Piezoelectric multilayer beam bending actuators: static and dynamic behaviour and aspects of sensor integration ; with 17 tables
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2007
|
| Series: | Microtechnology and MEMS
|
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 341 - 352 Microtechnology and MEMS |
| Physical Description: | XIV, 358 S. Ill., graph. Darst. |
| ISBN: | 9783540326410 3540326413 |
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MARC
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| 100 | 1 | |a Ballas, Rüdiger Gregor |d 1971- |e Verfasser |0 (DE-588)132275244 |4 aut | |
| 245 | 1 | 0 | |a Piezoelectric multilayer beam bending actuators |b static and dynamic behaviour and aspects of sensor integration ; with 17 tables |c R. G. Ballas |
| 246 | 1 | 3 | |a Microtechnology and MEMS |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2007 | |
| 300 | |a XIV, 358 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Microtechnology and MEMS | |
| 500 | |a Literaturverz. S. 341 - 352 | ||
| 500 | |a Microtechnology and MEMS | ||
| 650 | 4 | |a Actuators | |
| 650 | 4 | |a Piezoelectric ceramics | |
| 650 | 4 | |a Piezoelectric devices | |
| 650 | 0 | 7 | |a Lichtstrahl |0 (DE-588)4423037-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Schichtverbundwerkstoff |0 (DE-588)4311269-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Biegefestigkeit |0 (DE-588)4145333-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a MEMS |0 (DE-588)4824724-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Stoffeigenschaft |0 (DE-588)4192147-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Piezoelektrischer Aktor |0 (DE-588)4568836-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a MEMS |0 (DE-588)4824724-8 |D s |
| 689 | 0 | 1 | |a Piezoelektrischer Aktor |0 (DE-588)4568836-9 |D s |
| 689 | 0 | 2 | |a Schichtverbundwerkstoff |0 (DE-588)4311269-9 |D s |
| 689 | 0 | 3 | |a Stoffeigenschaft |0 (DE-588)4192147-1 |D s |
| 689 | 0 | 4 | |a Biegefestigkeit |0 (DE-588)4145333-5 |D s |
| 689 | 0 | 5 | |a Lichtstrahl |0 (DE-588)4423037-0 |D s |
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Record in the Search Index
| _version_ | 1804136553007546368 |
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| adam_text | IMAGE 1
R.G. BAILAS
PIEZOELECTRIC MULTILAYER
BEAM BENDING ACTUATORS STATIC AND DYNAMIC BEHAVIOR AND ASPECTS OF SENSOR
INTEGRATION
WITH 143 FIGURES AND 17 TABLES
SPRIN GER
IMAGE 2
CONTENTS
LIST OF SYMBOLS XV
PART I FOCUS OF THE BOOK
1 INTRODUCTION 3
1.1 APPLICATION AREAS OF PIEZOELECTRIC ACTUATORS 3
1.2 MOTIVATION AND AIM OF THE BOOK 4
1.3 STATE OF THE SCIENTIFIC RESEARCH 6
1.4 TEXTUAL FOCUS OF THE BOOK 11
PART II THEORETICAL ASPECTS AND CLOSED FORM ANALYSIS
2 PIEZOELECTRIC MATERIALS 17
2.1 DISCOVERY OF PIEZOELECTRICITY 17
2.2 DIRECT AND INVERSE PIEZOELECTRIC EFFECT 18
2.3 PIEZOELECTRIC CERAMICS 19
2.4 PEROVSKIT STRUCTURE OF PZT 20
2.5 DOMAIN AND REVERSION PROCESSES OF PZT 21
2.6 ELECTROMECHANICAL BEHAVIOR 24
2.7 PIEZOELECTRIC BEAM BENDING ACTUATORS 26
3 LINEAR THEORY OF PIEZOELECTRIC MATERIALS 31
3.1 ENERGY DENSITY OF THE ELASTIC DEFORMATION 31
