Ultrasonic motors : technologies and applications 9783642153051, 3642153054

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Mars prober

Automobile

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Cell pnncture

Optical III icroscope

Imegrated USM

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Mobi le phone

Walch

Color copier

Micro robot

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Aerial robot

Ultrasonic motors in applications

Space manipulator

Non-magnetic USM

V shape linear US

Ponable gasoline generator

USM with encoder

Non-contact USM

BUllerfty s hape linear USM

Surve il lance camera platfonn

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Three DOr USM

x- Y slage driven by rotarY USMs

Vacuum cleaning robot

Bar-type USM

Mode conversion type USMs

x-Y stage driven by line..."Ir

Joilll robot

Some ultrasonic motors developed by PDLab at NUAA and their applications

Active Il utter suppression system

MRI syringe

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Chunsheng Zhao

Ultrasonic Motors Technologies and Applications

Chunsheng Zhao

Ultrasonic Motors Technologies and Applications

Wi th 564 figures, 14 of them in eolor

e;e Science Press Beijing .dl

'.£l Springer

Author

Chunsheng Zhao Precision Driving La bora tory Nanjing University of Aeronautics and Astronautics Nanjing 210016, China Email: [email protected]

ISBN 978-7-03-029018-9 Science Press, Beijing Springer ISBN 978-3-642-15304-4 e-ISBN 978-3-642-15305-1 Springer Heidelberg Dordrech t London New Y or k Library of Congress Control Number: 2010932502

© Science Press Beijing and Springer- Verlag Berlin Heidelberg 2011 This work is subject to copyright. All rights arc reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9,1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The usc of general descriptive names, registered names, trademarks, etc. in this publication docs not imply, even in the absence of a specific statement, that such names arc exempt from the relevant protective laws and regulations and therefore free for general use.

Cover design: Frido Sleinen-Broo, EStudio Calamar, Spain Printed on acid- free paper Springer is part of Springer Science+Business MediaC www.springer.com)

Foreword by Jorg Wallaschek Piezoelectric Ultrasonic Motors are fascinating actuators. They combine fast dynamics and high force, can be adopted to a wide range of applications, and offer many advantages in comparison to electromagnetic and other motors. As a consequence, research in the field of piezoelectric ultrasonic motors has attracted scientists from all over the world, and many valuable contributions have been made during the past decades, while some open research questions still wait for an answer. Professor Chunsheng Zhao is a pioneer in the research of piezoelectric ultrasonic motors. His contributions to the scientific progress in this field inelude theoretical and experimental works, whose results arc documented in a large number of scientific papers and patents, and he has also developed many different prototypes of piezoelectric ultrasonic motors. Professor Chunsheng Zhao was the organizer of important international conferences and he also was the founder and director of a very successful research lab which has been recognized world wide. The present book summarizes not only the results of Prof. Zhao's work, but also provides an excellent survey on the state of the art of piezoelectric ultrasonic motors, which can be used as a textbook for teaching as well as a reference for experts in the field. I sincerely wish that it will be of practical usc to a hopefully very large number of readers and that it will also stimulate further research in the field. January 26th, 2010 Prof. Dr. - lng. habil. J brg Wallaschek

Leibniz Universitiit Hannover

Foreword by Bangchun Wen Vibratory utilization engineering is a new branch of vibration science which has been developing since the second half of the 20th century. Due to the academic significance and important applications of the field, the Vibratory Utilization Engineering Specialty Commission (VUESC) was founded in affiliation with the Chinese Association of Vibration Engineering in the last few years. It is aimed at promoting wider use and further development of the discipline through regular conferences and communication. Prof. Chunsheng Zhao, a well-known expert in vibration engineering, has researched vibration and vibration utilization engineering for more than 40 years, and has achieved fruitful results in both theory and engineering applications of vibration. For the past 15 years, Prof. Zhao has specialized in ultrasonic motors. He and his research team have developed more than 30 new types of the ultrasonic motors and corresponding drivers with proprietary intellectual rights, 71 invention patents awarded and pending in China and published more than 500 papers. The project of "Research on Ultrasonic Motor" was awarded multiple national awards and international recognition. Based on the author and his team's research on ultrasonic motors over the last 15 years, this book has summarized their achievements as follows: Firstly, the author explains the systematic theory and design methods in using vibration and wave theory, ineluding motion mechanism, electromechanical coupling model, optimal design of structural parameters, driving, control techniques, etc. Secondly, the author creatively applies advanced analytical methods and techniques into research on the ultrasonic motors, ineluding dynamic substructure, structure dynamic modification, modal identification and separation techniques, etc. Thirdly, this book introduces many key techniques on the ultrasonic motors, ineluding an effective frequency auto-tracking technique solved by the author's team, which has been the bottleneck for application of the ultrasonic motor. The new concept of "anti-resonance/ constant current" put forward by the author is applied to the traveling wave ultrasonic motor, which can promote comprehensive performances of ultrasonic motors. Fourthly, the book shows a series of testing devices developed by the author independently or cooperatively and a series of testing methods provided by the author, which are used for various tests of parts and completed motors. Finally, this book integrates theory with application. It not only ineludes sys-

V111

Ultrasonic Motors Technologies and Ap plicalions

tematic theories and methods, but also introduces many engineering and industrial applications, such as in robots, the active flutter suppression of a two-dimensional wing, an injector for nuclear magnetic resonance, a target recognition/ tracking system, etc. In addition, the author is meticulous and precise in writing. His formula deducing, experimental data and figures are also very convincing. In summary, this book comprehensivcly and systematically describes the technologies of ultrasonic motors and their applications. It will certainly make contributions to this area. I believe the publication of this book will promote the worldwide development and practical applications of ultrasonic motors. I greatly appreciate the effort of my close friend, Prof. Zhao, in writing this wonderful book. Here I cite a Chinese poem as our mutual encouragement: "Although the stabled steed is old, he dreams to run a thousand miles". Mar 1, 2010 Bangchun Wen

Academician of Chinese Academy of Sciences Professor of :'\Iortheastern University

Preface As a new type of micro-motor, the Ultrasonic Motor CUSM) has gained rapid dcvelopmcnt and wide applications sincc thc 1980's. Unlike traditional motors with electromagnetic effect, USM is driven by ultrasonic vibration and piezoelectric effcct. This new typc of motor covcrs a wide rangc of subjects, ineluding mechanical vibration, tribology, matcrials scicncc, mechanical design, elcctronics, automatic control, super-prccision process, etc. Ultrasonic motors havc many cxccllcnt pcrformances and fcaturcs, such as simplc construction, high torquc dcnsity at low specd, dircct drive without spccd reduction gears, quick rcsponsc, better elcctromagnetic compatibility, high holding torque while power off, quict running, efficiency insensitivc to thc sizc, ctc. They have been applicd to robots, precise facilities, medical instruments, etc. With the dcvelopmcnt of new matcrials, advanced technologies, and ncw structural types, the construction and performance of ultrasonic motors will be improvcd, and their applications will bc broadencd to encompass a wider arca ineluding space vehieles, MEMS, semiconductor manufacturing, life sciences, etc. During my visit at MIT from 1992 to 1991, I started research on ultrasonic motors. I came back to China in 1991 and continued my research at Nanjing University of Aeronautics and Astronautics CNUAA). I built a research group in 1995. My group designed and manufactured a traveling wave rotary ultrasonic motor with integrated construction that operated properly by the end of that year. In 1997, I founded the Ultrasonic Motors Rescarch Center CUMRC) in NUAA. In 1999 I organised the First Chinese Workshop on Ultrasonic Motor TechnologiesCCWUMT) with the support of National Natural Sciences Foundation of China C:'\JSFC). The research and development in this area has rapidly advanced since then, and our Research Center was further promoted to be the Ultrasonic Motors Enginecring Rcsearch Center of Jiangsu Provincc in 2001. Fivc years later, the Research Center was renamed the Precision Driving Laboratory CPDLab). The 4th International Workshop on Piczoelectric Materials and Applications in Actuators(IWPMA1) was held at :'\JUAA on September 2007. For the past 15 ycars, our rcscarch team has systcmatically studied ultrasonic motors in depth and obtained considerable achievements, ineluding motion mechanism, electromcchanical coupling modcl, optimal design of structural parametcrs, driving/control techniqucs, ctc. We havc developed more than 30 typcs of ncw ultrasonic motors with indcpendent intellcctual property rights and corresponding drivcrs. Wc have 71 invention patcnts cither awarded or pending in China and more than 500 papers published in journals and conferences. Our projcct of "Rescarch on Ultrasonic Motors" was awarded multiple national awards.

x

Ultrasonic Motors Technologies and Ap plicalions

The achievements of our team can be coneluded as follows:

1. In Theory On the basis of dynamic substructure theory, a comparatively well designed electromechanical coupling model of the traveling wave type rotary ultrasonic motor is built. A new friction interface model which takes the stator teeth and the radial sliding between the stator and rotor into consideration is proposed, and this model can precisely predict the output performances of the type of ultrasonic motors. Instead of the traditional concept of "resonance point/ constant voltage", a new concept of "anti-resonance point/constant current", which is more effective for improving the efficiency and stability of the traveling wave ultrasonic motor, is put forward. An effective frequency automatic tracking method which can lower the instability of ultrasonic motor's speed Cwi thin 5 %) is found, and this method succeeds in solving the bottleneck of the ultrasonic motor Cthe speed is down while the temperature is up). A method on solving the mode mixture in the ncar frequency of the ring stator or circular plate stator is obtained, and this method can improve the stability of the ultrasonic motor. The elliptical motion equation of a bar-type traveling wave ultrasonic motor is derived, and the concept of the effective ellipse orbit which provides a theoretical basis to the optimization of the bar-type ultrasonic motors is proposed. 2. Design Methods An optimal design of structure parameters for the ultrasonic motor put forward and the corresponding software is developed. By applying the sensitivity analysis of structure parameters and structural dynamic modification technique to the design of the ultrasonic motors, an effective method which can adjust the stator's two-phase or multi-phase modal frequencies to be the same. To propose that the design of piezoelectric ceramic components used for the ultrasonic motors should be in accordance with the strain mode of stator instead of its displacement mode; To put forward a method which simultaneously utilizes different types Cextension-contraction, bending and torsion) of vibration modes in-/out-of-planes for designing all types of ultrasonic motor; To point out that the design of the flexible rotor is very important, and to present some design methods for it; To provide the concept and design principles of the step ultrasonic motors. 3. Testing Techniques A series of test devices is developed independently or cooperatively. Some effective test methods have been proposed, ineluding modal tests with nm amplitude in ultrasonic frequency area, load characteristics tests in low speed and ultrasonic frequency area, response time tests at power on/off of the ultrasonic motors, measurement devices and methods of the dynamic friction between the stator and rotor, life test equipment and methods for the ultrasonic motor, test methods of the ultrasonic motor under an extreme environmentC vacuum, high/low temperatures), and performance measurement methods and preparation devices of new friction materials.

Preface

Xl

4. Applications Two series of the ultrasonie motors (TRUM and BTRUM) have been independently developed, and some of them are applied to industry, medical and precision instruments. Moreover, we have also provided prototypes of the ultrasonic motors to some companies. This creates favorable conditions for realizing the ultrasonic motor industrialization in China. At the same time, we have investigated some precision position and constant speed control systems with multi-variable (speed, frequency and phase) using the ultrasonic motors as actuators, ineluding a position control system used for suppressing a two-dimensional wing's flutter, a constant speed control system used for injector of nuelear magnetic resonance, a composite control system based on FN:'\J and Fuzzy control strategies which is used for drivel control a robot, a control system for automatically tracking targets based on vision, a fuzzy control system applied to portable gasoline generators, etc. In addition to the achievements and innovations mentioned above, this book also fully absorbs the most advanced and important results in this area over all world in order to enrich the content. There are 15 chapters in the book. Chapter 1 is an introduction, which describes the history, elassification, characteristics and applications of ultrasonic motors. Chapter 2 describes the fundamentals of piezoelectricity and piezoelectric materials used for ultrasonic motors, and emphasizes the influence of piezoelectric materials on the performance of ultrasonic motors. The knowledge on how to select the piezoelectric materials used for USM is also introduced. Chapter 3 introduces the fundamentals of tribology and tribomaterials used for ultrasonic motors. Some tribomaterials for ultrasonic motors are proposed. In addition, the components and produce process of two new kinds of friction materials are provided. Chapter 4 introduces the fundamentals of vibration and wave applied to ultrasonic motors. It expounds the displacement and strain modes of elastic bodies such as a common rectangular, circular, ring plates, and a cylindrical shell which are used for the stator of ultrasonic motors. The strain mode is a basis of the piezoelectric component polarization division for effectively exciting the stator. Moreover, some important concepts are analyzed, such as the relation between standing wave and traveling wave, mode superposition, mode separation, and wave propagation in elastic bodies. Chapters 5-11 describe the motion mechanism, electromechanical coupling model, optimal design of structure parameters, and testing for different types' ultrasonic motors, ineluding the disk- and bar-type traveling wave ultrasonic motors, the longitudinal-torsion hybrid type ultrasonic motor, the linear ultrasonic motor, the step ultrasonic motor, the non-contact ultrasonic motor, the surface wave ultrasonic motor, etc. These chapters are the most important as they represent our academic achievements and innovations. Chapters 12-13 describe the driving and control techniques of the ultrasonic

Xli

Ultrasonic Motors Technologies and Ap plicalions

motors. Chapter 13 introduces the drive principles and design methods of the drivers in detail, and provides an actual driver circuit which is in use at PDLab. Chapter 14 introduces various tests of the ultrasonic motors, ineluding testing principles, methods, equipment, and the analysis of testing results. Chapter 15 summarizes the practical applications of ultrasonic motors and looks to the future of this area. This book is a comprehensive tutorial for practicing engineers and researchers developing the ultrasonic motor technologies and applications. It is also an up-todate reference for graduates taking a course on ultrasonic motor technologies. Finally, I tell my readers that I will greatly appreciate your comments and s ugges tions. June 5, 2010 Chunsheng Zhao

)JUAA, Nanjing, China

Acknowledgements First, I would like to thank the ='Jational ='Jatural Seiences Foundation of China, 863 High-Tech Projects, and provincial and ministerial funding projects. Many achievements described in this book are credited to these funding sources. I also express my gratitude to my colleagues who have contributed to this book. The followings people are especially thanked for writing and translating some chapters of my manuscripts: H uafeng Li, Chao Chen, Zhiyuan Yao, H ua Zhu, Ying Yang, Zhijun Sun, Weiqing Huang, Jiamei Jin, Yunlai Shi , Lin Yang, Junhui Hu, Jianhui Zhang, Qingjun Ding, Shengqiang Zhou, Yiping Wang, Yi Ding, Congyun Shi, Yubao Li, Jiantao Zhang, Wei Zheng, Hanming Peng, Xiangdong Zhao, Guiqin Wang, Wei Hu, Jian Liu, Dan Lu, Yucong Yin, Qi Chen, Ping Wang, et al. I am grateful to Prof. Bangchun Wen, Prof. Shizhu Wen, Prof. Jue Zhong, Prof. Zhiyun Shen, Prof. Liding Wang, Prof. Haiyan H u, Prof. Tieying Zhou, Prof. Chenglin Gu, Prof. Zhigang Yang, Prof. Fengquan Wang, Prof. Jinhao Qiu, Prof. Zhendong Dai, Prof. Zexiang Li, Prof. Haosu Luo, Prof. Baoku Li, Prof. Shuxiang Dong, Prof. Fei Zhou, Prof. Xiangtao Fan, Prof. Yuhong Liu, Dr. Chunning Zhang, Prof. Zhong You, et al. for their helpful comments and s ugges tions. I also want to express my heartfelt thanks to Prof. Jbrg Wallaschek, Prof. Kenji Uchino, Prof. Piotr Vasiljev, Prof. Scok-Jing Yoon, Prof. Yo shiro Tomikawa, Prof. Minoru Kuribayashi Kurosawa, Prof. Takhiro Takano, Prof. Takshi Maeno, Prof. Aydin Dogan, Prof. J ian S Dai. Dr. Toshiiku Sashida, Dr. Ichiro Ohumura, Dr. David Henderson, and Dr. Ryan Lee. They have provided the book with some papers, data, and photos via the conferences or the lectures in our PDLab. I especially thank Prof. J brg Wallaschek for writing a Foreword in the book. Last but certainly not least, I am grateful to my wife Fengying Wang, my da ugh ter Dr. Ying Zhao, my son-in-law Dr. Charles Zhou, and my grandsons Derek and J esse for their understanding and support to my work, for their care to my life, and for their encouragement to my soul.

Contents 1

Introduction··· ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... 1

1. 1 History of Ultrasonic Motors ................................................ 2 1. 2 Characteristics of Ultrasonic Motors and Their Classification'" ...... 7 1. 2. 1

Characteristics of Ultrasonic Motors

1. 2. 2

Classification of Ultrasonic Motors'" ... ...... ... ...... ... ...... ... ... 8

...... ... ... ... ... ... ... ... ... ... 7

1. 3 Comparison with Electromagnetic Motors

.............................. 12

1. 3. 1

Load Characteristics ................................................... 13

1.3.2 1.3.3

Transient Response Characteristics

Energy Transform of Motors and Their Micromation

............ 13

................................. 14

1. 4 Applications and Development Trends of Ultrasonic Motors 1.4. 1

15

Applications .. · .. · .. · .. · .. · .. · .. · .. · .. · .. · .. · .. · .. · .. · .. · .. · .. · .. · .. · .. · 15

1.4.2 Development Trends ................................................... 15 References ........................................................................... 18

2

Fundamentals of Piezoelectricity and Piezoelectric Materials for Ultrasonic Motors ............................................................... 21

2. 1 Development and Classification of Piezoelectric Materials ............ 21 2.1. 1

Historical Development of Piezoelectric Materials .................. 21

2. 1. 2

Classification of Piezoelectric Materials'" ...... ... ...... ... ...... ... 22

2. 2 Electrical Properties of Piezoelectric Materials

... ... ...... ... ...... ... 23

2. 2. 1

Dielectric Properties and Dielectric Loss

...... ... ...... ... ...... ... 23

2. 2. 2

Ferroelectric Properties and Polarization

...... ... ...... ... ...... ... 25

2. 3 Properties and Constitutive Equations of Piezoelectric Materials

27 ........................... 27

2. 3. 1

Elastic Properties and Their Codficients

2. 3. 2

Piezoelectric Properties and Piezoelectric Equations

............... 28

2. 4 Vibration Types of Piezoelectric Vibrators .............................. 31 ............ 31

2.1. 1

Piezoelectric Vibrators and Their Equivalent Circuits

2. 4. 2

Characteristic Frequencies of Piezoelectric Vibrators ............... 33

2. 4. 3

Coupling Coefficient and Quality Factor

...... ... ...... ... ...... ... 35

2. 5 Applications of Piezoelectric Materials to Ultrasonic Motors 2.5. 1

Piezoelectric Ceramics Used for Ultrasonic Motors

2.5.2

Applications of Piezoelectric Materials to Other Actuators

38

............... 39 41

2. 6 Advances in Novel Piezoelectric Materials .............................. 45

Ultrasonic Motors Technologies and Ap plicalions

XVI

References

3

........................................................................... 17

Fundamentals of Tribology and Tribomaterials for Ultrasonic Motors ........................................................................... 50

3. 1 Basic Tribology

............................................................... 51

3. 1. 1

Surface of Tribomatcrials ............................................. 51

3.1.2

Friction and Its Classification

3. 1. 3

Friction Mechanism ................................................... 53

3.1.4

Wear Mechanism ...................................................... 56

3. 1. 5

Wear Surface for Stator and Rotor of Ultrasonic Motors

....................................... 52

3.2 Tribomaterials Used for Ultrasonic Motors

58

........................... 58

3.2. 1

Basic Requirement, Classification and Selection Principle ......... 58

3. 2. 2

Influence of Composition on Tribological Properties ............... 60

3. 2. 3

Preparation of Tribomaterial .......................................... 62

3. 3 Influence of Tribomaterials on Performance of USM .................. 67 3.3. 1

Influence of Elastic Modulus and Hardness

3. 3. 2

Influence of Friction Coefficient

3. 3. 3

Influence of Anisotropy

........................ 67

...... ... ...... ... ...... ... ...... ... 69

...... ... ...... ... ...... ... ...... ... ...... ... 70

3. 4 Friction Testing for Tribomaterials ....................................... 72 3.1. 1

Quasi-static Friction Testing .......................................... 72

3.4.2

Dynamic Friction Testing ............................................. 73

References

4

........................................................................... 71

Fundamentals of Vibration for Ultrasonic Motors ........................ 76

1. 1 Natural Vibration of Elastic Body··· .................................... 76 4. 1. 1

Longitudinal Vibration of Bars ....................................... 77

1. 1. 2

Characteristics of Natural Modes .................................... 78

4. 1. 3

Torsional Vibration of Shafts

4.1.4

Bending Vibration of Beam

.......................................... 81

... ...... ... ...... ... ...... ... ...... ... 80

1. 1. 5

:"Iatural Vibration of Plates

.......................................... 82

4.1. 6

:"Iatural Vibration of Cylindrical Shells .............................. 92

4. 2 Forced Vibration of Elastic Body··· ....................................... 95 1. 2. 1

Response of PZT Bar to Distributed Electric Field

... ... ...... ... 96

4.2.2

Metallic Bar Excited by Single or Multiple PZT Pieces ............ 99

1.2.3

Response of Beam to Constant Electric Field Intensity

4.2.4

Excitation of Simply Supported Beam by PZT Pieces ............ 101

1.2. 5

Response of Thin Plate to PZT Piece Excitation .................. 106

101

1. 3 Wave Propagation in Elastic Body··· .................................... 107 4.3.1

Basic Concept of Wave

1.3.2

Waves in Elastic Body··· .......................................... 108

............................................. 107

4.3.3

Superposition of Waves

............................................. 110

Contents

XVll

1. 3. 1

Formation of Traveling Waves

4.3. 5

Formation of Elliptical Trajectory··· .............................. ll4

... ...... ... ...... ... ...... ... ...... III

References ........................................................................... 115

5

Operating Mechanism and Modeling of Traveling Wave Rotary Ultrasonic Motor ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... 118 ....................................... ll9

5. 1 Operating Mechanism of TRUM

.................. ll9

5.1.1

Structure and Operation Mechanism of TRUM

5.1.2

Formation of Traveling Wave in Stator

5. 1. 3

Elliptical Motion Trajectory of Surface Points on Stator ......... 123

5. 1. 1

EHect of Amplitude and Phase on Elliptical Motion··· ...... ... ...... 121

........................... 121

5. 1. 5

Polarization Pattern of Piezoelectric Ceramic Components

5. 1. 6

Three-dimensional Motion Analysis of Points on Stator ......... 129

128

5. 2 Semi-Analytical Electromechanical Coupling Model of Stator ...... 132 5. 2. 1

Substructure Division of Stator

.................................... 133

5. 2. 2

Characteristic Matrix of Substructures a and b

5.2.3

Characteristic Matrix of Substructure c··· ........................ 139

... ...... ... ...... 133

5.2.4

Electromechanical Coupling Model of Stator

5.2. 5

Computation Example of Dynamic Characteristics of Stator ...... 141

..................... 110

5. 3 Contact Model Between Stator and Rotor .............................. 111 5.3. 1

Interface Assumptions

............................................. 145

5.3.2

Interface Force and Power Transmission ........................... 146

5.3.3

Interface Energy Loss and Power Transmission Efficiency··· ... 118

5.3.4

Contact Model Between Stator and Rotor

5.3. 5

Contact InterLace Simulation

........................ 149

....................................... 150

5.4 Electromechanical Coupling Model of TRUM and Its Simulation ...... 152 5.1. 1

Electromechanical Coupling Model of TRUM ........................ 152

5.4.2 Performance Simulation of Ultrasonic Motor ..................... 151 References ........................................................................... 158

6

Design and Manufacture of Traveling Wave Rotary Ultrasonic Motors ........................................................................... 161

6. 1 General Design Process of TRUMs

.................................... 161

6.1. 1

Structure Sizes of the Stator

6. 1. 2

Design of Rotor Size

....................................... 162

6.1.3

Choice of Materials ................................................... 166

................................................ 165

6. 2 Operating Modes of Stator and Polarization of PZT Ring 6.2. 1 Design of Modal Frequency .0

6.2.2

••

0

••

0

••

0

••

0

••

0

••

••

0

••

0

••

0

••

0

••

0

••

0.

