SAE R-395-2011 Principles of Vibration Analysis With Applications in Automotive Engineering (To Purchase Call 1-800-854-7179 USA Canada or 303-397-7956 Worldwide).pdf

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1、Principles of Vibration Analysis With Applications in Automotive Engineering i by C.Q.Liu and Ronald L. HustonPrinciples of Vibration Analysis with Applications in Automotive Engineering VibrationAnalysis_txt.indb i VibrationAnalysis_txt.indb i 11/24/10 11:43:29 AM 11/24/10 11:43:29 AMPrinciples of

2、Vibration Analysis with Applications in Automotive Engineering VibrationAnalysis_txt.indb i 11/24/10 11:43:29 AMOther Related Publications Available from SAE International: Vehicle Re nement By Matthew Harrison (Product Code: R-364) Vehicle Vibration and Sound By Gang Sheng (Product Code: R-400) Car

3、 Suspension and Handling, Fourth Edition By Geo rey Howard (Product Code R-318) For more information or to order a book, contact SAE International at 400 Commonwealth Drive, Warrendale, PA 15096-0001 USA; phone 877-606-7323 (U.S. and Canada only) or 724-776-4970 (outside U.S. and Canada); fax (724)

4、776-0790; e-mail CustomerServicesae.org; website http:/books.sae.org. VibrationAnalysis_txt.indb ii VibrationAnalysis_txt.indb ii 11/24/10 11:43:32 AM 11/24/10 11:43:32 AMPrinciples of Vibration Analysis with Applications in Automotive Engineering C. Q. Liu and Ronald L. Huston Warrendale, Pennsylva

5、nia USA VibrationAnalysis_txt.indb iii VibrationAnalysis_txt.indb iii 11/24/10 11:43:32 AM 11/24/10 11:43:32 AM Copyright 2011 SAE International eISBN: 978-0-7680-4608-3iv 400 Commonwealth Drive Warrendale, PA 15096-0001 USA E-mail: CustomerServicesae.org Phone: 877-606-7323 (inside USA and Canada)7

6、24-776-4970 (outside USA) Fax: 724-776-1615 Copyright 2011 SAE International. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, distributed, or transmitted, in any form or by any means without the prior written permission of SAE. For permission and lic

7、ensing requests, contact SAE Permissions, 400 Commonwealth Drive, Warrendale, PA 15096-0001 USA; e-mail: copyrightsae.org; phone: 724-772-4028; fax: 724-772-9765. ISBN 978-0-7680-3339-7 Library of Congress Catalog Number 2010940965 SAE Order No. R-395 Information contained in this work has been obta

8、ined by SAE International from sources believed to be reliable. However, neither SAE International nor its authors guarantee the accuracy or completeness of any information published herein and neither SAE International nor its authors shall be responsible for any errors, omissions, or damages arisi

9、ng out of use of this information. is work is published with the understanding that SAE International and its authors are supplying information, but are not attempting to render engineering or other professional services. If such services are required, the assistance of an appropriate professional s

10、hould be sought. To purchase bulk quantities, please contact: SAE Customer Service E-mail: CustomerServicesae.org Phone: 877-606-7323 (inside USA and Canada) 724-776-4970 (outside USA) Fax: 724-776-1615 Visit the SAE Bookstore at http:/store.sae.org VibrationAnalysis_txt.indb iv VibrationAnalysis_tx

11、t.indb iv 11/24/10 11:43:32 AM 11/24/10 11:43:32 AMv Contents Preface xiii Chapter One Introduction 11.1 What Is Vibration? 11.2 Classi cation of Vibration Studies 2(1) Vibration Analysis 2(2) System Design 2(3) Input Evaluation 2(4) System Identi cation 21.3 Classi cation of Vibration 3(1) Classi c

12、ation Based on Input 3(2) Classi cation Based on Output 4(3) Classi cation Based on the Degrees of Freedom of the System 7(4) Classi cation Based on Di erential Equation of Motion of the System 71.4 Harmonic Vibration 81.5 Harmonic Analysis 10Problems 16References 18 Chapter Two Vibration of a Singl

