Fig. 11.15 Valve distribution diagram of the front and rear chamber of DTH hammer

Table 11.11 Front and rear chamber valve distribution process Stage order

Piston stroke range

Front chamber state

Rear chamber state

Stage Stage Stage Stage Stage Stage Stage Stage Stage Stage

0  L\L5 L5  L\L4 L4  L\L3 L3  L\L2 L2  L\Lmax L2  L\Lmax L3  L\L2 L4  L\L3 L5  L\L4 0  L\L5

Intake Intake Enclosed Enclosed Exhaust Exhaust Enclosed Enclosed Intake Intake

Exhaust Enclosed Enclosed Intake Intake Intake Intake Enclosed Enclosed Exhaust

1 2 3 4 5 6 7 8 9 10

compression compression

compression compression

compression compression

compression compression

can be divided into two parts and ten stages, and the return part can be divided into five stages: front chamber intake and rear chamber exhaust stage, front chamber intake and rear chamber closure stage, front and rear chamber closure stage, front chamber closure and rear chamber intake stage, front chamber exhaust, and rear chamber intake stage. The stroke part is divided into five stages: front chamber exhaust and back chamber intake, front chamber closure and back chamber intake, front and back chamber closure, front chamber intake and back chamber closure, and front chamber intake and back chamber exhaust.

11.4

Dynamic Process and Theoretical Model of Large Diameter …

227

11.4.2 Theoretical Model of Large Diameter Pneumatic DTH Hammer 11.4.2.1

Hypothesis of Internal Dynamic Process of Pneumatic DTH Hammer

Figure 11.16 is a simplified model of pneumatic DTH hammer. The piston mass is M. The pressure, volume, and temperature in the front and rear chambers are p1 , V1 , T1 , p2 , V2 ; and T2 , respectively. Each chamber has an inlet and an exhaust port. G1 and G3 represent the unit time flow of the inlet and exhaust of the front chamber, while G2 and G4 represent the unit time flow of the inlet and exhaust of the rear chamber. The internal dynamic process of pneumatic DTH hammer is complex, and the following assumptions can be made: (1) Gases are ideal gases Ideal gas is a hypothetical gas. Gas molecules are elastic particles that do not occupy volume, and there is no interaction between molecules. The pneumatic impactor uses compressed air as the medium and the medium is far away from the liquid phase, so the distance between molecules is very large, the interaction force between molecules is very small, and the space occupied by the volume of molecules relative to the movement of gas molecules is extremely small. In this case, neglecting the volume of the molecule itself and the interaction force between the molecules will not cause great errors. Therefore, the medium in the pneumatic impactor can be regarded as an ideal gas. (2) Thermal process in air chamber is quasi-static Thermodynamic process refers to the whole process that the system changes from one equilibrium state to another through continuous intermediate state due to its interaction with the outside world. Thermodynamic process is the result of the destroyed equilibrium of the system. If the system transits from one equilibrium state to another through innumerable intermediate equilibrium states, that is, the system deviates from the equilibrium state infinitely small and restores the

Fig. 11.16 Simplified model of pneumatic DTH hammer

Intake Rear chamber

Piston

Intake

Front chamber Drilling bit

Exhaust Exhaust

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Pneumatic Down-the-Hole Hammer

equilibrium state at any time, the process is uniform, slow and without any sudden change, then the whole process can be regarded as a series of states very close to the equilibrium state. The thermodynamic process is called quasi-static process. In piston thermodynamic machinery, the piston speed is generally less than 10 m=s, but the velocity of pressure wave in gas is almost equal to that of sound, usually hundreds of meters per second. Relatively speaking, the piston’s motion speed is very slow. During the process, a series of force and heat equilibrium can be established in time, which will not be far away from the equilibrium state. Therefore, it can be used as quasi-static process calculation. Quasi-static process provides convenience for theoretical research and is also the basis of numerical calculation. (3) Process of gas change in gas chamber is adiabatic process The process of no heat exchange between the system and the outside world is adiabatic process. When the state of the gas changes very quickly, the heat exchange between the gas and the outside world can be neglected due to the short time of change. The change of the gas in the front and rear chamber of DTH hammer is very fast, and the numerical analysis by computer is based on the single step of microelement time (e.g., 0.0001 s), so it can be regarded as an adiabatic process in the analysis of the problem. (4) Ignoring the influence of friction resistance and DTH hammer rotation In large diameter DTH hammer, the big end of the piston contacts with the inner wall of outer cylinder, and the small end contacts with the inner wall of inner cylinder. Friction exists when piston moves up and down. Choosing reasonable matching tolerance and lubricating the friction surface with lubricating paste when working, the friction force is much smaller than that of the gas in the front and rear chamber, which can be neglected. Similarly, the influence of rotary motion of DTH hammer on gas state and piston motion is neglected.

11.4.2.2

Theoretical Model Equations of Pneumatic DTH Hammer

According to the model figure of DTH hammer shown in Fig. 11.16, the modeling mainly involves thermodynamics and dynamics theory, including solving the acceleration, velocity, and displacement of the piston in this time step and the volume of the front and rear chambers according to the differential equation of piston motion. The gas mass in the front and rear chamber entering and discharging is calculated by gas flow equation, and the change of gas pressure in the front and rear chamber entering and discharging is calculated by gas energy balance equation according to the change of gas mass, and then the change of temperature is calculated.

11.4

Dynamic Process and Theoretical Model of Large Diameter …

229

(1) Gas state equation pi Vi ¼ Mi RTi

ð11:31Þ

where pi Vi Mi R Ti

Absolute pressure of gas in front and rear chamber; Front and rear chamber volume; Gas mass in front and rear chambers; Gas constant; Thermodynamic temperatures of gases in front and rear chambers.

(2) Differential equation of piston acceleration d2 x 1 ¼ ð p1 A 1  p2 A 2 Þ  g 2 dt M

ð11:32Þ

(3) Differential equation of piston velocity   dx 1 ¼ V0 þ ðp1 A1  p2 A2 Þ  g dt dt M

ð11:33Þ

(4) Differential equation of piston displacement X ¼ S0 þ V0 Dt þ

  1 1 ðp1 A1  p2 A2 Þ  g dt2 2 M

where X M p1 ; p2 A1 ; A2 V0 S0 g

Piston displacement; Piston mass; Gas pressure in front and rear chamber; Piston effective area of front and rear chamber; Piston initial velocity; Piston initial displacement; Gravity acceleration.

ð11:34Þ

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(5) Gas flow equation dMi ¼ Gi dt

ð11:35Þ

where Mi Gas mass in front and rear chamber; Gi Gas mass per unit time. When calculating the gas flow rate inflow or exhaust the front and rear chamber, it is necessary to first calculate the wind speed through the throttle, determine what kind of sound speed it belongs to, and then select the corresponding calculation equation. The intake and exhaust process of the chamber is adiabatic expansion process, and the type of sound velocity can be determined by the critical pressure ratio e:
e¼

2 kþ1

k þk 1

ð11:36Þ

When p2 =p1 ¼ e, the velocity of gas flow is equal to the speed of sound; when 1  p2 =p1  e, the velocity of gas flow is less than the first velocity, i.e., subsonic velocity; when 0  p2 =p1  e, it is calculated as supersonic velocity. Equation for calculating when subsonic velocity vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi "
2
k þ 1 # u p1 u 2k p2 k p2 k t G ¼ CS pffiffiffiffiffiffi  p1 RT k  1 p1

ð11:37Þ

Equation for calculating when supersonic velocity p1 G ¼ CS pffiffiffiffiffiffi RT

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2
k1 2k 2 kþ1 kþ1

where k S p1 ; p2 T

Adiabatic process index; Section area of intake and exhaust port; Pressure at inlet and outlet of air chamber; Thermodynamic temperature of gas in front and rear chambers.

ð11:38Þ

11.4

Dynamic Process and Theoretical Model of Large Diameter …

231

(6) Gas energy equilibrium equation Calculating equation of gas pressure variation in gas chamber is dM dV dp RT0 dt  p dt ¼ dt V

ð11:39Þ

where dp V T0 dM dV

Variation of chamber pressure; Front and rear chamber volume; Absolute temperature of gas source; Gas mass variation in the chamber; Volume variation of chamber.   dT TR dM K  1 dV ¼ ðK  1ÞT0 T  dt pKV dt KV dt

ð11:40Þ

where dT Variation of temperature; other symbols have the same meaning as the previous.

11.4.3 Numerical Calculation of Large Diameter Pneumatic DTH Hammer Based on the above mathematical model and the principle of finite difference, the program is designed on the platform of MATLAB. The parameters used in the numerical calculation include valve distribution travel parameters, piston mass, area at both ends of piston, initial pressure and temperature of the front and rear chambers, initial displacement, velocity, and acceleration of the piston. For the pneumatic DTH hammer designed for 600 mm borehole diameter, the piston is usually made of alloy steel. The diameter of the big end is 285 mm, the diameter of the small end is 235 mm, and the mass is 230 kg. In the process of large diameter drilling, high wind pressure is needed to overcome high-pressure resistance. An air compressor with 1:6 MPa outlet pressure is matched for this design DTH hammer. When the check valve is opened with a loss of 0:2 MPa and the resistance loss along the way is neglected, the inlet pressure of the impactor is 1:4 MPa. The simulation step is set to 0:0001 s. Figure 11.17 shows the flow chart of the numerical simulation program for valveless pneumatic DTH hammer.

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Pneumatic Down-the-Hole Hammer

Fig. 11.17 Flow chart of numerical simulation program for valveless pneumatic DTH hammer

Variables in the program: L1 L2 L3

Structural stroke of piston (m); Front chamber expansion + intake length (m); Compression of rear chamber + exhaust length (m);

11.4

Dynamic Process and Theoretical Model of Large Diameter …

L4 L5 A1 A2 m pb ps p1 ; p2 Tb Tf T1 ; T2 x v a V1i ; V2i V1 ; V2 F1 F2 F3 F4 t

11.4.3.1

233

Inlet length of front chamber (m); Exhaust length of rear chamber (m); Forced area of piston front chamber (m2 ); Forced area of piston rear chamber (m2 ); Piston mass (kg); External environmental pressure (Pa); Air compressor supply pressure (Pa); Front and rear chamber pressure (Pa); External ambient temperature (K); Air compressor supply temperature (K); Front and rear chamber temperature (K); Piston displacement (m); Piston speed (m/s); Piston acceleration (m=s2 ); Initial volume of front and rear chambers (m3 ); Front and rear chamber volume (m3 ); Front chamber intake orifice flow area (m2 ); Front chamber exhaust orifice flow area (m2 ); Rear chamber intake orifice flow area (m2 ); Rear chamber exhaust orifice flow area (m2 ); Time step (s).

Analysis of the Results of the Whole Working Process

Set the return direction to be positive and the stroke direction to be negative. The simulation results are as follows. Figure 11.18 shows the velocity–displacement curve of the piston. The piston moves back from rest to upward with a maximum velocity of 5:67 m=s and a maximum displacement of 164:1 mm. After that, the piston starts to make stroke motion, and the velocity is negative (downward). When the displacement is zero (i.e., when the piston hits the bit), the velocity is 7:07 m=s, and the whole process takes 0:915 s. According to the above calculation results, important parameters such as drilling frequency and drilling power of DTH hammer can be obtained. Figure 11.19 is the pressure–time curve of the front and rear chambers. The front chambers undergo intake, closure, exhaust, and then closed and intake in a single cycle. Pressure p1 decreases from intake pressure 1:4 MPa to atmospheric pressure and then rises to intake pressure. Rear chamber pressure p2 undergoes the opposite process.

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Velocity v/(m/s)

(a)

Displacement x/s

(b)

Displacement-speed curve of piston 4

2 1 Piston speed

3 5

6 7 9 10

8

Piston displacement 1 Return: Front-chamber intake and rear-chamber exhaust 2 Return: Front-chamber intake and rear-chamber compression 3 Return: Front chamber expansion and rear chamber compression 4 Return: Front chamber expansion and rear chamber intake 5 Return: Exhaust from front chamber and inlet from rear chamber 6 Stroke: Exhaust from front chamber and inlet from rear chamber 7 Stroke: Front chamber compression and rear chamber intake 8 Stroke: Front chamber compression and rear chamber expansion 9 Stroke: Front-chamber intake and rear-chamber compression 10 Stroke: Front-chamber intake and rear-chamber exhaus Fig. 11.18 Speed–displacement curve of piston. a Computational results; b ten working stages

11.4

Dynamic Process and Theoretical Model of Large Diameter …

235

Fig. 11.19 Pressure–time curves of front and rear chamber

Pressure p/Pa

Rear chamber pressure

Front chamber pressure

Time t/s

11.4.3.2

Comparison of Performance Parameters of DTH Hammer Under Different Intake Pressure

Intake pressure p0 is an important factor to determine the impact energy and frequency, and therefore is also the main parameter affecting drilling speed. In large diameter drilling in complex formations, the appropriate supply pressure should be selected to achieve drilling efficiency. For the large diameter DTH hammer impactor designed in this paper, the initial matching intake pressure of the impactor is 1:4 MPa. The displacement and velocity curve of the piston with time is shown in Fig. 11.20. In Fig. 11.20, the piston reaches its maximum speed at the beginning of the fifth stage (front chamber exhaust and rear chamber intake) when it returns (the velocity is positive). At the end of this stage, the return displacement reaches the maximum, which does not exceed the range of travel (the maximum stroke designed is 170 mm), and the selected intake pressure meets the requirements. At stroke (speed is negative), the piston reaches its maximum speed at the beginning of the tenth

Displacement x/m

Fig. 11.20 Piston displacement and velocity– time curve at intake pressure of 1:4 MPa

Velocity

Displacement

Time t/s

11

Fig. 11.21 Comparison of piston velocity curves at intake pressure of 1:7; 1:4; 1:1; and 0:8 MPa

Pneumatic Down-the-Hole Hammer

Displacement x/m

236

Time t/s stage (front chamber intake and rear chamber exhaust), and then the velocity begins to decrease, and hits the bit at the end of this stage. In order to select the most reasonable intake pressure p0 for the large diameter pneumatic DTH hammer, the performances of DTH hammer impactors with p0 of 1:7; 1:4; 1:1 and 0:8 MPa were compared. As shown in Fig. 11.21, when the intake pressure p0 is 1:7 MPa, the motion curve of the piston is interrupted at the end of the return motion, which indicates that the return displacement of the piston has reached the maximum stroke designed, and the piston impacts the valve seat at the upper end of the impactor. For the other three intake pressures, the specific performance parameters of DTH hammer are shown in Table 11.12 (the mass of the piston is 230 kg for calculating the impact energy). It can be concluded that under the condition that the return displacement of the piston does not exceed the maximum stroke, the bigger the intake pressure, the bigger the impact power and frequency of the piston, the better the drilling effect.

11.4.3.3

Pressure Fluctuation Phenomenon Analysis and Parameter Optimization

From the simulation results of the impactor, it can be seen that the pressure of the front and rear chambers will fluctuate when the piston is at low speed. Figure 11.22 shows the pressure of the front chamber at the beginning of the return motion. The pressure fluctuates briefly at the beginning of the piston motion. Figure 11.23 shows the back chamber pressure at the end of the fifth stage and at the beginning of the sixth stage when the piston moves near top dead center. It can be seen that the fluctuations here are larger and take longer, accounting for 1/4 of the whole cycle. Analyzing the reasons, as shown in Formula 11.39, The change rate of gas pressure in the chamber increases with the increase of variation of gas mass in chamber dM=dt and decreases with the increase of volume change rate of chamber dV=dt. When the piston motion speed is low, the volume change rate of the

Maximum return displacement (m)

0.164 0.158 0.150

Intake pressure (MPa)

1.4 1.1 0.8

5.67 4.94 4.08

Maximum return speed (m/s) 7.55 6.47 5.23

Maximum stroke speed (m/s) 7.07 5.97 4.74

Impact bit speed (m/s) 292.16 224.68 190

Maximum return acceleration (m/s2 )

Table 11.12 Performance parameters of DTH hammer impactor under different intake pressure

225.86 173.46 122

Stroke maximum acceleration (m/s2 )

5748.3 4098.7 2583.8

Impact work of piston

10.93 9.79 8.47

Impact frequency

11.4 Dynamic Process and Theoretical Model of Large Diameter … 237

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Pneumatic Down-the-Hole Hammer

Pressure p/Pa

Fig. 11.22 Pressure–time curve of front chamber at the beginning of return journey

Time t/s

Pressure p/Pa

Fig. 11.23 Rear chamber pressure fluctuation at return end stroke initial stage

Time t/s chamber is relatively small, and the influence of dV=dt on dp=dt. is equal to that of dM=dt. dp=dt is positive and negative under the action of these two factors, so the pressure will fluctuate. When the piston speed increases, the value of dV=dt also increases. At this time, dV=dt plays a decisive role in dp=dt, so the pressure of the intake chamber changes in one direction, and there will be no fluctuation. The pressure fluctuation of the front chamber lasts for a very short time and has a small fluctuation range, so its influence can be neglected. The pressure fluctuation of the rear chamber lasts for a long time and has a large fluctuation amplitude, which may cause hidden danger to the construction of DTH hammer. It is found that the pressure fluctuation can be greatly reduced by increasing the inlet flow area of rear chamber. As shown in Fig. 11.24, the inlet passage of the rear chamber of the prototype is composed of four slots on the inner wall of the inner cylinder of the

11.4

Dynamic Process and Theoretical Model of Large Diameter …

239

Fig. 11.24 Inlet passage of rear chamber on cylinder inner surface of prototype

Inlet passage

Pressure p/Pa

Fig. 11.25 Rear chamber pressure fluctuation after increasing flow area

Time t/s impactor, which are uniformly distributed in the circumference. When the groove is machined, increasing the depth of the groove and increasing the flow area from 1:76  103 to 3:34  103 m2 will increase the air intake of the rear chamber at low piston speed, which will play a role in stabilizing the pressure of the rear chamber. Figure 11.25 shows the pressure of rear chamber at the end of return the beginning of stroke after increasing the flow area. The amplitude of pressure fluctuation decreases from 4  104 to 1:5  104 Pa, which achieves a better results.

11.4.4 Summary (1) The dynamic model of pneumatic DTH hammer needs to consider the influence of thermodynamic process on gas state. The numerical simulation of dynamic process of large diameter DTH hammer and the design of key structural parameters can be carried out through mathematical modeling and programming. (2) For the designed large diameter pneumatic DTH hammer, excessive air pressure will cause the piston to move beyond the maximum stroke, and too small

240

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will not produce the impact work required for drilling. Under the condition that the piston does not exceed the maximum stroke, the bigger the gas supply pressure selected, the better the drilling performance. (3) Pressure fluctuation will occur in the intake chamber at low piston speed, especially at the end of the stroke, which lasts for a long time. This fluctuation is unavoidable at low speed, but it can be greatly reduced by increasing the flow area of the chamber. This method is also easy to realize in technology. The analysis results can be used as a reference for the design theory and drilling technology development of large diameter pneumatic DTH hammer.

11.5

Design of Large Diameter DTH Hammer Bit and Spherical Tooth Layout

11.5.1 Rock-Breaking Process by Impact Reasonable arrangement of spherical teeth can effectively improve drilling efficiency, reduce energy consumption, ensure equal wear of spherical teeth, and improve bit life. It is of great significance for large diameter DTH hammer drilling. Through theoretical analysis and LS-DYNA simulation, the rule of rock breaking by two spherical teeth is obtained, and the reasonable spacing of spherical teeth and the arrangement scheme of spherical teeth for large diameter DTH bits in specific rock are obtained. As an important part of DTH hammer, the drilling bit directly acts with rock and soil, and its drilling performance and life affect the whole machine. Figure 11.26 shows various drilling bits of pneumatic DTH hammer. The interaction mechanism between drilling bit and soil and the optimization of drilling bit have always been the focus of research. Many scholars have studied the rock-breaking mechanism of single cylindrical teeth (spherical teeth, conical teeth, and warhead teeth) under impact, but seldom involved the combined impact breaking principle between two

Fig. 11.26 Pneumatic DTH hammer drilling bit. a DTH cylindrical drilling bit produced by Atlas Copco; b DTH drilling bit produced by Boart Long year; c DTH drilling bit produced by Sandvik; d DTH drilling bit produced by Ingersoll-Rand

11.5

Design of Large Diameter DTH Hammer Bit and Spherical Tooth Layout

241

(a) Atmosphere

Drill rod DTH Piston

(b) Drilling bit

Fig. 11.27 Working principle of pneumatic DTH hammer drilling machine

spherical teeth. In the past, according to the principle of equal volume crushing working conditions, the number of teeth of each ring column was determined. Because of the complex lithology, when determining the spacing between the cylinder teeth in each circle, the combined crushing effect of the two teeth should be considered, which needs to be studied. It is of great significance to study the mechanism of the two teeth and to optimize the spherical teeth layout of large diameter (generally  600 mm) bits. Figure 11.27 shows the working principle of a pneumatic DTH hammer drill. The pneumatic system of the pneumatic DTH hammer drives the piston to reciprocate up and down, and the hammer impacts on the rock, forming a pit on the rock as shown in Fig. 11.27b. At the same time, the drill bit of pneumatic DTH hammer can rotate. Under the action of drill bit rotation, the protruding part of rock pit can be removed to realize rock breakage. At present, there are three main theoretical analysis methods for rock bursting process by impact: 1. Empirical or semi-analytical method: combining similarity theory with dimensional analysis of a large number of experimental data to find the appropriate algebraic equation 2. Theoretical analysis method: using continuum physical equation, especially complex material constitutive equation. These equations are often nonlinear. Therefore, some phenomena in the process of rock bursting under impact are assumed and some empirical conclusions are added. 3. Numerical analysis method: in order to solve the problem of rock bursting by impact accurately, numerical method can be used to solve it. The numerical simulation method can fully reflect the changes of intermediate parameters and physical parameters during rock bursting by impact. The post-processing method of

242

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numerical simulation designed by computer image technology can visually demonstrate the changes of various parameters (shape, stress, strain, etc.) in the whole process of rock bursting by impact. Using the software program, different physical and geometric parameters can be selected to calculate, and the influence degree of different parameters on the results of the interaction between teeth and rock can be obtained, so as to give a more comprehensive result. The cylindrical teeth of DTH hammer bits are made of hard metal, which greatly improves the service life of DTH hammer bits. However, in the use process, there are still some phenomena such as broken teeth, dropping teeth, broken waist, split trousers, and so on. How to effectively reduce the fracture and breakage of cylindrical teeth has become a key factor to effectively improve the life of DTH hammer bits. In practice, it is found that the fracture and broken of the side teeth of DTH bits are the most common failure forms in the damage of the total cylindrical teeth. For example, when the bob-weight rock drill with Swedish /40 mm spherical teeth is used in a mine, the drop rate of the edge teeth reaches 23%, and the breakage rate of the edge teeth reaches 30%. The domestic /40 mm ball-tooth bit of pneumatic rock drill has an edge teeth drop rate of over 30% and an edge teeth crushing rate of 20%. However, other failure modes include broken middle teeth, broken waist and split trousers. The failure rates of falling middle teeth, capping, and inverted cone are all below 5%. The optimum structure parameters, high strength materials, and reasonable fixing technology are three effective means to improve the life of cylindrical teeth. However, the selection of high strength materials is not only limited by the existing level of material research but also by the cost funds of production and construction units. Simply depending on improving the strength of materials without optimizing the structural parameters cannot achieve the desired results. Starting from the force analysis of the edge teeth, the dangerous points on the edge teeth of the cylindrical bit are found and checked by the maximum shear stress criterion. The relationship between the stress and the inclination angle of the edge teeth, the height of the exposed teeth, the friction coefficient and the radius of the cylindrical teeth at each dangerous point is analyzed, so as to find a reasonable inclination angle and the exposed teeth height to reduce the stress at each point under the same working conditions, so as to reduce the failure probability of the edge teeth.

