RED BOX RULES ARE FOR PROOF STAGE ONLY. DELETE BEFORE FINAL PRINTING. Industrial, Aerospace and Automotive Applications Robert Bond Randall School of Mechanical and Manufacturing Engineering, University of New South Wales, Australia Without doubt the best modern and up-to-date text on the topic, written by one of the world leading experts in the field. Should be on the desk of any practitioner or researcher involved in the field of Machine Condition Monitoring. Simon Braun, Israel Institute of Technology Explaining complex ideas in an easy to understand way, Vibration-based Condition Monitoring provides a comprehensive survey of the application of vibration analysis to the condition monitoring of machines. Reflecting the natural progression of these systems by presenting the fundamental material and then moving onto detection, diagnosis and prognosis, Randall presents classic and state-of-the-art research results that cover vibration signals from rotating and reciprocating machines, basic signal processing techniques, fault detection, diagnostic techniques, and prognostics. Developed out of notes for a course in machine condition monitoring given by Robert Bond Randall over ten years at the University of New South Wales, Vibration-based Condition Monitoring is essential reading for graduate and postgraduate students/ researchers in machine condition monitoring and diagnostics as well as condition monitoring practitioners and machine manufacturers who want to include a machine monitoring service with their product. Includes a number of exercises for each chapter, many based on MATLAB, to illustrate basic points as well as to facilitate the use of the book as a textbook for courses in the topic. Accompanied by a website www.wiley.com/go/randall housing exercises along with data sets and implementation code in MATLAB for some of the methods as well as other pedagogical aids. Authored by an internationally recognised authority in the area of condition monitoring. Enjoyed this book? www.wiley.com/go/randall Cover design by Dan Jubb Why not tell others about it and write a review on your favourite online bookseller. Randall Vibration-based Condition Monitoring Vibration-based Condition Monitoring Robert Bond Randall Vibration-based Condition Monitoring Industrial, Aerospace and Automotive Applications
VIBRATION-BASED CONDITION MONITORING
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 first published 2011 C 2011 John Wiley & Sons, Ltd Registered office John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United Kingdom For details of our global editorial offices, 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 identified 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 book s 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. Vibration Testing. 2. Nondestructive testing. 3. Vibration Measurement. I. Title. TA355.R34 2010 621.8 11 dc22 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 xi xiii xv 1 Introduction and Background 1 1.1 Introduction 1 1.2 Maintenance Strategies 2 1.3 Condition Monitoring Methods 3 1.3.1 Vibration Analysis 3 1.3.2 Oil Analysis 4 1.3.3 Performance Analysis 5 1.3.4 Thermography 5 1.4 Types and Benefits of Vibration Analysis 6 1.4.1 Benefits Compared with Other Methods 6 1.4.2 Permanent vs Intermittent Monitoring 6 1.5 Vibration Transducers 8 1.5.1 Absolute vs Relative Vibration Measurement 8 1.5.2 Proximity Probes 9 1.5.3 Velocity Transducers 12 1.5.4 Accelerometers 13 1.5.5 Dual Vibration Probes 17 1.5.6 Laser Vibrometers 18 1.6 Torsional Vibration Transducers 18 1.6.1 Shaft encoders 19 1.6.2 Torsional Laser Vibrometers 19 1.7 Condition Monitoring the Basic Problem 20 References 23 2 Vibration Signals from Rotating and Reciprocating Machines 25 2.1 Signal Classification 25 2.1.1 Stationary Deterministic Signals 28 2.1.2 Stationary Random Signals 29 2.1.3 Cyclostationary signals 30
