Development of small footprint large amplitude tripod (three lambda) mode traveling wave generator

DEVELOPMENT OF SMALL-FOOTPRINT LARGEAMPLITUDE TRIPOD (3λ λ) MODE TRAVELING WAVE GENERATOR MOHAMMAD AHSAN ULLAH NATIONAL UNIVERSITY OF SINGAPORE 2010 DEVELOPMENT OF SMALL-FOOTPRINT LARGEAMPLITUDE TRIPOD (3λ λ) MODE TRAVELING WAVE GENERATOR MOHAMMAD AHSAN ULLAH (B.Sc.(Hons.), BUET) A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF ENGINEERING DEPARTMENT OF MECHANICAL ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2010 Acknowledgements I would like to express my heartfelt gratitude to my supervisor, Assoc. Prof Lim Leong Chew for his constant encouragements and invaluable advice and guidance throughout this research work. My gratitude also goes to Dr Jin Jing for his important suggestions and comments. My thanks and appreciation to technical staffs of Material Science Lab, namely, Thomas Tan, Ng Hon Wei, Abdul Karim, and Maung Aye Thein; technical staffs of Dynamics Lab namely, Cheng Kok Seng, Ahmad Bin Kasa, Amy Chee, and Priscilla Lee; technical staffs in Mechanical Engineering Fabrication Support Centre, namely, Lam Kim Song, Low Boo Kwan, and T. Rajah for their help in many ways. My appreciation also goes to Microfine staffs Paul Lim, Lenson Lim, and Joy Chuah for providing good supports. Thanks to my colleagues and friends for their hearted support through good times and bad times. Finally, I am especially indebted to my family for their love and continuous moral support. Without them this work would not have been completed. i Table of Contents Acknowledgements Table of contents Summary List of Tables List of Figures List of Symbols Chapter 1 Introduction 1 Chapter 2 Literature Review 6 2.1 Background 2.2 Non resonant piezoelectric actuator 8 2.2.1 Axial, Transverse, and Flexion actuator 2.2.2 Bimorph, Unimorph, Multimorph actuator 2.2.3 Stack actuator 2.2.4 Inchworm actuator 2.3 Resonant piezoelectric actuator 14 2.3.1 Different vibration modes used 2.3.2 Traveling wave and standing wave 2.3.3 Actuator generating traveling wave vibration excited by flexural vibration mode of ring 2.3.4 Cylindrical micromotors excited by bending vibration of a tubular stator 2.3.5 Ultrasonic motors excited by combined longitudinal-torsional vibrations ii 2.3.6 Micromotors excited by combined longitudinal-flexural vibrations 2.3.7 Standing wave elastic fin ultrasonic micromotors 2.3.8 Ultrasonic motors using torsional displacement – The windmill 2.3.9 Ultrasonic motor using shear mode 2.4 39 Summary Remarks 40 Chapter 3 Statement of Present Research 3.1 Objectives of present work 3.2 Organization of remaining chapters 44 Chapter 4 FEM Simulation of Vibrations of Cylindrical Stubs and Generation of Non-Rocking Tripod (3-crest) Traveling Wave 4.1 Mode shape and natural frequency of a vibrating body 4.2 Finite Element Analysis of free vibration of a cylindrical body 48 4.2.1 Free vibration of a slender cylindrical bar 4.2.2 Free vibration of short cylindrical stubs 4.3 Vibration mode of choice for traveling wave 54 4.4 Elaboration of the chosen mode shape 56 4.5 Forced vibration of cylindrical stub and generation of traveling wave – FEM results 57 4.5.1 Modeling of cylindrical stub vibrator 4.5.2 Forced vibration of the cylindrical stub vibrator 4.5.3 Generation of the traveling wave 4.6 Concluding Remarks 65 Chapter 5 Experimental Verification of Tripod (3λ λ) Traveling Wave Generation 5.1 Fabrication of Vibrator Assembly 5.1.1 Aluminium cylinder iii 66 5.1.2 Single Crystal 5.1.3 Bonding of crystals 5.1.4 Arrangement of crystals 5.1.5 Electrical cable connection 5.2 Resonance frequency of the vibrator in Impedance Analyzer 72 5.3 Vibration test results by means of Laser Vibrometry 73 5.3.1 Generation the mode shape by exciting respective sets of six crystals 5.3.2 Generation of traveling wave along the circumference of end face 5.3.2.1 Generation of the traveling wave in opposite direction 5.3.3 Displacement of traveling