vibration monitoring, testing, and instrumentationpreview.kingborn.net › 646000 ›...

53191mdash1432007mdash1849mdashVELUmdash246493mdash CRC ndash pp 1ndash15

copy 2007 by Taylor amp Francis Group LLC

Vibration MonitoringTesting and

Instrumentation


Mechanical Engineering SeriesFrank Kreith and Roop Mahajan - Series Editors

Published Titles

Computer Techniques in VibrationClarence W de SilvaDistributed Generation The Power Paradigm forthe New MillenniumAnne-Marie Borbely ampJan F KreiderElastoplasticity TheoryVlado A LubardaEnergy Audit of Building SystemsAn Engineering ApproachMoncefKrartiEngineering ExperimentationEuan SomerscalesEntropy Generation MinimizationAdrian BejanFinite Element Method Using MATLABreg2 n d EditionYoung W Kwon amp Hyochoong BangFluid Power Circuits and Controls Fundamentalsand ApplicationsJohn S CundiffFundamentals of Environmental DischargeModelingLorin R DavisHeat Transfer in Single and Multiphase SystemsGregF NatererIntroductory Finite Element MethodChandrakant S Desai amp Tribikram KunduIntelligent Transportation Systems New Principlesand ArchitecturesSumit Ghosh amp Tony LeeMathematical amp Physical Modeling of MaterialsProcessing OperationsOlusegun Johnson Ilegbusi Manabu Iguchi ampWalter E WahnsiedlerMechanics of Composite MaterialsAutarK Kaw

Mechanics of FatigueVladimir V BolotinMechanics of Solids and Shells Theories andApproximationsGerald Wempner amp Demosthenes TalaslidisMechanism Design Enumeration of KinematicStructures According to FunctionLung-Wen Tsai

The MEMS Handbook Second EditionMEMS Introduction and FundamentalsMEMS Design and FabricationMEMS Applications

Mohamed Gad-el-HakNanotechnology Understanding Small SystemsBen Rogers Jesse Adams amp Sumita PennathurNonlinear Analysis of StructuresM SathyamoorthyPractical Inverse Analysis in EngineeringDavid M Trujillo amp Henry R BusbyPressure Vessels Design and PracticeSomnath ChattopadhyayPrinciples of Solid MechanicsRowland Richards JrThermodynamics for EngineersKau-Fui WongVibration Damping Control and DesignClarence W de SilvaVibration Monitoring Testing and InstrumentationClarence W de SilvaVibration and Shock HandbookClarence W de SilvaViscoelastic SolidsRoderic S Lakes



Instrumentation

Edited by

Clarence W de SilvaThe University of British Columbia

Vancouver Canada

Ltfi) CRC PressVV^ J Taylor amp Francis Group

Boca Raton London New York

CRC Press is an imprint of theTaylor amp Francis Croup an informa business


This material was previously published in Vibration and Shock Handbook copy 2005 by CRC Press LLC

CRC PressTaylor amp Francis Group6000 Broken Sound Parkway NW Suite 300Boca Raton FL 33487-2742

copy 2007 by Taylor amp Francis Group LLCCRC Press is an imprint of Taylor amp Francis Group an Informa business

No claim to original US Government worksPrinted in the United States of America on acid-free paper10987654321

International Standard Book Number-101-4200-5319-1 (Hardcover)International Standard Book Number-13978-1-4200-5319-7 (Hardcover)

This book contains information obtained from authentic and highly regarded sources Reprinted material is quotedwith permission and sources are indicated A wide variety of references are listed Reasonable efforts have been made topublish reliable data and information but the author and the publisher cannot assume responsibility for the validity ofall materials or for the consequences of their use

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Library of Congress Cataloging-in-Publication Data

Vibration monitoring testing and instrumentation editor Clarence W de Silvap cm mdash (Mechanical engineering series)

Includes bibliographical references and indexISBN-13 978-1-4200-5319-7 (alk paper)ISBN-101-4200-5319-1 (alk paper)1 Vibration 2 Shock (Mechanics) I De Silva Clarence W II Title III Series

TA355V5228 200762030287-dc22 2006100139

Visit the Taylor amp Francis Web site athttpwwwtaylorandfranciscom

and the CRC Press Web site athttpwwwcrcpresscom


Preface

Individual chapters authored by distinguished leaders and experienced professionals in their

respective topics this book provides for engineers technicians designers researchers educators and

students a convenient thorough up-to-date and authoritative reference source on techniques tools

and data for monitoring testing and instrumentation of mechanical vibration and shock Included

are shock and vibration methodologies particularly for civil and mechanical engineering systems

instrumentation and testing methods including sensors exciters signal acquisition conditioning

and recording and LabVIEWw tools for virtual instrumentation testing and design for seismic

vibration and related regulatory issues and human response to vibration Important information

and results are summarized as windows tables graphs and lists throughout the chapters for easy

reference and information tracking References are given at the end of each chapter for further

information and study Cross-referencing is used throughout to indicate other places in the book

where further information on a particular topic is provided

In the book equal emphasis is given to theory and practical application Analytical

formulations design approaches monitoring and testing techniques and commercial software

tools are presented and illustrated Commercial equipment computer hardware and instrumenta-

tion are described analyzed and demonstrated for field application practical implementation and

experimentation Examples and case studies are given throughout the book to illustrate the use

and application of the included information The material is presented in a format that is

convenient for easy reference and recollection

Mechanical vibration is a manifestation of the oscillatory behavior in mechanical systems as a

result of either the repetitive interchange of kinetic and potential energies among components in

the system or a forcing excitation that is oscillatory Such oscillatory responses are not limited to

purely mechanical systems and are found in electrical and fluid systems as well In purely thermal

systems however free natural oscillations are not possible and an oscillatory excitation is needed

to obtain an oscillatory response Sock is vibration caused by brief abrupt and typically high-

intensity excitations Low levels of vibration mean reduced noise and improved work environment

Consequently a considerable effort is devoted today to monitoring studying and modifying the

vibration and shock generated by machinery components machine tools transit vehicles impact

processes civil engineering structures fluid flow systems and aircraft Before designing a system

for good vibratory or shock performance it is important to understand analyze and represent the

dynamic characteristics of the system This may be accomplished through monitoring testing and

analysis of test data which is the emphasis of this book

In recent years educators researchers and practitioners have devoted considerable effort towards

studying monitoring and testing vibration and shock in a range of applications in various branches

of engineering particularly civil mechanical aeronautical and aerospace and production and

v



manufacturing Specific applications are found in machine tools transit vehicles impact processes

civil engineering structures construction machinery industrial processes product qualification and

quality control fluid flow systems ships and aircraft This book is a contribution towards these

efforts

Clarence W de SilvaEditor-in-Chief

Vancouver Canada

Prefacevi



Acknowledgments

I wish to express my gratitude to the authors of the chapters for their valuable and highly professional

contributions I am very grateful to Michael Slaughter Acquisitions Editor-Engineering CRC Press for

his enthusiasm and support throughout the project Editorial and production staff at CRC Press have

done an excellent job in getting this volume out in print Finally I wish to lovingly acknowledge the

patience and understanding of my family

vii



Editor-in-Chief

Dr Clarence W de Silva PEng Fellow ASME Fellow IEEE Fellow Canadian Academy of

Engineering is Professor of Mechanical Engineering at the University of British Columbia Vancouver

Canada and has occupied the NSERC-BC Packers Research Chair in Industrial Automation since 1988

He has earned PhD degrees from the Massachusetts Institute of Technology and the University of

Cambridge England De Silva has also occupied the Mobil Endowed Chair Professorship in the

Department of Electrical and Computer Engineering at the National University of Singapore He has

served as a consultant to several companies including IBM and Westinghouse in US and has led the

development of eight industrial machines and devices He is recipient of the Henry M Paynter

Outstanding Investigator Award from the Dynamic Systems and Control Division of the American

Society of Mechanical Engineers (ASME) Killam Research Prize Lifetime Achievement Award from the

World Automation Congress Outstanding Engineering Educator Award of IEEE Canada Yasundo

Takahashi Education Award of the Dynamic Systems and Control Division of ASME IEEE Third

Millennium Medal Meritorious Achievement Award of the Association of Professional Engineers of BC

and the Outstanding Contribution Award of the Systems Man and Cybernetics Society of the Institute

of Electrical and Electronics Engineers (IEEE)

He has authored 16 technical books including Sensors and Actuators Control System Instrumentation

(Taylor amp Francis CRC Press 2007) MechatronicsmdashAn Integrated Approach (Taylor amp Francis CRC

Press Boca Raton FL 2005) Soft Computing and Intelligent Systems DesignmdashTheory Tools and

Applications (with F Karry Addison Wesley New York NY 2004) VIBRATION Fundamentals and

Practice (Taylor amp Francis CRC Press 2nd edition 2006) INTELLIGENT CONTROL Fuzzy Logic

Applications (Taylor amp Francis CRC Press 1995) Control Sensors and Actuators (Prentice Hall 1989) 14

edited volumes over 170 journal papers 200 conference papers and 12 book chapters He has served on

the editorial boards of 14 international journals in particular as the Editor-in-Chief of the International

Journal of Control and Intelligent Systems Editor-in-Chief of the International Journal of Knowledge-Based

Intelligent Engineering Systems Senior Technical Editor of Measurements and Control and Regional

Editor North America of Engineering Applications of Artificial Intelligence ndash the International Journal of

Intelligent Real-Time Automation He is a Lilly Fellow at Carnegie Mellon University NASA-ASEE Fellow

Senior Fulbright Fellow at Cambridge University ASI Fellow and a Killam Fellow Research and

development activities of Professor de Silva are primarily centered in the areas of process automation

robotics mechatronics intelligent control and sensors and actuators with cash funding of about $6

