Electromechanical Systems in Microtechnology and Mechatronics (eBook)

Preface 6
Contents 9
List of Symbols 14
Part I Focus of the Book 24
1 Introduction 25
1.1 Focus of the Book 26
1.2 Fields of Application and Examples for Electromechanical Systems 28
1.3 Design of Electromechanical Systems 31
1.4 Simulation Methods for Electromechanical Systems 32
1.4.1 Historical Overview 32
1.4.2 Design Methods 35
2 Electromechanical Networks and Interactions 37
2.1 Signal Description and Signal Transmission in Linear Networks 38
2.1.1 The Circular Function as Basic Module for Time Functions of Linear Networks 38
2.1.2 Fourier Expansion of Time Functions 42
2.1.3 The Fourier Transform 47
2.1.4 The Laplace Transform 55
2.2 Electrical Networks 58
2.3 Mechanical Networks 62
2.4 Interactions 66
2.4.1 Mechanical Interactions 66
2.4.2 Electromechanical Interactions 68
2.5 Structured Network Representation of Linear Dynamic Systems 78
2.6 Basic Equations of Linear Networks 80
Part II Network Representation of Systems with Lumped and Distributed Parameters 81
3 Mechanical and Acoustic Networks with Lumped Parameters 82
3.1 Mechanical Networks for Translational Motions 83
3.1.1 Arrangements 83
3.1.2 Coordinates 85
3.1.3 Components 87
3.1.4 Rules of Interconnection 95
3.1.5 Isomorphism between Mechanical and Electrical Circuits 98
3.1.6 Representation of Transient Characteristics of Mass Point Systems in the Frequency Domain (BODE diagram) 100
3.1.7 Network Representation of Mass Point Systems 106
3.1.8 Sample Applications 109
3.2 Mechanical Networks for Rotational Motions 120
3.2.1 Coordinates 121
3.2.2 Components and System Equations 122
3.2.3 Isomorphism between Mechanical and Electrical Circuits 123
3.2.4 Sample Application for a Rotational Network 127
3.3 Acoustic Networks 128
3.3.1 Coordinates 129
3.3.2 Acoustic Components 130
3.3.3 Network Representation of Acoustic Systems 131
3.3.4 Real Acoustic Components 135
3.3.5 Isomorphism between Acoustic and Electrical Circuits 141
3.3.6 Sample Applications 141
4 Abstract Linear Network 149
4.1 Coordinates 149
4.2 Components 150
4.3 Nodal and Loop Rules 152
4.4 Characteristics of the Abstract Linear Network 152
5 Mechanical Transducers 157
5.1 Translational-Rotational Transducer 157
5.1.1 Rigid Rod 157
5.1.2 Bending Rod 161
5.2 Mechanical-Acoustic Transducer 166
5.2.1 Ideal and Real Mechanical-Acoustic Piston Transducers 167
5.2.2 General Elastomechanical-Acoustic Plate Transducer 169
5.3 Characteristics of Selected Mechanical-AcousticTransducers 171
6 Mechanical and Acoustic Networks with Distributed Parameters 184
6.1 Representation of Mechanical Systems asone-dimensional Waveguides 184
6.1.1 Extensional Waves within a Rod 185
6.1.2 Approximate Calculation of the Input Impedance 191
6.1.3 Approximate Representation of an Impedance at Resonance 196
6.1.4 Approximated two-port Network Representation at Resonance 197
6.1.5 Flexural Vibrations within a Rod 202
6.2 Network Representation of Acoustic Systems as Linear Waveguides 211
6.3 Modeling of Transducer Structures with Finite Network Elements 214
6.3.1 Ultrasonic Microactuator with Capacitive Diaphragm Transducer 214
6.3.2 Fluid-filled Pressure Transmission System of a Differential Pressure Sensor 217
6.4 Combined Simulation with Network and Finite Element Methods 221
6.4.1 Applied Combination of Network Methods and Finite Element Methods 223
6.4.2 Combined Simulation using the Example of a Dipole Bass Loudspeaker 228
6.4.3 Combined Simulation using the Example of a Microphone with Thin Acoustic Damping Fabric 235