wave vibration at resonance 5.4 Concluding Remarks 83 84 Chapter 6 Generation of Tripod (3λ λ) Traveling Wave of Enhanced Amplitude by means of Flanged Cylindrical Stub Vibrators 6.1 Introduction 6.2 Determination of the dimensions of end flanges 86 6.2.1 End flanges of 0.5 mm thickness 6.2.2 End flanges of 1.0 mm thickness 6.3 89 Forced Vibration of the Flanged Cylindrical Vibrator 6.3.1 For 0.5 mm flange thickness 6.3.2 For 1 mm flange thickness 93 6.4 Fabrication of flanged cylinder vibrator assembly 6.5 Resonance frequency of the flanged cylinder vibrator in Impedance 6.6 Analyzer 94 Vibration test results by means of Laser Vibrometry 95 6.6.1 Generation the mode shape by exciting respective sets of six crystals iv 6.6.2 Generation of the traveling wave along the circumference of the flange 6.6.2.1 Generation of the traveling wave in opposite direction 6.6.3 Displacement of the traveling wave vibration at resonance 6.7 Concluding remarks Chapter 7 Conclusions and Recommendations 7.1 106 107 Summary of Main Results Obtained 7.1.1 Cylindrical stub vibrator 7.1.2 Flanged cylindrical stub vibrator 7.2 Recommendations 110 References 112 Appendix 121 v Summary Existing cylindrical micromotors are of bending vibration type in which the traveling wave generated at the end faces of the cylindrical stator has only one crest and one trough or of one-λ mode shape, λ being the wavelength. A rotor cap placed onto it is in contact with the cylinder end face at only one point. The resultant micromotor has large output torque but its rotor shaft will “rock” as a result. In this work, attempts have been made to design and test cylindrical vibrators which generate traveling wave of three crests and three troughs or 3λ mode shape of sufficiently large amplitude at their end faces for the realization of non-rocking micromotors. Extensive finite element analysis was carried out initially in search for a vibration mode for cylindrical stubs of the desired mode shape and a resonance frequency of 500 kHz and hence may not be suitable as actuators as the resultant axial displacement will be quite small. Table 4.2: Summary of FEM results on vibration of slender cylindrical bar Cylinder dimensions 1-cerst 1-trough 2-crest 2-trough 3-crest 3-trough 4-crest 4-trough O.D. = 3 mm I.D. = 2 mm L = 8 mm fr = 154 kHz Fig. 4.1 fr = 241 kHz Fig. 4.2 Occurs above 500 kHz Occurs above 500 kHz See Table 4.1 for properties of aluminum used in the simulation. 50 FEM Simulation 4.2.2 Free vibration of short cylindrical stubs In search for a vibration mode which can be used to generate a non-rocking traveling wave, the vibration characteristics of short cylindrical stubs are investigated. By changing the dimensions of the cylinder, their free vibration characteristics are investigated. Keeping the dimensions of the cylindrical stubs small where possible, attempts were made to study the various free vibration modes and the corresponding resonance frequencies. The physical and elastic properties of the cylinder material used in the simulation are the same as in Table 4.1. Our interest is to generate clear mode shapes with two-crest, three-crest, and four-crest at each end of the cylinder having resonance frequencies of [...]... the bending mode, radial mode, extensional mode, flexural mode of disc, longitudinal torsional mode, longitudinal bending mode, shear mode, torsional mode, etc Both standing and traveling waves have been utilized in piezoelectric actuators Standing wave requires one vibration source and it has fix nodal and antinodal points Traveling wave has moving nodal and antinodal points Traveling wave can be... although a combination of two modes may be used - flexural vibration mode - radial vibration mode - longitudinal vibration mode - torsional vibration mode (a) flexural vibration mode (c) longitudinal vibration mode (b) radial vibration mode (d) torsional vibration mode Figure 2.6: Different vibration mode (a) flexural mode, (b) radial