11.5.2 Mechanical Model of Side Tooth of Large Diameter Pneumatic DTH Hammer Bit As can be seen from Fig. 11.28, the spherical teeth of large diameter DTH bit are composed of solid hemisphere and cylinder. A part of the cylinder is embedded into the bit body through cold-pressed fixed teeth. The angle a with the axis of the bit is the inclination angle of the edge teeth, the radius of the spherical teeth is R, and the height of the exposed part of the cylinder is h. There are two main forces on

11.5

Design of Large Diameter DTH Hammer Bit and Spherical Tooth Layout

Tangential force produced by rotation, perpendicular to paper surface

243

Piston

Geotechnica l plane

Fig. 11.28 Total force acting on spherical edge teeth

spherical edge teeth: axial load P and tangential load F. The axial load comes from the impact force produced by the piston impacting the bit at the top of the bit. Therefore, the axial load direction of the rock on the spherical edge teeth is vertical upward, with the magnitude of P. When the edge teeth break the rock, they rotate with the drill bit, and the rock has tangential load on teeth, and the direction is vertical to the paper surface. Set the magnitude of F.

11.5.2.1

Hypothesis

The force acting on the edge teeth is complex. The edge teeth are subjected to impact load as well as static pressure produced by drilling pressure and reaction force produced by rock during rotary cutting. In order to facilitate analysis, the following assumptions need to be made: (1) The rock fragmented by drill bits is flat and uniform in structure, without considering the surface change of bottom rock when it is broken again. (2) The edge teeth are spherical teeth with radius R, the axial load (actually impact load and static pressure) is P, and the tangential load generated by rotary cutting is F. (3) The gas action at the bottom of the bit is neglected. (4) The influence of upper drill rod is neglected. (5) The influence of bit body is neglected, which is regarded as rigid body, and the embedded part of spherical teeth is fixed completely. Next, according to the principle of forces resultant, the forces acting on the edge teeth under the action of P and F are analyzed, respectively.

244

11.5.2.2

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Pneumatic Down-the-Hole Hammer

Force Model Under Axial Load

When DTH hammer bit drills rock, rock reacts on the bit, which makes the bit bear a reverse impact load. It is observed that the curvature of the bottom of the hole basically coincides with the curvature of the end of the bit after the ball tooth bit is drilled into the rock in normal drilling. The tougher the rock is, the better the coincidence degree is. It can be inferred that the axial impact stress is uniformly distributed along the contact surface when the bit is working. Therefore, the uniformly distributed force can be simplified as a concentrated force P, as shown in Fig. 11.29 (point B is the center of the loading surface). Force P acts at point A and can be decomposed into force Px and Py in both directions of X- and Y-axes. Py ¼ P sin a Px ¼ P cos a

ð11:41Þ

(1) Force analysis of side teeth acted by Px Px produces eccentric compression on the edge teeth, which can be decomposed 0 0 into Px along X-axis and bending moment Mx . P0x ¼ Px ð11:42Þ M0x ¼ Px R sin a

Fig. 11.29 Schematic diagram for force analysis of side teeth acted by P

11.5

Design of Large Diameter DTH Hammer Bit and Spherical Tooth Layout

245

0

Px produces compressive stress on the side teeth, so the compressive stress on I  I 0 section is as follows: P0 P0x P cos a rIC ¼ x ¼ ¼ ð11:43Þ 2 AI pðR sin aÞ pðR sin aÞ2 The compressive stress on J  J 0 section is as follows: rJC ¼

P0x P0 P cos a ¼ x2 ¼ pR2 AJ pR

ð11:44Þ

where AI and AJ —Area of I  I 0 and J  J 0 section. Mx0 produces bending stress. It can be seen that the maximum compressive stress is at point F and the maximum tensile stress is at point H on J  J 0 section. Its magnitude is Mx Px R sin a PR sin a cos a rxB ¼ ¼ ¼ Wy Wy Wy where Wy is section modulus in bending and d is the diameter of section. Here d ¼ 2R, so rxB ¼

PR sin a cos a pð2RÞ3 32

¼

4P sin a cos a pR2

ð11:45Þ

(2) Force analysis of side teeth acted by Py Bending stress AA and shear stress CC are produced in side teeth under Py action. The dangerous point is farthest from the neutral axis on the section with the largest bending moment, that is, the H and F points of contact between the spherical tooth edge and the bit body. Where point F is under tension and point H is under compression. For the sPy acting on the I  I 0 section, the maximum is at the neutral axis of section because it is a circular section. Because the exposed part of the teeth has a small span, it is necessary to check the shear stress at centroid point B of the loading surface. Bending stress: rPy B ¼

Mmax Py ðR cos a þ hÞ P sin aðR cos a þ hÞ ¼ ¼ Wy Wy Wy

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where Wy is section modulus in bending, Wy ¼ pd 32 and d is the diameter of section. Here d ¼ 2R, so 3

rPy B ¼

P sin aðR cos a þ hÞ 4P sin aðR cos a þ hÞ ¼ Wy pR3

ð11:46Þ

4Py 4P sina 4P ¼ ¼ 2 2 sina 3pR 3A 3pðR sinaÞ

ð11:47Þ

Shear stress: sPy ¼ where A Area of section of load point. (3) Equivalent Stress of Dangerous Points under Axial Load P From the analysis of (1) and (2), it is known that under the action of P, the dangerous points for the damage of edge teeth are B, F and H. Set a negative sign when the point is under compression and a positive sign when it is under tension, then the resultant stress at point F is rF ¼ rPy B  rxB  rJC

ð11:48Þ

The resultant stress at point H is rH ¼ rxB  rPy B  rJC

ð11:49Þ



a , because Rh3 is very small, the compressive stress rJC where rPy B  rxB ¼ 4PhpRsin 3 produced by Px is the main stress at point H and point F, and the section area is the largest, so this section is not a dangerous section. Point B is subjected to both bending shear stress sPy and compressive stress rIC . According to Fig. 11.30, the equivalent stress rBs of point B is qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 9   2 rx  ry þ 4s2x = r1 ¼ 12 rx þ ry þ 12 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi   2 rx  ry þ 4s2x ; r3 ¼ 12 rx þ ry  12

ð11:50Þ

Because of ry ¼ 0, rx ¼ rIC , sy ¼ sPy , substituting into Eq. (11.50), there is  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r1 ¼ 12 rIC þ r2IC  4s2Py r2 ¼ q0ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r3 ¼ 12 ðrIC  r2IC  4s2Py Þ

ð11:51Þ

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Design of Large Diameter DTH Hammer Bit and Spherical Tooth Layout

247

Fig. 11.30 Principal stress state of point B

From the failure mode of edge teeth, shear fracture is the main failure mode. According to the maximum shear stress criterion, point B is checked: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rBs ¼ r1  r3 , that is, r2IC þ 4s2Py  ½r, where ½r is the allowable stress: rBs

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 9 þ 55sin2 a P 55 2 csc a ¼ r1  r3 ¼ ¼ 2 csc4 a þ pR 9 3pR2 sin2 a P

ð11:52Þ

Equation (11.52) shows that since csc2 a is a decreasing function, if the load P and radius R of spherical teeth are fixed values, rBs decreases with the increase of a.

11.5.2.3

Force Model Under Tangential Load

While DTH hammer drills percussive drilling, it also cuts rock by rotation. F is the reaction force of rock to edge teeth in rotary cutting. It is assumed that it acts as a concentrated force on point A. The direction of F is parallel to the plane of rock, perpendicular to the axial load P and contrary to the bit steering. The magnitude of F is related to the static pressure of the edge teeth and the penetration depth and the bit speed. Similarly, by simplifying F to point B of the neutral axis, it can be transformed into vertical force F 0 and torque Mn , as shown in Fig. 11.31: F0 ¼ F Mn ¼ FR sin a

ð11:53Þ

248

11

Pneumatic Down-the-Hole Hammer

Fig. 11.31 Schematic diagram for force analysis of side teeth acted by F

(1) Force analysis under vertical force F 0 F 0 has a transverse bending effect on the edge teeth, producing a bending normal stress rMF 0 , and bending shear stress sF 0 on section I  I 0 . rMF 0 can be found as follows: ð11:54Þ MF 0 ¼ F 0 ðR cos a þ hÞ It produces the maximum bending normal stress in J  J 0 plane. rMF0 ¼

MF 0 F 0 ðR cos a þ hÞ 4F 0 ðR cos a þ hÞ ¼ ¼ WZ pR3 WZ

ð11:55Þ

0 where Wy ¼ pd 32 and d is the diameter of section J  J , and d ¼ 2R. Because MF 0 is perpendicular to the bending moment produced by the axial load P and reaches the maximum value in the same section, its maximum stress point is at the other two points of J  J 0 section, the two points of U and V shown in Fig. 11.32, and U is under compression and V is under tension. 3

sF 0 can be found as follows: The maximum shear stress produced by bending occurs at the centroid point B of I  I 0 section, but the direction is perpendicular to the shear force produced by the axial force P: sF 0 ¼

4F 0 4F 0 4F ¼ ¼ 2 3A 3pðR sin aÞ 3pðR sin aÞ2

ð11:56Þ

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Design of Large Diameter DTH Hammer Bit and Spherical Tooth Layout

249

Fig. 11.32 Views of points F; H; U; V

(2) Force analysis under torque Mn Torque Mn produces the maximum shear stress at the edge of each section, and at center is 0. Obviously, there is the maximum shear stress at the edge of I  I 0 section: sMn max ¼

Mn FR sin a 2F ¼ ¼ Wn Wn pðR sin aÞ2

ð11:57Þ

Wn is the section modulus in torsion, Wn ¼ pd 16 , d is the diameter of cross section, where d ¼ R sin a. The shear stress produced by Mn in J  J 0 section is as follows: 3

sJMn ¼

11.5.2.4

Mn FR sin a 2F sin a ¼ ¼ Wn pR2 Wn

ð11:58Þ

Force Model Under Combined Action of Axial and Tangential Loads

The process of the spherical teeth scraping at the bottom of the well can be seen as the process of sliding friction of the spherical teeth against the rock and ploughing the grooves on the rock surface. The shear failure of the teeth to the rock ridge in the crushing pit is actually the result of the pushing action. Therefore, the relationship between the axial load P and the tangential load F can be reflected by the relevant theory of tribology.

250

11

Pneumatic Down-the-Hole Hammer

Fig. 11.33 Relationship between F and P

Rotary cutting direction

F ¼f P

ð11:59Þ

where f is the scraping friction coefficient. Considering that the shear failure of rock by teeth is a dynamic process, f is closely related not only to the depth of teeth but also to the bit speed and rock properties. The mechanical model is shown in Fig. 11.33. From the analysis of the previous two sections, it can be seen that the most likely failure mode of the edge teeth is not compression and tension failure, but shear failure. Its failure point is related to the specific working conditions and drilling parameters. The stress of each dangerous point under the simultaneous action of two forces is analyzed below. (1) Equivalent stress at point B For point B of I  I 0 section, it is subjected to axial compressive stress rIC on the whole and two shear stresses sPy and sF 0 on the centroid. Combing sPy and sF 0 : qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4 sR ¼ s2Py  s2F 0 ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðP sin aÞ2 þ F 2 3pðR sin aÞ2

ð11:60Þ

Substituting F ¼ f  P into the above equation, there is sR ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4P ðsin aÞ2 þ f 2 3pðR sin aÞ2

ð11:61Þ

According to the maximum shear stress criterion, the equivalent stress at the centroid point B is obtained. rB ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2IA þ 4s2R ¼

P pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð9 þ 64f 2 Þcsc4 a þ 55csc2 a 3pR2

ð11:62Þ

11.5

Design of Large Diameter DTH Hammer Bit and Spherical Tooth Layout

251

(2) Equivalent stress at points U and V For points U and V on J  J 0 section, they are affected by rJC , sJMn and rMF0 together. According to the maximum shear stress criterion, the equivalent stress is obtained as follows: rJ ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rIC rMF0 þ 4s2JMn

ð11:63Þ

Substituting equations into the above equation, there are Point U
r2U

¼

P pR2





ð1 þ 8f Þcos a þ 8f þ 32f 2

2

h cos a R


2   R þ h2 2 þ 16 f ð11:64Þ R2

Point V
r2V

¼

P pR2





ð1  8f Þcos a  8f  32f 2

2

h cos a R


2   R þ h2 2 þ 16 f ð11:65Þ R2

(3) Equivalent stress at points F and H Points F and H are affected by four stresses rJC , rxB , rPy B , and sJMn . According to the maximum shear stress criterion, the equivalent stress is obtained as follows: Point F rJF ¼

ffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2 rPy B  rxB  rJC þ 4s2JMn

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P 16h2 sin2 a 8h sina cosa þ cos2 a þ 16f 2 sin2 a  ¼ 2 pR R2 R

ð11:66Þ

Point H rJH ¼

ffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 rxB  rPy B  rJC þ 4s2JMn

P ¼ 2 pR

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 16h2 sin2 a 8h sin a cos a þ cos2 a þ 16f 2 sin2 a þ R2 R

ð11:67Þ

(4) Equivalent stress at the edge points of I  I 0 section (including point A) The edge points of I  I 0 section are affected by rIC and sMn max . The equivalent stress is calculated as follows:

252

11

rII 0 ¼

Pneumatic Down-the-Hole Hammer

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2JC þ 4s2Mn max ¼ 2 ð1 þ 16f 2 Þcsc4 a  csc2 a pR

ð11:68Þ

It can be seen from the above equation that csc a is a decreasing function and is always greater than 1. Therefore, when the load P, inclination angle a and f are determined, the stress at the edge of I  I 0 section decreases with the increase of a. Point B and I  I 0 section edge points, under specific conditions who is the dangerous point, should be determined according to the specific axial load value and inclination a, and its change law can be obtained through the curve analysis. When estimating the axial load and tangential load, the axial load P comes from the impulse obtained when the piston impacts the drill bit. For convenience of calculation, it is assumed that during the collision process, the drill bit is rigid body, while the piston has elastic deformation and is completely elastic collision. The piston length is L, the cross-sectional area is A, the mass is m, the elastic modulus is E, and the initial impact velocity of the piston is v. From the piston just collided to the velocity decreased to 0, the impact force increases linearly from 0 to Q. When the velocity is 0, the piston has the maximum deformation DL, according to Hooke’s law, there is DL ¼

QL EA

ð11:69Þ

The piston-to-bit collision is completely elastic, that is, the work done by the bit reaction force is all converted into the deformation energy of the piston. Regardless of heat, according to the law of conservation of energy, there is 1 1 Q DL ¼ mv2 2 2

ð11:70Þ

From Eqs. (11.69) and (11.70), it is obtained that rffiffiffiffiffiffiffiffiffiffi mEA Q¼ v L

ð11:71Þ

The number of cylindrical teeth on large diameter DTH hammer is about 90, set n ¼ 90. According to the previous assumption, each cylindrical tooth is subjected to an average force, so P¼

Q n

ð11:72Þ

The piston mass m ¼ 248 kg, impact velocity v ¼ 7:1 m=s, cross-sectional area A ¼ 0:615 m2 , length L ¼ 0:6 m and E ¼ 2:1  1011 Pa of a DTH hammer

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Design of Large Diameter DTH Hammer Bit and Spherical Tooth Layout

253

impactor are used. By substituting Eqs. (11.71) and (11.72), an estimate of the axial force P is obtained P ¼ 1:82  105 N. The bits are made of hard metal YG11 with a compressive strength of 4600 MPa and shear strength of 80% of the compressive strength. Here, 3680 MPa is taken. The parameters of the original bit are a ¼ 40 ; h ¼ 0:009 m; R ¼ 0:01 m, and the friction coefficient f varies with different rock, soil and working conditions, with a range of 0:2
0:6. From the equations deduced above, it can be clearly seen that the equivalent stress at each dangerous point is related to load P, exposed tooth height h, inclination angle a, friction coefficient f of rotary cutting and radius R of spherical teeth. Obviously, with the increase of P, the stress at each point increases; with the increase of R, the stress at each point decreases. Next, the effects of the exposed tooth height h, the inclination a; and the friction coefficient f of rotary cutting on the stress at each point are discussed.

11.5.3 Layout Principle of Large Diameter Pneumatic DTH Hammer Bit The principle of DTH hammer drilling is percussive rotary drilling. The gas generated by the air compressor rushes into the piston and cylinder space to make the piston move. The drill bit is percussed periodically. The energy is transmitted to the drill bit in the form of stress wave, and the drill bit is percussed to destroy the rock. In the process of drilling, the drilling rig will also exert certain static pressure to prevent the efficiency reduction due to rebound from impact. So DTH hammer drilling is the result of combined action of static pressure, impact force, and rotating force. In the process of drilling hard rock with DTH hammer bit, impact plays a major role, with emphasis on rock breaking by impact.

11.5.3.1

Spherical Teeth Hydrostatic Rock Breaking

Figure 11.34 shows the principle diagram of spherical tooth hydrostatic rock crushing. The final force acting on the spherical teeth of DTH hammer piston is P, based on the model of spherical pressing into brittle rock, the process of rock fragmentation can be divided into the following stages. (1) Elastic deformation stage As shown in Fig. 11.34a, when P is small, a pressure surface is formed. Cracks a; b appear at the edge. When the force P is removed, the rock surface restores to its original state and the cracks at a; b disappear.

254

11

Pneumatic Down-the-Hole Hammer

Fig. 11.34 Principle of spherical tooth hydrostatic rock crushing. a Elastic deformation stage; b pressure crushing stage; c volume crushing stage

(2) Pressure crushing stage As shown in Fig. 11.34b, when P continues to increase, cracks a; b extend. The main pressure body of aob appears, which is called fatigue stage. The surface cracks no longer disappear and the rock surface breaks up. (3) Volume crushing stage As shown in Fig. 11.34c, when P increases to a certain extent, oA and oB cracks appear on the rock surface from point o to form shear bodies Aoa and Bob. With the increase of P, the shear body begins to collapse outwards, and the main pressure body aob is crushed to form a crushing pit.

11.5.3.2

Spherical Teeth Breaking Rock by One Impact

Figure 11.35 shows the principle diagram of spherical teeth impact crushing rock at one time. After a single impact of spherical teeth on rock, the rock will form three regions: one-time crushing pit, fatigue failure zone, and nondestructive zone. The size of fatigue failure zone is related to impact energy, geotechnical characteristics, and drilling pressure, which is a complex non-linear problem.

Fig. 11.35 Principle of spherical teeth impact crushing rock at one time

One-time crushing pit

Fatigue failure zone Non-destructive zone

11.5

Design of Large Diameter DTH Hammer Bit and Spherical Tooth Layout

255

It can be seen that the spherical teeth will cause damage to the rock under the action of static pressure or impact. The rock contacted with the top of the spherical teeth under static pressure will be destroyed and cracks will occur at both ends of the top of the spherical teeth. With the increase of the force, the rock will eventually cause damage. Under the impact force, the spherical teeth destroy the rock more obviously and quickly, not only forming a crushing crater, but also producing fatigue cracks on the rock near the crater, which provides favorable conditions for the next impact or rotary rock breaking.