viii Contents 2.2 Signals Generated by Rotating Machines 30 2.2.1 Low Shaft Orders and Subharmonics 31 2.2.2 Vibrations from Gears 40 2.2.3 Rolling Element Bearings 47 2.2.4 Bladed Machines 52 2.2.5 Electrical Machines 52 2.3 Signals Generated by Reciprocating Machines 56 2.3.1 Time Frequency Diagrams 57 2.3.2 Torsional Vibrations 60 References 61 3 Basic Signal Processing Techniques 63 3.1 Probability Distribution and Density 63 3.2 Fourier Analysis 66 3.2.1 Fourier Series 66 3.2.2 Fourier Integral Transform 69 3.2.3 Sampled Time Signals 69 3.2.4 The Discrete Fourier Transform 71 3.2.5 The Fast Fourier Transform 72 3.2.6 Convolution and the Convolution Theorem 74 3.2.7 Zoom FFT 84 3.2.8 Practical FFT Analysis 86 3.3 Hilbert Transform and Demodulation 95 3.3.1 Hilbert Transform 95 3.3.2 Demodulation 96 3.4 Cepstrum Analysis 103 3.4.1 Terminology and Definitions 105 3.4.2 Typical Applications of the Cepstrum 108 3.4.3 Practical Considerations with the Cepstrum 110 3.5 Digital Filtering 114 3.5.1 Realization of Digital Filters 115 3.6 Deterministic/Random Signal Separation 117 3.6.1 Order Tracking 117 3.6.2 Time Synchronous Averaging 120 3.6.3 Linear Prediction 122 3.6.4 Adaptive Noise Cancellation 125 3.6.5 Self-adaptive Noise Cancellation 125 3.6.6 Discrete/Random Separation DRS 128 3.7 Time Frequency Analysis 129 3.7.1 The Short Time Fourier Transform 130 3.7.2 The Wigner Ville Distribution 130 3.7.3 Wavelet Analysis 131 3.8 Cyclostationary Analysis and Spectral Correlation 134 3.8.1 Spectral Correlation 135
Contents ix 3.8.2 Spectral Correlation and Envelope Spectrum 138 3.8.3 Wigner Ville Spectrum 139 References 139 4 Fault Detection 143 4.1 Introduction 143 4.2 Rotating Machines 143 4.2.1 Vibration Criteria 143 4.2.2 Use of Frequency Spectra 148 4.2.3 CPB Spectrum Comparison 149 4.3 Reciprocating Machines 155 4.3.1 Vibration Criteria for Reciprocating Machines 155 4.3.2 Time Frequency Diagrams 156 4.3.3 Torsional Vibration 160 References 165 5 Diagnostic Techniques 167 5.1 Harmonic and Sideband Cursors 167 5.1.1 Examples of Cursor Application 167 5.2 Minimum Entropy Deconvolution 169 5.3 Spectral Kurtosis and the Kurtogram 172 5.3.1 SK Definition and Calculation 172 5.3.2 Use of SK as a Filter 174 5.3.3 The Kurtogram 176 5.4 Gear Diagnostics 178 5.4.1 Techniques Based on the TSA 179 5.4.2 Transmission Error as a Diagnostic Tool 181 5.4.3 Cepstrum Analysis 187 5.4.4 Separation of Spalls and Cracks 196 5.4.5 Diagnostics of Gears with Varying Speed and Load 199 5.5 Rolling Element Bearing Diagnostics 200 5.5.1 Signal Models for Bearing Faults 203 5.5.2 A Semi-automated Bearing Diagnostic Procedure 207 5.6 Reciprocating Machine and IC Engine Diagnostics 214 5.6.1 Time Frequency Methods 214 5.6.2 Cylinder Pressure Identification 217 References 225 6 Fault Trending and Prognostics 229 6.1 Introduction 229 6.2 Trend Analysis 229 6.2.1 Trending of Simple Parameters 230 6.2.2 Trending of Impulsiveness 234 6.3 Determination of Spall Size in Bearings 238 6.4 Advanced Prognostics 243 6.4.1 Physics-Based Models 244
x Contents 6.4.2 Data-Driven Models 245 6.4.3 Hybrid Models 247 References 250 Appendix: Exercises and Tutorial Questions 253 A.1 Introduction and Background 253 A.1.1 Exam Questions 253 A.2 Vibration Signals from Machines 254 A.2.1 Exam Questions 254 A.3 Basic Signal Processing 256 A.3.1 Tutorial and Exam Questions 256 A.4 Fault Detection 270 A.4.1 Tutorial and Exam Questions 270 A.4.2 Assignment 273 A.5 Diagnostic Techniques 275 A.5.1 Tutorial and Exam Questions 275 A.5.2 Assignments 280 A.6 Prognostics 284 A.6.1 Tutorial and Exam Questions 284 Index 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 briefly described. The text is the result of the author s years of involvement in the development, practice, and teaching of techniques used in the field, 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 first 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 refined 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 difficult and complex cases as a result of FFT analyzers that had greater resolution than analog filtered instruments. Portable tape recorders were used to acquire vibration data on defined routes; sometimes heavy analyzers were hauled into the field on carts and trucks. Blake and Jackson published the first 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 efficiency and effectiveness
xii Foreword 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 first 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 Brüel & Kjær 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 fields 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.