million as principal investigator

ix



Contributors

xi

Kourosh DanaiUniversity of Massachusetts

Amherst Massachusetts


Vancouver British Columbia Canada

P S HeynsUniversity of Pretoria

Pretoria South Africa

S HuangNational University of Singapore

Singapore

Hirokazu IemuraKyoto University

Kyoto Japan

Sarvesh Kumar JainMadhav Institute of Technology and

Science

Madhya Pradesh India

Christian LalanneEngineering Consultant

Jalles France

TH LeeNational University of Singapore

Singapore

YP LeowSingapore Institute of Manufacturing

Technology

Singapore

SY LimSingapore Institute of Manufacturing

Technology

Singapore

Jiaohao LinDalian University of Technology

Liaoning Peoplersquos Republic of China

W LinSingapore Institute of Manufacturing

Technology

Singapore

Chris K MechefskeQueenrsquos University

Kingston Ontario Canada

Priyan MendisUniversity of Melbourne

Melbourne Victoria Australia

Tuan NgoUniversity of Melbourne


Mulyo Harris PradonoKyoto University

Kyoto Japan

C SchefferUniversity of Stellenbosch


KK TanNational University of Singapore

Singapore

KZ TangNational University of Singapore

Singapore

Yahui ZhangDalian University of Technology




Contents

1 Vibration Instrumentation Clarence W de Silva 1-1

11 Introduction 1-1

12 Vibration Exciters 1-3

13 Control System 1-15

14 Performance Specification 1-21

15 Motion Sensors and Transducers 1-27

16 Torque Force and Other Sensors 1-50

Appendix 1A Virtual Instrumentation for Data Acquisition Analysis

and Presentation 1-73

2 Signal Conditioning and Modification Clarence W de Silva 2-1

21 Introduction 2-2

22 Amplifiers 2-2

23 Analog Filters 2-15

24 Modulators and Demodulators 2-29

25 AnalogndashDigital Conversion 2-37

26 Bridge Circuits 2-43

27 Linearizing Devices 2-49

28 Miscellaneous Signal Modification Circuitry 2-56

29 Signal Analyzers and Display Devices 2-62

3 Vibration Testing Clarence W de Silva 3-1

31 Introduction 3-1

32 Representation of a Vibration Environment 3-3

33 Pretest Procedures 3-24

34 Testing Procedures 3-37

35 Some Practical Information 3-52

4 Experimental Modal Analysis Clarence W de Silva 4-1

41 Introduction 4-1

42 Frequency-Domain Formulation 4-2

43 Experimental Model Development 4-8

44 Curve Fitting of Transfer Functions 4-10

45 Laboratory Experiments 4-18

46 Commercial EMA Systems 4-24

xiii



5 Mechanical Shock Christian Lalanne 5-1

51 Definitions 5-2

52 Description in the Time Domain 5-3

53 Shock Response Spectrum 5-4

54 Pyroshocks 5-17

55 Use of Shock Response Spectra 5-18

56 Standards 5-24

57 Damage Boundary Curve 5-26

58 Shock Machines 5-28

59 Generation of Shock Using Shakers 5-44

510 Control by a Shock Response Spectrum 5-52

511 Pyrotechnic Shock Simulation 5-58

6 Machine Condition Monitoring and Fault Diagnostics Chris K Mechefske 6-1

61 Introduction 6-2

62 Machinery Failure 6-2

63 Basic Maintenance Strategies 6-4

64 Factors Which Influence Maintenance Strategy 6-7

65 Machine Condition Monitoring 6-8

66 Transducer Selection 6-10

67 Transducer Location 6-14

68 Recording and Analysis Instrumentation 6-14

69 Display Formats and Analysis Tools 6-16

610 Fault Detection 6-21

611 Fault Diagnostics 6-25

7 Vibration-Based Tool Condition Monitoring Systems C Scheffer and PS Heyns 7-1

71 Introduction 7-1

72 Mechanics of Turning 7-2

73 Vibration Signal Recording 7-7

74 Signal Processing for Sensor-Based Tool Condition Monitoring 7-11

75 Wear ModelDecision-Making for Sensor-Based Tool Condition Monitoring 7-15

76 Conclusion 7-20

8 Fault Diagnosis of Helicopter Gearboxes Kourosh Danai 8-1

81 Introduction 8-1

82 Abnormality Scaling 8-5

83 The Structure-Based Connectionist Network 8-8

84 Sensor Location Selection 8-11

85 A Case Study 8-14

86 Conclusion 8-23

9 Vibration Suppression and Monitoring in Precision Motion Systems KK Tan

TH Lee KZ Tang S Huang SY Lim W Lin and YP Leow 9-1

91 Introduction 9-1

92 Mechanical Design to Minimize Vibration 9-2

93 Adaptive Notch Filter 9-10

94 Real-Time Vibration Analyzer 9-17

Contentsxiv



95 Practical Insights and Case Study 9-29

96 Conclusions 9-35

10 Vibration and Shock Problems of Civil Engineering Structures Priyan Mendis

and Tuan Ngo 10-1

101 Introduction 10-2

102 Earthquake-Induced Vibration of Structures 10-3

103 Dynamic Effects of Wind Loading on Structures 10-22

104 Vibrations Due to FluidndashStructure Interaction 10-33

105 Blast Loading and Blast Effects on Structures 10-34

106 Impact Loading 10-47

107 Floor Vibration 10-51

11 Seismic Base Isolation and Vibration Control Hirokazu Iemura Sarvesh Kumar Jain

and Mulyo Harris Pradono 11-1


112 Seismic Base Isolation 11-4

113 Seismic Vibration Control 11-33

12 Seismic Random Vibration of Long-Span Structures Jiahao Lin and Yahui Zhang 12-1


122 Seismic Random-Excitation Fields 12-11

123 Pseudoexcitation Method for Structural Random Vibration Analysis 12-16

124 Long-Span Structures Subjected to Stationary Random Ground Excitations 12-27

125 Long-Span Structures Subjected to Nonstationary Random Ground Excitations 12-34

126 Conclusions 12-39

13 Seismic Qualification of Equipment Clarence W de Silva 13-1


132 Distribution Qualification 13-1

133 Seismic Qualification 13-6

14 Human Response to Vibration Clarence W de Silva 14-1


142 Vibration Excitations on Humans 14-2

143 Human Response to Vibration 14-3

144 Regulation of Human Vibration 14-6

Contents xv



1Vibration

Instrumentation


11 Introduction 1-1

12 Vibration Exciters 1-3Shaker Selection dagger Dynamics of Electromagnetic Shakers

13 Control System 1-15Components of a Shaker Controller dagger Signal-Generating

Equipment

14 Performance Specification 1-21Parameters for Performance Specification dagger Linearity dagger

Instrument Ratings dagger Accuracy and Precision

15 Motion Sensors and Transducers 1-27Potentiometer dagger Variable-Inductance Transducers dagger

Mutual-Induction Proximity Sensor dagger Selfinduction

Transducers dagger Permanent-Magnet Transducers dagger

Alternating Current Permanent-Magnet Tachometer dagger

Alternating Current Induction Tachometer dagger Eddy Current

Transducers dagger Variable-Capacitance Transducers dagger

Piezoelectric Transducers

16 Torque Force and Other Sensors 1-50Strain Gage Sensors dagger Miscellaneous Sensors

Appendix 1A Virtual Instrumentation for DataAcquisition Analysis and Presentation 1-73

Summary

Devices useful in instrumenting a mechanical vibrating system are presented in this chapter Shakers whichgenerate vibration excitations are discussed and compared A variety of sensors including motion sensorsproximity sensors forcetorque sensors and other miscellaneous sensors are considered Performance specificationin the time domain and the frequency domain is addressed Rating parameters of instruments are given

11 Introduction

Measurement and associated experimental techniques play a significant role in the practice of vibration

Academic exposure to vibration instrumentation usually arises in laboratories in the context of learning

training and research In vibration practice perhaps the most important task of instrumentation is the

measurement or sensing of vibration Vibration sensing is useful in the following applications

1 Design and development of a product

2 Testing (screening) of a finished product for quality assurance

3 Qualification of a good-quality product to determine its suitability for a specific application

1-1

53191mdash522007mdash1201mdashSENTHILKUMARmdash246494mdash CRC ndash pp 1ndash112


4 Mechanical aging of a product prior to carrying out a test program

5 Exploratory testing of a product to determine its dynamic characteristics such as resonances

mode shapes and even a complete dynamic model

6 Vibration monitoring for performance evaluation

7 Control and suppression of vibration

Figure 11 indicates a procedure typical of experimental vibration highlighting the essential

instrumentation Vibrations are generated in a device the test object in response to some excitation In

some experimental procedures primarily in vibration testing (see Figure 11) the excitation signal has

to be generated in a signal generator in accordance with some requirement (specification) and applied to

the object through an exciter after amplification and conditioning In some other situations primarily in

performance monitoring and vibration control the excitations are generated as an integral part of the

operating environment of the vibrating object and may originate either within the object (eg engine

excitations in an automobile) or in the environment with which the object interacts during operation

(eg road disturbances on an automobile) Sensors are needed to measure vibrations in the test object In

particular a control sensor is used to check whether the specified excitation is applied to the object

and one or more response sensors may be used to measure the resulting vibrations at key locations of

the object

The sensor signals have to be properly conditioned for example by filtering and amplification and

modified for example through modulation demodulation and analog-to-digital conversion prior to

recording analyzing and display The purpose of the controller is to guarantee that the excitation is

correctly applied to the test object If the signal from the control sensor deviates from the required

excitation the controller modifies the signal to the exciter so as to reduce this deviation Furthermore the

controller will stabilize or limit (compress) the vibrations in the object It follows that instruments in

experimental vibration may be generally classified into the following categories

1 Signal-generating devices

2 Vibration exciters

3 Sensors and transducers

4 Signal conditioningmodifying devices

5 Signal analysis devices

6 Control devices

7 Vibration recording and display devices

AnalogDigital

Interface

DigitalSignal

RecorderAnalyzerDisplay

FilterAmplifier

FilterAmplifier

SignalGenerator

and ExciterController

Reference (Required)Signal (Specification)

PowerAmplifier

MountingFixtures

TestObject

ResponseSensor

ControlSensor

Exciter

SwivelBase

FIGURE 11 Typical instrumentation in experimental vibration

Vibration Monitoring Testing and Instrumentation1-2



Note that one instrument may perform the tasks

of more than one category listed here Also more

than one instrument may be needed to carry out

tasks in a single category In the following sections

we will provide some examples of the types of

vibration instrumentation giving characteristics

operating principles and important practical

considerations Also we will describe several

experiments which can be found in a typical

vibration laboratory

An experimental vibration system generally

consists of four main subsystems

1 Test object

2 Excitation system

3 Control system

4 Signal acquisition and modification system

These are schematically shown in Figure 12 Note that various components shown in Figure 11 may

be incorporated into one of these subsystems In particular component matching hardware and object

mounting fixtures may be considered interfacing devices that are introduced through the interaction

between the main subsystems as shown in Figure 12 Some important issues of vibration testing and

instrumentation are summarized in Box 11

12 Vibration Exciters

Vibration experimentation may require an external exciter to generate the necessary vibration This is the

case in controlled experiments such as product testing where a specified level of vibration is applied to the

test object and the resulting response is monitored A variety of vibration exciters are available with

different capabilities and principles of operation

Three basic types of vibration exciters (shakers) are widely used hydraulic shakers inertial shakers

and electromagnetic shakers The operation-capability ranges of typical exciters in these three categories

are summarized in Table 11 Stroke or maximum displacement is the largest displacement the exciter

is capable of imparting onto a test object whose weight is assumed to be within its design load limit

Maximum velocity and acceleration are similarly defined Maximum force is the largest force that could

be applied by the shaker to a test object of acceptable weight (one within the design load) The values

given in Table 11 should be interpreted with caution Maximum displacement is achieved only at very

low frequencies The achievement of maximum velocity corresponds to intermediate frequencies in the

operating frequency range of the shaker Maximum acceleration and force ratings are usually achieved at

high frequencies It is not feasible for example to operate a vibration exciter at its maximum

displacement and its maximum acceleration simultaneously

Consider a loaded exciter that is executing harmonic motion Its displacement is given by

x frac14 s sin vt eth11THORN

in which s is the displacement amplitude (or stroke) Corresponding velocity and acceleration are

_x frac14 sv cos vt eth12THORN

eurox frac14 2sv2sin vt eth13THORN

SignalModification

System

TestObject

ControlSystem

VibrationExciter (Shaker)

System

FIGURE 12 Interactions between major subsystems of

an experimental vibration system

Vibration Instrumentation 1-3



If the velocity amplitude is denoted by v and the acceleration amplitude by a it follows from Equation

12 and Equation 13 thatv frac14 vs eth14THORN

and

a frac14 vv eth15THORN

Box 11

VIBRATION INSTRUMENTATION

Vibration Testing Applications for Products

Design and Development Production Screening and Quality Assessment Utilization and Qualification for Special Applications

Testing Instrumentation

Exciter (excites the test object) Controller (controls the exciter for accurate excitation) Sensors and Transducers (measure excitations and responses and provide excitation error

signals to controller) Signal Conditioning (converts signals to appropriate form) Recording and Display (perform processing storage and documentation)

Exciters

Shakers

1 Electrodynamic (high bandwidth moderate power complex and multifrequency

excitations)

2 Hydraulic (moderate to high bandwidth high power complex and multifrequency

excitations)

3 Inertial (low bandwidth low power single-frequency harmonic excitations)

TransientInitial Condition

1 Hammers (impulsive bump tests)

2 Cable Release (step excitations)

3 Drop (impulsive)

Signal Conditioning

Filters Amplifiers Amplifiers ModulatorsDemodulators ADCDAC

Sensors

Motion (displacement velocity acceleration) Force (strain torque)




TABLE 11 Typical Operation-Capability Ranges for Various Shaker Types

Shaker Type Typical Operational Capabilities

Frequency Maximum Displacement

(Stroke)

Maximum

Velocity

Maximum

Acceleration

Maximum

Force

Excitation

Waveform

Hydraulic

(electrohydraulic)

Low

(01ndash500 Hz)

High (20 in 50 cm) Intermediate

(50 insec

125 cmsec)

Intermediate

(20 g)

High (100000 lbf

450000 N)

Average flexibility (simple

to complex and random)

Inertial

(counter-rotating mass)

Intermediate

(2ndash50 Hz)

Low (1 in 25 cm) Intermediate

(50 insec

125 cmsec)

Intermediate

(20 g)

Intermediate

(1000 lbf 4500 N)

Sinusoidal only

Electromagnetic

(electrodynamic)

High

(2ndash10000 Hz)


(50 insec

125 cmsec)

High (100 g) Low to intermediate

(450 lbf 2000 N)

High flexibility and accuracy

(simple to complex and

random)

VibrationInstru

mentation

1-5

53191mdash522007mdash

1201mdashSENTHILKUMARmdash246494mdash

CRCndashpp1ndash112


An idealized performance curve of a shaker

has a constant displacementndashamplitude region a

constant velocityndashamplitude region and a con-

stant accelerationndashamplitude region for low

intermediate and high frequencies respectively

in the operating frequency range Such an ideal

performance curve is shown in Figure 13(a) on a

frequencyndashvelocity plane Logarithmic axes are

used In practice typical shaker performance

curves would be fairly smooth yet nonlinear

curves similar to those shown in Figure 13(b)

As the mass increases the performance curve

compresses Note that the acceleration limit of a

shaker depends on the mass of the test object

(load) Full load corresponds to the heaviest object

that could be tested The ldquono loadrdquo condition

corresponds to a shaker without a test object To

standardize the performance curves they are

usually defined at the rated load of the shaker A

performance curve in the frequencyndashvelocity

plane may be converted to a curve in the

frequencyndashacceleration plane simply by increasing

the slope of the curve by a unit magnitude (ie

20 dbdecade)

Several general observations can be made from

Equation 14 and Equation 15 In the constant-

peak displacement region of the performance

curve the peak velocity increases proportionally

with the excitation frequency and the peak

acceleration increases with the square of the excitation frequency In the constant-peak velocity region

the peak displacement varies inversely with the excitation frequency and the peak acceleration increases

proportionately In the constant-peak acceleration region the peak displacement varies inversely with the

square of the excitation frequency and the peak velocity varies inversely with the excitation frequency

This further explains why rated stroke maximum velocity and maximum acceleration values are not

simultaneously realized

121 Shaker Selection

Vibration testing is accomplished by applying a specified excitation to the test package using a shaker

apparatus and monitoring the response of the test object Test excitation may be represented by its

response spectrum The test requires that the response spectrum of the actual excitation known as the

test response spectrum (TRS) envelops the response spectrum specified for the particular test known as

the required response spectrum (RRS)

A major step in the planning of any vibration testing program is the selection of a proper shaker

(exciter) system for a given test package The three specifications that are of primary importance in

selecting a shaker are the force rating the power rating and the stroke (maximum displacement) rating

Force and power ratings are particularly useful in moderate to high frequency excitations and the stroke

rating is the determining factor for low frequency excitations In this section a procedure is given to

determine conservative estimates for these parameters in a specified test for a given test package

Frequency domain considerations are used here

Stroke

Limit M

ax

Acceleration

MaxVelocity

Peak

Vel

ocity

(cm

s)

01 1 10 100

FullLoad

NoLoad

Frequency (Hz)(a)

Peak

Vel

ocity

(cm

s)

100

10

1

100

10

1

01 1 10 100

FullLoad

NoLoad

Frequency (Hz)(b)

FIGURE 13 Performance curve of a vibration exciter

in the frequencyndashvelocity plane (log) (a) ideal (b)

typical




1211 Force Rating

In the frequency domain the (complex) force at the exciter (shaker) head is given by

F frac14 mHethvTHORNasethvTHORN eth16THORNin which v is the excitation frequency variable m is the total mass of the test package including

mounting fixture and attachments asethvTHORN is the Fourier spectrum of the support-location (exciter head)

acceleration and H(v) is frequency response function that takes into account the flexibility and

damping effects (dynamics) of the test package apart from its inertia In the simplified case where the

test package can be represented by a simple oscillator of natural frequency vn and damping ratio by zt

this function becomes

HethvTHORN frac14 1thorn 2jztv=vn=12 ethv=vnTHORN2 thorn 2jztv=vn eth17THORNin which j frac14 ffiffiffiffi