13、e-Degree-of-Freedom System 212.1 Introduction: Modeling 212.2 Free Vibration of a Single-Degree-of-Freedom System 24(1) Governing Di erential Equation of Motion 24(2) Equivalent Spring Sti ness 282.3 e Energy Method 33(1) e Law of Conservation of Energy 33(2) e Rayleigh Method 342.4 E ective Mass 40

14、2.5 Damped Free Vibration of a Single-Degree-of-Freedom System 41(1) Damping Forces 41(2) Di erential Equation of Motion 41(3) Discussion of the Solution 43Problems 50References 53 VibrationAnalysis_txt.indb v VibrationAnalysis_txt.indb v 11/24/10 11:43:33 AM 11/24/10 11:43:33 AMvi Chapter Three Har

15、monically Excited Motion 553.1 Introduction 553.2 Forced Harmonic Vibration of Damped Systems 553.3 Forced Harmonic Vibration of Undamped Systems 63(1) Beating 64(2) Resonance 663.4 Forced Vibration Caused by Rotating Unbalance 673.5 Forced Vibration Caused by Support Motion 693.6 Vibration Isolatio

16、n 72(1) Isolation of the Machine from the Foundation 73(2) Isolation of the Foundation from the Machine 733.7 Damping 76(1) Energy Dissipation Due to a Viscous Damping Force 76(2) Structural (Hysteretic) Damping 78(3) Complex Sti ness and Lost Factor 79(4) Sharpness of Resonance 803.8 Forced Vibrati

17、on Under Periodic Excitation 813.9 Response to Arbitrary Excitation 82Problems 87References 92 Chapter Four Balancing of Rotors 934.1 Unbalance 93(1) Static Unbalance 93(2) Dynamic Unbalance 944.2 Whirling of Rotating Sha 954.3 Experimental Balancing 98(1) e In uence Coe cient Method: Single-Plane B

18、alancing 98(2) e In uence Coe cient Method: Two-Plane Balancing 1004.4 Inertia Forces in a Single-Cylinder Engine 1044.5 Inertia Forces and Couples of Multicylinder Engines 1104.6 Balancing of Cranksha s 120Problems 126References 133 VibrationAnalysis_txt.indb vi VibrationAnalysis_txt.indb vi 11/24/

19、10 11:43:33 AM 11/24/10 11:43:33 AMvii Chapter Five Multi-Degree-of-Freedom Systems 1375.1 Introduction 1375.2 Two-Degree-of-Freedom Systems 137(1) Equations of Motion 137(2) Characteristic Equation and Natural Frequency 138(3) Mode Shapes 1385.3 Eigenvalues and Eigenvectors 1405.4 Orthogonal Proper

20、ties of the Modal Vectors 1435.5 Zero Eigenvalues and Repeated Roots 146(1) Zero Eigenvalues 146(2) Repeated Roots 1475.6 Response of a System to Initial Conditions 1505.7 Coordinate Coupling 1525.8 Undamped Systems and Coordinate Decoupling 155(1) Forced Response and Coordinate Decoupling 155(2) In

21、itial Value Problem and Coordinate Decoupling 1575.9 Damped Systems and Coordinate Decoupling 159(1) Coordinate Decoupling with Forced Response 159(2) Coordinate Decoupling with Initial Value Problems 1625.10 Lagranges Equations 164(1) Generalized Coordinates and Virtual Displacements 165(2) Virtual

22、 Work and Generalized Forces 165(3) Lagranges Equations 1665.11 Kanes Equations 169(1) Partial Velocities and Partial Angular Velocities 170(2) Inertia Forces 170(3) Generalized Applied Forces 172(4) Kanes Equations 172Problems 174References 177 Chapter Six Numerical Methods 1796.1 Introduction 1796

23、.2 Various Eigenvalue Analyses 179(1) e Generalized Eigenvalue Problem 179(2) e Algebraic Eigenvalue Problem 180 VibrationAnalysis_txt.indb vii VibrationAnalysis_txt.indb vii 11/24/10 11:43:33 AM 11/24/10 11:43:33 AMviii (3) e Symmetric Eigenvalue Problem 180(4) e Standard Eigenvalue Problem in Stat

24、e Space 183(5) e Generalized Eigenvalue Problem in State Space 1856.3 Numerical Evaluation of the Time Response 197Problems 210References 214 Chapter Seven Transfer Functions and Frequency Response Functions 2177.1 Introduction 2177.2 e Laplace Transformation and Fourier Transformation 217(1) e Lapl

