G.Gautschi

Piezoelectric Sensorics

Springer-Verlag Berlin Heidelberg GmbH

G. Gautschi

Piezoeleetrie Sensories Force Strain Pressure Acceleration and Acoustic Emission Sensors Materials and Amplifiers

With 175 Figures

Springer

Dipl.-Ing. ETH Gustav Gautschi Oetlisbergstr. 25 CH-8053 Zürich Switzerland e-mail: gustav.gautschi@alumni.ethz.ch

ISBN 978-3-642-07600-8 ISBN 978-3-662-04732-3 (eBook)

DOI 10.1007/978-3-662-04732-3

Library of Congress Cataloging -in -Publieation -Data

Gautsehi, G. (Gustav), 1936-Piezoelectrie sensories : force, strain, pressure, acceleration and acoustie emission sensors, materials and amplifiers / G. Gautschi. p.em. Rev. and enlarged translation of chapters 6 - 12 of German text by Jan Tiehy and Gustav Gautsehi. Includes bibliographieal references and index.

1. Piezoelectrie transducers.1. Title. TK7872.P54 G38 2002 681'.2-dc21

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Originally published by Springer-Verlag Berlin Heidelberg New York in 2002. Softcover reprint of the hardcover I st edition 2002 The use of general descriptive names, registered names trademarks, ete. in this publieation does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

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Preface

Sensors are the key to life and survival - and to the success of modern technology. Nature has provided living creatures with a wealth of sensors for a variety of measurands, such as light, sound, temperature, speed, motion, distance, force, pressure, acceleration, odor and so on - sensors, whose performance and specifications have often not been matched yet by man-made devices. Even at today's high level of electronics and information technology, sensors remain the crucial and decisive interface needed to reliably relate phenomena occurring in the environment to corresponding electric signals that can be processed to obtain the desired information and subsequent correct reaction of systems.

Although the literature on sensors is extremely vast, there is one type of sensors which so far has received little attention: the piezoelectric sensor. Certainly, most handbooks on measurement mention briefly this type of sensor yet there is not a single book in the English language dedicated entirelyto piezoelectric sensors and giving a reasonably complete overview. There are only the books by [Gohlke 1955 and 1959] and [Tichy and Gautschi 1980], all in German.

The information and explanation given on piezoelectric sensors in measurement handbooks is - regrettably - rather terse and often quite limited. In particular there are certain prejudices and even misconceptions about piezoelectric sensors that have been perpetuated over many years and still persist today, such as: "piezoelectric sensors can only be used for dynamic measurements and are usually limited to measuring vibration". My practical experience of over 30 years in the field and elose contact with countless users of sensors worldwide, has confirmed again and again that there is indeed a widespread lack of full understanding of the nature of piezoelectric sensors and their applications, both in academia and industry.

Therefore the goal of this book is to give a comprehensive overview of piezoelectric sensors, their characteristics and their proven practical applications. The book is not intended to be an instruction on how to build piezoelectric sensors. Rather, their properties and their "behavior" as sensing devices are presented with the aim to enable the reader to make a better and more objective choice when looking for a suitable sensor to fulfill a given measuring task. For each type of sensor, some exemplary applications are described to illustrate the possibilities offered and to give the reader ideas for his own work.

In chapter 1, abrief comparison of the piezoelectric sensing principle with other types of sensors illustrates the possibilities offered. The historic background

VI Preface

highlighted in chapter 2 describes a number of interesting facts whieh are not so weIl known generally. The piezoelectric materials and their physical properties currently used in sensors are presented in chapter 3. An important but often neglected subject is the terminology for correctly defining and comparing the characteristies (specifications) of sensors, the topic of chapter 4. Chapter 5 gives an overview of the parts and the basie design of sensors. Sensors for the measurands force, strain, pressure, acceleration and acoustic emission are presented in chapters 6 to 10. These chapters are intentionally weIl illustrated to show the reader the great variety of applications existing for piezoelectrie sensors.

