Piezoelectric Sensors and Actuators (eBook)

Preface 6
Acknowledgements 7
Contents 8
1 Introduction 14
1.1 Fundamentals of Sensors and Actuators 14
1.2 History of Piezoelectricity and Piezoelectric Materials 15
1.3 Practical Applications of Piezoelectricity 16
1.4 Chapter Overview 17
2 Physical Basics 20
2.1 Electromagnetics 20
2.1.1 Maxwell's Equations 20
2.1.2 Electrostatic Field 22
2.1.3 Interface Conditions for Electric Field 23
2.1.4 Lumped Circuit Elements 25
2.2 Continuum Mechanics 28
2.2.1 Navier's Equation 28
2.2.2 Mechanical Strain 31
2.2.3 Constitutive Equations and Material Behavior 34
2.2.4 Elastic Waves in Solids 36
2.3 Acoustics 39
2.3.1 Fundamental Quantities 40
2.3.2 Wave Theory of Sound 41
2.3.3 Linear Acoustic Wave Equation 46
2.3.4 Reflection and Refraction of Sound 48
2.3.5 Sound Absorption 51
References 53
3 Piezoelectricity 55
3.1 Principle of Piezoelectric Effect 55
3.2 Thermodynamical Considerations 57
3.3 Material Law for Linear Piezoelectricity 61
3.4 Classification of Electromechanical Coupling 65
3.4.1 Intrinsic Effects 65
3.4.2 Extrinsic Effects 66
3.4.3 Modes of Piezoelectric Effect 67
3.5 Electromechanical Coupling Factors 69
3.5.1 Conversion from Mechanical into Electrical Energy 70
3.5.2 Conversion from Electrical into Mechanical Energy 72
3.6 Piezoelectric Materials 75
3.6.1 Single Crystals 76
3.6.2 Polycrystalline Ceramic Materials 81
3.6.3 Polymers 89
References 92
4 Simulation of Piezoelectric Sensor and Actuator Devices 94
4.1 Basic Steps of Finite Element Method 95
4.1.1 Finite Element Method for a One-Dimensional Problem 96
4.1.2 Spatial Discretization and Efficient Computation 100
4.1.3 Ansatz Functions 102
4.1.4 Time Discretization 105
4.2 Electrostatics 106
4.3 Mechanical Field 109
4.3.1 Types of Analysis 112
4.3.2 Attenuation within Mechanical Systems 115
4.3.3 Example 116
4.4 Acoustic Field 119
4.4.1 Open Domain Problems 121
4.4.2 Example 124
4.5 Coupled Fields 126
4.5.1 Piezoelectricity 126
4.5.2 Mechanical–Acoustic Coupling 133
References 136
5 Characterization of Sensor and Actuator Materials 138
5.1 Standard Approaches for Characterization 139
5.1.1 IEEE/CENELEC Standard on Piezoelectricity 139
5.1.2 Characterization Approaches for Passive Materials 147
5.2 Fundamentals of Inverse Method 152
5.2.1 Definition of Inverse Problems 152
5.2.2 Inverse Method for Material Characterization 153
5.2.3 Tikhonov Regularization 154
5.2.4 Iteratively Regularized Gauss–Newton Method 156
5.3 Inverse Method for Piezoceramic Materials 158
5.3.1 Material Parameters and Modeling of Attenuation 160
5.3.2 Feasible Input Quantities 161
5.3.3 Test Samples 161
5.3.4 Mathematical Procedure 166
5.3.5 Efficient Implementation 168
5.3.6 Results for Selected Piezoceramic Materials 169
5.4 Inverse Method for Passive Materials 176
5.4.1 Material Model and Modeling of Attenuation 177
5.4.2 Feasible Input Quantities 183
5.4.3 Test Samples 184
5.4.4 Efficient Implementation 191
5.4.5 Identified Parameters for Selected Materials 195
References 201
6 Phenomenological Modeling for Large-Signal Behavior of Ferroelectric Materials 205
6.1 Mathematical Definition of Hysteresis 207
6.2 Modeling Approaches on Different Length Scales 208
6.3 Phenomenological Modeling Approaches 211
6.4 Modeling of Preisach Hysteresis Operator 214
6.4.1 Preisach Hysteresis Model 214
6.4.2 Efficient Numerical Calculation 219
6.5 Weighting Procedures for Switching Operators 223
6.5.1 Spatially Discretized Weighting Distribution 224
6.5.2 Analytical Weighting Distribution 228
6.6 Generalized Preisach Hysteresis Model 234
6.6.1 Reversible Parts 234
6.6.2 Asymmetric Behavior 236
6.6.3 Mechanical Deformations 238
6.6.4 Rate-Dependent Behavior 240
6.6.5 Uniaxial Mechanical Stresses 244
6.7 Parameter Identification for Preisach Modeling 249
6.7.1 Identification Strategy for Model Parameters 249
6.7.2 Application to Piezoceramic Disk 252
6.8 Inversion of Preisach Hysteresis Model 252
6.8.1 Inversion Procedure 255
6.8.2 Characterization of Inversion Procedure 259
6.8.3 Inverting Generalized Preisach Hysteresis Model 262
6.8.4 Hysteresis Compensation for Piezoceramic Disk 262
References 264
