VIBRATION-BASED CONDITION MONITORING

Vibration-based Condition Monitoring: Industrial, Aerospace and Automotive Applications 2011 John Wiley & Sons, Ltd. ISBN: 978-0-470-74785-8

Robert Bond Randall

VIBRATION-BASED CONDITION MONITORING

INDUSTRIAL, AEROSPACE AND AUTOMOTIVE APPLICATIONS

Robert Bond Randall

School of Mechanical and Manufacturing Engineering, University of New South Wales, Australia

A John Wiley and Sons, Ltd., Publication

This edition rst published 2011 C 2011 John Wiley & Sons, Ltd Registered ofce John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United Kingdom For details of our global editorial ofces, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com. The right of the author to be identied as the author of this work has been asserted in accordance with the Copyright, Designs and Patents Act 1988. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by the UK Copyright, Designs and Patents Act 1988, without the prior permission of the publisher. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. Designations used by companies to distinguish their products are often claimed as trademarks. All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners. The publisher is not associated with any product or vendor mentioned in this book. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold on the understanding that the publisher is not engaged in rendering professional services. If professional advice or other expert assistance is required, the services of a competent professional should be sought. MATLAB R is a trademark of The MathWorks, Inc., and is used with permission. The MathWorks does not warrant the accuracy of the text or exercises in this book. This books use or discussion of MATLAB R software or related products does not constitute endorsement or sponsorship by The MathWorks of a particular pedagogical approach or particular use of MATLAB R software. Library of Congress Cataloging-in-Publication Data Randall, Robert Bond. Vibration-based condition monitoring : industrial, aerospace and automotive applications / Robert Bond Randall. p. cm. Includes index. ISBN 978-0-470-74785-8 (hardback) 1. VibrationTesting. 2. Nondestructive testing. 3. VibrationMeasurement. I. Title. TA355.R34 2010 621.8 11dc22 2010034835 A catalogue record for this book is available from the British Library. Print ISBN: 978-0-470-74785-8 ePDF ISBN: 978-0-470-97765-1 oBook ISBN: 978-0-470-97766-8 ePub ISBN: 978-0-470-97758-3 Typeset in 10/12pt Times by Aptara Inc., New Delhi, India

To my daughters Katrina and Deborah.

Contents
Foreword About the Author Preface 1 1.1 1.2 1.3 Introduction and Background Introduction Maintenance Strategies Condition Monitoring Methods 1.3.1 Vibration Analysis 1.3.2 Oil Analysis 1.3.3 Performance Analysis 1.3.4 Thermography Types and Benets of Vibration Analysis 1.4.1 Benets Compared with Other Methods 1.4.2 Permanent vs Intermittent Monitoring Vibration Transducers 1.5.1 Absolute vs Relative Vibration Measurement 1.5.2 Proximity Probes 1.5.3 Velocity Transducers 1.5.4 Accelerometers 1.5.5 Dual Vibration Probes 1.5.6 Laser Vibrometers Torsional Vibration Transducers 1.6.1 Shaft encoders 1.6.2 Torsional Laser Vibrometers Condition Monitoring the Basic Problem References Vibration Signals from Rotating and Reciprocating Machines Signal Classication 2.1.1 Stationary Deterministic Signals 2.1.2 Stationary Random Signals 2.1.3 Cyclostationary signals xi xiii xv 1 1 2 3 3 4 5 5 6 6 6 8 8 9 12 13 17 18 18 19 19 20 23 25 25 28 29 30

1.4

1.5

1.6

1.7

2 2.1

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2.2

2.3

Signals Generated by Rotating Machines 2.2.1 Low Shaft Orders and Subharmonics 2.2.2 Vibrations from Gears 2.2.3 Rolling Element Bearings 2.2.4 Bladed Machines 2.2.5 Electrical Machines Signals Generated by Reciprocating Machines 2.3.1 TimeFrequency Diagrams 2.3.2 Torsional Vibrations References Basic Signal Processing Techniques Probability Distribution and Density Fourier Analysis 3.2.1 Fourier Series 3.2.2 Fourier Integral Transform 3.2.3 Sampled Time Signals 3.2.4 The Discrete Fourier Transform 3.2.5 The Fast Fourier Transform 3.2.6 Convolution and the Convolution Theorem 3.2.7 Zoom FFT 3.2.8 Practical FFT Analysis Hilbert Transform and Demodulation 3.3.1 Hilbert Transform 3.3.2 Demodulation Cepstrum Analysis 3.4.1 Terminology and Denitions 3.4.2 Typical Applications of the Cepstrum 3.4.3 Practical Considerations with the Cepstrum Digital Filtering 3.5.1 Realization of Digital Filters Deterministic/Random Signal Separation 3.6.1 Order Tracking 3.6.2 Time Synchronous Averaging 3.6.3 Linear Prediction 3.6.4 Adaptive Noise Cancellation 3.6.5 Self-adaptive Noise Cancellation 3.6.6 Discrete/Random Separation DRS TimeFrequency Analysis 3.7.1 The Short Time Fourier Transform 3.7.2 The WignerVille Distribution 3.7.3 Wavelet Analysis Cyclostationary Analysis and Spectral Correlation 3.8.1 Spectral Correlation