21p

This approximation is adequate for most practical purposes The static weight of the

test object is not included in Equation 16 Most heavy-duty shakers which are typically hydraulic

have static load support systems such as pneumatic cushion arrangements that can exactly balance the

dead load The exciter provides only the dynamic force In cases where shaker directly supports the

gravity load in the vertical test configuration Equation 16 should be modified by adding a term to

represent this weight

A common practice in vibration test applications is to specify the excitation signal by its response

spectrum This is simply the peak response of a simple oscillator expressed as a function of its natural

frequency when its support location is excited by the specified signal Clearly the damping of the simple

oscillator is an added parameter in a response spectrum specification Typical damping ratios ethzrTHORN used inresponse spectra specifications are less than 01 (or 10) It follows that an approximate relationship

between the Fourier spectrum of the support acceleration and its response spectrum is

as frac14 2jzrarethvTHORN eth18THORNThe magnitude larethvTHORNl is the response spectrumEquation 18 substituted into Equation 16 gives

F frac14 mHethvTHORN2jzrarethvTHORN eth19THORNIn view of Equation 17 for test packages having low damping the peak value of H(v) is

approximately 1=eth2jztTHORN this should be used in computing the force rating if the test package has a

resonance within the frequency range of testing On the other hand if the test package is assumed to be

rigid then HethvTHORN oslash 1 A conservative estimate for the force rating is

Fmax frac14 methzr=ztTHORNlarethvTHORNlmax eth110THORNIt should be noted that larethvTHORNlmax is the peak value of the specified (required) response spectrum (RRS)

for acceleration

1212 Power Rating

The exciter head does not develop its maximum force when driven at maximum velocity Output power

is determined by using

p frac14 Refrac12FvsethvTHORN eth111THORNin which vsethvTHORN is the Fourier spectrum of the exciter velocity and Re [ ] denotes the real part of a complex

function Note that as frac14 jvvs Substituting Equation 16 and Equation 18 into Equation 111 gives

p frac14 eth4mz2r =vTHORNRefrac12jHethvTHORNa2r ethvTHORN eth112THORNIt follows that a conservative estimate for the power rating is

pmax frac14 2methz2r =ztTHORNfrac12larethvTHORNl2=v max eth113THORN




Representative segments of typical acceleration RRS curves have slope n as given by

a frac14 k1vn eth114THORN

It should be clear from Equation 113 that the maximum output power is given by

pmax frac14 k2v2n21 eth115THORN

This is an increasing function for n 1=2 and a decreasing function for n 1=2 It follows that the power

rating corresponds to the highest point of contact between the acceleration RRS curve and a line of slope

equal to 12 A similar relationship may be derived if velocity RRS curves (having slopes n2 1) are used

1213 Stroke Rating

From Equation 18 it should be clear that the Fourier spectrum xs of the exciter displacement time

history can be expressed as

xs frac14 2zrarethvTHORN=jv2 eth116THORNAn estimate for stroke rating is

xmax frac14 2zrfrac12larethvTHORNl=v2 max eth117THORNThis is of the form

xmax frac14 kvn22 eth118THORNIt follows that the stroke rating corresponds to the highest point of contact between the acceleration

RRS curve and a line of slope equal to two

Example 11

A test package of overall mass 100 kg is to be

subjected to dynamic excitation represented by the

acceleration RRS (at 5 damping) as shown in

Figure 14 The estimated damping of the test

package is 7 The test package is known to have a

resonance within the frequency range of the

specified test Determine the exciter specifications

for the test

Solution

From the development presented in the previous

section it is clear that the point F (or P) in

Figure 14 corresponds to the force and output

power ratings and the point S corresponds to

the stroke rating The co-ordinates of these

critical points are F P frac14 eth42 Hz 40 gTHORN and S frac14 eth08 Hz 075 gTHORN Equation 110 gives the force

rating as

Fmax frac14 100 pound eth005=007THORN pound 40 pound 981 N frac14 2803 N

Equation 113 gives the power rating as

pmax frac14 2 pound 100 pound eth0052=007THORN pound frac12eth40 pound 981THORN2=42 pound 2p watts frac14 417 W

Equation 117 gives the stroke rating as

xmax frac14 2 pound 005 pound frac12eth075 pound 98THORN=eth08 pound 2pTHORN2 m frac14 3 cm

Acc

eler

atio

n(g

)

Con

stan

t Dis

plac

emen

t

Constant Velo

city

Frequency (Hz)

S

FP

0101

10 10 100

10

10

FIGURE 14 Test excitation specified by an accelera-

tion RRS (5 damping)




1214 Hydraulic Shakers

A typical hydraulic shaker consists of a piston-cylinder arrangement (also called a ram) a servo-valve a

fluid pump and a driving electric motor Hydraulic fluid (oil) is pressurized (typical operating pressure

4000 psi) and pumped into the cylinder through a servo-valve by means of a pump that is driven by an

electric motor (typical power 150 hp) The flow (typical rate 100 galmin) that enters the cylinder is

controlled (modulated) by the servo-valve which in effect controls the resulting piston (ram) motion

A typical servo-valve consists of a two-stage spool valve which provides a pressure difference and a

controlled (modulated) flow to the piston which sets it in motion

The servo-valve itself is moved by means of a linear torque motor which is driven by the excitation-

input signal (electrical) A primary function of the servo-valve is to provide a stabilizing feedback to the

ram In this respect the servo-valve complements the main control system of the test setup The ram is

coupled to the shaker table by means of a link with some flexibility The cylinder frame is mounted on the

support foundation with swivel joints This allows for some angular and lateral misalignment which

might be caused primarily by test-object dynamics as the table moves

Two-degree-of-freedom (Two-DoF) testing requires two independent sets of actuators and three-DoF

testing requires three independent actuator sets Each independent actuator set can consist of several

actuators operated in parallel using the same pump and the same excitation-input signal to the torque

motors

If the test table is directly supported on the vertical actuators they must withstand the total dead

weight (ie the weight of the test table the test object the mounting fixtures and the instrumentation)

This is requirement is usually prevented by providing a pressurized air cushion in the gap between the

test table and the foundation walls Air should be pressurized so as to balance the total dead weight

exactly (typical required gage pressure 3 psi)

Figure 15(a) shows the basic components of a typical hydraulic shaker The corresponding

operational block diagram is shown in Figure 15(b) It is desirable to locate the actuators in a pit in the

test laboratory so that the test tabletop is flushed with the test laboratory floor under no-load conditions

This minimizes the effort required to place the test object on the test table Otherwise the test object has

to be lifted onto the test table with a forklift Also installation of an aircushion to support the system

dead weight is difficult under these circumstances of elevated mounting

Hydraulic actuators are most suitable for heavy load testing and are widely used in industrial and civil

engineering applications They canbeoperated at very low frequencies (almost direct current [DC]) aswell

as at intermediate frequencies (see Table 11) Large displacements (stroke) are possible at low frequencies

Hydraulic shakers have the advantage of providing high flexibility of operation during the test their

capabilities include variable-force and constant-force testing and wide-band random-input testing The

velocity and acceleration capabilities of hydraulic shakers are moderate Although any general excitation-

input motion (for example sine wave sine beat wide-band random) can be used in hydraulic shakers

faithful reproduction of these signals is virtually impossible at high frequencies because of distortion and

higher-order harmonics introduced by the high noise levels that are common in hydraulic systems This

is only a minor drawback in heavy-duty intermediate-frequency applications Dynamic interactions are

reduced through feedback control

1215 Inertial Shakers

In inertial shakers or ldquomechanical excitersrdquo the force that causes the shaker-table motion is generated by

inertia forces (accelerating masses) Counter-rotating-mass inertial shakers are typical in this category

To understand their principle of operation consider two equal masses rotating in opposite directions at

the same angular speed v and in the same circle of radius r (see Figure 16) This produces a resultant

force equal to 2mv2r cos vt in a fixed direction (the direction of symmetry of the two rotating arms)

Consequently a sinusoidal force with a frequency of v and an amplitude proportional to v2 is generated

This reaction force is applied to the shaker table

Figure 17 shows a sketch of a typical counter-rotating-mass inertial shaker It consists of two identical

rods rotating at the same speed in opposite directions Each rod has a series of slots in which to




place weights In this manner the magnitude of

the eccentric mass can be varied to achieve various

force capabilities The rods are driven by a

variable-speed electric motor through a gear

mechanism that usually provides several speed

ratios A speed ratio is selected depending on the

required test-frequency range The whole system is

symmetrically supported on a carriage that is

directly connected to the test table The test object

is mounted on the test table The preferred

mounting configuration is horizontal so that the

excitation force is applied to the test object in a

horizontal direction In this configuration there

are no variable gravity moments (weight pounddistance to center of gravity) acting on the drive

mechanism Figure 17 shows the vertical con-

figuration In dynamic testing of large structures

the carriage can be mounted directly on the

structure at a location where the excitation force

should be applied By incorporating two pairs of

counter-rotating masses it is possible to generate

test moments as well as test forces

FIGURE 15 A typical hydraulic shaker arrangement (a) schematic diagram (b) operational block diagram

m m

2mw2r cos wt

wtw w

wt

FIGURE 16 Principle of operation of a counter-

rotating-mass inertial shaker




Reaction-type shakers driven by inertia are widely used for the prototype testing of civil engineering

structures Their first application dates back to 1935 Inertial shakers are capable of producing

intermediate excitation forces The force generated is limited by the strength of the carriage frame The

frequency range of operation and the maximum velocity and acceleration capabilities are also

intermediate for inertial shakers whereas the maximum displacement capability is typically low A major

limitation of inertial shakers is that their excitation force is exclusively sinusoidal and that the force

amplitude is directly proportional to the square of the excitation frequency As a result complex and

random excitation testing constant-force testing (for example transmissibility tests and constant-force

sine-sweep tests) and flexibility to vary the force amplitude or the displacement amplitude during a test

are not generally feasible with this type of shakers Excitation frequency and amplitude can be varied

during testing however by incorporating a variable-speed drive for the motor The sinusoidal excitation

generated by inertial shakers is virtually undistorted which gives them an advantage over the other types

of shakers when used in sine-dwell and sine-sweep tests Small portable shakers with low-force capability

are available for use in on-site testing

1216 Electromagnetic Shakers

In electromagnetic shakers or ldquoelectrodynamic excitersrdquo the motion is generated using the principle of

operation of an electric motor Specifically the excitation force is produced when a variable excitation

signal (electrical) is passed through a moving coil placed in a magnetic field

The components of a commercial electromagnetic shaker are shown in Figure 18 A steady magnetic

field is generated by a stationary electromagnet that consists of field coils wound on a ferromagnetic base

that is rigidly attached to a protective shell structure The shaker head has a coil wound around it When

the excitation electrical signal is passed through this drive coil the shaker head which is supported on

flexure mounts will be set in motion The shaker head consists of the test table on which the test object

is mounted Shakers with interchangeable heads are available The choice of appropriate shaker head is

based on the geometry and mounting features of the test object The shaker head can be turned to

different angles by means of a swivel joint In this manner different directions of excitation (in biaxial

and triaxial testing) can be obtained

FIGURE 17 Sketch of a counter-rotating-mass inertial shaker




122 Dynamics of Electromagnetic Shakers

Consider a single axis electromagnetic shaker (Figure 18) with a test object having a single natural

frequency of importance within the test frequency range The dynamic interactions between the shaker

and the test object give rise to two significant natural frequencies (and correspondingly two significant

resonances) These appear as peaks in the frequency response curve of the test setup Furthermore the

natural frequency (resonance) of the test package alone causes a ldquotroughrdquo or depression (antiresonance)

in the frequency response curve of the overall test setup To explain this characteristic consider the

dynamic model shown in Figure 19 The following mechanical parameters are defined for

Figure 19(a) m k and b are the mass stiffness and equivalent viscous damping constant respectively

of the test package and me ke and be are the corresponding parameters of the exciter (shaker) Also in

the equivalent electrical circuit of the shaker head as shown in Figure 19(b) the following electrical

parameters are defined Re and Le are the resistance and (leakage) inductance and kb is the back

electromotive force (back emf) of the linear motor Assuming that the gravitational forces are supported

FIGURE 18 Schematic sectional view of a typical electromagnetic shaker manufactured by Bruel and Kjaer

Denmark




by the static deflections of the flexible elements and that the displacements are measured from the static

equilibrium position we have the following system equations

Test object meuroy frac14 2kethy2 yeTHORN2 beth_y2 _yeTHORN eth119THORNShaker head me euroye frac14 fe thorn kethy2 yeTHORN thorn beth_y2 _yeTHORN2 key 2 be _ye eth120THORN

Electrical Lediedt

thorn Reie thorn kb _ye frac14 vethtTHORN eth121THORN

The electromagnetic force fe generated in the shaker head is a result of the interaction of the magnetic

field generated by the current ie with coil of the moving shaker head and the constant magnetic field

(stator) in which the head coil is located Here we have

fe frac14 kbie eth122THORNNote that v(t) is the voltage signal that is applied by the amplifier to the shaker coil ye is the displacement

of the shaker head and y is the displacement response of the test package

It is assumed that kb has consistent electrical and mechanical units (Vmsec and NA) Usually

the electrical time constant of the shaker is quite small compared with the primarily mechanical

time constants of the shaker and the test package In such cases the Ledie=dt term in Equation 121 may

be neglected Consequently the equations from Equation 119 through Equation 122 may be

expressed in the Laplace (frequency) domain with the Laplace variable s taking the place of the derivative

d=dt as

ethms2 thorn bsthorn kTHORNy frac14 ethbsthorn kTHORNye eth123THORN

FIGURE 19 Dynamic models of an electromagnetic shaker and a flexible test package (a) mechanical model

(b) electrical model




frac12mes2 thorn ethbthorn beTHORNsthorn ethkthorn keTHORN ye frac14 ethbsthorn kTHORNy thorn kb

