G. Gautschi

Piezoelectric SensoricsForceStrainPressureAcceleration and Acoustic Emission SensorsMaterials and Amplifiers

With 175 Figures

Springer

Contents

Symbols, Quantities and Units XI

1 Introduction 1

2 Background of Piezoelectric Sensors 5

2.1 Direct and Converse Piezoelectric Effect 52.2 Discovery of the Piezoelectric Effect 62.3 Applications of the Converse Piezoelectric Effect 82.4 History of Piezoelectric Sensors 9

3 Piezoelectric Materials for Sensors 133.1 Requirements of Piezoelectric Materials for Sensors 133.2 Quartz 143.2.1 Choice of Coordinate System 153.2.2 Physical Properties 173.2.3 Synthetic Quartz Crystals 203.2.4 Twinning 213.2.5 Suppressing Secondary Twinning 263.2.6 Temperature Dependence of Piezoelectric Constants 273.2.7 Nonlinear Electromechanical Properties of a-Quartz 293.2.8 Piezoelectric Properties of ^-Quartz 303.3 Tourmaline 313.4 Gallium Orthophosphate 353.5 Crystals of the CGG Group 373.6 Other Piezoelectric Single Crystals 403.7 Piezoelectric Textures 433.7.1 Piezoelectric Ceramics 433.7.2 Piezoelectricity in Thin Films 50

4 Piezoelectric Sensor Terminology 514.1 Definition of a Sensor 524.2 Properties of Sensors 534.2.1 Static Characteristics 534.2.1.1 Properties Relating to the Measurand 534.2.1.2 Properties of the Relationship Between Measurand

and Output 55

VIII Contents

4.2.1.3 Influence of Temperature on the Relationship BetweenMeasurand and Output 60

4.2.1.4 Influence of Acceleration and Vibration on the RelationshipBetween Measurand and Output 65

4.2.1.5 Drift, Stability and Repeatability 654.2.2 Dynamic Characteristics 664.2.3 Electrical Characteristics 704.2.4 Effects of Sensor Mounting 704.2.5 Lifetime of a Sensor 714.2.6 Cross Talk 72

5 Piezoelectric Sensors 735.1 Introduction 735.2 Fundamental Observations on Measuring Force 745.3 Basic Design of a Sensor 765.4 General Review of Practical Sensor Designs 815.5 Components of a Sensor 855.5.1 Transduction Elements 855.5.1.1 Quartz 855.5.1.2 Tourmaline 875.5.1.3 Crystals of the CGG-Group and Gallium Orthophosphate 875.5.1.4 Piezoelectric Ceramics 875.5.2 Electrodes 885.5.3 Insulating Materials 895.5.4 Preloading Elements 895.5.5 Sensor Housings 905.5.6 Connectors 90

6 Force and Torque Sensors 936.1 Quantity, Units of Measurement, and Coordinate Systems 936.2 Force Sensors 946.2.1 Sensors for Compression Force 946.2.2 Linear Compression Force Sensors 956.2.3 Measuring Tension Force with Preloaded Force Sensors 976.3 Multicomponent Force Sensors 1026.4 Torque Sensors 1056.5 Cross Talk in Single- and Multicomponent Force Sensors 1066.6 Mounting Force Sensors 1096.7 Measuring 3 Forces and 3 Moments (6 Components) 1126.8 Calibration of Force Sensors 123

7 Strain Sensors 1277.1 Quantity and Units of Measurement 1277.2 Working Principle of Piezoelectric Strain Sensors 127

Contents IX

7.3 Surface Strain Sensors 1287.4 Strain Pins for Internal Strain 1307.4.1 Longitudinal Strain Pins 1307.4.1.1 Measuring Tie Bar Loading 1317.4.1.2 Measuring Pressure Variations in Thick-Walled Pipes 1327.4.2 Transverse Strain Pins 1347.5 Omnidirectional Strain Sensors 1367.6 Piezoelectric "Strain Gage" 1377.7 Multiaxial Strain Sensors 1387.8 Calibration of Piezoelectric Strain Sensors 139