167 168

Polarization of Piezoelectric Ceramics .............................. 168

6. 3 Structure Form of Stator and Its Modal Analysis 6. 3. 1

0

Structure Form of Stator

... ...... ... ...... 170

...... ... ...... ... ...... ... ...... ... ...... 170

Ultrasonic Motors Technologies and Ap plicalions

XV111

6. 3. 2

Modal Analysis of Stator

...... ... ...... ... ...... ... ...... ... ...... 170

6.4 Sensitivity Analysis and Avoiding of Mode Mixture of Stator ...... 172 6.1. 1

Principle of Sensitivity Analysis .................................... 172

6.4.2

Sensitivity Analysis of Stator for TRUM-60

6. 1. 3

Mode Separation of Stator for TRUM-60

..................... 173 ...... ... ...... ... ...... 174

6. 5 Optimal Design of Stator ................................................... 176 6.5. 1

Optimal Model of Stator ............................................. 176

6. 5. 2

Example of Optimal Design of Stator .............................. 177

6. 6 Adjustment of Two Phase Modal Frequencies of Stator ............ 179 6. 6. 1

Method of Adjusting of Two Phase Modal Frequencies

180

6. 6. 2 Example of Adjusting of Two Phase Modal Frequencies 182 6. 7 Analysis of Flexible Rotor ................................................ 183 6.7. 1

Importance of Rotor's Flexibility for Performance of Motor

185

6.7.2

Comparison of Contact Area of Rigid and Flexible Rotor

188

6.7.3

EHect of Rigid and Flexible Rotors on Mechanical Characteristics

189

6.7.4

Design and Manufacture of Flexible Stator ........................ 189

6.8 Manufacturing Techniques of TRUM ................................. 191 References ........................................................................... 193

7

Bar-type Traveling Wave Rotary Ultrasonic Motors ..................... 195

7. 1 Review of Bar-type Ultrasonic Motor

................................. 195

7. 2 Construction and Motion Mechanism of SDOF Motor ............... 196 7.2. 1 Construction ......................................................... 196 7.2.2

Motion Mechanism ................................................... 197

7. 3 Optimal Design for SDOF Motor

....................................... 201

7.3. 1

Design Principle ...................................................... 201

7.3.2

Dynamic Model

7.3.3

Sensitivity Analysis

7.3.4

Objective Function ................................................... 208

7.3. 5

Optimal Algorithm and Results

...................................................... 203 ................................................ 207 .................................... 208

7.3.6

Modal Frequency Modification of Stator ........................... 210

7. 3. 7

Design of Flexible Rotor ............................................. 213

7. 1 Performance Simulation for SDOF Motor .............................. 211 7. 4. 1

Dynamic Model

...................................................... 214

7.1.2

Contact Analysis

7.4.3

Performance Simulation ............................................. 216

................................................... 215

7.5 Motion Mechanism of 3-DOF Motor .................................... 219 7.5.1

Construction and Operating Modes ................................. 219

7.5.2

Motion Mechanism ................................................... 219

7. 6 Optimal Design of Stator of 3-DOF Motor 7.6. 1

Construction and Objective Function

........................... 221 .............................. 221

Contents 7.6.2

XIX

Optimal Algorithm and Results

.................................... 223

7. 7 Performance Measurement of 3-DOF Motor ........................... 225 7.7. 1

Testing Equipment and Results .................................... 225

7.7.2

Effect of Pre-pressure on Mechanical Performance ............... 226

7. 8 Driving and Control Techniques of 3-DOF Motor

.................. 227

7.8. 1

Configuration of the Control System

7.8.2

Control for Trajectory Tracking .................................... 227

.............................. 227

References······ ... ...... ... ...... ... ...... ...... ... ...... ... ...... ... ...... ... ...... 229

8

Ultrasonic Motor Using Longitudinal-Torsional Hybrid Vibration

8. 1 Current Research of LTUM 8. 2 Multi-mode Type LTUM

... 232 ... ...... ... ...... ... ...... ... ...... ... ...... 232

...... ...... ... ...... ... ...... ... ...... ... ...... 235

8. 2. 1

Motion Mechanism ................................................... 235

8.2.2

Structure Design of Multi-mode Type LTUM ..................... 239

8. 3 Contact Model between Stator and Rotor .............................. 213 8. 3. 1

Modeling of Contact Interface··· ... ...... ... ...... ... ...... ... ...... 243

8. 3. 2

Friction Loss on Interface and Efficiency of LTUM

8.3.3

Simulation of Performance of LTUM .............................. 219

... ... ...... 218

8. 4 Mode Conversion Type Ultrasonic Motor .............................. 255 8.1. 1

Structure and Operation Modes

8.4.2

Principle of Mode Conversion ....................................... 256

.................................... 255

8.1.3 8.4.4

Design of Mode Conversion Type LTUM with Holes ............ 258 Testing ............................................................... 259

References ........................................................................... 262

9

Linear Ultrasonic Motors

.................................................. . 265

9. 1 State of the Art of Linear Ultrasonic Motors

266 9. 2 Linear Ultrasonic Motors Based on d'l Effect ........................ 270 9.2. 1

Linear Ultrasonic Motor with Double Driving Feet ............... 270

9.2.2

Linear Ultrasonic Motor with Single Driving Foot ............... 278

9. 3 Linear Ultrasonic Motors Based on d" Effect ........................ 281 9. 3. 1

Linear Ultrasonic Motor with Butterfly Shaped Stator

9. 3. 2

Linear Ultrasonic Motor with Wheel Shaped Stator

9.4 Contact Model of Standing Wave Type LUSMs 9.1. 1

Steady State Characteristics

282 ... ... ...... 288

..................... 292

....................................... 292

9.4.2

Transient Responses

................................................ 293

9.1.3

Simulation Examples

................................................ 294

9. 5 Synergetic Operation Technique of LUSMs ........................... 296 References ........................................................................... 298

Ultrasonic Motors Technologies and Ap plicalions

xx

10

Step Ultrasonic Motors ...................................................... 300

10. 1 Step Control of USM ...................................................... 301 10. 1. 1 10.1.2

Startup and Shutdown Characteristics of USM ............... 301 Step Control for USM ............................................. 303

10. 1. 3 Factors Impacting on Single-step Positioning Accuracy 308 10. 2 Step USM with Fixed Step length ....................................... 309 10.2. 1 10.2.2

Standing Wave USM Used for Constructing Step USM 309 Modal Rotary Type Step USM ................................. 312

10.2.3

Self-correction Peak Type Step USM

........................... 322

References······ ... ...... ... ...... ... ...... ...... ... ...... ... ...... ... ...... ... ...... 325

11

Other Ultrasonic Motors

................................................... 327

11. 1 )Jon-Contact Type Ultrasonic Motors ................................. 327 11. 1. 1

Classification and Development

11. 1. 2

Operating Principle ................................................ 331

...... ... ...... ... ...... ... ...... 328

11. 1. 3

Design of Non-contact USM

11. 1. 1

Performance Measurement of Non-contact USM ............... 336

... ...... ... ...... ... ...... ... ...... 335

11.1. 5

Design of Non-contact Type USM with Disk Stator

11. 1. 6

Testing of :'\fon-contact USM with Disk Stator

11. 2 Linear Surface Acoustic Wave Motor

337

...... ... ...... 338

................................. 310

11. 2. 1

State of the Art ................................................... 340

11. 2. 2

Surface Acoustic Wave and Its Generation

11.2.3

Operation Mechanism ............................................. 316

..................... 343

References······ ... ...... ... ...... ... ...... ...... ... ...... ... ...... ... ...... ... ...... 349

12

Driving Techniques for Ultrasonic Motors .............................. 351

12.1 Design Requirements for Drivers ....................................... 351 12. 2 Signal Generator ............................................................ 353 12.2. 1

RC Multivibrator

................................................ 353

12.2.2

555 Multivibrator

................................................ 351

12. 2. 3

Voltage Controlled Oscillator .................................... 355

12. 3 Frequency Divider and Phase Splitter ................................. 356 12.3. 1

FDPS Composed by Shift Register .............................. 356

12.3.2

FDPS Composed by CPLD ....................................... 358

12.1 Power Amplifier Techniques ............................................. 359 12. 5 Electrical Characteristics of Ultrasonic Motors

..................... 362

12.5. 1

Experimental Results and System Description .................. 362

12.5.2 12.5.3

Analysis of Vibration States and Driving Method ............ 361 Experimental Results ............................................. 364

12. 6 Influence of Matching Circuit on Performance of Driver 367 12.6. 1 Influence of Matching Capacitor ................................. 368

Contents

XX!

12.6.2

Influence of Matching Inductors ................................. 371

12.6.3

Influence of USM on Driver

.................................... 373

12.7 :'\Jon-transformer Driver with Resonance Voltage Step-up ......... 376 References······ ... ...... ... ...... ... ...... ... ...... ... ...... ...... ... ...... ... ...... 383

13

Control Techniques for Ultrasonic Motors

.............................. 385

13. 1 Classification of Control for Ultrasonic Motors ..................... 385 13. 2 Speed Adjusting Mechanism and Control Methods of USM ...... 387 13.2. 1 Voltage Amplitude Adjusting .................................... 387 13.2.2

Frequency Adjusting

13.2.3

Phase Difference Adjusting ....................................... 389

............................................. 388

13. 3 Stability Control Techniques for Ultrasonic Motor 13.3. 1

............... 390

Principle of Frequency Automatic Tracking ..................... 390

13.3.2

Detection of Amplitude

13.3.3

Implementation of FAT System ................................. 392

.......................................... 392

13.4 Ultrasonic Motors Used as Servo Motors 13.1. 1

Ideal Servo Actuator- USM

........................... 393

.................................... 393

13.4.2

Requirements of Servo Control Using USM

13.4.3

Servo Control System Using USM .............................. 395

.................. 391

13.1.1

PID Controller Using USM ....................................... 397

13.4. 5

Adaptive Controller Using USM ................................. 404

13.1. 6 Fuzzy Controller Using USM .................................... 411 References ........................................................................... 117

14

Testing Techniques for Ultrasonic Motors

... ... ...... ... ...... ... ...... 119

14. 1 Modal Testing for Parts and Assemblies .............................. 419 11. 2 Measurements of Pre-pressure .......................................... 123 11. 3 Measurement of Transient Characteristics ........................... 121 14. 3. 1

Testing Principle··· ...... ...... ... ...... ... ...... ... ...... ... ...... 424

11. 3. 2

Transient Characteristics of USMs .............................. 126

14.4 Measurement of Load Characteristics ................................. 427 11. 1. 1

Measurement System for Load Characteristics··· ...... ... ...... 427

11. 1. 2

Measured Results for TRUM-60 Load Characteristics ......... 129

14. 5 Environmental Testing for Ultrasonic Motors

..................... 430

14.5.2

High/Low Temperature Environmental Testing ............... 130 Vacuum Environment Testing .................................... 132

11.5.3

Load Characteristics of USMs in Vibration Environment······ 434

11.5. 1

11.5.1

Load Characteristics of USMs under Strong Shock ............ 137

14. 5. 5

Test and Analysis of :'\roise from Ultrasonic Motors

438

11.5. 6 Testing of USMs in Hygrothermal Environment ............... 110 11. 6 Life Testing for USMs ................................................... 112

Ultrasonic Motors Technologies and Ap plicalions

XXll

11.6. 1

Design 01 Life Testing System

................................. 112

Life Testing Results and Analysis for TRUM .................. 444 References ........................................................................... 115

14. 6. 2

15

Applications of Ultrasonic Motors in Engineering ..................... 448

15. 1 Applications in Domestic Engineering ................................. 119 15.1. 1

Application in Camera ............................................. 449

15.1.2

Application in Cell Phone

15.1.3

Application in Watch

....................................... 151

............................................. 151

15. 2 Applications in Industrial Engineering ................................. 452 .............................. 152

15.2. 1

Application in Gasoline Generator

15.2.2

Applications in Automobile ....................................... 153

15.2.3

Applications in Robot ............................................. 156

15.2.1

Application in Surveillance Camera PlatIorm

15.2. 5

Applications in Precision Positioning Stage ..................... 159

15. 3 Applications in Biological and Medical Engineering

.................. 458 ............... 461

15.3. 1

Applications in Medical Facility··· .............................. 161

15.3.2

Applications in Biomedical Engineering

15.4 Applications in Aerospace Engineering 15.1. 1

Applications in Aircraft

15.4.2

Applications in Aerospace

........................ 162

.............................. 464

.......................................... 161 ....................................... 466

References ........................................................................... 168

Index ....................................................................................... 469 Appendix A

Natural Vibration Frequencies and Mode Shape Functions of Bars Shafts, Beams, and Plates ... ... ... ... ... ... ... ... ... ... ... 477

Appendix B

Natural Vibration Mode Shapes of Bars, Shafts, and Beams .............................................................................. 179

Appendix C

Natural Vibration Displacement and Strain Mode Shapes of Plates, and Their Nephogram .................................... 187

Symbols The following symbols arc commonly used with the attached definitions. unless otherwise specified in the text. .1':.y.z

Spatial coordinates in a global system

u,v,w

Displacements in

.1':.

U o .Vo .Wo

Ampli tudes in

y. z directions

U o ,Va ,Wo

Displacements of neutral layer

u,v,w

V eloci ties in

u,v,w

Accelerations in

.1':.

.1':.

y. z directions

y. z directions .1':.

y. z directions

Tangential velocity Rotating speed (Speed) Length Width

b

h

Height. thickness

r(r, )

Radius

D(d)

Diameter

m

Mass

Mi

i th modal mass

Ki

i th modal stiffness

Fi

i th modal force

Ci

i th modal darning

S

Area

P E

Density of material

/1

Poisson ratio

G

Shear modulus of elasticity

lUx .Iy .Ie .Ip)

Inertia moment

A k

Wave length

Young's modulus

V clocity of wave propagation Wave number

/1 (/1d •/1, )

Friction coefficient

u(ai • Til )

Stress matrix

(Ci )

F( Fn.F,)

Strain matrix External force

Ultrasonic Motors Technolof{ies and Ap plicalions

XXIV

Friction force

Fr f(x) ,fey) ,fez)

Distributed forces in x, y, z directions

P(P o )

Pre-pressure (Preload)

M(M" Mx,

ｍｾＩ＠

Bending moment Torque

MT

Temporal variable Voltage sign function of the polarization of phase A Voltage sign function of the polarization of phase B Code of the tooth cell

e

Shape function of annular cell Mass matrix of annular cell /j"

Displacement column matrix of substructure a

M"

Mass matrix of substructure a

K"

Stiffness matrix of substructure a

M'

Mass matrix of tooth e

a'

Displacement column matrix of nodes of tooth e Displacement column matrix of inner nodes of tooth e

r

Condensed matrix of tooth e

K'

Condensed stiffness matrix of tooth e

T

Kinetic energy

V

Potential energy

f

Frequency (Friction force) Angular frequency

W

¢n (x)

,

¢n

nth mode shape

fn (W n ) c;p

nth mode frequency

cp( cpn)

Phase angle

q(t)

Mode shape matrix Modal coordinate Bending mode Mechanical quality factor Force coefficient matrix Shape function matrix Variable for structure design Sensitivity with respect to p; Relative sensitivity with respect to Pi Radial shape function matrix Node column matrix of annular cell Stiffness matrix of annular cell Displacement column of substructure b Mass matrix of substructure b Stiffness matrix of substructure b

Symbols

xxv

K'

Stiffness matrix of tooth e

aj

Displacement column matrix of boundary nodes of tooth e Static condensed matrix of tooth e

M'

Condensed mass matrix of tooth e Dielectric constant matrix under

E=

constant

Lagrange function Variational Work Charge on electrode Generalized coordinate column matrix K,

Generalized stiffness matrix

e,

Radial unit vector Axial unit vector Circumferential unit vector

PCP)

Polariza tion in tensi ty vector

E( Ei )

Electric field intensity vector

D( D i

Electric displacement vector

)

S(5,)

Strain tensor

TCTi)

Stress tensor

(Sij)

S

Flexibility coefficient matrix

c (e i})

Stiffness coefficient matrix

k

Electromechanical coupling coefficient

dedi} )

Piezoelectric constant matrix

im in i, i, i,

Minimum impedance frequency Series resonance frequency

i

p

Parallel resonance frequency

(Ei)

Dielectric constant matrix

Maximum impedance frequency Resonance frequency Anti-resonance frequency

v

Voltage

V pp

Peak-peak value of voltage

Vo VA,VB

Voltage amplitude

I (i. io )

Current matrix

Vol tage of phase A or B

I

Unit matrix

R(R l .Rd .Rm)

Resistance

C(Ca ,Cl .Cm ) L(L .Lm .Lp .L,)

Capacitance

Y

Admittance

j

Inductance

XXVI

Ultrasonic Motors Technolof{ies and Ap plicalions

Z(Zn,)

Impedance (Mechanical impendance)

W(W k )

Work (electric potential energy)

D

Duty cycle

1']

Integral time constant

Til

Differential time constant

K]

Integral coefficient

Kn Kp

Differential coefficient

VI

Isolated electrode voltage

Scale factor

Chapter 1

Introduction Traditional motors based on the electromagnetic principle have been invented and developed for more than one hundred years. As actuators and power sources, the motors have been widely used in many fields all over the world and have made a great contribution to our society. Over the years, the theories, design methods and manufacturing technologies of traditional motors have been developed so successfully that little improvement can be made to them.

However, due to ad-

vanced science and technology, especially in hi-tech products such as spaceships, satellites, launch vehicles, various electronic equipment, and precision instruments, many new requirements for motors have been raised, including a small size, light weight, low noise, no electromagnetic interference, etc. Due to limitations on the principle and structure, traditional motors are difficult to meet these requirements. Many countries in the world strive to explore various new, small, and special motors such as electrostatic motors, ultrasonic motors (USMs) , bionic motors, photo-thermal motors, shape memory alloy motors, microwave motors, etc. As integrated hi-tech products, the new, small, and special motors apply a variety of new technologies, including computers, automatic control, precision machinery, new material and modern manufacturing. They are increasingly becoming indispensable devices not only in the development of aerospace equipment, but also in the achievement of industrial automation, office automation and home automation. The ultrasonic motor is relatively mature among these new, small, and special motors. USMs have been developed as a new concept of motors since the 1980's. It utilizes the vibration of the elastic body (stator) in the ultrasonic frequency band and the reverse piezoelectric effect of piezoelectric materials. The mechanical movement and torque are obtained by means of the frictional contact force between the stator and rotor or slider. USMs can meet many new requirements for small and special motors because of advantages such as small size, light weight, compact structure, fast response, low noise, and no electromagnetic interference. )Jowadays, this kind of motors is being developed very quickly and applied to more and more fields. As an introduction to the book, this chapter summarizes the history, features, classification and applications of ultrasonic motors.

C. Zhao, Ultrasonic Motors © Science Press Beijing and Springer-Verlag Berlin Heidelberg 2011

2

1.1

Ultrasonic Motors Technologies and Ap plicalions

History of Ultrasonic Motors L1J

In 1940s, scientists discovered the ceramic material of BaTi0 3

•

which is easy to

be processed and can be made into piezoelectric elements of special shape and can be poled in arbitrary direction. This discovery greatly promoted the development of piezoelectric actuator technology. As early as in 1948, Williams and Brown applied for the first patent of "piezomotor" in history-2-, whose structure is shown in Fig. 1. 1. Their invention reveals the basic tenets and creates a new period of ultrasonic motor. However, ultrasonic motors were not rapidly developed because of the limitations of materials and processing technology at that time. Man's attempt to use vibration of elastic bodies to obtain the power began with the clock and watch industry. In 1960, Swiss Bulova watch Co., Ltd. used the reciprocating displacement of a metal tuning fork to drive watch gears: 3 : , as shown in Fig. 1. 2. This clock's operating frequency is 360Hz. This watch has an error of one minute per month. which created a record at that time. About ten years later, roughly in 1970-1972, Siemens and Matsushita Electrical Industries developed a kind of linear actuator and step motor, which used the key component such as piezoelectric vibrator. Because the piezoelectric vibrator's resonant frequency is as high as tens of thousands hertz and vibration amplitude is very small. the motor can not obtain a large torque or power. Drive coil

Drive coil Vibration direction

Fig. 1. 1

Sta tor of the first ultrasonic motor

Fig. 1. 2 Driving mechanism of tuning fork watch

In 1965. Lavrinenko from the Soviet Union designed a kind of ultrasonic motor, as shown in Fig. 1. 3, which used the vibration of piezoelectric plate to drive the rotor. He was granted an invention patent: 4J and summed up the characteristics of the ultrasonic motor: simple structure, low cost, low speed, high torque, large energy density, high precision, and high energy conversion efficiency. In 1973, Barth in IBM proposed a structural design scheme with the principle of modern ultrasonic motor[3: , as shown in Fig. 1. 4. He used two piezoelectric actuators to produce longitudinal vibration of horns. The contact friction between the rotor surface and horns end drives the rotor. In 1975, Vishnevsky also proposed a design scheme similar to Barth' S[6 J • They used a spring to press the edge

Chapter 1

Introduction

3

of a rectangular piezoelectric composite stator, which excited a longitudinal bra tion modc to drive the rotor, as shown in Fig. 1. 5.

Vl-

Rotor Output shaft

P iezoelectTi c actuator 2

Piezoelectric actu ator I

Fig. 1. 3

Lavrinenko's USM

Fig. 1. 4

Barth's design of USM

Excitat ion i b'l131

Fig. 1. 5

Vishnevsky's design of USM

In 1981, Lithuanian Vasiliev successfully developed an ultrasonic motor with the ability of driving larger loads L7J , as shown in Fig. 1. 6. The stator of this motor is a Langevin vibrator, which excites the longitudinal vibration mode of the metal shect contacting with thc rotor that is driven by thc friction force bctwcen the sheet and rotor. This structure of the motor can decrease the operating frequency and amplify thc vibration amplitude at the samc time. Thc usc of such motors to thc wheel of gramophonc becamc the first practical application of piczoelectric actuator in that cra. Aftcr Vasiljev's rescarch findings, Sashida in 1982 dcsigncd and made a standing wavc ultrasonic motor:"], as shown in Fig. 1. 7. This motor uscd a Langcvin vibrator. Its driving frequency was 27. 8kHz, input electric power 90W, output mechanical power SOW, output torque O. 5:'\J-m, output rotational speed 2800 r/ min, and the efficiency 60 %. It can be said that this piezoelectric ultrasonic motor met the performance requirements for actual applications at the first time. Because this motor's metal film and the rotor were fixed at the same position, serious wears existed on the contact surfaces. To solve this problem, in 1983 Sashida designed and manufactured another traveling wave ultrasonic motor, and in 1985 was granted a patent: 9: in USA, as shown in Fig. 1. 8. This motor realizcd the rotor rotation through thc traveling wavc instcad of the standing wavc. The formcr drivcs thc rotor continuously, while the lattcr drives the rotor discontinuously, so thc abrasion on the contact

Ultrasonic Motors Technologies and Ap plicalions

4

surface is decreased uSing the traveling wave. The successful development of such motors paved the way towards practical applications of ultrasonic motors. In the same year, Sashida put forward two design schemes of traveling wave linear ultrasonic motors(LUSMs) based on the same principle llo -: one is straight beam type, as shown in Fig. 1. 9, and the other is ring beam type, as shown in Fig. 1. 10. Piezoccralllic Metallic

Rotor Beari ng

Flexible sheet

Fig. 1. 6

Vasiliev's structure of USM

Sashida's standing wave USM

Rotor

, : ｾ＠

Fig. 1. 7

Moving direction of rotor

)- - - - ｾ＠ ｾ＠ ...-,.-;..- - - - - - - - - - - - -: ;;;>.,.,;-.u

., to

"u i::

20

= ｾ＠ u ｾ＠

UJ

10

ｏｌＭｾ＠

.. t ,,

200

ｾ＠

30

250

,, ,,

o

ｾ＠ '"

Ci

- - - - " Electromagnetic motor - - Ultrasonic motor

5

10

15

20

Relationship

and size for and USM

of

150

(

II I

,

I

•

j

1'\

"

I

100

I I I

50 00

I

" ---- Electromagnetic actua tor ",,/ - - Ullrasonic actuator

0.01

0.D2

0.03

0.04

0.05

Re ponse timeJs

Motor diameter/mm

Fig. 1. 21

I

I

efficiency

electromagnetic

motor

Fig. 1. 22 Comparison of start-up characteristics between electromagnetic and ultrasonic actuator

Chapter 1

1.4 1. 4. 1

Introduction

15

Applications and Development Trends of Ultrasonic Motors Applications

As mentioned above. ultrasonic motors have some unique advantages. So it promises a broad application prospects in many fields such as micro-robot. automobile, aerospace, precision positioning system, optical instrument, and medical endoscope. Color Fig. 1 lists some successful application examples in the world. Ultrasonic motors show strong vitality and board market potential sincc they are invented. Starting from the 1980's. many Japanese scientists have dedicated to commercializc the prototypc motor developcd by Amcrican or Soviet rescarchers. At present, many Japanese famous universities and companies are researching and producing ultrasonic motors. Japan now holds many invention patcnts of ultrasonic motors in the world. Canon Co., Ltd. has established a special production line of ultrasonic motors. USA. Germany. France, Britain, etc. have been putting in a lot of manpower and resources to develop ultrasonic motorsL31-32J. Applications of ultrasonic motors are gradually promoted in China. As shown in Figs. 1. 23 and 1. 21, PDLab successfully uses ultrasonic motors in the injector of MRI systcm and two-dimcnsional wing flutter modcl. Some other applications are introduced in Chap. 16 in details.

Fig. 1. 23 USM used in the injector of MRI system

1. 4. 2

Fig. 1. 24

USM used in airfoil flutter

model

Development Trends

As several types of linear ultrasonic motors and the ultrasonic motors with multi degrees of freedom have been developed in recent years, the development trend of USMs can bc summarizcd as follows:

1. Development of new frictional and piezoelectric materials for improving ultrasonic motors' adaptability to the extreme environment. Because ultrasonic motors transfer torque through the friction coupling. thc abrasion and fatigue problem of friction material on the contacting surface is incvitablc, which greatly limits applications of the motors. At prcsent, ultrasonic

16

Ultrasonic Motors Technologies and Ap plicalions

motors are only applied to the intermittent operating occasions, for example, total operational time of the ultrasonic motor in camera focus system is less than 15 hours, total operational time in car window switches or scat adjusting devices is less than 500 hours. In the last two years, Canon Co., Ltd. has used traveling wave ultrasonic motor for color copiers and the required operational life of the motor is more than 3 000 hours. Some applications also request longer life. To that end, many researchers are trying to find the new friction materials in order to increase the life of ultrasonic motors. Take the ultrasonic motors of Shinsei Corporation as an example: the biggest improvement for the past 10 years could be the friction materials including the material formula, manufacture, and adhesive bonding techniques. In order to use ultrasonic motors for aerospace engineering, the research on motors' adaptability to the environmental conditions is necessary. To complex environment of the space, National Aeronautics and Space Administration (NASA) and jet Propulsion Laboratory (jPL) have done a lot of research on the operating motors in the high/low temperature and vacuum environment C03 :. They applied USR-30 ultrasonic motors of Shinsei Corporation for a destructive testing of 67-hour operating in Cryovae conditions of - 80°C and 25mtorr (1 torr = 1. 33322 X 10 2 Pa). Based on testing results, taking a number of special measures, :'\JASA and jPL developed their SRPD type USM, which experienced the operating of 336 hours (65 hours in the conditions of -80°C and 25mtorr, 271 hours in the ones of -150°C and 16mtorr) and exhibited a good Cryovac characteristics. The researches show that in order to achieve good low temperature properties, in addition to improve adhesive materials and adhesive bonding techniques, it is necessary to improve the low temperature performance of frictional and piezoelectric materials and develop some new materials suitable for low-temperature environment. When the temperature drops to -10°C, the performance of series of PZT piezoelectric ceramics may decrease because of the increase of hysteresis loss. Piezoelectric ceramics remains only 25 % capability at the temperature of - 210°C. However, The piezoelectric properties of single-crystal relaxor ferroelectric piezoelectric ceramics (1 - .z:) Pb( Mg1/O Nb2/3 ) 0, - .z:PbTiO, (solid solutions of lead magnesium niobate-lead titanate, abbreviations PMN-PT) and (1.z:)Pb(ZnJ/3:'\Jb'!3)03 -.z:PbTi03 (solid solutions of lead zincum niobate-lead titanate, abbreviations PZN-PT) in the temperature - 240°C arc still better than the ones of piezoelectric ceramics in 30°C L31 . • Obviously, PMN-PT single crystal will effectively take the place of the traditional piezoelectric ceramic materials.

2. Miniaturization and integration of ultrasonic motors As mentioned above, the ultrasonic motor has no coil and its structure is simple, so it is easy for manufacture and it possesses higher energy density compared with the traditional motor. From Fig 1. 21, we can sec the efficiency of USMs is nearly independent of their sizes, which makes USMs extremly useful as actuators of micro-electro-mechanical system (MEMS). Therefore, miniaturization and integration are important development trends of ultrasonic motors. Though there is another small and special electrostatic motor, which can be

Chapter 1

Introduction

17

manufactured based on the Ie processing and can also be integrated together with the driving circuit, but its output torque is very small because of the limit of operating principle. The energy density of electrostatic motor is Eo E' /2. where Eo denotes the air dielectric constant and E denotes electric field intensity. When the size of the gap is IfLm, E::::::::IOR(V/m). The energy density of ultrasonic motors using the reverse piezoelectric effect of PZT can also be calculated by EE' /2, where E denotes the dielectric constant of piezoelectric ceramics and E is I 300Eo. Therefore, it can be said that ultrasonic motors have higher energy density[os:. For example, output torque of 5. 5mm in diameter electrostatic motor presented by Ref. [36Jwas only 25n)J'm, which was difficult to meet the needs of practical engineering applications. Miniature linear ultrasonic motor presented by Yoon is shown in Fig. 1. 25: shaft diameter is Imm. length is 6mm, its output force is 160mN, and velocity is 12mm/ s. Miniature bar-type ultrasonic motor presented by Ref. [37J is shown in Fig. 1. 26: diameter is 2. 1mm, length is 10mm, rotational speed is 570r/min, output torque is 1. 8mN'm, and efficiency is 25%.