3.2 ENERGY DENSITY OF THE ELECTROSTATIC FIELD 35
3.3 THERMODYNAMICS OF DEFORMATION 36
3.3.1 INTERNAL ENERGY OF ELASTIC PIEZOELECTRIC MATERIALS 38
3.3.2 LINEAR CONSTITUTIVE EQUATIONS AND ELECTRICAL ENTHALPY . 39 3.3.3
CONDENSED NOTATION OF ELASTIC AND PIEZOELECTRIC TENSORS 43
IMAGE 3
CONTENTS
THEORY OF THE STATIC BEHAVIOR OF PIEZOELECTRIC B E AM BENDING ACTUATORS
47
4.1 SECTIONAL QUANTITIES OF A BENDING BEAM 47
4.2 BERNOULLI HYPOTHESIS OF BEAM BENDING THEORY 49
4.3 NEUTRAL AXIS POSITION OF A MULTILAYERED BEAM BENDER 51
4.4 FORCES AND MOMENTS WITHIN A MULTILAYER SYSTEM 54
4.5 TOTAL STORED ENERGY WITHIN A MULTILAYER SYSTEM 55
4.5.1 TOTAL ENERGY IN A SINGLE LAYER 56
4.5.2 ENERGY IN AN N-LAYERED SYSTEM 57
4.6 CANONICAL CONJUGATES AND COUPLING MATRIX 58
4.7 PRINCIPLE OF VIRTUAL WORK 60
4.8 THEOREM OF MINIMUM TOTAL POTENTIAL ENERGY 61
4.9 DERIVATION OF THE COUPLING MATRIX 62
4.9.1 MULTILAYER BEAM BENDER SUBJECTED TO AN EXTERNAL STATIC MOMENT 63
4.9.2 MULTILAYER BEAM BENDER SUBJECTED TO AN EXTERNAL STATIC FORCE 65
4.9.3 MULTILAYER BEAM BENDER SUBJECTED TO A UNIFORM PRESSURE LOAD 67
4.9.4 ELECTRICAL CHARGE GENERATED BY THE EXTENSIVE PARAMETERS 69
4.10 THE CONSTITUENT EQUATIONS 75
PIEZOELECTRIC B E AM BENDING ACTUATORS AND HAMILTON S PRINCIPLE 77
5.1 CONSTRAINTS AND GENERALIZED COORDINATES 77
5.2 D ALEMBERT S PRINCIPLE 78
5.3 LAGRANGE S EQUATIONS 80
5.4 EULER-LAGRANGE DIFFERENTIAL EQUATION 83
5.5 HAMILTON S PRINCIPLE 87
5.6 CONSIDERATION OF NON-CONSERVATIVE FORCES 88
5.7 LAGRANGE FUNCTION OF PIEZOELECTRIC BEAM BENDING ACTUATORS . . 91 5.8
MECHANICAL WORK DONE BY EXTENSIVE QUANTITIES AND FRICTIONAL FORCE 95
5.9 VARIATION OF THE LAGRANGE FUNCTION 98
5.10 VARIATION OF THE MECHANICAL WORK 99
5.11 DIFFERENTIAL EQUATIONS OF A PIEZOELECTRIC MULTILAYER BEAM BENDER
100
THEORY OF THE DYNAMIC BEHAVIOR OF PIEZOELECTRIC B E AM BENDING ACTUATORS
103
6.1 EIGENMODES OF A CLAMPED-FREE BEAM BENDER 103
6.2 ORTHOGONALITY OF EIGENFUNCTIONS 107
6.3 DESCRIPTION OF FLEXURAL VIBRATIONS WITH RESPECT TO TIME 109
6.4 THE FREE DAMPED FLEXURAL VIBRATION HO
IMAGE 4
CONTENTS XI
6.5 EXCITATION BY A HARMONIE FORCE 112
6.6 EXCITATION BY A HARMONIE MOMENT 114
6.7 EXCITATION BY A HARMONIE UNIFORM PRESSURE LOAD 116
6.8 EXCITATION BY A HARMONIE DRIVING VOLTAGE 117
6.9 ELECTRICAL CHARGE GENERATED BY HARMONIE EXTENSIVE PARAMETERS 118
6.10 DYNAMIC ADMITTANCE MATRIX 121
7 NETWORK REPRESENTATION OF PIEZOELECTRIC MULTILAYERED BENDING ACTUATORS
123
7.1 THE IDEAL ROD AS TRANSDUCER FOR TRANSLATORY AND ROTATORY QUANTITIES
124
7.2 BENDING OF A DIFFERENTIAL BEAM SEGMENT 126
7.3 THE DIFFERENTIAL BEAM SEGMENT AND CORRESPONDING CORRELATIONS 129
7.4 SOLUTION APPROACH TO THE COMPLEX EQUATION OF FLEXURAL VIBRATIONS 133
7.5 GENERAL SOLUTION OF THE EQUATION FOR FLEXURAL VIBRATIONS 135
7.5.1 REFERENCE VALUES OF A MULTILAYERED BEAM BENDER 136
7.6 SOLUTION OF THE EQUATION OF FLEXURAL VIBRATIONS BY MEANS OF
REFERENCE VALUES 137
7.7 ADMITTANCE MATRIX OF A BEAM BENDER 137
7.7.1 EXCITATION BY A HARMONIE FORCE F_ X 138
7.7.2 EXCITATION BY A HARMONIE FORCE F_ 2 139
7.7.3 EXCITATION BY A HARMONIE MOMENT M_ X 140
7.7.4 EXCITATION BY A HARMONIE MOMENT M 2 141
7.8 TRANSITION TO THE PIEZOELECTRIC MULTILAYER BEAM BENDING ACTUATOR 142