Chapter 11 treats the amplifiers used with piezoelectrie sensors and their partieular nature. Here again there are still widespread misconceptions about these amplifiers because the output signal of piezoelectric sensors - electrie charge - is not so often encountered in other fields of measuring electronies.

The number of references cited had to be kept within reasonable limits and is far from exhaustive. Readers may also refer to the included list of manufacturers of piezoelectrie sensors from whom more information can be obtained.

The first book written together with Jan Tiehy [Tiehy and Gautschi 1980] covered both, the theory of the physics of crystals, and the piezoelectrie sensors and their applications. Practieal considerations prompted us to split the book into two volumes. This book corresponds to the second part (chapters 6 ... 12) ofthe previous book, considerably enlarged and brought up to date. The chapters on the measurands strain and acoustic emission are new. The first part of the previous book authored by Jan Tichy (chapters 1 ... 6) has also been rewritten, enlarged and updated by Jid Erhart, Jan Fousek, Vaclav Janovec, Jana Privratska and Jan Tichy [Erhard et al 2002]. Therefore, the two new volumes are complementary, but can be used separately, too.

I am highly indebted to a number of friends and colleagues who significantly contributed to the manuscript. Claudio Cavalloni reviewed the manuscript and wrote the chapter 3.5 on the new materials of the CGG group while Roland Sommer contributed to the chapter 3.7 on piezoelectrie ceramies and thin films. Wolfgang Wallnöfer and Peter Worsch provided the chapter 3.4 on gallium orthophosphate. The manuscript was also critieally reviewed and commented on by Christoph Gossweiler, Karl-Heinz Martini and Jan Tiehy, co-author of our first book in German.

My thanks go to a number of sensor manufacturers who generously contributed material that serves to exemplify the vast range and variety of applications. Throughout the project, the staff of the Springer-Verlag offered an excellent co operation and continuous support for which I am especially grateful.

Although this book is based on the previous German edition and has been enlarged, it is a first attempt to cover the entire field of piezoelectric sensors in a single volume. There is certainly room for improvement and I greatly welcome comments, criticism and suggestions (gustav.gautschi@alumni.ethz.ch) to consider for further enhancing a next edition.

Zurich, November 2001 Gustav H. Gautschi

Contents

Symbols, Quantities and Units ...................................... XI

1 Introduction ............................................. 1

2 Background of Piezoelectric Sensors ........................ 5 2.1 Direct and Converse Piezoelectric Effect ..................... 5 2.2 Discovery of the Piezoelectric Effect ........................ 6 2.3 Applications of the Converse Piezoelectric Effect ............. 8 2.4 History of Piezoelectric Sensors ............................ 9

3 3.1 3.2 3.2.1 3.2.2 3.2.3 3.2.4 3.2.5 3.2.6 3.2.7 3.2.8 3.3 3.4 3.5 3.6 3.7 3.7.1 3.7.2

4 4.1 4.2 4.2.1 4.2.1.1 4.2.1.2

Piezoelectric Materials for Sensors ......................... 13 Requirements of Piezoelectric Materials for Sensors ........... 13 Quartz .................................................. 14 Choice of Co ordinate System ............................... 15 Physical Properties ....................................... 17 Synthetic Quartz Crystals .................................. 20 Twinning ................................................ 21 Suppressing Secondary Twinning ........................... 26 Temperature Dependence of Piezoelectric Constants .......... 27 Nonlinear Electromechanical Properties of a-Quartz .......... 29 Piezoelectric Properties of ß-Quartz ........................ 30 Tourmaline .............................................. 31 Gallium Orthophosphate .................................. 35 Crystals of the CGG Group ................................. 37 Other Piezoelectric Single Crystals .......................... 40 Piezoelectric Textures ..................................... 43 Piezoelectric Ceramics .................................... 43 Piezoelectricity in Thin Films .............................. 50

Piezoelectric Sensor Terminology .......................... 51 Definition of a Sensor ..................................... 52 Properties of Sensors ..................................... 53 Static Characteristics ..................................... 53 Properties Relating to the Measurand ....................... 53 Properties of the Relationship Between Measurand and Output .............................................. 55

