Foundations of Ultraprecision Mechanism Design

Transcription

1 Foundations of Ultraprecision Mechanism Design S.T. Smith University of North Carolina at Charlotte, USA and D.G. Chetwynd University of Warwick, UK GORDON AND BREACH SCIENCE PUBLISHERS Switzerland Australia Belgium France Germany Great Britain India Japan Malaysia Netherlands Russia Singapore USA

2 INTRODUCTION TO THE SERIES xi PREFACE xiii CHAPTER 1 INTRODUCTION The scale of ultraprecision Instrumentation terms Errors Random errors and noise Error combination 13 References 15 CHAPTER 2 INTRODUCTORY MECHANICS 17 Introduction Statics, elasticity and beam distortion Elementary elasticity Bending of symmetrical beams Rigid body dynamics and Lagrange's equation Vibration behaviour of beams Longitudinal vibration of a beam Transverse vibration of beams Rayleigh's method 38 References 41 v

3 CHAPTER 3 FUNDAMENTAL CONCEPTS IN PRECISION DESIGN 43 Introduction Kinematics of constraint Coordinate systems Basic point constraints Point constraints and relative freedom Kinematic clamps Mobility and the kinematics of mechanisms Mechanism mobility Kinematics of plane mechanisms Pseudo-kinematic design or elastic design Load bearing, area contact and elastic averaging Kinematic analogy to real systems Measurement and force loops Principles of alignment 'Cosine' errors Abbe offset Nulling Compensation Mechanical compensation strategies Computer compensation of systematic errors Symmetry The effects of scaling: Stiffness and dynamic response Case study: A proposed nanohardness indentation instrument References 93 CHAPTER 4 FLEXURE DESIGN FOR POSITIONING AND CONTROL A simple flexure design The pros and cons of flexure design The advantages of flexures The disadvantages of flexures Linear spring mechanisms Simple and compound leaf spring mechanisms 100 vi

4 4.3.2 Notch type spring mechanisms Kinematic analysis of linear spring mechanisms Additional considerations with compound spring designs Angular motion flexures Dynamic characteristics of flexure mechanisms Case studies X-ray interferometry The measurement of friction between a diamond stylus and specimen 126 References 128 CHAPTER 5 DRIVE COUPLINGS AND THE MECHANICS OF CONTACT 131 Introduction Surface contact under different load conditions Stationary and sliding contacts of a sphere and a flat Rolling contacts Linear drive couplings Rotary drive couplings Elastic rotary couplings Rolling rotary couplings (the knife edge) The sliding rotary coupling Case study: Irving Langmuir's surface tension instrument for the determination of the molecular sizes of fatty acids 150 References 153 CHAPTER 6 LEVER MECHANISMS OF HIGH RESOLUTION 155 Introduction: Generalized leverage The effects of levers Angular levers The pulley drive The wedge Angular gearboxes and friction drives Balanced torque actuation 168 vii

5 6.3 Linearievers Case studies The Marsh micro-tensile tester The Ängstrom ruler 178 References 180 CHAPTER 7 ACTUATORS AND SENSORS FOR CONTROLLED DISPLACEMENTS 181 Introduction Types of actuator Piezoelectric drives Electrostrictive Mechanical micrometers Friction drives Magnetostrictive Magnetoelasticity Shape memory alloys and bimetallic strips Electromagnetic Electrostatic Hydraulic The Poisson's ratio drive Summary of actuator performance Nanometric displacement sensors Inductive gauging Capacitive gauging Optical transducers Proximity probes for scanning tip microscopes Eddy current sensors Strain gauges 213 References 215 CHAPTER 8 MATERIALS SELECTION IN PRECISION MECHANICAL DESIGN 221 Introduction 221 viii

6 8.1 Design, materials and function Property groupings and charts Property profiles in precision engineering Mechanical property groups Thermal property groups Material profiles Materials properties Metals Ceramics and glasses Polymers and composites Non-conventional materials for small devices Materials for transducers Case studies Simple flexure mechanism Talystep revisited 248 References 253 CHAPTER 9 SLIDEWAYS FOR LONG RANGE PRECISION MOTION 255 Introduction Sources of error in bearing slideways Fluid film bearings Air or oil hydrostatic bearings Hydrodynamic rotary bearings Lubrication with lamellar solids Frictional behaviour of graphite Frictional behaviour of molybdenum disulphide Dry or boundary lubrication Liquid film boundary lubrication Polymer bearings Case studies Nanosurfll Molecular measuring machine Super stiff grinding machine slides 280 References 281 ix

7 CHAPTER 10 THE DYNAMICS OF INSTRUMENTATION MECHANISMS The simple oscillator Response of a second order spring/mass/viscous damper system Standard forms of the equation of motion Response to a step change of force Steady state response to a harmonically varying input force Response to a harmonic displacement: Seismic isolation Harmonic response of series spring-mass-damper systems Response of two stage seismic isolator Multi-stage isolation Measurement of the viscous damping coefficient The design of resonant systems: Followers and isolators Stylus tracking Vibration isolation Noise isolation Damping of small vibrations Casestudies An atomic force probe A gravity wave antenna 319 References 320 APPENDIX A 323 Airy point mounting of datum bars 323 AUTHOR INDEX 325 SUBJECT INDEX 333 x