11.5.3.3

Basic Principles for Bit Layout of Large Diameter DTH Hammer

The arrangement of large diameter DTH hammer bits should consider the rock-breaking efficiency and energy utilization efficiency of spherical teeth, as well as the restriction of bit structure, such as the location of slag discharge port. The basic principles are as follows. (1) Equal Volume Crushing Principle In order to make the life of each spherical tooth equal, the cutting volume should be equal. As shown in Fig. 11.36, the cutting areas of spherical teeth at r1 and r2 are A1 ¼ pðr1 þ B1 Þ2 pr12

Fig. 11.36 Cutting area of spherical teeth with different diameters

ð11:73Þ

256

11

Pneumatic Down-the-Hole Hammer

A2 ¼ pðr2 þ B2 Þ2 pr22

ð11:74Þ

where r1 , r2 Minimum distance of spherical teeth from the center of bit; B1 , B2 Cutting width of spherical teeth. If B1 þ B2 ¼ D (D is spherical tooth diameter), then A1 \A2 . If the cutting depth S1 ¼ S2 , then the cutting volume V1 \V2 . In order to make the life of each spherical tooth equal, the cutting volume must be equal. There are two ways to realize the equal life at r1 and r2 . Firstly, from the angle of coverage (the working contours of adjacent cutting teeth intersect in the direction of drill radius are called coverage), B2 can be reduced by adjusting the coverage, and A1 ¼ A2 is obtained. Secondly, from the point of view of overlap (several cutting teeth on the same circumference cutting strata at the same time called overlap), it is to distribute several cutting teeth of the same size on the area A2 of spherical teeth passing through r2 . The two methods mentioned above can make the volume of rock cut by each cutting tooth equal and the wear degree equal. (2) Principle of total sectional excision In rotary drilling, the bit layout can ensure that there is no uncut clearance between the bits. The cylindrical teeth of DTH hammer bits are arranged in concentric circles. Considering the overlap coefficient between cylindrical teeth, the spacing of each circle should be less than the diameter of cylindrical teeth. That is to say, the projection of the alloy teeth in a certain direction should be interlaced (Fig. 11.37). Fig. 11.37 Projection overlap diagram of spherical teeth of each ring

11.5

Design of Large Diameter DTH Hammer Bit and Spherical Tooth Layout

257

There should be no clearance between the teeth, so as to avoid the presence of unresected rocks in the work, which will affect the driving speed and even cause unnecessary damage.

11.5.3.4

Example of Rock-Breaking Dynamic Process Analysis of Bit

The impact of spherical teeth on rock is a transient action. The dynamic analysis of the impact system of spherical teeth is needed to determine the displacement, stress, and strain of rocks varying with time under impact load, so as to determine the spacing of spherical teeth. LS-DYNA, nonlinear dynamic analysis software, can simulate real complex problems and is suitable for solving the impact, penetration, and pierce through problems of two-dimensional and three-dimensional nonlinear structures. According to Newton’s law and Hamilton’s variational principle, the second-order differential equation of structural dynamic response after finite element discretization can be obtained. € þ CU € þ KU ¼ F MU

ð11:75Þ

where, M Mass matrix of impact system; K Stiffness matrix of system; € U; _ U System node displacement, system velocity vector and system accelerU; ation vector; F Transient impact load of system; C Damping coefficient matrix of system determined by experiments. The damping coefficient matrix is usually calculated by proportional damping method, i.e., C ¼ a 0 M þ a1 K

ð11:76Þ

where coefficients a0 ; a1 are determined by experiments. The difference in direct integration method is used to solve the nonlinear transient dynamic response. Figure 11.38 is a model diagram of rock breaking by combined impact of two spherical teeth. (1) Material Model Assuming that the material of drill spherical teeth is YG8 hard metal, rigid body model is adopted: density is 14500 kg=m3 , elastic modulus is 5:88  1011 Pa, Poisson’s ratio is 0:22. The rock is modeled by a plastic kinematic model with a density of 2700 kg=m3 , an elastic modulus of 4:55  1010 Pa, a Poisson ratio of 0:26, a yield strength of 50 MPa and a failure strain of 0:06. The constitutive relation is simple and the parameters are few. The parameters of material model can be

258

11

Pneumatic Down-the-Hole Hammer

Fig. 11.38 Schematic diagram of rock breaking by combined impact of two spherical teeth (D is the diameter of spherical teeth; t is the spacing between two spherical teeth)

obtained by material handbook. The application fields of large diameter DTH hammer are mainly complex geology, driftstone, pebble, hard rock, soil, and granite. (2) Element properties and mesh generation The elements used for spherical teeth and rocks are hexahedral solid element SOLID164. Because the focus of attention is not on the force exerted on the spherical tooth bit, and in order to speed up the analysis and reduce the memory occupation, the bit is set as a rigid body. As a whole, all the forces exerted on the spherical teeth act on the center of mass of the bit, which reduces the requirement for the bit meshing. The spherical teeth are divided into free meshes. The division of rock is relatively simple. Considering that the middle area is the main stress area, the mesh of the middle area is subdivided. The meshing is shown in Fig. 11.39. (3) Contact and boundary conditions The contact model between spherical teeth and soil is defined as automatic contact. The process of two spherical teeth penetrating into soil is simulated, and static and dynamic friction coefficients between spherical teeth and soil are defined. The model sets a wide enough boundary to simulate the actual situation in the infinite domain. For the process of rock impact and rebound, there are two kinds of initial loading conditions. One is given initial impact velocity, and the other is given drilling displacement. Considering that the impact velocity has no reference value, and it is

Fig. 11.39 Meshing

11.5

Design of Large Diameter DTH Hammer Bit and Spherical Tooth Layout

259

not easy to control the direction of the bit movement by the velocity, the method of applying displacement to the bit is adopted in the simulation. The magnitude of the applied displacement can refer to the data of experiment and field construction. (4) Results and analysis The other conditions remain unchanged. LS-DYNA is used to simulate the different spacing of two spherical teeth. The simulation results are shown in Figs. 11.40 and 11.41. Result analysis: From the isostress curve and stress nephrogram, it can be seen that under the impact, the rock will form a crushing pit, fatigue damage zone and nondestructive zone not affected by the impact. The rock is destroyed by impact force in the form of stress wave. As shown in Fig. 11.40a, when the spacing between the two spherical teeth is small (t ¼ 0:5D), the stress wave between the two spherical teeth has coincided. This disadvantage lies in the excessive number of bits, resulting in energy waste and efficiency reduction. Increasing the spacing between the two spherical teeth (t ¼ 1D), it can be

Fig. 11.40 Isostress curve. a t ¼ 0:5D; b t ¼ 1D; c t ¼ 1:5D; d t ¼ 2D

Fig. 11.41 Stress nephogram. a t ¼ 1D; b t ¼ 1:5D; c t ¼ 2D

260

11

Pneumatic Down-the-Hole Hammer

seen from the isostress curve Fig. 11.40b that the fatigue failure zone of rock is still in a large coincidence state after one impact. The spacing between the two spherical teeth continues to increase (t ¼ 1:5D). It can be seen from the isostress curve Fig. 11.40c that the fatigue failure zone of rock has begun to separate after one impact. If the tooth spacing is increased to t ¼ 2D (Fig. 11.40d), it can be seen that the fatigue failure zone of the damaged rock has basically separated. From the stress nephrogram, it can be more intuitively observed that when t ¼ 1D (Fig. 11.41a), the stress waves overlap in the middle of the spherical teeth, which results in a high stress in the middle. As shown in Fig. 11.41b, when t ¼ 1:5D, the most superficial rock in the middle of the spherical teeth has begun to appear nondestructive zone. When t ¼ 2D, the non-damaged zone in the middle can be clearly seen from the stress nephrogram of Fig. 11.41c. In this case, the rock between the two spherical teeth will produce a “ridge” because of not reach the failure strength, which will undoubtedly reduce the drilling efficiency. From the analysis of isostress diagram and the comparison of Fig. 11.41, it can be concluded that when the spacing of spherical teeth is slightly larger than t ¼ 1:5D, the spacing is reasonable. The calculation in this case is only a reasonable pitch under this kind of rock and working condition. According to the specific rock characteristics and working conditions, the appropriate parameters can be set in the simulation analysis, so as to get a reasonable pitch. (5) Spherical Tooth Layout of Large Diameter DTH Bit Based on the above basic layout principles and the simulation results—reasonable spacing of spherical teeth, combined with the structure of the bit itself, such as the size and location of exhaust holes and slag suction holes, a reasonable layout of spherical teeth of a 600 mm DTH hammer bit can be designed, as shown in Fig. 11.42. Fig. 11.42 1/4 diagram of reasonable layout of a 600 mm pneumatic DTH hammer bit

11.6

Typical Engineering Cases

11.6

261

Typical Engineering Cases

11.6.1 Project Site The project site is located at the west of Dayou Street, south of Middle East Road, east of Youshan road and north of Xiahe Village, Xiahe District, Lishui City, Zhejiang Province. The building area is about 83;000 m2 , of which the underground area is 19;900 m2 . Construction is undertaken by Wenzhou Great Wall Foundation Engineering Company. The diameter of piles is 600, 700 mm, the number of piles is 550, the length of piles is about 14 m, the amount of concrete works is 2715 m3 , and the amount of concrete reinforcing bars is 187 t. Located in the south of Lishui Basin, the site belongs to the landform of big creek flood alluvial plain. Stratigraphic geology is roughly distributed as follows. (1) Layer miscellaneous fill: Recent backfill, backfill time is less than 6 years, layer thickness 4:5
6:5 m. (2) Layer silty clay: flood alluvial origin, 1:5
2:5 m thickness, soft plastic, silt content is high, the property is close to silt, local transformation into silt, formation bearing capacity characteristic value fak ¼ 120
130 kPa. (3) Layer pebbles: alluvial origin, 6:0
10:0 m thickness, medium density structure, characteristic value of bearing capacity fak ¼ 280 kPa. (4) It can be divided into three types: (a) One layer of strong weathered siltstone: dark purple, 0:8
1:5 m thickness, medium density, characteristic value of bearing capacity of stratum fak ¼ 300 kPa. (b) Two layers of medium-weathered siltstone: dark red, 1:0
2:5 m thick, fak ¼ 10
15:0 MPa, soft rock, rock basic quality grade V. (c) Three layers of slightly weathered siltstone: purple red, fak ¼ 20
35:0 MPa, which belongs to softer to harder rocks, and the basic quality grade of rock is grade III to IV.

11.6.2 Model and Parameters of Pneumatic DTH Hammer Large diameter pneumatic DTH hammer double rotary drilling rig is used for drilling. The upper power head drives the DTH hammer and the lower power head drives the outer sleeve. The large diameter DTH is hammered onto the long screw drill rod. The drilling efficiency of this construction method is higher than that of wave impact and rotary drilling by 5–10 times. The slag is discharged by wind speed and the bottom of the hole is clean. During the drilling process, the steel casing keeps track of the guard wall, and there is no collapse of the hole wall, which ensures the construction quality and progress, and no slurry discharge and pollution of the environment. As shown in Fig. 11.43, the main components of large diameter

262

11

Pneumatic Down-the-Hole Hammer

Fig. 11.43 Main components of large diameter pneumatic DTH hammer

Outer cylinder Piston

Valve seat Inner cylinder Spring

Spiral tube

Check valve Lower joint

Upper joint

Lower joint Drilling bit

Hafu

Snap ring

Seal ring

Circlip

pneumatic DTH hammer are piston, valve distribution, inner cylinder, outer cylinder, screw rod, and upper and lower joints. In addition to the large diameter multifunction double rotary drilling rig and pneumatic DTH hammer, other equipment shown in Table 11.13 is also used. Fifty-five tons crawler crane and hole-type vibration hammer are selected for casing lifting machine.

11.6.3 Construction Process The construction technology of large diameter pneumatic DTH hammer drill is shown in Fig. 11.44. The site of each main construction technology is shown in Fig. 11.45. The technological process includes setting-out of pile position, positioning of pile machine, drilling and slag discharging, including stopping after drilling outer casing into bedrock surface, then drilling bedrock with inner spiral rod and DTH hammer to design hole depth, final hole, hole clearing, hanging and installing steel cage, downward pipe, grouting underwater concrete, piling, pulling out steel casing, and shifting of pile machine.

11.6

Typical Engineering Cases

263

Table 11.13 Equipment name and model parameters Name of device

Model and specification

Unit

Amount

Engineering rig Air compressor Steel bar cutter Crawler crane Excavating machinery Steel sleeve Concrete conduit Plug-in vibrator Vibration hammer Initial irrigation bucket

150PW LUY238D GQ-4 50T 120 600*1 000 mm 250 mm /50 60 1.5M3

Set Set Set Set Set Meter Meter Set Set Piece

1 2 1 1 1 300 30 1 1 1

Fig. 11.44 Sketch map of construction process of large diameter pneumatic DTH hammer drill

Before construction, theodolite is used to measure and place the pile position by polar coordinate method, and steelhead or wooden pile is inserted into the center of the measured pile position as a sign. The error of pile position measurement is controlled within 1 cm. When the pile machine is installed in place, the chassis of the machine frame should be flat and stable on the ground. The machine base should be adjusted horizontally and the machine frame should be vertical. The instrument should be used to check and correct the chassis so as to meet the requirement that the deviation of drilling verticality is not more than 1%. The deviation between the center point of steel casing and the center point of pile is not more than 20 mm. During construction, the air compressor is started first, and when the air pressure reaches a certain value, the drilling rig’s internal and external power heads are started for impact drilling. The speed is generally controlled at 17 r=min

264

11

Pneumatic Down-the-Hole Hammer

Fig. 11.45 Pictures of construction site of large diameter pneumatic DTH hammer. a Drill hole; b arriving drill depth; c drill pipe hoisting; d casting concrete; e pile-pulling

11.6

Typical Engineering Cases

265

for the inner screw rod and 7
8 r=min for the outer casing. The screw rod should be lifted to remove the drilling slag once when the drilling footage reaches 5
8 m. When DTH hammer drills into bedrock or bearing stratum, its footage becomes slower and vibration and impulse induction is obvious. After reaching the designed hole depth, the hole is cleared by high-speed air pressure through the bottom slag discharge channel of DTH hammer for 2
3 minutes, and the screw rod is lifted. The drilling slag can be directly discharged out of the hole to complete the hole clearing work. The DTH hammer is put out of the hole.

11.6.4 Analysis of Bit Usage and Phenomenon In the process of drilling 20 drill pipes with large diameter pneumatic DTH hammer, the work of the pneumatic DTH hammer and its bit is generally normal, the spherical teeth of the bit are normal wear and tear, the center teeth are normal, and there is no loss of teeth. This shows that the overall design of the bit is normal and the tooth arrangement design and fixing technology are reasonable. However, the following problems are still found in use: (1) Fracture of Edge Teeth As shown in Fig. 11.46a and b, the fracture of individual edge teeth occurs in use, and the location of the fracture occurs from the fixed position of edge teeth and the bit to the spherical tooth surface, which is consistent with the previous analysis. Under the impact fatigue load, the dangerous point (H point) of the edge teeth may break. As shown in Fig. 11.46c, the fracture failure of the edge teeth can be further

(a)

(c)

(b)

Fracture zone

Fig. 11.46 Fracture of edge teeth in practical use and comparison with theoretical analysis

266

11

Pneumatic Down-the-Hole Hammer

Fig. 11.47 Central spherical tooth unequal working conditions

reduced from the heat treatment and processing technology of the material of the cylindrical teeth. (2) Unmatched design of bottom lip and rock properties As shown in Fig. 11.47, the spherical teeth on the most central arc top have less contact with rock and soil, which means that these spherical teeth do not work under the same working conditions as other teeth. This not only wastes energy but also affects the drilling efficiency of DTH bit. On the one hand, this problem is due to the too large radian of concave surface in bit design. On the other hand, it is also related to the geotechnical properties of drilling. It can be seen that the arc of the drill should be reduced appropriately in the design of the drill bit, and the appropriate type of drill bit can be selected according to the specific geotechnical properties in the construction.

Bibliography 1. Yin Y, Shuai H, Hongjuan L (2013) Analysis of sealing characteristics of pneumatic check valve used for down-the-hole hammer. Fluid Power Trans Control 5:1–4 2. Yin Y (2013) R&D and industrialization of key equipment for construction of underground diaphragm wall and pile foundation of complex stratum. National science and technology support plan, 2012 The report 3. Yin Y-B,Yu L, Zhang H. Hydraulic pneumatic pilehammer: 201020676102.2, 23 Dec 2010 4. Yin Y-B, Wu J, Yue Y. Hydraulic pile extractor device: 200810201704.X, 24 Oct 2008 5. Yin Y-B, Yaobao C. Fundamental research on aerodynamic asymmetry mechanism and high-speed aerodynamic control of gas resistance and gas capacity. Project supported by national natural science foundation of China, Annual report 2012,2013

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6. Huang S (2013) Research on large diameter pneumatic DTH hammer impactor. Master’s thesis of Tongji university 7. Zhang C (2013) Research and design of large-diameter pneumatic downhole hammer ball tooth bit. Master’s thesis of Tongji university 8. Yin Y-B, Luo J-Y, Zhou G-P, Guo C-X (2007) Development of a powder injection pile drawing device with quadrant combination steel pipe. Build Mach (10):71–74 9. Yin Y-B, Huang J-Q, Hu X-H, Guo C-X (2012) A compare of several typical foreign hydraulic system of hydraulic hammers. Build Mach (2):63–66 10. Yaobao Y, Zhichao L, Shuai H, Chuanxin G (2012) Analysis of fast dropping process of hydraulic-pneumatic hammer. Fluid Power Transm Control 2:10–13 11. Yin Y-B, Huang J-Q, Zhang X-Q, Guo C-X, Shen Y-C (2012) Analysis of hydraulic-pneumatic hammer working process. Build Mach (4): 67–71 12. Yin Y-B, Huang J-Q, Wang H-Q, Shen Y-C, Guo C-X (2011) Pile—soil contact analysis via hydraulic hammering process. Chin J Constr Mach 9(4):379–385 13. Yin Y, Hu X, Li Y et al (2010) Mathematical modeling and analysis of hydraulic and pneumatic composite hammer. In: Proceedings of 2010 China construction machinery association piling machinery industry annual meeting, China construction machinery industry association piling machinery branch, Hangzhou, China, vol 11, no 18–19, pp 175–180 14. Yin Y, Huang J, Xiong W et al (2012) Modeling and analysis of hydraulic pile .hammer system. In: Proceedings of the 2011 international conference on advances in construction machinery and vehicle engineering, Chinese construction machinery society, vol 3, pp 90–94 15. Guo C, Yin Y, Ye Y et al. The status quo and development tendency of construction machinery and its hydraulic components in china. In: Proceedings of 7th JFPS international symposium on fluid power Toyama 2008, Sept 15–18, 2008, The Japan fluid power system society, pp 77–82 16. Yin Y, Luo J, Guo C (2007) Challenge of a powder injection pile- drawing device with a quadrant combination steel pipe. In: Proceedings of the 2007 international conference on advances in construction machinery and vehicle engineering, Tongji University Press, pp 257–261 17. Jianzhong W, Yaobao Y (2007) Trend of hydraulic technology in Tongji University. Hydraul Pneum (Japan Industry Press) 46(13):31–37 18. Yaobao YIN (2012) Electro-hydraulic servo control theory and application technology in extreme environment. Shanghai Scientific & Technical Publishers, Shanghai 19. Yin Y. Above 45 MPa research on hydrogen supercharging pressure control and regulation technology. Subject acceptance report of national high-tech research and development plan (National 863 Program)(2017AA05Z119), 30 June 2010 20. Yaobao Y, Mizuno Takeshi W, Jianzhong AK (2007) Pressure characteristics of an asymmetric pneumatic servovalve with uneven underlaps. China Mech Eng 18(18):2169– 2173 21. Yaobao Y, Kenji A (2009) Modelling and analysis of a pneumatic force control system with an asymmetric servovalve. China Mech Eng 20(17):2107–2112 22. Yin Y, Mizuno T, Araki K (2007) Research on an asymmetric pneumatic servovalve. Fluid Power Transm Control (3):7–11 23. Yin Y-B, Li C-M, Araki K (2010) Characteristics of the pneumatic servovalve with symmetric uneven underlaps. J Shanghai Jiaotong University, 44(4):500–505 24. Yin Y, Li C, Han X, Araki K (2008) Flow characteristics at neutral position of pneumatic servovalve with symmetric even underlaps. Fluid Power Transm Control (6):9–12 25. Yaobao Y, Yanpei Z, Phamxuan H (2011) Analysis of a pneumatic high pressure-reducing valve with throttle spool. Fluid Power Transm Control 2:1–5 26. Yin Y-B, Shen L, Zhao Y-P, Dai Y (2010) Research on flow field of high pressure reducing valve of hydrogen vehicle based on CFD. Fluid Mach 38(1):23–26 27. Yin Y-B (2007) Pressure characteristics of a pneumatic servovalve with uneven underlaps of the spool. Chinese Hydraulics and Pneumatics 3:74–77

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28. Xiong Q,Yin K (2011) Development and application of simulation computer software for pneumatic downhole hammer. Petroleum industry press, Beijing 29. Xiong Q,Yin K, Xia H (2005) The development of ZWC—95 mid-pressure air DTH hammer. Rock Drill Mech Pneum Tools (3):22–27 30. Jiang R, Qing S,Wang M (1999) Discussion on large diameter hard rock drilling technique. Explor Eng (Rock Soil Drill Eng) (S1):330–334 31. Zhang G (1991) Pneumatic impact equipment and its design. Mechanical engineering press, Beijing 32. Yang G,Yin H, Fu F (2005) Discussion on large diameter hard rock drilling technique. J Changchun Inst Technol (Science edition) 6(3):7–9 33. Zhao W, Wu X-J, Zheng P, Liu M-H, Cheng C-Y (2009) The application and research of the large diameter air operated down hole hammer in guiding-hole for pile-sinking at the layer of gravel and boulders mixed together. Guangzhou Build 37(5):70–72 34. Jinshi P (2010) Research on drilling process optimization of through DTH hammer. Doctoral dissertation of Jilin University, Changchun 35. Rixin L (2007) Research on drilling technology of DTH hammer and pipe in complex formation. Doctoral dissertation of Chengdu University of technology, Chengdu 36. Dongjiu S (2008) Development of cj-130 two-way pneumatic submersible hammer. Central south university, Changsha 37. Xin J (2005) Rock breaking mechanism—dynamics study and structural improvement of geophysical exploration DTH bit. Southwest petroleum institute 38. Zupei Z, Baochang L (ed) (2004) Rock fragmentation. Beijing: geology press 39. Li H, Sun Y-H (1998) Optimization of the insert arrangement for button bits. Explor Eng (Rock Soil Drill Eng) (3):56–59 40. Xueshe Z, Shengli T (1998) Study on rational tooth distribution of centreless drill bit in geological PDC. Drill Eng Drill Mach 3:56–59 41. Tongwu Z (1996) Impact drilling dynamics. Metallurgical industry press, Beijing 42. Korea Dongyu Machinery co. LTD. Large diameter pneumatic submersible hammer products. http://www.dwdth.com/ 43. Korea Top Drill company. Large diameter pneumatic submersible hammer products. http:// www.dwdth.com/ 44. Lyons WC (2001) Air and gas drilling manual. The McGraw- Hill Companies 45. Chiang LE, Elias DA (2008) A 3D FEM methodology for simulating the impact in rock-drilling hammers.Int J Rock Mech Mining Sci 45(5):701–711 46. Benamar A (2000) Dynamic pile response using two pile- driving techniques. Soil Dyn Earthq Eng 20(4):243–247 47. Chiang LE, Elias DA (2003) Modeling impact in down-the- hole rock drilling. Int J Rock Mech Min Sci 37(4):599–613 48. Hallquist JO (1998) LS- DYNA theoretical manual V970. Livermore Software Technology Corporation, Livermore

Chapter 12

Pneumatic–Hydraulic Pile Driving Hammer

In the early fifteenth century, people used ropes to lift heavy objects for piling. Various diesel hammers and hydraulic hammers emerged as the times require. This chapter introduces a pneumatic–hydraulic pile hammer which combines pneumatic technology with hydraulic technology, including its historical origin, domestic and foreign products, basic principles and key technologies, and the interaction mechanism between pile and soil.