Fig. 1. 25 Micro linear USM developed by Yo on

Micro bar-type traveling wave USM developed by Koe

Fig. 1. 26

3. Combination of piezoelectric actuator and biomedical engineering In modern biomedical engineering, it is indispensable to manipulate cells such as processing. transfer, separation, and fusion. or cellular materials (karyons. chromosomes, genes) transfers, restructuring, stretch, and fixation. For cells of micro size. a key technique is the precise positioning one and i t always requires the resolution of dozens of nanometers. Driving devices with high positioning accuracy and fine resolution are needed to accomplish this kind of manipulation. At present, these operations are manually implemented by professionally trained technical personnel with low efficiency and low success rate. USMs with high positioning resolution and fast response can successfully solve the problem. It can be deduced from the fact that Japan developed three-dimensional micro system which operates on the leukocyte, its positioning resolution is o. IfLm and operating range is 582fLm X 582fLm X 52fLm because human leukocyte diameter is about IOfLm. This system used laminated piezoelectric ceramics as actuator, had two-finger micro manipulator and could imitate the movement of chopsticks[08:.

Ultrasonic Motors Technologies and Ap plicalions

18

This system can also be used for surgery operating to manipulate the glass ball of diameter 2f1-m. The adoption of precision driving technique can improve efficieney, simplify the operating and realize the automation of the bioengineering. In the laboratory, Japanese scholars recently developed a set of automated cellpuncture operating system based on the nano-positioning technique of an inertia type linear ultrasonic motor and image processing technique, as shown in Fig. 1. 27: 39J • Using the modern micro-fabrication technique, the concept of drug delivery is proposed and can greatly improve the traditional delivery method for oral peptide and oral protein. Fig. 1. 28 shows Drug Delivery System based on the linear ultrasonic motor developed by New Scale Technology, Inc. in USA.

USM used in cell-puncture micro operating system

Fig. 1. 27

Fig. 1. 28

USM used in drug delivery system

In particular, it should be pointed out that the surface acoustic wave ultrasonic motor developed by Kurosawa possesses smaller loss, higher efficiency, and smaller volume compared with the traveling wave ultrasonic motor. At present, the surface acoustic wave motor with dimensions of 4mmX 4mmX 3mm has been developed, and its operating frequency range is lO-lOOMHz. When it is used as a step motor, O. Snm stepping motions and every step's response time of O. 2ms can be achieved: 40J • This ultrasonic motor with high spatial resolution has shown broad application potential in the fields of computer science and biomedical engineenng.

References [ 1]

[ 2] [ 3]

J Wallasehek. Ultrasonic motor research in Germany-past, present, future. Proceedings of the First International Workshop on Ultrasonic Motors and Actuators. Yokohama, Japan: Tokyo Institute of Technology, 2005. W Willams, W Brown. Piezoelectric motor. US Patent, 2439499, 1942-08-20. F J Britten. Britten's Watch and Clock Maker's Handbook: Dictionary and Guide. )lew York:

[ 4] [ 5] [ 6]

Areo Publishing Co., 1978: 109. V V Lavrinenko, M )lekrasov. Piezoelectric motor. Soviet Patent, 217509, 1965. H V Barth. Ultrasonic drive motor. IBM Technical Disclosure Bulletin, 1973,16(7): 2263. V Vishncvsky, V Kavertsev, I Kartashev, ct al. Piezoelectric motor structures. US Patent, 4019073, 1975-08-12.

[ 7]

P Vasiliev, R Klimavichjus, A Kondratiev, et al. Vibration motor control. UK Patent, GB

Chapter 1

[ 8J [9 J [lOJ [l1J [l2J [l3J

[14J [15J [l6J

Introduction

19

2020857A, 1979-11-21. T Sashida. Trial construction and opcration of an ultrasonic vibration drivcn motor. Oyo Butsiuri, 1982, 51(6): 713-718. T Sashida. Motor dcvicc utilizing ultrasonic oscillation. US Patent, 1562371, 1981-05-16. Takashi Kenjyo, :'-Icnsei Sashida. Introduction of Ultrasonic Motor. Japan: Sougou-Dcnshi Publishcr, 1991. (in Japanese) A Kumada. A piezoelectric ultrasonic motor. Japanese] ournal of Applied Physics, Supplement, 1985, 24(2): 739-741. Isc Yukihiko. Ultrasonic motor. Journal of the Acoustical Society of] apan, 1987, 13 (3): 184-188. K Uehino. Piezoelcetrie actuators/ultrasonic motors-thcir dcvelopments and markcts. IEEE International Symposium on Applications of Ferroelectrics. PA, USA: University Park, 1994: 319-324. J Wallaschek. Piezoelectric ultrasonic motors. Journal of Intelligence Material Systems and Structure, 1995, 6(1): 71-83. Tieying Zhou, Shuxiang Dong. Circular ultrasonic vibrator and the micro-motor driven by this vibrator. Chinese Invention Patent, ZL89109320, 1989-12-21. (in Chines c) M K Kurosawa, 0 Kodaira, Y Tsuehitoi, ct at. Transducer for high speed and large thrust ultrasonic linear motor using two sandwich-type vibrators. IEEE Transactions on Ultrasun-

ics, Ferroelectrics, and Frequency Control, 1998, 15(5): 1188-1195.

[17J [l8J [l9J [20J [21J

[22J

Y Tomikawa, T Ogasawara, T Takano. Ultrasonic motors-constructions /characteristics/ applications. Ferroelectrics, 1989, 91:163-178. Kazumasa Onishi. Principle and mcchanism of ultrasonic linear actuator. Labor-saving and Robotization, 1990, 112: 165-170. (inJapanesc) M Kurosawa, S Ueha. Hybrid transducer type ultrasonic motor. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 1991, 38(2): 89-92. S Ucha, Y Tomikawa. Ultrasonic Motors-Theory and Applications. USA: Oxford University Press, 1994. Zhcng Tao. Study on Hybrid Ultrasonic Motor Using Longitudinal and Torsional Vibration Modes. Dissertation for thc Dcgrec of Doctor of Philosophy. Nanjing: :'-Ianjing Univcrsity of Aeronautics and Astronautics, 2006. (in Chincsc) M Kurosawa, K Nakamura, T Okamoto. An ultrasonic motor using bcnding vibrations of a short cylinder.

[23J

transducer).

[21J

[25J [26J [27J

IEEE Transactions un [lltrasonics, Ferroelectric>; and Frequency Cuntrol,

1989, 36(5): 517-521. T Morita, M K Kurosawa, T Higuchi. A cylindrical micro-ultrasonic motor using PZT thin film depositcd by single process hydrothermal mcthod (Diametcr 2.1mm, L10mm Stator IEEE Transactions un [lltrasonics, Ferruelectric'i and Frequency Cuntrol,

1998,45(5): 1178-1187. T Morita, M K Kurosawa, T Higuchi. A cylindrical shaped micro ultrasonic motor utilizing PZT thin film (Diameter 1. 4mm and L5. Omm stator transducer). Sensors and Actuators A: Physical, 2000, 83 (3): 225-230. Hua Zhu, Chunsheng Zhao. The review of rotational ultrasonic micro-motor. Piezoelectrics & Acuustooptics, 2005, 27(6): 627-630,642. (in Chinese) T Sashida, T Kenjo. An Introduction to Ultrasonic Motors. Oxford: Clarendon Press, 1993. Tieying Zhou. An integrated optical auto-focus system driven by a nut-type USM. 5 th International Workshop on Piezoelectric Materials and Applications in Actuators. PA, USA:

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Pann. State University, 2008. A Kumada. A piezoelectric ultrasonic motor. Japanese] ournal of Applied Physics, Supplement, 1985, 24(2): 739-741. P Bouchilloux, B Koc, K Uchino. New concept for resonant longitudinal-shear ultrasonic motor. Materials for Srnart Systerns, Syrnpusiurn (Materials Research Society Pruceedings) ,

2000, 604: 71-78. [:jOJ

A Henke, M A Kummel, J Wallaschck. A piezoelectrically drivcn wire fceding systcm for

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[31]

Chunshcng Zhao. Ultrasonic motor tcchniqucs for 21" ccntury. Engineering Science, 2002,

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Chunsheng Zhao. Some proposals for development of ultrasonic motor techniques in China. Micromotors Servo Technique, 2005, 8: 64-69. (in Chinese)

[33J

S S Lih, B C Yoscph, W Grandia. Rotary ultrasonic motors actuatcd by traveling flcxural

[34J

S Dong, L Yan, N Wang, et al. A small, linear, piezoelectric ultrasonic cryomotor. Applied

[35J

A M Flynn, L S Tavrow, SF Bart, ct at. Piczoelcctric micromotors for microrobots. Jour-

1(2): 86-91. (in Chincsc)

waves. SPIE, 2004, 3041: 912-917. Physics Letters 86, 053501 (2005). nal of Microelectromechanical System, 1992, l( 1): 44-5l.

[36J

A Fujimoto, M Sakata, M Hirano, et al. Miniature electrostatic motor. Sensor and Actuators A, 1990, 21(1): 13-16.

[37J

[38J [39J [40J

B Koc, S Cagatay, K Uchino. A piezoelectric motor using two orthogonal bending modes of a hollow cylindcr. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 2002, 1(19): 195-500. T Tanikawa, T Arai. Development of a micro-manipulation system having a two-fingered micro-hand. IEEE Trans. Robot. Autom. , 1999, 15: 152-162. T Higuchi. Automatic micro manipulation systcm for ccll manipulation. [2007-05-23]. http: / /www.intellcct.pc.u-tokyo.ac.jp/rcscarch/manipulator/manipulator_c.htm!. T Shigematsu, M Kurosawa, K Asai. Sub-nanometer stepping drive of surface acoustic ultrasonic motor. IEEE Int. Conf. Nanotechnology. San Francisco, CA, 2003, 2: 299-302.

Chapter 2

Fundamentals of Piezoelectricity and Piezoelectric Materials for Ultrasonic Motors The development of ultrasonic motors is a highlight in the application of piezoelectric materials. Ultrasonic motors take advantage of converse piezoelectricity of piezoelectric materials to yield mechanical output from converting electrical energy. It is no doubt that piezoelectric materials are in the central position that controls thc pcrformancc of thc dcviccs. In this chaptcr, wc will rcvicw piczoelcctric materials and their properties from the aspect of their applications in ultrasonic motors. The chapter begins with a brief overview of historical development of piczoelcctric matcrials, and thcn a dctailcd cxplanation of thc elcctrical and mcchanical properties of piezoelectric materials will be discussed in the second and thc third scctions, whcrc thc piczoelcctric constitutivc cquations arc spccially strcsscd. Piczoelcctric vibrators, as basic units of piczoelcctric dcviccs, and thcir vibration types will be described in sequence. In the last two sections, the application of piczoelcctric matcrials in ultrasonic motors and somc advanccs in novel materials will be introduced.

2. 1

2. 1. 1

Development and Classification of Piezoelectric Materials Historical Development of Piezoelectric Materials

In 1880, Pierre Curie and] acques Curie reported a number of crystals such as quartz, topaz, tourmalinc and Rochcllc salt that could display surfacc chargcs when they were mechanically stressed. This phenomenon that materials produce elcctricity in rcsponsc to applicd strcss is defincd as thc dircct piczoelcctric cffcct, of which thc discovcry is thcreforc crcditcd to thc Curic brothcrs. Thc inverse process of the piezoelectric effect, that is say, an external electric field applicd to piczoelcctric matcrial gcncratcs deformation in thc matcrial, is defincd as the converse piezoelectric effect- 1- 6J • Frcnch scicntist Langcvin thcn dcvelopcd thc first scrious application for piczoelectric materials in 1916 by using quartz crystals to build transducers for submarinc dctccting. Thc discovcry of BaTi03 piczoelcctric ccramic in World War II was rcgardcd as a milcstonc of thc dcvelopmcnt of piczoelcctric matcrials. In contrast with piczoelcctric singlc crystals, BaTi03 ccramic is rathcr casy to prcparc, and can bc form cd into spccific shapcs and pol cd in arbitrary dircctions.

C. Zhao, Ultrasonic Motors © Science Press Beijing and Springer-Verlag Berlin Heidelberg 2011

22

Ultrasonic Motors Technologies and Ap plicalions

These advantages brought BaTi03 to be rapidly applied in ultrasonic transducers, high-frequency transducers, pressure sensors and other piezoelectric devices. It has gone through three stages in discovering and understanding the piezoelectricity of ceramics: the first stage was the discovery of high dielectric constant in the ceramics; then at the second stage it was realized that the high dielectric constant was originated from the ferro electricity of the materials; poling processing for the ceramics was finally established at the third stage. Lead zireonate-lead titanate (PZT) system is another progress in the field of piezoelectric materials. In 1951, ] affe et al from the United States reported much better piezoelectric properties found in PZT solid solution ceramics and proposed the concept of morphotropic phase boundary (MPB)L1J. Based on this concept series of the currently most widely used piezoelectric ceramics were developed. Recent research focus of piezoelectric materials is on the relaxor ferroelectrics of Pb (Mg x Nb j - x ) 0 3 -PbTi0 3 (PMN-PT) and Pb(ZnE:'\Jbl-E)03-PbTiO, (PZ:'\J-PT) single crystals, which were reported with outstanding electromechanical coupling properties L5 -

2. 1. 2

Classification of Piezoelectric Materials

The currently used piezoelectric materials cover three classes: CD Inorganic piezoelectric materials, including piezoelectric monocrystalline materials and piezoelectric ceramics which consist of massive fine crystals. Piezoelectric ceramics present advantages such as strong piezoelectricity, high dielectric constant and can be easily formed into various shapes. But they arc usually with low mechanical quality factor, large electric loss and poor stability. These characteristics make piezoelectric ceramics suitable for high-power transducers, wide-band filters and so on. Piezoelectric single crystals provide high mechanical quality factor and excellent stability but low piezoelectric coefficient and low dielectric constant, and their shapes for devices arc restricted because of the difficulty in machining these crystals. Piezoelectric single crystals can be used in devices such as vibrators to control standard frequencies, high-selectivity filters (usually with high frequency and narrow-band), high-temperature ultrasonic transducers and so on. CZ)Organic piezoelectric materials, also known as piezoelectric polymers, e. g., polyvinylidene fluoride (PVDF). ] ust like other polymers, piezoelectric polymers possess excellent flexibility, low density, small impedance, as well as reasonable piezoelectric coefficient. Piezoelectric polymers have been rapidly applied in devices for underwater ultrasonic measuring, pressure sensing, and explosion igniting. However, the low piezoelectric stain constant of piezoelectric polymers has restricted their applications as active transducers. Gil Piezoelectric composites, in which piezoelectric ceramics and polymers are incorporated together. As a result, the piezoelectric properties of the composites are enhanced comparing with their initial components. Furthermore, the composites may present novel properties that do not exist in these single components. Piezoelectric composites can ha ve large piezoelectricity, strong strength and low density, and their outstanding machinability makes them easy to be fabricated into large area films or other complicated forms. Nowadays, piezoelectric composites have already been widely

Chapter 2

Fundamentals of Piezoelectricity and Piezoelectric'"

23

used in hydroaeoustie. eleetroacoustic. ultrasonic and medical applications.

Electrical Properties of Piezoelectric Materials

2.2

This section is concerned with some important electrical properties of piezoelectric materials. Parameters such as dielectric constant. dielectric loss. electrical quality factor. ferroelectric polarization and Curie temperature will be explained in detail, with which the dielectric and ferroelectric properties of piezoelectric materials are described.

2. 2. 1

Dielectric Properties and Dielectric Loss

1. Dielectric polarization and dielectric constant[l, :1, 7J All piezoelectric materials are dielectrics. Response of dielectric materials to external electric field will produce net dipole moments or produce changes in dipole moments along the electric field direction. This process is called the polarization of dielectrics. The induced and orientational polarization in external electric field is responsible for the mechanism of polarization. As a result of polarization. electric charges appear on the outside surfaces of the dielectrics. The quantity P is the basic parameter describing the polarization of the dielectric and denotes the dipole moment per unit volume. Under moderate external field. the polarization P is proportional to the electric field strength and can be expressed by the linear equation

P where

Eo =

=

(2. 1)

EoXE

8.85 X 10- 12 F/m is the permittivity (or dielectric constant) of free

space and the dimensionless constant X is called the susceptibility of the medium. which is a second-rank tensor. When P and E are collinear. and X is simply a scalar. the electric displacement vector D can be written as D

If we define

Eo E, =

E.

=

Eo E

+P

=

Eo

(1

+ X) E

=

EoE,E

(2. 2)

then (2. 3)

where E referring to the dielectric constant of the material. is an important parameter used to describe the dielectric property of the material in static electric fields. In isotropic materials. E is simplified as a scalar. In anisotropic materials such as single crystals. P. D. and E are vectors. precisely. are first-rank tensors. The coefficients E and X connecting them are then second-rank tensors. The number of the independent components of a dielectric constant tensor depends on the symmetry of the crystal structure. Materials with higher crystallographic symmetry always have fewer independent components in the dielectric

24

Ultrasonic Motors Technologies and Ap plicalions

constant matrix. For example, triclinic crystal, which is with the poorest symmetry, has six independent components of £jj, £22 , £33 , £j2 , £j3 , and £23' On the other hand, cubic crystal has the highest symmetry so that only one independent component exists. Unpolarizcd polycrystallinc ceramic is isotropic and presents identical dielectric constant in all directions. However, the poled piezoelectric ceramic presents anisotropy because of the existence of remnant polarization along the poling direction. The dielectric constant component in this direction is different from these of the other two directions. In practice, the expression of dielectric constant for hexagonal crystal system can be taken to describe the poled piezoelectric ceramic, in which two independent components £jj =£22 and £33 arc used. Taking into account different boundary conditions during test, dielectric constants can be sorted into the stress-free dielectric constant and the mechanically clamped dielectric constant, symbolized as £;j , £i; and £fj , d3' respectively.

2. Dielectric loss and electrical quality jactor[l, 3, 6, 8J When an electric field applied to dielectrics, energy loss always occurs because of polarization relaxation or leakage and other reasons. This energy loss in dielectrics is defined as the dielectric loss. If a dielectric is suddenly exposed to an electrostatic field, the polarization building up from zero to the final value is not instantaneous but takes a finite time. This phenomenon is described by dielectric relaxation and the finite time is defined as relaxation time. In a high frequency AC field, the response of the dielectric may not follow the change of the field, the polarization therefore lags behind the field and leads to dielectric loss. The polarization relaxation will also result in a difference between the dynamic dielectric constant and the static dielectric constant in the material. Part of the energy of dielectric loss is consumed to rotate the dipole moments because of polarization lag. The energy finally transforms into heat energy and dissipates. Current leakage in dielectric is another factor that causes dielectric loss, especially at high temperature or in strong electric field strength. The energy also dissipates in the form of thermal effect. In ideal dielectrics without dielectric loss, the phase of the current inside leads 90° ahead of the phase of the voltage. However, in actual piezoelectric materials, the energy loss makes this leading angle rp less than 90 degrees. The complementary angle G of the angle rp is then defined as the loss angle. Tangent of the loss angle tanG is defined as the quotient between the active power P and the reactive power Q in a dielectric. One can image that there is a resistance R in the dielectric to consume part of energy. The current in the dielectric is then divided into two parts: IR goes through the resistance to cause energy loss; Ie passes the capacitor without losing. The tangent of the loss angle of dielectrics can be written as tanG

IR =

Ie

1

=

wCR

(2. 1)

In which w stands for the angular frequency of the alternating electric field, and C is the static capacitance of the dielectric with electrodes.

Chapter 2

Fundamentals of Piezoelectricity and Piezoelectric'"

25

Since tanB is proportional to the energy loss, naturally it is used to characterize thc dielcctric loss of matcrials. In gcneral, thc more is thc dielectric loss, thc worsc is thc pcrformancc of the material. Dielectric loss is also scnsitive to thc temperature, the strength and the frequency of the electric field. Thc rcciprocal of thc tangcnt of loss anglc is defined as the electrical quality factor Q" which is shown as Q,

2. 2. 2

1 tanB

---(JJ

CR

(2. 5)

Ferroelectric Properties and Polarization

1. Ferroelectricityrl.

3, 781

The function parts uscd in ultrasonic motors and other actuators actually arc fcrroelcctric matcrials. As wc know from solid statc physics, thc structural symmetries of crystalline solids are described by 32 point groups. Dielectrics can be belonged to any of these groups. Of the 32 point groups, there are 21 non-centrosymmetric point groups. Among them, 20 point groups exhibit piezoelectric effcct as the polarization of thcse crystals varics with elastic strain. Furthermore, 10 point groups in thc crystal structurcs of piezoelectrics prcsent only onc polar axis. Crystals with the structures falling into this 10 point groups can present spontaneous polarization even without external electric field. Bcsides stress, tcmperaturc gradicnt may also inducc elcctric polarization variation in thesc crystals. The generation of polarization by temperature gradient is referred as the pyroelectricity. Among pyroelectric materials, some materials possess spontaneous polarization and the spontaneous polarization is switchable by external electric field. During switch the polarization P and thc external elcctric filed E prescnt a hysteresis loop. This property of materials is referred as the ferroelectricity. A ferroelectric crystal consists of many fine regions defined as domains, where thc spontaneous polarizations arc aligned in samc directions.

Thc boundary

bctwccn domains is callcd thc domain wall. The polarization P of a ferroelcctric prescnts a nonlinear characteristic under a strong altcrnating elcctric field and displays a ferroelectric hysteresis loop with the variation of electric field E, as shown in Fig. 2. 1, in which P is a doublc-valued function of E . Thesc behaviors makc fcrroelcctrics bc analogous to fcrromagnet in many physical propertics. The ferroelectric phase is limited to below the Curie temperature Te' Above T"

the spontaneous polarization disappcars and thc fcrroelcctric phasc turns to

paraelectric phase. Thc electric pcrmittivity of fcrroelectrics dcmonstratcs quitc complex temperature dependence. At the Curie temperature, the permittivity of the material reaches its maximum and then decreases with the increase of temperature, which can be described by the Curie-Weiss law E=

(2. 6)

Ultrasonic Motors Technologies and Ap plicalions

26

p

H

C

ＭｾｌＫｅ＠

H

Ferroelectric hysteresis loop of ferroelectric materials

Fig. 2. 1

2. Poling of piezoelectric ceramic/:J· 9-10Many single crystals can naturally present piezoelectricity. However, as their crystal grains are randomly oriented, the sintered ferroelectric ceramics have to be polarized before they can exhibit piezoelectricity. The fine grains in the ceramics may be single-domain or multi-domain structures, the spontaneous polarizations of the domains distribute randomly and compensate each other so that no net electric dipole moments are shown. If the strength of the external electric filed is larger than the coercivity of the material, the spontaneous polarizations of the domains will be switched as much as possible to the electric filed direction. The polarized ceramics will keep a remanent polarization even the electric field is removed. Ceramics with macro electric polarizations then present piezoelectric behavior. Fig. 2. 2 displays the evolution of domain structures of ferroelectric ceramics during poling process. Before polarization, domains with spontaneous polarizations point all possible directions and the net polarization of the ceramics is zero, as shown in Fig. 2. 2(a). After polarization, the ceramics present net polarization at zero electric field, which is the remanent polarization P, of the ferroelectric ceramics, as shown in Fig. 2. 2 (c).

ｾ＠

1

I

ｾ＠

P,

Remnant prolongation caused prolongation

(a) Domains oriented randomly prior to polarization

Fig. 2. 2

(b) Domains rearrange along electric fie ld direction during poling proce

(c) Remnant polarization remai ns afte r remQval of DC field

Domain structures of piezoelectric ceramics before and after poling process

Chapter 2

2. 3

Fundamentals of Piezoelectricity and Piezoelectric'"

27

Properties Constitutive Equations of Piezoelectric Materials

2. 3. 1

Elastic Properties and Their Coefficients- 7 , 910_

In general, an object will make two behaviors in response to an external force. One is the position movement, including translation and rotation. The other is the deformation of volume or shape, which includes elastic deformation and plastic deformation. Considering the deformation is small enough during the performance of piezoelectric materials, we can deal with it as the elastic deformation. The elastic state of piezoelectric materials is described by stress (T) and strain(S). Fig. 2. 3 depicts the interior stress of a unit volume of piezoeleetries. As it can be seen in the figure, the stress relics on the orientation of the force as well as the plane where the force acts. The stress T can be described by a second-rank stress tensor which consists of 9 components. These components are indexed by notations with double subscript, as shown in Fig. 2. 3. Sometimes, notations of single subscript arc also used. The conversions between the indexes of double subscript and single subscript arc listed on Table 2. 1.

, 7'," 'j:,, 7'--", --- -- --ｾＬＢｏ

Ｍ

ｩｾ＠

72 ,J-- -.. y

J.-- --------

"I-- -.. y

// 0

x

x

Fig. 2. 3 Table 2. 1

FI_

i

Ｗｾ Ｌ＠

:

Indexes of stress components in a piezoelectric bulk

Conversions between indexes with double subscript and single subscript

Double subscript

Double subscript

.II

11

Single subscript

yy

22

2

zz

33

yz

Z.T

y.T

zy

xz

xy

23

31

12

32

13

21

1

From Table 2. 1, we have

TXE = I'll = 1'1' Tyy = 1'22 = 1'2' 1'= = 1'" = 1', , Tyx = Txy = 1'12 = 1'6 , 1'= = 1'= = 1'13 = 1'5' l'yz = Toy = 1'23 = 1', Of the stress tensor components, only six ones are independent. These independent components usually are expressed by a matrix.

28

Ultrasonic Motors Technologies and Ap plicalions (2. 7)

Similarly we have six independent components in the strain tensor, expressed by the following matrix (2. 8)

In linear elastic range, the relationship between stress and strain is described by the Hooke's law that the strain component is a linear function of the stress components 6

Si =

ｾｓｩ｝ｔ＠

1,2,···,6 )

(2. 9)

(i=1,2,···,6)

(2. 10)

(i

=

]-1

By a linear transformation, we also have 6

Ti =

ｾｃｩ｝ｓｪ＠ ;'=1

where Si] is the flexibility coefficient and Si]=S]i; c i] is the stiffness coefficient and we also have C i] = C]i. It is not hard to find that these elements in the matrix of flexibility coefficients and the matrix of stiffness coefficients have a relation: [Si] J=[c i]

J- 1 •

The symmetry of poled piezoelectric ceramics is approximate to those of hexagonal crystal system. The elastic constant matrix of piezoceramics is then similar to that of crystals with structural symmetry of 6mm point group. Five independent flexibility coefficients ( Sl1 , SI2 , SB , S" , s,,) are left in the matrix. The flexibility matrix of piezoelectric ceramics is as follows Sl1

s=

0

0

0

S12

S13

Sl2

S11

S12

0

0

0

S13

S13

S33

0

0

0

0

0

0

S44-

0

0

0

0

0

0

S44-

0

0

0

0

0

0

2(Sll-SI')

(2. 11)

Similarly, there are five independent stiffness coefficients in the stiffness matrix of piezoceramics, C ll , C 12 , C 13 ' C 33 ' c11 • The stiffness matrix is similar to Eq. (2. 11) in form but replacing Sij with Cij and replacing 2 with 1/2.