7.9 THE CLAMPED-FREE PIEZOELECTRIC MULTIMORPH 149
7.9.1 CIRCUIT REPRESENTATION OF A PIEZOELECTRIC MULTIMORPH WITH RESPECT
TO THE FUNDAMENTAL MODE 153
7.9.2 CANONICAL CIRCUIT REPRESENTATION OF A PIEZOELECTRIC MULTIMORPH 157
PART III MEASUREMENT SETUP AND VALIDATION OF THEORETICAL ASPECTS
8 MEASUREMENT SETUP FOR PIEZOELECTRIC B E AM BENDING ACTUATORS 163
8.1 MEASUREMENT SETUP 163
8.2 AUTOMATION OF MEASUREMENT SETUP 167
8.2.1 STABILIZATION OF THE BEAM BENDING ACTUATOR 168
8.2.2 ELECTRICAL ACTUATION OF THE BENDING ACTUATOR 169
8.2.3 DEFLECTION MEASUREMENT BY MEANS OF TRIANGULATION . . .. 169 8.2.4
CONTROL OF THE LINEAR STAGES 170
IMAGE 5
XII CONTENTS
8.2.5 CONTROL OF THE VOICE-COIL-MOTOR 170
9 MEASUREMENTS AND ANALYTICAL CALCULATIONS 173
9.1 USED MULTILAYER BEAM BENDING STRUCTURE FOR EXPERIMENTAL
INVESTIGATIONS 173
9.2 STATIC AND QUASI-STATIC MEASUREMENTS 175
9.2.1 HYSTERESIS MEASUREMENT 175
9.2.2 MEASUREMENT AND ANALYTICAL CALCULATION OF BENDING CURVATURES UNDER
DIFFERENT EXCITATION VOLTAGES 178
9.2.3 MEASUREMENT AND ANALYTICAL CALCULATION OF FORCE-DEFLECTION
CHARACTERISTICS 180
9.2.4 DRIFT AND CREEP MEASUREMENTS 182
9.3 DYNAMIC MEASUREMENTS 184
9.3.1 EXPERIMENTAL EVALUATION OF THE COEFFICIENT OF FRICTION . 184 9.3.2
MEASUREMENT AND ANALYTICAL CALCULATION OF THE FIRST AND SECOND EIGENMODE
187
9.3.3 MEASUREMENT AND ANALYTICAL CALCULATION OF THE TRANSFER FUNCTION
191
PART IV SENSOR INTEGRATION FOR TIP DEFLECTION MEASUREMENTS
10 PIEZOELECTRIC B E AM BENDING ACTUATOR WITH INTEGRATED SENSOR 199
10.1 SMART PNEUMATIC MICRO VALVE 200
10.2 SENSOR REQUIREMENTS 201
11 TIP DEFLECTION MEASUREMENT - CAPACITIVE SENSOR PRINCIPLE 203 11.1
SENSOR POSITIONING 203
11.2 SENSOR ELECTRONICS FOR CAPACITIVE STRAIN SENSORS 206
11.2.1 ELECTRONIC CIRCUIT 206
11.2.2 STATIC SENSOR PERFORMANCE AND UNCERTAINTY OF MEASUREMENT 212
11.2.3 MEASUREMENT RESULTS 213
12 TIP DEFLECTION MEASUREMENT - INDUCTIVE SENSOR PRINCIPLE . 217 12.1
MEASUREMENT SETUP AND BASIC STRUCTURE OF THE INDUCTIVE PROXIMITY SENSOR
217
12.2 FUNCTIONING OF THE INDUCTIVE PROXIMITY SENSOR 219
12.2.1 OUTPUT SIGNAL PERFORMANCE 220
12.3 EQUIVALENT NETWORK REPRESENTATION 223
12.4 INDUCTANCE OF A CIRCULAR LOOP INFLUENCED BY A CONDUCTIVE LAYER 227
12.4.1 SOLUTION APPROACH 227
12.4.2 MAGNETIC FIELD OF A CIRCULAR LOOP 229
IMAGE 6
CONTENTS XIII
12.4.3 INFLUENCE OF A CONDUCTIVE LAYER 230
12.4.4 RELATIVE INDUCTANCE CHANGE OF A CIRCULAR LOOP IN PRESENCE OF A
CONDUCTIVE LAYER 231
12.5 MEASUREMENT RESULTS 234
12.5.1 RELATIVE INDUCTANCE CHANGE OF THE SENSING COIL WITH RESPECT TO A
CONDUCTIVE COPPER LAYER 235
12.5.2 PERFORMANCE OF THE INDUCTIVE PROXIMITY SENSOR 240
13 CONCLUSION 249
13.1 SUMMARY AND RESULTS 249
13.2 OUTLOOK 253
PART V APPENDIX
A WORK DONE BY STRESSES ACTING ON AN INFINITESIMAL VOLUME ELEMENT 257
B DERIVATION OF THE COUPLING MATRIX ELEMENTS 261
B.L MULTILAYER BEAM BENDER SUBJECTED TO AN EXTERNAL STATIC MOMENT 261
B.2 MULTILAYER BEAM BENDER SUBJECTED TO AN EXTERNAL STATIC FORCE 264 B.3
MULTILAYER BEAM BENDER SUBJECTED TO A UNIFORM PRESSURE LOAD 266
B.4 ELECTRICAL CHARGE GENERATED BY THE EXTENSIVE PARAMETERS 268 B.4.1
EXTERNAL STATIC MOMENT 272