Rev2

k2bs

Reye eth124THORN

It follows that the transfer function of the shaker head motion with respect to the excitation voltage is

given by

yevfrac14 kb

Re

DethsTHORNDdethsTHORN eth125THORN

where DethsTHORN is the characteristic function of the primary dynamics of the test object

DethsTHORN frac14 ms2 thorn bsthorn k eth126THORN

and DdethsTHORN is the characteristic function of the primary dynamic interactions between the shaker and thetest object

DcethsTHORN frac14 mmes4 thorn frac12methbe thorn bthorn boTHORN thornmeb s

3 thorn frac12methke thorn kTHORN thornmekthorn bethbe thorn boTHORN s2thorn frac12bke thorn ethbe thorn boTHORNk sthorn kke

eth127THORN

where

bo frac14 k2bRe

eth128THORN

It is clear that under low damping conditions DdethsTHORN will produce two resonances as it is fourth order in sand similarly DethsTHORN will produce one antiresonance (trough) corresponding to the resonance of the testobject Note that in the frequency domain s frac14 jv and hence the frequency response function given by

Equation 125 is in fact

yevfrac14 kb

Rb

DethjvTHORNDdethjvTHORN eth129THORN

The magnitude of this frequency response function for a typical test system is sketched in Figure 110

Note that this curve is for the ldquoopen-looprdquo case where there is no feedback from the shaker controller

In practice the shaker controller will be able

to compensate for the resonances and anti-

resonances to some degree depending on its

effectiveness

The main advantages of electromagnetic

shakers are their high frequency range of

operation their high degree of operating flexi-

bility and the high level of accuracy of the

generated shaker motion Faithful reproduction

of complex excitations is possible because of the

advanced electronics and control systems used in

this type of shakers Electromagnetic shakers are

not suitable for heavy-duty applications (large test

objects) however High test-input accelerations

are possible at high frequencies when electromag-

netic shakers are used but their displacement and

velocity capabilities are limited to low or

intermediate values (see Table 11)

100

10

1 10 100Excitation Frequency (Hz)

Antiresonance

Resonance

Shak

erD

ispl

acem

entM

agni

tude

Resonance

1000

FIGURE 110 Frequency response curve of a typical

electromagnetic shaker with a test object




1221 Transient Exciters

Other varieties of exciters are commonly used in

transient-type vibration testing In these tests

either an impulsive force or an initial excitation is

applied to the test object and the resulting

response is monitored The excitations and the

responses are ldquotransientrdquo in this case Hammer

test drop tests and pluck tests fall into this

category For example a hammer test may be

conducted by hitting the object with an instru-

mented hammer and then measuring the response

of the object The hammer has a force sensor at its

tip as sketched in Figure 111 A piezoelectric or

strain-gage type force sensor may be used More

sophisticated hammers have impedance heads in

place of force sensors An impedance head

measures force and acceleration simultaneously

The results of a hammer test will depend on many

factors for example the dynamics of the hammer

body how firmly the hammer is held during the

impact how quickly the impact is applied and

whether there are multiple impacts

13 Control System

The two primary functions of the shaker control system in vibration testing are (1) to guarantee that the

specified excitation is applied to the test object and (2) to ensure that the dynamic stability (motion

constraints) of the test setup is preserved An operational block diagram illustrating these control

functions is given in Figure 112 The reference input to the control system represents the desired

excitation force that should be applied to the test object In the absence of any control however the force

reaching the test object will be distorted primarily because of (1) dynamic interactions and

nonlinearities of the shaker the test table the mounting fixtures the auxiliary instruments and the test

object itself (2) noise and errors in the signal generator amplifiers filters and other equipment and (3)

external loads and disturbances acting on the test object and other components (for example external

restraints aerodynamic forces friction) To compensate for these distorting factors response

measurements (displacements velocities acceleration and so on) are made at various locations in the

test setup and are used to control the system dynamics In particular the responses of the shaker the test

table and the test object are measured These responses are used to compare the actual excitation felt by

FIGURE 111 An instrumented hammer used in bump

tests or hammer tests

ExcitationInput

(Reference)

Feedback Paths

DriveSignal

ShakerResponse

TestTable

TestObject

Test ObjectResponse

Test TableResponseExciter

(Shaker)(Ram)

Controllerand

Amplifier

FIGURE 112 Operational block diagram illustrating a general shaker control system




the test object at the shaker interface with the desired (specified) input The drive signal to the shaker is

modified depending on the error that is present

Two types of control are commonly employed in shaker apparatus simple manual control and

complex automatic control Manual control normally consists of simple open-loop trial-and-error

methods of manual adjustments (or calibration) of the control equipment to obtain a desired dynamic

response The actual response is usually monitored (on an oscilloscope or frequency analyzer screen for

example) during manual-control operations The pretest adjustments in manual control can be very

time-consuming as a result the test object might be subjected to overtesting which could produce

cumulative damage is undesirable and could defeat the test purpose Furthermore the calibration

procedure for the experimental setup must be repeated for each new test object

The disadvantages ofmanual control suggest that automatic control is desirable in complex test schemes

in which high accuracy of testing is desired The first step of automatic control involves automatic

measurement of the system response using control sensors and transducers The measurement is then fed

back into the control system which instantaneously determines the best drive signal to actuate the shaker

in order to get the desired excitation This may be done by either analog or digital methods

Primitive control systems require an accurate mathematical description of the test object This

dependency of the control system on the knowledge of test-object dynamics is clearly undesirable

Performance of a good control system should not be considerably affected by the dynamic interactions

and nonlinearities of the test object or by the nature of the excitation Proper selection of feedback signals

and control-system components can reduce such effects and will make the system robust

In the response-spectrum method of vibration testing it is customary to use displacement control at

low frequencies velocity control at intermediate frequency and acceleration control at high frequencies

This necessitates feedback of displacement velocity and acceleration responses Generally however the

most important feedback is the velocity feedback In sine-sweep tests the shaker velocity must change

steadily over the frequency band of interest In particular the velocity control must be precise near the

resonances of the test object Velocity (speed) feedback has a stabilizing effect on the dynamics which is

desirable This effect is particularly useful in ensuring stability in motion when testing is done near

resonances of lightly damped test objects On the contrary displacement (position) feedback can have a

destabilizing effect on some systems particularly when high feedback gains are used

The controller usually consists of various instruments equipment and computation hardware and

software Often the functions of the data-acquisition and processing system overlap with those of the

controller to some extent As an example consider the digital-controller of vibration testing apparatus

First the responses are measured through sensors (and transducers) filtered and amplified

(conditioned) These data channels may be passed through a multiplexer whose purpose is to select

one data channel at a time for processing Most modern data acquisition hardware does not need a

separate multiplexer to handle multiple signals The analog data are converted into digital data using

analog-to-digital converters (ADCs) The resulting sampled data are stored on a disk or as a block data in

the computer memory The reference input signal (typically a signal recorded on an FM tape) is also

sampled (if it is not already in the digital form) using an ADC and fed into the computer Digital

processing is done on the reference signal and the response data with the objective of computing the

command signal to drive the shaker The digital command signal is converted into an analog signal using

a digital-to-analog converter (DAC) and amplified (conditioned) before it is used to drive the exciter

The nature of the control components depends to a large extent on the nature and objectives of the

particular test to be conducted Some of the basic components in a shaker controller are described in

the following subsections

131 Components of a Shaker Controller

1311 Compressor

A compressor circuit is incorporated in automatic excitation control devices to control the excitation-

input level automatically The level of control depends on the feedback signal from a control sensor and




the specified (reference) excitation signal Usually the compressor circuit is included in the excitation-

signal generator (for example in a sine generator) The control by this means may be done on the basis of

a single-frequency component (eg the fundamental frequency)

1312 Equalizer (Spectrum Shaper)

Random-signal equalizers are used to shape the spectrum of a random signal in a desired manner In

essence and equalizer consists of a bank of narrow-band filters (for example 80 filters) in parallel over

the operating frequency range By passing the signal through each filter the spectral density (or the mean

square value) of the signal in that narrow frequency band (for example each one-third-octave band) is

determined This is compared with the desired spectral level and automatic adjustment is made in that

filter in case there is an error In some systems response-spectrum analysis is made in place of power

spectral density analysis In that case the equalizer consists of a bank of simple oscillators whose

resonant frequencies are distributed over the operating frequency range of the equalizer The feedback

signal is passed through each oscillator and the peak value of its output is determined This value is

compared with the desired response spectrum value at that frequency If there is an error automatic gain

adjustment is made in the appropriate excitation signal components

Random-noise equalizers are used in conjunction with random signal generators They receive

feedback signals from the control sensors In some digital control systems there are algorithms (software)

that are used to iteratively converge the spectrum of the excitation signal felt by the test object into the

desired spectrum

1313 Tracking Filter

Many vibration tests are based on single-frequency excitations In such cases the control functions

should be performed on the basis of the amplitudes of the fundamental-frequency component of the

signal A tracking filter is simply a frequency-tuned band-pass filter It automatically tunes the center

frequency of its very narrow-band-pass filter to the frequency of a carrier signal Then when a noisy

signal is passed through the tuned filter the output of the filter will be the required fundamental

frequency component in the signal Tracking filters also are useful in obtaining amplitudendashfrequency

plots using an XndashY plotter In such cases the frequency value comes from the signal generator (sweep

oscillator) which produces the carrier signal to the tracking filter The tracking filter then determines the

corresponding amplitude of a signal that is fed into it Most tracking filters have dual channels so that two

signals can be handled (tracked) simultaneously

1314 Excitation Controller (Amplitude Servo-Monitor)

An excitation controller is typically an integral part of the signal generator It can be set so that automatic

sweep between two frequency limits can be performed at a selected sweep rate (linear or logarithmic)

More advanced excitation controllers have the capability of an automatic switch-over between constant-

displacement constant-velocity and constant-acceleration excitation-input control at specified

frequencies over the sweep frequency interval Consequently integrator circuits should be present

within the excitation controller unit to determine velocities and displacements from acceleration signals

Sometimes integration is performed by a separate unit called a vibration meter This unit also offers

the operator the capability of selecting the desired level of each signal (acceleration velocity or

displacement) There is an automatic cut-off level for large displacement values that could result from

noise in acceleration signals A compressor is also a subcomponent of the excitation controller The

complete unit is sometimes known as an amplitude servo-monitor

132 Signal-Generating Equipment

Shakers are force-generating devices that are operated using drive (excitation) signals generated from a

source The excitation-signal source is known as the signal generator Three major types of signal

generators are used in vibration testing applications (1) oscillators (2) random-signal generators and

(3) storage devices In some units oscillators and random-signal generators are combined We shall




discuss these two generators separately however because of their difference in function It also should be

noted that almost any digital signal (deterministic or random) can be generated by a digital computer

using a suitable computer program the signal eventually can be passed through a DAC to obtain

the corresponding analog signal These lsquodigitalrsquo signal generators along with analog sources such as

magnetic tape players (FM) are classified into the category of storage devices

The dynamic range of equipment is the ratio of the maximum and minimum output levels (expressed

in decibels) at which it is capable of operating without significant error This is an important specification

for many types of equipment particularly for signal-generating devices The output level of the signal

generator should be set to a value within its dynamic range

1321 Oscillators

Oscillators are essentially single-frequency generators Typically sine signals are generated but other

waveforms (such as rectangular and triangular pulses) are also available in most oscillators Normally

an oscillator has two modes of operation (1) sweeping up and down between two frequency limits and

(2) dwelling at a specified frequency In the sweep operation the sweep rate should be specified This can

be done either on a linear scale (Hzmin) or on a logarithmic scale (octavesmin) In the dwell operation

the frequency points (or intervals) should be specified In either case a desired signal level can be chosen

using the gain-control knob An oscillator that is operated exclusively in the sweep mode is called a sweep

oscillator

The early generation of oscillators employed variable inductor-capacitor types of electronic circuits to

generate signals oscillating at a desired frequency The oscillator is tuned to the required frequency by

varying the capacitance or inductance parameters A DC voltage is applied to energize the capacitor

and to obtain the desired oscillating voltage signal which subsequently is amplified and conditioned

Modern oscillators use operational amplifier circuits along with resistor capacitor and semiconductor

(SC) elements Also common are crystal (quartz) parallel-resonance oscillators used to generate voltage

signals accurately at a fixed frequency The circuit is activated using a DC-voltage source Other

frequencies of interest are obtained by passing this high-frequency signal through a frequency converter

The signal is then conditioned (amplified and filtered) Required shaping (for example rectangular

pulse) is obtained using a shape circuit Finally the required signal level is obtained by passing the

resulting signal through a variable-gain amplifier A block diagram of an oscillator illustrating various

stages in the generation of a periodic signal is given in Figure 113

A typical oscillator offers a choice of several (typically six) linear and logarithmic frequency ranges and

a sizable level of control capability (for example 80 dB) Upper and lower frequency limits in a sweep can

be preset on the front panel to any of the available frequency ranges Sweep-rate settings are continuously