2. 3. 2

Piezoelectric Properties and Piezoelectric Equations

1. Piezoelectricity The ability of materials to develop or vary electric polarization when they are mechanically stressed has been known as piezoelectricity. When a piezoelectric is strained with external stress, charges displace from their equilibrium position to both surfaces, causing bound charges on the surfaces of the material. The produced charge density is proportional to the stress. This effect is the direct piezoelectricity and its mechanism is shown in Fig. 2. 4.

Chapter 2

Fundamentals of Piezoelectricity and Piezoelectric···

29

The mechanism of the converse piezoelectricity is shown in Fig. 2. 5, where an external electric field induces elastic displacemcnt of charges, producing deformation in thc material.

r----------- -----------. ++++++++++

i+- -+--+--;-+--;-+--+--.:;:-+--;-+ ---:

:

tPolarization

I

t Polarization

E 1 I

++++++++++++

Direct piezoelectric effect of a piezoelectric element responding to external force

Fig. 2. 4

Converse piezoelectric effect of a piezoelectric element responding to external electric field

Fig. 2. 5

2. Piezoelectric equations The functional intcrrelations bctween elcctric paramctcrs (E, D) and mechanical parameters (T, S) of the piezoelectric effect are known as the equations of state for piezoelectric materials. The forms of the equations are dependent on boundary conditions and indepcndcnt variablcs. The electrical and mechanical boundary conditions of piezoelectric elements depend on the tcsting methods or thcir application circumstances. Strcss-frcc mechanical boundary condition and elamped (fixed) mechanical boundary condition, along with short-circuit and open-circuit electrical boundary conditions, are commonly used in piczoelectric equations. Free dielectric constant and elamped dielectric constant are the dielectric constants mcasurcd undcr stress-frcc mechanical boundary condition and elamped mechanical boundary conditions, symbolized as ｅｾｮ＠

and ｅｾｮＧ＠

rcspectively. Thc

electrical boundary conditions are defined by electrodes, circuit states and geometrical shapes of the piezoelectric elements. During measurement, if the electric field strength E inside the material is maintained to zero but the electric displacement is variable (for example, the electrodes arc shorted or the potential of the sample surface keeps constant by grounding), this boundary condition is called the short-circuit boundary condition. The measured elastic compliance and stiffness arc the short-circuit compliance and short-circuit stiffness, expressed as ｳｾ＠

and ｣ｾＬ＠

respectively. Similarly,

if the electric displacement D remains constant but the electric field strength inside the piezoelectric element is variable, the corresponding boundary condition is the open-circuit boundary condition, and the measured elastic compliance and stiffness arc the open-circuit compliance and open-circuit stiffness, expressed as ｳｾ＠

and ｣ｾＬ＠

respectively.

Four typical boundary conditions can be obtained through combining the two mechanical boundary conditions and two electrical boundary conditions, thus leading to four types of piezoelectric equations, which are listed on Table 2. 2.

Ultrasonic Motors Technologies and Ap plicalions

30 Table 2.2 Name

Type 1

Type 2

Type 3

Type 1

Four types of boundary conditions of piezoelectric vibrators

Boundary conditions and corresponding coefficients

Piezoelectric equations with

Loading

Short-circuit compliance coefficients

sE

Short-circuit stiffness coefficients c E

Open-circuit compliance coefficients ,IJ

cD

Clamped impermittivity components

T

j

+ ｅ［ｾｮ＠

dmJ T J

= =

Si = En

ｃｾｓｩ＠

enjEn

-

+ E;mEn s;;TJ + gmiDm gnj T + /tnDm

=-

j

T j = Cf,Si - hmjDm

S. D

{f

•

Dm = emiSi

T,D

Stress-free impermittivity components (3T Open-circuit stiffness coefficients

Dm

S,E

ES

Sll bseripts

Si = s5TJ +dniEn

T.E

Stress-free dielectric constants e T

Clamped dielectric constants

shortened

En

=-

hniS i

+ {f",nDm

* i,j=1,2,3,1,5,6; m,n=1,2,3.

The specific forms of the piezoelectric equations listed in the table are also related with the forms of piezoelectric coefficient, elastic compliance and permittivity. As mentioned before, materials with different crystal structures have diffcrcnt indcpcndcnt componcnts in thcir matriccs, so that thc cxprcssions of piczoelectric equations change correspondingly. Furthermore, the piezoelectric cquations may vary cvcn in thc samc piczoelcctric crystal if it is cut into diffcrcnt forms since the piezoelectric coefficient, elastic compliance and dielectric constant will changc in various coordinatc systcms with diffcrcnt rotation symmctrics. For spccific vibration typcs, piczoelcctric cquations may bc furthcr simplificd.

3. Applications of piezoelectric equations zn piezoelectric elements[ll: Here we consider a piezoelectric element as an example of using the piezoelectric cquations. From thc piczoelcctric cquations, it can bc elcarly sccn that thc coupling between electric parameters (E, D) and mechanical parameters (T, S) will inducc elcctromcchanical coupling cffcct in piczoelcctric elcmcnts. Dcpcnding on boundary conditions, thcrc arc two basic piczoelcctric cqua tions in piczoelcctric ccramics. Thc first onc is thc piczoelcctric cquation dcscribing thc dircct piczoclectric effect under short-circuit electrical boundary conditions (E 1 = E2 = E, = 0). If transforming thc piczoelcctric cquation Dm = d mj T J Ｋｅｾｮ＠ (listcd in Tablc 2.2) into matrix form, we have

D=

ｲｚｬｾ＠

D3

r d" d'l d'l

d l, d 22 d"

d 13

dl1

d 15

d'3 d"

d" d34

d'5 d,s

T1 T,

d"1 d'6 d'5

T3 Tl T,

E,

E3

0)

T6 (2. 12) In the equation, D" Ei(i=l, 2, 3) are the electric displacement and electric field in thc polar planc of thc piczoelcctric body along Xi (i = 1, 2, 3) axcs. Thc

Chapter 2

Fundamentals of Piezoelectricity and Piezoelectric···

31

electric displacement vector D = [D l D2 D 3 ]I'; d is a matrix retrieved from the reduced piezoelectric constant tensors. where the component of piezoelectric constant d i} signifies the electric displacement developed along the i-axis when the material is stressed along the j-axis. The form of matrix d is determined according to the specific material and its crystal structure. The second one is the piezoelectric equation describing the converse piezoelectric effect at stress-free mechanical boundary conditions (Ti = O. i = 1-6). By the piezoelectric equation 5 i = ｳｾｔｽ＠ + dmEn listed in Table 2. 2. the electric field E3 along the .1':3 axis. and electric fields El and E2 along axes of .1':1 and .1':2 will generate strains in piezoelectric bodies. This is the converse piezoelectric effect.

s=

51 52 53 51 55 56

=

dTE

=

dJJ d 12

d 21

d 31

d 22

d 32

d 13

d23

d 33

du

d"

d 15

d" d 26

d 16

d 35

[E' E2

(Ti

= O.i =

1.2.··· .6)

E3

d 36

(2. 13) In piezoelectric elements. the polarization direction is usually referred as .1':3 axis. For piezoelectric ceramics with polaxis parallel to X3 • the plane perpendicular to the polaxis is isotropic. so that there are only three independent piezoelectric constant components d 31 • d 33 • and d 15 in piezoelectric constant matrix. The piezoelectric constant matrix can be written as

d=

[1,

0 0

0 0

0

d 13

d 13

0

d 31

d 33

0

0

ｾＱ＠

(2. 14)

Meanwhile. at the stress-free boundary conditions. piezoelectric ceramics can be regarded as capacitors so that they should satisfy the dielectric equations. Similarly. under the condition of short circuit. piezoelectric ceramics also need to comply with the constitutive equations. These equations are not listed here.

2. 4 2. 4. 1

Vibration Types of Piezoelectric Vibrators Piezoelectric Vibrators and Their Equivalent Circuits

Piezoelectric vibrator is simply a piezoelectric bulk with electrodes coated on its two opposite surfaces. which is the most elementary piezoelectric unit used in ultrasonic motors or other actuators. As an elastic body. it has infinite natural vibration frequencies. Once the frequency of the applied electric field equals to one of the natural frequencies. mechanical resonance will be activated in the vibrator due to the converse piezoelectric effect. Vibration types are defined by the relations between polarization directions and vibration directions. We can refer to the type as the longitudinal vibration type if the vibration direction is parallel to the polarization direction. For a transverse vibration type. the vibration direction

Ultrasonic Motors Technologies and Ap plicalions

32

is perpendicular to the polarization direction. Table 2. 3 lists several vibration types observed from some regular vibrators, where the hollow arrow represents the polarization direction and the solid arrows point to the vibrating directions. Among them, diagrams (a) to (g) show length-extension(contraction) types (The extensions(contractions) may be along length, width or radial directions) whose vibration is perpendicular to the polarization direction (LE type). Table 2. 3 (h) presents a transverse-thickness shear vibration type(TS type) in a piezoelectric plate whose vibration is normal to the polarization direction. As a comparison. a longitudinal-thickness shear vibration type is given in Table 2.3 (1) (LS) , where the vibration is parallel to the polarization direction. Those thickness-extension ( contraction) vibrations parallel to polarization directions arc shown in Table 2. 3(i)-(k) (TE types). Table 2. 3

ｉｾ＠

---( ｾ＠ .,

(a) Length exten ion

Vibration types of piezoelectric vibrators

a

0

ｾｏ＠

u

(b) Width exten ion

ｾ＠

'c"'

1:;

r:

I-

U

ｾ＠ .,

ｾｏ＠

(e) Radial exten ion

Obviously, the parameter Qm of a vibrator is also dependent on its vibration type. Here Qm is the mechanical quality factor of the radial vibration type if without special clarification. From the equivalent circuit, we can determine Qrn by the cleetrieal parameters of the vibrator

1

Qrn

=

4rr(Co

+ C] )R] t::.j

(2. 23)

Ultrasonic Motors Technologies and Ap plicalions

38

Co: the static capacitor of the piezoelectric vibrator; R I : the equivalent resistance of the vibrator in the resonant state; C I : the equivalent capacitor of the vibrator in the resonant state; 6.j: the difference between the resonant frequency j, and the anti-resonant frequency j,.

2.5

Applications of Piezoelectric Materials to Ultrasonic Motors

Piezoelectric materials playa key role in ultrasonic motors and other piezoelectric actuators because of their function to transform electrical energy into mechanical energy. Several parameters of some important piezoelectric materials are listed in Table 2. 6 for reference- IIJ • Since the properties of piezoelectrics can be widely adjusted by substituting or doping additives, the data show only a rough range. In the table, To is the Curie temperature and Eo is the coercive field. Table 2. 6

Some main parameters of several typical piezoelectric materials Parameters

Materials

T,

E§3

rC

d 33

diS

I (pC/")

l(pC/")

k33

Qm

E, l(kV lern)

Pb(Zr, Ti)03 (PZT)

330

1 800

117

710

0.73

75

(BaPb) Nb z 0 3 (BPN)

100

300

85

100

0.30

15

PbTi 0 3 (PT)

490

190

56

68

0.45

1 300

Bi4 Ti4 Ole (NBT)

600

110

18

-

O. 15

100

(Bio. 5 Nao. s) Ti0 3 (BNT)

315

300

70

-

O. 10

210

73

LiNb0 3 (L") Crystal

1 150

25

6

69

0.23

NR

200

SiO, (Quartz) Crystal

573

4.5

2(d ll )

NR

10 5

-

10-12 -

> >

40 50

-

The requirements in properties of piezoelectric materials have to be determined according to their specific purposes of the devices. These used in ultra-high-frequency (UHF) and high-frequency devices require the material to have low permittivity and small high-frequency dielectric loss. For energy transducer application, the coupling coefficient and acoustic impedance of the material arc often stressed. Materials with excellent frequency stability and high Qm values can be used as standard frequency oscillators. To satisfy the application of delay line, the materials have to be stable in frequency, and the velocity of sound in the materials should also be considered. Ceramics used in the electro-acoustic field should have a large permittivity, high kp value and high elastic compliance coefficient, and their dielectric loss doesn't matter too much to the devices. For hydroacoustic transducer applications, if used as receivers, it is necessary that the material has a large piezoelectric coefficient of g33 or g31 , large permittivity, high kp value and high compliance constant, but its Qrn value is not seriously required; if

Chapter 2

Fundamentals of Piezoelectricity and Piezoelectric'"

39

used as high-power emitters, it is important that the material has a low dielectric loss tanO' and a high Qrn undcr a rong elcctric field, additionally with a largc diclectric constant, high kp value and large piezoelectric constant. For materials uscd as filtcrs, thcy arc cxpcctcd to bc not only with cxccllcnt duration stability and temperature stability, but also with high Qm and low tanO'; the requirement in kp valuc dcpcnds on thc bandwidth of filtcrs. High-voltagc gcncrators and igniters require the materials to have large values of g33 and k33' a large permittivity, a moderately high Qm' as well as a low tan 0'. :'\Jowadays, by means of doping and substituting, thc propcrtics of piczoelcctric ccramics can bc adjustcd in a wide range to meet diverse application occasions.

2.5. 1

Piezoelectric Ceramics Used for Ultrasonic Motors

1. Piezoelectric ceramics for ultrasonic motors So far, piezoelectric ceramics, instead of piezoelectric single crystals, are mainly thc functional matcrials uscd in ultrasonic motors. Among thcm, Pb(Zrx TilE) 0, (PZT) bascd systcm is thc most important onc duc to its cxtraordinary propcrtics and is currcntly thc first choicc for ultrasonic motors. The preparation of PZT ceramics follows a standard ceramic process ineluding stcps of powdcr prcparing, forming and sintcring, succccdcd by a poling proccss which is requisite for piezoelectric ceramics to get piezoelectricity. Ulltrasonic motors are typical high-power devices, so that the used piezoelectric ccramics should bc with a low dielcctric loss tani) and a high mcchanical quality factor Qm under a strong electric field, as well as a reasonable piezoelectric constant d 33 and an elcctromcchanical coupling factor k p • Unfortunately, for PZT-based piezoelectric ceramics, in most cases the improvement in Qrn simultaneously induces degradations in d" and k p • Up to now, researchers from all over thc world havc conductcd a grcat dcal of fruitful work, which aim cd at cnhancing the piezoelectric constant and electromechanical coupling coefficient but without impairing the mechanical quality factor. Multi-constituent doped PZT ceramics havc bccn dcvelopcd for high powcr piczoelcctric dcviccs, and thc improvcmcnt in properties still continues. Ultrasonic motors now have been used in tremendous occasions to satisfy many applications. For different motors with specific purposes, piezoelectric elements wi th particular properties, dimensions and structures are required. The piezoelcctric elcmcnts thcn havc to bc shapcd into spccific dimcnsions and forms. Fig. 2. 10 (a) shows somc PZT piczoelcctric elcmcnts from industrial companics, and Fig. 2. 10 (b) displays PZT components used for ultrasonic motors designed by our PDLab at :'\JUAA. 2. Stability of Piezoelectric ceramics used in ultrasonic motors[1-2, 11-l2J During thc scrvicc of ultrasonic motors, thc uscd piczoelcctric matcrials havc bccn found fluctuant in thcir physical propcrtics with elapsc of durations and fluctuation of tcmpcraturcs. Somctimcs thc variation in propcrtics can bc pro-

40

Ultrasonic Motors Technologies and Ap plicalions

(a) PiezoeleCTric ceramic elemCIlIs(Xinchang Silver River Electronic Co. Lid in China)

Fig. 2. 10

(b) PZT components lISed in ultrasonic molors developed by PDLab

PZT piezoelectric ceramic components

nounced enough to cause failure of the whole devices. Therefore, the stability of piczoelectric ccramics is utterly significant for thcir applications. (1) Aging stability Stabilities of piezoelectric ceramics with duration elapse and temperature fluctuation are called aging stability and tcmperaturc stability, rcspectively. Variations of physical propertics induccd by aging effcct will accumulatc in thc polarizcd ccramics at a gradually slowing-down ratc. Thc accumulation is irrevcrsible unlcss thc ccramics cxperience a ncw cxcitation such as a rcpolarization. Generally, as a result of aging, samples present decreases in dielectric constant, dielectric loss, piezoelcctric coefficicnt and elastic compliance and increases in mechanical quality factor and frequcncy factor. It is also found that such changes are roughly proportional to the logarithm of the duration. The aging curvc of the pol cd piezoelcctric ccramics may bc interfercd by environmental factors. To deal with possible disturbances, a prior artificial aging treatment is usually employed to stabilize the poled ceramics so that the ceramics won't fluctuate in properties with the environmental interferences. In practical manufactures, the poled piezoelectric ceramics are aged by heat treatment or heat cyeles. The prior heat treatment can help the ceramics to stabilize from other heat excitements. This stabilization is attributed to the mechanism that domain motions of the ceramic are enhanced and its internal stress is largely released during the artificial aging processing. Other artificial aging methods such as elcctric aging, mechanical aging and exposure to y-ray radiation of Co", can also achicvc similar cffects. (2) Thermal depolarization Thermal depolarization will occur during heating the piezoelectric ceramIcs. Dipolcs get in disorder gradually with the tempcraturc elevating, dcteriorating the piezoelectric performance simultaneously. Once the temperature reaches abovc the Curic point, whcre thc piczoelectricity disappcars thoroughly, the ultrasonic motor is irreversiblc dcstroyed. Consequcntly, it is ncccssary that thc divices operatc at tcmpcraturcs far below the Curie point. Thc tcmpcraturc limitation whcrc piezoelectric ccramics can safely work without rcmarkablc reduction in piczoelectric activity is approximately set at half of thc Curie point.

Chapter 2

Fundamentals of Piezoelectricity and Piezoelectric···

41

(3) Electric depolarization Electric dcpolarization happcns if a strong invcrse electric field is applicd on a polcd ccramic. Whcther the elcctric field will cause scrious dcpolarization in thc material depends on the material itself and the applying duration of the electric field. as well as the temperature that the material stays. For a direct current electric field. thc strcngth thrcshold causing dcpolarization is around 5001 OOOv Imm. Thc readers have also to notice that thc material can bc depolarizcd during the other half period when applying an altering current field to drive ultrasonic motors. (4) Mcchanical dcpolarization Excessive mechanical strcss can disarrange dipolcs in piczoelectric ceramIcs. leading to a failure in piczoelectric pcrformancc. This process is referrcd to as mechanical depolarization. Piczoelectric ceramics with differcnt compositions may allow different limitations of the safe mechanical stress. Reliable data and information have to be referred for reasonable application of materials.

2. 5. 2

Applications of Piezoelectric Materials to Other Actuators

Besides ultrasonic motors. other piezoelectric actuators based on different forms of piezoelectric materials havc also been widely applied in many fields. Considcring their application importancc and their distinct opcrating mcchanisms in contrast with ultrasonic motors, we will then launch a brief introduction for these piezoelectric actuators.

1. Piezoelectric stack actuators In conventional piezoelectric actuators. the displacements of single layer piezoelcctric actuators are found to bc too small to fulfilllargc strokc driving. Thc idca thcn comes naturally to stack several piezoelcctric ceramic pieccs together to form a piezoelectric stack actuator. As shown in Fig. 2. 11, the piezoelectric stack actuators are fabricated by agglutinating piezoelectric ceramic pieces in serics. Thcse picces are electrically parallel but mcchanically scrial. When a voltage IS applicd along the poling direction. each singlc picce produces a displacement, and all displacements sum up to the total output of the stack actuator.

Fig. 2. 11

Piezoelectric stack actuators [PI (Physik Instrument) L. P. ]

Current concerns for piczoelectric stack actuators are mainly on to compensatc thc hysteresis characteristic of the dcviccs. This bchavior refcrring to thc nonlin-

42

Ultrasonic Motors Technologies and Ap plicalions

ear hysteresis between the input voltages and the output displacements, is an intrinsic trait of piezoelectric materials. Therefore, some compensation methods have to be adopted to improve the positioning precision of the actuators.

2. Piezoelectric bimorph actuators Piezoelectric bimorph was firstly invented by Baldwin Sawyer in 1931. Now it has been frequently used in piezoelectric elements for acoustic detections, USMs, laser beam deflectors, filters, accelerometers, optical choppers, etc l3J • There are four structures commonly used in piezoelectric bimorphs, whose schematic diagrams arc presented in Fig. 2.12. In diagrams (a) and (b) two identical piezoelectric plates arc bonded to each other, with their poling directions oppositely arranged. Electrodes are coated on both sides of the bimorph. These two structures arc therefore called antiparallel-type piezoelectric bimorphs or continuous-type piezoelectric bimorphs. The bimorph in Fig. 2. 12 (c) contains an extra electrode between two plates, and both plates are poled along the direction of the driving voltage. Contrastively, this structure is named as parallel-type piezoelectric bimorph. The actuator in Fig. 2. 12 (d) consists of a non-piezoelectric plate and a piezoelectric vibrator coated with electrodes.

{jJ U ｾ＠

{jJ ｴｾ＠

(a)

(b)

f[ ｦｾ＠ (e)

Fig. 2. 12

ff' (d)

Structures of piezoelectric bimorphs

When applied with an electric field, owing to the converse piezoelectric effect, the bimorphs in (a), (b) and (c) start to bend since one vibrator inside the structures extends and the other contracts. The working voltage of the bimorph in (c) is twice as large as those of the bimorphs in (a) and (b), so the bending deforma tion of the bimorph in (c) is also twice as large as those of the bimorphs in (a) and (b). The behavior of the fourth one in (d) is similar with that of the former three ones, but its motion and output is tunable by varying thickness ratios between the piezoelectric plate and the non-piezoelectric one or by changing the elasticity modulus of the non-piezoelectric material.

3. Functionally graded piezoelectric actuators For functionally graded piezoelectric materials, the composItions and structures are controlled to change gradually from one side to the other side. Correspondingly, the properties and functions of the materials change gradually too. A structural comparison between the bimorph and the functionally graded device is shown in Fig. 2. 13. In bimorph structure, the sharp interface is easy to concen-

Chapter 2

Fundamentals of Piezoelectricity and Piezoelectric···

43

trate stress and induce interface cracks. However, these disadvantages can be effectively avoided in the gradient interface of the functionally graded material. Ｍｾ＠

Ｍｶ

Ｍ

________________________ｾ＠

Ｋｶ

ｾ＠

________________________ｾ＠ (a) Piezoelectric bimorph

(b) Functionally graded piezoelectric material

Fig. 2. 13 A comparison between the structures of piezoelectric bimorph and functionally graded piezoelectric material

Figure 2. 14 shows the working mechanisms of a multi-layer functionally graded piezoelectric actuator[14:. Four layers with different compositions and properties are sintered together to form a structure without evident interfaces. The piezoelectric coefficients and dielectric constants vary from bottom to top in a positive and negative gradient. respectively. Under a DC voltage in thickness direction. the layers of smaller dielectric constants will have larger electric-field intensity distributions. As a result, each layer deforms in the way as the Fig. 2. l1(b) shows. The deformations then integrate into a uniform deformation in the whole device. as shown in Fig. 2. 14(c). Apparently, the internal stresses are greatly depressed in the device owing to the structural gradient. Furthermore, higher mechanical strength can be obtained for the absence of adhesive between the interfaces.

(a) Schematic structllre ofa functionally graded piezoelectric actuator with four piezoelectric layers

(b) The defomlation of each layer under applied voltage

(c) Total defomlation of the fu nctionally graded piezoelectric aCllmtor

Fig. 2. 14

Deformation mechanism of the functionally graded piezoelectric actuator

4. Piezoelectric fiber actuators The brittleness of piezoelectric ceramics restrains their applications in nonplanar devices. For this reason, active fiber composites (AFe) and macro fiber compos-

Ultrasonic Motors Technologies and Ap plicalions

44

ites (MFC) were designed by American scientists from MIT and NASA in the 1990' s. These composites arc generally called piezoelectric fiber compositesL 15J . In AFC structures, arrays of piezoelectric fibers with round cross sections arc embedded in epoxy resin matrix. Interdigital electrodes are arranged perpendicularly to the axial direction of the fibers. The fabrication of MFC is analogical to that of AFC except that the piezoelectric fibers inside arc with rectangular cross sections. Large stains can be obtained in AFC and MFC by utilizing their axial d" piezoelectric characteristics. Comparing with piezoelectric ceramics, piezoelectric fiber composites possess better flexibility so that they can satisfy the applications in bending planes(Fig. 2.15).

Piezoelectric active fiber composites (left) and macro fiber composites (right)

Fig. 2. 15

Recently. metal core piezoelectric fibers (MPF) are developed to fabricate new piezoelectric sensors and actuatorS[16 17J. A typical structure of MPF is shown in Fig. 2. 16, where the piezoelectric fiber with diameter O. 15-0. 25mm is coated with a layer of metal electrode on the surface. In the center of the piezoelectric fiber, a metal core of O. 05mm in diameter, usually platinum. acts as another electrode. This metal core can also act as a medium that enhances the strength of the fiber.

Metal COre

Piezoelectric cCl'1lmic

T/ ｾ＠

Fig. 2. 16

..... -

I

I

I

1 - .....

J-_I_

ｾＭｊ＠

'1

Piezoelectric ceramic fiber with a metal core inside

We refer the fiber to as the full-electrode piezoelectric fiber if its surface is entirely coated with metal electrode. The piezoelectric fiber is polarized along the radial direction, so that the fiber will produce a radial extension vibration type under an applied electric field. A half-plated fiber is called the half-electrode piezoelectric fiber. Bending distortions will be produced in the half-electrode piezoelectric fiber after applying electric field. These tiny dimensional MPF can be con-

Chapter 2

Fundamentals of Piezoelectricity and Piezoelectric···

45

veniently embedded into composites to drive deformations in the composites.

2.6

Advances in Novel Piezoelectric Materials

With the fast-growing application of ultrasonic motors and other piezoelectric devices, the demand for new piezoelectric materials is getting more and more imperative. Here we present some progress in the research on piezoelectric materials that are promising for future potential applications.

