Piezoelectric Multilayer Beam Bending Actuators:

Static and Dynamic Behavior and Aspects of Sensor Integration

Springer, 1 janv. 2007 - 358 pages

An important aim of the presented book is the explanation of the application of piezoelectric materials such as piezoceramics within the wide field of electromechanical actuators and sensor technology. The reader should be presented the physical and mechanical properties of piezoceramics in a distinct way. In a next step, the reader is introduced into the mechanical description of the static behavior of piezoelectric multilayer beam bending actuators. The description of the dynamic behavior of piezoelectric multilayered bending actuators is effected on the basis of Lagrange s formalism and Hamilton s principle. The achieved insights are used for the systematic development of the electromechanical circuit representation within the scope of the network theory for any design of piezoelectric bending actuators. The applications of piezoelectric multilayer beam bending actuators can be extended by means of special displacement sensors allowing for the compensation of effects such as hysteresis, creep and drift being typical for piezoelectric actuators. Within the scope of the presented book, two different sensor-actuator-systems are presented being based on an integrated capacitive and inductive displacement sensor, respectively. Analytical simulations of the static and dynamic behavior are compared to real measurement results of a specially developed piezoelectric multilayer beam bender. Here, the suitability of the developed theoretical aspects is shown in an outstanding way.

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Index

Références

Table des matières

Introduction	3

12 Motivation and Aim of the Book	4

13 State of the Scientiﬁc Research	6

14 Textual Focus of the Book	11

Theoretical Aspects and Closed Form Analysis	14

Piezoelectric Materials	17

22 Direct and Inverse Piezoelectric Effect	18

23 Piezoelectric Ceramics	19

82 Automation of Measurement Setup	167

821 Stabilization of the Beam Bending Actuator	168

822 Electrical Actuation of the Bending Actuator	169

824 Control of the Linear Stages	170

Measurements and Analytical Calculations	173

92 Static and Quasistatic Measurements	175

922 Measurement and Analytical Calculation of Bending Curvatures Under Different Excitation Voltages	178

923 Measurement and Analytical Calculation of ForceDeﬂection Characteristics	180

24 Perovskit Structure of PZT	20

25 Domain and Reversion Processes of PZT	21

26 Electromechanical Behavior	24

27 Piezoelectric Beam Bending Actuators	26

Linear Theory of Piezoelectric Materials	31

32 Energy Density of the Electrostatic Field	35

33 Thermodynamics of Deformation	36

331 Internal Energy of Elastic Piezoelectric Materials	38

332 Linear Constitutive Equations and Electrical Enthalpy	39

333 Condensed Notation of Elastic and Piezoelectric Tensors	43

Theory of the Static Behavior of Piezoelectric Beam Bending Actuators	46

42 Bernoulli Hypothesis of Beam Bending Theory	49

43 Neutral Axis Position of a Multilayered Beam Bender	51

44 Forces and Moments within a Multilayer System	54

45 Total Stored Energy within a Multilayer System	55

451 Total Energy in a Single Layer	56

452 Energy in an nlayered System	57

46 Canonical Conjugates and Coupling Matrix	58

47 Principle of Virtual Work	60

48 Theorem of Minimum Total Potential Energy	61

49 Derivation of the Coupling Matrix	62

491 Multilayer Beam Bender Subjected to an External Static Moment	63

492 Multilayer Beam Bender Subjected to an External Static Force	65

493 Multilayer Beam Bender Subjected to a Uniform Pressure Load	67

494 Electrical Charge Generated by the Extensive Parameters	69

410 The Constituent Equations	75

Piezoelectric Beam Bending Actuators and Hamiltons Principle	77

52 DAlemberts Principle	78

53 Lagranges Equations	80

54 EulerLagrange Differential Equation	83

55 Hamiltons Principle	87

56 Consideration of NonConservative Forces	88

57 Lagrange Function of Piezoelectric Beam Bending Actuators	91

58 Mechanical Work Done by Extensive Quantities and Frictional Force	95

59 Variation of the Lagrange Function	98

510 Variation of the Mechanical Work	99

511 Differential Equations of a Piezoelectric Multilayer Beam Bender	100

Theory of the Dynamic Behavior of Piezoelectric Beam Bending Actuators	103

62 Orthogonality of Eigenfunctions	107

63 Description of Flexural Vibrations with Respect to Time	109

64 The Free Damped Flexural Vibration	110

65 Excitation by a Harmonic Force	112

66 Excitation by a Harmonic Moment	114

67 Excitation by a Harmonic Uniform Pressure Load	116

68 Excitation by a Harmonic Driving Voltage	117

69 Electrical Charge Generated by Harmonic Extensive Parameters	118

610 Dynamic Admittance Matrix	121

Network Representation of Piezoelectric Multilayered Bending Actuators	123

71 The Ideal Rod as Transducer for Translatory and Rotatory Quantities	124

72 Bending of a Differential Beam Segment	126

73 The Differential Beam Segment and Corresponding Correlations	129

74 Solution Approach to the Complex Equation of Flexural Vibrations	133

75 General Solution of the Equation for Flexural Vibrations	135

751 Reference Values of a Multilayered Beam Bender	136

76 Solution of the Equation of Flexural Vibrations by Means of Reference Values	137

771 Excitation by a Harmonic Force F2	138

772 Excitation by a Harmonic Force F2	139