25、ace Transform 217(2) e Fourier Transform 2197.3 Laplace Domain: Transfer Function 2207.4 Frequency Domain: Frequency Response Function 223(1) Receptance (or Admittance, or Dynamic Compliance) 223(2) Mobility 223(3) Accelerance (or Inertance) 223(4) e Bode Diagrams 226(5) e Nyquist Diagrams 2287.5 Ti

26、me Domain: Impulse Response Function 2307.6 FRFs of Multi-Degree-of-Freedom Systems 234(1) Laplace Domain: Transfer Function Matrix 235(2) Frequency Domain: Frequency Response Function Matrix 238(3) Time Domain: Impulse Response Functions 2417.7 Determination of Residues and Poles in State Space 248

27、Problems 254References 257 Chapter Eight Lumped Parameter Systems 2598.1 Introduction 2598.2 e Flexibility and Sti ness Matrices 2598.3 Maxwells Reciprocity eorem 2618.4 Eigenvalue Analysis 2658.5 Dunkerleys Equation 2698.6 Rayleigh Principle 2718.7 Method of Matrix Iteration 2748.8 Determining of H

28、igher-Order Modes and Frequencies 277 VibrationAnalysis_txt.indb viii VibrationAnalysis_txt.indb viii 11/24/10 11:43:33 AM 11/24/10 11:43:33 AMix 8.9 Transfer Matrix Method 279(1) A Spring-Mass System 280(2) Torsional Systems 286(3) A Geared System 289(4) Branched Systems 2908.10 Beams Modeled as Lu

29、mped Masses 292(1) Flexural Vibration 292(2) Rotating Beams 301Problems 304References 308 Chapter Nine Continuous Systems 3099.1 Introduction 3099.2 Lateral Vibration of a String 310(1) d Alemberts Solution 310(2) Separation of Variables 3129.3 Longitudinal Vibration of Rods 3159.4 Torsional Vibrati

30、on of Rods 3209.5. Lateral Vibration of Beams 3239.6 Orthogonal Relations 3319.7 E ects of Rotary Inertia, Shear, and Axial Loading 336(1) e E ect of Rotary Inertia and Shearing Deformation 336(2) e E ect of Axial Force on Lateral Vibration 3399.8 Forced Vibration 3409.9 Ritz Method 344Problems 348R

31、eferences 351 Chapter Ten Engine Mounting Systems 35310.1 Introduction 35310.2 Inertia Properties of an Engine 354(1) Reference Frame and Direction Cosines 358(2) Inertia Matrix 358(3) Mass Center 36110.3 Orientation Angles and Transformation Matrix 36310.4 Equations of Motion 372(1) Forces and Torq

32、ues Produced by an Engine Mount due to Translational Motion of the Engine 374 VibrationAnalysis_txt.indb ix VibrationAnalysis_txt.indb ix 11/24/10 11:43:33 AM 11/24/10 11:43:33 AMx (2) Forces and Torques Produced by an Engine Mount due to Rotational Motion of the Engine 37610.5 Mode Shapes and Natur

33、al Frequencies 37910.6 Decoupling and Optimization 382(1) Two-Degree-of-Freedom Coupled System 384(2) ree-Degree-of-Freedom Coupled System 387(3) Optimization 38910.7 Torque Roll Axis (TRA) 39510.8 Torque Roll Axis (TRA) Mode Decoupling 397Problems 398References 402 Chapter Eleven Experimental Modal

34、 Analysis 40511.1 Introduction 40511.2 Modal Analysis eory 40611.3 e Complex Exponential Algorithm 40811.4 e Least-Squares Complex Exponential Method 41211.5 e Polyreference Time Domain Method 41211.6 e Ibrahim Time Domain Method 41911.7 e Eigensystem Realization Algorithm 42211.8 Estimation of Moda

35、l Vectors 42611.9 Estimation of Frequency Response Functions 428(1) H 1Estimator of FRF 430(2) H 2Estimator of FRF 431(3) H vEstimator of FRF 43211.10 Coherence Function 433(1) Ordinary Coherence Function 433(2) Multiple Coherence Function 434(3) Partial Coherence Function 43511.11 Discrete Fourier