1. Multi-constituent doped PbCZr x Ti 1- x )()3CPZT) ceramics[1820: Multi-constituent doped PZT ceramics have been intensively investigated for long duration since its electrical and mechanical properties of the ceramics can be greatly varied by doping PZT with acceptors, donors, or isovalent dopant. It was verified that doping of Mn' I in PZT could improve the mechanical quality factor Qm; and its electromechanical coupling coefficient k" could be improved by Sb 5 - doping. So that PZT based ceramics doped with both Mn'- and Sb'- have been constantly attended. By these efforts some trinary and quaternary PZTbased materials with excellent sintcring property and repeatability have been found. Materials applied for high-power piezoelectric devices have been reported based on these systems. For example, in Mn'· doped quaternary PS:'\J-PZ:'\J-PZT system, experiments reveal that pure perovskitc phase can be formed within a wide range of Mn' I additives. Proper amounts of Mn'· additives can optimize the piezoelectric properties of the PS:'\J-PZ:'\J-PZT quaternary system for improving the mechanical quality factor Qm and decreasing the dielectric loss tanB. The ceramics with o. 5 % (mass fraction) dopant possess the best electromechanical properties that satisfy the requirement for USM and transformer applications. Recently a new series of quaternary PZT-based ceramics doped with Ba" and Sr'· have been developed with properties greatly improved. Among them, d 33 = 406pC/:'\J, kp

=

o. 55,

E=

2183, Qm = 1077, and tani) = 2. 7 %, respectively.

2. Relaxor ferroelectric single crystals[5] Relaxor ferroelcctrics such as lead magnesium niobate-lcad titanate (PM:'\J-PT) and lead zinc niobate-lead titanate (PZ:'\J-PT) single crystals exhibit much higher piezoelectric coefficients and electromechanical coupling coefficients than conventional piezoelectric ceramics- 5-. For example, the strain of these crystals reaches to 1. 7 %, almost an order larger in magnitude of the conventional piezoelectric ceramics. Furthermore, it has been verified that even temperature down to -200'C, the property of PMN-PT and PZN-PT single crystals are still comparable with the room-temperature property of PZT ceramics['l 24:. This nature enables PMN-PT and PZN-PT suitable for USM running at extreme-temperature conditions. Relaxor ferroelectric single crystals are promising to replace conventional piezoelectric ceramics in many devices, such as acoustic detectors, ultrasonic imaging devices, high-strain actuator, and ultrasonic motors used in extreme circumstances- 25 - 31J •

3. Lead- free piezoelectric materials[35] The lead-containing piezoelectric ceramics may cause serious hazard to the envi-

46

Ultrasonic Motors Technologies and Ap plicalions

ronment and human health during their manufacturing, serving and disposing after failure. Therefore the development of environment-friendly lead-free piezoelectric ceramics is indispensable from the perspective of the global environment protection. Recent research on lead-free piezoelectric materials has been focused mainly on two promising systems: perovskite structural piezoelectric ceramics and bismuthlayered structural piezoelectric ceramics. The former family ineludes the solid solutions of Ko 5 :'\lao. 5 :'\Ib03 - LiTa0 3 , BaTi03 - Bio 5 Ko. 5 Ti0 3 , and Bio. 5 Nao. 5 Ti0 3 Bio. 5 Ko. 5 TiO, , with their compositions near the morpho tropic phase boundary. In optimized compositions the piezoelectric constant d 33 of these systems can reach 300pC/:'\I, which is elose to the value of PZT ceramics. The bismuth-layered structural solid solutions such as the donor-doped Bi4 Ti3 0 12 or Bi, TiTaO g systems are featured with high Curie point and relatively large piezoelectric coefficient, as well as the less temperature dependence of their resonant frequencies. These traits make them suitable for sensor and resonator applications.

4. Piezoelectric composites[6, 18: Piezoelectric composites have been developed since the late 70s of last century. The preparation of piezoelectric composites involves to incorporate piezoelectric ceramics and piezoelectric polymers with designed connectivity, mass/volume ratios and spatial distributions to form certain microstructures. Piezoelectric ceramics have disadvantages such as high density, extreme brittleness, easy fracture to mechanical impacts and poor capability to form complex shapes. On the other hand, piezoelectric polymers possess properties of excellent flexibility, low density and great machinability but poor temperature endurance and high cost. However, the properties of piezoelectric composites can be remarkable improved by taking advantage of the composition effect elaborately, so that piezoelectric composites keep the merits of both components of piezoelectric ceramic and polymer and overcome their disadvantages, offering excellent piezoelectric performance and mechanical flexibility. The manner of each phase connects with itself in composites is known as the "connectivity" of the composites, which is proposed by Newnham et al. in 1978. Fig. 2. 17 lists all ten types of connectivity of piezoelectric composites. These connectivity types are: 0-0, 0-1, 0-2, 0-3, 1-1, 1-2, 1-3, 2-2, 2-3, and 3-3. The first number in the expression represents the connecting dimension of the piezoelectric phase and the second number is the connecting dimension of the polymer phase. Different connectivity types mean different spatial distributions of the ceramic phase and the polymer phase and correspondingly different dielectric and piezoelectric properties in the composites.

5. Piezoelectric thin jilms[36 37J The progress in thin film deposition methods has provided the possibility of application thin films in almost all fields of modern science and technology. Now bunch of techniques have been employed to prepare piezoelectric materials from high-quality epitaxial films to large-area polycrystalline films. Among them,

Chapter 2

Fundamentals of Piezoelectricity and Piezoelectric'"

---__ ---0-0

0- I

0-2

0-3

I- I

1-2

2 -2

2 -3

1-3

Fig. 2. 17

47

3-3 (Two views)

Ten connectivity types of piezoelectric composites

sputter deposition, sol-gel, chemical vapor deposition (CVD), molecular-beam epitaxy (MBE) and pulsed laser deposition (PLD) are well established for piezoelectric films preparation. Piezoelectric films could have many important applications due to their versatile properties. For example, in surface acoustic wave ( SAW) devices. piezoelectric films have been widely used as the functional parts. The combination of micro sensors and actuators onto the surfaces of semiconductor integrated circuits creates a new research highlight of piezoelectric film micro mechanic-electric systems. Devices based on bulk piezoelectric materials usually operate with operating frequencies no more than hundreds hertz due to their dimension restrictions. On the other hand. devices based on piezoelectric films offer much higher operating frequency, extra flexibility in designing and shaping the device dimensions, as well as additional advantage in device miniaturization and integration. In various applications, piezoelectric films can replace their single crystal or ceramic counterparts, to provide similar functions with considerable satisfaction.

References [ 1] [2] [ 3] [ 4] [ 5] [ 6] [ 7] [ 8] [ 9]

Zhiwcn Yin. Physics of Dielectrics (Second Edition). Bcijing: Prcss, 2005:1-8. (in Chincsc) B Jaffe, W R Cook, H Jaffe. Piezoelectric Ceramics. "few York: Academic Press, 1971: 1-5. Duan Fcng, Changxu Shi, Zhiguo Liu. Introduction to Material Science-An Integrated Approach. Beijing: Chemical Industry Press, 2002:324-350. (in Chinese) B Jaffe, R S Roth, S Marzullo. Piezoelectric properties of lead zirconate-Iead titanate solid solution ccramies. J. Appl. Phys., 1951,25: 809-100. R F Service. Shape-changing crystals get shifter. Science, 1997, 275: 1878. Changxu Shi, Hengde Li, Lian Zhou. Handbook of Materials Science and Engineering. Beijing: Chcmieal Industry Prcss, 2006: 7-76. (in Chincse) Shenghe Lin, Zhibi Ye, Yubin Wang. Piezoelectric Ceramics. Beijing: Defense Industry Press, 1980: 17-40. (in Chinese) Statc burcau of technical supcrvision. National Standards of the People's Republic of China CElT 3389. 1-1996. Bcijing: Standards Prcss of China, 1997: 2-3. Daorcn Song, Mingshan Xiao. Piezoelectricity and Its Application. Bcijing: Popular Sciencc

Ultrasonic Motors Technologies and Ap plicalions

48

[IOJ [l1J [I2J [13J [I1J [I5J [16J

[17J [I8J

[I9J

[20J [21J [22J [23J [21J [25J [26J [27J

[28J [29J [30J

Press, 1980:19-38. (in Chinese) Yuan Li, Zikai Qin, Zhigang Zhou. Measurement for Piezoelectric and Ferroelectric Materials. Beijing: Science Press, 2001:19-21. (in Chinese) Yuhuan Xu. Ferroelectric and Piezoelectric Materials. Beijing: Science Press, 1978: 118202. (in Chinese) Weilie Zhong. Physics of Ferroelectrics. Beijing: Science Press, 1996: 310-311. (in Chinese) J G Smits, S I Dalke, T K Cooney. The constituent equations of piezoelectric bimorphs. Sensors and Actuators A, 1991, 28: 41-61. J Qiu, J Tani, Ueno, et al. Fabrication and high durability of functionally graded piezoelectric bending actuators. Journal of Smart Materials and Structures, 2003, 12: 115-12l. R B Williams, G Park, D J Inman. An overview of composite actuators with piezoelectric fibers. Proc. of SP IE- The International Society of Optical Structures, 2002, 1753: 121-127. J Qiu, N Yamada, J Tani, et al. Fabrication of piezoelectric fibers with metal core. Pmc. of SP IE's 10th International Symposium on Smart Structures and Materials. San Diego, CA. , Active Materials: Behavior and Mechanics. DC Lagoudas, Ed., 2003, 5053: 175-183. G Sebald, J H Qiu, D Guyomar. Modeling the lateral resonance mode of piezoelectric fibers with metal core. Journal of Physics D, 2005, 38: 3733-3710. Qian Li, Ying Yang, Dandan Wan, et al. Microstructural characteristics and electrical properties of x Pb(Mg 1n Ta'/3)O,-(0. 1-.T)Pb(Mnl/3Sb2/')O,-0. 9Pb(Zr0.5zTio.48)03 high power piezoelectric ceramics. Materials Science and Engineering B, 2009, 163: 115-150. (in Chinese) J Ryu, D SPark, D Y Jeong. Effect of LazO, doping on the piezoelectric properties of PbZr03-PbTi03-Pb(Zn1l3 :'-Ib2/3) 03-Pb(Snl/3 Nbz/3) 03-yMn03 ceramics for high-power applications. Journal of Ceramic Processing Research, 2009, 10: 386-390. (in Chinese) G H Hacrtling. Ferroelectric ceramics: history and technology. Journal of the American Ceramic Society, 1999, 82: 797-818. (in Chinese) Fuxue Zhang, Likun Wang. Modern Piezoelectricity (Volume 1, Second Edition). Beijing: Science Press, 2003: 97-98. (in Chinese) J Van Randeraat, R B Setterington. Piezoelectric Ceramics. Mullard Limited, 1971: 15-16. S E Park, T R Shrout. Ultrahigh strain and piezoelectric behavior in relaxor based ferroelectric single crystals. Journal of Applied Physics, 1997, 82: 1801-1811. G Roger, D Busch. A survey of micro-actuator technologies for future spacecraft missions. [2009-05-26]. http://www.robotstore.eom/support. asp. S E Park, W Hackenberger. High performance single crystal piezoeleetries: applications and issues. Current Opinion in Solid State &. Materials Science, 2002, 6: 11-18. M Levy, S Ghimire, A K Bandyopadhyay, et al. PZ:'-I-PT single-crystal thin film monomorph actuator. Ferroelectrics Letters Section, 2002, 29 (3-4): 29-40. K S Moon, M Levy, Y K Hong, et al. Axial displacement measurement of a single-crystal actuator using phase-shift interferometry. IEEE Transactions on Industrial Electronics, 2005, 52 (4): 953-959. M Yang, M Zhu, C Robert, et al. Design and evaluation of linear ultrasonic motors for a cardiac compression assist device. Sensors and Actuators A, 2005, 119: 214-220. S Dong, L Yan, :'-I Wang. A small, linear, piezoelectric ultrasonic eryomotor. Applied Physics Letters, 86: 200505350l. Z Y Feng, T H He, H Q Xu, et al. High eleetrie-field-indueed strain of Pb(Mg 1/ 3Nbz/3)O,PbTi0 3 crystals in multilayer actuators. Solid State Communications, 2001, 130 (8): 557-562.

[31J [32J

S E Park, T R Shrout. Relaxor based ferroelectric single crystals for electro-mechanical actuators. Materials Research Innovations, 1997, 1 (1): 20-25. S Genti, D Damjanovie, :'-I Setter. Pb(Mg 1/3Nbz/3)O, and (1-x) Pb(Mg1n:'-lb'n)O,-.T PbTi03 relaxor ferroelectric thick films: processing and electrical characterization. Journal of Electroceramics, 2004,12 (3): 151-16l.

[:l3J

V Y Topolov. Orientation relationships between electromechanical properties of monoelinic

Chapter 2

Fundamentals of Piezoelectricity and Piezoelectric'"

O. 91Pb (Znl!' Nbz/,) 0,-0. 09PbTi0 3 single crystals.

[31J

[35J [36J [37J

49

Sensors and Actuators A-Physical.

2005.121 (1):118-155. S C Woody. S T Smith. X N Jiang, ct al. Pcrformancc of single-crystal Pb(Mgl/ 3 Nb z/3 ()3)32%PbTi0 3 stacked actuators with application to adaptive structures. Review of Scientific Instruments, 2005, 76 (7): 075112(1-8). T Takenaka, H :'-Iagata. Current status and prospects of lead-free piezoelectric ccramics, J. Euro. Ceramic. Society, 2005, 25: 2693-2700. Zhiwen Yin. Physics of Dielectrics (Second Edition). Beijing: Science Press, 2005: 778-831. C P Araujo, J F Scott, G W Taylor. Ferroelectric Thin Films: Synthesis and Basic Properties. Amsterdam: Gordon and Breach Scicnce Publishcrs, 1996: 1-8.

Chapter 3

Fundamentals of Tribology and Tribomaterials for Ultrasonic Motors Tribology is defined as "the sCIence and technology of phenomena occurnng at the contact interface between objects", and its main topics are friction and wear of materials. Ultrasonic motor is a new tribological actuator, which uses the friction at a contact area between a stator and rotor to convert the ultrasonic vibration of the stator into the linear or rotational motion of the rotor. It is evident that the ultrasonic motor with friction drive possesses features such as self-lock without power and a high self-lock torque. As far as the locking property of USM is concerned, the self-lock torque is higher than its stall torque, while the rotor's inertia is low. This indicates that the ultrasonic motor has rapid (millisecond scale) response property. Because USM transmits the power via friction at the contact area between the stator and rotor, stable and relatively high friction force at the contact interface is required. Since sliding wear between the rotor and stator is inevitable,

high wear resistance of tribomaterials in USMs (stator and rotor) is then essential to maintain precision control, because their wear causes changes in the contact condition between the stator and rotor and leads to a decrease in control accuracy. Generally, friction characteristics include output power property of friction surfaces, the microstructure of wear surface and the tribological property at contact surfaces, whereas the phys-chemical properties of tribomaterials include an elastic modulus, wear resistance, anisotropy, dependence to environments, etc.: 1 RJ Therefore, how to match the friction and wear characteristics between stator and rotor pairs is a key to guaranteeing the performance of USMs. Currently, the tribological behaviors of tribosystems without vibrations have been investigated. If the vertical and tangential high-frequency vibration components along .1':, y, and z axial directions are superimposed on the tribosystem, the friction and wear behaviors become sophisticated. Thus, it is imperative to study the friction and wear behaviors of tribomaterials under ultrasonic vibration. To improve the reliability and stability of USM, an advanced functional surface technology and nanotechnology must be used to adjust and enhance the tribological properties between the stator and rotor in adverse circumstances. Furthermore, it is important to devclop experimental methods for estimating tribomaterial life and efficiency because the life and the efficiency of USM largely depend on the tribological properties of the stator and rotor pairs. It is obvious

C. Zhao, Ultrasonic Motors © Science Press Beijing and Springer-Verlag Berlin Heidelberg 2011

Chapter 3

Fundamentals of Tribology and Tribomaterials···

51

that friction interfaces for different ultrasonic motors exhibit various action fashions. However. due to the rotor or mover being impelled to move according to the elliptical motion at the contact points between the stator and rotor. the influences of the different action fashions on the stator and rotor are identical[9-15]. Therefore. it is of vital importance to analyze the tribological effect of the stator and rotor pair if we want to prolong the life of USM. In this chapter. the basic tribology will be first introduced. and then the preparation of tribomaterials in USM will be addressed. The influence of the phys-ehemieal properties of the tribomaterials on tribologic characteristics will be analyzed. After that. the experimental methods to determine the tribomaterial performance will be discussed.

3. 1 3. 1. 1

Basic Tribology Surface of Tribomaterials

In a viewpoint of tribology. the friction between two sliding surfaces is largely governed by physical conditions and chemical interactions between sliding surfaces and environments. Physically. rough surfaces could create higher friction coefficient. while chemical interactions between two sliding surfaces and the environment can play an important role in the friction and wear behavior of tribocouples in different environments. Usually. the practical solid surfaces arc formed by cutting. grinding and polishing. These surfaces look smooth and arc sometimes called mirrors. But even a mirror surface is still rough microscopically. Since the solid surface has microasperities. the surface roughness is estimated by peaks and valleys with various amplitude and space. These microasperities with long wavelengths on the surface arc formed owing to the vibration of the work piece or tools during processing. The micro asperities arc distributed directionally or isotropically on the surface depending on processing methods. When the solid surfaces are processed via turning. milling and planning. the asperities arc distributed directionally. whereas the asperities arc distributed isotropic ally or equiprobably as the surfaces arc processed via electropolishing and lapping. The surface roughness is determined by R, (centerline average roughness). Ry (average roughness at ten points) andR,(maximum altitude roughness). respectively. Normally. R, is more often used to show the roughness value of surfaces. For the stator and the rotor in USM. their surface roughness R, is lower than 0. 51l-m. In order to measure the roughness value for such solid surface. a surface profilometer is popularly used. and the cross-sectional profile of the surface is measured as shown in Fig. 3. 1. Furthermore. the surface microstructure of metal will be changed during cutting process. The surface of metals usually consists of several layers which arc formed during their machining processes[16] • as shown in Fig. 3. 2. From the metal matrix. the first layer is the deformation layer(also known as the strain hardening layer) with about l0ll-m thickness. and then the Bielby layer is formed on the deformation layer due to the surface melting. flowing and quenching. Thus. the microstructure of Bielby layer is amorphous or microcrystal. The oxide layer is formed by the chemical reaction between metal

52

Ultrasonic Motors Technologies and Ap plicalions

surface and oxygen in air. The outside layer is the absorption layer or contamination layer formed by the absorption of gas or liquid polar molecule on the solid surface in environments. It is obvious that the surface roughness and microstructure of tribomaterials have more influenees on the tribologieal properties of tribomaterials.

o

o

Dusl panicle wilh dia meter of ｉ

ｾｭ＠

Oxide laye r

-I

0. I

0.2 0 .3 0.4 0.5

0.6 0 .7

0 .8

x/ mm

Fig. 3. 1

3. 1. 2

Surfacc morphology of a stator

Fig. 3. 2

Typical surface of metal

Friction and Its Classification

The importance of friction may be seen in daily life. To decrease energy consumption in overcoming friction during sliding, the reduction of friction is extremcly important in modern technologies. However, when people walk or car moves. they need sufficiently high friction to push their body to move forward. Thus, it is imperative to control friction in our modern life. If friction effect exits on the contact surface between two sliding objects. which are called as a tribopair. Fig. 3. 3 shows a tribosystem constituted by objects A and B. It is clear that the object A is pressed firmly on the object B at a normal load of P. When object A is pushed by an external force F. a rclative motion or motion trend occurs at the contact surface between A and B. At this moment, A phenomenon to impede the rclative motion appears at the contact area.

This phenomenon is

called as friction. The force impeding the object motion at the contact surface is called as friction force, marked as Fr. The magnitude of Fr is related to the normal load. the contact surface status and the tribopairs.

Fig. 3. 3

Tribosystem

The following Coulomb's friction law:]6] is the most classical equation to

Chapter 3

Fundamentals of Tribology and Tribomaterials···

53

describe the above tribosystem (3.1)

where /1 is a friction coefficient. In the viewpoint of the macro-motion state, frictions can be classified into static friction and dynamic friction. As seen in Fig. 3. 3, thc two objects A and B arc initially kcpt in relativcly stationary statc at thc normal prcssure P. When thc extcrnal force F is zcro, therc is no friction between A and B. When F increases gradually in a certain rang, the relative micro-motion will occur between A and B. In this case, the friction force Fr is callcd as a static friction force, which corresponds to a static friction cocfficicnt /1,. When F is higher than the maximal friction forcc, the rela ti ve macro-movc bctwccn A and B will occur. Thcn this friction force is called as a dynamic friction force, which corrcspond to a dynamic friction cocfficicnt /1d. According to the relative motion of the tribopair, the friction is classified as sliding friction, rolling friction, rolling and sliding friction: (1) Sliding friction is thc friction state that thc relativc spccd on thc contact surfacc of the tribopairs are not cqual to zcro. (2) Rolling friction is thc friction statc that the relativc specd at somc actual contact points are zero. (3) Rolling and sliding friction is the friction state that combines sliding friction and rolling friction. According to thc friction states of thc contact surface of tribopairs, thc friction can be classified into dry, boundary, fluid and mixed frictions: (1) Dry friction is the friction condition that there is no lubricant between two objccts; usually the object surfacc absorbs gas, aqucous vapors and so on. (2) Boundary friction is thc friction condition that thc cxtremely thin film of the lubrication oil separates the sliding surfaces of two objects. (3) Fluid friction is the friction condition of which the surface of two objects is completely separated by fluid film and the friction characteristics is decided by the fluid viscosity. (1) Mixed friction is the mixed conditions including dry friction, boundary friction and fluid friction.

3. 1. 3

Friction Mechanism

To cxplain thc occurrcncc of friction, Amontons put forward the mechanical junction thcory in 1699, while Tomlinson and Hardy put forward the molecular attraction theory in 1929 and 1936, respectively. Since 1938, Bowden had done detailed works about tribology. For example, Bowden and Tabor have distinguished the large difference bctwcen cffectivc contact arca and true contact arca in 1942. Finally, the adhcsion thcory had becn propos cd by Bowdcn in 1950 to elucidate the friction mechanism. Now, the adhesion theory and its development are reviewed here- 16 -.

1. Simple adhesion theory Even in the case of a mirror surface, the surface displays rough asperities

54

Ultrasonic Motors Technologies and Ap plicalions

microscopically. When one solid contacts with the other, the surface mlcroasperisties will weld together due to the adhesive between a tribopair. When one of the solids moves on the other, the microweld junctions will break. So the entire friction process changes from the adhesion of asperities to the shear fracture of junctions alternatively. At the normal load pressure of p, the contact stresses at some contact asperities are so high that the plastic deformation occurs at contact zone, and then the contact area increases to the all area bearing load P. Suppose the yield strength of an ideal elastic-plastic material is rr, and the true contact area between two solids is S" then it has P=rr,S,. Once an object slides relatively against the other, the adhesive junctions arc fractured via shearing. This indicates that the shear force of the junctions is the main part of the friction force F. So the friction Fr force can be expressed as FI

S,T;,

=

=

(Plrr,)r;,

(3. 2)

and the dynamic friction coefficient (friction coefficient) is calculated as fl.d

=

FrlP

=

T:/rr,

(3. 3)

where T;' is the shear strength of the adhesive junction. It is obvious from Eq. (3. 3) that the friction coefficient is independent of the effective contact area, but is directly proportional to the shear strength of adhesive junction and inversely proportional to the yield strength of the ideal elastic-plastic material. If we consider the strain-hardening effect of tribomaterials, the shear strength Tb of the softer material is used to replace T;, in Eq. (3.3). Then (3. 1)

according to Eq. (3. 4), the friction coefficients of o. 2 for most metals arc acquired, but experimental results are mostly between O. 2-0. 5. This difference indicates that the simple adhesion theory has to be modified L16_

2. Modified adhesion theory In the situation of static friction, the true contact area S, is directly proportional to the normal load P. When the two objects in the tribosystem slide relatively, the true contact area S, will increase. Assuming the adhesive junction's yield is related to the composite stress of the compressive stress given by the normal load P and the shear stress given by tangential force, as shown in Fig. 3. 1, an empIrical equation for the modified model is introduced as (3. 5)

where a is an experimental constant. When a natural contamination film is formed on the contact surface and its shear strength is TI' there is (3. 6)

where Tb is the shear strength of the softer material in tribosystem. f3 is less than 1. When the ratio of Fr I S, is lower than Tr' with P increasing the contact area increases, while the contact area stops increasing as the ratio of FilS, equals to Tr. If the adhesive junction is sheared, the tribopairs start to slide over each other. If T in Eq. (3. 5) is replaced by Tr' the sliding criterion of the tribopair can be

Chapter 3

Fundamentals of Tribology and Tribomaterials···

55

s,

Fig. 3. 4

Compressive stress and shear stress at junction

expressed as (3.7) it is known from Eq. (3. 7) that the number of adhesive junctions will increase if F is very high. Then aｔｾ＠ ""=' a; or a = a; / ｔｾＧ＠ so a; = ari / f3 2. Combining those with Eq. (3. 7), the friction coefficient can be derived as /1d

f3 /aCl-f32)

(3. 8)

If the contact surfaces are well cleaned and the contact interface has good adhesion, Tr is close to a, of the softer material in contact and f3 is close to unit. It is clear from Eq. (3. 8) that /1d becomes infinite when f3 is equal to 1. When f3 decreases from one, /1d decreases quickly. Due to the shear strength of the contamination film lower than that of metal and the cease of junction growth, f3 is close to zero. Thus, Eq. (3. 8) can be represented as /1d = Tr / a" which agrees with the simple adhesive theory. Although the modified adhesion theory can explain the tribologieal phenomena of metals, it has been criticized because of the following questions such as: CDthe agreement between the theoretical calculation and the experimental results of the friction coefficient is not good; (2)the effect of surface roughness on friction is not considered in this theory; Gil there is a lack of evidence that strength is necessary for the junction formed. To overcome the shortcomings of the adhesion theory, Kragclskii proposed the molecular-mechanical theory based on the adhesion theory and the molecule attraction theory in 1939. Under very high pressure, the mieroasperities on the real contact surface for a tribopair arc mutual chimerism, and the micro asperities of the harder object arc impressed into the softer one. Moreover, the molecular attraction force is existed at the contact zone. Because the motion process is to overcome the mechanical chimerism of mieroasperities, ploughing and the molecular attraction force in the tribosystem, thus, the friction force is a sum of all tangential stresses induced by the mechanical chimerism of mieroasperities, ploughing and the molecule attraction of the contact junction, and expressed as (3. 9)

Ultrasonic Motors Technologies and Ap plicalions

56

where a and yare related to phys-mechanical properties of contact surface. Combining Eqs.(3. 9) and (3. 1). the friction coefficient can be derived as

y+ aS,1 P

{1d =

(3. 10)

where y is the constant friction coefficient obtained from the mechanical chimerism theory. while ,I P is the variable of y after considering the influence of molecular attraction. This theory considers each factor comprehensively. and is usef ul not only to elucidate the mechanism of dry friction and boundary friction. but also to explain the tribology of metal and polymer material. The experimental friction coefficients arc listed in Table 3. 1. which shows the static and dynamic friction coefficients of tribomaterials with smooth surface.

as

Table 3. 1

Friction coefficient for normal tribopairs Static friction coefficients

Dynamic friction coefficients

Materials "fo lubricant

0.15

Steel-steel

o.