12.1

Pneumatic–Hydraulic Composite Pile Driving Hammer

Pile hammers date back to the fifteenth century (Fig. 12.1). Hydraulic piling hammer has been widely used in the foundation construction of prefabricated piles such as bridges, buildings, ports and wharfs. Compared with traditional diesel pile hammer, hydraulic pile hammer has the characteristics of high efficiency, no exhaust gas emission, low noise, adjustable impact energy, wide range of adaptability, and can be used for underwater pile driving and inclined pile driving. According to the falling mode of hammer head, hydraulic hammer can be divided into single acting hydraulic hammer and double acting hydraulic hammer. Single acting hydraulic hammer, i.e., pile hammer, falls freely under the action of self-weight, such as HH357 series of BSP in Britain and Model 650-3505 hydraulic hammer of HPSI in the United States. Dual acting hydraulic hammer, i.e., pile hammer, under the combined action of self-weight and hydraulic–pneumatic force, falls faster than the acceleration of free falling body, such as S series of IHC in the Netherlands, NH series of Japanese vehicles and HHKA series of JUNTTAN in Finland. According to the tonnage of pile hammer, hydraulic hammer can be divided into three types: large, medium, and small. The weight of pile hammer less than 3 t is small hydraulic hammer, for medium hydraulic hammers the weight of © Springer Nature Singapore Pte Ltd. and Shanghai Scientific and Technical Publishers 2020 Y. Yin, High Speed Pneumatic Theory and Technology Volume II, https://doi.org/10.1007/978-981-15-2202-4_12

269

270

12 Pneumatic–Hydraulic Pile Driving Hammer

Fig. 12.1 Pile driver for lifting heavy objects by rope in the fifteenth century

pile hammer is between 3 and 10 t, and large hydraulic hammers whose weights exceed 10 t. Small hydraulic hammers are suitable for steel and concrete piles with smaller cross-sectional sizes; medium and large hydraulic hammers are suitable for pile foundation construction of port wharf, high-rise buildings, bridges, and other projects. Foreign hydraulic hammer series products have been formed to meet the needs of various foundation constructions. In recent years, the research and development of hydraulic hammers have been carried out in the domestic pile machinery industry, but there are not many large tonnage and high-performance hydraulic hammers, which cannot meet the growing engineering needs. For this reason, foreign hydraulic hammers have been introduced and adopted in domestic foundation construction. Domestic enterprises have successively studied and developed hydraulic hammers. This section compares and analyzes the hydraulic system characteristics, performance, strike frequency and strike energy of several typical foreign hydraulic hammers.

12.1.1 Hydraulic System of Typical Hydraulic Pile Driving Hammer 12.1.1.1

British BSP Single Acting Hydraulic Hammer

British BSP Company produces a single acting hydraulic hammer. Figure 12.2 shows the hydraulic system and outline of CGL370 hydraulic hammer. During the rising stage of the pile hammer, the electromagnetic directional valve 9 is electrified

12.1

Pneumatic–Hydraulic Composite Pile Driving Hammer

271

Fig. 12.2 British BSP single acting hydraulic hammer. a CGL370 hydraulic hammer hydraulic system diagram; b CGL370 hydraulic hammer profile diagram (1—Variable displacement pump; 2—One-way throttle valve; 3, 7, 9—Electromagnetic directional valve; 4—High-pressure accumulator; 5—Hydraulic cylinder; 6—Pilot control valve; 8—Low-pressure accumulator; 10—Electro-hydraulic proportional valve)

and operates in the left position. The electro-hydraulic proportional valve 10 acts as a relief valve to regulate the working pressure of the hydraulic system. The solenoid directional valve 3 is cut off and the upper position is connected. The outlet oil of the high-pressure accumulator 4 and variable pump 1 flows into the left and right cavities of the pilot control valve 6 control cylinder. The left position of the main valve of the pilot control valve 6 works. At this time, the electromagnetic directional valve 7 is electrified, and the left position works. The high-pressure oil flows into the lower chamber of the hydraulic cylinder 5 through the left position of the reversing valve 7. Variable displacement pump and high-pressure accumulator 4 supply oil at the same time, and the piston rod accelerates to rise. The pressure oil in the upper chamber of the hydraulic cylinder 5 passes through the pilot control valve 6, flows into the low-pressure accumulator 8, and returns to the oil tank through the one-way valve. Low-pressure accumulator 8 absorbs return oil and reduces pressure fluctuation. In the descending stage of pile hammer, the electromagnetic directional valve 3 is electrified and the lower position works. The hydraulic oil enters the right chamber of the pilot control valve 6 control cylinder, which makes the pilot control valve 6 work at the right position. The hydraulic oil in the lower chamber of the hydraulic cylinder 5 enters the upper chamber of the hydraulic cylinder 5 through the left chamber of the reversing valve 7, the large chamber of the pilot control valve 6 and the lower position of the electromagnetic directional valve 3, and jointly supplies oil to the upper chamber of the hydraulic cylinder with the hydraulic pump. The hammer body falls freely under the action of gravity. After the

272

12 Pneumatic–Hydraulic Pile Driving Hammer

Fig. 12.3 Finnish JUNTTAN single acting hydraulic hammer. a HHKA hydraulic hammer hydraulic system diagram; b HHKA hydraulic hammer profile diagram (1—Variable displacement pump; 2—Relief valve; 3—One-way valve; 4—Unloading valve; 5—High-pressure accumulator; 6—Electromagnetic reversing valve; 7—Main reversing valve; 8—Hydraulic cylinder; 9—Low-pressure accumulator)

action of pile hammer impacting the pile head is completed, it enters the pressure-retaining stage. After pressure holding, the electromagnetic directional valve 9 is energized and a new working cycle is started.

12.1.1.2

Finnish JUNTTAN Single Acting Hydraulic Hammer

JUNTTAN Finland produces a single acting hydraulic hammer. Figure 12.3 shows the hydraulic system and outline of HHKA hydraulic hammer. During the rising stage of pile hammer, the electromagnetic reversing valve 6 is electrified, and the upper part works, while the main reversing valve 7 lower part works. At this time, variable displacement pump 1 and high-pressure accumulator 5 simultaneously supply oil to the lower chamber of hydraulic cylinder 8. The piston rod accelerates to rise and drives the hammer head to rise. The hydraulic cylinder 8 upper chamber hydraulic oil flows into the low-pressure accumulator 9 return tank. In the descending stage of pile hammer, when the pile hammer reaches the height set by the system, the lower position of electromagnetic reversing valve 6 works. At this time, the upper position of main reversing valve 7 is controlled. High-pressure oil flows into the upper chamber of hydraulic cylinder 8, forming a differential circuit, and the pile hammer drops accelerated. Pressure retention stage of pile hammer. In order to prevent pile rebound, the pile hammer stays on the pile for a very short period of time, that is, the holding time. After the pressure retention, the electromagnetic reversing valve 6 moves to make the main reversing valve 7 change direction, and the pile hammer starts to rise and

12.1

Pneumatic–Hydraulic Composite Pile Driving Hammer

273

Fig. 12.4 Dutch IHC double acting hydraulic hammer. a S-type hydraulic hammer hydraulic system diagram; b S-type hydraulic hammer profile diagram (1—Hammer head; 2—Hydraulic cylinder; 3—One-way valve; 4—Low-pressure accumulator; 5, 7—Directional valve; 6—Nitrogen chamber; 8—High-pressure accumulator; 9—Hydraulic pump; 10—Relief valve)

start a new cycle. When the pile hammer stops working, the relief valve 2 and the unloading valve 4 are opened and connected with the oil tank. The pressure oil from the variable pump 1 flows directly back to the oil tank. The upper and lower chambers of the hydraulic cylinder 8 are connected with the same pressure. The piston stops at the lowest end of the hydraulic cylinder 8.

12.1.1.3

Dutch IHC Double Acting Hydraulic Hammer

Dutch IHC company has introduced a double acting hydraulic hammer. Figure 12.4 shows the hydraulic system and outline of S-type hydraulic hammer. During the rising stage of the pile hammer, the electromagnetic reversing valve 7 closes, the electromagnetic reversing valve 5 is disconnected, the hydraulic cylinder 9 and the high-pressure accumulator 8 simultaneously supply oil to the lower chamber of the cylinder, and the hammer head 1 is raised. At this time, the gas in the nitrogen chamber 6 is compressed to store energy. During the descending stage of the pile hammer, the electromagnetic reversing valve 7 was disconnected, the electromagnetic reversing valve 5 was closed, and the pile hammer began to descend. High-pressure nitrogen in nitrogen chamber releases its stored energy. Under the dual effects of self-weight and nitrogen chamber 6, the pile hammer accelerates to drop and impacts the pile body to complete the impact. During the descending stage of the pile hammer, the hydraulic cylinder 9 simultaneously supplies hydraulic oil to the high-pressure accumulator 8. Because of the long return pipeline, the low-pressure accumulator 4 absorbs the hydraulic oil

274

12 Pneumatic–Hydraulic Pile Driving Hammer

discharged from the hydraulic hammer to ensure the accelerated drop of the pile hammer. When the two solenoid reversing valves are in the closed position, the hydraulic oil returns to the tank and the hydraulic system unloads.

12.1.2 Strike Frequency and Strike Energy 12.1.2.1

Strike Frequency

The strike frequency of hydraulic pile hammer depends on the working time of each stage of pile hammer. The shorter the working time, the higher the strike frequency is. Because the falling acceleration of hydraulic pile hammer is usually designed at a gravitational acceleration or above, the falling time is very short, and the strike frequency mainly depends on the rising time. During the rising process of single acting hydraulic hammer, hydraulic pump and high-pressure accumulator supply oil at the same time, with fast rising speed and high striking frequency, such as CGL370 hydraulic hammer of British BSP Company. When the double acting hydraulic hammer rises, the hydraulic pump simultaneously supplies oil to the cylinder and the high-pressure accumulator. The pile hammer rises slowly and the strike frequency is low, such as the NH hydraulic hammer of Japan Vehicle Company. For Dutch IHC S-type double acting hydraulic hammer and Finnish JUNTTAN HHKA single acting hydraulic hammer, in the rising stage, the hydraulic pump and high-pressure accumulator simultaneously supply oil to the lower chamber of the hydraulic cylinder, with a high strike frequency of 60 beats per minute.

12.1.2.2

Strike Energy

The strike energy is related to the weight of the hammer, the rising height, the pressure of the oil (or gas) in the upper chamber of the hydraulic cylinder, and the magnitude of the strike acceleration. When single acting hydraulic hammer drives piles, the upper chamber of the cylinder is a low-pressure chamber, which is connected with the return oil circuit. It mainly relies on self-weight to strike the pile by approximate free falling, and the impact energy is low. Double acting hydraulic hammer relies on hydraulic pressure or aerodynamic force plus the weight of the hammer body, which generally has larger impact energy. Table 12.1 compares the main performances of several typical hydraulic hammers.

12.1.3 Main Characteristics and Parameters BSP Company, founded in 1905, is the earliest company to develop hydraulic hammer. Its hydraulic hammer is mainly suitable for steel and concrete piles on

12.1

Pneumatic–Hydraulic Composite Pile Driving Hammer

275

Table 12.1 Comparison of main performance of several typical hydraulic hammers Manufacturer

Dutch IHC

JUNTTAN, Finland

British BSP

Model Piling method

S-type Dual action mode

Number of accumulator Cylinder

3 Single acting piston rod

Hydraulic pump Control valve

Variable pump Electromagnetic directional valve Stepless adjustable

2.0 g

HHKA型 Single acting mode 2 Dual acting piston rod Variable pump Pilot control slide valve Stepless adjustable 40 beats per minute 1.2 g

CGL370型 Single acting mode 2 Dual acting piston rod Variable pump Pilot control slide valve Stepless adjustable 38 beats per minute 1.0 g

Maximum

Less

Minimum

Stroke itinerary Maximum stroke strike frequency Maximum falling acceleration Strike energy

60 beats per minute

land or offshore. Its strike energy ranges from 20 to 300 kN
m. Its hydraulic hammer allows the crane to suspend. JUNTTAN Company of Finland began to produce hydraulic pile driver in 1976. The hydraulic hammer is mainly suitable for steel pile, sheet pile and precast concrete pile. The stroke and strike energy of the hammer head can be adjusted steplessly to achieve the best strike efficiency, and the weight of the hammer head can be changed to meet different construction requirements. Dutch IHC Company began to produce double acting hydraulic hammers in 1970. Piling is carried out through the double effects of the weight of the hammer head and the gas pressure in the nitrogen chamber of the hydraulic hammer. The hammer core of the pile driving hammer is forged as a whole, and the fully enclosed hammer structure can be used to drive piles on land and underwater guided by the upper and lower bearings. Its hydraulic hammer can be divided into S series and S C series. It is suitable for steel pile and concrete pile. Its strike energy ranges from 3 to 2300 kN
m. It has been used in large-scale piling projects of CNOOC Ocean Engineering Company, Shengli Oilfield, China Harbor Construction Group First Navigation Engineering Bureau, China Harbor Construction Group Second Navigation Engineering Bureau and China Harbor Construction Group Third Navigation Engineering Bureau. At present, the typical foreign hydraulic hammer products mainly include HH, CX, CG series of BSP in Britain, S and SC series of IHC in the Netherlands and HHK and HHKA series of JUNTTAN in Finland. Table 12.2 is a comparison table of working parameters of several typical hydraulic hammers.

S-90 S-150 SC-50 SC-75 SC-150 HH3 HH5 HH7 CX85 CG165 CG240 HHK 9S HHK 12S HHK 16S HHK 18S HHK 20S

Dutch IHC

JUNTTAN, Finland

British BSP

Hydraulic hammer type

Manufacturer

90 150 50 75 150 35.28 58.8 82.32 883 165 240 132 176 235 265 294

Maximum strike energy/ðkN
m) 50 45 50 45 38 46 42 40 40 34 31 30 30 30 30 30

Maximum stroke frequency/(beats/min) 4.5 7.5 3.3 5.7 11 5.25 7.25 9.25 7 11 16 9 12 16 18 20

Hammer weight/t

Table 12.2 Comparison table of main parameters of several typical hydraulic hammers

2.02 2.02 1.54 1.37 1.37 1.21 1.21 1.21 1.2 1.52 1.52 1.5 1.5 1.5 1.5 1.5

Maximum fall height/m 23 26 20–24 23–27 25–29 16 21 24 24 26 28.5 26 17.5 23 26 27

Working pressure/MPa

220 460 200 250 410 152 180 190 200 385 370 350 603 750 750 750

Hydraulic oil flow rate/(L/min)

276 12 Pneumatic–Hydraulic Pile Driving Hammer

12.1

Pneumatic–Hydraulic Composite Pile Driving Hammer

277

12.1.4 Conclusions (1) By comparing several typical foreign hydraulic hammers, it can be seen that CGL370 type of British BSP and Dutch IHC S-type have higher strike frequency, while HHKA type of JUNTTAN hydraulic hammer in Finland has lower strike frequency. (2) The Dutch IHC S-type and HHKA type of JUNTTAN in Finland both have high impact energy and can be adjusted in a wide range. The CGL370 series of British BSP are single acting hydraulic pile hammers with low impact energy and limited adjustable range. (3) The hydraulic system of Dutch IHC S-type hydraulic hammer is simple and compact. The hydraulic system of other companies is relatively complex. The cylinder of IHC hydraulic hammer is equipped with nitrogen chamber to adjust the pressure so as to adjust the strike energy. The maximum strike acceleration can reach 2 g, which is suitable for large tonnage pile driving.

12.2

High-Speed Pneumatic–Hydraulic Composite Hammer

Pile foundations are widely used in high-rise buildings, bridges, ports, offshore oil production platforms and nuclear power plants. Pile foundations have become the most important form of foundation in China’s engineering construction. In the past, diesel pile hammer was widely used, but because of its shortcomings such as high noise, high pollution, and low efficiency, it has been unable to meet the actual needs of the environment and energy. Now, hydraulic pile hammer and pneumatic–hydraulic composite pile hammer have been gradually adopted. This section analyzes the hydraulic circuit of the pneumatic–hydraulic pile hammer, establishes the dynamic equation of the rising and falling process, analyzes the influence of the main parameters on the working performance of the hydraulic hammer, determines the parameters that meet the design conditions, and the calculation results will play a guiding role in the design and development of the hydraulic hammer.

278

12 Pneumatic–Hydraulic Pile Driving Hammer

12.2.1 Hydraulic System of Pneumatic–Hydraulic Pile Driving Hammer 12.2.1.1

Principle of Pneumatic–Hydraulic Pile Driving Hammer

A complete working cycle of hydraulic–pneumatic pile driving hammer includes three stages: rising, falling and retaining pressure. Figure 12.5 shows the hydraulic circuit diagram of the hydraulic hammer rising stage. The reversing valve 8 opens, the reversing valve 6 closes, and the hydraulic pump 10 starts to supply high-pressure oil to the system. In the initial stage, because the hammer body rises slowly, the high-pressure oil needed for the rod chamber of the hydraulic cylinder is less. Some of the high-pressure oil output from the pump enters the rod chamber of the hydraulic cylinder 2, some enters the high-pressure accumulator 9, and even some of the high-pressure oil may overflow into the tank through the relief valve 11. When the speed of hammer body increases to the point that the fuel supplied by pump alone cannot meet the requirement, the high-pressure accumulator stops filling oil and begins to supply oil to the rod chamber of the hydraulic cylinder. The nitrogen chamber was compressed and stored energy throughout the rise. After the hammer body rises to the maximum stroke, the valve 8 closes and the valve 6 opens. The hammer body accelerates its descent under the double action of

Fig. 12.5 Hydraulic circuit of hydraulic–pneumatic pile driving hammer in rising process (1—Hammer body; 2—Rod cavity of hydraulic cylinder; 3—One-way valve; 4—Back pressure valve; 5—Low-pressure accumulator; 6, 8—Reversing valve; 7—Nitrogen chamber; 9—High-pressure accumulator; 10—Hydraulic pump; 11—Relief valve)

12.2

High-Speed Pneumatic–Hydraulic Composite Hammer

279

Fig. 12.6 Hydraulic circuit of hydraulic–pneumatic pile driving hammer in descending process

compressed nitrogen and its own gravity. When the hammer body descends to the lowest stroke, it hits the pile head. The hydraulic circuit in the descending stage is shown in Fig. 12.6. In this process, the pump 10 still supplies oil to the system. First, it fills the high-pressure accumulator with oil, so that the high-pressure accumulator can reach the predetermined initial working pressure for use in the next cycle, and then the excess high-pressure oil flows back to the tank through the relief valve. In the pressure-retaining stage, in order to prevent the hammer body from bouncing back after the strike action is completed, the reversing valves 6 and 8 are closed at the same time, so that the hammer body stays on the pile for a period of time. After the pressure-retaining stage, the reversing valve 8 is opened, the reversing valve 6 is still closed, and the system enters the next working cycle.

12.2.1.2

Dynamics Model of Rising Process

In the rising stage, high-pressure oil is supplied by hydraulic pump, and the flow equation is satisfied. QP ¼ QR þ QA þ QC where QP Pump output flow; QR Overflow discharge flow;

ð12:1Þ

280

12 Pneumatic–Hydraulic Pile Driving Hammer

QA Flow rate provided by pump to high-pressure accumulator; QC Flow into rod chamber of hydraulic cylinder. The overflow flow of the relief valve is Cd AR x QR ¼ ð p  pc Þ js þ 2PCd x cos R

sffiffiffiffiffi 2p q

ð12:2Þ

where q Cd x AR js R p

Hydraulic oil density; Flow coefficient; Valve orifice perimeter length, x ¼ pdR ; Valve orifice area, AR ¼ p4 dR2 ; Spring stiffness; Angle between the direction of liquid flow and the axis of valve core; Inlet pressure of relief valve, the numerical value is equal to the pressure of accumulator and hydraulic cylinder with rod cavity at the same time; Opening pressure of relief valve.

pc

According to the ideal gas equation, the accumulator gas has n n ¼ pHA VHA pHA0 VHA0

ð12:3Þ

The change of hydraulic oil quantity of high-pressure accumulator is equal to the change of working volume of high-pressure accumulator: "

Z QA dt ¼ DV ¼ VHA  VHA0 ¼

pHA0 pHA

1n

# 1 VHA0

ð12:4Þ

where DV pHA0 ; VHA0 pHA ; VHA n

Accumulator working volume change, for positive oil discharge, for negative oil filling; Inflatable pressure and volume of gas under inflatable pressure of high-pressure accumulator; Pressure of high-pressure accumulator at a certain working hour and volume of gas under that pressure; Gas state index, assumed to be an adiabatic process, is 1.4.