DC Voltage

Oscillator

FrequencySpecification

FrequencyConverter

FilterAmplifier

ShaperPeriodicSignal

FrequencyCounter

Fixed-FrequencySignal

Variable-GainOutput

Amplifier

SignalSpecification

LevelSpecification

FIGURE 113 Block diagram of an oscillator-type signal generator




53191fm

Vibration Monitoring Testing and Instrumentation

Preface

Acknowledgments

Editor-in-Chief

Contributors

Contents

Related Titles

53191ch1

Table of Contents

Chapter 1 Vibration Instrumentation

Summary

11 Introduction



1211 Force Rating

1212 Power Rating

1213 Stroke Rating






13 Control System


1311 Compressor





1321 Oscillators

1322 Random Signal Generators

1323 Tape Players

1324 Data Processing

14 Performance Specification

141 Parameters for Performance Specification

1411 Time-Domain Specifications

1412 Frequency-Domain Specifications

142 Linearity

143 Instrument Ratings

1431 Rating Parameters

144 Accuracy and Precision

15 Motion Sensors and Transducers

151 Potentiometer

1511 Potentiometer Resolution

1512 Optical Potentiometer

152 Variable-Inductance Transducers

1521 Mutual-Induction Transducers

1522 Linear-Variable Differential Transformer

1523 Signal Conditioning

153 Mutual-Induction Proximity Sensor

154 Selfinduction Transducers

155 Permanent-Magnet Transducers

156 Alternating Current Permanent-Magnet Tachometer

157 Alternating Current Induction Tachometer

158 Eddy Current Transducers

159 Variable-Capacitance Transducers

1591 Capacitive Displacement Sensors

1592 Capacitive Angular Velocity Sensor

1593 Capacitance Bridge Circuit

1510 Piezoelectric Transducers

15101 Sensitivity

15102 Piezoelectric Accelerometer

15103 Charge Amplifier

16 Torque Force and Other Sensors

161 Strain Gage Sensors

1611 Equations for Strain Gage Measurements

1612 Bridge Sensitivity

1613 The Bridge Constant

1614 The Calibration Constant

1615 Data Acquisition

1616 Accuracy Considerations

1617 Semiconductor Strain Gages

1618 Force and Torque Sensors

1619 Strain Gage Torque Sensors

16110 Deflection Torque Sensors

16111 Variable-Reluctance Torque Sensor

16112 Reaction Torque Sensors

162 Miscellaneous Sensors

1621 Stroboscope

1622 Fiber Optic Sensors and Lasers

1623 Fiber-Optic Gyroscope

1624 Laser Doppler Interferometer

1625 Ultrasonic Sensors

1626 Gyroscopic Sensors

References

Appendix 1A Virtual Instrumentation for Data Acquisition Analysis and Presentation

Summary

List of Abbreviations

1A1 Dynamic Signals

1A11 Acquiring and Simulating Dynamic Signals

1A111 Aliasing

1A112 Time Continuity

1A2 Measurement Configuration Considerations

1A21 Input Signal Considerations

1A211 Input Pseudodifferential and Differential Configuration

1A212 Gain

1A213 Input Coupling

1A214 Integrated Electronic Piezoelectric Excitation

1A215 Nyquist Frequency and Bandwidth

1A216 Analog-to-Digital Conversion

1A217 Antialias Filters

1A218 Input Filter Delay

1A219 Overload Detection

1A22 Output Signal Considerations

1A221 Output Pseudodifferential and Differential Configuration

1A222 Attenuation

1A223 Digital-to-Analog Conversion

1A224 Anti-imaging and Interpolation Filters

1A225 Output Filter Delay

1A3 Scaling and Calibration

1A31 Scaling to Engineering Units

1A32 Performing System Calibration

1A321 Propagation Delay Calibration

1A4 Limit Testing Analysis

1A41 Limit Testing Overview

1A42 Using the SVT Limit Testing VI

1A5 Integration

1A51 Introduction to Integration

1A52 Implementing Integration

1A521 Challenges when Integrating Vibration Data

1A53 Time-Domain Integration

1A531 Single-Shot Acquisition and Integration

1A532 Continuous Acquisition and Integration

1A54 Frequency-Domain Integration

1A6 Vibration-Level Measurements

1A61 Measuring the Root Mean Square Level

1A611 Single-Shot Buffered Acquisition

1A612 Continuous Signal Acquisition

1A62 Performing a Running RMS Level Measurement

1A63 Computing the Peak Level

1A64 Computing the Crest Factor

1A7 Frequency Analysis

1A71 FFT Fundamentals

1A711 Number of Samples

1A712 Frequency Resolution

1A713 Maximum Resolvable Frequency

1A714 Minimum Resolvable Frequency

1A715 Number of Spectral Lines

1A716 Relationship between Time-Domain and Frequency-Domain Specifications and Parameters