Part III Electromechanical Transducers 245
7Electromechanical Interactions 246
7.1 Classification of Electromechanical Interactions 246
7.2 Network Representation of Electromechanical Interactions 250
8 Magnetic Transducers 264
8.1 Electrodynamic Transducer 264
8.1.1 Derivation of the Two-Port Transducer Network 264
8.1.2 Sample Applications 268
8.2 Electromagnetic Transducer 284
8.2.1 Derivation of the Two-Port Transducer Network 285
8.2.2 Sample Applications 292
8.3 Piezomagnetic Transducer 302
8.3.1 Derivation of the Two-Port Transducer Network 303
8.3.2 Sample Applications 313
8.3.3 Piezomagnetic Unimorph Bending Elements 319
9 Electrical Transducers 329
9.1 Electrostatic Transducer 329
9.1.1 Electrostatic Plate Transducer 329
9.1.2 Sample Applications 339
9.1.3 Electrostatic Diaphragm Transducer 347
9.1.4 Sample Applications 350
9.1.5 Electrostatic Solid Body Transducers 355
9.1.6 Sample Application 357
9.2 Piezoelectric Transducers with Lumped Parameters 361
9.2.1 Model Representation of the Piezoelectric Effect 361
9.2.2 Piezoelectric Equations of State and Circuit Diagram forLongitudinal Coupling 364
9.2.3 General Piezoelectric Equations of State 366
9.2.4 Piezoelectric Transducers and Corresponding EquivalentParameters 369
9.2.5 Piezoelectric Bending Bimorph Elements 374
9.2.6 Piezoelectric Materials 376
9.2.7 Sample Applications 381
9.3 Piezoelectric Transducer as one-dimensional Waveguide 386
9.3.1 Transition from Lumped Parameters to the Waveguide usingthe Example of an Accelerometer 387
9.3.2 Piezoelectric Longitudinal Oscillator as Waveguide 391
9.3.3 Piezoelectric Thickness Oscillator as Waveguide 391
9.3.4 Sample Applications of Piezoelectric Longitudinal andThickness Oscillators 397
9.3.5 Piezoelectric Beam Bending Element as Waveguide 408
9.3.6 Sample Applications of Piezoelectric Beam BendingElements 409
10 Reciprocity in Linear Networks 429
10.1 Reciprocity Relations in Networks with only One Physical Structure 429
10.2 Reciprocity Relations in General Linear Two-Port Networks 431
10.3 Electromechanical Transducers 433
10.4 Mechanical-Acoustic Transducers 436
Part IV Appendix 438
A Characteristics of Selected Materials 439
A.1 Material Characteristics of Crystalline Quartz 439
A.2 Piezoelectric Constants of Sensor Materials 440
A.3 Characteristics of Metallic Structural Materials 441
A.4 Material Characteristics of Silicon and Passivation Layers 442
A.4.1 Comparison of Main Characteristics of Silicon, Silicon Dioxide and Silicone Nitride Layers 442
A.4.2 Characteristics of Silicon Dioxide Layers 443
A.4.3 Characteristics of Silicon Nitride Layers 444
A.5 Characteristics of Ceramic Structural Materials 445
A.6 Material Characteristics of Selected Polymers 446
A.7 Characteristics of Plastics as Structural Materials 447
A.8 Composition and Material Characteristics of Selected Glasses 448
A.9 Material Characteristics of Metallic Solders and Glass Solders 449
A.10 Sound Velocity and Characteristic Impedance 450
B Signal Description and Transfer within LinearNetworks 451
B.1 Fourier Expansion of Time Functions 451
B.1.1 Estimate of Approximation Error with Numerical Analyses of Fourier Series 451
B.1.2 Sample Application for the Periodic Iteration of Singular Processes 454
B.2 Ideal Impulse and Step Functions 456
B.2.1 Problem Definition 456
B.2.2 Ideal Impulses and their System Response 457
B.2.3 The Ideal Step Function and its System Response 462
B.3 The Convolution Integral 463
References 466
Index 471