Piezoelectric Multilayer Beam Bending Actuators (eBook)

Static and Dynamic Behavior and Aspects of Sensor Integration

Rüdiger G. Ballas (Autor)

eBook Download: PDF

2007 | 2007
XXIII, 358 Seiten
Springer Berlin (Verlag)
978-3-540-32642-7 (ISBN)

Infos

This book describes the application of piezoelectric materials, particularly piezoceramics, in the wide field of actuators and sensors. It gives a step-by-step introduction to the structure and mechanics of piezoelectric beam bending actuators in multilayer technology, which are of increasing importance for industrial applications. The book presents the suitability of the developed theoretical aspects in a memorable way.

Rüdiger G. Ballas was born in 1971 in Blieskastel, Germany. After finishing education as an assistant in physics at the Technical School for Natural Sciences Ludwigshafen, Germany, he received the diploma in microsystemtechnology in 1999 from the University of Applied Sciences Kaiserslautern, Germany. From 1999 until 2001 he worked with Tele Quarz in Neckarbischofsheim, Germany, where he was head of the group concerning microstructuring of AT-quartz crystals and development of high-frequency inverted MESA-quartzes. From 2001 until 2006 he worked as a Ph.D. student at Darmstadt University of Technology in the field of piezoelectric bending multilayer actuators with integrated sensors for tip deflection measurements. He received the Ph.D. degree in electrical engineering in 2006 from Darmstadt University of Technology. His actual research fields are theoretical mechanics, electromechanical system theory and modeling of the nonlinear behavior of piezoelectric actuators.