Lubricant

No lubricant

10-0. 12

o. o. o. o.

Steel-soft steel Steel-cast iron

0.30

Steel-bronze

0.15

Sol t steel-cast iron

0.20

Sol t steel-bronze

0.20

o.

18

Cast iron-bronze

o.

Bronze-bronze

Ebonite-steel

o.

0.05-0.10

20

o.

18

0.05-0.15

15

0.05-0.15

10

o. o. o. o.

18

0.07-0. 15

15

0.07-0. 12

15-0.20

0.07-0. 15

20

0.07-0. 10

10

0.01

Pure aluminum-brass hardened

o. o. o.

Steel-polycarbonate hardened

0.30

Steel-polyformaldehyde powder

0.16

Metallurgy-steel powder

o. 10 o. 10

Pure aluminum-steel

Bronze-bakelite

Metallurgy-cast iron

3.1.4

10-0.20

0.05-0. 15

o.

Cast iron-cast iron

10-0. 15

Lubricant

15

17 24 27

Wear Mechanism 1l718 -

Wear is the successive removal of surface materials by repeated friction and is mainly caused by microscopic mechanical fracture. Even when surface has some chemical reaction products. such as oxides. the volume loss from surface occurs mechanically in many cases. Although the various wear mechanisms have been proposed. it is difficult to predict the wear loss. It is elear that the wear process involves fatigue. fracture. corrosion and plastic deformation of tribomaterials. The wear mechanism is elassified by Burwell. Main wear mechanisms arc ad-

Chapter 3

Fundamentals of Tribology and Tribomatcrials···

57

hesive wear, abrasive wear, fatigue wear and corrosIve wear, respectively, which arc elucidated as follows.

1. Adhesive wear Adhesive wear is a form of wear which occurs when two smooth surfaces arc slid against each other, and the fragments arc pulled off from one surface to adhere to the other. Adhesive wear always arises from the formation and shear fracture of the junction. When the adhesive junction strength is lower than that of tribomaterials, shear fracture occurs at the joint interface, and the transfer of material is not obvious and wear rate is low. When the adhesive strength is higher than the yield strength of softer material in tribosystem, fracture takes place in the subsurface of softer metal ncar joint, and then wear become mild. When the junction strength is higher than those of tribomaterials, shear failure mainly occurs in the subsurface of soft metal. The fragments adhered to the hard metal make the softer surface scratched. If the junction strength is much higher than the shear strength of tribomaterials, shear fracture occurs at the deeper position of one or two metals, and then wear become severe. 2. Abrasive wear Abrasive wear is the form of wear which occurs when a rough hard surface slides on a softer surface, and ploughs a series grooves. The material originally in the grooves is normally removed in the form of loose fragments. Abrasive wear can also arise when hard and abrasive particles are introduced between sliding surface. In this situation, the abrasive grains adhere temporarily to one of the sliding surfaces, or else arc embedded into it, and plow out grooves in the other. The form of wear is generally called as the three-body abrasive wear. Usually there is the extremely high stress at contact area between abrasive grain and sliding surfaces, which makes the tribomaterials deform plastically and fatigue or fragment. If abrasive wear is caused by hard and rough surface, the form of wear is referred to as the two-body abrasive wear. When the motion direction of particles is parallel to the solid surface, the stress at contact zone between particle and smooth surface is low, which is characterized by the scratch line and shallow grooves on the surface. If the motion direction of particles is vertical to the solid surface, the collision contact stress at interface between particles and surfaces is high, which is characterized by the deeper groove on the surface and large size particles peeled off.

3. Fatigue wear Fatigue wear is observed during repeated sliding or rolling over a track. The repeated loading-unloading cyeles may induce the formation of surface or subsurface cracks, which eventually results in the break-up of the surface with the formation of large fragments, leaving large pits in the surface. Fatigue failure depends on the amplitude of the cycle shear stress. If the shear stress exceeds the endurance strength of materials during rolling, the wear particles arc generated by the initiation and propagation of crack. For the rolling contact, cracks arc usually initiated in subsurface. If the contact condition is the mixture of rolling

58

Ultrasonic Motors Technologies and Ap plicalions

and a little sliding, the damage will occur close to surface. 4. Corrosive wear The mechanical-chemical reaction occurs at a sliding contact zone in the corrosive environment. and the corrosion elements are observed on the sliding friction surface. During sliding friction, the corrosion clements on the sliding surface arc worn away so that the corrosive attack can continue. This indicates that the corrosion and friction are promoted mutually in corrosive wear.

3. 1. 5

Wear Surface for Stator and Rotor of Ultrasonic Motors

Generally, wear occurs as a result of friction. For TRUM-60, its rotor surface is covered with the tribomaterial, and its stator is made of copper. Fig. 3. S shows the microstructure of wear track on a stator and rotor. As seen in Fig. 3. 5. it is clear that the plough grooves are formed on the worn surface owing to adding hard minerals such as alumina into the friction material as reinforced phase. Fig. 3. S (a) shows the optical microscope of a copper stator. The plough grooves arc generated on the worn surface of the stator owing to friction, and their direction is identical to the rotation direction of the rotor. If the hardness of tribomaterials (base materials) was lower than that of substrate metal, the plough grooves are formed on the rotor's surface. Thus, the wear mechanism is abrasive wear. It is obvious from Fig. 3. 5 (b) that the plough grooves arc formed on the rotor's surface owing to the friction effect, and the grooves' direction is the same as that of the rotor's rotation. Fig. 3. S(c) shows SEM image of polytetrafluoroethylene-based tribomaterials for rotor. As seen in Fig. 3. S (c), besides the plough grooves. the fragments arc observed to be pulled off the surface. This indicates that the wear mechanism is the mix wear including abrasive wear, fatigue wear and adhesive wear for the tribomaterials in USM.

(a) 0pl icalmi eroscopic ofstalor

(b) 0pliealmieroscopie ofrolor

Fig. 3. 5

3.2 3. 2. 1

(e) Scanning e el ctron microscopic ofrolor

Microscopic image of wear track

Tribomaterials Used for Ultrasonic Motors Basic Requirement, Classification and Selection Principle

In order to increase the mechanical characteristics and running life of ultrasonic

Chapter 3

Fundamentals of Tribology and Tribomaterials···

59

motor, the surface of a stator or rotor is usually coated with tribomaterial or modificd using othcr surface processing methods. Currcntly, therc arc two elcments in the criteria to evaluate the ultrasonic motor's performances: CDthe ultrasonic motor posscsscs thc good output pcrformancc and running stability; @thc ultrasonic motor has the excellcnt reliability and running lifc. It is realized that the factors to influence the energy transmission are the situation of contact sur face (roughness, contact area), tangent friction force, longitudinal vibration velocity; but onc of main factors to induce thc ultrasonic motor running unstably and its life shortening is its tribology of its tribopairs.

1. Basic requirement and selection principle of tribomaterials in ultrasonic motors According to before-mentioned designing requirements, tribomaterials for USM should meet the following basic conditions: CD appropriatc static friction coefficient (0.15-0.3 for TRUM, greater than 0.2 for LUSM) , the coefficients of dynamic friction close to that of static friction, and thcre is no creep or crawl at low velocity; @good wcar-rcsistant pcrformancc and lcss wcar ratc for tribopairs surfaces; ®low frictional noise «15dB); @good surfaces hardness match of tribopairs; Ql) stablc phys-chcmical propcrties at room, high and low tempcraturc, low or high temperature tolerance; ® good vibration resistance and impact resistance propertics. The selection of friction coefficient will depend on the designing requirement of ultrasonic motors. For the motor of short-stroke, discontinuous working and short lifc, it is suitable to selcct thc tribomaterials with high cocfficicnts. But for the motor of long-stroke, continuous working and long life, it is suitable to select the tribomaterials with lower coefficients. Furthcrmore, thc tribomaterials' lifc is one of thc important factors deciding the running-life of ultrasonic motors, so it is especially important for the tribomaterials to have high wear-resistance ability. Due to the generation of frictional hcat, tcmpcraturc on thc friction surface will incrcasc with the running timc, and finally approach to a balance temperature higher than 100'C. Thus, it is more important to guarantee ultrasonic motors running stably if the tribomaterials havc good tcmperature stability of phys-chemical propcrties. 2. Classification of tribomaterials Tribomaterials for USM are often composites, which consist of matrix, relllforced filler and friction regulator. Matrix is used to form the main-body of tribomaterials, whilc rcinforced fillcr is used to cnhancc the mechanical charactcristics, and friction regulator is used to regulate the friction coefficients so as to enhance thc output torque and cfficicncy of USM. Morcovcr metal coating is also uscd as the tribomatcrials of TRUM to keep it running discontinuously. For cxample, the elinvar coating is used in the TRUM of camera. For thc tribomaterials uscd in USM, wc must consider how to match thcir friction cocfficient and wear rcsistance. Although the addition of hard assist materials could enhance the hardness of tribomaterial, the high content of hard assist materials leads to thc mating pair's surface becoming worn. If a little of

60

Ultrasonic Motors Technologies and Ap plicalions

friction regulator is added into the matrix, the wear resistance and stability of tribomaterials would be enhanced. Then no stick-slip occurs, and vibration and noisy will be reduced. Based on the above-mentioned guiding theory, the tribomaterials used for USM could be classified as: CD polymer matrix; @ ceramic coatings; ® powder metallurgy; @metal coatings. There arc many kinds of tribomaterials for USM in the world. In Japan, Endo and Sasakp9: have reported a tribomaterial mainly made of neoprene, while in Germany, Rehbein and Wallasehek[2°:have devcloped a PTFE-based tribomaterial consisting of PTFE, polyimide, carbon fiber and steel. And in China, according to adhesive method, Baoku rjC21: has developed a tribomaterial with the main components of bisphenol type epoxy resin, phenol-formaldehyde epoxy resin, modified imidazole curing, frictional coefficient regulator, KH500 silane coupling agent and hardness regulator. Xuejun Liu, Tongsheng Li, et aI L22 - have developed an aromatic polyamide-based tribomaterial, and its main components are aromatic polyamide, cuprous chloride, graphite and carbon fiber. lianjun QUL23-21_ has reported a tribomaterials with the modified PTFE or nano PTFE. Recently, Zhiyuan Yao, Qingjun Ding and the author"-26 J have developed a series of tribomaterials used for the rotor and the stator. For coatings used in USM, Seok-Jin Yoon in Korea has indicated that the TiAI)J, Ti)J, DLC and Si-DLC coatings could be used on the stator- 27 -.

3. 2. 2

Influence of Composition on Tribological Properties

For TRUM, the matrix materials arc epoxy resin, phenol-formaldehyde reSin, PTFE, polyimide, neoprene, acrylonitrile-butadiene rubber (NBR) , etc., while reinforced fillers are aramid fiber, carbon fiber, wear resistance powder (mineral), wollastonite, calcium carbonate, alumina, etc. The proper addition of reinforced fiber will change the elastic modulus and the anisotropy of materials, and increase frictional coefficient as well as enhance the locked torque of motors. Due to the aramid fiber having high tensile strength as well as good thermal resistance and its friction coefficient higher than carbon fiber, so that aramid fiber is an ideal reinforced fiber. If the anti-wear powder is added into the tribomaterials made of phenol-formaldehyde resin modified by nitrile-butadiene rubber, the tribomaterials exhibit the high friction coefficient and then the locked torque of ultrasonic motor increases:"]. However, after the ultrasonic motor run for some time, its locked torque will decrease. This indicated that the frictional properties of the stator and rotor tribopair are not stable and the anti-wear ability of the stator/rotor tribopair is poor. In order to improve the anti-wear property of the material, the frictional regulator is added into the tribomaterial. At present, frictional regulators arc PTFE, copper oxide, molybdenum disulfide, graphite and copper powder etc., which can adjust the frictional coefficient. They arc absorbed on the surface of the anti-wear powder and distributed into the soft adhesive matrix to form the particle with specific function, and then could regulate the macroscopical friction property of tribomaterials. Table 3. 2 shows related properties of

Chapter 3

Fundamentals of Tribology and Tribomaterials'"

61

some raw materials [or tribomaterials based on polymers. Table 3. 2 Related properties of some raw materials for tribomaterials based on polymers Raw materials

Related properties

Epoxy resin

Middle friction coefficient, brittle. good wear resist anee with fillers, bad temperature stability, high polarity, easy adbesion

Phenolic resin

Middle friction coefficient, brittle, middle wear resistanee with fillers, bad temperature stability, high polarity, easy adhesion

Polytetrafluoroethylene

perature stability, tiny surface tension, small com-

Low friction coefficient, high self-lubricity, good tempression modulus, friction regulator

Matrix

Polyimide

Chloroprene rubber

Butadiene-arylonitrile rubber

Polyphenyl ester Highdensity polyethylene

Aramid fiber

Reinforcing filler

Carbon fiber

Alumina

Middle friction coefficient, brittle, good wear resist ance, good temperature stability

Good toughness, bad high temperature stability, good wear resistance with fillers, low efficiency

Good toughness, bad bigb temperature stability, good wear resistance with fillers, low efficiency

Tiny wear loss, tiny creep deformation, good radiation resistance, tiny injury to coupled part, brittle

Low friction coefficient, bad temperature stability

High tensile strength, high friction coeffeient, good temperature stability High tensile strength, low friction coeffeient, good radiation resistance, good temperature stability

high hardness, good wear resistance, good temperature stability

Molybdenum

Solid lubricant, low friction eoeffcient, high friction coefficient at high temperature

Graphite

Solid lubricant, low friction coefficient, good temperature stability, good chemistry stability, conducting

Friction regulator

Copper oxide

High friction coefficient, good temperature stability

Ceramic composites and metal coatings arc used for LUSM. Moreover ceramic composites arc mainly alumina-, titania-, chromium oxide-based composites, etc. As is known, alumina has high hardness, high brittleness, and low wear

62

Ultrasonic Motors Technologies and Ap plicalions

loss. If the alumina ceramics contains a certain amount titania, the alumina composites have good toughness, low wear loss and excellent heat insulation performance. The chromium oxide ceramics has low friction coefficient, good polishing performance and low wear loss. Recently, metal coatings are often used as tribomaterial for TRUM and LUSM, and their main components are nickel, chrome or their alloy. But short life is their shortcoming, so discontinuous condition is suitable for this technology. As above-mentioned, the composition of tribomaterials will have major influence on their tribological properties. The best composition of tribomaterial should be determined by using orthogonal matrix design with a few experiments.

3. 2. 3

Preparation of Tribomaterial

According to the type of tribomaterials, their preparation process method and the process equipment are different. The main equipment to prepare the epoxy resinbased tribomaterial is ordinary oven, while the main apparatuses to prepare PTFE-based tribomaterial arc hydraulic pressure machine bclow 20 ton and a high temperature sintering furnace above 100 'C. For the ceramic coatings, the main equipment is a plasma spraying device. Now, the preparations of the PTFE-based tribomaterial, epoxy resin-based tribomaterial and alumina-based tribomaterial arc introduced in detail here.

1. PTFE-based composite tribomaterial on rotor PTFE-based tribomaterials consist of the PTFE matrix, the reinforced agent of nano diamond powder and the regulator of copper powder. Its common compositions (molar percentage) are: CDPTFE matrix(60%-70%); @reinforcing agent 0%-25%); (3)regulator(5%-30%). It is clear that the matrix content is up to 60%. If the filler content is too high, the increase of hardness for tribomaterials will cause the abrasion wear of tribopair. There are three procedures to prepare the PTFE-based tribomaterial: CD three kinds of raw powders according to their molar ratios are mixed, stirred uniformly and dried up; @ the above mixture is filled into the mold, and pressed by the hydraulic machine to form an embryo of tribomaterial, then kept it at 40-60'C for 21-18h; C]the molding product is sintered at 370-380'C. As the temperature increases from 20 to 330'C, the heat speed is 40'C/h, while that is 30'C/h when the temperature rise from 330 to 380'C. When the temperature approaches to 380'C, it is kept for 4h. Figure 3. 6 shows the PTFE-based tribomaterial developed by PDLab. The PTFE-based tribomaterial is often adhered to a rotor. Firstly, the rotor is made via machining aluminum alloy. Then the sinter cd tribomaterial is cut into sheet (with the thickness of o. 2-0. 3mm) and adhibited on the rotor (as seen in Fig. 3. 7). 2. Epoxy resin-based tribomaterial on stator Epoxy resin-based tribomaterial consists of epoxy resin matrix, nano alumina reinforcing agent and PTFE regulator. Its common composition (molar percentage) are: CDmatrix of epoxy resin: 50%-60%; @reinforcing agent: 20%-35%;

Chapter 3

Fundamentals of Tribology and Tribomaterials'"

Tribomaterials based on polymers

Fig. 3. 6

Stators of TRUM with tribomaterials

Fig. 3. 8

63

Rotors with tribomaterials based on polymers

Fig. 3. 7

Rotors of BTRUM with tribomaterials

Fig. 3. 9

@regulator: 5%-30%. These raw materials including epoxy resin, PTFE, alumina, carbon fiber and curing agent arc cohered on the stator's surface and rotor's surface after being mixed up, and then lathe processes them to the required size after the composite is cured in heat at 80"C for 2 hours, as shown in Fig. 3. 8 and Fig. 3. 9. The frequency response experiments of stator arc performed with PSV-300F vibration measurement system using laser Doppler. A rotary tribometer designed by PDLab is used to test the wear and the friction of the samples. After running-in period of 10 hours, friction coefficients are tested under two different conditions: CD20"C, preload 100-250)J; @20"C ,prcload 100-250)J , voltage imposed on single face 15 V, frequency 37. 4kHz. The apparatus is located in a clean room with the relative humidity of 25%-50%. The rotor rotates at 12r/min, and the stator is fixed to the tribometer. Prior to testing, the eounterfaees are cleaned with ethanol, and dried. The normal load is continuously monitored and controlled with computer via using an eleetropneumatie valve. The data of normal load and friction force arc collected instantaneously. Table 3. 3 shows the friction coefficient of tribomaterials against the anodized aluminum rotor. It is obvious that the friction coefficient is not a constant value at different preload, and the higher the preload is, the higher the friction coefficient is. It indicates that the contact area increases with an increase of the preload due to the tribomaterial's toughness.

Ultrasonic Motors Technologies and Ap plicalions

64

Table 3.3

Friction coefficient between tribomaterial and aluminum rotor anodized Friction coefficient

Variation ratc/ %

Preload/)! Ordinary state

Under ultrasonic vibration

100

o.

150 7

O. 119 4

-20.7

150

0.153 1

0.123 2

-19.7

180

0.151 3

0.131 6

-11.7

200

O. 158 1

O. 140 7

-11. 0

250

O. 160 7

O. 113 8

-10.5

The friction coefficient decreases 10 %-20 % under ultrasonic vibration in comparison to that of the ordinary state- 10J • Due to ultrasonic vibration and impact, the contact area between tribomaterial and rotor under ultrasonic vibration is less than that of the ordinary state, and the preload decreases, thus the friction force and the apparent friction coefficient all decrease. As seen in Table 3. 3, it is evident that the more the preload is, the less the decrease degree is. The rotor is impacted by the stator coated with tribomaterial. When the pre-pressure increases, the effects of impact to contact area makes reduce. This indicates that the decrease degree of the friction coefficient is little. Figure 3. 10 shows that SEM images of friction surface of epoxy resin-based tribomaterial on stator. There arc some microcracks after running for 200 hours, while there is obvious delamination after running for 600 hours. However, there are no ploughing grooves. It could be coneluded that the wear mechanism of epoxy resin composite are fatigue wear and adhesive wear. Therefore, the antifatigue performance and high cohesion energy density of the tribomaterials should be investigated when they are used in ultrasonic motors. In addition, the hardness, thermal stability and friction coefficient of the tribomaterials are usually considered as key factors of effecting or wear resistance of the tribomaterials.

(a) 200h

Fig. 3. 10

(b) 600h

SEM images of friction surface

Because the variation of temperature results in the migration of frequency response, thus, one of key factors affecting the stability and adjustability of ultra-

Chapter 3

Fundamentals of Tribology and Tribomaterials'"

65

sonic motor is the width of frequency response. With increasing the width of frequency response, the stability and adjustability of ultrasonic motor increase. Fig. 3. 11 shows frequency responses of the stators. It is obvious that there is no migration for the frequency response when the stator( Fig. 3. 11 (b)) is covered with epoxy resin composite and the half-peak width of frequency response increases about 2 times of that of the stator (Fig. 3.11 (a)) without the composite. This indicates that the stability and adjustability of ultrasonic motor increase significantly via coating tribomaterial on the stator.

rL 1 1 1 f L Ll1 20

30

40

50

FrequencylkHz

20

30

40

Trioomatcria ll iner

l(b'

50

Frequency/kHz

Fig. 3. 11

Frequency response for stator

The experimental results show that the half-power bandwidth of working mode responding curve is widened if the tribomaterial is adhered on the surface of stator (Fig. 3. 11 (b)). This causes the ultrasonic motor having more stable rotation speed. Besides PTFE type the other tribomaterials developed by PDLab can meet the requirement for all kinds of ultrasonic motors (Fig. 3. 9). 3. Alumina composite as friction material on stator of LUSM Compared with traditional electromagnetic motor, one of the advantages of ultrasonic motors is excellent transient property, mainly in rapid response, self-locking performance and precise positioning. At present, linear ultrasonic motors have been used in rapid response unit, high-grade instruments, and precision control devices. One of the key factors effecting on transient property is hardness of tribomaterial. Tribomaterials based on polymers will delay the response time because of the polymers' toughness and heat deformation. So inorganic composites are often used as tribomaterials in linear ultrasonic motors. Because it is difficult to bond inorganic composites to the stator of ultrasonic motor without any tackiness agent. The plasma spray process is basically the spraying of molten or heat softened material onto a surface to provide a coating. Material in the form of powder is inj ected into a very high temperature plasma flame, where it is rapidly heated and accelerated to a high velocity. The hot material impacts on the substrate surface and rapidly cools forming a coating. This

66

Ultrasonic Motors Technologies and Ap plicalions

plasma spray process carried out correctly is called a "cold process" (relative to the substrate material being coated) as the substrate temperature can be kept low during processing avoiding damage, metallurgical changes and distortion to the substrate material. Plasma spraying has the advantage that it can spray very high melting point materials such as refractory metals like tungsten, ceramics and zirconia unlike combustion processes. Plasma sprayed coatings arc generally much denser, stronger and cleaner than the other thermal spray processes with the exception of HVOF and detonation processes. Plasma spray coatings probably account for the widest range of thermal spray coatings and applications and makes this process the most versatile. The tribomaterial based on alumina is composition of the matrix of alumina and the regulator agent of titanium dioxide, etc. Its common composition (molar percentage) is: (1) matrix of alumina: 55%-80%; (2) the regulator agent of titanium dioxide: 10 %-10 %; (3) others: 0%-10%. Although in the prescription above, the ratio of matrix is up to 55%, however, the study shows that the ratio of the regulator agent of titanium dioxide has great effect on the friction properties of tribomaterial. It is clear that the high speed, torque, output efficiency and the efficiency of interface dynamical transmission would be acquired when adjusting the content of titanium dioxide in a certain range. The commercially available AI,O, powders with an average particle size of ＴＰｾＷｦｌｭ＠ arc used as a feedstock in the present study. The raw feedstock has the purity >99. Owt% of Al,0 3 component. And titanium dioxide powders with an average particle size of 50fLm are used as an additive to prepare the other feedstock of AI, 0, -TiO, composite. The composite powders with a content of around 20 % TiO, arc mechanically mixed in a rotary-vibrationmill, alcohol being used as a binder, and then suffered sieving and drying prior to the spraying.

Fig. 3. 12

AI, 0 3 - Ti0 2 tribomaterial

The DH-2080 atmospheric plasma spraying equipment made by Shanghai Dahao :'\Ianomaterials &. Thermal Spray Co., Ltd. in China is applied to prepare AI 2 0 3 -TiO, compositc coatings. Thc fcedstock powdcrs arc fed with a Twin-Systcm 1O-C. A mixturc of argon and hydrogen is uscd as plasma gas. During spra-

Chapter 3

Fundamentals of Tribology and Tribomaterials···

67

ymg. the substrates and coatings are cooled using compressed air. Stainless steel coupons arc uscd as substrates. Beforc spraying. the substratcs are dcgrcascd ultrasonically in acctonc and grit blasted with corundum. In addition. the plasma torch is utilized to spray powders onto the unheated quartz substrate in order to observe the spreading and flattening morphology of impacted droplets. Disadvantagcs of the plasma spray process are relativc high cost and complcxity of process.

3.3 3. 3. 1

Influence of Tribomaterials on Performance of USM Influence of Elastic Modulus and Hardness

Elastic modulus E and hardness H are two essential parameters of materials. Elastic modulus is relatcd to the material atom composition. whilc hardncss has relevancc to the organization structurc of materials. It is elcar that hcat trcatment has no influcncc on the elastic modulus. but has grcat cffect on hardness. espccially for mctal alloy. Gencrally. hardness depends on the local elastic-plastic deformation of solid material during indentation loading. and the elastic modulus can be calculated from unloading process. Based on the conventional depthsensing indentation method proposed by Oliver and Pharr. Chinese researchers dcrivcd an analytical relationship between the reduccd modulus and hardncss for solid materials. It is found that the hardness and thc elastic modulus are interrelated to each other through the recovery resistance of materials. Experimental results show two important features: CD the reduced modulus predicted by the new E'- H relationship is the same as that obtained by the conventional method; CZ) the elastic modulus and hardness determined by the simple set of procedures arc comparable to thosc obtaincd by using thc convcntional method: 2"J.