1A72 Increasing Frequency Resolution

1A721 Zoom FFT Analysis

1A722 Frequency Resolution of the Zoom FFT VIs

1A723 Zoom Measurement

1A724 Zoom Settings

1A725 Subset Analysis

1A8 Transient Analysis

1A81 Transient Analysis with the Sound and Vibration Toolkit

1A82 Performing an STFT vs Time

1A821 Selecting the FFT Block Size

1A822 Overlapping

1A823 Using the SVT STFT vs Time VI

1A83 Performing an STFT vs Rotational Speed

1A831 Converting the Pulse Train to Rotational Speed

1A832 STFT vs RPM

1A84 Measuring a Shock Response Spectrum

1A9 Waterfall Display

1A91 Using the Display VIs

1A911 Initializing the Display

1A912 Sending Data to the Display

1A913 Waterfall Display for Frequency Analysis

1A914 Waterfall Display for Transient Analysis

1A915 Waterfall Display for Octave Spectra

1A10 Swept-Sine Measurements

1A101 Swept-Sine Overview

1A102 Choosing Swept-Sine vs FFT Measurements

1A103 Taking a Swept-Sine Measurement

1A104 Swept-Sine Measurement Example

Bibliography

Related Titles

53191ch2

Table of Contents

Chapter 2 Signal Conditioning and Modification

Summary

21 Introduction

22 Amplifiers

221 Operational Amplifier

222 Use of Feedback in Opamp

223 Voltage Current and Power Amplifiers

2231 Charge Amplifiers

224 Instrumentation Amplifiers

2241 Differential Amplifier

2242 Common Mode

225 Amplifier Performance Ratings

2251 Common-Mode Rejection Ratio

226 Component Interconnection

2261 Impedance Characteristics

2262 Cascade Connection of Devices

2263 AC-Coupled Ampliers

23 Analog Filters

231 Passive Filters and Active Filters

2311 Number of Poles

232 Low-Pass Filters

2321 Low-Pass Butterworth Filter

233 High-Pass Filters

234 Band-Pass Filters

2341 Resonance-Type Band-Pass Filters

235 Band-Reject Filters

24 Modulators and Demodulators

241 Amplitude Modulation

2411 Modulation Theorem

2412 Side Frequencies and Side Bands

242 Application of Amplitude Modulation

2421 Fault Detection and Diagnosis

243 Demodulation

25 Analog ndashDigital Conversion

251 Digital-to-Analog Conversion

2511 DAC Error Sources

252 Analog-to-Digital Conversion

253 Analog-to-Digital Converter Performance Characteristics

2531 Resolution and Quantization Error

2532 Monotonicity Nonlinearity and Offset Error

2533 Analog-to-Digital Converter Conversion Rate

254 Sample-and-Hold Circuitry

255 Digital Filters

2551 Software Implementation and Hardware Implementation

26 Bridge Circuits

261 Wheatstone Bridge

262 Constant-Current Bridge

263 Bridge Amplifiers

2631 Half-Bridge Circuits

264 Impedance Bridges

2641 Owen Bridge

2642 Wien-Bridge Oscillator

27 Linearizing Devices

271 Linearization by Software

272 Linearization by Hardware Logic

273 Analog Linearizing Circuitry

274 Offsetting Circuitry

275 Proportional-Output Circuitry

2751 Curve-Shaping Circuitry

28 Miscellaneous Signal Modification Circuitry

281 Phase Shifters

282 Voltage-to-Frequency Converter

283 Frequency-to-Voltage Converter

284 Voltage-to-Current Converters

285 Peak-Hold Circuits

29 Signal Analyzers and Display Devices

291 Signal Analyzers

292 Oscilloscopes

2921 Triggering

2922 Lissajous Patterns

2923 Digital Oscilloscopes

Bibliography

Related Titles

53191ch3

Table of Contents

Chapter 3 Vibration Testing

Summary

31 Introduction

32 Representation of a Vibration Environment

321 Test Signals

3211 Stochastic vs Deterministic Signals

322 Deterministic Signal Representation

3221 Single-Frequency Signals

3222 Sine Sweep

3223 Sine Dwell

3224 Decaying Sine

3225 Sine Beat

3226 Sine Beat with Pauses

3227 Multifrequency Signals

3228 Actual Excitation Records

3229 Simulated Excitation Signals

323 Stochastic Signal Representation

3231 Ergodic Random Signals

3232 Stationary Random Signals

3233 Independent and Uncorrelated Signals

3234 Transmission of Random Excitations

324 Frequency-Domain Representations

3241 Fourier Spectrum Method

3242 Power Spectral Density Method

325 Response Spectrum

3251 Displacement Velocity and Acceleration Spectra

3252 Response-Spectra Plotting Paper

3253 Zero-Period Acceleration

3254 Uses of Response Spectra

326 Comparison of Various Representations

33 Pretest Procedures

331 Purpose of Testing

332 Service Functions

3321 Active Equipment

3322 Passive Equipment

3323 Functional Testing

333 Information Acquisition

3331 Interface Details

3332 Effect of Neglecting Interface Dynamics

3333 Effects of Damping

3334 Effects of Inertia

3335 Effect of Natural Frequency

3336 Effect of Excitation Frequency

3337 Other Effects of Interface

334 Test-Program Planning

3341 Testing of Cabinet-Mounted Equipment

335 Pretest Inspection

34 Testing Procedures

341 Resonance Search

342 Methods of Determining Frequency-Response Functions

3421 Fourier Transform Method

3422 Spectral Density Method

3423 Harmonic Excitation Method

343 Resonance-Search Test Methods

3431 Hammer (Bump) Test and Drop Test

3432 Pluck Test

3433 Shaker Tests

344 Mechanical Aging

3441 Equivalence for Mechanical Aging

3442 Excitation-Intensity Equivalence

3443 Dynamic-Excitation Equivalence

3444 Cumulative Damage Theory

345 Test-Response Spectrum Generation

346 Instrument Calibration

347 Test-Object Mounting

348 Test-Input Considerations

3481 Test Nomenclature

3482 Testing with Uncorrelated Excitations

3483 Symmetrical Rectilinear Testing

3484 Geometry vs Dynamics

3485 Some Limitations

3486 Testing Black Boxes

3487 Phasing of Excitations

3488 Testing a Gray or White Box

3489 Overtesting in Multitest Sequences

35 Some Practical Information

351 Random Vibration Test Example

352 Vibration Shakers and Control Systems

Bibliography

Related Titles

53191ch4

Table of Contents

Chapter 4 Experimental Modal Analysis

Summary

41 Introduction

42 Frequency-Domain Formulation

421 Transfer-Function Matrix

422 Principle of Reciprocity

43 Experimental Model Development

431 Extraction of the Time-Domain Model

44 Curve Fitting of Transfer Functions

441 Problem Identification

442 Single- and Multi-Degree-of-Freedom Techniques

443 Single-Degree-of-Freedom Parameter Extraction in the Frequency Domain

4431 Circle-Fit Method

Case of Viscous Damping

Case of Hysteretic Damping

4432 Peak-Picking Method

444 Multi-Degree of Freedom Curve Fitting

4441 Formulation of the Method

445 A Comment on Static Modes and Rigid-Body Modes

446 Residue Extraction

45 Laboratory Experiments

451 Lumped-Parameter System

4511 Frequency-Domain Test

4512 Time-Domain Tests

452 Distributed-Parameter System

46 Commercial EMA Systems

461 System Configuration

4611 FFT Analysis Options

4612 Modal Analysis Components

Bibliography

Related Titles

53191ch5

Table of Contents

Chapter 5 Mechanical Shock

Summary

51 Definitions

511 Shock

512 Simple (or Perfect) Shock

513 Half-Sine Shock

514 Versed-Sine (or Haversine) Shock

515 Terminal Peak Sawtooth Shock or Final Peak Sawtooth Shock

516 Rectangular Shock

5161 Trapezoidal Shock

52 Description in the Time Domain

53 Shock Response Spectrum

531 Need

532 Shock Response Spectrum Definition

533 Response of a Linear One-Degree-of-Freedom System

5331 Shock Defined by a Force

5332 Shock Defined by an Acceleration

534 Definitions


5342 Absolute Acceleration Shock Response Spectrum

5343 Relative Displacement Shock Spectrum

5344 Primary Positive Shock Response Spectrum or Initial Positive Shock Response Spectrum

5345 Primary (or Initial) Negative Shock Response Spectrum

5346 Secondary (or Residual) Shock Response Spectrum

5347 Positive (or Maximum Positive) Shock Response Spectrum

5348 Negative (or Maximum Negative) Shock Response Spectrum

5349 Maximax Shock Response Spectrum

53410 Choice of Shock Response Spectrum

535 Standardized Shock Response Spectrum

5351 Definition

5352 Standardized Shock Response Spectra of Simple Shocks

53521 Half-Sine Pulse

53522 Versed Sine Pulse

53523 Terminal Peak Sawtooth Pulse

53524 Rectangular Pulse

53525 Trapezoidal Pulse

536 Choice of Damping

537 Shock Response Spectra Domains

538 Algorithms for Calculation of the Shock Response Spectra

539 Choice of the Digitization Frequency of the Signal

5310 Use of Shock Response Spectra for the Study of Systems with Several Degrees of Freedom

54 Pyroshocks

55 Use of Shock Response Spectra

551 Severity Comparison of Several Shocks

552 Test Specification Development from Real Environment Data

5521 Synthesis of Spectra

5522 Nature of the Specification

5523 Choice of Shape

5524 Amplitude

5525 Duration

5526 Difficulties

56 Standards

561 Types of Standards

562 Installation Conditions of Test Item

563 Uncertainty Factor

564 Bump Test

57 Damage Boundary Curve

571 Definition

572 Analysis of Test Results

58 Shock Machines

581 Main Types

582 Impact Shock Machines

5821 Universal Shock-Test Machines

58211 Impact Mode

58212 Impulse Mode

583 Shock Simulators (Programmers)


58311 Shock Duration

58312 Impact Velocity

58313 Maximum Deformation of the Shock Simulator (Programmer)

58314 Shock Amplitude

58315 Characteristics of the Target

5832 Terminal Peak Sawtooth Shock Pulse

5833 Rectangular Pulse ndash Trapezoidal Pulse

5834 Universal Shock Simulator (Programmer)

58341 Generating a Half-Sine Shock Pulse

58342 Generating a Terminal Peak Sawtooth Shock Pulse

58343 Trapezoidal Shock Pulse

584 Limitations

5841 Limitations of the Shock Machines

5842 Limitations of Shock Simulators

585 Pneumatic Machines

586 High Impact Shock Machines

5861 Lightweight High Impact Shock Machine

5862 Medium Weight High Impact Shock Machine

587 Specific Test Facilities

59 Generation of Shock Using Shakers

591 Principle Behind the Generation of a Simple Shape Signal versus Time

592 Main Advantages

593 Pre- and Postshocks

5931 Requirements

5932 Solutions

59321 Optimized Pre- and Postpulses

5933 Incidence on the Shock Response Spectra

594 Limitations of Electrodynamic Shakers

5941 Mechanical Limitations

59411 Abacuses

5942 Electronic Limitations

595 The Use of Electrohydraulic Shakers

510 Control by a Shock Response Spectrum

5101 Principle

5102 Principal Shapes of Elementary Signals

51021 Decaying Sinusoid

51022 ZERD Function

51023 WAVSIN Waveform

5103 Comparison of WAVSIN SHOC Waveforms and Decaying Sinusoid

5104 Criticism of Control by a Shock Response Spectrum

511 Pyrotechnic Shock Simulation

5111 Simulation Using Pyrotechnic Facilities

5112 Simulation Using Metal-to-Metal Impact

5113 Simulation Using Electrodynamic Shakers

5114 Simulation Using Conventional Shock Machines

References

Related Titles

53191ch6

Table of Contents

Chapter 6 Machine Condition Monitoring and Fault Diagnostics

Summary

61 Introduction

62 Machinery Failure

621 Causes of Failure

622 Types of Failure

623 Frequency of Failure

63 Basic Maintenance Strategies

631 Run-to-Failure (Breakdown) Maintenance

632 Scheduled (Preventative) Maintenance

633 Condition-Based (Predictive Proactive Reliability Centered On-Condition) Maintenance

64 Factors Which Influence Maintenance Strategy

65 Machine Condition Monitoring

651 Periodic Monitoring

652 Continuous Monitoring

66 Transducer Selection

661 Noncontact Displacement Transducers

662 Velocity Transducers

663 Acceleration Transducers

67 Transducer Location

68 Recording and Analysis Instrumentation

681 Vibration Meters

682 Data Collectors

683 Frequency-Domain Analyzers

684 Time-Domain Instruments

685 Tracking Analyzers

69 Display Formats and Analysis Tools

691 Time Domain

6911 Time-Waveform Analysis

6912 Time-Waveform Indices

6913 Time-Synchronous Averaging

6914 Negative Averaging

6915 Orbits

6916 Probability Density Functions

6917 Probability Density Moments

692 Frequency Domain

6921 Band-Pass Analysis

6922 Shock Pulse (Spike Energy)

6923 Enveloped Spectrum

6924 Signature Spectrum

6925 Cascades (Waterfall Plots)

6926 Masks

6927 Frequency-Domain Indices

693 Modal Domain

694 Quefrency Domain

610 Fault Detection

6101 Standards

61011 Standards Based on Machinery Type

61012 Standards Based on Vibration Severity

6102 Acceptance Limits

61021 Statistical Limits

6103 Frequency-Domain Limits

61031 Limited Band Monitoring

61032 Constant Bandwidth Limits

61033 Constant Percentage Bandwidth Limits

611 Fault Diagnostics

6111 Forcing Functions

61111 Unbalance

61112 Misalignment

61113 Mechanical Looseness

61114 Soft Foot

61115 Rubs

61116 Resonances

61117 Oil Whirl

61118 Oil Whip

61119 Structural Vibrations

611110 Foundation Problems

6112 Specific Machine Components

61121 Damaged or Worn Rolling-Element Bearings

61122 Damaged or Worn Gears

6113 Specific Machine Types

61131 Pumps

61132 Fans

61133 Electric Motors

61134 Steam and Gas Turbines

61135 Compressors

61136 Reciprocating Machines

6114 Advanced Fault Diagnostic Techniques

References

Related Titles

53191ch7

Table of Contents

Chapter 7 Vibration-Based Tool Condition Monitoring Systems

Summary

71 Introduction

72 Mechanics of Turning

721 General Terms

722 Chatter Vibrations

723 Tool Wear

7231 Tool Failure Mechanisms

7232 Tool Failure Modes

7233 Tool Wear Measurement

7234 Tool Wear Stages

73 Vibration Signal Recording

731 Direct and Indirect Systems

732 Sensor Requirements for Tool Wear Monitoring

733 Force Measurement

7331 Direct Measurement Dynamometers

7332 Indirect Force Sensors

7333 Piezoelectric Strain Sensors

7334 Resistance Strain Gauges

7335 Customized Force Sensors

734 Acceleration Measurement

735 Acoustic Emission Measurement

736 Sensor Comparisons

74 Signal Processing for Sensor-Based Tool Condition Monitoring

741 Feature Extraction

7411 Time Domain


7413 Statistical Processing

7414 TimendashFrequency Domain

742 Feature Selection

75 Wear ModelDecision-Making for Sensor-Based Tool Condition Monitoring

751 Trending Threshold

752 Neural Networks

7521 Unsupervised Networks

7522 Supervised Networks

753 Fuzzy Logic

754 Other Methods

76 Conclusion

References

Related Titles

53191ch8

Table of Contents

Chapter 8 Fault Diagnosis of Helicopter Gearboxes

Summary

81 Introduction

82 Abnormality Scaling

83 The Structure-Based Connectionist Network

84 Sensor Location Selection

841 Coverage Index

842 Overlap Index

843 Monitoring Effectiveness

85 A Case Study

851 Structural and Featural Influences

852 Evaluation of Influences

853 Fault Detection Results

854 Fault Diagnostic Results

8541 Faulty Subsystem Isolation

8542 Faulty Component Isolation

855 Sensor Location Evaluation

856 Sensor Location Validation

86 Conclusion

References

Related Titles

53191ch9

Table of Contents

Chapter 9 Vibration Suppression and Monitoring in Precision Motion Systems

Summary

91 Introduction

92 Mechanical Design to Minimize Vibration

921 Stability and Static Determinacy of Machine Structures

922 Two-Dimensional Structures

923 Three-Dimensional Structures

93 Adaptive Notch Filter

931 Fast Fourier Transform

932 Simulation and Experiments

94 Real-Time Vibration Analyzer

941 Learning Mode

942 Monitoring Mode

943 Diagnostic Mode

944 Experiments

9441 Input Variables mdash the Evaluation Criteria

94411 Monitoring Mode

94412 Diagnostic Mode

9442 Evaluation Rules



9443 Tests



95 Practical Insights and Case Study

96 Conclusions

References

Related Titles

53191ch10

Table of Contents

Chapter 10 Vibration and Shock Problems of Civil Engineering Structures

Summary

101 Introduction

102 Earthquake-Induced Vibration of Structures

1021 Seismicity and Ground Motions

1022 Influence of Local Site Conditions

1023 Response of Structures to Ground Motions

1024 Dynamic Analysis

10241 Equations of Motion for Linear Single-Degree-of-Freedom Systems

10242 Equations of Motion for Linear Multiple-Degree-of-Freedom Systems

1025 Earthquake Response Spectra

10251 Elastic Response Spectra

10252 Smoothed Design Spectra

10253 Ductility-Modified Response Spectrum Analysis

1026 Design Philosophy and the Code Approach

10261 Performance-Based Design

1027 Analysis Options for Earthquake Effects

10271 Dynamic Time History Analysis

10272 Response Spectrum Analysis

102721 Response Spectrum Analysis of Single-Degree-of-Freedom Systems

102722 Response Spectrum Analysis of Multi-Degree-of-Freedom Systems

10273 Equivalent Static Analysis (Force-Based Approach)

10274 Displacement-Based Approach

1028 SoilndashStructure Interaction

1029 Active and Passive Control Systems

10210 Worked Examples

103 Dynamic Effects of Wind Loading on Structures

1031 Introduction

1032 Wind Speed

1033 Design Structures for Wind Loading

10331 Types of Wind Design

10332 Design Criteria

10333 Static Analysis

1034 Along and Across-Wind Loading

10341 Along-Wind Loading

10342 Across-Wind Loading

1035 Wind Tunnel Tests

1036 Comfort Criteria Human Response to Building Motion

1037 Dampers

1038 Comparison with Earthquake Loading

104 Vibrations Due to Fluid ndashStructure Interaction

1041 Added Mass and Inertial Coupling

1042 Wave-Induced Vibration of Structure

105 Blast Loading and Blast Effects on Structures

1051 Explosions and Blast Phenomenon

1052 Explosive Air-Blast Loading

10521 Blast Wave Scaling Laws

10522 Prediction of Blast Pressure

1053 Gas Explosion Loading and Effect of Internal Explosions

1054 Structural Response to Blast Loading

10541 Elastic Single-Degree-of-Freedom Systems

10542 Elasto-Plastic Single-Degree-of-Freedom Systems

1055 Material Behaviors at High Strain Rate

10551 Dynamic Properties of Concrete under High Strain Rates

10552 Dynamic Properties of Reinforcing Steel under High Strain Rates

1056 Failure Modes of Blast-Loaded Structures

10561 Global Structural Behavior

10562 Localized Structural Behavior

10563 PressurendashImpulse ( PndashI ) Diagrams

1057 Blast WavendashStructure Interaction

1058 Effect of Ground Shocks

10581 Loads from Air-Induced Ground Shock

10582 Loads from Direct Ground Shock

1059 Technical Design Manuals for Blast-Resistant Design

10510 Computer Programs for Blast and Shock Effects

106 Impact Loading

1061 Structural Impact between Two Bodies mdash Hard Impact and Soft Impact

1062 Example mdash Aircraft Impact

107 Floor Vibration

1071 Introduction

1072 Types of Vibration

10721 Walking

10722 Rhythmic Activities

10723 Mechanical Equipment

10724 Analysis Methods

1073 Natural Frequency of Vibration

10731 Computing the Natural Frequency

10732 Computing Deflection

10733 Damping

10734 Resonance

1074 Vibration Caused by Walking

10741 Minimum Natural Frequency

1075 Design for Rhythmic Excitation

10751 Harmonics


1076 Example mdash Vibration Analysis of a Reinforced Concrete Floor