7 Piezoelectric Ultrasonic Transducers 270
7.1 Calculation of Sound Fields and Electrical Transducer Outputs 271
7.1.1 Diffraction at Point-Like Target 272
7.1.2 Spatial Impulse Response (SIR) 274
7.1.3 SIR of Piston-Type Transducer 276
7.1.4 SIR of Spherically Focused Transducer 278
7.2 Sound Fields and Directional Characteristics 281
7.2.1 Piston-Type Transducer 283
7.2.2 Spherically Focused Transducer 290
7.3 Spatial Resolution in Pulse-Echo Mode 298
7.3.1 Transducer Excitation and Resulting Output 298
7.3.2 Axial Resolution 300
7.3.3 Lateral Resolution 301
7.4 General Structure 304
7.4.1 Single-Element Transducers 305
7.4.2 Transducer Arrays 310
7.4.3 Piezoelectric Composite Transducers 315
7.5 Analytical Modeling 317
7.5.1 Equivalent Electrical Circuits 320
7.5.2 Calculation Procedure 321
7.5.3 Exemplary Results 325
7.6 Examples for Piezoelectric Ultrasonic Transducers 328
7.6.1 Airborne Ultrasound 328
7.6.2 Underwater Ultrasound 333
7.6.3 Medical Diagnostics 339
7.7 Ultrasonic Imaging 340
7.7.1 A-Mode and M-Mode Imaging 341
7.7.2 B-Mode Imaging 342
7.7.3 C-Mode Imaging 343
References 345
8 Characterization of Sound Fields Generated by Ultrasonic Transducers 349
8.1 Conventional Measurement Principles 349
8.1.1 Hydrophones 350
8.1.2 Microphones 351
8.1.3 Pellicle-Based Optical Interferometry 353
8.1.4 Schlieren Optical Methods 354
8.1.5 Light Diffraction Tomography 355
8.1.6 Comparison 356
8.2 History of Light Refractive Tomography 356
8.3 Fundamentals of Light Refractive Tomography 357
8.3.1 Measurement Principle 357
8.3.2 Tomographic Imaging 360
8.3.3 Measurement Procedure and Realized Setup 364
8.3.4 Decisive Parameters for LRT Measurements 366
8.3.5 Sources for Measurement Deviations 372
8.3.6 Measurable Sound Frequency Range 378
8.4 Sound Fields in Water 380
8.4.1 Piston-Type Ultrasonic Transducer 381
8.4.2 Cylindrically Focused Ultrasonic Transducer 384
8.4.3 Acceleration of Measurement Process 386
8.4.4 Disturbed Sound Field due to Hydrophones 390
8.5 Sound Fields in Air 395
8.5.1 Piezo-optic Coefficient in Air 395
8.5.2 Experimental Setup 396
8.5.3 Results for Piston-Type Ultrasonic Transducer 398
8.6 Mechanical Waves in Optically Transparent Solids 402
8.6.1 Normal Stress in Isotropic Solids 402
8.6.2 Experimental Setup 403
8.6.3 Results for Different Ultrasonic Transducers 404
8.6.4 Verification of Experimental Results 409
References 412
9 Measurement of Physical Quantities and Process Measurement Technology 415
9.1 Force, Torque, Pressure, and Acceleration 417
9.1.1 Fundamentals 417
9.1.2 Force and Torque 420
9.1.3 Pressure 423
9.1.4 Acceleration 426
9.1.5 Readout of Piezoelectric Sensors 430
9.2 Determination of Plate Thickness and Speed of Sound 436
9.2.1 Measurement Principle 437
9.2.2 Transmission Line Model for Plate 439
9.2.3 Excitation Signal of Transmitter 442
9.2.4 Pulse Compression 448
9.2.5 Experiments 454
9.3 Fluid Flow 460
9.3.1 Fundamentals of Fluid Flow Measurements 461
9.3.2 Measurement Principles of Ultrasonic Flow Meters 464
9.3.3 Arrangement of Ultrasonic Transducers 473
9.3.4 Modeling of Clamp-on Transit Time Ultrasonic Flow Meters in Frequency–Wavenumber Domain 477
9.4 Cavitation Sensor for Ultrasonic Cleaning 492
9.4.1 Fundamentals of Acoustic Cavitation and Ultrasonic Cleaning 492
9.4.2 Conventional Measurements of Cavitation Activity 500
9.4.3 Realized Sensor Array 501
9.4.4 Characterization of Sensor Array 503
9.4.5 Experimental Results 509
References 513
10 Piezoelectric Positioning Systems and Motors 518
10.1 Piezoelectric Stack Actuators 519
10.1.1 Fundamentals 519
10.1.2 Effect of Mechanical Prestress on Stack Performance 523
10.1.3 Preisach Hysteresis Modeling for Prestressed Stack 525
10.2 Amplified Piezoelectric Actuators 528
10.2.1 Working Principle 529
10.2.2 Numerical Simulations for Parameter Studies 530
10.2.3 Experimental Verification 535
10.3 Piezoelectric Trimorph Actuators 538
10.3.1 Preisach Hysteresis Modeling for Trimorph 538
10.3.2 Model-Based Hysteresis Compensation for Trimorph 540
10.4 Piezoelectric Motors 545
10.4.1 Linear Piezoelectric Motors 546
10.4.2 Rotary Piezoelectric Motors 551
References 555
Index 558