773 Excitation by a Harmonic Moment M1	140

774 Excitation by a Harmonic Moment M2	141

78 Transition to the Piezoelectric Multilayer Beam Bending Actuator	142

79 The ClampedFree Piezoelectric Multimorph	149

791 Circuit Representation of a Piezoelectric Multimorph with Respect to the Fundamental Mode	153

792 Canonical Circuit Representation of a Piezoelectric Multimorph	157

Measurement Setup and Validation of Theoretical Aspects	160

Measurement Setup for Piezoelectric Beam Bending Actuators	161

924 Drift and Creep Measurements	182

93 Dynamic Measurements	184

932 Measurement and Analytical Calculation of the First and Second Eigenmode	187

933 Measurement and Analytical Calculation of the Transfer Function	191

Sensor Integration for Tip Deﬂection Measurements	197

Piezoelectric Beam Bending Actuator with Integrated Sensor	198

101 Smart Pneumatic Micro Valve	200

102 Sensor Requirements	201

Tip Deﬂection Measurement Capacitive Sensor Principle	203

112 Sensor Electronics for Capacitive Strain Sensors	206

1122 Static Sensor Performance and Uncertainty of Measurement	212

1123 Measurement Results	213

Tip Deﬂection Measurement Inductive Sensor Principle	217

122 Functioning of the Inductive Proximity Sensor	219

1221 Output Signal Performance	220

123 Equivalent Network Representation	223

124 Inductance of a Circular Loop Inﬂuenced by a Conductive Layer	227

1242 Magnetic Field of a Circular Loop	229

1243 Inﬂuence of a Conductive Layer	230

1244 Relative Inductance Change of a Circular Loop in Presence of a Conductive Layer	231

125 Measurement Results	234

1251 Relative Inductance Change of the Sensing Coil with Respect to a Conductive Copper Layer	235

1252 Performance of the Inductive Proximity Sensor	240

Conclusion	249

132 Outlook	253

Appendix	255

Work Done by Stresses Acting on an Infinitesimal Volume Element	257

Derivation of the Coupling Matrix Elements	260

B2 Multilayer Beam Bender Subjected to an External Static Force	264

B3 Multilayer Beam Bender Subjected to a Uniform Pressure Load	266

B4 Electrical Charge Generated by the Extensive Parameters	268

B41 External Static Moment	272

B42 External Static Force	273

B43 External Uniform Pressure Load	275

Mechanical Potential and Kinetic Energy	279

Derivation of the Electrical Enthalpy	281

Correlation Between Material Parameters	283

Work Done by Extensive Dynamic Quantities	285

F2 Work Done by a Moment	286

F3 Work Done by a Driving Voltage	287

On the Variation of the Lagrange Function	289

On the Variation of the Work Done by Extensive Quantities	294

On the Excitation by a Periodic Force	297

Particular Solution of the Differential Equation for Flexural Vibrations	299

Transition to the Differential Equations in Complex Form	301

Orthogonality of Different Boundary Conditions	305

Logarithmic Decrement	308

Favored Sensor Principles and Sensor Signal Estimation	311

N1 Resisitive Distance Sensors	312

N11 Metallic Strain Gages	313

N12 Semiconductor Strain Gages	314

N2 Capacitive Distance Sensors	316

N22 Interdigital Electrodes doublesided	318

N3 Piezoelectric Distance Sensor	321

N4 Inductive Distance Sensor	323

Methods of Measuring Small Capacitances with High Resolution	327

O2 Selfbalancing Capacitance Bridge	328

O3 Charge Measurement	330

O4 Measurement of the Integration Time	331

To the Output Signal of the Instrumentation Amplifier	333

Alternating Magnetic Field Within a Conductive Layer	335

Magnetic Field Calculation of a Circular Loop	337

References	341

Index	353

Droits d'auteur

Autres éditions - Tout afficher

Piezoelectric Multilayer Beam Bending Actuators: Static and Dynamic Behavior ...

Rüdiger G. Ballas
Aucun aperçu disponible - 2007

Piezoelectric Multilayer Beam Bending Actuators: Static and Dynamic Behavior ...

Rüdiger G. Ballas
Aucun aperçu disponible - 2010

Expressions et termes fréquents

according admittance matrix analytical calculations ansatz function beam bender beam bending actuator behavior of piezoelectric bender’s tip bending angle bending segment capacitance change ceramics cient of friction circuit representation circular loop clamping coe cient constitutive equations correlation coupling matrix deﬁned derived Dirac delta function driving voltage dynamic behavior eigenmodes electric ﬁeld electrical enthalpy electromechanical enthalpy erence erential equation extensive quantities external F F F ferroelectric ﬁrst formulated frequency hysteresis illustrated in ﬁgure inductive proximity sensor inﬂuence instrumentation amplifier integration magnetic ﬁeld matrix elements measurement setup mechanical stress monomorph multilayer beam bending neutral axis oscillation output signal Piezo piezoceramic piezoelectric beam bending piezoelectric bending actuator piezoelectric multilayer beam polarization pressure load relative inductance change respect sensing coil sensor electronics shown in ﬁgure Slh}r static behavior strain gages structure total potential energy transfer function transient characteristics translatory two-port network unit length

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QR code for Piezoelectric Multilayer Beam Bending Actuators

Titre	Piezoelectric Multilayer Beam Bending Actuators: Static and Dynamic Behavior and Aspects of Sensor Integration Microtechnology and MEMS
Auteur	R. G. Ballas
Éditeur	Springer, 2007
ISBN	3540326421, 9783540326427
Longueur	358 pages

Exporter la citation	BiBTeX EndNote RefMan

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