Flow rate of rod cavity in hydraulic cylinder is Z QC dt1 ¼

 p 2 D  d 2 yr 4

ð12:5Þ

12.2

High-Speed Pneumatic–Hydraulic Composite Hammer

281

where D Piston diameter; d Piston rod diameter; yr Rising displacement of hammer. The ideal gas equation of nitrogen chamber of pile hammer is n ¼ pA VAn pA0 VA0

ð12:6Þ

p DV ¼ VA0  VA ¼ D2 yr 4

ð12:7Þ

where pA0 ; VA0 Inflatable pressure of nitrogen chamber and volume at that pressure is applied; pA ; V A Pressure of nitrogen chamber at work and volume at that pressure. Substituting Eq. (12.7) into Eq. (12.6), the pressure of nitrogen chamber in a certain working moment is  pA ¼ pA0

VA0 VA0  p4 D2 yr

n

ð12:8Þ

Substituting Eqs. (12.2), (12.4), and (12.5) into Eq. (12.1), the flow equation is sffiffiffiffiffiffiffiffiffiffiffiffi Z Cd AR x 2pHA0 dt Qp t1 ¼ ðpHA0  pc Þ js þ 2PHA0 Cd x cos R q ð12:9Þ " 1 #  pHA0 n p 2 2 D  d yr þ 1 VHA0 þ 4 pHA where t1 —Rising time. The dynamic equation of the rising stage of the hammer body is as follows: m

 d2 y r p p ¼ pHA D2  d 2  pA D2  mg  Bv 4 4 dt2

ð12:10Þ

where B v m g

Viscous damping coefficient, empirical value; Rising speed of hammer body; Weight of hammer body, including hammer core, piston rod and piston; Gravity acceleration.

Because Bv value is small, the influence of Bv value is neglected in preliminary design. Substituting Eq. (12.8) into Eq. (12.10), it is obtained

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12 Pneumatic–Hydraulic Pile Driving Hammer

m

 n  d2 y r p 2 VA0 p 2 2 D D  mg ¼ p  d  p HA A0 p 2 2 4 dt VA0  4 D yr 4

ð12:11Þ

Simultaneous solving Eqs. (12.10) and (12.11), the dynamic model of the rising stage is obtained as follows: sffiffiffiffiffiffiffiffiffiffiffiffi Cd AR x 2pHA0 Q p t1 ¼ dt ðpHA0  pc Þ js þ 2PHA0 Cd xcosR q " 1 #  pHA0 n p 2 D  d 2 yr þ 1 VHA0 þ 4 pHA  n  d2 y r p VA0 p 2 D  mg m 2 ¼ pHA D2  d 2  pA0 4 dt VA0  p4 D2 yr 4 Z

12.2.1.3

ð12:12Þ

Dynamics Model of Descending Process

In the descent stage, the hammer core accelerates to descend under the double action of compressed nitrogen and gravity. The dynamic equation is as follows: m

 d 2 yf p p ¼ mg þ pA1 D2  Bv  pLA D2  d 2 4 4 dt2

ð12:13Þ

where pA1 Pressure of a certain working moment in nitrogen chamber; pLA Pressure of low-pressure accumulator at a certain working moment; yf Descending displacement of hammer core. The ideal gas equations of the nitrogen chamber are n n pA1 VA1 ¼ pA0 VA0

ð12:14Þ

VA1 ¼ VA0  DV

ð12:15Þ

 p  DV ¼ D2 H  yf 4

ð12:16Þ

where H—Hammer stroke. Substituting Eqs. (12.15) and (12.16) into Eq. (12.14), the pressure of nitrogen chamber in a certain working moment is " pA1 ¼ pA0

VA0   p 2 VA1  4 D H  yf

#n ð12:17Þ

12.2

High-Speed Pneumatic–Hydraulic Composite Hammer

283

where pA1 ; VA1 —Pressure of nitrogen chamber at a certain working moment and gas volume at that pressure in descending stage. For low-pressure accumulators, there are n n ¼ pLA VLA pLA0 VLA0

" DV ¼ VLA  VLA0 ¼

pLA0 pLA

1n

ð12:18Þ

# 1 VLA0

 Z  Z  dyf  p 2 p D  d2  QH dt ¼ D2  d 2 yf  QH dt ¼ 4 4 dt sffiffiffiffiffiffiffi QH d1  4:61 vp

ð12:19Þ

ð12:20Þ

where QH Average flow rate of outlet pipe; vp Average flow rate of hydraulic oil in tubing. Check the hydraulic technical manual, the speed of oil return pipeline is 1:7  4:5 m=s, take 3 m=s; d1 Oil tubing diameter. Substituting Eqs. (12.19) and (12.20) into Eq. (12.18), the hydraulic pressure of the oil in the low-pressure accumulator at a certain working hour is obtained.

pLA

8 > >  n < VLA0 ¼ pLA0 ¼ pLA0 > VLA > :V

LA0

þ

R h

9n > > =

VLA0 p 2 4D



d2

i>  dy f > ;  Q H dt

ð12:21Þ

where pLA0 ; VLA0 Inflatable pressure of low-pressure accumulator and volume at that pressure is applied; pLA ; VLA Pressure of low-pressure accumulator at work and volume at that pressure. Substituting Eqs. (12.17) and (12.21) into Eq. (12.13), the dynamic model of the descending stage is obtained as follows: " #n d 2 yr VA0 p 2   m 2 ¼ mg þ pA0 D 4 dt VA0 þ p4 D2 H  yf " #n  VLA0 p 2 R D  d2  pLA0 p VLA0 þ 4 ðD2  d 2 Þyf  QH dt 4

ð12:22Þ

284

12 Pneumatic–Hydraulic Pile Driving Hammer

12.2.2 Strike Energy The hammer body descends to the lowest position and has the largest descending speed. According to the kinetic energy theorem, the strike energy of the hammer is as follows:  2 1 dyf E¼ m 2 dt

ð12:23Þ

12.2.3 Characteristics of Pneumatic–Hydraulic Pile Driving Hammer According to the hydraulic circuit, the model shown in Fig. 12.7 is built AMESIM test platform. Because of the high pressure and high flow rate of hydraulic system, all valves in the design are cartridge valves. Relative to reversing valve, relief valve, and back pressure valve have less influence on

Fig. 12.7 AMESIM model of hydraulic pile driving hammer

on the the the

12.2

High-Speed Pneumatic–Hydraulic Composite Hammer

285

whole hydraulic system, so only the cartridge valve model of two reversing valves is established on the platform. According to the design requirements, some important parameters can be calculated, such as hammer body mass and stroke, piston rod diameter, strike frequency, etc. For those that cannot be calculated directly, a rough value is obtained by consulting the relevant design criteria, and then the model is run in batches and revised repeatedly. Finally, a set of parameters to meet the design requirements are determined: the maximum working pressure of the system is 32 MPa; the maximum flow rate of the hydraulic pump is 1400 L=min; the inflatable pressure of the high-pressure accumulator is 15 MPa; the nominal volume is 96 L; the low-pressure accumulator inflatable pressure is 0.5 MPa; the nominal volume is 64 L; the hammer core mass is 30 t; the piston diameter is 230 mm; the piston rod diameter is 180 mm; the nitrogen chamber initial volume is 75 L; the nitrogen chamber preload pressure is 16 MPa; the rising time is 1 s; and the falling time is 0.34 s. The main characteristic curves of a working cycle include the velocity, acceleration, displacement, and strike energy of the hammer. Figures 12.8, 12.9, 12.10 and 12.11 show the variation curves of the main performance parameters, respectively. Figure 12.8 is a velocity–time curve, which describes the trend of velocity change in a work cycle; Fig. 12.9 is an acceleration–time curve, which describes the trend of acceleration change in a work cycle; Fig. 12.10 is a displacement–time curve, which describes the trend of displacement change in a period, and reflects the working position of hammer at a certain time. Figure 12.11 is a time curve of strike energy derived from the velocity curve. In the rising stage, the initial velocity of hammer is zero, the pressure of nitrogen chamber is minimum (Fig. 12.8), and the acceleration is maximum. As the hammer rises, the nitrogen chamber is compressed and the acceleration decreases gradually, but the velocity increases. When the velocity reaches its maximum, the acceleration decreases to zero (Fig. 12.9). After that, the hammer began to decelerate, the nitrogen chamber continued to be compressed, and the reverse acceleration gradually increased, so that the hammer’s

Velocity v/(m/s)

Fig. 12.8 Velocity–time curves for a working cycle

Time t/s

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12 Pneumatic–Hydraulic Pile Driving Hammer

Acceleration v/(m/s2 )

Fig. 12.9 Acceleration–time curves for a working cycle

Time t/s

Displacement m

Fig. 12.10 Displacement– time curves for a working cycle

Time t/s

rising speed gradually decreased to zero, at which time the hammer reached its maximum stroke (Fig. 12.10). After that, the hammer body begins to decline, and the acceleration of the hammer body suddenly changes due to the instantaneous decrease of the high-pressure oil pressure in the rod chamber (Fig. 12.9). At this time, the acceleration is the largest. As the nitrogen chamber gradually releases energy, the acceleration decreases, and the speed of the hammer increases until the hammer reaches its maximum at the lowest stroke, when the impact energy reaches its maximum (Fig. 12.11). Through simulation analysis, the parameters obtained meet the design requirements, and the design values are compared with the theoretical values as shown in Table 12.3.

High-Speed Pneumatic–Hydraulic Composite Hammer

287

Strike energy /(kN m)

12.2

Time t/s Fig. 12.11 Strike energy–time curves for a working cycle

Table 12.3 Comparison of design and simulation values Comparison items

Design value

Theoretical value

Comparison items

Design value

Theoretical value

Strike energy

600 kN m

633.3 kN m

1.2 m

1.4 m

Strike frequency

45 Hz

44 Hz

Descending journey Average acceleration

2g

1.84 g

12.2.4 Conclusions (1) Hydraulic–pneumatic composite hammering technology can realize the hammering ability of hydraulic hammer with acceleration of more than 1 g. The average acceleration of the example can reach 1.8 g. Hydraulic–pneumatic composite technology has higher strike frequency and energy under the same stroke and hammer weight. (2) The accumulator of hydraulic hammer plays an important role in reducing pressure fluctuation and increasing strike frequency. (3) Hydraulic cylinder piston, piston rod diameter, nitrogen chamber initial pressure and volume, high and low-pressure accumulator initial pressure and volume parameters directly affect the strike energy of hydraulic hammer, through appropriate parameter design and cooperation to achieve a better design and use effect of hydraulic hammer.

288

12.3

12 Pneumatic–Hydraulic Pile Driving Hammer

Mathematical Model of High-Speed Pneumatic– Hydraulic Composite Hammer

Based on the working principle and structural characteristics of the pneumatic– hydraulic composite hammer, the dynamic mathematical model of the rising and falling stages of the hammer body is established, which can be used as the basis for the research and development of the new type of hydraulic hammer. Pneumatic– hydraulic composite hammering technology can realize the function of pile hitting with acceleration of more than 1G. The strike energy is related to the weight of hammer, acceleration, gas pressure in nitrogen chamber of hydraulic cylinder, maximum height of hammer, and resistance of oil return pipeline.

12.3.1 Overview At present, the hammer theory research based on hydraulic and pneumatic technology is rare. This section mainly analyzes the hydraulic and pneumatic composite hammer theory, mathematical model and basic characteristics of hydraulic hammer based on hydraulic and pneumatic technology. Figure 12.12 shows the schematic diagram of the hydraulic system of the hydraulic–pneumatic acceleration compound hammer. A complete working cycle of hydraulic–pneumatic compound hammer consists of three stages: the rising stage, the descending stage and the pressure-retaining stage of the hammer body. During the rising stage of the hammer body, the electromagnetic reversing valve 6 closes, the electromagnetic reversing valve 4 disconnects, the hydraulic pump 8 and the high-pressure accumulator 7 simultaneously output the hydraulic oil, which is supplied to the lower chamber of the cylinder through the electromagnetic reversing valve 6 to push the piston and drive the hammer body 1 to achieve accelerated lifting. At this time, the gas in the nitrogen chamber 5 at the upper end of the hydraulic cylinder 2 is continuously compressed to store energy. During the descending stage of hammer body, when the hammer body rises to the set stroke height, the electromagnetic reversing valve 6 is disconnected, the electromagnetic reversing valve 4 is closed, and the hammer body begins to descend. In the process of hammer falling, the hydraulic oil in the lower chamber of the hydraulic cylinder is returned to the oil tank through the electromagnetic reversing valve 4 and the pipeline. The high-pressure nitrogen in the nitrogen chamber releases the stored energy and accelerates the drop of the hammer due to the weight of the hammer. When the hammer and the pile contact, it impacts the pile body and completes the impact between the hammer and the pile. In the pressure-retaining stage, after hitting the pile head, the hammer body uses aerodynamic force and gravity to continue to exert pressure on the pile. During the descending stage of the hammer, the hydraulic pump 8 simultaneously supplies hydraulic oil to the high-pressure accumulator 7. Due to the long return pipeline and certain pressure loss, the

12.3

Mathematical Model of High-Speed Pneumatic–Hydraulic Composite Hammer

289

Fig. 12.12 Schematic diagram of hydraulic system of hydraulic–pneumatic acceleration hammer (1—Hammer body; 2—Hydraulic cylinder; 3—Low-pressure accumulator; 4, 6—Electromagnetic directional valve; 5—Nitrogen chamber; 7—High-pressure accumulator; 8—Hydraulic pump; 9— Relief valve). pp —Pump outlet pressure; Qp —Pump flow; pha ; Vha —Pressure and volume of gas in high-pressure accumulator; Qha —Flow rate of hydraulic oil supplied by high-pressure accumulator to hydraulic cylinder; pu —Pressure of nitrogen chamber in upper chamber of hydraulic cylinder; pd —Hydraulic oil pressure in lower chamber of hydraulic cylinder; Au ; Ad —Effective area of rodless cavity and rod cavity of piston rod; Qd —Flow rate of hydraulic oil flowing into lower chamber of hydraulic cylinder; pla ; Vla —Pressure and volume of gas in low-pressure accumulator; Qla —Hydraulic oil flow into low-pressure accumulator; Qh —Hydraulic oil flow to tank; Dp1 ; Dp2 —Pressure loss of electromagnetic direction valve and pipeline working

low-pressure accumulator 3 absorbs part of the hydraulic oil from the lower chamber of the hydraulic cylinder to accelerate the downward movement of the hammer. When the two solenoid reversing valves are in the closed position, the hydraulic oil enters the hydraulic cylinder from the hydraulic pump 8 through the electromagnetic reversing valve 6, and unloads the hydraulic system through the electromagnetic reversing valve 4 return tank and the low-pressure accumulator 3 and the hydraulic oil return tank. The hydraulic–pneumatic acceleration hammer is equipped with a nitrogen chamber in the upper structure of the hydraulic cylinder. The gas pressure can be set independently of the hydraulic system to change the falling acceleration of the hammer and realize stepless control of the hammer energy. Utilizing the compressibility of nitrogen gas, energy is absorbed and stored in the process of hammer rising. The hammer head and piston can adopt the whole forged alloy steel structure and be installed in the fully enclosed cylinder body. The structure of the hammer head and piston is simple and compact. The strike energy of the hydraulic hammer is mainly related to the weight of the hammer, the lifting height of the hammer and the acceleration of the hammer. When the hydraulic hammer drops, the acceleration of the hammer body can reach more than 2.0 g through the dual action of

290

12 Pneumatic–Hydraulic Pile Driving Hammer

compressed gas and the weight of the hammer body, which has larger strike energy. Hydraulic system has high strike frequency through the fast alternation of electromagnetic reversing valve, oil supply and drainage of hydraulic cylinder and nitrogen chamber of hydraulic cylinder. The closed structure can also meet the special requirements of underwater pile driving and inclined pile driving. The stroke of the hammer head can be adjusted arbitrarily according to the soil condition and the strength of the pile, and the strike energy of the hammer can be adjusted. Hydraulic–pneumatic composite hammer components require higher precision and higher price.

12.3.2 Mathematical Model 12.3.2.1

Hammer Body Rising Stage

As shown in Fig. 12.12, during the rising stage of the hammer body, the hydraulic pump and high-pressure accumulator simultaneously supply oil to the lower chamber of the hydraulic cylinder through the electromagnetic directional valve, and the hammer body is lifted. Ignoring the compressibility of hydraulic oil, pipeline expansion and leakage, the flow continuity equation of hammer body in rising stage is as follows: Qd ¼ Qha þ Qp

ð12:24Þ

The flow Rate of hydraulic cylinder is Qd ¼ Ad vu

ð12:25Þ

where vu Qp n q

Rising speed of hammer body; Output flow of hydraulic pump, Qp ¼ nq; Motor speed; Pump displacement.

From Eqs. (12.24) and (12.25), the flow equation of high-pressure accumulator is obtained as follows. Qha ¼ Ad vu  Qp

ð12:26Þ

It is assumed that the pre-charging pressure and volume of high-pressure accumulator are pha0 and Vha0 respectively. When the hydraulic hammer is in the highest working position, the gas pressure of the high-pressure accumulator is the lowest and the volume is the largest, which are pha1 and Vha1 , respectively. When

12.3

Mathematical Model of High-Speed Pneumatic–Hydraulic Composite Hammer

291

the hydraulic hammer is in the lowest working position, the gas pressure of the high-pressure accumulator is the highest and the volume is the smallest, which are pha2 and Vha2 , respectively. Assuming that the gas in the high-pressure accumulator is adiabatic, the equation of state is n1 n1 n1 ¼ pha1 Vha1 ¼ pha2 Vha2 pha0 Vha0

ð12:27Þ

where n1 —Gas variability index of high-pressure accumulator. When the hydraulic hammer is in the highest working position, the gas pressure of the nitrogen chamber of hydraulic cylinder is the highest and the volume is the smallest, which are pa1 and Va1 , respectively. When the hydraulic hammer is in the lowest working position, the gas pressure of the nitrogen chamber of hydraulic cylinder is the lowest and the volume is the largest, which are pa2 and Va2 , respectively. Assuming that the gas in the nitrogen chamber is adiabatic, the equation of state is n2 n2 ¼ pa2 Va2 pa1 Va1

ð12:28Þ

where n2 —Gas variability index of nitrogen chamber. The dynamic equation of hammer body is pd Ad  pu Au  mg ¼ m

d2 y dy þ B þ k ð y þ y0 Þ dt2 dt

ð12:29Þ

where m g y t B k y0

Mass of hammer body; Gravity acceleration; Rising stroke of hammer body; Time of hammer body rises; Viscous damping coefficient; Spring stiffness; Spring precompression.

2 The initial conditions are yð0Þ ¼ 0; ddyt ¼ 0; dd ty2 ¼ 0. t¼0 t¼0

12.3.2.2

Hammer Body Descending Stage

As shown in Fig. 12.12, during the descending stage, the hammer body falls with variable acceleration under the action of gas pressure in the nitrogen chamber and the weight of the hammer body.

292

12 Pneumatic–Hydraulic Pile Driving Hammer

The flow continuity equation of hammer body in descending stage is as follows. Qd ¼ Qla þ Qh

ð12:30Þ

Hydraulic hammers and hydraulic energy devices are often located at different locations ten or even tens of meters apart, and oil return pipelines are generally long. At this time, the pressure loss of oil return pipeline cannot be neglected. When the pressure loss of the return pipeline is considered, the Bernoulli equation can be used to obtain the pressure loss Dp of the fluid flowing through the pipeline with diameter d and length L. It is Dp ¼ k

L qv2 d 2

ð12:31Þ

where k v q d

Resistance loss coefficient along the pipeline; 2 Average flow velocity of oil in return pipeline, and it meets Qh ¼ pd4 v; Liquid density; Pipeline diameter. The flow rate of hydraulic cylinder is Qd ¼ Ad vd

ð12:32Þ

where vd —Hammer body descending speed. The flow equation of low-pressure accumulator is Qla ¼ Ad vd  Qh

ð12:33Þ

It is assumed that the pre-charging pressure and volume of low-pressure accumulator are pla0 and Vla0 , respectively. When the hydraulic hammer is in the highest working position, the gas pressure of the low-pressure accumulator is the lowest and the volume is the largest, which are pla1 and Vla1 , respectively. When the hydraulic hammer is in the lowest working position, the gas pressure of the low-pressure accumulator is the highest and the volume is the smallest, which are pla2 and Vla2 , respectively. Assuming that the gas in the low-pressure accumulator is adiabatic, the equation of state is n3 n3 n3 pla0 Vla0 ¼ pla1 Vla1 ¼ pla2 Vla2

ð12:34Þ

where n3 —Gas variability index of low-pressure accumulator. In the descending stage of hammer body, the gas in nitrogen chamber of hydraulic cylinder satisfies state Eq. (12.28).

12.3

Mathematical Model of High-Speed Pneumatic–Hydraulic Composite Hammer

293

The dynamic equation of the hammer body is mg þ pu Au  pd Ad ¼ m

12.3.2.3

d2y dy þ B þ k ðy þ y 0 Þ dt2 dt

ð12:35Þ

Strike Energy

Assuming that the friction loss and the energy loss during impact are not taken into account when the hammer drops, the kinetic energy of the hammer drops is converted into the strike energy E, the following equation is satisfied: 1 E ¼ mv2d g 2

ð12:36Þ

where g—Piling efficiency.

