Vibration measurement

MECHANICS : DYNAMICAL SYSTEMS Editors : L M eirovitch and G lE Ora vas

E. H. Dowell, Aeroelasticity of Plates and Shells. 197 4. ISBN 90-286-0404-9.

D. G.B. Edelen, Lagrangian Mechanics of Noncomervative Nonho­lonomic Systems. 1977. ISBN 90-286-0077-9.

J. L .. Junkins, An Introduction to Optical Estimation of Dynamical Systems. 1978. ISBN 90-286-0067-1.

E. H. Dowell et al., A l\Iodern Course in Aeroelasticity. 1978.

ISBN 90-286-00.'57-4. L. Meirovitch, Computational Methods in Structural Dynamics.

1980. ISBN 90-286-0580-0. B. Skalmierski and A. Tylikowski, Stochastic Processes in Dynamics.

1982. ISBN 90-247-2686-7. P. C. Mi.iller and W. 0. Schiehlen, Linear Vibrations. 1985.

ISBN 90-247-2983-1. Gh. Buzdugan, E. Mihi1ilescu and M. Rade~, Vibration measure­

ment. 1986. ISBN 90-247-3111-9.

Vibration measurement

Gheorghe Buzdugan Elena Mihailescu Mircea Rade$ Strength of Materials Chair Polytechnic Institute of Bucharest Romania

lrr..Af SPRINGER-SCIENCE+BUSINESS MEDIA, B.V. 1986 '"

Library of Congres!'> Cataloging in Publication Data

Buzdugan, Gh. Vibration measurement.

(lVIechanics, dynamical systems; 8) Updated English version of: Măsurarea vibraţiilor. Includes bibliographies and index. 1. Vibration-l\Ieasurement. 1. Mihăilescu, Elena.

II. Radeş, Mircea. III. Title. IV. Series : Monographs and textbooks on mechanics of solids and fluids. Mechanics, dynamical systems; 8. TA355.B8313 1986 620.3'2 84-25523 ISBN 978-90-481-8287-9 ISBN 978-94-017-3645-9 (eBook) DOI 10.1007/978-94-017-3645-9

Book information

The English version represents the revised and updated translation of the Romanian 'york Măsurarea vibraţiilor published in 1979 by Editura Academiei.

Copyright

© 1986 by Springer Science+Business Media Dordrecht Originally published by Martinus Nijhoff Publishers, Dordrecht in 1986

AlI rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, mechanical, photocopying, recording, or otherwise, without the prior written permis sion of the publishers, Springer-Science+Business Media, B.V.

Contents

Preface xiii

1. Introduction 1

1.1 Definitions 1

1. 2 Object of vibration measurements 3

1.3 Components of the instrumentation system. 5

1. 4 Measured mechanical quantities 8

References for Chapter 1 . . . 10

2. Elements of the theory of vibrations 13

2.1 Classification of vibrations . . . 13

2. 2 Characteristic vibration parameters 14

2. 2.1 Quantities describing the signal waveform . 14 2. 2 .. 2 Correlation functions . . . . . 16 2. 2. 3 Frequency domain description of time sig-

nals . . . . . . . . . . . . . . . . 17 2. 2. 3 .1 Frequency analysis of periodic sig-

nals . . . . . . . . . . . . 18 2. 2. 3 . 2 Frequency analysis of non periodic

signals . . . . . . . . . . . 19 2. 2. 3. 3 Frequency analysis of random sig-

nals . . . . . . . . . . . . . 21 2. 2. 3. 4 The Discrete Fourier Transform . 23

2. 2. 4 Probability density function . . . . . . 25

2. 3 Estimation errors at random data analysis . . 26

2. 3.1 Confidence probability. Confidence interval 27 2. 3 . 2 Standard error . . . . . . . . . . . . 28

v

Contents

2. 4 Response of vibrating systems to various excitations 30 2. 4.1 Harmonic excitation . . . . . . 31 2.4.2 Periodic excitation . . . . 36 2.4. 3 Transient excitation and shocks 37 2. 4. 4 Stationary random excitation 42

2.5 Natural frequencies . . . 44

2.6 Spring constants. . . . . 48

References for Chapter 2 50

3. Effects of vibrations 51

3 .1 Effects of vibrations on man . 51

3. 2 Effects of vibrations on buildings 55

3. 3 Effects of vibrations on machinery 56

References for Chapter 3 . . . . 70

4. Transducers and pickups for vibration measurement 71

4.1 Transducers for electrical measurement of vibrations 71 4 .1 .1 Passive transducers . . . . . . . . . . 73

4 .1.1.1. Variable resistance transducers . 73 4.1.1.2. Capacitive transducers 75 4 .1.1. 3. Inductive transducers 77