30 31 40 47 52 52 56 57 60 61 63 63 66 66 69 69 71 72 74 84 86 95 95 96 103 105 108 110 114 115 117 117 120 122 125 125 128 129 130 130 131 134 135

3 3.1 3.2

3.3

3.4

3.5 3.6

3.7

3.8

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3.8.2 Spectral Correlation and Envelope Spectrum 3.8.3 WignerVille Spectrum References 4 4.1 4.2 Fault Detection Introduction Rotating Machines 4.2.1 Vibration Criteria 4.2.2 Use of Frequency Spectra 4.2.3 CPB Spectrum Comparison Reciprocating Machines 4.3.1 Vibration Criteria for Reciprocating Machines 4.3.2 TimeFrequency Diagrams 4.3.3 Torsional Vibration References Diagnostic Techniques Harmonic and Sideband Cursors 5.1.1 Examples of Cursor Application Minimum Entropy Deconvolution Spectral Kurtosis and the Kurtogram 5.3.1 SK Denition and Calculation 5.3.2 Use of SK as a Filter 5.3.3 The Kurtogram Gear Diagnostics 5.4.1 Techniques Based on the TSA 5.4.2 Transmission Error as a Diagnostic Tool 5.4.3 Cepstrum Analysis 5.4.4 Separation of Spalls and Cracks 5.4.5 Diagnostics of Gears with Varying Speed and Load Rolling Element Bearing Diagnostics 5.5.1 Signal Models for Bearing Faults 5.5.2 A Semi-automated Bearing Diagnostic Procedure Reciprocating Machine and IC Engine Diagnostics 5.6.1 TimeFrequency Methods 5.6.2 Cylinder Pressure Identication References Fault Trending and Prognostics Introduction Trend Analysis 6.2.1 Trending of Simple Parameters 6.2.2 Trending of Impulsiveness Determination of Spall Size in Bearings Advanced Prognostics 6.4.1 Physics-Based Models

138 139 139 143 143 143 143 148 149 155 155 156 160 165 167 167 167 169 172 172 174 176 178 179 181 187 196 199 200 203 207 214 214 217 225 229 229 229 230 234 238 243 244

4.3

5 5.1 5.2 5.3

5.4

5.5

5.6

6 6.1 6.2

6.3 6.4

Contents

6.4.2 Data-Driven Models 6.4.3 Hybrid Models References Appendix: Exercises and Tutorial Questions A.1 Introduction and Background A.1.1 Exam Questions A.2 Vibration Signals from Machines A.2.1 Exam Questions A.3 Basic Signal Processing A.3.1 Tutorial and Exam Questions A.4 Fault Detection A.4.1 Tutorial and Exam Questions A.4.2 Assignment A.5 Diagnostic Techniques A.5.1 Tutorial and Exam Questions A.5.2 Assignments A.6 Prognostics A.6.1 Tutorial and Exam Questions Index