Bibliography

Related Titles

53191ch11

Table of Contents

Chapter 11 Seismic Base Isolation and Vibration Control

Summary

111 Introduction

1111 From Ductility Design to Base Isolation and Control Design

1112 The Importance of Reducing Seismic Input and Response

112 Seismic Base Isolation

1121 Historical Development of Base Isolation

1122 Basic Principle

1123 Issues in Seismic Base Isolation

11231 Performance Criteria

11232 Type of Structure

11233 Site Characteristics

11234 Retrofit Issues

11235 Design of Building Services

11236 Expected Life of Isolator

1124 Seismic Isolation Devices

11241 Laminated Rubber Bearings

11242 Lead Rubber Bearing

11243 Friction-Based Systems

11244 Other Systems

1125 Design of Isolation Devices

11251 High-Damping Rubber Bearing

112511 Stability against Buckling

112512 Stability against Roll Out

11252 Lead Rubber Bearings

112521 Design of Lead Plug

112522 Design of Laminated Rubber Bearing

11253 Design of Friction Pendulum System

1126 Verification of Properties of Isolation Systems

11261 Tests for Isolation Systems

112611 System Characterization Tests

112612 Prototype Tests

112613 Quality Control Tests

11262 Uniform Building Code Recommendations

112621 Units Dependent on Loading Rates

112622 Units Dependent on Bilateral Load

112623 System Adequacy

1127 Analysis of Base-Isolated Structures

11271 Modeling of a Superstructure

11272 Modeling of Isolation System

11273 Static Analysis Procedure

11274 Dynamic Analysis Procedure

112741 Response Spectrum Method

112742 Time-History Analysis

11275 Software for Analysis

1128 Experimental Methods for Isolated Structures

1129 Implementation of Seismic Isolation

11291 New Construction

112911 Buildings

112912 Bridges

11292 Seismic Retrofit

112921 Buildings

112922 Bridges

11293 Other Implementations

11210 Performance during Past Earthquakes

112101 Performance of Buildings

112102 Performance of Bridges

113 Seismic Vibration Control

1131 Historical Development of Seismic Vibration Control

1132 Basic Principles

11321 Passive Control System

11322 Active Control System

11323 Semiactive Control System

11324 Hybrid Control System

11325 Categorization of Basic Principles

1133 Important Issues in Vibration Control


11332 DevicendashStructure Interaction and Time Delay

11333 Design Guidelines

1134 Vibration-Control Devices

11341 Passive Control Systems

113411 Metallic Yielding Dampers

113412 Friction Dampers

113413 Viscoelastic Dampers

113414 Viscous Fluid Dampers

113415 Tuned Mass Dampers


113421 Electromagnetic Actuator

113422 Hydraulic Actuators


113431 Variable-Orifice Hydraulic Dampers

113432 Controllable Fluid Dampers

113433 Controllable Friction Dampers


1135 Control Algorithm



113521 Common Control Schemes for Controllable Dampers

113522 Special Control Schemes for Controllable Damper

1136 Experimental Performance Verification

11361 Shaking Table Tests of a Flexible Structural Model with TMD AMD and ATMD

11362 Substructure Hybrid Test

113621 Hybrid Tests Using Hydraulic Actuator

113622 Hybrid Tests Using Shaking Table

113623 Hybrid Tests Using Inertia-Force-Driven Loading System

1137 Implementations

11371 Semiactive Control of Full-Scale Structures Using Variable Joint Damper System

113711 Background of Study

113712 Test System Set Up


113714 Test Results

11372 Application of Structural Control Technologies to Seismic Retrofit of a Cable-Stayed Bridge


113722 Basic Concept of Seismic Retrofit

113723 Modal Shape Analysis


113725 Soil ndash Structure Interaction Effect

113726 Semiactive Control

Bibliography

Related Titles

53191ch12

Table of Contents

Chapter 12 Seismic Random Vibration of Long-Span Structures

Summary

121 Introduction

1211 Basic Concepts of Random Vibration

12111 Stationary Random Process

12112 Nonstationary Random Process

1212 Three Methods for Structural Seismic Analysis


12122 Time-History Method

12123 Random Vibration Method

121231 Davenport Approach

121232 Vanmarcke Approach

12124 Comparisons of the Three Seismic-Analysis Methods

122 Seismic Random-Excitation Fields

1221 Power Spectral Density of Spatially Varying Ground Acceleration

1222 Several Coherence Models

12221 FengndashHu Model

12222 Harichandran ndashVanmarcke Model

12223 LohndashYeh Model

12224 OliveirandashHaondashPenzien Model

12225 LucondashWong Model

12226 QundashWangndashWang Model

1223 Generation of Ground Acceleration Power Spectral Density Curves from Acceleration Response Spectrum Curves

12231 Kaul Method

12232 Iteration Scheme

1224 Seismic Equations of Motion of Long-Span Structures

1225 Seismic Waves and Their Geometrical Expressions

123 Pseudoexcitation Method for Structural Random Vibration Analysis

1231 Structures Subjected to Stationary Random Excitations

12311 Single Stationary Random Excitations

12312 Multiple Stationary Random Excitations

1232 Structures Subjected to Nonstationary Random Vibration

12321 Structures Subjected to Uniformly Modulated Evolutionary Random Excitations

123211 Single Excitation Problems

123212 Multiple Excitation Problems

12322 Structures Subjected to Nonuniformly Modulated Evolutionary Random Excitations



1233 Precise Integration Method

12331 Precise Integration of Exponential Matrices

12332 Particular Solutions and Precise Integration Formulas for Various Forms of Loading

123321 Linear Loading Form (HPD-L Form)

123322 Sinusoidal Loading Form (HPD-S Form)

123323 Exponentially Decaying Sinusoidal Loading Form (HPD-E Form)

124 Long-Span Structures Subjected to Stationary Random Ground Excitations

1241 The Solution of Equations of Motion Using the Pseudoexcitation Method

1242 Numerical Comparisons with Other Methods

12421 Song-Hua-Jiang Suspension Bridge

124211 All Supports Move Uniformly

124212 Wave Passage Effect Is Taken into Account

124213 Wave-Passage Effect and Incoherence Effect Are Jointly Taken into Account

12422 San Joaquin Concrete Bridge

125 Long-Span Structures Subjected to Nonstationary Random Ground Excitations

1251 Modulation Functions

1252 The Formulas for Nonstationary Multiexcitation Analysis

1253 Expected Extreme Values of Nonstationary Random Processes

1254 Numerical Comparisons with the Corresponding Stationary Analysis

126 Conclusions

References

Related Titles

53191ch13

Table of Contents

Chapter 13 Seismic Qualification of Equipment

Summary

131 Introduction

132 Distribution Qualification

1321 Drive-Signal Generation

1322 Distribution Spectra

1323 Test Procedures

133 Seismic Qualification

1331 Stages of Seismic Qualification

1332 Test Preliminaries

1333 Single-Frequency Testing

1334 Multifrequency Testing

1335 Generation of RRS Specifications

Bibliography

Related Titles

53191ch14

Table of Contents

Chapter 14 Human Response to Vibration

Summary

141 Introduction

142 Vibration Excitations on Humans

1421 Excitation Characteristics

143 Human Response to Vibration

1431 Vibration Perception

1432 Frequency Weighting Curve

1433 Iso-Perception Curves

1434 Detection Threshold Curve

144 Regulation of Human Vibration

1441 Acceptable Vibration Levels in Buildings

1442 Whole-Body Vibration

1443 HandndashArm Vibration

Bibliography

Related Titles

Mechanical Engineering SeriesFrank Kreith and Roop Mahajan - Series Editors

Published Titles

Computer Techniques in VibrationClarence W de SilvaDistributed Generation The Power Paradigm forthe New MillenniumAnne-Marie Borbely ampJan F KreiderElastoplasticity TheoryVlado A LubardaEnergy Audit of Building SystemsAn Engineering ApproachMoncefKrartiEngineering ExperimentationEuan SomerscalesEntropy Generation MinimizationAdrian BejanFinite Element Method Using MATLABreg2 n d EditionYoung W Kwon amp Hyochoong BangFluid Power Circuits and Controls Fundamentalsand ApplicationsJohn S CundiffFundamentals of Environmental DischargeModelingLorin R DavisHeat Transfer in Single and Multiphase SystemsGregF NatererIntroductory Finite Element MethodChandrakant S Desai amp Tribikram KunduIntelligent Transportation Systems New Principlesand ArchitecturesSumit Ghosh amp Tony LeeMathematical amp Physical Modeling of MaterialsProcessing OperationsOlusegun Johnson Ilegbusi Manabu Iguchi ampWalter E WahnsiedlerMechanics of Composite MaterialsAutarK Kaw

Mechanics of FatigueVladimir V BolotinMechanics of Solids and Shells Theories andApproximationsGerald Wempner amp Demosthenes TalaslidisMechanism Design Enumeration of KinematicStructures According to FunctionLung-Wen Tsai

The MEMS Handbook Second EditionMEMS Introduction and FundamentalsMEMS Design and FabricationMEMS Applications

Mohamed Gad-el-HakNanotechnology Understanding Small SystemsBen Rogers Jesse Adams amp Sumita PennathurNonlinear Analysis of StructuresM SathyamoorthyPractical Inverse Analysis in EngineeringDavid M Trujillo amp Henry R BusbyPressure Vessels Design and PracticeSomnath ChattopadhyayPrinciples of Solid MechanicsRowland Richards JrThermodynamics for EngineersKau-Fui WongVibration Damping Control and DesignClarence W de SilvaVibration Monitoring Testing and InstrumentationClarence W de SilvaVibration and Shock HandbookClarence W de SilvaViscoelastic SolidsRoderic S Lakes



Instrumentation

Edited by


Vancouver Canada

















TA355V5228 200762030287-dc22 2006100139




Preface




































v






efforts


Vancouver Canada

Prefacevi



Acknowledgments






vii



Editor-in-Chief
































ix



Contributors

xi








Singapore


Kyoto Japan


Science



Jalles France


Singapore


Technology

Singapore


Technology

Singapore




Technology

Singapore








Kyoto Japan




Singapore


Singapore





Contents


11 Introduction 1-1









21 Introduction 2-2

22 Amplifiers 2-2









31 Introduction 3-1






41 Introduction 4-1






xiii




51 Definitions 5-2



54 Pyroshocks 5-17


56 Standards 5-24







61 Introduction 6-2












71 Introduction 7-1





76 Conclusion 7-20


81 Introduction 8-1





86 Conclusion 8-23



91 Introduction 9-1




Contentsxiv




96 Conclusions 9-35


and Tuan Ngo 10-1





























Contents xv



1Vibration

Instrumentation


11 Introduction 1-1



Equipment












Summary


11 Introduction








1-1



















the object













6 Control devices


AnalogDigital

Interface

DigitalSignal


FilterAmplifier

FilterAmplifier

SignalGenerator



PowerAmplifier

MountingFixtures

TestObject

ResponseSensor

ControlSensor

Exciter

SwivelBase

















1 Test object

2 Excitation system

3 Control system




























SignalModification

System

TestObject

ControlSystem


System








and


Box 11







Exciters

Shakers


excitations)


excitations)





3 Drop (impulsive)

Signal Conditioning


Sensors








(Stroke)

Maximum

Velocity

Maximum

Acceleration

Maximum

Force

Excitation

Waveform

Hydraulic

(electrohydraulic)

Low

(01ndash500 Hz)


(50 insec

125 cmsec)

Intermediate

(20 g)

High (100000 lbf

450000 N)



Inertial


Intermediate

(2ndash50 Hz)


(50 insec

125 cmsec)

Intermediate

(20 g)

Intermediate

(1000 lbf 4500 N)

Sinusoidal only

Electromagnetic

(electrodynamic)

High

(2ndash10000 Hz)


(50 insec

125 cmsec)


(450 lbf 2000 N)



random)

VibrationInstru

mentation

1-5



CRCndashpp1ndash112

























20 dbdecade)

























Stroke

Limit M

ax

Acceleration

MaxVelocity

Peak

Vel

ocity

(cm

s)

01 1 10 100

FullLoad

NoLoad

Frequency (Hz)(a)

Peak

Vel

ocity

(cm

s)

100

10

1

100

10

1

01 1 10 100

FullLoad

NoLoad

Frequency (Hz)(b)



typical




1211 Force Rating









21p


















for acceleration

1212 Power Rating

















1213 Stroke Rating







Example 11








for the test

Solution







rating as






Acc

eler

atio

n(g

)

Con

stan

t Dis

plac

emen

t

Constant Velo

city

Frequency (Hz)

S

FP

0101

10 10 100

10

10























motors


























































m m

2mw2r cos wt

wtw w

wt



















































Denmark







Electrical Lediedt












d=dt as








Rev2

k2bs

Reye eth124THORN


given by

yevfrac14 kb

Re







eth127THORN

where

bo frac14 k2bRe

eth128THORN



yevfrac14 kb

Rb







effectiveness















100

10


Antiresonance

Resonance

Shak

erD

ispl

acem

entM

agni

tude

Resonance

1000




























13 Control System
















ExcitationInput

(Reference)

Feedback Paths

DriveSignal

ShakerResponse

TestTable

TestObject

Test ObjectResponse


(Shaker)(Ram)

Controllerand

Amplifier



















































1311 Compressor
























desired spectrum









































1321 Oscillators








oscillator
















DC Voltage

Oscillator


FrequencyConverter

FilterAmplifier


FrequencyCounter


Variable-GainOutput

Amplifier

SignalSpecification

LevelSpecification





53191fm


Preface

Acknowledgments

Editor-in-Chief

Contributors

Contents

Related Titles

53191ch1

Table of Contents


Summary

11 Introduction



1211 Force Rating

1212 Power Rating

1213 Stroke Rating






13 Control System


1311 Compressor





1321 Oscillators


1323 Tape Players






142 Linearity





151 Potentiometer


















15101 Sensitivity


















1621 Stroboscope






References


Summary


1A1 Dynamic Signals


1A111 Aliasing





1A212 Gain










1A222 Attenuation











1A5 Integration



























1A724 Zoom Settings






1A822 Overlapping




1A832 STFT vs RPM














Bibliography

Related Titles

53191ch2

Table of Contents


Summary

21 Introduction

22 Amplifiers







2242 Common Mode







23 Analog Filters















243 Demodulation










255 Digital Filters


26 Bridge Circuits






2641 Owen Bridge










281 Phase Shifters







292 Oscilloscopes

2921 Triggering



Bibliography

Related Titles

53191ch3

Table of Contents


Summary

31 Introduction


321 Test Signals




3222 Sine Sweep

3223 Sine Dwell

3224 Decaying Sine

3225 Sine Beat












































3432 Pluck Test

3433 Shaker Tests






















Bibliography

Related Titles

53191ch4

Table of Contents


Summary

41 Introduction



























Bibliography

Related Titles

53191ch5

Table of Contents


Summary

51 Definitions

511 Shock


513 Half-Sine Shock







531 Need





534 Definitions












5351 Definition












54 Pyroshocks







5524 Amplitude

5525 Duration

5526 Difficulties

56 Standards




564 Bump Test


571 Definition


58 Shock Machines

581 Main Types



58211 Impact Mode

58212 Impulse Mode














584 Limitations










592 Main Advantages


5931 Requirements

5932 Solutions





59411 Abacuses




5101 Principle



51022 ZERD Function









References

Related Titles

53191ch6

Table of Contents


Summary

61 Introduction




















682 Data Collectors





691 Time Domain





6915 Orbits









6926 Masks


693 Modal Domain


610 Fault Detection

6101 Standards











61111 Unbalance

61112 Misalignment


61114 Soft Foot

61115 Rubs

61116 Resonances

61117 Oil Whirl

61118 Oil Whip







61131 Pumps

61132 Fans



61135 Compressors



References

Related Titles

53191ch7

Table of Contents


Summary

71 Introduction


721 General Terms


723 Tool Wear



















7411 Time Domain







752 Neural Networks



753 Fuzzy Logic

754 Other Methods

76 Conclusion

References

Related Titles

53191ch8

Table of Contents


Summary

81 Introduction




841 Coverage Index

842 Overlap Index


85 A Case Study









86 Conclusion

References

Related Titles

53191ch9

Table of Contents


Summary

91 Introduction









941 Learning Mode

942 Monitoring Mode

943 Diagnostic Mode

944 Experiments







9443 Tests




96 Conclusions

References

Related Titles

53191ch10

Table of Contents


Summary

101 Introduction

























1031 Introduction

1032 Wind Speed










1037 Dampers



























106 Impact Loading



107 Floor Vibration

1071 Introduction


10721 Walking







10733 Damping

10734 Resonance




10751 Harmonics



Bibliography

Related Titles

53191ch11

Table of Contents


Summary

111 Introduction

















11244 Other Systems





























112911 Buildings

112912 Bridges


112921 Buildings

112922 Bridges
















































113714 Test Results








Bibliography

Related Titles

53191ch12

Table of Contents


Summary

121 Introduction





















12231 Kaul Method


































126 Conclusions

References

Related Titles

53191ch13

Table of Contents


Summary

131 Introduction











Bibliography

Related Titles

53191ch14

Table of Contents


Summary

141 Introduction












Bibliography

Related Titles


Instrumentation

Edited by


Vancouver Canada

















TA355V5228 200762030287-dc22 2006100139




Preface




































v






efforts


Vancouver Canada

Prefacevi



Acknowledgments






vii



Editor-in-Chief
































ix



Contributors

xi








Singapore


Kyoto Japan


Science



Jalles France


Singapore


Technology

Singapore


Technology

Singapore




Technology

Singapore








Kyoto Japan




Singapore


Singapore





Contents


11 Introduction 1-1









21 Introduction 2-2

22 Amplifiers 2-2









31 Introduction 3-1






41 Introduction 4-1






xiii




51 Definitions 5-2



54 Pyroshocks 5-17


56 Standards 5-24







61 Introduction 6-2












71 Introduction 7-1





76 Conclusion 7-20


81 Introduction 8-1





86 Conclusion 8-23



91 Introduction 9-1




Contentsxiv




96 Conclusions 9-35


and Tuan Ngo 10-1





























Contents xv



1Vibration

Instrumentation


11 Introduction 1-1



Equipment












Summary


11 Introduction








1-1



















the object













6 Control devices


AnalogDigital

Interface

DigitalSignal


FilterAmplifier

FilterAmplifier

SignalGenerator



PowerAmplifier

MountingFixtures

TestObject

ResponseSensor

ControlSensor

Exciter

SwivelBase

















1 Test object

2 Excitation system

3 Control system




























SignalModification

System

TestObject

ControlSystem


System








and


Box 11







Exciters

Shakers


excitations)


excitations)