12.3.3 Characteristic and Example of Pneumatic–Hydraulic Composite Pile Driving Hammer Software Simulink is used to simulate the rising process of hammer body from Eqs. (12.24)*(12.32) and initial conditions. Equations (12.28), (12.30)*(12.36) can be used to simulate the falling process of hammer. The basic parameters of the simulation are the flow rate of the hydraulic pump is 1400 L=min, the initial pressure of the hydraulic cylinder is 29.5 MPa, the maximum stroke of the hammer head is 1.33 m, the minimum working pressure of the nitrogen chamber is 1.9 MPa, and the maximum volume is 68.2 L. Figures 12.13, 12.14, 12.15 and 12.16 show the simulation results of the hammer, the nitrogen chamber of the hydraulic cylinder and the high-pressure accumulator in the rising stage. From Figs. 12.13 and 12.14, it can be seen that the velocity of the hammer increases first and then decreases during the rising stage, and the maximum velocity reaches 2:5 m=s. When the maximum stroke is reached,

Velocity v/(m

Velocity

s)

Displacement

Displacement y/m

Fig. 12.13 Displacement, velocity–time curve of hammer in rising stage

Time t/s

Acceleration

Flow Q/(L min)

Fig. 12.14 Acceleration of hammer and flow–time curve of hydraulic cylinder in rising stage

12 Pneumatic–Hydraulic Pile Driving Hammer

Acceleration v/(m/s 2 )

294

Flow

Time t/s

Pressure Volume Volume V/L

Pressure p/MPa

Fig. 12.15 Gas pressure, volume–time curve of nitrogen chamber of hydraulic cylinder in rising stage

Time t/s

the velocity can be close to zero. The rising acceleration first decreases and then increases in reverse. The maximum forward acceleration is 5:26 m=s2 and the maximum reverse acceleration is 19:9 m=s2 . The rise time of hammer is 0:83 s. As can be seen from Fig. 12.14, the maximum demand flow reaches 2792 L=min. From Fig. 12.15, it can be seen that the gas in the nitrogen chamber is continuously compressed and the pressure is constantly rising, from 1.9 to 19 MPa, and the volume is reduced from 68 to 13 L. From Fig. 12.16, it can be seen that the pressure of high-pressure accumulator increases slightly, then decreases gradually, from the maximum 30.5–27.4 MPa, and its gas volume increases from 95.4 to 103.2 L. Figures 12.17, 12.18, 12.19 and 12.20 show the simulation results of hammer body, nitrogen chamber of hydraulic cylinder, low-pressure accumulator and hammer strike energy in the descending stage. The speed of the hammer body increases continuously during its descent, reaching the lowest point and reaching the speed of 6:4 m=s. The acceleration decreases gradually from the maximum 35:4 to 11:3 m=s2 . The average acceleration of the descent process is 20:1 m=s2 , which is equivalent to the acceleration of 2.05 g and the descent time is 0.33 s. The gas pressure in the nitrogen chamber of the hydraulic cylinder decreases continuously, and the volume of it increases continuously. The pressure of the low-pressure accumulator decreases slightly, then increases continuously, from 1 to 1.3 MPa, and the volume of the accumulator decreases from 24 to 19.5 L. The strike energy can reach 655 kN
m, which meets the predetermined requirements of piling.

Mathematical Model of High-Speed Pneumatic–Hydraulic Composite Hammer

295

Pressure Volume

Volume V/L

Fig. 12.16 Gas pressure, volume–time curve of high-pressure accumulator in rising stage

Pressure p/MPa

12.3

Time t/s

Velocity v/(m

Velocity

s)

Displacement Displacement y/m

Fig. 12.17 Displacement, velocity–time curve of hammer in descending stage

Strike energy

m)

Acceleration

Strike energy E/(kN

Fig. 12.18 Acceleration and strike energy–time curve of hammer in descending stage

Acceleration v/(m/s2 )

Time t/s

Pressure Volume

Velocity v/(m

Pressure p/MPa

Fig. 12.19 Pressure, volume–time curve of nitrogen chamber of hydraulic cylinder in descending stage

s)

Time t/s

Time t/s

12 Pneumatic–Hydraulic Pile Driving Hammer

Pressure Volume

Velocity v/(m

Pressure p/MPa

Fig. 12.20 Pressure, volume–time curve of low voltage accumulator in descending stage

s)

296

Time t/s

12.3.4 Conclusions (1) Hydraulic–pneumatic composite hammering technology can realize the impact capacity of piles with acceleration of more than 1 g. The strike energy is related to hammer mass, strike acceleration, gas pressure in nitrogen chamber of hydraulic cylinder, maximum height of hammer and resistance of return pipeline. A series of pile hammers with various strike energies can be realized by proper design. (2) In the rising stage of hammer body, high-pressure accumulator and hydraulic pump supply oil to the hydraulic cylinder at the same time. The hammer body accelerates to rise, which shortens the rising time of hammer body and increases the strike frequency. When the hammer body rises to its maximum stroke, the volume compression of gas in the nitrogen chamber is the largest and the pressure is the largest. When switching solenoid valve at the maximum stroke, proper design can ensure that the hammer speed is close to zero during switching, and can reduce the impact of hammer on nitrogen chamber. (3) The average acceleration of hammer can be 2 g in the process of falling. Under the condition of the same stroke and hammer weight, the hydraulic–pneumatic composite hammer can achieve greater strike energy and frequency.

12.4

Rapid Piling Process of High-Speed Pneumatic– Hydraulic Composite Hammer

The return oil pipeline of pneumatic–hydraulic hammer is generally over 50 m long. The pressure loss of the pipeline is large and the return oil pressure is high. In the process of hydraulic–pneumatic hammer dropping, the pipeline directly affects the speed of hydraulic hammer dropping, and then affects the strike energy of the system. For this reason, low-pressure accumulator is used to absorb the oil drainage from hydraulic hammer and realize rapid drop. The dynamic model of hydraulic hammer in descending stage is established, and the influence of parameters of return

12.4

Rapid Piling Process of High-Speed Pneumatic–Hydraulic Composite Hammer

297

pipeline and low-pressure accumulator on descending speed and strike energy is analyzed. The law of influence of return pipeline and accumulator parameters on driving speed and strike energy of hydraulic hammer is obtained. This section mainly analyzes the influence of pressure loss of oil return pipeline and its solution. It also analyzes the working process, hammer speed and strike energy with and without low-pressure accumulator in the descending process. It provides theoretical basis for engineering application and new product development.

12.4.1 Principle of Rapid Piling The working process of pneumatic–hydraulic composite pile hammer can be divided into four working stages.

12.4.1.1

Rising Stage

Figure 12.21 shows the hydraulic system diagram of the rising stage of the hydraulic hammer piling process. In the process of pile hammer rising, the electromagnetic reversing valve 7 closes, the electromagnetic reversing valve 5

Fig. 12.21 Hydraulic system diagram of rising stage of hydraulic hammer piling process (1— Hammer head; 2—Hydraulic cylinder; 3—Check valve, 4—Low-pressure accumulator; 5, 7— Electromagnetic directional valve; 6—Nitrogen chamber; 8—High-pressure accumulator; 9— Hydraulic pump; 10—Relief valve). pu —Pressure of nitrogen chamber of hydraulic hammer; Au — Area of rodless cavity of piston; pd —Pressure of hydraulic cylinder; Ad —Area of rod cavity of piston; Qd —Flow rate of hydraulic cylinder

298

12 Pneumatic–Hydraulic Pile Driving Hammer

Fig. 12.22 Hydraulic system diagram of inertia rising stage of hydraulic hammer piling process

disconnects, the hydraulic pump 9 and the high-pressure accumulator 8 jointly output the hydraulic oil, and through the reversing valve 7 enters the lower chamber of the cylinder, the hammer head accelerates to rise. In the rising stage, the hydraulic oil of the low-pressure accumulator 4 flows back to the tank through the long pipeline of the return pipe.

12.4.1.2

Inertial Rising Stage

Figure 12.22 shows the hydraulic system diagram of the inertia rising stage of the hydraulic hammer piling process. When the hydraulic hammer is about to reach the set height, the electromagnetic reversing valve 7 is disconnected. At this time, the hammer head has a certain speed. In order to make full use of energy, the reversing valve 5 is closed, and the hammer head continues to rise relying on inertia. At this time, the hydraulic oil needed in the lower chamber of the hydraulic cylinder 2 is supplied by the low-pressure accumulator 4 through the one-way valve 3. When the hammer reaches the set height, the reversing valve 5 opens.

12.4.1.3

Descending Stage

Figure 12.23 shows the hydraulic system diagram of the descending stage of the hydraulic hammer piling process. The electromagnetic reversing valve 5 opens and the hammer begins to drop. The energy released by nitrogen compressed and stored in nitrogen chamber accelerates the drop of pile hammer under the dual effects of

12.4

Rapid Piling Process of High-Speed Pneumatic–Hydraulic Composite Hammer

299

Fig. 12.23 Hydraulic system diagram for descending stage of hydraulic hammer piling process

gas pressure in nitrogen chamber and weight of hammer body. In the descending stage, the hydraulic oil in the lower chamber of the hydraulic cylinder 2 flows back to the tank through the reversing valve 5 and the long return pipeline. At this time, the low-pressure accumulator 5 is used to absorb the hydraulic oil in the lower chamber of the hydraulic cylinder, so as to realize the rapid descent of the hammer body. During the descending process, the hydraulic pump supplies oil to the high-pressure accumulator 6. The acceleration of hammer striking pile body can reach 2 g. After the hammer strikes the pile body, the reversing valve 5 closes, and the hammer continues to exert pressure on the pile for a certain period of time, that is, to turn into the pressure-retaining stage.

12.4.1.4

Pressure-Retaining Stage

Figure 12.24 shows the hydraulic system diagram of the pressure-retaining stage of the hydraulic hammer piling process. In order to maintain a certain force on the pile body and prevent the elastic rebound of the pile body, after the hydraulic hammer strikes the pile body, the electromagnetic reversing valves 7 and 5 are closed and enter a certain period of pressure-retaining stage. The pressure-retaining time is determined by the holding delay relay in the electrical control system. After the pressure-retaining time is over, the electro-hydraulic reversing valve 7 is energized and transferred to the rising stage for a new round of work cycle.

300

12 Pneumatic–Hydraulic Pile Driving Hammer

Fig. 12.24 Hydraulic system diagram of pressure-retaining stage in hydraulic hammer piling process

12.4.2 Mathematical Model for Descending Stage of Rapid Piling This section mainly establishes the mathematical model of hydraulic–pneumatic pile driving hammer in descending stage. (1) Taking the direction of gravity as the positive direction, the force equilibrium equation of the hydraulic hammer in the descending stage is as follows. mg þ pu Au  pd Ad ¼ m

d2y dy þ B þ Ky dt2 dt

  Ad ¼ p D2  d 2 =4; Ad ¼ pD2 =4 where m B y t K D d

Mass of movable part of hydraulic hammer; Viscous damping coefficient; Drop displacement of hammer body; Descending time; Spring stiffness coefficient; Piston diameter; Piston rod diameter.

ð12:37Þ ð12:38Þ

12.4

Rapid Piling Process of High-Speed Pneumatic–Hydraulic Composite Hammer

301

(2) In the dropping process of hydraulic hammer, the pressure equation between the hydraulic oil from hydraulic cylinder, reversing valve, low-pressure accumulator and return pipeline is as follows. pd ¼ pL þ Dp2 ; pL ¼ Dp1

ð12:39Þ

where Dp1 Pressure drop of return pipeline; Dp2 Pressure drop of reversing valve; pL Pressure of low-pressure accumulator. (3) Low-pressure accumulator plays different roles in different stages of hydraulic hammer. In the rising stage, the absorbed hydraulic oil is flowed back to the tank through the return pipeline by the low-pressure accumulator. In the inertia rising stage, the low-pressure accumulator supplies hydraulic oil to the hydraulic hammer through a one-way valve to prevent suction. In the descending stage, the low-pressure accumulator absorbs oil from the lower chamber of the hydraulic hammer, so that the hammer body can descend rapidly. In the pressure-retaining stage, the absorbed hydraulic oil is flowed back to the tank through the return pipeline by the low-pressure accumulator. The accumulator should be as close as possible to the hydraulic hammer. Due to the short drop time of hydraulic hammer, the variable process of gas in accumulator satisfies the following equation: p0 V0n ¼ p1 V1n ¼ pL VLn

ð12:40Þ

where p0 p1 pL V0 ; V1 ; VL n

Charging pressure of accumulator; Maximum working pressure of accumulator; Working pressure of accumulator at a certain moment; Accumulator gas volume under three different pressures; Gas Variability Index. Because of the short working time, it can be regarded as adiabatic condition, taking n ¼ 1:4.

The flow rate of low-pressure accumulator can be obtained by derivative both sides of Eq. (12.40). Qa ¼

dVL VL dpL ¼ dt npL dt

ð12:41Þ

302

12 Pneumatic–Hydraulic Pile Driving Hammer

Because the drop time of hammer body is very short, the hydraulic oil first flows into the low-pressure accumulator near the hydraulic cylinder. At this time, the pressure loss of the return pipeline is large, and it is too late to flow back to the tank through the return pipeline. Therefore, the low-pressure accumulator has been in the state of oil filling during the drop process. (4) Flow equation of long return pipeline is

Qp ¼

pdp2 4

vp

ð12:42Þ

where dp Long return pipe diameter; vp Average flow rate of hydraulic oil in long return pipeline. (5) Pressure loss of long oil return pipeline is composed of pressure loss along the pipeline and local pressure loss, and its calculation equation is as follows:

Dp1 ¼

X

k

2 2 L qvp X qvp þ n dp 2 2

ð12:43Þ

where k Pressure loss coefficient along pipeline. When the flow state is laminar, k ¼ Re and Re is Reynolds number; n Local pressure loss coefficient; q Density of hydraulic oil, q ¼ 890 kg=m3 . (6) Considering the volume elasticity of the oil in the lower chamber of the hydraulic hammer, the flow continuity equation of the oil is as follows: Ad

dy V dpd  ¼ Qa þ Qp dt b dt

where V Oil volume in lower chamber of hydraulic hammer; b Volumetric modulus of elasticity of hydraulic oil.

ð12:44Þ

12.4

Rapid Piling Process of High-Speed Pneumatic–Hydraulic Composite Hammer

303

(7) The equation of state and the equation of flow of gas in the upper chamber of hydraulic hammer are, respectively, n ¼ pu Vun pu0 Vu0

Qu ¼

dVu Vu dpu dy ¼ ¼ Au dt dt npu dt

ð12:45Þ ð12:46Þ

where pu0 ; Vu0 Inflation pressure and volume of air chamber of hydraulic–pneumatic composite hammer; Vu Volume of air chamber of hydraulic–pneumatic composite hammer when working. (8) Strike energy of hydraulic hammer: Assuming that the friction loss of hydraulic hammer and the energy loss during impact are not considered, the kinetic energy of falling hammer is converted into strike energy, and the energy satisfies the following equation:  2 1 dy E¼ m g 2 dt

ð12:47Þ

where g—Pile efficiency of absorbing strike energy, i.e., pile driving efficiency.

12.4.3 Influencing Factors of Rapid Piling From the above mathematical model Eqs. (12.37)*(12.47), the influence of length and diameter of oil return pipeline and low-pressure accumulator on the descending process and strike energy of hydraulic hammer can be calculated.

12.4.3.1

Influence of Diameter and Length of Oil Return Pipeline

(1) If the length and diameter of the pipeline are different, and the inflatable pressure of the low-pressure accumulator is different. The inflatable pressure of low-pressure accumulator is generally 0:8  0:85 times of the working pressure. The length and diameter of oil return pipe directly affect the pressure loss along the oil return pipeline, but have little influence on the local pressure loss.

12 Pneumatic–Hydraulic Pile Driving Hammer

Velocity v/(m/s)

Displacement y/m

304

Time t/s Fig. 12.25 Influence of diameter of return tubing on displacement and velocity in descending stage v1 ; y1 L ¼ 50 m; dp ¼ 50 mm; v2 ; y2 L ¼ 50 m; dp ¼ 150 mm; v3 ; y3 L ¼ 50 m; dp ¼ 250 mm

(2) The results show that As shown in Fig. 12.25 and Fig. 12.26, the displacement ðy1 ; y2 ; y3 Þ, velocity ðv1 ; v2 ; v3 Þ curves and strike energy diagrams of the pipeline with a length of 50 m and a diameter of 50 mm; 150 mm, and 250 mm, respectively. It can be seen that the thicker the pipeline is, the faster the descent is, the shorter the time is, and the greater the strike energy is. As shown in Fig. 12.27 and Fig. 12.28, the displacement ðy1 ; y2 ; y3 Þ, velocity ðv1 ; v2 ; v3 Þ curves and strike energy charts of the pipeline with a diameter of 150 mm and a length of 100 m; 50 m; and 20 m, respectively. The shorter the pipeline is, the faster the descent is, the shorter the time is, and the greater the strike energy is.

12.4.3.2

Influence of Low-Pressure Accumulator

When the diameter of oil return pipeline is 150 mm and the length is 50 m, the simulation calculation can be carried out with accumulator and without accumulator, respectively, and the strike energy curve of hydraulic hammer shown in Fig. 12.29 can be obtained. It can be seen that when there is no low-pressure accumulator, the hydraulic hammer drops slowly and the strike energy is low. The main reason is that when the hydraulic hammer drops, the return pipeline is too long to drain oil, which leads to the decrease of the speed of the hydraulic hammer and seriously affects the strike energy.

Rapid Piling Process of High-Speed Pneumatic–Hydraulic Composite Hammer

305

Energy E/(N m)

12.4

Time t/s

Displacement y/m

Velocity v/(m/s)

Fig. 12.26 Influence of diameter of return tubing on strike energy 1L ¼ 50 m; dp ¼ 50 mm; 2L ¼ 50 m; dp ¼ 150 mm; 3L ¼ 50 m; dp ¼ 250 mm

Time t/s Fig. 12.27 Influence of length of return tubing on displacement and velocity in descending stage v3 ; y3 dp ¼ 150 mm; v1 ; y1 dp ¼ 150 mm; L ¼ 100 m; v2 ; y2 dp ¼ 150 mm; L ¼ 50 m; L ¼ 20 m

12 Pneumatic–Hydraulic Pile Driving Hammer

Energy E/(N m)

306

Time t/s

Energy E/(N m)

Fig. 12.28 Energy and time curves of descending stages at different return pipe lengths 1dp ¼ 150 mm; L ¼ 100 m; 2dp ¼ 150 mm; L ¼ 50 m; 3dp ¼ 150 mm; L ¼ 20 m

Time t/s Fig. 12.29 Hammer strike energy and time curve in descending stage 1—With low-pressure accumulator; 2—Without low-pressure accumulator

12.4

Rapid Piling Process of High-Speed Pneumatic–Hydraulic Composite Hammer

307

12.4.4 Conclusions Hydraulic–pneumatic pile driving hammer can effectively achieve the impact of large diameter and tonnage piles. The falling speed and strike energy of the hydraulic hammer depend on the parameters of the low-pressure accumulator and the diameter and length of the oil return pipeline. The shorter the length of the return pipe and the larger the diameter are, the greater the strike energy of the hydraulic hammer is. Low-pressure accumulator can quickly absorb the hydraulic oil discharged from the hydraulic hammer, so that the hydraulic hammer drops rapidly, thereby improving the strike energy of the hydraulic hammer.

12.5

Contact Model Pile and Soil

Pneumatic–hydraulic hammer uses the combined action of weight of hammer and pneumatic–hydraulic pressure to achieve the impact of hammer and pile and penetrate the pile into the soil. This section mainly analyzes the impact process of hammer and pile, and the contact between pile and soil after impact. The mathematical model of pile-soil contact process is established by software ANSYS, and the distribution of displacement, stress, shear force and strain in pile-soil contact is obtained by simulation calculation. The comparison between theoretical results and field application shows that the proposed theory and method can well explain the pile penetration process and the changing trend of soil parameters. According to the research results of this section, the phenomena of pile collapse and pile breakage in pile driving construction can also be predicted, prevented and evaluated, which can provide technical support for pile foundation construction.