B.4.2 EXTERNAL STATIC FORCE 273
B.4.3 EXTERNAL UNIFORM PRESSURE LOAD 275
C MECHANICAL POTENTIAL AND KINETIC ENERGY 279
D DERIVATION OF THE ELECTRICAL ENTHALPY 281
E CORRELATION BETWEEN MATERIAL PARAMETERS 283
F WORK DONE BY EXTENSIVE DYNAMIC QUANTITIES 285
F.L WORK DONE BY A FORCE 285
F.2 WORK DONE BY A MOMENT 286
F.3 WORK DONE BY A DRIVING VOLTAGE 287
G ON THE VARIATION OF THE LAGRANGE FUNCTION 289
H ON THE VARIATION OF THE WORK DONE BY EXTENSIVE
QUANTITIES 295
I ON THE EXCITATION BY A PERIODIC FORCE 297
IMAGE 7
XIV CONTENTS
J PARTICULAR SOLUTION OF THE DIFFERENTIAL EQUATION FOR
FLEXURAL VIBRATIONS 299
K TRANSITION TO THE DIFFERENTIAL EQUATIONS IN COMPLEX FORM 301
L ORTHOGONALITY OF DIFFERENT BOUNDARY CONDITIONS 305
M LOGARITHMIC DECREMENT 309
N FAVORED SENSOR PRINCIPFES AND SENSOR SIGNAL ESTIMATION . . 311 N.L
RESISITIVE DISTANCE SENSORS 312
N.L.L METALLIC STRAIN GAGES 313
N.L.2 SEMICONDUCTOR STRAIN GAGES 314
N.2 CAPACITIVE DISTANCE SENSORS 316
N.2.1 ALL OVER COVERING ELECTRODES (DOUBLE-SIDED) 316
N.2.2 INTERDIGITAL ELECTRODES (DOUBLE-SIDED) 318
N.3 PIEZOELECTRIC DISTANCE SENSOR 321
N.4 INDUCTIVE DISTANCE SENSOR 323
O METHODS OF MEASURING SMALL CAPACITANCES WITH HIGH RESOLUTION 327
0.1 DIRECT METHOD 327
0.2 SELF-BALANCING CAPACITANCE BRIDGE 328
0.3 CHARGE MEASUREMENT 330
0.4 MEASUREMENT OF THE INTEGRATION TIME 331
0.5 OSCILLATOR METHOD 331
P TO THE OUTPUT SIGNAL OF THE INSTRUMENTATION AMPLIFIER . .. 333
Q ALTERNATING MAGNETIC FIELD WITHIN A CONDUCTIVE LAYER . .. 335
R MAGNETIC FIELD CALCULATION OF A CIRCULAR LOOP 337
REFERENCES 341
INDEX
|
| adam_txt |
IMAGE 1
R.G. BAILAS
PIEZOELECTRIC MULTILAYER
BEAM BENDING ACTUATORS STATIC AND DYNAMIC BEHAVIOR AND ASPECTS OF SENSOR
INTEGRATION
WITH 143 FIGURES AND 17 TABLES
SPRIN GER
IMAGE 2
CONTENTS
LIST OF SYMBOLS XV
PART I FOCUS OF THE BOOK
1 INTRODUCTION 3
1.1 APPLICATION AREAS OF PIEZOELECTRIC ACTUATORS 3
1.2 MOTIVATION AND AIM OF THE BOOK 4
1.3 STATE OF THE SCIENTIFIC RESEARCH 6
1.4 TEXTUAL FOCUS OF THE BOOK 11
PART II THEORETICAL ASPECTS AND CLOSED FORM ANALYSIS
2 PIEZOELECTRIC MATERIALS 17
2.1 DISCOVERY OF PIEZOELECTRICITY 17
2.2 DIRECT AND INVERSE PIEZOELECTRIC EFFECT 18
2.3 PIEZOELECTRIC CERAMICS 19
2.4 PEROVSKIT STRUCTURE OF PZT 20
2.5 DOMAIN AND REVERSION PROCESSES OF PZT 21
2.6 ELECTROMECHANICAL BEHAVIOR 24
2.7 PIEZOELECTRIC BEAM BENDING ACTUATORS 26
3 LINEAR THEORY OF PIEZOELECTRIC MATERIALS 31
3.1 ENERGY DENSITY OF THE ELASTIC DEFORMATION 31
3.2 ENERGY DENSITY OF THE ELECTROSTATIC FIELD 35
3.3 THERMODYNAMICS OF DEFORMATION 36
3.3.1 INTERNAL ENERGY OF ELASTIC PIEZOELECTRIC MATERIALS 38
3.3.2 LINEAR CONSTITUTIVE EQUATIONS AND ELECTRICAL ENTHALPY . 39 3.3.3
CONDENSED NOTATION OF ELASTIC AND PIEZOELECTRIC TENSORS 43
IMAGE 3
CONTENTS
THEORY OF THE STATIC BEHAVIOR OF PIEZOELECTRIC B E AM BENDING ACTUATORS
47
4.1 SECTIONAL QUANTITIES OF A BENDING BEAM 47
4.2 BERNOULLI HYPOTHESIS OF BEAM BENDING THEORY 49
4.3 NEUTRAL AXIS POSITION OF A MULTILAYERED BEAM BENDER 51
4.4 FORCES AND MOMENTS WITHIN A MULTILAYER SYSTEM 54
4.5 TOTAL STORED ENERGY WITHIN A MULTILAYER SYSTEM 55
4.5.1 TOTAL ENERGY IN A SINGLE LAYER 56
4.5.2 ENERGY IN AN N-LAYERED SYSTEM 57