4 .1. 2 Self-generating transducers 80 4 .1. 2 .1 . Piezoelectric transducers 80 4 .1 . 2. 2. Electrodvnamic transducers 83 4 .1. 2. 3. Electromagnetic transducers 83

4. 2 Vibration pickups . . . . . . . . . . 84 4. 2.1 Theory of seismic instruments . 84

4. 2 .1: 1. Principle of operation 84 4. 2 .1. 2. Amplitude distortions . 88 4. 2 .1 . 3 . Phase distortions . . . 89

4. 2. 2 Displacement and acceleration pickups 90 4. 2. 2 .1 . Displacement-measuring pickups . . 91 4. 2. 2. 2. Accelerometers 99

4. 2. 3 Velocity pickups . . . . . . 105 4. 2. 4 Force and torque gauges 107 4. 2. 3 Dynamic pressure transducers . 110 4. 2. 6 Limits of vibration pickup performance 113 4. 2. 7 l\lounting . . . . . . . . 113

References for Chapter 4 115

vi

Content8

5 Instrumentation for vibration measurement . . . 117

5 .1 General properties of measuring instruments . 117 5. 2 Mechanical instrument!'\ for vibration meai'\urement 120

5.2.1 Tastograph . . . . . 120 5. 2. 2 Stoppani vibrograph 120 5. 2. 3 Geiger vibrograph 121

5. 3 Conversion instruments 122 5. 3 .1 Measuring bridges 122

5. 3 .1.1. Bridge circuits 122 5. 3 .1. 2. Detection circuits 125

5. 3. 2 Frequency discriminator circuits 128 5 . 3. 3 .Amplifiers. . . . . . . . . . . 130

5. 3. 3 .1 Voltage amplifiers 130 5. 3. 3. 2 .Amplifiers with feedback 131 5. 3. 3. 3 Charge amplifiers . . . . 131 :) . 3. 3. 4 Impedance-transforming amplifiers. 132

5.3.4 Integrators . .Analog low-pass and high-pass filters . . . . . . . . . . . . . 13 2

5. 3. 5 .Analog-to- digital converters . . . . 135 5 . 3. 5 .1 Sampling rate. Aliasing . . 136 5.3.5.2 Number of discrete samples 139

5.3.6 Averagers . . . . . . . . . . . . 141 5. 3 . 6 .1 Time averaging/integration of analog

signals . . . . . . . . . . . . . 141 5. 3. 6. 2 Time averaging/integration of digital

signals . . . . 143 5.3.7 R.M.S. detectors. . . . 144

;) . 4 Instruments for signal analysis 145 5 :4 .1 COITelators . . . . . . 145

:3 . 4 .1.1 Stepped correla tors 145 :3.4.1.2 On-line correlators 146 5.4.1.3 Real time correlators 148

5. 4. 2 Bandpass filters . . . . . . . 149 5. 4. 2 .1 Constant percentage bandwidth

filters . . . . . . 150 5. 4. 2. 2 Constant bandwidth filters 151 5. 4. 2. 3 Filter response time 152

5.4.3 Non-real time spectrum analyzers 152 5. 4. 3.1 Noise analyzers . . . . 152 5. 4. 3. 2 Tunable bandpass filters 153

vii

Contents

5 . 4 . 3 . 3 Heterodyne analyzers 5 .4. 3. 4 Synchronous filters

5. 4. 4 Real time spectrum analyzers 5. 4. 4 .1 Parallel filter analyzers. 5 . 4. 4 . 2 Time compression analyzers 5.4.4.3 Weighting .... 5.4.4.4 Digital analyzers

5 . 4 . 5 Shock spectrum analyzers 5. 4. 6 Amplitude distribution analyzers 5. 4. 7 Resolved component indicators

5. 5 Display and recording instruments 5. 5.1 Stroboscopes . . . . . . . .5 . 5 . 2 Analog meters . . . . . . 5. 5. 3 Digital meters and printers 5. 5. 4 Analog strip-chart recorders 5. 5. 5 X-Y recorders 5. 5. 6 Graphic level recorders . .5. 5. 7 Magnetic oscillographs 5. 5. 8 Cathode-ray oscilloscopes 5. 5. 9 Magnetic tape recorders 5. 5.10 Digital recorders . . . .