12.5.1 Finite Element Analysis Model of Pile and Soil The pile driving process of hydraulic hammer can be divided into two stages: the first stage is the impact process of hydraulic hammer on the pile body, in which the pile body obtains certain strike energy; the second stage is the process of pile penetration into soil under strike energy. The energy of the hydraulic hammer before hitting the pile body is related to the instantaneous velocity and the mass of the movable part of the hydraulic hammer body. The expression of the strike energy of the hydraulic hammer is as follows. 1 Et ¼ Mv2 2

ð12:48Þ

308

12 Pneumatic–Hydraulic Pile Driving Hammer

where Et Energy of hydraulic hammer before hitting, that is, strike energy of pile hammer; M Mass of Hammer; v Pre-impact velocity of hydraulic hammer. The energy received by the pile is related to the efficiency coefficient g of the hydraulic hammer in the process of driving the pile. The key to the finite element analysis of bearing capacity of single pile is to determine the mechanical properties of soil and the contact condition between pile and soil. The mechanical properties of soil materials are complex and changeable, and the stress–strain relationship of the same soil body is nonlinear. In this section, Drucker–Prager model for elastic– plastic soil and degree of freedom elastic body model for pile are adopted, and friction characteristics between soil and pile are considered. It is assumed that the interface between pile and soil is a contact element without thickness or thin layer, and it is a rigid–flexible contact form. In the process of modeling and calculation, the following assumptions are made: (1) The hammer body is rigid and the pile is a mass-free deformed body. The material deformation obeys Hooke’s law during the impact process, and the impact coefficient is zero during the impact process. (2) In the process of impact, only the transformation between kinetic energy, potential energy and deformation energy is possible, and other energy losses are neglected. (3) Without considering the propagation of stress wave in the component, it is assumed that the component deforms at the same time everywhere in every instant. The energy method is used to calculate the impact of hammer and pile. When the hammer impacts the pile head with velocity v, the impact force Fd obtained by the pile can be expressed as Fd ¼ kdd

ð12:49Þ

k ¼ EA=l

ð12:50Þ

dd ¼ Kd dst ¼

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi! v2 1þ 1þ dst gdst

dst ¼ G=k

ð12:51Þ ð12:52Þ

where k dd E A l Kd

Stiffness of pile as elastic bar; Maximum deformation of piles under impact load when they are elastic rods. Elastic modulus of pile as impact member; Section area of impact member; Length of pile as impact member; Dynamic load coefficient of pile under impact;

12.5

Contact Model Pile and Soil

309

dst Static displacement produced by gravity acting on an elastic rod in the form of static load; G Hammer weight. Taking a cylindrical steel pipe pile manufactured by a company as an example, the material is Q345C, the elastic modulus E is 206 GPa and the shear modulus G is 79 GPa, Poisson’s ratio l is 0.3, diameter D ¼ 1200 mm, wall thickness d ¼ 150 mm, total length l is 10 m, in which the length of soil infiltration is l1 ¼ 2 m. Figure 12.30 shows a schematic diagram of a cylindrical steel pipe pile in soil. The hydraulic hammer with strike energy of 600 kN
m and hammer weight of 30 t is used to drive the steel pipe pile. From formula (12.48)–(12.52), it can be calculated that the impact force of steel pipe pile is Fd ¼ 1:068  105 kN, and the drop displacement of the pile after each hammering is about 10 mm. The mechanical change process of soil belongs to the problem of material nonlinearity. Because the soil area tends to be infinite, the soil in the semicircular area which is large enough relative to the cross-sectional area of steel piles is taken as the research object in this section. The relationship between this area and the outside soil can be simulated by spring element. When setting up the DP (Drucker– Prager) model in ANSYS, three parameters need to be input: cohesion, internal friction angle, and expansion angle. Table 12.4 shows the soil material parameters of a soft soil foundation in Shanghai. Pile top

Steel pile Soil

Pile tip

Fig. 12.30 Schematic diagram of cylindrical steel pipe pile in soil Table 12.4 Parameters of soil materials Parameter

Modulus of elasticity EX/GPa

Poisson’s ratio PRXY

Cohesion c

Internal friction angle u

Expansion angle /f

Parameter value

5

0.38

10

30

30

310

12 Pneumatic–Hydraulic Pile Driving Hammer

12.5.2 Finite Element Solution of Pile and Soil 12.5.2.1

Dynamic Model Parameter Setting

During the impact process of hydraulic hammer and pile, the hammer transfers the strike energy to the pile through the form of impact. After the impact process, the strike energy propagates in the form of stress wave in the pile and soil. First, the energy is transmitted in the pile, and then the energy is transmitted to the whole soil through the contact between the pile and the soil. Soil is in a complex stress state, and yield condition is a function of stress or strain state. In the theoretical analysis of soil elastic–plastic constitutive relationship, it is assumed that the soil material is isotropic, so the principal stress can be transferred to all directions of action. As long as the magnitude of the principal stress acting at a point is studied, the magnitude of the stress transferred in all directions can be known. The three principal stresses can be described intuitively in three-dimensional space. The Cartesian space coordinate system consisting of three principal stresses as axes is called principal stress space. In the principal stress space, the space diagonal line which is equal to the three coordinate axes is called the isobaric line, while the plane perpendicular to the isobaric line is called the partial plane, and the intersection line between the yield surface and the partial plane is called the yield curve. Drucker–Prager (D-P) yield criterion of DP soil material is adopted in ANSYS. The plastic behavior of soil is assumed to be ideal elastic–plastic and the yield function of soil is  pffiffiffiffiffi pffiffiffiffiffi f I1 ; J2 ¼ J2  aI1  k ¼ 0

ð12:53Þ

where a; k Constants related to cohesion C and internal friction angle u of soil materials; First invariant of soil stress tensor; I1 J2 Second invariant of soil stress tensor. The expressions of I1 , J2 , a; k are as follows: I1 ¼ r1 þ r2 þ r3 J2 ¼

i 1h ðr1  r2 Þ2 þ ðr2  r3 Þ2 þ ðr3  r1 Þ2 6

ð12:54Þ ð12:55Þ

sin u  a ¼ pffiffiffipffiffiffi 3 3 cos hr  sin hr sin u

ð12:56Þ

pffiffiffi 3c cos u p ffiffi ffi k¼ 3 cos hr  sin hr sin u

ð12:57Þ

12.5

Contact Model Pile and Soil

311

Among them, 2r2  r1  r3 hr ¼ a tan pffiffiffi 3ðr1  r3 Þ

! ð12:58Þ

where hr r1 ; r2 ; r3 C

Lode angle, which reflects material’s stress state parameters, ranges 30  30 ; First, second, and third principal stresses in principal stress space; Soil material cohesion.

When hr ¼ 30 , the soil material is in the state of pure tension; when hr ¼ 0 , the soil material is in the state of pure shear; when hr ¼ 30 , the soil material is in the state of pure compression. In the process of Lode angle changing from 30 to 30 , the stress state of soil will change from tension type to compression type. Soil Mohr–Coulomb (M-C) yield criterion can be regarded as a function of Lode angle hr , while D-P yield criterion is M-C criterion when certain hr values are taken. Therefore, according to the different values of hr , the position relationship between D-P criterion and M-C criterion on the partial plane can be obtained. Table 12.5 shows the parametric expressions commonly used in the D-P failure criterion. This table lists several common expressions of a; k. The soil discussed in this section is pure pressure type, and hr is 30 . The ANSYS software first defines the element type and soil parameters, and then creates the grid model for geometric analysis. By utilizing the symmetry of pile and soil, the number of elements can be greatly reduced, the degree of freedom can be reduced, and the solving time can be reduced. In the system composed of soil and pile body, the coordinate origin of the geometric model is the intersection point of the center line of pile body and soil plane, and the cross section of foundation soil is OXY plane. The horizontal direction is X-direction, the right direction is positive, the vertical direction is Y direction, the upward direction is positive, and the radius thickness direction is Z direction. Figure 12.31 shows the finite element meshing model. The geometric model is meshed, then the impact load F is applied, and then the ANSYS solver is used to solve the problem, and the simulation results are obtained.

Table 12.5 Common parametric expressions for D-P failure criteria Category and serial number of criterions

Outer cone

Inner cone

Inner tangential cone

a

pffiffi2 sin u 3ð3sin uÞ

pffiffi 2 sin u 3ð3 þ sin uÞ

sin u pffiffipffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 ð3 þ sin2 uÞ

k

pffiffi6 sin u 3ð3sin uÞ

pffiffi 6c sin u 3ð3 þ sin uÞ

3c sin u pffiffipffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 ð3 þ sin2 uÞ

Equal area cone pffiffi 2 3 sin u ffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffi 2 3pð9sin2 uÞ pffiffi 6 3c sin u ffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffi 2 3pð9sin2 uÞ

312

12 Pneumatic–Hydraulic Pile Driving Hammer

Fig. 12.31 Finite element mesh generation model

12.5.2.2

Results

(1) Figures 12.32, 12.33 and 12.34 show the horizontal displacement contour map, the vertical displacement contour map, and the total displacement contour map, in unit of mm. From the displacement contour map, it can be seen that: As shown in Fig. 12.32, in the horizontal displacement X-direction, the displacement field distribution diffuses outward in a layered form. The soil displacement near the pile tip is the smallest, and gradually increases with the distance from the pile tip, but the displacement distribution area becomes smaller and smaller. The maximum displacement is 96:96 mm and the minimum displacement is 10:85 mm. As shown in Fig. 12.33, in the Y-direction of vertical displacement, the displacement of the pile body and the soil near the pile body is the largest due to the downward impact load of the hammer body on the top of the pile. The displacement at the top of the pile reaches 654:6 mm, and the farther away from the pile, the smaller the displacement of the soil layer. As shown in Fig. 12.34, the total displacement contour map is similar to the Y-direction displacement distribution. The displacement of the pile body and the area near the pile body is the largest. The farther away from the pile, the smaller the displacement is. At a certain distance, the displacement is zero.

12.5

Contact Model Pile and Soil

Fig. 12.32 X-direction (horizontal) displacement contour map

Fig. 12.33 Y-direction (vertical) displacement contour map

313

314

12 Pneumatic–Hydraulic Pile Driving Hammer

Fig. 12.34 Total displacement contour map

(2) Figures 12.35, 12.36, 12.37 and 12.38 show the horizontal stress contour map, the vertical stress contour map, the radial stress contour map and the comprehensive equivalent stress contour map in unit of MPa. From the stress contour map, it can be seen that: As shown in Fig. 12.35, in the X direction of the horizontal stress contour map, the large stress area is concentrated at the pile bottom and around the pile body. The stress of the soil in the central area of the pile bottom is the largest, 255:8 MPa. With the distance from the steel pipe piles, the stress on the soil decreases and the distribution area enlarges gradually. As shown in Fig. 12.36, in the Y-direction of the vertical stress contour map, the stress gradually decreases from the top of the pile to the bottom of the pile and then to the contact soil, and the maximum stress is at the top of the pile, reaching gigapa. As shown in Fig. 12.38, the total stress distribution is similar to that in the Y-direction. The stress decreases gradually from the top of the pile to the bottom of the pile and then to the contact soil, and the maximum stress is at the top of the pile, reaching gigapa. It can be seen that the stress at the contact point between the hammer and the pile is the greatest. Usually, the replacement device is set between the hammer and the top of the pile when driving the pile. (3) Figure 12.39 shows the shear stress contour map in unit of MPa. From the shear stress contour diagram, it can be seen that: The maximum shear stress is 159:6 MPa on the outside of the pile. The soil around the pile gradually diffuses

12.5

Contact Model Pile and Soil

Fig. 12.35 X-direction (horizontal) stress contour map

Fig. 12.36 Y-direction (vertical) stress contour map

315

316

12 Pneumatic–Hydraulic Pile Driving Hammer

Fig. 12.37 Z-direction (radius thickness) stress contour map

Fig. 12.38 Equivalent stress contour map

12.5

Contact Model Pile and Soil

317

Fig. 12.39 Shear stress contour map

outward, and the shear stress decreases gradually, and the distribution area becomes larger and larger. On the contrary, the shear stress of the soil at the bottom of the pile is not large, 17:7 MPa, and there is no obvious change in the Y-direction. (4) Figures 12.40, 12.41 and 12.42 show the horizontal strain contour, the vertical strain contour and the equivalent strain contour, respectively. From the strain contour diagram, it can be seen that: As shown in Fig. 12.40, in the direction of horizontal strain X, the large strain region appears in the soil around the pile body. The strain of pile tip and soil surface near pile body is the largest, reaching 0.31. The strain gradually diffuses outward from the core of the area, and the minimum value is 0.016. As shown in Fig. 12.41, in the vertical strain Y-direction, the maximum strain appears in the soil around the pile body nearest to the ground. It can be seen that it is also the area with the largest deformation, and its value is 0.043. The maximum strain in the opposite direction appears in the soil at the bottom of the pile, and its value is 0.099. As shown in Fig. 12.42, on the contour map of total strain, the maximum strain of the soil penetrating around the pile body is 0.47. The sub-large strain area is the soil around the pile body, and its value is about 0.26. With these two parts as the core, the strain gradually diffuses outward and decreases.

318

12 Pneumatic–Hydraulic Pile Driving Hammer

Fig. 12.40 X-direction (horizontal) strain contour map

Fig. 12.41 Y-direction (vertical) strain contour map

12.5

Contact Model Pile and Soil

319

Fig. 12.42 Equivalent strain contour map

The above theoretical calculation results are consistent with the penetration process of pile driver and the variation trend of soil parameters. According to the research method in this paper, the phenomena of pile collapse and pile breakage in piling construction can also be predicted, prevented, and evaluated.

12.5.3 Conclusions (1) In the process of impact between hydraulic hammer and pile, hydraulic hammer transfers the strike energy to pile through the form of pile driving impact. After the impact of hammer and pile, energy propagates in the form of stress wave in the pile and soil, first in the pile and then to the whole soil. In the process of energy transfer, due to the constant dissipation, the distribution of displacement, stress, shear force and strain of pile and soil changes regularly, and the maximum value appears near the pile body or pile body. With the gradual distance from the pile body, the value gradually decreases, and the distribution range gradually enlarges. (2) In the process of hydraulic hammer piling, the stress distribution of different parts of the pile is quite different. Pile top stress is the largest and pile bottom is the smallest. The penetrating soil part is obviously different from the

320

12 Pneumatic–Hydraulic Pile Driving Hammer

non-penetrating soil part. Replacement driving can be set between pile and hammer to improve the anti-impact performance of pile hammer. From the strain distribution, it can be seen that the strain is the same everywhere in the pile body, which indicates that the deformation intensity of each part is the same. The displacement of the whole pile can be divided into two parts. One is the overall decline caused by impact, the other is the deformation caused by stress, which is different according to different stress. During piling, the displacement field distribution shows that the displacement from pile top to pile bottom decreases gradually. (3) In the process of hydraulic hammer piling, the maximum displacement and stress of soil occur around the pile body, including the pile side and the pile bottom, while the maximum shear force and strain occur around the pile body. The soil around the pile is compressed and deformed by the penetration process of the pile, and the soil on the surface is uplifted upward, which has obvious soil compaction effect. No matter the displacement, stress, shear force or strain are in accordance with the distribution law, that is, the maximum deformation appears around the pile body, and gradually diffuses outward with the maximum area as the core. The farther away from the pile, the smaller the deformation value is. The comparison between the theoretical calculation results and the field application shows that the proposed theory and analysis method can well explain the pile penetration process and the changing trend of soil parameters. According to the above research results, the phenomena of pile collapse and pile breakage in pile driving construction can be predicted, prevented and evaluated, which can provide technical support for pile foundation construction.

Bibliography 1. Yin Y-B, Luo J-Y, Zhou G-P, Guo C-X (2007) Development of a powder injection pile drawing device with quadrant combination steel pipe. Build mach (10):71–74 2. Yin Y-B, Yu L, Zhang H Hydraulic pneumatic pilehammer:201020676102.2[P], 3 Aug 2011 3. Yin Y, Hu X, Li Y, Others (2010) Mathematical modeling and analysis on hydraulic-pneumatic-compound hammers. Chin J Constr Mach 8(4):379–384 4. Yin Y-B, Huang J-Q, Wang H-Q, Shen Y-C, Guo C-X (2011) Pile—soil contact analysis via hydraulic hammering process. Chin J Constr Mach 8(4):67–71 5. Yin Y-B, Huang J-Q, Xiong W, et al (2012) Modeling and analysis of hydraulic pile. hammer system. In: Proceedings of the 2011 international conference on advances in construction machinery and vehicle engineering, Chinese Construction Machinery Society, Shanghai Scientific &Technical Publishers, pp 90–94 6. Yin Y-B, Huang J-Q, Zhang X-Q, Guo C-X, Shen Y-C (2012) Analysis of hydraulic-pneumatic hammer working process. Build Mach (4):67–71 7. Yin Y-B, Huang J-Q, Hu X-H, Guo C-X (2012) A compare of several typical foreign hydraulic system of hydraulic hammers. Build Mach (2):10–13 8. Yin Y-B, Liang Z, Huang S, Guo C-X (2012) Analysis of fast dropping process of hydraulic-pneumatic hammer. Fluid Power Transm Control (2):10–13

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Chapter 13

Application of Pneumatic Technology in Fuel Cell Vehicles

Hydrogen energy was first used in space rocket engines. As a reference theoretical basis for equipment development of self-contained energy devices, this chapter analyzes the application of aerospace hydrogen energy and ultrahigh pressure pneumatic control technology for fuel cell vehicles, studies the key technical problems of carbon fiber wrapped cylinder with aluminum alloy liner and hydrogen delivery system for fuel cell vehicles, and studies the relationship between the driving distance of hydrogen fuel cell vehicle, the hydrogen supply of high-pressure hydrogen transmission system on vehicle and the driving speed and distance. The application of Van der Waals equation of real gas in high-pressure hydrogen transmissionation system in vehicle environment is discussed.

13.1

Pneumatic System and Fuel Cell Hydrogen Transmission System

13.1.1 Overview W. Grove, an Englishman, first put forward the principle of generating electricity by hydrogen and oxygen reaction in 1839, and formed the present hydrogen–oxygen fuel cell. Since the twentieth century, small fuel cells consisting of liquid hydrogen and liquid oxygen have been used in space engines to provide power for space flight. In recent years, environmental protection, global warming, and energy shortage have become an important research topic for the joint efforts of all countries in the world. Especially with the continuous depletion of oil resources in the world, scientists all over the world are competing to study new energy vehicle using hydrogen-based fuel cell to replace oil. Car manufacturers have developed carbon fiber wound aluminum alloy inner liner composite cylinders to store gaseous

© Springer Nature Singapore Pte Ltd. and Shanghai Scientific and Technical Publishers 2020 Y. Yin, High Speed Pneumatic Theory and Technology Volume II, https://doi.org/10.1007/978-981-15-2202-4_13

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hydrogen fuels, and developed ultrahigh pressure pneumatic hydrogen transmission system. Hydrogen storage technology is considered to be the key to the practical utilization of hydrogen energy. The main hydrogen storage modes are high-pressure hydrogen storage, liquefaction hydrogen storage, metal hydride hydrogen storage, activated carbon adsorption hydrogen storage at low temperature, carbon nanotubes hydrogen storage, car-borne methanol reforming for hydrogen production, etc. At present, under the organization of the Ministry of Science and Technology of China, Tsinghua University, Dalian Institute of Chemistry, Chinese Academy of Sciences, Beijing Flying Green Energy, Shanghai Shenli, etc. have carried out research on fuel cell vehicles, and some products have been published. Overseas, most fuel cell vehicle prototypes launched by automobile companies adopt ultrahigh pressure gaseous hydrogen storage, followed by liquid hydrogen storage and methanol catalytic reforming for hydrogen production, and a few adopt metal hydride hydrogen storage and indirect hydrogen production. In order to increase the driving distance and power–weight ratio after one hydrogenation, fuel cell vehicles of major automobile companies have developed 70 MPa ultrahigh pressure hydrogen storage vessel and fuel cell unit by using aerospace composite materials, lightweight high-power solid motor and the filament winding technology of high-pressure gas storage cylinder for reference. Compared with 35 MPa hydrogen storage vessel, the hydrogen storage mass can be increased by 30% and the driving distance can reach 500 km. However, with the commercialization and practicality of fuel cell vehicles, the safety of ultrahigh pressure hydrogen storage vessel in vehicle extreme environment has become a key problem to be solved and studied urgently.

13.1.2 Space Hydrogen Energy Technology and Its Application 13.1.2.1

Application of Hydrogen Energy Technology in Spacecraft

Since the discovery of hydrogen 250 years ago, hydrogen and hydrogen energy have been widely used in industry. Since the twentieth century, with the development of human space industry, hydrogen energy has been successfully used in human space, using liquid hydrogen to launch rockets and space shuttles to explore the mystery of space. China’s self-developed Long March rocket CZ-3A, which employs high thrust hydrogen–oxygen engine, cold helium heating and pressurization technology, low-temperature hydrogen energy double pendulum servo mechanism technology and other key technologies to utilize hydrogen energy, has been comparable to the advanced technology in the world. Among them, the high thrust hydrogen–oxygen engine uses liquid hydrogen and liquid oxygen as the propeller fuel. The specific impulse of the hydrogen–oxygen engine is high, and the

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fuel is nontoxic and pollution-free. The non-coaxial two-turbine pneumatic series structure is adopted in the structure. The helical tube bundle type hydrogen emission cooling and large nozzle with an area ratio of 80:1 are adopted in the nozzle, which effectively improves the performance and reliability of the engine. The cold helium heating and pressurization system use the tank pressurization system to ensure that the inlet of the engine pump has a certain pressure, so that the liquid propellant is continuously supplied to the engine. Using advanced cold helium pressurization technology, the cylinder with high-pressure helium is installed in the liquid hydrogen tank. After liquid hydrogen filling, the cylinder is immersed in liquid hydrogen, and the helium in the cylinder is cooled to the liquid hydrogen temperature (20.3 K). When the engine is working, the cold helium gas is heated through the cold helium heater to the liquid oxygen temperature and then introduced into the liquid oxygen tank for pressurization. The hydrogen energy pneumatic servo mechanism uses the hydrogen pneumatic engine as its energy source. The hydrogen flows from the engine combustion chamber head through the flow limiting tube, and blow the pneumatic blade through a one-way valve, thus driving the hydraulic pump and the two-way swing servo mechanism to achieve three-stage flight attitude control. The servo mechanism uses low-temperature hydrogen as medium and adopts low-temperature hydrogen aero-engine technology with high power–mass ratio. In addition, the autopilot rudder of air defense missile often uses gas rudder. For example, the Soviet S-300 missile initially used gas steering gear; the American Sparrow missile series used solid gas generator to drive gas–liquid accumulator seeker energy and nitrogen to drive gas–liquid accumulator pilot; the British sea javelin ship-to-air missile used gas motor-driven hydraulic steering gear; the Italian Aspide Army general air defense missile used gas turbopump electro-hydraulic energy pilot. The nitrogen cylinder pressure of the air-conditioned actuator of an aircraft is over 65 MPa. The multistage decompression control schemes of pressure 10 and 2.5 MPa are adopted to control gas pressurization and ultrahigh pressure so as to solve the problems of gas storage and transmissionation. Japan is studying passenger aircraft powered by liquid hydrogen and biofuels. In order to prevent the residual gas from mixing into the original system, vacuum filling method is adopted when the hydraulic or pneumatic actuator in the control cabin of missile and rocket is filled with working medium. The high temperature and high-pressure gas pressure used by the aircraft are about 5 MPa and the temperature is 1200 °C. The nitrogen gas storage cylinder pressure of the cold air steering gear is over 65 MPa. A series of key technological breakthroughs have been made in gas pressurization and ultrahigh pressure control technology by adopting two-stage decompression control scheme with pressure of 10 and 2.5 MPa and flow rate of 50 L/min. Hydrogen can be safely stored and transmissioned at ground atmospheric pressure. Space scientists are studying the key technologies of hydrogen storage vessels, control devices and thrusters in the near space and space extreme environment, including the performance of various special pneumatic control valves in the extreme environment, hydrogen storage materials, gas filling and releasing rules and hydrogen aerodynamic thrusters.