245 247 250 253 253 253 254 254 256 256 270 270 273 275 275 280 284 284 285

Foreword
Robert Randall uses state-of-the-art vibration measurement and analysis in this book about condition-based monitoring of machinery; other forms of condition monitoring, including oil analysis and infrared thermography are briey described. The text is the result of the authors years of involvement in the development, practice, and teaching of techniques used in the eld, including contributions to digital signal analysis. A highly sophisticated methodology for assessing machine condition has evolved in the last 70 years with respect to techniques, digital instruments, and computer chips. Despite many years of effort, the technique that every maintenance manager yearns for prognostics (run time to failure) does not yet exist in a usable form. However, condition monitoring of machinery using vibration measurements and analysis is a major component of all manufacturing processes (chemical, petroleum, automobile, paper, and power) as well as military and airline operations. The relationship between vibration signals and machine condition was rst recognized by Rathbone in his 1939 paper on Vibration Tolerance. The Rathbone chart that appeared in the paper was a plot of amplitude versus frequency based on the concept that machine condition is related to vibration amplitude. His zones of severity (six dB apart) were based on constant velocity and applied over the common frequency range of most machines. The chart was later rened by IRD Mechanalysis, the U.S. Navy, Blake, and others. Blake developed a chart containing plots of displacement, velocity, and acceleration versus frequency with severity levels spaced at 10 dB and service factors for various machines. During this period simple meters and oscilloscopes were used to extract vibration levels from transducers. Overall vibration levels were used non-systematically until 1960 to identify machine condition. By this time it had been recognized that periodic monitoring could be useful in avoiding costly machine failures and improving return on investment. A meter and clipboard were used to measure and record vibration levels, another development the proximity probe by Bently for non-contacting shaft vibration measurement allowed permanent machine monitoring. Although screening involved overall vibration levels until the 1970s, vibration analysis expanded to address difcult and complex cases as a result of FFT analyzers that had greater resolution than analog ltered instruments. Portable tape recorders were used to acquire vibration data on dened routes; sometimes heavy analyzers were hauled into the eld on carts and trucks. Blake and Jackson published the rst texts related to condition monitoring in 1972 and 1979 respectively. Data collectors that use high-frequency accelerometers interfaced with digital computers were developed in the 1980s. They had a higher level of efciency and effectiveness

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and spurred development of new monitoring and analysis techniques using innovative signal processing. Recent improvements in condition monitoring include more sophisticated miniaturized data acquisition systems, physics and experience-based expert systems, Internet data sharing, and wireless data transmission. Unfortunately, progress with prognostic techniques has not produced practical techniques. Randall has written an authoritative monograph on state-of-the-art methods for evaluating the condition of machinery using vibration analysis. For the rst time practitioners can refer to one source for the techniques commonly used. Because machines are complex and the range of application of signal processing techniques is wide, the user must be aware of their power and limitations. The text is interesting, well written, and well illustrated. This work on vibration signals, signal processing techniques, fault detection, diagnostic techniques, and fault trending and prognostics will provide guidance for individuals struggling to keep down maintenance costs on complex machines using the art and science of condition monitoring. Ronald L. Eshleman Vibration Institute Willowbrook, Illinois, USA October 2010

About the Author

Bob Randall is a visiting Emeritus Professor in the School of Mechanical and Manufacturing Engineering at the University of New South Wales (UNSW), Sydney, Australia, which he joined as a Senior Lecturer in 1988. Prior to that, he worked for the Danish company Br el & u Kjr for 17 years, after 10 years experience in the chemical and rubber industries in Australia, Canada and Sweden. He was promoted to Associate Professor in 1996 and to Professor in 2001, retiring in 2008. He has degrees in Mechanical Engineering and Arts (Mathematics, Swedish) from the Universities of Adelaide and Melbourne, respectively. He is the invited author of chapters on vibration measurement and analysis in a number of handbooks and encyclopaedias and a member of the editorial boards of four journals, including Mechanical Systems and Signal Processing and Transactions of the IMechE Part C. He is the author of more than 190 papers in the elds of vibration analysis and machine diagnostics, and has supervised 14 PhD and 3 Masters projects to completion in those and related areas. Since 1996, he has been Director of the DSTO (Defence Science and Technology Organisation) Centre of Expertise in Helicopter Structures and Diagnostics at UNSW.

Preface
This book is based largely on a course on machine condition monitoring taught at the University of New South Wales (UNSW), Sydney, Australia, from 1997 to 2006. However, its origins date back to courses I developed while working for the Danish company Br el & Kjr, from u 1971 to 1987. In conjunction with a number of colleagues, in particular Hans Mrsk-Mller and Roger Upton, a four-day course was given about 40 times in 20 countries. Perhaps half the material comes from my contributions to those courses and from my book Frequency Analysis, published by Br el & Kjr, the last edition in 1987. u My reasons for writing this book are not only because Frequency Analysis is now out of print, but also because of my frustration at not being able to nd a suitable textbook for the machine condition monitoring course at UNSW. I acknowledge with thanks the permission given by Br el & Kjr Sound and Vibration Measurement A/S to reuse much of the material u from the earlier Br el & Kjr publications. u The other and much more up-to-date half of the material comes from research work carried out since I have been at UNSW, and owes a great deal to the contributions of my PhD students at UNSW, in particular those who worked with machine diagnostic topics. Although all of my students have contributed greatly to my understanding of a range of topics, with respect to the material of the book I would like to acknowledge specially the contributions of Drs Peter Sweeney, Shu Du and Hiroaki Endo in gear diagnostics, Dominique Ho and Nader Sawalhi in bearing diagnostics, and Yaping Ren in engine diagnostics. As will be seen in the references, a number of undergraduate students have also made valuable contributions in their Bachelor of Engineering theses. While at UNSW, I have enjoyed a considerable amount of interaction and collaboration with overseas universities and research establishments, with sabbatical periods at inter alia CETIM (Centre Technique des Industries M caniques), Senlis, France; lUniversit` di Roma e a La Sapienza, Italy; Katholieke Universiteit Leuven, Belgium; the University of Manchester, UK; and a number of universities in France. These include lUniversit de Technologie de e Compi` gne (UTC); the laboratory LASPI of lUniversit Jean Monnet de St Etienne, Roanne; e e and lUniversit dOrl ans at IUT Chartres. There has also been a close collaboration with e e the French universities lInstitut National Polytechnique de Grenoble (INPG) and lInstitut National des Sciences Appliqu es (INSA) Lyon, as well as Lule Tekniska Universitet (LTU), e a Sweden. A number of my students have spent time at UTC and INSA Lyon, in the former case arranged on the French side by Professor M nad Sidahmed, and I have received a number of e exchange PhD students from UTC, LASPI, INPG and LTH.