5. 6 Computerized vibration · analysis systems

References for Chapter 5

153 154 155 156 157 160 164 171 171 172 174 174 174 174 177 177 179 179 180 181 182

183

184

6 Vibration exciters . . . . . 187

viii

6.1 Mechanical vibration exciters 6 .1.1 Reciprocating vibration exciters • 6 .1. 2 Rotating unbalance vibration exciters

187 187 188

6. 2 Electromagnetic vibration exciters . . . 192

6. 2.1 Force generated by an electromagnet 192 6. 2. 2 Measurement of electromagnet force 195 6. 2. 3 General performance characteristics 197

6.3 Electrodynamic vibration exciters . . 198 6.3 .1 Principle of operation . . . . 198 6. 3. 2 Interaction between vibrator and tested

structure . . . . . 200 6 . 3. 3 Frequency response . . . . . 202

Contents

6 . 3. 4 Measurement of the force applied to the struc-ture . . . . . . . . . . . . . . . . . . 203

6 . 3. 5 Features of a vibrator used in structural test-ing . . . . . . . . 205

6. 3. 6 Application . . . . 206 6. 4 Hydraulic vibration exciters

6 . 4 .1 Construction 6 . 4. 2 Frequency response 6 . 4. 3 General performance References for Chapter 6 .

characteristics

7 Instrument set-ups and techniques for vibration measure-

207 207 208 208

209

ment . . . . . . . . . . 211

I .1 Selection of equipment . . . . . . . . . . . 211

7. 2 Basic set-ups for signal waveform. measurement 213 7 . 3 Procedures for analysing random vibration records 217

7 . 3 .1 Analysis of a single record . . . 218 7 . 3 . 2 Analysis of a collection of records . . . 220

7. 4 Frequency analysis . . . . . . . . . . . . 221 7. 4.1 Frequency analysis of stationary signals 222

7. 4 .1 .1 Selective filtering . . . . . . 222 7. 4 .1. 2 Time compression analysis . . 223 7. 4 .1. 3 Digital analysis . . . . . . . 225 7. 4 .1. 4 Analysis of stationary random signals 226

7. 4. 2 Frequency analysis of shocks . . . 227 7. 4. 2.1 Pulse transformation into a pulse

train . . . . . . . . . . . . 227 7. 4. 2. 2 Response of a very narrow bandpass

filter 230 7. 5 Vibration testing . . . . . . . . . . 231

7 . . 5 .1 Sinusoidal tests . . . . . . . . . 232 7. ;) . 2 Broadband random vibration tests 237 7.5.3 Sweepnarrowbandrandomvibrationtests. 239 7 . 5 .4 Shock tests . . . . . . . . 240

7. 6 Frequency response measurement 7. 6 .1 Frequency response functions 7 . 6 . 2 Sinusoidal test techniques .

7.6.2.1 Single-point excitation 7. 6. 2. 2 l\Iulti-point excitation .

240 240 242 242 247

ix

Contents

7. 6. 3 Transient. test techniques . . . . . . . . . 250 7. 6 . 3 .1 Impact test technique . . . . . . 250 7. 6. 3. 2 Step relaxation technique . . . . 253 7. 6. 3. 3 Rapid frequency sweep excitation

technique . . . . . . . . . . . . 2:)4 7. 6. 4 Random excitation techniques . . . . . . . 255

7.6 .4 .1 Measurementofthefrequencyrespon-se function . . . . . . . . . . . 257

7. 6. 4 . 2 l\Ieasurement of the impulse response function . . . . . . . . . . . 259

7. 6 . 5 Experimental modal analysis . . . . . . . 260 7. 6. 5.1 Single-degree-of-freedom techniques 260 7.6.5.2 Multi-degree-of-freedom techniques 263

References for Chapter 7 267

8 Calibration oi transducers and instrumentation systems 269

8.1 Calibration of vibration pickups . . . 8 .1.1 Static calibrat ion . . . . . . . .

269 270

8 .1. 2 "Direct" dynamic calibration . . . 270 8 .1. 2.1 Calibration of a piezoelectric accele-

rometer . . . . . . . . . . . 271 8 .1. 2. 2 Calibration of a piezoelectric force

transducer . . . . 273 8 .1. 3 R eciprocity calibration . . . . . 275

8.1 .3.1 Reciprocity·procedure . 276 8 .1. 3 . 2 Theoretical background. 27 7

8 .1. 4 Optical interferometry calibration 279 8 .1 . 5 Comparison calibration . . . . 281

8. 2 Simulation calibration of auxiliary circuits 8. 2.1 Substitution calibration 8. 2 .. 2 Insert calibration . . . . 8. 2. 3 Shunt-resistor calibration

References for Chapter 8 . . .