1. Influence of elastic modulus on USM The elastic modulus of tribomaterials is one of the major physical parameters determining the friction characteristics. The results show that the elastic modulus affects the no-load speed. output torque. output power and start-stop characteristic of ultrasonic motors. Thc variation of opcrating spccd with the elastic modulus is not simply lincar relationship. The prescnt theory :29J indicates that undcr the condition of no-load and thc certain prc-prcssure in the range(250-300N). it is available that thc contact area between a stator and rotor would decrease as the elastic modulus of material increases in the range( o. 2-1. 5GPa) • which induces the average tangential velocity of thc rotor increasing at thc contact arca. With thc incrcase of thc avcrage tangential velocity and the decrcase in elasticity sliding motion. thc noload speed of ultrasonic motors would incrcascs. If the elastic modulus excecds thc above-mcntioned rangc. the averagc speed at contact area increascs and thc elastic sliding decreases. However. the high elastic modulus makes the interface area between the stator and rotor decreased. which causes a friction drive force and cnergy convcrsion rate bcing lower. In this casc. thc no load speed of ultra-

Ultrasonic Motors Technologies and Ap plicalions

68

sonic motors decreases. The author29 J analyzes the influence of vanous elastic moduli on the output performance of ultrasonic motors using the simulation software for the traveling wave ultrasonic motor, and the results indicate that the contact width of the stator and rotor pair in a wavelcngth and the deformation strain of tribolaycr bccomc wide and large, with decreasing the elastic modulus of tribomaterials. On the contrary, the contact width between the stator and rotor will decrease with the increase of the elastic modulus or the contact stiffness. When the elastic modulus varies in thc rangc of o. 1-0. 5GPa, the no-load spced incrcases with mcreasmg the elastic modulus. The elastic modulus of tribomaterials also affects the locked torque and the output cfficicncy of USMs. According to thc contact models, if the tribolayer is soft and the contact area extend to the area beyond the points with the same circumferetial spccd of stator and rotor, the contact area includcs impcding area which weakcns thc stator's driving effect on rotor. Whcn the contact stiffncss of tribolayer is high, the contact arca would decrcase and becomc thc driving zone, and then thc locked torque incrcascs obviously. In meanwhilc, thc radial componcnt of thc contact forcc on this zone will bc low, and thc sliding loss on the intcrfacc will also decrcase. Thereforc, the output cfficiency of ultrasonic motors bccomcs high. From the above analysis, it is clcar that thc high rotational spccd, torque, output efficiency and thc cfficiency of dynamical transmission on thc intcrfacc would be acquircd whcn the elastic modulus of tribolayer properly incrcascs in a ccrtain rangc.

2. Influence of hardness The hardness of tribomaterials affects not only running speed and output torque, but also frictional noise. The influence of tribomaterials' hardness on the opcrating performance of somc linear ultrasonic motors has bcen rcported by Endo[19:. Thc author prepared several tribomatcrials, and studied the influence of hardness on the performance of USM. PTFE compositc, cpoxy composite, phcnolic composites, hard aluminum alloy, ccmented carbide as tribomatcrials on rotors are respectively paired to the stator made of phosphor bronze and piezoelectric ceramic. By controlling fillers and roughness, their friction coefficient can be adjusted to a similar valuc. Table 3. 4 shows the Vickcrs hardncss of fivc kinds of tribomaterials. It can bc seen that the rank of hardness is arranged from low to high: PTFE composite< epoxy composites < phenolic compositcs < anodizcd aluminum alloy < cemcnted carbidc. Table 3. 4 Tribomaterial

PTFE

Vickers hardness (HV)

11

Vickers hardness of tribomaterials Epoxy

Phenolic

Anodized

reSln

reSln

aluminum

Cemented carbide

39

80

453

1 120

Chapter 3

Fundamentals of Tribology and Tribomaterials···

69

Figure 3. 13 shows the curves o[ speed vs. torque [or the ultrasonic motor with five kinds of tribomaterials. It is evident that with an increase of the hardness of tribomaterials, the no-load speed increases, while the stalling torque decreases. Moreover, the difference o[ the no-load speed also decreases. In other words, the hard tribomaterials could be applied to the ultrasonic motors with high speed, while the soft tribomaterials could be used in the ultrasonic motors with high stalling torque. Because the ultrasonic motors with hard tribomaterials often run with high noise, thus polymer composites are a main kind o[ tribomaterials especially used [or traveling wave rotary ultrasonic motors.

220 200

"'-.-,

.. .:....... ' :":':-- ...."

180 160

'2 140 120 0::

"'!l" c.

Vl

ｾ＠

, ....

Anodized al uminu m Cemented carbibe

..... . '.;: : ....

Ｎｾ＠

-E ."

.

PTF E Epoxy resin Phenolic resi n

ｾ＠ .

100

.:- ....ｾ＠ .... ,.. .... . ., ... . . ..... '" .. , ... ｾ＠

80 60 40 20 0 00

0_2

0.4

0.6

0_8

1.0

L2

IA

Output torqu (N -m)

Fig. 3. 13

3. 3. 2

Mechanical characteristics for an ultrasonic motor

Influence of Friction Coefficient

The output torque of ultrasonic motors will increase with the friction coefficient in a certain range. The increase o[ output torque will stop as the friction coefficient increases to a certain value. If the friction coefficient becomes higher. the torque could not increase obviously. In this situation. the wear rate of tribolayer becomes high, and the noise of ultrasonic motors become aloud. Thus, the running life o[ USMs becomes short. In the viewpoint o[ tribology. there are primarily two friction mechanisms: the first is the sliding resistance caused by the mechanical chimerism of asperities for tribopair. This is a mechanical component in friction force. The second is the shearing resistance caused by the adhesion [unction o[ molecules at contact area. It is a molecular component in friction force. In order to enhance the friction force of the stator and rotor pair at a certain pre-pressure, the friction coefficient of the stator and rotor tribopair should be high. The simple method to raise the friction coefficient is the addition o[ hard particles into the tribomaterials. The hard particles can increase the sliding resistance caused by the mechanical chimerism of asperities. When the surface with hard micro-asperities is pressed to the

70

Ultrasonic Motors Technologies and Ap plicalions

soft surface, the friction force is formed owmg to the ploughing resistance. In this casc, thcrc arc many ploughing groovcs and thc powdcr loss on thc surfacc of tribopairs in USM. The friction coefficient is increased using the second method, which decreases the surface roughness of tribopairs and augments the adhesion force between the molecules. In this case, the powder loss becomes slight. The above analysis indicates that the high-speed, high-torque, high-output power and interfacial dynamic transmission efficiency can be gained as the elastic modulus of the tribolayer increases in a certain range, and the output torque, efficiency, rotation speed, and power of ultrasonic motors can be enhanced by increasing the friction coefficient of tribomaterials.

3. 3. 3

Influence of Anisotropy

The tribolayer on stators or rotors with a certain thickness

IS

distributed on the

annular area. This area is r 2 ｾ＠ ｲｾ＠ r3 , as shown in Fig. 3. 14. The sand {} denote arc-length and angel respectively. The contact model between the stators and rotors of ultrasonic motors is very complicated (see Chap. 5). One simple model is that the tribolayers arc supposed as the axial and circumferential independent springs. If the elastic coefficients of axial and circumferential springs are k n and k., respectively, the dynamic friction coefficient is !1d and the deformation of the friction layer is 0, the pre-load of Po is equal to kno under static status, as shown in Fig. 3. 15. Tribomaterial

r

Fig. 3. 14 Rotor of traveling wanc USM

Fig. 3. 15 Deformation status of rotor and stator

If the tribomaterial is pasted on the rotor, the free surface of the tribolayer is against the surface of the stator. In the situation of the ultrasonic motor operating, the stator affects the rotor through tribolayer. Assuming that the axial(normal) pressure f.(r,{},t) and circumferential shear force f.(r,{},t) have influences on the rotor in the friction area, they arc respectively expressed as

f ( r, {} ,t) -- {kn (w + 0) , n

f, (r, {}, t)

0,

=

w+O>o ｷＫｯｾｏ＠

sign(V" - V) !1dn (r,{), t)

(3. 11) (3. 12)

where w is the displacement (z direction) of points on the surface of the stator,

Chapter 3

Fundamentals of Tribology and Tribomaterials···

71

V" is the corresponding circumferential velocity, V, is the circumference speed at the contact point between the rotor and stator. In the above-mentioned model, k n and /1d have different effects on the interaction between stators and rotor. Eq. (3.11) shows that the value of k n influences the contact state of the stator and rotor pair. When thc stator and rotor contact mutually, Eq. (3. 11) is exprcsscd as fn(r,{),t)=knw+k,J'j, where the constant forcc of k,J'j is cqual to Po as prcload, while k n w is alternating force, which represents the interaction between the stator and rotor during operating, and

o. 5k

n

w' is the work done by alterna-

ting force in axial direction. When k n is high, k nwand o. 5k nw' become high. Due to ineffcctive work done by thc ultrasonic motor along axial dircction, the ultrasonic motor's energy would lose. When the stator and rotor contact mutually, Eq. (3. 12) is changed as f,(r,{),t)

=

sign(V" - V,)/1dkn (w+ 0)

(3. 13)

It is clcar from Eq. (3. 13) that the valuc of /1dkn affects the transmission of thc energy from the stator to the rotor. With an increase in the values of /1dkn' the tangential force between the stator and rotor increases at the proper pre-load. Actually, with a decrease in the value of kn' the deformation amount of the tribolayer increascs and the contact width bctween thc stator and rotor in a wavelength enlarges gradually. This indicated that the value of k n should vary in a suitable rangc. If Lt is a contact time in which the point G on the stator contacts with the rotor in one period, the work done by this point to the rotor is

(3. 14) wherc hi is thc distance from thc stator surfacc to thc neutral layer. It is indicated that the stator transmits the cffectivc encrgy to the rotor though thc tribolaycr along circumfcrential dircction. In herc, the tribolayer in circumfercntial direction is considered as the spring with the elastic coefficient of k" which decidcs the output cfficiency of thc ultrasonic motors. Thc output efficiency usually incrcascs with an increasc in thc value of k,. The above-mentioned analysis indicates that in order to increase the operating efficiency of ultrasonic motors, it is necessary to make the anisotropic tribomaterials with low vertical elastic modulus. But in order to obtain the high output torque, the friction coefficient and the circumferential elastic coefficient k, for tribomaterials should be high. The anisotropic tribomaterials prepared in this way are beneficial to improving the output characteristics of ultrasonic motors. Based on the preparation of isotropic tribomaterials, the anisotropic tribomaterials can be prepared increasing the circumferential elastic modulus k,. After glass or carbon fibers are added into the isotropic tribomaterials, the fibers are distributed and stirred circumferentially, and then the anisotropic tribomaterials arc acquired.

Ultrasonic Motors Technologies and Ap plicalions

72

3.4

Friction Testing for Tribomaterials

Currently, there are two methods to measure the friction coefficients of tribomaterials: The first method is to determine the traditional static friction coefficients. The second method is to measure the dynamic friction coefficients based on the operating principle of USM.

3. 4. 1

Quasi-static Friction Testing

1. Summary Quasi-static tribometer, as shown in Fig. 3. 16, is used to measure friction coefficients of tribomaterials at low speed. The friction coefficient measured by the method is called a quasi-static friction coefficient.

.. ｾ＠

Sensor

ＬＭｾ

ＡｾｉＧ＠

Signal amplifier

Data acquisition card

Motion control card

Motion loading: vert ical, el vel , rotational;

Fig. 3. 16

Data acquisition : adhesive force, friction force(moment), friction coefficient

Schematic diagram of quasi-static tribometer

The tribometer is controlled by a computer, whose software system IS wmdows interface in Chinese, and operated easily. Its data analysis software can accomplish the data acquisition and storage, and translate the test data into Word, Excel or other general software. Data record system adopts 12bits AID converter, the record speed can reach to 1000kHz as the experimental curve is shown and the dynamic saving disk works. According to the configurations of different sensors, the tribometer can accomplish the adhesion, friction and wear experiments.

2. Operating principle The tribometer includes hardware and software systems. The hardware system consists of 5 parts: the level moving part, the vertical moving part, the rotation part, the force sensor, and the control box of the motor. Meanwhile the attachments to the tribometer include the motion control card of motors, the signal amplified card of sensors, the data acquisition card, computer, and so on. The motion compartments such as level motion, vertical motion and rotation parts all arc driven by step motors. Software system consists of the drive and control system of step motors, the data acquisition and the data analysis software.

Chapter 3

Fundamentals 01 Tribology and Tribomaterials···

73

As seen in Fig. 3. 16, the relative movement between tribopairs is generated via moving parts, and a ccrtain prc-prcssurc is imposcd to thc stator. Thc rcaltimc data collcction and storagc of prc-prcssurc and friction forcc arc carricd out by using sensor, signal amplifier, and data collection card. The control system includes computer, motion control card, and control program, and controls the motion dircction and spccd of motion parts and thc prc-prcssurc bctwccn tribopairs.

3.4.2

Dynamic Friction Testing

1. Summary The dynamic friction test is used to measure the dynamic friction coefficients of tribomaterials during friction. For the running USM, there are macroscopic and microscopic rclativc motion at thc contact arca of thc stator and rotor tribopairs simultancously. Thc microscopic relativc motion shows two aspccts: CD thc stators and rotors are in the contact state with pulsation variation, which makes the contact stress of the stator and rotor tribopair to change periodically; @there is altcrnating rclativc motion along circumfcrcntial dircction. This motion statc causcs thc intcraction bctwccn thc stators and rotors bcing complicatcd, and thcn thc uniquc friction charactcristics arc cxhibitcd. To analyzc friction cocfficicnt of tribomaterials during running, a dynamic friction test machine is made and provided by Harbin Institute of technology. This machine can simulate the motion at thc contact point of thc stator and rotor pair for ultrasonic motors, and thcn mcasurc thc dynamic friction cocfficicnts for ultrasonic motors. 2. Work mechanism Thc dynamic tribomctcr utilizcs thc front cnd of bar with longitudinal and flcxural vibration modes to simulate the elliptical motion of a surface point on a stator for ultrasonic motor. When the bar excites a composite ultrasonic vibration made of a longitudinal and a flcxural vibration, thcn thc bar front cnd producc a highfrcqucncy microscopic clliptical motion, and thcn thc clliptical functions arc simulated. The dynamic tribometer consists of mechanical system, signal output, and data collcction and transfcr systcm, ctc. Thc mcchanical systcm is a vcrtical structurc. It is convcnicnt for loading prc-prcssurc and thc amplificd output of thc instant friction driving force as the ultrasonic micro-tribo test is done. As seen in Fig. 3. 17, the tribometer includes the ultrasonic vibration parts to simulate the high-frcqucncy clliptical motion of thc point on thc stator for thc traveling wavc ultrasonic motors, thc prc-tightcning structurc to adjust thc prc-load and thc position of instant kinetic positive pressure sensor, the pre-tightening part to regulate the position of output and sensor, the supporting and position structures of transmission output axis and cxpcrimcntal tablc. Thc signal transfcr and output parts includc thc piczoelcctric scnsor to mcasurc thc instant dynamic driving force, and corresponding electric charge amplifier.

74

Ultrasonic Motors Technologies and Ap plicalions

ｉｓｰＢ｣

ｩ ｮ ｬ ｾ ｾ ｾｺＢ

ｉ ｾ ｴｮ ｩ｣ｳ･

ｮ ｳｯｲ＠

I

sensor 2 Operation simulation equipment for TRUM

Fig. 3. 17

Data acquisition card

Computer

Charge amplifier

Schematic diagrams 01 dynamic tribomctcr

References [ 1

J

[ 2

[3

J J

[ 4

J

[ 5

J

[ 6

J

[ 7

J

[ 8

J

[ 9

J

[IOJ [llJ

[I2J

[13J

[14J

[15J

Shizhu Wen. Existing state and development of tribology research in China. Chinese Journal of Mechanical Engineering, 2004, 40 (11): 1-6. Zhongrong Zhou, Leo Vincent. Fretting Wear. Beijing: Scicncc Prcss, 2002. (in Chines c) T Ishii, S Ueha, K "Iakamura. Wear properties and life prediction of frictional material for ultrasonic motor. Japanese J oumal of Applied Physics, 1995, 34: 2765-2770. H Storck, W Littmann, J Wallasehek. The effect of friction reduction in presence of ultrasonic vibration and its relevance to traveling wave ultrasonic molors. [lltrasonics, 2002, 40: 379-383. T Yamaguchi, K Adachi, Y Ishimine, et a1. Wear mode control of drive tip of ultrasonic motor for prccision positioning. Wear, 2001, 256: 115-152. M Kurosawa. Efficiency of traveling wave type ultrasonic motors. J. Acoust. Soc. J pn, 1988,11(1): 10-16. N M Hagood, A J McFarland. Modeling of piezoelectric rotary ultrasonic motor. IEEE Trans. Ultrason., Ferroelee!., Freq. Contr., 1995, 42(2): 210-224. P Hagcdorn, T Sattel, D Spcziari, ct a1. The importance of motor flcxibility in traveling wave ultrasonic motors. Smart Mater. Struct., 1998, 7: 352-368. Hcming Sun, Chunshcng Zhao, Xiaodong Zhu. Simulation on friction characteristic of ultrasonic motor using longitudinal and torsional modc. Journal of Southeast University (Natural Science Edition), 2002, 32(1): 621-626. (in Chincse) Heming Sun, Hui Guo. Thc relation of preprcssure and output-torquc of longitudinal and torsional ultrasonic motor. Tribology, 2001, 21( 1): 52-54. (in Chinese) Hui Guo, Taizhc Tan, Xinbao "ling. Moving track of the surfacc particlc and torquc for thc ultrasonic motor using thc traveling wavc in the plane. Tribology, 2002, 22(5): 386-390. (in Chincse) Xiangdong Zhao, Changqing Liu, Hcming Sun, ct a1. Output characteristics of thc frictional interface of traveling wave type ultrasonic motors. Small & Special Machines, 2000, 21 (3): 21-22. (in Chinese) Xiangdong Zhao, Bo Chen, Chunsheng Zhao. "Ionlinearly frictional interface model of rotated traveling wave typc ultrasonic motor. Journal of Nanjing University of Aeronautics & Astronautics, 2003, 35(6): 629-633. (in Chinese) Hai Xu, Chunsheng Zhao. Contact process and friction analysis of linear ultrasonic motor. Journal of Nanjing University of Aeronautics & Astronautics, 2005, 37(2): 144-149. (in Chinese) Qianwci Chcn, Wciqing Huang, Chunshcng Zhao. Mcasurcmcnt of scrviec lifc of ultrasonic

Chapter 3

[l6J [17J [l8J [19J [20J [21J [22J [23J

[24J [25J

[26J

[27J

[28J

[29J

Fundamentals 01 Tribology and Tribomaterials'"

75

motors. Journal of Vibration, Measurement & Diagnosis, 2004, 24 (l): 19-22. (in Chinese) J Halling. Principles of Tribology. Beijing: China Machine Press, 1981. (in Chinese) Shizhu Wen. Principles of Tribology. Beijing: Tsinghua University Press, 1990. (in Chinese) Zhendong Dai, Min Wang, Qunji Xue. Introduction to the Thermodynamics of Friction Systems. Beijing: National Defense Industry Press, 2002. A Endo, N Sasaki. Investigation o[ [rietional material [or ultrasonic motor. Japanese Journal of Applied Physics, 1987, 26: 197-199. P Rhbein, J Wallasehek. Friction and wear behavior of polymer/steel and alumina/ alumina under high-fretting conditions. Wear, 1998, 216(2): 97-105. Baoku Li. Preparation [or new [rietion material. Technology on Adhesion & Sealing, 2001, 22(3): 7-8. (in Chinese) Xujun Liu, Tongsheng Li, Tian Nong, et al. Manufacture and application of aromatic polyamide based [rietional material. China Plastics Industry, 1999, 27(3): 25-26. (in Chinese) Jianjun Qu. Friction Driving Mechanism and Friction Material Research on Ultrasonic Motor. Dissertation for the Degree of Doctor of Philosophy. Harbin: Harbin Institute of Technology, 1998. (in Chinese) Jianjun Qu. The Contact Model and the Properties of the Friction Materials for Ultrasonic Motors. Post-doctoral Report. Beijing: Tsinghua University, 2001. (in Chinese) Zhiyuan Yao, Qingjun Ding, Chunsheng Zhao. Preparation and auxiliary tools of thermoset resin-based friction material and friction layer of ultrasonic motors. Chinese Invention Patent, CN200610040708. 5, 2006. Zhiyuan Yao, Qingjun Ding, Chunsheng Zhao. Using PTFE-based filled with carbon fiber as friction material of ultrasonic motors and its fabrication. Chinese Invention Patent, CN200610010709. X, 2006. H-P Ko, SKim, J-S Kim, et al. Wear and dynamic properties o[ piezoelectric ultrasonic motor with [rietional materials coated stator. Materials Chemistry and Physics, 2005 (90): 391395. Y W Bao, W Wang, Y C Zhou. Investigation of the relationship between elastic modulus and hardness based on depth-sensing indentation measurements. Acta Material, 2004, 52 (18) : 5397-5404. Chao Chen. The Research on Theory Model for the Rotary Driveling Wave Ultrasonic Motor. Dissertation for the Degree of Doctor of Philosophy. Nanjing: :'-Ianjing University of Aeronautics and Astronautics, 2005. (in Chinese)

Chapter 4

Fundamentals of Vibration for Ultrasonic Motors An ultrasonic motor is onc of thc most typical cxamplcs of utilizing vibration. In order to understand its motion mechanisms and design principles, it is necessary to start with clastic body vibrations. Vibration is a classic topic in mcchanical cngineering and many references can be found 11-2J. In this chapter the vibration of clastic bodics is discusscd. It providcs thc ncccssary thcorctical foundation for the subsequent chapters of this book and for readers who are interested in ultrasonic motor technologies, but have little exposure to mechanical vibration. In general, structures (including an ultrasonic motor's structure) are made of simplc componcnts such as bcams, platcs, and shclls. Thcy havc a continuous distribution of mass and stiffness, called a continuous system (elastic body), that has an infinitc numbcr of natural modcs (natural frcqucncics and corrcsponding mode shapes). Analytical solutions to an elastic body vibration equation arc limitcd to only simplc gcomctrics with spccific boundary conditions. In most other cases, numerical methods are used instead to obtain approximate solutions. Thc Finitc Elcmcnt Mcthod (FEM) is thc most cffcctivc onc, of which somc highly sophisticated software, such as NASTRA:'\J, A:'\JSYS, ATILA, etc., is bascd on. Most of thc numcrical analysis in this book wcrc donc by ANSYS, which is a powerful package capable of static and dynamic analysis, modal analysis, timc domain analysis of structurcs, ctc. Ultrasonic motors utilize the inverse piezoelectric effect of piezoelectric ceramic clcmcnts to gcncratc strcss or strain, which cxcitcs a stator (clastic body) to produce forced vibration response. The response is converted into the rotational or lincar motion of a rotor or slidcr by thc friction bctwccn thc stator and rotor. Thcreforc, in ordcr to dcsign ultrasonic motors, pcoplc must also mastcr thc forccd vibration of clastic bodics c, 4J.

4. 1

Natural Vibration of Elastic Body

In the section, we will introduce the natural vibration of elastic body, including bars (shafts, beams), plates, shells, etc. A straight elastic strut can undergo longitudinal, torsional, and latcral vibration. If x dcnotcs thc longitudinal (ccn-

C. Zhao, Ultrasonic Motors © Science Press Beijing and Springer-Verlag Berlin Heidelberg 2011

Chapter 1

Fundamentals of Vibration for Ultrasonic Motors

77

troidaD aXIs, and y and z represent the directions of principal axes of a cross section, the longitudinal vibrations take place in the x direction, the torsional vibrations occur about the x axis, and the lateral vibrations involve motion in either the

.Ly

plane or the

.LZ

plane. The strut subjected to longitudinal vibration is of-

ten called a bar. We consider first the longitudinal vibration of a uniform bar using a simple theory.

4, 1. 1

Longitudinal Vibration of Bars

In the condition of no external force and no damping, we can obtain the equation governing the natural vibration of the bar in the longitudinal direction:

psa2u at'

=

ｾＨｅｓ｡ｕＩ＠

a.L

(4. 1)

ax

where u(x, t) is the displacement function of the bar in axial direction; S(x) , E(x) , and P(.L) are the cross section area, elastic modulus of material, and mass density of the bar, respectively. For a uniform bar, Eq. (4. 1) can be simplified as

au at' 2

E a'u

(1. 2)

p a.L'

The solution of the above equation can be obtained through the separation of variables. Assume that the solution can be expressed as (1. 3)

Substituting Eq. (4.3) into Eq. (4.2) and using the method of separation of variables can yield

､ＲｘｴｾＩ＠

+w'q(t)

d'KL) dx'

0

=

+ WE'I'·L '13...--I.( )

(1. 1)

0

(1. 5)

+ Bcoswt

(1. 6)

+ Dcosw J"f-.L

(1. 7)

=

From Eqs. (1.1) and (1.5), we can obtain

q(t)

ｾＨＮｌＩ＠

=

=

Asinwt

Csinw J"f-.L

The complete solution of Eq. (1. 2) becomes

U(.L, t)

=

(Asinwt

+ Bcoswt) (Csinw J"f-.L + Dcosw J"f-.L)

where w denotes the frequency of vibration, the function ｾＨＮｌＩ＠

(1. 8)

represents the

mode shape, the constants C and D can be evaluated from the boundary conditions, the function q (t) indicates harmonic motion, and the constants A and B can be determined from the initial conditions of the bar. The general solution of Eq. (4.2) becomes

Ultrasonic Motors Technologies and Ap plicalions

78

11-]

According to boundary conditions of bars, we obtain the natural frequency of vibrationwn(n = 1,2,3,···) and corresponding modc shapes ｾｮＨｸＩ＠ , which arc summarizcd in Tablc A. 1 and Fig. B. 1 in Appcndixes A and B, respcctively.

4. 1. 2

Characteristics of Natural Modes

All of ultrasonic motors make use of thc "mode" of elastic bodics. Thc word "mode" is used to describe either the natural mode of vibration ( W n ' ｾｮ＠ ) or the mode shape ｾｮＮ＠ In other words, the nth mode refers to the nth natural frequency and corresponding mode shape, or refers only to the mode shape ｾｮＮ＠ It has been noted that usc of word "modc" has becn very loosc in litcratures. From Tablc A. 1 and Fig. B. 1, it can be observcd that the mode is in fact a wavc in spacc whosc amplitude ratio of various points along axis direction of the uniform bar holds a constant for all time. The certain points (called nodes) on the bar undergo zero amplitude, whereas other points (called antinodes) attain maximum amplitude. The nodes and antinodes occur at regular spaces along the bar and remain the fixcd positions for all timc. This form of vibration is callcd a standing wavc, which is widely utilized in dcsign of ultrasonic motors. The modcs posscss thc following important characteristics:

1. Infinite number of natural modes An elastic body is a continuous system with an infinitc numbcr of dcgrces of frcedom. The system possesses an infinite number of natural frequencies (modal frequencics) and modc shapcs, i. c., wc ha vc modal parameters (w n , ｾｮＩＧ＠

n

=

1, 2,3, ...

In general, each natural frequency corresponds with one mode shape.

2. Dependence of modal parameters Gcnerally, modal paramctcrs dcpend on mass, stiffness distribution of thc elastic body, and its boundary conditions. 3. Orthogonality of mode shapes Whcn a bar vibratcs longitudinally, from Eq. (4. 5) any of the modcs must satisfy

-.! (E S dx Therefore for modes

(Wi'

ｾｩＩ＠

and (w j

d¢) d.L '

ｾｪＩＧ＠

p Sw 2 ｾ＠

= -

ｾ＠

=

ｾＨｸＩ＠

(1. 10)

there are

d d.L

(E 'd.L S d¢i)

d d.L

(ES d¢j )S dx - - P

=-

P

S

2-1.

Wi't'i

2-1.