Inhalt

Preface 7
Contents 9
List of Symbols 15
Focus of the Book 24
1 Introduction 25
1.1 Application Areas of Piezoelectric Actuators 25
1.2 Motivation and Aim of the Book 26
1.3 State of the Scientific Research 28
1.4 Textual Focus of the Book 33
Theoretical Aspects and Closed Form Analysis 36
2 Piezoelectric Materials 37
2.1 Discovery of Piezoelectricity 37
2.2 Direct and Inverse Piezoelectric Effect 38
2.3 Piezoelectric Ceramics 39
2.4 Perovskit Structure of PZT 40
2.5 Domain and Reversion Processes of PZT 41
2.6 Electromechanical Behavior 44
2.7 Piezoelectric Beam Bending Actuators 46
3 Linear Theory of Piezoelectric Materials 51
3.1 Energy Density of the Elastic Deformation 51
3.2 Energy Density of the Electrostatic Field 55
3.3 Thermodynamics of Deformation 56
4 Theory of the Static Behavior of Piezoelectric Beam Bending Actuators 66
4.1 Sectional Quantities of a Bending Beam 66
4.2 Bernoulli Hypothesis of Beam Bending Theory 68
4.3 Neutral Axis Position of a Multilayered Beam Bender 70
4.4 Forces and Moments within a Multilayer System 73
4.5 Total Stored Energy within a Multilayer System 74
4.6 Canonical Conjugates and Coupling Matrix 77
4.7 Principle of Virtual Work 79
4.8 Theorem of Minimum Total Potential Energy 80
4.9 Derivation of the Coupling Matrix 81
4.10 The Constituent Equations 94
5 Piezoelectric Beam Bending Actuators and Hamilton’s Principle 96
5.1 Constraints and Generalized Coordinates 96
5.2 D’Alembert’s Principle 97
5.3 Lagrange’s Equations 99
5.4 Euler-Lagrange Differential Equation 102
5.5 Hamilton’s Principle 106
5.6 Consideration of Non-Conservative Forces 107
5.7 Lagrange Function of Piezoelectric Beam Bending Actuators 110
5.8 Mechanical Work Done by Extensive Quantities and Frictional Force 114
5.9 Variation of the Lagrange Function 117
5.10 Variation of the Mechanical Work 118
5.11 Differential Equations of a Piezoelectric Multilayer Beam Bender 119
6 Theory of the Dynamic Behavior of Piezoelectric Beam Bending Actuators 122
6.1 Eigenmodes of a Clamped-Free Beam Bender 122
6.2 Orthogonality of Eigenfunctions 126
6.3 Description of Flexural Vibrations with Respect to Time 128
6.4 The Free Damped Flexural Vibration 129
6.5 Excitation by a Harmonic Force 131
6.6 Excitation by a Harmonic Moment 133
6.7 Excitation by a Harmonic Uniform Pressure Load 135
6.8 Excitation by a Harmonic Driving Voltage 136
6.9 Electrical Charge Generated by Harmonic Extensive Parameters 137
6.10 Dynamic Admittance Matrix 140
7 Network Representation of Piezoelectric Multilayered Bending Actuators 142
7.1 The Ideal Rod as Transducer for Translatory and Rotatory Quantities 143
7.2 Bending of a Differential Beam Segment 145
7.3 The Differential Beam Segment and Corresponding Correlations 148
7.4 Solution Approach to the Complex Equation of Flexural Vibrations 152
7.5 General Solution of the Equation for Flexural Vibrations 154
7.6 Solution of the Equation of Flexural Vibrations by Means of Reference Values 156
7.7 Admittance Matrix of a Beam Bender 156
7.8 Transition to the Piezoelectric Multilayer Beam Bending Actuator 161
7.9 The Clamped-Free Piezoelectric Multimorph 168
Measurement Setup and Validation of Theoretical Aspects 179
8 Measurement Setup for Piezoelectric Beam Bending Actuators 180
8.1 Measurement Setup 180
8.2 Automation of Measurement Setup 184
9 Measurements and Analytical Calculations 189
9.1 Used Multilayer Beam Bending Structure for Experimental Investigations 189
9.2 Static and Quasi-static Measurements 191
9.3 Dynamic Measurements 200
Sensor Integration for Tip Deflection Measurements 213
10 Piezoelectric Beam Bending Actuator with Integrated Sensor 214
10.1 Smart Pneumatic Micro Valve 215
10.2 Sensor Requirements 216
11 Tip Deflection Measurement - Capacitive Sensor Principle 218
11.1 Sensor Positioning 218
11.2 Sensor Electronics for Capacitive Strain Sensors 221
12 Tip Deflection Measurement - Inductive Sensor Principle 232
12.1 Measurement Setup and Basic Structure of the Inductive Proximity Sensor 232
12.2 Functioning of the Inductive Proximity Sensor 234
12.3 Equivalent Network Representation 238
12.4 Inductance of a Circular Loop Influenced by a Conductive Layer 242
12.5 Measurement Results 249
13 Conclusion 264
13.1 Summary and Results 264
13.2 Outlook 268
Appendix 270
A Work Done by Stresses Acting on an Infinitesimal Volume Element 271
B Derivation of the Coupling Matrix Elements 274
B.1 Multilayer Beam Bender Subjected to an External Static Moment 274
B.2 Multilayer Beam Bender Subjected to an External Static Force 277
B.3 Multilayer Beam Bender Subjected to a Uniform Pressure Load 279
B.4 Electrical Charge Generated by the Extensive Parameters 281
C Mechanical Potential and Kinetic Energy 291
D Derivation of the Electrical Enthalpy 293
E Correlation Between Material Parameters 295
F Work Done by Extensive Dynamic Quantities 297
F.1 Work Done by a Force 297
F.2 Work Done by a Moment 298
F.3 Work Done by a Driving Voltage 299
G On the Variation of the Lagrange Function 301
H On the Variation of the Work Done by Extensive Quantities 306
I On the Excitation by a Periodic Force 308
J Particular Solution of the Differential Equation for Flexural Vibrations 310
K Transition to the Differential Equations in Complex Form 312
L Orthogonality of Different Boundary Conditions 315
M Logarithmic Decrement 318
N Favored Sensor Principles and Sensor Signal Estimation 320
N.1 Resisitive Distance Sensors 321
N.2 Capacitive Distance Sensors 325
N.3 Piezoelectric Distance Sensor 330
N.4 Inductive Distance Sensor 332
O Methods of Measuring Small Capacitances with High Resolution 336
O.1 Direct Method 336
O.2 Self-balancing Capacitance Bridge 337
O.3 Charge Measurement 339
O.4 Measurement of the Integration Time 340
O.5 Oscillator Method 340
P To the Output Signal of the Instrumentation Amplifier 342
Q Alternating Magnetic Field Within a Conductive Layer 344
R Magnetic Field Calculation of a Circular Loop 346
References 350
Index 362

Produkt-Details

• Erscheint lt. Verlag: 6.3.2007
• Reihe/Serie: Microtechnology and MEMS
• Zusatzinfo: XXIII, 358 p.
• Verlagsort: Berlin
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• Themenwelt: Technik ► Bauwesen
• Themenwelt: Technik ► Elektrotechnik / Energietechnik
• Themenwelt: Technik ► Maschinenbau
• Schlagworte: Actuator • Actuators • beam benders • beam bending actuators • Drift • electromagnetic field theory • electromechanical circuit representation • Electronics • Mechatronics • MEMS • micro electromechnical systems • Microsystems technology • Multilayer • piezoceramics • piezoelectricity • senor electronics • Sensor • sensor characteristics • sensors • transducer • Transit
• ISBN-10: 3-540-32642-1 / 3540326421
• ISBN-13: 978-3-540-32642-7 / 9783540326427