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The contacts with France have been particularly valuable, as I believe that France leads the world in many areas of signal processing, in particular as applied to mechanical problems. Most important has been my contact with Professor J r me Antoni, of UTC, who rst visited UNSW eo during his PhD candidature at LASPI and INPG. Many of the more recent developments in the book have been introduced or inspired by J r me. eo Over many years I have received research support from the Australian governments Defence Science and Technology Organisation (DSTO) which set up the Centre of Expertise in Vibration Analysis at UNSW in 1996, with a name change to the Centre of Expertise in Helicopter Structures and Diagnostics in the year 2000. I have also received support from the Australian Research Council, with a number of Discovery and Linkage grants. The research supported by such grants has given rise to much of the newer material in the book, in particular the sections on the diagnostics of helicopter gearboxes. DSTO has itself been responsible for much of the development of diagnostic techniques for helicopter gearboxes, including the pioneering work of researchers such as Peter McFadden and David Forrester. My association with the Elsevier journal Mechanical Systems and Signal Processing, as a member of the editorial board, has been very valuable in allowing me to keep up with the latest developments in the application of signal processing to machine diagnostics. I have received much encouragement and support from the Editor-in-Chief, Professor Simon Braun, which is gratefully acknowledged. The book has been written to appeal to condition monitoring practitioners as well as researchers and academics. Thus, mathematics is kept to a minimum and explained where possible by analogy with mechanical and graphical concepts. Certainly, this is the way I, as a mechanical engineer, best understand it myself. The book is written primarily for mechanical engineers, who are most likely to be responsible for the condition monitoring of machines, and so quite a bit of fundamental knowledge of machine function and operation is assumed. On the other hand, specialists in electrical engineering and signal processing might nd some of the explanations somewhat simplistic. The layout of the book is as follows:

Chapter 1 Introduction to machine condition monitoring, by a range of methods, and its application in predictive maintenance. Explanation of the primary role of the analysis of vibration, and in particular accelerometer signals, for the detection, diagnosis and prognosis of incipient faults in machines. Chapter 2 Discussion of the vibration signals produced by rotating and reciprocating machines, and machine components, both with and without faults. Chapter 3 Basic signal processing in the time domain, frequency domain and timefrequency domain, giving generally applicable methods for separating different signal constituents, such as deterministic, stationary random and cyclostationary random components, and source and transmission path effects (either of which might be indicative of failure), as well as performing amplitude and phase/frequency demodulation.

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xvii

Chapter 4 Widely applicable methods for fault detection, on both rotating and reciprocating machines. Detection is the rst stage in the three-stage process, detectiondiagnosisprognosis, and must be efcient so it can be applied to a large number of signals, and if possible automated. Chapter 5 Specic but widely applicable diagnostic techniques, illustrated by application to a number of specic cases such as gears, rolling element bearings and internal combustion engines. Chapter 6 Prognostics, starting with trend analysis of a range of simple and more complicated parameters, and extraction of such parameters. Introduction to more advanced prognostic techniques based on relating vibration symptoms to degree of degradation and theories of failure. Appendix Tutorial and examination questions and assignments. The book can be used as a text for Masters courses at both a fundamental and more advanced level. For that reason the Appendix contains a selection of tutorial and examination questions, as well as assignments using real data. The data and further details are to be found on the web site www.wiley.com/go/randall, where new examples will be added from time to time. Finally, I would like to acknowledge the support of my wife, Helen, who encouraged me to keep writing at all times, even when it threw a greater load on her.