36、Transfer (DFT) and Fast Fourier Transfer (FFT) 436(1) Aliasing 438(2) Leakage 43811.12 Window Functions 44011.13 Averaging 442(1) Linear Average 443(2) Stable Average 443 VibrationAnalysis_txt.indb x VibrationAnalysis_txt.indb x 11/24/10 11:43:34 AM 11/24/10 11:43:34 AMxi 11.14 Overlapping Signal An

37、alysis 44311.15 Modal Data Acquisition 444(1) Test Structure 445(2) Exciter 447(3) Data Acquisition System 451(4) Analyzer 45311.16 Operational Modal Analysis 453(1) Stochastic Subspace Identi cation Method 454(2) e Natural Excitation Technique (NExT) 45711.17 Running Modes Analysis 458Problems 460R

38、eferences 463 Chapter Twelve Special Topics 46712.1 Introduction 46712.2 Complex Structure Analysis Using the FRFs of Substructures 467(1) Equations of Motion 468(2) Solution Method 46912.3 Translational Vibration Absorber 475(1) Absorber Tuning Based on the Primary System FRF 476(2) Special Cases:

39、A Single-Degree-of-Freedom System 48012.4 Torsional Vibration Absorber 48612.5 Experimental Measurement of the Torsional FRF 48712.6 HYFEX Method 48812.7 Sensitivity Analysis 495(1) Eigenvalue Derivatives 496(2) Eigenvector Derivatives 497References 503 Appendix A 507 Appendix B 509 Appendix C 513 N

40、otation 519 Index 537 VibrationAnalysis_txt.indb xi VibrationAnalysis_txt.indb xi 11/24/10 11:43:34 AM 11/24/10 11:43:34 AMVibrationAnalysis_txt.indb xii VibrationAnalysis_txt.indb xii 11/24/10 11:43:34 AM 11/24/10 11:43:34 AMxiii Preface Over the years there have been many outstanding books written

41、 on vibrations, including textbooks, books on analysis and design, and theoretical treatises. Why then should there be another, and, speci cally, why this book? ere are several reasons: First, vibrations, as with all science and engineering subjects, is continually evolving. As new discoveries and n

42、ew analyses and new experimental procedures are developed, there is an ongoing need to document these advances. Next, with the evolution in the subject, many of the older procedures become obsolete. Traditional topical emphases become less important, and are superseded by advances in computational a

43、nd measurement methods. Consequently, new topical emphases are emerging. ere is a need to document these new methods for students and for practicing engineers. Finally, it is always helpful to have a state-of-the-art treatise on fundamentals enabling future research and application. We wrote this bo

44、ok attempting to satisfy each of these needs. e book summarizes basic concepts and established analytical methodologies. We then illustrate these ideas and procedures via worked-out examples. Numerous examples using Matlab are presented throughout the text. e various chapters contain problems (with

45、answers) for readers studying the subject for the rst time, and for those seeking additional expertise and/ or review. In the later chapters, we illustrate application in automotive engineering with a focus upon engine balancing and engine mounting systems. Finally, the book is intended to be a quic

46、k reference for current (circa 2010) modeling and analysis methods. e book is divided into twelve chapters, with the rst of these providing an introduction to vibration terminology. In the second chapter we review the fundamentals of single-degree-of-freedom systems, and in the third chapter we cons

47、ider harmonically excited motion. e fourth chapter applies these concepts with rotors, outlining balancing methods. In the h chapter we study multi-degree-of-freedom systems, and then we devote a chapter to numerical methods. In the seventh chapter we introduce the concept of transfer functions and

48、frequency response functions together with a detailed discussion about these functions. Chapter eight explores lumped parameter modeling and chapter nine follows with analyses of continuous systems. Chapter ten provides an extensive exposition of engine mounting systems. VibrationAnalysis_txt.indb x

49、iii VibrationAnalysis_txt.indb xiii 11/24/10 11:43:34 AM 11/24/10 11:43:34 AMxiv Chapter eleven summarizes experimental modal analysis methods, including the basic theory and an account of signal processing and test procedures. In the nal chapter, we conclude with some special topics, such as the frequency response function (FRF)-based substructure method, the hybrid nite element and experimental (HYFEX) method, system sensitivity analysis, and vibration absorber t