Wj 't'j

(4. 11)

(4. 12)

Chapter 1

Fundamentals of Vibration for Ultrasonic Motors

79

The two end positions of the bar are denoted by 0 and l, respectively. Multiplying Eqs. (1. 11) and (1. 12) by ｾｪ＠ and ｾｩ＠ , respectively, and carrying out integration yields

I' I'

ｾｊ＠

o

o ｾｩ＠

M)

d ( E5 -d' d.r -d

=-

X.T

w;

I' I'

0

ｰＵｾｩｊ､Ｎｲ＠

(1. 13)

d ( E5 MJ - - WJ2 ｯｐＵｾｊｩ､Ｎｲ＠ dx dx ) d.r -

(1.11)

Applying integration by parts to Eqs. (4. 13) and (4. 14), respectively, and using the free boundary condition ( E5M/d.r = 0) or the fixed boundary condition Ｈｾ＠ = 0) of the bar, the following results can be obtained:

t

Mi -d MJd x - - Wi'It P5-1.'l'i'l'j -I. d X - I E5 -d .T.T 0 o

(4. 15)

t Mi -d Mjdx - - Wj'It P5-1.'l'i'l'j -I. d - I E5 -d X .T.T 0 o

(4. 16)

Subtracting Eq. (1. 16) from Eq. (1.15), the remainder is

Ｈｷｾ＠

Ｍｷ［Ｉｉ＾Ｕｾｩｊ､Ｎｲ＠

(1. 17)

0

=

Because Wi cFW J ' we have (1. 18a) For a uniform bar we obtain (4. 18b) Comparing Eq. (1. 18a) with Eq. (1.16) gives

MJ dx I to E 5 Mi dx dx

0

=

(4. 19a)

For a uniform bar, there is

MJdx I to Mi d.r d.r

=

0

(4. 19b)

Eq. (1.18) or (1. 19) is the orthogonal condition of mode shapes. More precisely speaking, Eq. (4.18) is the orthogonal condition of displacement mode shapes. Similarly, multiplying both sides of Eq. (1.11) by ｾｩ＠ and then integrating from 0 to l results in

I 'o ｾｩ＠

dd (E5

､ｾｩ＠

X.T

)d.r

=-

W;I' ｰＵｾ［＠

d.r

(1.20)

0

Integrating it by parts and then applying the boundary conditions, there is

Ki Mi

(1.21)

Ultrasonic Motors Technologies and Ap plicalions

80

Ki

I' ,

(dcPi) 2 oES dx d.1':

=

(1. 22) (4. 23)

where Ki and Mi are the ith (order) modal stiffness and modal mass of the bar. respeetively. Sometimes they are also ealled as the ith (order) generalized stiffness and generalized mass of the bar. From Eqs. (1.22) and (1.23). it can be observed that each natural frequency Wi corresponds to both the modal stiffness Ki and modal mass Mi. The three modal properties given above arc universal to the vibration system. not only for bars. shafts. and beams. but also for plates. shells. and more complex vibration systems. 4. Normalization of modes The mode describes the amplitude distribution of an elastic body at corresponding natural frequency. It shows that the amplitudes of all points on the elastic body are not independent. with being proportional to each other. The process used to select the specific ratio or multiples is called normalization. Currently there arc three major methods for normalization L5J : (1) The maximum amplitude of a mode shape is regulated to 1. (2) The modal mass is taken as 1, that is. Mi (3)

J: ¢;

d.1':

=

=

I>S¢;

dx

=

1.

1.

5. Strain modes The stress-strain relation of a bar is (J

=

F

-

S

=

au

E-

a.1':

=

EE

(4. 24)

For the nth (order) mode shape function of the bar. the corresponding strain function of the bar can be deduced as En =

au: a.1'

=

dcPn(X)qn(t) d.1':

=

¢'()

()

n .1': qn t

(1. 25)

¢:

(X) is defined as the nth (order) strain mode shape function of longitudinal vibration or the nth strain mode. 'Table A.2 represents the natural frequencies and corresponding strain mode shape functions of the bar with three boundary conditions. Fig. B. 2 denotes the first four (order) mode shapes of the bar with the boundary conditions. From Eq. (4. 19) the strain modes also possess orthogonality. The modal characteristics mentioned above exist in the natural vibration of bars. as well as in those of shafts. beams. plates. and shells. but which possess different expressions in their displacement and strain mode functions.

4. 1. 3

Torsional Vibration of Shafts

The strut subjected to torsional vibration is often called a shaft. The equation

Chapter 1

Fundamentals of Vibration for Ultrasonic Motors

81

governing the natural vibration of the shaft about its axis can be described by (4. 26)

where e(x, t) = e is the twist angle of the shaft around x axis, Ie (x) = Ie indicates the mass moment of inertia of the unit length of the shaft around :r axis, Ger) = G and J Cd = J represent the shear modulus of the material and the aera moment of inertia of the shaft about :r axis, respectively. For a uniform shaft, Eq. (1.26) reduces to I a'e Oat'

=

GJ a'e

(1.27)

a.x'

When the shaft has a circular section, Io=pJ , Eq. (4.27) becomes

G a'e

a'e at

(4. 28)

p a.x'

Note that Eqs. (4.28) and (4.2) arc mathematically the same. So the characteristics of the torsional and longitudinal vibrations of a bar behave in the same form. Hence detailed discussion of the torsional vibration of the shaft is omitted and only the final results are given in Table A. 3. :'\Iote that the e.xpressions of natural frequencies are only suitable for shafts with a circular section.

4. 1. 4

Bending Vibration of Beam

The strut subjected to bending vibration is often called a beam. We consider the thin beam for which the length is much large than depth (at least 10 times) and the deflections arc small compared to the depth. Then, the rotation of cross sections of the beam is neglected compared to the translation, and the angular distortion due to shear is negligible compared to the bending deformation. Applying Euler-Bernoulli theory, the equation governing the natural vibration of the beam in its lateral direction can be described by

ｾ＠ ax'

(E1 a'w)+ 5 a 2 w a.x' Pat'

=

0

(1. 29)

where w(.x, t) = w is the lateral vibration displacement of the beam, I (.x) = 1 denotes the area moment of inertia of the beam's cross section about the neutral axis, S(.x), E(.x), and p(.x) represent the cross section area, the elastic modulus of the material, and the mass density of the beam, respectively. For a uniform beam, we have (4. 30)

Letting w(x,t)

=

cp(x)q(t)

(4. 31)

Substituting Eq. (1. 31) into Eq. (1. 30) and using the method of separation of variables, we can obtain the general solution of Eq. (4. 30)

82

Ultrasonic Motors Technologies and Ap plicalions

W(.T, t)

where the constants An and En can be determined from the initial conditions, the constants C and Dn can be evaluated from the boundary conditions, from which we can obtain following characteristic equation, natural frequencies, and corresponding mode shapes for a uniform beam simply supported, respectively: sinX n _ ｘｾ＠ Wn

-

(1. 33)

=

0, n

l'

{IT '\j ps

(4. 34)

Fnsinpnx

(4. 35)

S¢i(xH; (x)dx (4.98)

;'-1

f>S¢i(xH;(x)dx.

Taking the actual damping into account, the consumption function can be expressed as

Chapter 1

Fundamentals of Vibration for Ultrasonic Motors

D where C i}

C}i

=

=

J:

ｾ＠ ｾ＠ ｾ＠

=

103

(4. 99)

Ci}ej,(t)q} (t) I-J

)-1

C¢i (x) ¢j (x) dx.

Substituting Eqs. (4.95) - (4.99) into the Lagrange Eq. (4.76) produces Mij(t) +Cq(t) +Kq(t)

=

(1.100)

F(t)

where M = [m i} J, C= [e i} J, and K = [k i} ] are the generalized mass, damping and stiffness matrices of the beam, respectively. kij = k;; kt, F(t) = b hh"

. [J:

+

e3l E3 rfl: (.T) d.TJ is the column matrix of the generalized force.

According to the orthogonality conditions of displacement and bending strain modal shapes of the beam: 1 '] , we can obtain

or (4.101) where M n , C , and Kn are the nth modal mass, damping, and stiffness of the beam, respectively, and its modal force is

Fn (t) = bhh p

f:

e31 E3 rfl}n (.T) d.T = bhe 31 e iwt

J:

Vo rfl: (.T) d.T = Fn e iwt

(1.102)

where

Fn

=

bhe 3 1

J:

Vo ｲｦｬｾ＠

(4.103)

(x) dx

Subjected to the excitation of the PZT strip, the steady-state bending vibration response of the beam can be expressed as w(x,t) =

2.:Fn¢n(X)/[Kn

Jo-w:) + (2Sn wj

]eiCwt-.n)

11=]

(4.104) 11-]

where (4.105) Comparison of Eqs. (1.105) and (1.82) reveals that they are identical in formation, and thus the same eonelusions can be drawn, which are not to be repeated here. It is important to note the followings: (1) The content of the modal force amplitude Fn of Eq. (1.102) is different from that of Eq. (1.80).

If Vo

=

ｅｎＧｾ＠

(x)

=

Vex) n

=

m

n

=F

m

(1.106)

104

Ultrasonic Motors Technologies and Ap plicalions

Then, the mth pure modal response of the beam can be excited, and the response is proportional to the width of the PZT strip b, the eonstant e31 , and the height of beam h. (2) It is known from Eq. (1. 106) that in order to obtain the "pure" mode of a uniform beam, distribution of V(.L) must be the same as the strain distribution. It ean be learnt by comparing Figs. B. 3 with B. 4 that among four typical boundary eonditions, the displacement mode and strain modes are identical only in the simple supported beam, whereas in the other three conditions the two kind of modes are different. (3) In reality, it is difficult to impose a distributed voltage identically to strain modal function of a beam. In genera), a number of PZT strips (pieces) are affixed on a beam to approximately achieve "pure" mode excitation.

4. 2. 4

Excitation of Simply Supported Beam by PZT Pieces

As shown in Fig. 4. 17, the simply supported beam is excited by one PZT strip (piece). Let a,b, and hI' denote the length, width, and thickness of the PZT piece, respectively, and the characteristic coordinate of the excitation PZT is .L o • The excitation effect of the PZT piece at point .Lo is expressed as "distributed foree" by the unit pulse function with variable (x- x o ). For a simply supported beam, we can obtain from Eq. (1. 102): Fn(t)

bhe3IVoeiw'J:B(x-xo)1«x)dx

=

2

=-

nIT) . nIT iw' b h eol V 0 ( T sIn Txoe

(4.107)

xo

h

0 ,d; ｾ＠

xCI)

_. g"""

;1 ｾ＠ ｾｅＳ＠ I

A metallic beam excited by single PZT piece

Fig. 4. 17

Thus, the steady-state bending vibration response of the beam to one PZT piece excitation is W(.L, t)

2

ex:

ｾ＠

=

-

b h e 31 Vo (nt) sin nlIT.Lo ( sin nlITx)

n=l

I[K n ｾＨｬＭｷＩ＠ =

ｾ＠

AnB nei(w'-.n)

+

(2l;"n wj

ｊ･ｩＨｷｴＭｾｮＩ＠ (4.108)

Chapter 1

Fundamentals 01 Vibration Ior Ultrasonic Motors

105

where

{

An

=-

En -

bh

e VO (T) 3l

(,jCl - ｩｌｉｾＩ＠

2

sin

TXo sin nZ'I[x

(1.109)

+ (2Sn iLlY)

The form of Eq. (4.89) is similar to that of Eq. (4.109) about the longitudinal vibration response to one single point excitation, and hence related conclusions are not repeated here. The displacement and strain modes possess the same shape in the simply supported beam. Therefore, one PZT piece is placed wi thin the range of the half wavelength of its mode, the polarization direction of the PZT matches with the "+" and" - " of the mode, and PZT piece's width beam's width and its length a ,1./2. as shown in Fig. 1. 18.

b
01

[4. 29

=

2. 92

- o. 96

- 1. 0

-

1. 13

-

o. 72

-

o. 37 o. 54

-

o. 56 o.

0.02

50

r

Here. taking i = 16. the first 16 modal frequencies and the corresponding MAC values can be calculated. The first 6 modes are rigid motion modes and the corresponding frequency values are equal to zero. So Table 7. 2 only lists 7-16 order modes. The eighth mode with the largest MAC value is the first bending mode. while the seventh mode with the almost same MAC value as that of the eighth mode is the orthogonal mode of the eighth mode. Mode calculation and corresponding MAC value MAC value Order flHz MAC value

Table 7. 2

Order

flHz

7 8

31 31 31 50 50

10 11

o. o. o. o.

537 538 656 499 499

996 998 670

12

022 O. 044

15 16

58 59 59 62 68

13

11

0.611 o. 177 0.251

898 553 551 554 238

o. 884 o. 888

As shown m Fig. 7. 9. the relation between the numbers of physical parameters and dimensions can be shown in Table 7. 3. Parameters PI • P, • P,. P5' and P7 are selected as the optimal variables based on the sensitivity analysis method in Section 6. 3. 2. Table 7. 3 Parameters and numbers

Dimension of the structural parameters

Structural design parameters of the stator

PI

pz

P,

P,

P5

P6

P7

rz

r3

r6

hi

hz

h3

hs

208

7.3.4

Ultrasonic Motors Technologies and Ap plicalions

Objective Function

The design requirements for the vibration mode of the BTRUM have been discussed in Section 7. 3. 1. Doing the optimal design, these requirements must be considered in the objective function F for the optimization algorithm, which ineludes: (1) The first bending modal frequency fbi and the target design frequency ft should be as elose as possible, that is FI

=

I

fbi - ft

(7.18)

I

(2) The amplitude of points on the driving surface should be as large as possible, while the amplitude of points on the lower mass should be as small as possible. If ¢tr and ¢tt x represent the first bending mode shape values in the x direction of Node 1 and :'\Jode 11 in Fig. 7. 9, respectively, this means

F

2

-I ¢i,i" 1

(7.49)

ﾢｩＬｾ＠

-

(3) Piezoelectric ceramics group should be placed on the antinode( with maximum strain) of the first bending mode of the stator, which means the position of Node 7 should be ncar the middle of the antinode, that is

(7.50) where ﾢ［Ｌｾ＠ and ﾢｴｾ＠ represent the bending mode shape values in the 01': direction of Nodes 6 and 8 in Fig. 7. 9, respectively. (4) The difference between the bending mode frequency and the nearest interference one should be as large as possible, that is

F,

=

I

1 fO

(7.51)

fO

_ ill -

_ iut

Based on the above four requirements and taking into account differences of orders of magnitude, the partial objective functions arc multiplied by weighted coeffieients, and the global objective function for the stator design can be expressed as

(7.52) i=l

where Pi stands for the weighted coefficients. The mathematical model of the optimal design of the stator can be expressed as a minimum problem with boundary constraints:

,

min F

=

b PiFi

(7.53)

i-"j

j

=

1,2,1,5,7

where p;b and P't' represent the lower and upper boundaries of the optimal variables, respectively.

7.3.5

Optimal Algorithm and Results

The pattern search algorithm in Matlab toolbox is used in the optimization mod-

Chapter 7

Bar-type Traveling Wave Rotary Ultrasonic Motors

209

el L37 .• and the boundary of the design variables is defined as plb

=

[7

pub

=

[9. 5

1. 5

1

6. 5

6 1

1J 10

(7.54)

5J

The start values of the pattern search algorithm are p"

=

[7.75

6

2.7

8

(7.55)

3J

The vector in Eqs. (7.54) and (7.55) represents the dimensions of the design variables PI • P, • P4 , Pc , and P7 in mm. The stator modal frequency at the start point is 31 538Hz. the design goal frequency is 36 OOOHz and the weighted coefficients arc f31 = 1. f32 = 1. 5 X 10' • f33 = 50, and f3, = 1. 2 X 10 5. Figure 7. 10 shows the iterative process and the optimal results of the design variables. The values of the partial objective functions arc compared in Table 7. 4. where F represents frequency of first bending mode, A represents amplitude ratio of point on the driving surface to the one on the bottom of stator, D represents distance between Node 7 and the middle of the antinode of the bending mode, and T represents tolerance between the frequency of operating mode and interference mode. It can be the seen that after the optimization, the modal frequency of the stator is 36 003Hz, the piezoelectric ceramic group is closer to the center of the antinode of the bending mode, and the difference between the frequencies of the operating mode and the interference mode becomes larger. In addition, the amplitude ratio of the point on the driving surface to the one on the bottom of the s ta tor increases to 10. 79, as shown in Fig. 7. 11.

-§

7000

l I

0

Iｾｉ＠ (b) Stretch-out view of response fu nction

Fig. 8. 8

Driving procedure in one cycle

Ｚｾ＠

Chapter 8

Ultrasonic Motor Using Longitudinal-Torsional···

237

CW can not transfer to the rotor. But the rotor can continue to rotate due to inertia. In the second, third···, nth cycle, the above procedure will be repeated and the micro angular displacement of the rotor obtained in each cycle will be accumulated to form macro rotation of the rotor. Only when one phase of the voltage is antiphase, the rotor will rotate in CWo According to the driving procedure in one cycle of the motor shown in Fig. 8. 8(a) and the stretch-out view of the longitudinal displacement u< (t) = U< sinwt, the torsional displacement ux(t) =Uxcoswt and the torsional vcloeityitx(t) = - w Uxsinwt shown in Fig. 8. 8 (b), we can get the amplitude value of U x (t) , itx (t) and u< (t) in one cycle in table 8.1. In order to write simply, let U x 1. Table 8. 1

o ｾ｟Ｌｦｩ＠

3

5 Ｔｲｾ＠

ＭＬｦｩｷｾｏ＠

6

1

7

1 ｾＬｦｩ＠

ｏｾＬｦｩｷ＠

,fi ｾ＠ 2

1

Ｌｦｩｷｾｏ＠

ＭＬｦｩｾｏ＠

2

ＨＲＩｾｇｊ＠

ｇｊＩｾｃｄ＠

From contact state to crit-

0

｀ｾｇＩ＠

ical state Stator separate [rom ro-

2

-1 ｾ｟Ｌｦｩ＠

w-----Zw

ｃｄｾＨＲＩ＠

becoming worse

ｇＺｊｾﾮ＠

tor gradually Stator separate from ro-

2

,fi

2

to

Best contact state

_,fi ｾＭＱ＠

Ｒｷｾ＠

state state

Contact state is

o ｾ｟Ｌｦｩ＠

,fi

o ｾＬｦｩ＠

1

2

2

critical

contact state

2

,fi ｾ＠

2

2

2

2

2

,fi

ＭＬｦｩｾｏ＠

From

,fi ｾ＠

ＭｷｾＲ＠

2

-1 ｾ｟Ｌｦｩ＠

6

o ｾＬｦｩ＠

w

ＭＲｷｾ＠

2

5

2

,fi

0

_,fi ｾＭＱ＠

3

ｲｾＱ＠

ｾｲＲ＠

,fi ｾ＠

rr

o ｾ｟Ｌｦｩ＠

2

Driving

Contact state

Uz

U.r.

2

Ｔｲｾ＠

Ｑｲｾ＠

1 ｾＬｦｩ＠

1

rr ＲｾＴｲ＠

Uz

rr ＱｾＲ＠

Uz =

Contact state between stator and rotor and driving procedure in one cycle

wt ｏｾ＠

=

ﾮｾｃｖ＠

tor completely Stator separate [rom ro-

2

Stator still separate [rom

2

ｃｖｾﾮ＠

tor completely

rotor completely

ﾮｾｃｄ＠

2. Elliptic motion of points on the driving sur face In order to analyze the elliptic motion of points on the driving surface of the motor, the simplified modcl shown in Fig. 8. 9 is adopted. When the motor runs, the stator will generate the torsional vibration ux(t) around z axis, as shown m Fig. 8. 9(a), and the extension-contraction vibration uz(t) along z direction, as shown in Fig. 8. 9(b). Therefore, the vibration of point P can be expressed as Ux

=

Uxsin(wt)

Uz

=

U z sin(wt

+ rp)

(8. 1) (8. 2)

where rp is the phase difference between the longitudinal and torsional vibration, ' U z arc their amplitudes of point p, respeetivcly.

Ux

Ultrasonic Motors Technologies and Ap plicalions

238

P P'

-

: : : :: :

I'

:

:

(b)

Fig. 8. 9

ＱｉＬ

ｾ ｕＬｳ

ｩｮ

ＨＯｬＩ

ｉ Ｋ ＹＧＩ＠

Vibration response of multi-mode type LTUM

Eliminating wt from Eqs. (8. 1) and (8. 2), we can get 2

ｵｾ＠

U,

-

2 uxu ｾ＠

UxU, cosrp

+

2

.

u,

U; =

Sill

2

(8. 3)

rp

From Eq. (8. 3) , we can see that the motion locus of point P is an ellipse. Taking various numerical values for cp, we can get various loci, as shown in Fig. 8. 10.

(b)

(a)

(d)

(g) -TCq:»-1I/2

Fig. 8. 10

(e)

Motion loci of point P under various phase differences

IT

When rp= 2 and rp= -

IT 2'

the motion loci of point P can be simplified as an

ideal elliptic equation

1

(8. 4)

Chapter 8

Ultrasonic Motor Using Longitudinal-Torsional···

239

We note that the directions of the motion are opposite under the two phase diffcrences

({J= ;

and

({J= -

;.

Accordingly, wc can changc

({J

to control the di-

rection of the motion. In addition, we can control the output characteristics by changing thc phasc difference of two cxciting voltages, bccausc its long and short axes of the ellipse are related to the longitudinal and torsional vibration, respectively. When ({J= 0 or ({J= IT, the equation of motion track is u::'

""!:l

Q.

g

Ｎ Ｘ＠

0.6

100

-0.005

« -2

-0.01 -0.015

-3 ＧＭｾ＠

o

2 Tim s (a) Acoustic intcnsity 43dB(42 .5 kH z)

-40 Time!s (b) Acoustic intcnsily 92 dB (ncar to re onance frequency 39kHz)

Fig. 14.30 :'\raise measurement results for TRUM-60 at two different driving frequencies

In fact, the piezoeleetric material is depicted by the nonlinear constitution equation under strong electric field. The stator's response will become more complex due to the nonlinear effect of the piezoelectric material, which can obtain the sharp noise of the USM. The experiments show that noise will be greatly decreased as long as the driving frequency is a little higher than the resonance frequency. So the driving frequency should keep away from the resonance frequency.

2. Influence of pre-pressure on noise Fixing the driving frequency of 35kHz and gradually increasing pre-pressure, we have conducted a series of experiments in which the results corresponding to the pre-pressure of 20)J and 210N are illustrated in Figs. 14. 31(a) and (b). respectively. It is found that small pre-pressure will produce quite louder noise. For example, the pre-pressure of 20)J results in 86dB. However with the increasing pre-pressure the noise of high frequency vanishes. The noise without the high frequency components decreases to 53dB at the pre-pressure of 210N. The experiments illustrate that the noise of the ultrasonic motor decreases remarkably with the increasing pre-pressure. It can also prove that the high prepressure can improve the contact characteristics between the stator and rotor and enlarge the structure stiffness. 3. Influence of friction material on noise Due to the application of macromolecule friction material, the noise of USM can be reduced to below 30dB. Moreover, the smooth finish of friction material has an effect on not only the life of the USM, but also its noise. Usually the friction material with the coarse finish results in the noise with low frequencies; on the other hand the noise with high frequencies is produced by the good smooth finish, which will reduce the noise level. 4. Influence of manufacture and assembly quality on noise Manufacture and assembly errors lead to the contact nonuniformity between

Ultrasonic Motors Technologies and Ap plicalions

440

0. 15 ｲＭｾＮＬ＠ 0. 1

ｾ＠

0.05 ｾ＠

ｾ＠ ｾ＠

.'" ii

...:"

Q.

'" -0.05

8

- 05

...:

-I

- 0. 1 - 0. 15 - 0.2 ＧＭｾ

Ｎ＠

o

2 Time/s

Time/s

(a) Acorstic intensity 86dB at pre-pressure 20N

Fig. 14. 31

(b) Acorst ic intensity 53 dB at pre-pressure 21 ON

Noise measurement results of ultrasonic motor with various pre-pressure

the stator and rotor, then the impure traveling wave appears in the stator. In this case the noise of the USM can be produced. So we have to improve the smooth finish, reduce assembly errors, and adj ust appropriate pre-pressure, so as to decrease the noise. Then TRUM-60 and TRUM-10 developed by PDLab were chosen as noise testing samples, which were placed in anechoic room of Aerodynamic Institute of )JUAA. The experimental results show that the noise level of TRUM-60 and TRUM-40 are 38. 5dB and 29dB. respectively.

14. 5. 6

Testing of USMs in Hygrothermal Environment

The experiments are proposed to research on the adaptability of USM simulated hygrothermal environment. The key of the hygrothermal test is how to simulate the natural humidity of the envionment under a shortening testing period. Considering the testing features, the moisture absorption characteristics of friction materials will be measured besides the mechanical characteristics of the USM. Some special methods can be applied to shorten the testing period. such as increasing temperature and enhancing relative humidity. Fig. 11. 32 illustrates the alternation of the temperature and humidity in the hygrothermal testing. ._._._._._._._._._._._. _._._._._._.- 95 95 ＭＮｾ＠ -·_·-Humidity -: 85 85 ---------Temperature : :

55

I: 30

, - - - - i..

I

I

Ii

:1

ｾ＠

:: 1112

24

36

48

Timeih Notice: Humidity retains over 85% with decreasing temperature

Fig. 14.32

Experimental conditions in hygrothermal environment

Chaptcr 11

Tcsting Tcchniqucs for Ultrasonic Motors

441

1. Test chamber and project In the hygrothermal experiment, the available room should accord with the testing rules and allowable errors. The water used in the experiment must be purified. The condensation water on the top of the testing chamber should fall on the tested samples drop by drop, so as to avoid the seepcr on the samples. Of course. this is very distinct from the natural hygrothcrmal environment. The high/low temperature hygrothermal test chamber from ACS Co. of Italy is applied and the available temperature ranges from -75"C to 180"C, and humidity from 10 percent to 98 percent. The experiments inelude the mechanical characteristics of the USM before and after the hygrothermal environment and the moisture absorption characteristics of friction materials. 2. Mechanical characteristics of the ultrasonic motor in the hygrothermal environment Figure 14. 33 depicts the mechanical characteristics of the USM in different hygrothermal environments. We notice that a normal USM is first measured before the hygrothcrmal environment. then once again after 24h storage in the hygrothermal environment. Moreover the USM is measured after 18h storage in the hygrothermal environment, and then measured once again after the hygrothcrmal environment. It is found that the USM can operate well in the hygrothcrmal environment. 3. Moisture absorption characteristics testing of friction materials Due to the contact mechanism of USM. the moisture absorption of friction materials with a long time storage can lead to the adhesion between the stator and rotor. In this case the USM's startup is more difficult and so the moisture absorption characteristics testing of friction material is very necessary. By weighing the tested samples before and after the storage in humid environment. we measured and calculated the moisture absorption characteristics of three kinds of friction materials, respectively. based on poly(cthcr-cther-ketone) (denoted by No. 1), 150 ;:R ｾ＠

125

ｾ＠

::

ｾ＠

Ｎ ｾ＠

e Ｎ ｾ＠ e-ｾ＠

100 75

g "'-

(rJ

.0

'"g

50

0.9 0.8 0.7 0.6 0.5 0.4 0.3

;;; 0.2