VIII

4.2.1.3

4.2.1.4

4.2.1.5 4.2.2 4.2.3 4.2.4 4.2.5 4.2.6

5 5.1 5.2 5.3 5.4 5.5 5.5.1 5.5.1.1 5.5.1.2 5.5.1.3 5.5.1.4 5.5.2 5.5.3 5.5.4 5.5.5 5.5.6

6 6.1 6.2 6.2.1 6.2.2 6.2.3 6.3 6.4 6.5 6.6 6.7 6.8

Contents

Influence of Temperature on the Relationship Between Measurand and Output .................................... 60 Influence of Acceleration and Vibration on the Relationship Between Measurand and Output ............................ 65 Drift, Stability and Repeatability ............................ 65 Dynamic Characteristics .................................. 66 Electrical Characteristics .................................. 70 Effects of Sensor Mounting ................................ 70 Lifetime of a Sensor ....................................... 71 Cross Talk ............................................... 72

Piezoelectric Sensors ..................................... 73 Introduction ............................................. 73 Fundamental Observations on Measuring Force .............. 74 Basic Design of a Sensor ................................... 76 General Review of Practical Sensor Designs .................. 81 Components of a Sensor ................................... 85 Transduction Elements .................................... 85 Quartz .................................................. 85 Tourmaline .............................................. 87 Crystals of the CGG-Group and Gallium Orthophosphate ...... 87 Piezoelectric Ceramics .................................... 87 Electrodes ............................................... 88 Insulating Materials ...................................... 89 Preloading Elements ...................................... 89 Sensor Housings ......................................... 90 Connectors .............................................. 90

Force and Torque Sensors ................................. 93 Quantity, Units of Measurement, and Co ordinate Systems ...... 93 Force Sensors ............................................ 94 Sensors for Compression Force ............................. 94 Linear Compression Force Sensors .......................... 95 Measuring Tension Force with Preloaded Force Sensors ....... 97 Multicomponent Force Sensors ............................. 102 Torque Sensors ........................................... 105 Cross Talk in Single- and Multicomponent Force Sensors ...... 106 Mounting Force Sensors ................................... 109 Measuring 3 Forces and 3 Moments (6 Components) .......... 112 Calibration of Force Sensors ............................... 123

7 Strain Sensors ........................................... 127 7.1 Quantity and Units of Measurement ........................ 127 7.2 Working Principle of Piezoelectric Strain Sensors ............. 127

Contents

7.3 7.4 7.4.1 7.4.1.1 7.4.1.2 7.4.2 7.5 7.6 7.7 7.8

IX

Surface Strain Sensors .................................... 128 Strain Pins for Internal Strain .............................. 130 Longitudinal Strain Pins ................................... 130 Measuring Tie Bar Loading ................................ 131 Measuring Pressure Variations in Thick-Walled Pipes ......... 132 Transverse Strain Pins ..................................... 134 Omnidirectional Strain Sensors ............................ 136 Piezoelectric "Strain Gage" ................................. 137 Multiaxial Strain Sensors .................................. 138 Calibration of Piezoelectric Strain Sensors ................... 139

8 Pressure Sensors ......................................... 141 8.1 Quantity and Units of Measurement ........................ 141 8.2 Design of Piezoelectric Pressure Sensors ..................... 142 8.3 Low-Pressure Sensors ..................................... 144 8.4 Pressure Sensors for General Applications ................... 146 8.5 High-Pressure Sensors .................................... 148 8.6 Pressure Sensors with Acceleration Compensation ............ 150 8.7 Pressure Sensors for High Temperature ...................... 155 8.8 Sensors for Cylinder Pressure in Internal Combustion Engines .. 156 8.9 Sensors for Cavity Pressure in Plastics Processing and in

Die Casting of Metals ..................................... 159 8.10 Calibration of Pressure Sensors ............................. 161