4.6 CANONICAL CONJUGATES AND COUPLING MATRIX 58
4.7 PRINCIPLE OF VIRTUAL WORK 60
4.8 THEOREM OF MINIMUM TOTAL POTENTIAL ENERGY 61
4.9 DERIVATION OF THE COUPLING MATRIX 62
4.9.1 MULTILAYER BEAM BENDER SUBJECTED TO AN EXTERNAL STATIC MOMENT 63
4.9.2 MULTILAYER BEAM BENDER SUBJECTED TO AN EXTERNAL STATIC FORCE 65
4.9.3 MULTILAYER BEAM BENDER SUBJECTED TO A UNIFORM PRESSURE LOAD 67
4.9.4 ELECTRICAL CHARGE GENERATED BY THE EXTENSIVE PARAMETERS 69
4.10 THE CONSTITUENT EQUATIONS 75
PIEZOELECTRIC B E AM BENDING ACTUATORS AND HAMILTON'S PRINCIPLE 77
5.1 CONSTRAINTS AND GENERALIZED COORDINATES 77
5.2 D'ALEMBERT'S PRINCIPLE 78
5.3 LAGRANGE'S EQUATIONS 80
5.4 EULER-LAGRANGE DIFFERENTIAL EQUATION 83
5.5 HAMILTON'S PRINCIPLE 87
5.6 CONSIDERATION OF NON-CONSERVATIVE FORCES 88
5.7 LAGRANGE FUNCTION OF PIEZOELECTRIC BEAM BENDING ACTUATORS . . 91 5.8
MECHANICAL WORK DONE BY EXTENSIVE QUANTITIES AND FRICTIONAL FORCE 95
5.9 VARIATION OF THE LAGRANGE FUNCTION 98
5.10 VARIATION OF THE MECHANICAL WORK 99
5.11 DIFFERENTIAL EQUATIONS OF A PIEZOELECTRIC MULTILAYER BEAM BENDER
100
THEORY OF THE DYNAMIC BEHAVIOR OF PIEZOELECTRIC B E AM BENDING ACTUATORS
103
6.1 EIGENMODES OF A CLAMPED-FREE BEAM BENDER 103
6.2 ORTHOGONALITY OF EIGENFUNCTIONS 107
6.3 DESCRIPTION OF FLEXURAL VIBRATIONS WITH RESPECT TO TIME 109
6.4 THE FREE DAMPED FLEXURAL VIBRATION HO
IMAGE 4
CONTENTS XI
6.5 EXCITATION BY A HARMONIE FORCE 112
6.6 EXCITATION BY A HARMONIE MOMENT 114
6.7 EXCITATION BY A HARMONIE UNIFORM PRESSURE LOAD 116
6.8 EXCITATION BY A HARMONIE DRIVING VOLTAGE 117
6.9 ELECTRICAL CHARGE GENERATED BY HARMONIE EXTENSIVE PARAMETERS 118
6.10 DYNAMIC ADMITTANCE MATRIX 121
7 NETWORK REPRESENTATION OF PIEZOELECTRIC MULTILAYERED BENDING ACTUATORS
123
7.1 THE IDEAL ROD AS TRANSDUCER FOR TRANSLATORY AND ROTATORY QUANTITIES
124
7.2 BENDING OF A DIFFERENTIAL BEAM SEGMENT 126
7.3 THE DIFFERENTIAL BEAM SEGMENT AND CORRESPONDING CORRELATIONS 129
7.4 SOLUTION APPROACH TO THE COMPLEX EQUATION OF FLEXURAL VIBRATIONS 133
7.5 GENERAL SOLUTION OF THE EQUATION FOR FLEXURAL VIBRATIONS 135
7.5.1 REFERENCE VALUES OF A MULTILAYERED BEAM BENDER 136
7.6 SOLUTION OF THE EQUATION OF FLEXURAL VIBRATIONS BY MEANS OF
REFERENCE VALUES 137
7.7 ADMITTANCE MATRIX OF A BEAM BENDER 137
7.7.1 EXCITATION BY A HARMONIE FORCE F_ X 138
7.7.2 EXCITATION BY A HARMONIE FORCE F_ 2 139
7.7.3 EXCITATION BY A HARMONIE MOMENT M_ X 140
7.7.4 EXCITATION BY A HARMONIE MOMENT M 2 141
7.8 TRANSITION TO THE PIEZOELECTRIC MULTILAYER BEAM BENDING ACTUATOR 142
7.9 THE CLAMPED-FREE PIEZOELECTRIC MULTIMORPH 149
7.9.1 CIRCUIT REPRESENTATION OF A PIEZOELECTRIC MULTIMORPH WITH RESPECT
TO THE FUNDAMENTAL MODE 153
7.9.2 CANONICAL CIRCUIT REPRESENTATION OF A PIEZOELECTRIC MULTIMORPH 157
PART III MEASUREMENT SETUP AND VALIDATION OF THEORETICAL ASPECTS
8 MEASUREMENT SETUP FOR PIEZOELECTRIC B E AM BENDING ACTUATORS 163
8.1 MEASUREMENT SETUP 163
8.2 AUTOMATION OF MEASUREMENT SETUP 167
8.2.1 STABILIZATION OF THE BEAM BENDING ACTUATOR 168
8.2.2 ELECTRICAL ACTUATION OF THE BENDING ACTUATOR 169
8.2.3 DEFLECTION MEASUREMENT BY MEANS OF TRIANGULATION . . . 169 8.2.4
CONTROL OF THE LINEAR STAGES 170
IMAGE 5
XII CONTENTS
8.2.5 CONTROL OF THE VOICE-COIL-MOTOR 170
