Vibration measurement

Transcription

1 Vibration measurement

2 MECHANICS : DYNAMICAL SYSTEMS Editors : L M eirovitch and G le Ora vas E. H. Dowell, Aeroelasticity of Plates and Shells ISBN D. G.B. Edelen, Lagrangian Mechanics of Noncomervative Nonholonomic Systems ISBN J. L.. Junkins, An Introduction to Optical Estimation of Dynamical Systems ISBN E. H. Dowell et al., A l\iodern Course in Aeroelasticity ISBN '57-4. L. Meirovitch, Computational Methods in Structural Dynamics ISBN B. Skalmierski and A. Tylikowski, Stochastic Processes in Dynamics ISBN P. C. Mi.iller and W. 0. Schiehlen, Linear Vibrations ISBN Gh. Buzdugan, E. Mihi1ilescu and M. Rade~, Vibration measurement ISBN

3 Vibration measurement Gheorghe Buzdugan Elena Mihailescu Mircea Rade$ Strength of Materials Chair Polytechnic Institute of Bucharest Romania SPRINGER-SCIENCE+BUSINESS MEDIA, B.V lrr..af '"

4 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.B ' ISBN ISBN (ebook) DOI / 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.

5 Contents Preface xiii 1. Introduction Definitions Object of vibration measurements Components of the instrumentation system Measured mechanical quantities 8 References for Chapter Elements of the theory of vibrations Classification of vibrations Characteristic vibration parameters Quantities describing the signal waveform Correlation functions Frequency domain description of time signals Frequency analysis of periodic signals Frequency analysis of non periodic signals Frequency analysis of random signals The Discrete Fourier Transform Probability density function Estimation errors at random data analysis Confidence probability. Confidence interval Standard error v

6 Contents 2. 4 Response of vibrating systems to various excitations Harmonic excitation Periodic excitation Transient excitation and shocks Stationary random excitation Natural frequencies Spring constants References for Chapter Effects of vibrations Effects of vibrations on man Effects of vibrations on buildings Effects of vibrations on machinery 56 References for Chapter Transducers and pickups for vibration measurement 71 vi 4.1 Transducers for electrical measurement of vibrations Passive transducers Variable resistance transducers Capacitive transducers Inductive transducers Self-generating transducers Piezoelectric transducers Electrodvnamic transducers Electromagnetic transducers Vibration pickups Theory of seismic instruments : 1. Principle of operation Amplitude distortions Phase distortions Displacement and acceleration pickups Displacement-measuring pickups Accelerometers Velocity pickups Force and torque gauges Dynamic pressure transducers Limits of vibration pickup performance l\lounting References for Chapter 4 115

7 Content8 5 Instrumentation for vibration measurement General properties of measuring instruments Mechanical instrument!'\ for vibration meai'\urement Tastograph Stoppani vibrograph Geiger vibrograph Conversion instruments Measuring bridges Bridge circuits Detection circuits Frequency discriminator circuits Amplifiers Voltage amplifiers Amplifiers with feedback Charge amplifiers :) Impedance-transforming amplifiers Integrators..Analog low-pass and high-pass filters Analog-to- digital converters Sampling rate. Aliasing Number of discrete samples Averagers Time averaging/integration of analog signals Time averaging/integration of digital signals R.M.S. detectors ;). 4 Instruments for signal analysis :4.1 COITelators : Stepped correla tors 145 : On-line correlators Real time correlators Bandpass filters Constant percentage bandwidth filters Constant bandwidth filters Filter response time Non-real time spectrum analyzers Noise analyzers Tunable bandpass filters 153 vii

8 Contents Heterodyne analyzers Synchronous filters Real time spectrum analyzers Parallel filter analyzers Time compression analyzers Weighting Digital analyzers Shock spectrum analyzers Amplitude distribution analyzers Resolved component indicators 5. 5 Display and recording instruments Stroboscopes Analog meters Digital meters and printers Analog strip-chart recorders X-Y recorders Graphic level recorders Magnetic oscillographs Cathode-ray oscilloscopes Magnetic tape recorders Digital recorders Computerized vibration analysis systems References for Chapter Vibration exciters viii 6.1 Mechanical vibration exciters Reciprocating vibration exciters Rotating unbalance vibration exciters Electromagnetic vibration exciters Force generated by an electromagnet Measurement of electromagnet force General performance characteristics Electrodynamic vibration exciters Principle of operation Interaction between vibrator and tested structure Frequency response

9 Contents Measurement of the force applied to the structure Features of a vibrator used in structural testing Application Hydraulic vibration exciters Construction Frequency response General performance References for Chapter 6. characteristics Instrument set-ups and techniques for vibration measurement I.1 Selection of equipment Basic set-ups for signal waveform. measurement Procedures for analysing random vibration records Analysis of a single record Analysis of a collection of records Frequency analysis Frequency analysis of stationary signals Selective filtering Time compression analysis Digital analysis Analysis of stationary random signals Frequency analysis of shocks Pulse transformation into a pulse train Response of a very narrow bandpass filter Vibration testing Sinusoidal tests ;). 2 Broadband random vibration tests Sweepnarrowbandrandomvibrationtests Shock tests Frequency response measurement Frequency response functions Sinusoidal test techniques Single-point excitation l\iulti-point excitation ix

10 Contents Transient. test techniques Impact test technique Step relaxation technique Rapid frequency sweep excitation technique :) Random excitation techniques Measurementofthefrequencyresponse function l\ieasurement of the impulse response function Experimental modal analysis Single-degree-of-freedom techniques Multi-degree-of-freedom techniques 263 References for Chapter Calibration oi transducers and instrumentation systems Calibration of vibration pickups Static calibration "Direct" dynamic calibration Calibration of a piezoelectric accelerometer Calibration of a piezoelectric force transducer R eciprocity calibration Reciprocity procedure Theoretical background Optical interferometry calibration Comparison calibration Simulation calibration of auxiliary circuits Substitution calibration Insert calibration Shunt-resistor calibration References for Chapter Examples oi vibration measurements 9.1 Identification of vibration sources 9. 2 Measurements on prototypes Machine tools Rolling hoisting cranes

11 Contents Suspended pipelines Rotating machinery Cargo ships Measurements for production control and acceptance Machine tools Reciprocating compressor piping Measurements during machinery operation Forge hammers and machine foundations Machinery condition monitoring Measurement of vibrations produced by blasting Measurement of the dvnamic characteristics of materials , Measurement of soil elastic characteristics by vibration methods Spring constants for rigid footings resting on 333 soil Measurement of elastic constants for soils Resonance technique for determining the dynamic coefficients of subgrade reaction. 336 References for Oha,pter Subject index xi

12 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 vibration 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, having 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

13 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 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