9 Acceleration Sensors ...................................... 167 9.1 Quantity and Units of Measurement ........................ 167 9.2 Basic Properties of Acceleration Sensors ..................... 167 9.3 Designs of Piezoelectric Acceleration Sensors ................ 177 9.4 Characteristics of Sensors with Piezoelectric Ceramic or

Tourmaline Elements ..................................... 181 9.5 Acceleration Sensors with High Sensitivity ................... 183 9.6 Acceleration Sensors for General Applications ................ 184 9.7 Acceleration Sensors for Measuring Shock ................... 186 9.8 Acceleration Sensors for High Temperature .................. 188 9.9 Acceleration Sensors for Low Temperature ................... 190 9.10 Acceleration Sensors for Modal Analysis ..................... 190 9.11 Triaxial Acceleration Sensors ............................... 193 9.12 Calibration of Acceleration Sensors ......................... 194

10 Acoustic Emission Sensors ................................ 199 10.1 Quantity and Units of Measurement ........................ 199 10.2 Background of AE as Process Parameter ..................... 200 10.3 Design of AE Sensors ..................................... 201 10.4 AE Sensors for Process Monitoring ......................... 203

X Contents

10.5 AE Sensors Applied to Metalworking ........................ 203 10.6 AE Sensors for Nondestructive Testing ...................... 205 10.7 Calibration of AE Sensors .................................. 205

11 11.1 11.2 11.2.1 11.2.2 11.2.3 11.2.4 11.3 11.4 11.5 11.6 11.6.1 11.6.2 11.6.3 11.6.4 11.6.5 11.6.5.1 11.6.5.2 11.6.5.3 11.6.5.4 11.6.5.5 11.6.5.6

11.6.5.7

11.6.5.8 11.6.5.9 11.6.6 11.6.7 11.6.8 11.6.9 11.7 11.8 11.9

Amplifiers for Piezoelectric Sensors ........................ 209 Quantity and Units of Measurement ........................ 209 Principles of Measuring Electric Charge ..................... 210 Piezoelectric Sensor as an Active Capacitor .................. 210 Discharge of a Capacitor, Time Constant, Insulation Resistance .. 211 Lower Frequency Limit of an RC-Circuit ..................... 213 Zero Point of a Measurement ............................... 214 Ideal Electrometer Amplifier ............................... 215 Real Electrometer Amplifier ............................... 216 Ideal Charge Amplifier .................................... 219 Real Charge Amplifier ..................................... 222 Sensitivity Setting, Scale and Measuring Range ............... 222 Lower Frequency Limit of aCharge Amplifier ................ 225 Resetting and Choosing the Zero of aCharge Amplifier ........ 227 Upper Frequency Limit of aCharge Amplifier ................ 227 Quasistatic Measuring, Stability and Drift .................... 228 Phenomenon "Drift" ...................................... 229 Time Constant of the Feedback Circuit ...................... 230 Dielectric Memory Effect in Capacitors and Cables ............ 231 Leakage Current at the Input ............................... 232 Zero Point Stability ....................................... 233 Leakage Currents Over the Insulation Resistance in the Input Circuit due to Offset Voltages ......................... 233 Output Voltage with Poor Insulation Resistance at the Input and Short Time Constant ............................. 234 "Operate Jump" .......................................... 235 Equalization of Electric Charge After Manipulations .......... 236 Influence of Cables ....................................... 236 Properties of Currently Used Input Stages ................... 237 Capacitive Coupling for Measuring at High Temperature ....... 238 Protecting the MOS-FET at the Input from Overload .......... 238 Connecting Several Sensors to One Amplifier ................ 239 Cables and Connectors .................................... 240 Calibration of Charge Amplifiers ........................... 241

References ....................................................... 245

List of Manufacturers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 255

Index ........................................................... 259

Symbols, Quantities and Units

Note 1: Quantities, units and symbols are represented in this book in accordance with the Standards ISO 31-0 ... ISO 31-13:1992 and ISO 1000:1992 [ISO 1993], valid at the time of printing this book. In particular, the reader should note that ISO 31-0: 1992, Section 3.3.2, states:

The decimal sign is a comma on the line. If the magnitude of the number is less than unity, the decimal sign should be preceded by a zero. Note: In documents in the English language, a dot is often used instead of a comma. If a dot is used, it should be on the line. In accordance with an ISO Council decision, the decimal sign is a comma in ISO documents.