9 MEASUREMENTS AND ANALYTICAL CALCULATIONS 173
9.1 USED MULTILAYER BEAM BENDING STRUCTURE FOR EXPERIMENTAL
INVESTIGATIONS 173
9.2 STATIC AND QUASI-STATIC MEASUREMENTS 175
9.2.1 HYSTERESIS MEASUREMENT 175
9.2.2 MEASUREMENT AND ANALYTICAL CALCULATION OF BENDING CURVATURES UNDER
DIFFERENT EXCITATION VOLTAGES 178
9.2.3 MEASUREMENT AND ANALYTICAL CALCULATION OF FORCE-DEFLECTION
CHARACTERISTICS 180
9.2.4 DRIFT AND CREEP MEASUREMENTS 182
9.3 DYNAMIC MEASUREMENTS 184
9.3.1 EXPERIMENTAL EVALUATION OF THE COEFFICIENT OF FRICTION . 184 9.3.2
MEASUREMENT AND ANALYTICAL CALCULATION OF THE FIRST AND SECOND EIGENMODE
187
9.3.3 MEASUREMENT AND ANALYTICAL CALCULATION OF THE TRANSFER FUNCTION
191
PART IV SENSOR INTEGRATION FOR TIP DEFLECTION MEASUREMENTS
10 PIEZOELECTRIC B E AM BENDING ACTUATOR WITH INTEGRATED SENSOR 199
10.1 SMART PNEUMATIC MICRO VALVE 200
10.2 SENSOR REQUIREMENTS 201
11 TIP DEFLECTION MEASUREMENT - CAPACITIVE SENSOR PRINCIPLE 203 11.1
SENSOR POSITIONING 203
11.2 SENSOR ELECTRONICS FOR CAPACITIVE STRAIN SENSORS 206
11.2.1 ELECTRONIC CIRCUIT 206
11.2.2 STATIC SENSOR PERFORMANCE AND UNCERTAINTY OF MEASUREMENT 212
11.2.3 MEASUREMENT RESULTS 213
12 TIP DEFLECTION MEASUREMENT - INDUCTIVE SENSOR PRINCIPLE . 217 12.1
MEASUREMENT SETUP AND BASIC STRUCTURE OF THE INDUCTIVE PROXIMITY SENSOR
217
12.2 FUNCTIONING OF THE INDUCTIVE PROXIMITY SENSOR 219
12.2.1 OUTPUT SIGNAL PERFORMANCE 220
12.3 EQUIVALENT NETWORK REPRESENTATION 223
12.4 INDUCTANCE OF A CIRCULAR LOOP INFLUENCED BY A CONDUCTIVE LAYER 227
12.4.1 SOLUTION APPROACH 227
12.4.2 MAGNETIC FIELD OF A CIRCULAR LOOP 229
IMAGE 6
CONTENTS XIII
12.4.3 INFLUENCE OF A CONDUCTIVE LAYER 230
12.4.4 RELATIVE INDUCTANCE CHANGE OF A CIRCULAR LOOP IN PRESENCE OF A
CONDUCTIVE LAYER 231
12.5 MEASUREMENT RESULTS 234
12.5.1 RELATIVE INDUCTANCE CHANGE OF THE SENSING COIL WITH RESPECT TO A
CONDUCTIVE COPPER LAYER 235
12.5.2 PERFORMANCE OF THE INDUCTIVE PROXIMITY SENSOR 240
13 CONCLUSION 249
13.1 SUMMARY AND RESULTS 249
13.2 OUTLOOK '253
PART V APPENDIX
A WORK DONE BY STRESSES ACTING ON AN INFINITESIMAL VOLUME ELEMENT 257
B DERIVATION OF THE COUPLING MATRIX ELEMENTS 261
B.L MULTILAYER BEAM BENDER SUBJECTED TO AN EXTERNAL STATIC MOMENT 261
B.2 MULTILAYER BEAM BENDER SUBJECTED TO AN EXTERNAL STATIC FORCE 264 B.3
MULTILAYER BEAM BENDER SUBJECTED TO A UNIFORM PRESSURE LOAD 266
B.4 ELECTRICAL CHARGE GENERATED BY THE EXTENSIVE PARAMETERS 268 B.4.1
EXTERNAL STATIC MOMENT 272
B.4.2 EXTERNAL STATIC FORCE 273
B.4.3 EXTERNAL UNIFORM PRESSURE LOAD 275
C MECHANICAL POTENTIAL AND KINETIC ENERGY 279
D DERIVATION OF THE ELECTRICAL ENTHALPY 281
E CORRELATION BETWEEN MATERIAL PARAMETERS 283
F WORK DONE BY EXTENSIVE DYNAMIC QUANTITIES 285
F.L WORK DONE BY A FORCE 285
F.2 WORK DONE BY A MOMENT 286
F.3 WORK DONE BY A DRIVING VOLTAGE 287
G ON THE VARIATION OF THE LAGRANGE FUNCTION 289
H ON THE VARIATION OF THE WORK DONE BY EXTENSIVE
QUANTITIES 295
I ON THE EXCITATION BY A PERIODIC FORCE 297
IMAGE 7
XIV CONTENTS
J PARTICULAR SOLUTION OF THE DIFFERENTIAL EQUATION FOR
FLEXURAL VIBRATIONS 299
K TRANSITION TO THE DIFFERENTIAL EQUATIONS IN COMPLEX FORM 301
L ORTHOGONALITY OF DIFFERENT BOUNDARY CONDITIONS 305