mode, (c) longitudinal mode, and (d) torsional mode [48] 14 Literature... excitation frequency Figure 5.9 Schematic for the generation of the traveling wave by simultaneously applying 90° out -of- phase voltage signals (at 65 kHz) to respective sets of crystals from Channel A and Channel B of the function generator Figure 5.10 Evidence of the generation of traveling wave The entire circumference of the end face consists of three wave lengths (i.e 3 crests and 3 troughs) The relative... frequency 70 kHz Figure 6.15 Schematic for the generation of the traveling wave by simultaneously applying 90° out -of- phase voltage signals (at 70 kHz) to respective sets of crystals from Channel A and Channel B of the function generator Figure 6.16 Evidence of the generation of traveling wave The entire circumference of the end face consists of three wave lengths (i.e 3 crests and 3 troughs) The relative... types: traveling wave type and standing wave type In fact, these two types are related to each other Traveling wave can be generated by superimposing two standing waves with a phase shift (i) Traveling wave: Traveling wave types are certainly one of the most advanced actuator Invented by Sashida in 1982 [30], this actuator marked the beginning of a period of intense research This type of actuator requires... generated by superimposing two standing waves of a given phase shift, such as by two voltage signals of 90 degree phase difference with each other Flexural mode of discs or rings has been used to construct traveling wave motion in actuators For instance, Sashida et al., (1983) used nine-wavelength flexural mode of a ring and successfully developed traveling wave micromotors for the first time Hagood... generate traveling wave Two vibration sources generate two standing waves, and these two waves are superimposed with 900 phase difference to generate the traveling wave Traveling wave in the opposite direction can be generated by changing the phase difference to -90° In traveling wave there is no fixed nodal or antinodal point Hence, mounting the actuator requires careful considerations for traveling wave. .. Combinations of these two standing waves generate the traveling wave xi Figure 4.13 Generation of the traveling wave by superimposing 2 standing waves differing by 90° both spatially and temporally The amount of angular distance traveled by each crest along circumferential direction in one cycle of input voltage signal is shown here The phase angles given pertain to those applied to the set of “white”... frequency of the vibrator Figure 5.5 Schematic of electrical connection from Channel A of the function generator to the crystals of the vibrator Incident laser scans the end face of the vibrator Figure 5.6 Mode shape of the end face of the vibrating cylinder, taken from laser vibrometer, when the set of 6 blue-colored crystals are excited with a sinusoidal ac voltage signal The maximum displacement of vibration... successfully developed traveling wave micromotors for the first time Hagood et al (1995) reported the construction of traveling wave in an actuator utilizing fourwavelength flexural mode of discs and Chau et al (2004) a standing wave actuator using 8th vibration mode of rings Actuators using bending mode of cylinders have been constructed with PZT discs (Kurosawa et al., 1989) and PZT thin films (Morita et al., ... difference, a traveling wave of the mode shape is generated The FEA results give an axial displacement of the traveling wave of ±84 nm at ±20 V The generation of tripod vi (3λ) traveling wave was... bending mode, radial mode, extensional mode, flexural mode of disc, longitudinal torsional mode, longitudinal bending mode, shear mode, torsional mode, etc Both standing and traveling waves have.. .DEVELOPMENT OF SMALL-FOOTPRINT LARGEAMPLITUDE TRIPOD (3λ λ) MODE TRAVELING WAVE GENERATOR MOHAMMAD AHSAN ULLAH (B.Sc.(Hons.), BUET) A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF ENGINEERING