Therefore, it was decided to use a comma as decimal sign in this book, too. In accordance with section 3.3.1 ofISO 31-0:1992, the reading of numbers with many digits is facilitated by separating them in groups of three, separated by a small space, and never by a comma or a point, nor by any other means.

Note 2: For indicating a range of values, the mathematical sign " .. :' is used, i.e. a ... b me ans from a to b, limits included.

Symbol Quantity Unit

A factor of proportionality amplitude m area, surface m2

a thickness m acceleration ms-2

a, b, c crystallographic axis b width m C spring constant Nm-1

capacitance F

Cijkb CA/1 modulus of elasticity Nm-2

D electric flux density Cm-2

dh coefficient of the hydrostatic piezoelectric effect CN-l du piezoelectric coefficient CN-l E Young's modulus of elasticity Nm-2

XII

gu gup H

ho" I k I M m nI. n2J n3

o P P Ps P Pi Q

qi %}.., r r}"'k S

Sijkb s}"'tL T U u V V

w W

XI. X2J X3

XI. X2J X3

x,y, Z

a aij,a}..,

Symbols, Quantities and Units

electric field strength electric field strength of the local field base of the naturallogarithms (e=2,718 281 ... ) elementarycharge (e = (l,602177 33 ± 0,000 000 49) .10-19 C) piezoelectric modulus Cm-2

fu~ N frequency Hz shear modulus Nm-2

acceleration of free fall ms-2

standard acceleration of free fall {gn = 9,80665 m/s2

(exact1y), usually simply designated as g} piezoelectric coefficient electroelastic coefficient magnetic field strength piezoelectric modulus electric current spring constant length moment mass integers origin of coordinates point electric polarization spontaneous polarization pressure pyroelectric coefficient electric charge pyroelectric modulus electrostrictive coefficient radius electrooptic constant dis placement elasticity coefficients torque tension displacement volume speed gain (amplification factor) work energy density co ordinate axes, material or Lagrange's coordinates co ordinate axes, spatial or Euler's coordinates cartesian co ordinate axes damping constant thermal expansion coefficients

m 2C-1 Cm2N-2

Am-1

NC-1

A Nm-1

m Nm kg

Cm-2

Cm-2

Pa Cm-2K-1

C m 2C-1

m 2y-2

m my-1

m m2N-1 Nm y

m m3

ms-1

1 J Jm-3

Symbols, Quantities and Units XIII

Ll 8 E

Co Eijk B B Be 8

v ~, 1], ,

II IIA/.l n n n P

Pi (j

(jij, (j/

T

T

Tij, TA

qJ m

logarithmic decrement damping coefficient S-l

permittivity Fm-1

electric constant, permittivity of vacuum (eo = 8,854 188 pF/m) electrooptic coefficient CV-2

angle temperature Curie temperature angle damping coefficient Poisson ratio angles of rotation about the Xi> X2> X3 axes hydrostatic pressure piezooptic constant Ludolf number (n = 3,141 5926 ... ) pyroelectric coefficient piezomagnetic coefficient density (mass) density (charge) pyroelectric modulus normal stress thermal expansion modulus shear stress time constant thermal tension coefficient phase angle angular frequency

K,OC K,oC

1

Vm-1K-1

A-1m kgm-3

Cm-3

V-1m Nm-2

Nm-2

Nm-2

Decimal prefixes (SI)

Factor Name Symbol Factor Name Symbol

1024 yotta Y 10-3 milli m 1021 zetta Z 10-6 micro J.L 1018 exa E 10-9 nano n 1015 peta P 10-12 pico P 1012 te ra T 10-15 femto f 109 giga G 10-18 atto a 106 mega M 10-21 zepto z 103 kilo k 10-24 yocto Y

102 hecto h 10 deca da 10-1 deci d 10-2 centi c