M LOGARITHMIC DECREMENT 309
N FAVORED SENSOR PRINCIPFES AND SENSOR SIGNAL ESTIMATION . . 311 N.L
RESISITIVE DISTANCE SENSORS 312
N.L.L METALLIC STRAIN GAGES 313
N.L.2 SEMICONDUCTOR STRAIN GAGES 314
N.2 CAPACITIVE DISTANCE SENSORS 316
N.2.1 ALL OVER COVERING ELECTRODES (DOUBLE-SIDED) 316
N.2.2 INTERDIGITAL ELECTRODES (DOUBLE-SIDED) 318
N.3 PIEZOELECTRIC DISTANCE SENSOR 321
N.4 INDUCTIVE DISTANCE SENSOR 323
O METHODS OF MEASURING SMALL CAPACITANCES WITH HIGH RESOLUTION 327
0.1 DIRECT METHOD 327
0.2 SELF-BALANCING CAPACITANCE BRIDGE 328
0.3 CHARGE MEASUREMENT 330
0.4 MEASUREMENT OF THE INTEGRATION TIME 331
0.5 OSCILLATOR METHOD 331
P TO THE OUTPUT SIGNAL OF THE INSTRUMENTATION AMPLIFIER . . 333
Q ALTERNATING MAGNETIC FIELD WITHIN A CONDUCTIVE LAYER . . 335
R MAGNETIC FIELD CALCULATION OF A CIRCULAR LOOP 337
REFERENCES 341
INDEX |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Ballas, Rüdiger Gregor 1971- |
| author_GND | (DE-588)132275244 |
| author_facet | Ballas, Rüdiger Gregor 1971- |
| author_role | aut |
| author_sort | Ballas, Rüdiger Gregor 1971- |
| author_variant | r g b rg rgb |
| building | Verbundindex |
| bvnumber | BV022467311 |
| classification_rvk | UP 4900 |
| ctrlnum | (OCoLC)180906335 (DE-599)DNB979111749 |
| dewey-full | 620.14 621.3815 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 620 - Engineering and allied operations 621 - Applied physics |
| dewey-raw | 620.14 621.3815 |
| dewey-search | 620.14 621.3815 |
| dewey-sort | 3620.14 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Maschinenbau / Maschinenwesen Physik Elektrotechnik / Elektronik / Nachrichtentechnik |
| discipline_str_mv | Maschinenbau / Maschinenwesen Physik Elektrotechnik / Elektronik / Nachrichtentechnik |
| format | Book |
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| id | DE-604.BV022467311 |
| illustrated | Illustrated |
| index_date | 2024-07-02T17:43:02Z |
| indexdate | 2024-07-09T20:58:13Z |
| institution | BVB |
| isbn | 9783540326410 3540326413 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015674875 |
| oclc_num | 180906335 |
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| owner | DE-703 DE-634 DE-858 |
| owner_facet | DE-703 DE-634 DE-858 |
| physical | XIV, 358 S. Ill., graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Springer |
| record_format | marc |
| series2 | Microtechnology and MEMS |
| spelling | Ballas, Rüdiger Gregor 1971- Verfasser (DE-588)132275244 aut Piezoelectric multilayer beam bending actuators static and dynamic behaviour and aspects of sensor integration ; with 17 tables R. G. Ballas Microtechnology and MEMS Berlin [u.a.] Springer 2007 XIV, 358 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 341 - 352 Actuators Piezoelectric ceramics Piezoelectric devices Lichtstrahl (DE-588)4423037-0 gnd rswk-swf Schichtverbundwerkstoff (DE-588)4311269-9 gnd rswk-swf Biegefestigkeit (DE-588)4145333-5 gnd rswk-swf MEMS (DE-588)4824724-8 gnd rswk-swf Stoffeigenschaft (DE-588)4192147-1 gnd rswk-swf Piezoelektrischer Aktor (DE-588)4568836-9 gnd rswk-swf MEMS (DE-588)4824724-8 s Piezoelektrischer Aktor (DE-588)4568836-9 s Schichtverbundwerkstoff (DE-588)4311269-9 