9 Examples oi vibration measurements

9.1 Identification of vibration sources

9. 2 Measurements on prototypes . 9 . 2 .1 Machine tools . . . . . 9. 2. 2 Rolling hoisting cranes

282 282 283 285

286

287

287

297 297 300

Contents

9. 2. 3 Suspended pipelines 302 9. 2.4 Rotating machinery 303 9. 2. 5 Cargo ships . . . . 310

9. 3 Measurements for production control and accept-ance . . . . . . . . . . . . . . 313 9. 3 .1 Machine tools . . . . . . . 313 9. 3. 2 Reciprocating compressor piping 316

9. 4 Measurements during machinery operat ion 318 9. 4.1 Forge hammers and machine foundations . . . 318 9. 4. 2 Machinery condition monitoring . . . . . . 320

9. 5 Measurement of vibrations produced by blasting . . 324

9. 6 Measurement of the dvnamic characteristics of mate-rials . . . . . . . . ,. . . . . . . . . . . . . . 326

9. 7 Measurement of soil elastic characteristics by vibra-tion methods . . . . . . . . . . . . . . . . . 333 9. 7.1 Spring constants for rigid foot ings resting on

soil . . . . . . . . . . . . . . . . 333 9. 7. 2 Measurement of elastic constants for soils 334 9. 7. 3 Resonance technique for determining the

dynamic coefficients of subgrade reaction . 336 References for Oha,pter 9 339

Subject index . . . . 345

x i

Preface

Nowadays, the engineering practice raises far more vibration problems than can be theoretically explained or modelled. Because Df this, measurements are used in almost all fields of industry, transportation and civil engineering in studies of mechanical and structural vibration. They are an invaluable tool for designing products and machines with high reliability and low noise level, vehicles and buildings with improved comfort and resistance to dynamic loads, as well as for obtaining increased safety of opera­tion and optimum running parameters.

In order to cope with the increasing demand for experimental measurement of vibration characteristics, young engineers and designers need an introductory book with emphasis on "what has to be measured" and "by what means" before learning "how measurements are done". The expertise to perform v ibration measurements must be gained in time, with every new investi­gation and studied problem .

.A detailed presentation of instrumentation and measuring techniques is beyond the aim of this book. Such information can be found in product data sheets, application manuals and hand­books supplied by equipment manufacturers. Only general princi­ples and widely used methods are presented herein, in order to provide the reader with an overview of the instrumentation and techniques encountered in vibration measurement.

The instrumentation had a rather spectacular development, from the purely mechanical vibrographs, used 40 years ago, to the analogic electrical equipment and, today, to the digital instru­ments, hav ing high accuracy and increased operating speed. The -advent of FFT analyzers, minicomputer-based data acquisition and data processing systems, and more recently of microprocessor­based measuring systems, had changed the conventional methods <>f vibration analysis.

The experimental techniques had a corresponding develop­ment, namely: 1) from the graphical analysis of time history

xiii

Preface

records and frequency rcf;ponse diagrams plotted J)Oint by point, to the modern real time on-line analysis and computer ~ti(led

testing; 2) from the analysit'> of i;imple harmonic or periodic vibrations to the measurement and analysis of transient or ran­dom vibrations.

Herein, while considerable attention is paid to analogic instru­ments, detailed description is also given to the basic features of some digital instruments. As for the presented examples of appli­cation, these are somewhat limited to the authors' area of intere.st. Topics not treated include acoustic measurements, dynamic ba­lancing, shock and vibration testing machines.

The book is organized in nine chapters covering the following topics : some elements from the theory of vibration, effect~; of vibrat.ion and allo-,vable limits, t.ransducers and pickups used in vibration measurement, instruments for signal conditioning·, ana­lysis, display and recording, exciter:;; used in vibration testing sys­tems, basic measurement set-ups and teehniques, transducer and system calibration methodi\, example:; of application of vibration measurement.

Although the book i:.; written primarily for mechanical engi­neers, it is hoped that it will prove useful to students and research­ers, as well as to specialists from all fields of engineering confronteu with vibration problem:o..

The book is an updated English version of the original edition in Romanian publi:-;heu by Editura Academiei, Bucharest, in 1979. It is the result of author:.;' experience gained during the long term research activity in the benefit of industry_

The authors 1vish to thank all those who gave the permission to reproduce material from their publications or about their products. Thanks are alRo due to the publishers for their care and attention during the editing of this book.

THE AUTHORS

:xiv