8 Pressure Sensors 1418.1 Quantity and Units of Measurement 1418.2 Design of Piezoelectric Pressure Sensors 1428.3 Low-Pressure Sensors 1448.4 Pressure Sensors for General Applications 1468.5 High-Pressure Sensors 1488.6 Pressure Sensors with Acceleration Compensation 1508.7 Pressure Sensors for High Temperature 1558.8 Sensors for Cylinder Pressure in Internal Combustion Engines . . 1568.9 Sensors for Cavity Pressure in Plastics Processing and in

Die Casting of Metals 1598.10 Calibration of Pressure Sensors 161

9 Acceleration Sensors 1679.1 Quantity and Units of Measurement 1679.2 Basic Properties of Acceleration Sensors 1679.3 Designs of Piezoelectric Acceleration Sensors 1779.4 Characteristics of Sensors with Piezoelectric Ceramic or

Tourmaline Elements 1819.5 Acceleration Sensors with High Sensitivity 1839.6 Acceleration Sensors for General Applications 1849.7 Acceleration Sensors for Measuring Shock 1869.8 Acceleration Sensors for High Temperature 1889.9 Acceleration Sensors for Low Temperature 1909.10 Acceleration Sensors for Modal Analysis 1909.11 Triaxial Acceleration Sensors 1939.12 Calibration of Acceleration Sensors 194

10 Acoustic Emission Sensors 19910.1 Quantity and Units of Measurement 19910.2 Background of AE as Process Parameter 20010.3 Design of AE Sensors 20110.4 AE Sensors for Process Monitoring 203

X Contents

10.5 AE Sensors Applied to Metalworking 20310.6 AE Sensors for Nondestructive Testing 20510.7 Calibration of AE Sensors 205

11 Amplifiers for Piezoelectric Sensors 20911.1 Quantity and Units of Measurement 20911.2 Principles of Measuring Electric Charge 21011.2.1 Piezoelectric Sensor as an Active Capacitor 21011.2.2 Discharge of a Capacitor, Time Constant, Insulation Resistance . . 21111.2.3 Lower Frequency Limit of an .RC-Circuit 21311.2.4 Zero Point of a Measurement 21411.3 Ideal Electrometer Amplifier 21511.4 Real Electrometer Amplifier 21611.5 Ideal Charge Amplifier 21911.6 Real Charge Amplifier 22211.6.1 Sensitivity Setting, Scale and Measuring Range 22211.6.2 Lower Frequency Limit of a Charge Amplifier 22511.6.3 Resetting and Choosing the Zero of a Charge Amplifier 22711.6.4 Upper Frequency Limit of a Charge Amplifier 22711.6.5 Quasistatic Measuring, Stability and Drift 22811.6.5.1 Phenomenon "Drift" 22911.6.5.2 Time Constant of the Feedback Circuit 23011.6.5.3 Dielectric Memory Effect in Capacitors and Cables 23111.6.5.4 Leakage Current at the Input 23211.6.5.5 Zero Point Stability 23311.6.5.6 Leakage Currents Over the Insulation Resistance in the

Input Circuit due to Offset Voltages 23311.6.5.7 Output Voltage with Poor Insulation Resistance at the

Input and Short Time Constant 23411.6.5.8 "Operate Jump" 23511.6.5.9 Equalization of Electric Charge After Manipulations 23611.6.6 Influence of Cables 23611.6.7 Properties of Currently Used Input Stages 23711.6.8 Capacitive Coupling for Measuring at High Temperature 23811.6.9 Protecting the MOS-FET at the Input from Overload 23811.7 Connecting Several Sensors to One Amplifier 23911.8 Cables and Connectors 24011.9 Calibration of Charge Amplifiers 241

References 245

List of Manufacturers 255

Index 259