s Stoffeigenschaft (DE-588)4192147-1 s Biegefestigkeit (DE-588)4145333-5 s Lichtstrahl (DE-588)4423037-0 s DE-604 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2789600&prov=M&dok_var=1&dok_ext=htm Inhaltstext GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015674875&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ballas, Rüdiger Gregor 1971- Piezoelectric multilayer beam bending actuators static and dynamic behaviour and aspects of sensor integration ; with 17 tables Actuators Piezoelectric ceramics Piezoelectric devices Lichtstrahl (DE-588)4423037-0 gnd Schichtverbundwerkstoff (DE-588)4311269-9 gnd Biegefestigkeit (DE-588)4145333-5 gnd MEMS (DE-588)4824724-8 gnd Stoffeigenschaft (DE-588)4192147-1 gnd Piezoelektrischer Aktor (DE-588)4568836-9 gnd |
| subject_GND | (DE-588)4423037-0 (DE-588)4311269-9 (DE-588)4145333-5 (DE-588)4824724-8 (DE-588)4192147-1 (DE-588)4568836-9 |
| title | Piezoelectric multilayer beam bending actuators static and dynamic behaviour and aspects of sensor integration ; with 17 tables |
| title_alt | Microtechnology and MEMS |
| title_auth | Piezoelectric multilayer beam bending actuators static and dynamic behaviour and aspects of sensor integration ; with 17 tables |
| title_exact_search | Piezoelectric multilayer beam bending actuators static and dynamic behaviour and aspects of sensor integration ; with 17 tables |
| title_exact_search_txtP | Piezoelectric multilayer beam bending actuators static and dynamic behaviour and aspects of sensor integration ; with 17 tables |
| title_full | Piezoelectric multilayer beam bending actuators static and dynamic behaviour and aspects of sensor integration ; with 17 tables R. G. Ballas |
| title_fullStr | Piezoelectric multilayer beam bending actuators static and dynamic behaviour and aspects of sensor integration ; with 17 tables R. G. Ballas |
| title_full_unstemmed | Piezoelectric multilayer beam bending actuators static and dynamic behaviour and aspects of sensor integration ; with 17 tables R. G. Ballas |
| title_short | Piezoelectric multilayer beam bending actuators |
| title_sort | piezoelectric multilayer beam bending actuators static and dynamic behaviour and aspects of sensor integration with 17 tables |
| title_sub | static and dynamic behaviour and aspects of sensor integration ; with 17 tables |
| topic | Actuators Piezoelectric ceramics Piezoelectric devices Lichtstrahl (DE-588)4423037-0 gnd Schichtverbundwerkstoff (DE-588)4311269-9 gnd Biegefestigkeit (DE-588)4145333-5 gnd MEMS (DE-588)4824724-8 gnd Stoffeigenschaft (DE-588)4192147-1 gnd Piezoelektrischer Aktor (DE-588)4568836-9 gnd |
| topic_facet | Actuators Piezoelectric ceramics Piezoelectric devices Lichtstrahl Schichtverbundwerkstoff Biegefestigkeit MEMS Stoffeigenschaft Piezoelektrischer Aktor |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=2789600&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015674875&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT ballasrudigergregor piezoelectricmultilayerbeambendingactuatorsstaticanddynamicbehaviourandaspectsofsensorintegrationwith17tables AT ballasrudigergregor microtechnologyandmems |