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13 Application of Pneumatic Technology in Fuel Cell Vehicles

High-Pressure Cylinders for Self-contained Energy Plants

Most aircraft and mobile equipment require self-contained energy for power plant, so high-pressure cylinders become the preferred object. High-pressure cylinders are classified by materials as steel cylinders, titanium alloy cylinders, plastic inner liner winding cylinders, aluminum alloy inner liner winding cylinders and so on. Conventional cylinders or titanium cylinders were used in the early high-pressure hydrogen storage cylinders, but the heavy weight of the tanks could not meet the requirements of high power–weight ratio of self-contained energy devices. In 1946, the filament wound pressure vessel was first manufactured in the United States by filament winding technology. In 1960, filament winding technology was used in large space solid rocket motor shells, such as Polaris and Saturn, to achieve lightweight and high-strength structure. The U.S. Air Force studied PBO aramid fibers in 1970. Bruswick uses PBO filament wound spherical vessel with an inner diameter of 250 mm and a pressure of 91 MPa. Since the end of 1960s, fiber composite light pressure vessels with metal lining have gradually replaced the traditional all-metal pressure vessels in the field of aerospace. In 1975, the United States began to develop light composite material cylinders, using S-glass fiber/ epoxy, Kevlar/epoxy wound composite cylinders. With the improvement of carbon fiber performance and the decrease of cost, the production of high-pressure vessels with low cost, lightweight, high performance, and good reliability becomes a reality by combining carbon fiber with low-cost manufacturing technology of aluminum lining. Since 1970, Aerospace scientists have developed various advanced composite materials for the extreme environment and high power-to-weight ratio of aircraft, rockets, satellites and spacecraft, such as glass fiber, carbon fiber, silicon carbide fiber, alumina fiber, boron fiber, aramid fiber, high-density polyethylene fiber, and other high-performance reinforcing materials, using high-performance resin, metal, and ceramics as the basal body. Carbon fiber wound case is often used in engine. For example, the combustion chamber shell of the three-stage engine of the American small ground-to-ground intercontinental ballistic missile Dwarf is made of IM-7 carbon fiber/HBRF-55A epoxy resin, and the first stage of the American submarine-launched missile Trident used carbon fiber shell. The United States, Britain, and France began to develop civil composite cylinders in the mid-1980s. There are three main types: circumferential winding or full-winding high-strength glass fiber steel inner cylinder; full-winding aramid fiber or carbon fiber aluminum inner cylinder; full-winding high-strength glass fiber or carbon fiber plastic inner cylinder. In 1991, the Swedes first used carbon fibers instead of glass fibers to wrap aluminum alloy inner liner, which further reduced the mass of wrapped cylinders. In the 1990s, the United States and the United Kingdom mainly developed full-winding carbon fiber aluminum liner cylinders. At present, remarkable progress has been made in the manufacture of ultrahigh pressure gas storage tanks. Internationally, the major companies that started to produce composite cylinders for automobiles earlier are LINCON Company of the United States and DYNETEK Company of Canada. In 2000, Qiantum Company and Lavrence Livermore National Laboratory cooperated to develop an ultrahigh pressure

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hydrogen storage vessel with a pressure of 35 MPa and a hydrogen storage density of 11.3 wt%. After that, an ultrahigh pressure storage tank with a pressure of 70 MPa was developed. IMPCO, California, USA, has increased the pressure of ultralight gas storage tanks to 69 MPa, with a hydrogen storage capacity of 7.5wt%. China began to produce composite materials in 1958. In 1961, glass fiber phenolic resin ablation heat-proof device was used in long-range rocket. Glass fiber and aramid fiber were successfully used in solid motor shell. Glass fiber pressure vessel, aramid fiber and carbon fiber pressure vessel, carbon fiber wound metal inner liner cylinder, etc. are used in various aerospace products. However, high-performance carbon fibers have not yet been fully localized and their applications are limited.

13.1.2.3

Pneumatic Servo Control Technology

Pneumatic servo control originated from attitude control system of missile and rocket vehicle before and after World War II. At that time, gas generator, pneumatic servo valve, and gas motor were used as gas servo system. In the past 50 years, in order to develop space, the United States, the Soviet Union and Europe have used cold air or hot gas-driven pneumatic servo actuators or hydraulic actuators for servo control in thrust vector control and attitude control of space rockets and spacecraft. The actuator of rocket attitude control system uses cylinder output gas source to drive pneumatic blade and hydraulic pump or motor pump to generate hydraulic energy. The storage and emission of gases, gas drive and reliability of gas cylinder system are very important in the extreme environment of aircraft. With the development of aerospace and national defense industry, aerodynamic control with slow response in general industry has developed into pneumatic servo control. Servo control technology with certain response speed, high precision, and high power has emerged as the times require. About 15 years ago, foreign manufacturers successively used hydraulic servo valves to make pneumatic servo valves. Since then, commercial pneumatic servo valves have come out and began to be used in remote control of industrial processes. The study of pneumatic servo mechanism began in 1956. J. L. Shearer of the United States studied the characteristics of pneumatic valve-controlled motor. In 1971, 1979, Araki Kenji, Japan, studied the pneumatic servo valve with force feedback and proposed a compensation scheme of spring and chamber to increase the bandwidth from 70 Hz to 190 Hz. The unequal overlap (positive overlap, zero overlap, and negative overlap) of the sliding valve was also studied. A prototype of small flow pneumatic servo valve was developed in 1981 by Tanaka Hirohisa, Japan, with response time up to 30 ms. In 1997, the author put forward the theory of pneumatic asymmetry control, and successfully developed a prototype of asymmetric high-speed electronic pneumatic servo valve for pneumatic asymmetry phenomenon. The high-speed control of pneumatic system was realized and used in resistance welding machine. Later, pneumatic technology began with the cylinder and its control valve of resistance welding machine. The general industrial pneumatic control pressure is

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0.5 MPa, and the high-pressure control pressure is only about 5 MPa. It is necessary to study the characteristics of ultrahigh pressure gas above 35 MPa and the basic theory of pneumatic control. In recent years, with the transfer of overseas manufacturing industry to China, domestic universities have begun to study aerodynamic control technology. The research on ultrahigh pressure pneumatic technology is rare in China. At present, the main problems that need to be studied in the field of aerodynamic control are as follows: (1) Usually, the pneumatic control pressure is 0.5 MPa, and the high-pressure control pressure is only about 5 MPa. However, most hydrogen-powered vehicles use ultrahigh pressure hydrogen storage. In order to ensure a driving distance of 200 km after one hydrogenation, the hydrogen storage pressure is usually more than 35 MPa. The hydrogen storage pressure should be as high as 70 MPa to ensure the driving distance of 500 km after one hydrogenation. Therefore, it is necessary to study the ultrahigh pressure pneumatic control technology to meet the needs of high-pressure hydrogen storage. (2) In the extreme environment of large temperature range, vibration, impact and centrifuge, the air chamber and its aerodynamic control characteristics will become extremely complex. At present, the research in this field is rare. In addition, aerodynamic asymmetry has seriously hindered the development of high-speed and high-pressure pneumatic control technology, especially the rapid inflation and deflation of high-pressure hydrogen.

13.1.3 Carbon Fiber Winding Cylinder for Fuel Cell Vehicle 13.1.3.1

Fuel Cell Vehicle Hydrogen Storage Device

Fuel cell vehicle (FCV) drives the vehicle directly by the electric energy generated by the chemical reaction between hydrogen and oxygen. The exhaust is pure water, which achieves zero emission. It is a new energy vehicle with high efficiency and cleanliness. Among them, hydrogen storage technology is the key to the practical utilization of hydrogen energy. Nissan Automobile Company started to develop fuel cell vehicles in 1996. In December 2002, Nissan obtained the recognition of high-pressure hydrogen fuel cell vehicles from the Ministry of Land and Resources of Japan. In December 2003, it began to sell fuel cell vehicles X-TRAIL FCV, which was equipped with 35 MPa high-pressure hydrogen fuel device and traveled 350 km. The fuel cell vehicle launched in December 2005 is equipped with 70 MPa hydrogen storage container and fuel cell unit. The hydrogen storage quality has increased by 30% and the driving distance has reached 500 km. Among them, 70 MPa hydrogen storage vessel is made of aluminum alloy inner liner and carbon fiber reinforced plastics (C-FRP) outer winding. C-FRP cylinder adopts high-strength and high-elasticity

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reinforced carbon fibers. The optimum design of full-winding mode is carried out. The cylinder reaches 70 MPa of working pressure. Car running-in test has been carried out in Canada since 2006. At present, the company is carrying out research on the urgent problems to be solved in the industrialization of fuel cell vehicles, such as simplification of complex systems of fuel cell vehicles, practicality of materials, durability and long-life fuel cells. In 2000, General Motors (GM) used metal hydride to store hydrogen. The driving distance of fuel cell vehicles reached 800 km. Dyke Motor Company uses liquid hydrogen storage at a distance of 450 km. Honda Motor Company of Japan launched hydrogen fuel cell vehicle FCX-V by adopting metal hydride hydrogen storage container (LaNi5) in June 1999. In September 2000, it was changed to a 25 MPa high-pressure hydrogen storage vessel with a volume of 100 L. FCX-ZC2 hydrogen fuel cell vehicle was launched in 2006. It uses high-pressure hydrogen storage vessel with working pressure of 34.4 MPa, vessel volume of 156 L (68 + 88), hydrogen storage mass of 3.75 kg and driving distance of 430 km. Toyota Motor Company of Japan began to develop fuel cell vehicles in 1992, and began to develop fuel cell vehicles with high-pressure hydrogen storage containers in 2001. In the same year, a fuel cell bus with a high-pressure hydrogen storage container was launched jointly with Hino Motor Company. In recent years, 35 and 70 MPa high-pressure hydrogen storage containers have been developed, which were certified by Japan High Pressure Gas Safety Association in April 2004 and January 2005 respectively, and used in fuel cell vehicles. Among them, 35 MPa high-pressure hydrogen storage vessel meets the Japanese “Technical Standard for Vehicle Compressed Hydrogen Fuel Device Vessel”. The high-pressure hydrogen storage vessel adopts a new technology to prevent hydrogen penetration, and a layer of nylon resin to prevent hydrogen leakage is added to the inner side of the aluminum liner. The outer side of the aluminum liner adopts high-strength carbon fiber winding technology, which realizes lightweight and high strength. Especially after adding a layer of nylon resin to prevent hydrogen leakage, the hydrogen storage capacity of 35 MPa storage container with the same volume increased by about 10%, and the driving distance of the car increased from 300 to 330 km. Compared with 35 MPa high-pressure hydrogen storage vessel, 70 MPa high-pressure hydrogen storage vessel can increase hydrogen storage to 1.7 times and travel distance to 500 km. In particular, the reliability of hydrogen storage is improved by equipping solenoid shutoff valves in hydrogen storage containers. Toyota is investigating how the freezing of water generated by fuel cells will affect vehicle driving distances, and plans to develop pumps and control valves that work normally at low temperatures of −20 °C.

13.1.3.2

Carbon Fiber Winding Composite Gas Cylinder for Domestic Fuel Cell Vehicle

China began to produce composite materials in 1958 and used glass fiber phenolic resin ablation heat-proof warheads for military long-range rockets in 1961.

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Forty-three Institutes of China Aerospace have successfully adopted glass fibers and aramid fibers on solid motor shells. Glass fiber pressure vessel, aramid fiber pressure vessel and carbon fiber pressure vessel developed independently have been applied to various aerospace products. In the development of metal inner liner pressure vessel, 50 L carbon fiber high-pressure composite winding super high-pressure cylinder for DFH-4 satellite platform has been successfully developed in China. Since 1987, a large number of foreign advanced technologies have been introduced. At present, domestic production capacity of filament wound metal inner liner super high-pressure composite cylinder has been developed, such as raw materials and production technology of various grades of resin and auxiliary materials, large winding system, pultrusion process production line, sheet molding production line, resin reaction injection molding production line, etc. However, high-performance carbon fibers have not yet been domesticated and their applications are limited, and the shell process control means are not advanced. In 1980, the Institute of Composite Materials Hydrogen Storage and High-Pressure Vessel of Tongji University began to study the mechanics of composite materials. The finite element analysis of filament wound rocket engine shell of the Fourth Academy of the Ministry of Space was successfully completed. A 30 MPa carbon fiber wound aluminum liner cylinder was developed independently in China and put into production in Shanghai. Shanghai Aerospace Vehicle Electrical and Mechanical Company began to study various advanced winding high-pressure cylinders in 1999 by using the winding technology of solid rocket motor shell of space launch vehicle. Advanced winding production line has been introduced from the United States, and the certificate of pressure vessel production issued by the National Quality and Technical Supervision Bureau has been obtained. It specializes in manufacturing vehicle-mounted composite material high-pressure vessel. For example, LPG, CNG and other high safety and lightweight composite material high-pressure cylinders, working pressure 20*30 MPa; 30 MPa hydrogen storage composite cylinder has been used in hydrogen energy vehicle of Tongji University. The 35 MPa composite cylinder production line is currently in operation. Beijing Ketaike Technology Co., Ltd. began to produce composite cylinders for automobiles in 2003, which were used in the first hydrogen fuel cell bus in China. The composite cylinder adopts spinning forming aluminum alloy sealed inner liner and carbon fiber composite material as outer layer to ensure the lightweight and high strength of the cylinder. The cylinder has also obtained two national patents, i.e., “Vehicle Composite Gas Cylinder” and “Aluminum Liner for Composite Gas Cylinder”. In 2004, 35 MPa hydrogen cylinder was developed. In addition, Tongji University and Shanghai Aerospace Energy Co., Ltd. began to develop hydrogenation station equipment and carbon fiber wound high-pressure composite cylinders (“863” high-tech project), but the pressure is still only 30 MPa. The hydrogenation pressure of various hydrogenation stations in Japan is 70 MPa. At present, high-pressure hydrogen storage and transmissionation mainly have the following two important topics: The first is the control of ultrahigh pressure hydrogen pressure and its safety; the second is the complex and high cost of high-pressure hydrogenation station and its pneumatic system. Nevertheless, most

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Pneumatic System and Fuel Cell Hydrogen Transmission System

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Fig. 13.1 Carbon fiber wound composite cylinder (Shanghai Aerospace)

of the fuel cell vehicle prototypes launched by major automobile companies in the world use high-pressure gaseous hydrogen storage. In August 2005, the first fuel cell hybrid car “Chao Yue No. 1” developed by China passed the acceptance of “863” project. The car uses reinforced carbon fiber wound aluminum alloy inner liner with cylinder pressure of 30 MPa. The maximum speed is 110 km per hour, and it can drive 210 km continuously. In 2004, the 863 fuel cell city bus developed by Tsinghua University used the high-pressure cylinder developed by Space 625 Research Institute to store hydrogen. The cylinder is an aluminum container, the outer layer is strengthened with carbon fibers, and the inner liner is polymer material resistant to hydrogen embrittlement. The working pressure is 20 MPa and 9 cylinders with volume of 100 L were used. In addition, the city bus is equipped with hydrogen supply safety system, vehicle hydrogen safety system, garage hydrogen safety system and so on. Figure 13.1 shows a carbon fiber wound composite cylinder (Shanghai Aerospace).

13.1.4 Fuel Cell Vehicle Hydrogen Transmission System Figure 13.2 shows the hydrogen delivery system of the Chao Yue Fuel Cell Vehicle developed by Tongji University. Low-pressure hydrogen is supplied to fuel cells through high-pressure hydrogen storage cylinders, cylinder valves and pipelines. Figure 13.3 shows the schematic diagram of a two-stage pneumatic hydrogen transmission system for a hydrogen-powered vehicle. Two-stage high-pressure pneumatic pressure relief valve group is used for pressure relief. When working, the first decompression of the hydrogen delivery system is completed by the high-pressure gas source through the first-stage decompression valve and throttle, and the gas pressure is reduced from 35 to 5 MPa. After the secondary pressure relief valve and throttle, the gas pressure is reduced to 0.16 MPa of the working pressure of the proton exchange membrane fuel cell.

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Fig. 13.2 Fuel cell vehicle hydrogen transmission system (Tongji University)

Fig. 13.3 Schematic diagram of vehicle-borne pneumatic hydrogen transmission system

Inlet

First-stage pressure relief valve Slender orifice 1

Second-stage pressure relief valve Slender orifice 1

Outlet

Grasping the law of hydrogen storage process, following the safety technical specifications of hydrogen storage and strictly following the technical standards of hydrogen energy utilization are the keys to the safe utilization of hydrogen energy. At present, countries are competing to develop fuel cell vehicles with ultrahigh pressure hydrogen storage vessels and carry out road running-in tests around the world, but the evaluation methods of vehicle safety and environmental performance have not yet been unified in the manufacturing industry, domestic and international. The formulation of relevant regulations and norms is an important issue to be solved urgently by cooperation of all countries. Japan has formulated fuel cell vehicle certification and safety standards for fuel cell vehicles since 2003, including safety standards for compressed hydrogen containers for vehicles. The Japan Automobile Industry Association organizes the joint efforts of various domestic automobile manufacturers to formulate various safety standards and technical specifications, and plans to obtain the priority of participating in the formulation of

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relevant international standards. Japan’s Toyota, Nissan, Honda, GM, Hino, Mitsubishi, Suzuki and other automobile companies are conducting road driving tests and data collection of fuel cell vehicles, preparing to develop fuel cell vehicle industry standards and Japan’s fuel cell vehicle national standards. With the advent of the hydrogen energy society, countries are planning to start infrastructure construction such as hydrogen production, hydrogen storage and hydrogen station development. For vehicle-mounted high-pressure hydrogen transmission system, the main problems that need to be studied at present are as follows: 35 and 70 MPa high-pressure pneumatic control devices; aerodynamic control of vehicles in extreme environments such as large temperature range, vibration, impact and centrifuge. At present, the Van der Waals equation of real gas, which was discovered by Dutch in 1873 and won the Nobel Prize in Physics in 1910, is used to calculate the state parameters of high-pressure gases. The revised terms of gas intermolecular force and molecular volume are considered, but there is a big error between the calculated results and the experimental results of Van der Waals equation for high-pressure gas with pressure above 35 MPa. Since the discovery of hydrogen energy technology, researchers at home and abroad have used mature space technology for reference to develop mobile equipment which need self-contained energy, such as fuel cell vehicles, hydrogen energy aircraft, and fuel cell hybrid power engineering machinery. The basic research and development of pneumatic control devices above 35 MPa and ultrahigh pressure hydrogen storage cylinders will become an important research direction in the field of pneumatic control.

13.2

Hydrogen Transmission and Hydrogenation Characteristics of Vehicle-Borne High-Pressure Hydrogen Transmission System Cylinders

Advanced and applicable hydrogen transmission technology is one of the key technologies for hydrogen energy utilization. Hydrogen energy vehicles mostly use high-pressure hydrogen storage. In order to ensure a driving distance of 200 km after one hydrogenation, the hydrogen storage pressure is usually above 35 MPa at present. The hydrogen storage pressure should be as high as 70 MPa to ensure the driving distance of 500 km after one hydrogenation. According to the requirement of driving distance of hydrogen fuel cell vehicle, a mathematical model of the relationship between hydrogen supply of vehicle-mounted high-pressure hydrogen transmission system and driving speed and distance based on the basic theory of charging and discharging gas from fixed container is established, and the parameters relationship of hydrogen storage, hydrogen supply, and driving distance are obtained. The Van der Waals equation of real gas is introduced into the vehicle-mounted high-pressure hydrogen transmission system, and the hydrogen

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transmissionation and hydrogenation characteristics are obtained by comparing the theoretical results with the experimental results. This section establishes the mathematical model of the relationship between working time and pressure in the process of hydrogen transmissionation and hydrogenation of high-pressure cylinders, and obtains the parameters relationship of hydrogen storage mass of cylinders, working time of hydrogenation and driving distance of vehicles in the hydrogen transmission system of clean energy vehicles.

13.2.1 Characteristics of Vehicle-Borne Hydrogen Transmission and Storage System 13.2.1.1

Hydrogen Storage Mode

The main physical properties of gaseous hydrogen and liquid hydrogen are shown in Table 13.1. The comparison of various hydrogen storage modes for fuel cell vehicles is shown in Table 13.2. Gaseous high-pressure hydrogen storage has low cost and easy preparation. Aluminum alloy inner liner and carbon fiber resin reinforced outer layer are commonly used for high-pressure hydrogen storage. Because hydrogen has a very low density, it must be compressed at a higher pressure to store enough mass of gas in a certain volume. At present, the cylinder pressure of fuel cell vehicles abroad is 35 and 70 MPa.

13.2.1.2

Hydrogen Supply Capacity

(1) Working Principle of Fuel Cell Vehicle Fuel cell vehicles generate electricity directly from the chemical reactions of hydrogen and oxygen (or air) in fuel cell stacks. The electric energy generated by fuel cell is supplied to the motor by means of inverters, controllers and other devices. The electric energy is converted into mechanical energy by the motor. Table 13.1 Physical properties of gaseous and liquid hydrogen Hydrogen storage mode Gaseous hydrogen storage Liquid hydrogen storage

Physical property Density/(kg/m3) Temperature/°C 0.0899 70.8

Energy density

Production cost

>−258.2

Low

Relative low

−258.2*259.1

Relative high

High