3 Drop (impulsive)

Signal Conditioning


Sensors








(Stroke)

Maximum

Velocity

Maximum

Acceleration

Maximum

Force

Excitation

Waveform

Hydraulic

(electrohydraulic)

Low

(01ndash500 Hz)


(50 insec

125 cmsec)

Intermediate

(20 g)

High (100000 lbf

450000 N)



Inertial


Intermediate

(2ndash50 Hz)


(50 insec

125 cmsec)

Intermediate

(20 g)

Intermediate

(1000 lbf 4500 N)

Sinusoidal only

Electromagnetic

(electrodynamic)

High

(2ndash10000 Hz)


(50 insec

125 cmsec)


(450 lbf 2000 N)



random)

VibrationInstru

mentation

1-5



CRCndashpp1ndash112

























20 dbdecade)

























Stroke

Limit M

ax

Acceleration

MaxVelocity

Peak

Vel

ocity

(cm

s)

01 1 10 100

FullLoad

NoLoad

Frequency (Hz)(a)

Peak

Vel

ocity

(cm

s)

100

10

1

100

10

1

01 1 10 100

FullLoad

NoLoad

Frequency (Hz)(b)



typical




1211 Force Rating









21p


















for acceleration

1212 Power Rating

















1213 Stroke Rating







Example 11








for the test

Solution







rating as






Acc

eler

atio

n(g

)

Con

stan

t Dis

plac

emen

t

Constant Velo

city

Frequency (Hz)

S

FP

0101

10 10 100

10

10























motors


























































m m

2mw2r cos wt

wtw w

wt



















































Denmark







Electrical Lediedt












d=dt as








Rev2

k2bs

Reye eth124THORN


given by

yevfrac14 kb

Re







eth127THORN

where

bo frac14 k2bRe

eth128THORN



yevfrac14 kb

Rb







effectiveness















100

10


Antiresonance

Resonance

Shak

erD

ispl

acem

entM

agni

tude

Resonance

1000




























13 Control System
















ExcitationInput

(Reference)

Feedback Paths

DriveSignal

ShakerResponse

TestTable

TestObject

Test ObjectResponse


(Shaker)(Ram)

Controllerand

Amplifier



















































1311 Compressor
























desired spectrum









































1321 Oscillators








oscillator
















DC Voltage

Oscillator


FrequencyConverter

FilterAmplifier


FrequencyCounter


Variable-GainOutput

Amplifier

SignalSpecification

LevelSpecification





53191fm


Preface

Acknowledgments

Editor-in-Chief

Contributors

Contents

Related Titles

53191ch1

Table of Contents


Summary

11 Introduction



1211 Force Rating

1212 Power Rating

1213 Stroke Rating






13 Control System


1311 Compressor





1321 Oscillators


1323 Tape Players






142 Linearity





151 Potentiometer


















15101 Sensitivity


















1621 Stroboscope






References


Summary


1A1 Dynamic Signals


1A111 Aliasing





1A212 Gain










1A222 Attenuation











1A5 Integration



























1A724 Zoom Settings






1A822 Overlapping




1A832 STFT vs RPM














Bibliography

Related Titles

53191ch2

Table of Contents


Summary

21 Introduction

22 Amplifiers







2242 Common Mode







23 Analog Filters















243 Demodulation










255 Digital Filters


26 Bridge Circuits






2641 Owen Bridge










281 Phase Shifters







292 Oscilloscopes

2921 Triggering



Bibliography

Related Titles

53191ch3

Table of Contents


Summary

31 Introduction


321 Test Signals




3222 Sine Sweep

3223 Sine Dwell

3224 Decaying Sine

3225 Sine Beat












































3432 Pluck Test

3433 Shaker Tests






















Bibliography

Related Titles

53191ch4

Table of Contents


Summary

41 Introduction



























Bibliography

Related Titles

53191ch5

Table of Contents


Summary

51 Definitions

511 Shock


513 Half-Sine Shock







531 Need





534 Definitions












5351 Definition












54 Pyroshocks







5524 Amplitude

5525 Duration

5526 Difficulties

56 Standards




564 Bump Test


571 Definition


58 Shock Machines

581 Main Types



58211 Impact Mode

58212 Impulse Mode














584 Limitations










592 Main Advantages


5931 Requirements

5932 Solutions





59411 Abacuses




5101 Principle



51022 ZERD Function









References

Related Titles

53191ch6

Table of Contents


Summary

61 Introduction




















682 Data Collectors





691 Time Domain





6915 Orbits









6926 Masks


693 Modal Domain


610 Fault Detection

6101 Standards











61111 Unbalance

61112 Misalignment


61114 Soft Foot

61115 Rubs

61116 Resonances

61117 Oil Whirl

61118 Oil Whip







61131 Pumps

61132 Fans



61135 Compressors



References

Related Titles

53191ch7

Table of Contents


Summary

71 Introduction


721 General Terms


723 Tool Wear



















7411 Time Domain







752 Neural Networks



753 Fuzzy Logic

754 Other Methods

76 Conclusion

References

Related Titles

53191ch8

Table of Contents


Summary

81 Introduction




841 Coverage Index

842 Overlap Index


85 A Case Study









86 Conclusion

References

Related Titles

53191ch9

Table of Contents


Summary

91 Introduction









941 Learning Mode

942 Monitoring Mode

943 Diagnostic Mode

944 Experiments







9443 Tests




96 Conclusions

References

Related Titles

53191ch10

Table of Contents


Summary

101 Introduction

























1031 Introduction

1032 Wind Speed










1037 Dampers



























106 Impact Loading



107 Floor Vibration

1071 Introduction


10721 Walking







10733 Damping

10734 Resonance




10751 Harmonics



Bibliography

Related Titles

53191ch11

Table of Contents


Summary

111 Introduction

















11244 Other Systems





























112911 Buildings

112912 Bridges


112921 Buildings

112922 Bridges
















































113714 Test Results








Bibliography

Related Titles

53191ch12

Table of Contents


Summary

121 Introduction





















12231 Kaul Method


































126 Conclusions

References

Related Titles

53191ch13

Table of Contents


Summary

131 Introduction











Bibliography

Related Titles

53191ch14

Table of Contents


Summary

141 Introduction












Bibliography

Related Titles













TA355V5228 200762030287-dc22 2006100139




Preface




































v






efforts


Vancouver Canada

Prefacevi



Acknowledgments






vii



Editor-in-Chief
































ix



Contributors

xi








Singapore


Kyoto Japan


Science



Jalles France


Singapore


Technology

Singapore


Technology

Singapore




Technology

Singapore








Kyoto Japan




Singapore


Singapore





Contents


11 Introduction 1-1









21 Introduction 2-2

22 Amplifiers 2-2









31 Introduction 3-1






41 Introduction 4-1






xiii




51 Definitions 5-2



54 Pyroshocks 5-17


56 Standards 5-24







61 Introduction 6-2












71 Introduction 7-1





76 Conclusion 7-20


81 Introduction 8-1





86 Conclusion 8-23



91 Introduction 9-1




Contentsxiv




96 Conclusions 9-35


and Tuan Ngo 10-1





























Contents xv



1Vibration

Instrumentation


11 Introduction 1-1



Equipment












Summary


11 Introduction








1-1



















the object













6 Control devices


AnalogDigital

Interface

DigitalSignal


FilterAmplifier

FilterAmplifier

SignalGenerator



PowerAmplifier

MountingFixtures

TestObject

ResponseSensor

ControlSensor

Exciter

SwivelBase

















1 Test object

2 Excitation system

3 Control system




























SignalModification

System

TestObject

ControlSystem


System








and


Box 11







Exciters

Shakers


excitations)


excitations)





3 Drop (impulsive)

Signal Conditioning


Sensors








(Stroke)

Maximum

Velocity

Maximum

Acceleration

Maximum

Force

Excitation

Waveform

Hydraulic

(electrohydraulic)

Low

(01ndash500 Hz)


(50 insec

125 cmsec)

Intermediate

(20 g)

High (100000 lbf

450000 N)



Inertial


Intermediate

(2ndash50 Hz)


(50 insec

125 cmsec)

Intermediate

(20 g)

Intermediate

(1000 lbf 4500 N)

Sinusoidal only

Electromagnetic

(electrodynamic)

High

(2ndash10000 Hz)


(50 insec

125 cmsec)


(450 lbf 2000 N)



random)

VibrationInstru

mentation

1-5



CRCndashpp1ndash112

























20 dbdecade)

























Stroke

Limit M

ax

Acceleration

MaxVelocity

Peak

Vel

ocity

(cm

s)

01 1 10 100

FullLoad

NoLoad

Frequency (Hz)(a)

Peak

Vel

ocity

(cm

s)

100

10

1

100

10

1

01 1 10 100

FullLoad

NoLoad

Frequency (Hz)(b)



typical




1211 Force Rating









21p


















for acceleration

1212 Power Rating

















1213 Stroke Rating







Example 11








for the test

Solution







rating as






Acc

eler

atio

n(g

)

Con

stan

t Dis

plac

emen

t

Constant Velo

city

Frequency (Hz)

S

FP

0101

10 10 100

10

10























motors


























































m m

2mw2r cos wt

wtw w

wt



















































Denmark







Electrical Lediedt












d=dt as








Rev2

k2bs

Reye eth124THORN


given by

yevfrac14 kb

Re







eth127THORN

where

bo frac14 k2bRe

eth128THORN



yevfrac14 kb

Rb







effectiveness















100

10


Antiresonance

Resonance

Shak

erD

ispl

acem

entM

agni

tude

Resonance

1000




























13 Control System
















ExcitationInput

(Reference)

Feedback Paths

DriveSignal

ShakerResponse

TestTable

TestObject

Test ObjectResponse


(Shaker)(Ram)

Controllerand

Amplifier



















































1311 Compressor
























desired spectrum









































1321 Oscillators








oscillator
















DC Voltage

Oscillator


FrequencyConverter

FilterAmplifier


FrequencyCounter


Variable-GainOutput

Amplifier

SignalSpecification

LevelSpecification





53191fm


Preface

Acknowledgments

Editor-in-Chief

Contributors

Contents

Related Titles

53191ch1

Table of Contents


Summary

11 Introduction



1211 Force Rating

1212 Power Rating

1213 Stroke Rating






13 Control System


1311 Compressor





1321 Oscillators


1323 Tape Players






142 Linearity





151 Potentiometer


















15101 Sensitivity


















1621 Stroboscope






References


Summary


1A1 Dynamic Signals


1A111 Aliasing





1A212 Gain










1A222 Attenuation











1A5 Integration



























1A724 Zoom Settings






1A822 Overlapping




1A832 STFT vs RPM














Bibliography

Related Titles

53191ch2

Table of Contents


Summary

21 Introduction

22 Amplifiers







2242 Common Mode







23 Analog Filters















243 Demodulation










255 Digital Filters


26 Bridge Circuits






2641 Owen Bridge










281 Phase Shifters







292 Oscilloscopes

2921 Triggering



Bibliography

Related Titles

53191ch3

Table of Contents


Summary

31 Introduction


321 Test Signals




3222 Sine Sweep

3223 Sine Dwell

3224 Decaying Sine

3225 Sine Beat












































3432 Pluck Test

3433 Shaker Tests






















Bibliography

Related Titles

53191ch4

Table of Contents


Summary

41 Introduction



























Bibliography

Related Titles

53191ch5

Table of Contents


Summary

51 Definitions

511 Shock


513 Half-Sine Shock







531 Need





534 Definitions












5351 Definition












54 Pyroshocks







5524 Amplitude

5525 Duration

5526 Difficulties

56 Standards




564 Bump Test


571 Definition


58 Shock Machines

581 Main Types



58211 Impact Mode

58212 Impulse Mode














584 Limitations










592 Main Advantages


5931 Requirements

5932 Solutions





59411 Abacuses




5101 Principle



51022 ZERD Function









References

Related Titles

53191ch6

Table of Contents


Summary

61 Introduction




















682 Data Collectors





691 Time Domain





6915 Orbits









6926 Masks


693 Modal Domain


610 Fault Detection

6101 Standards











61111 Unbalance

61112 Misalignment


61114 Soft Foot

61115 Rubs

61116 Resonances

61117 Oil Whirl

61118 Oil Whip







61131 Pumps

61132 Fans



61135 Compressors



References

Related Titles

53191ch7

Table of Contents


Summary

71 Introduction


721 General Terms


723 Tool Wear



















7411 Time Domain







752 Neural Networks



753 Fuzzy Logic

754 Other Methods

76 Conclusion

References

Related Titles

53191ch8

Table of Contents


Summary

81 Introduction




841 Coverage Index

842 Overlap Index


85 A Case Study









86 Conclusion

References

Related Titles

53191ch9

Table of Contents


Summary

91 Introduction









941 Learning Mode

942 Monitoring Mode

943 Diagnostic Mode

944 Experiments







9443 Tests




96 Conclusions

References

Related Titles

53191ch10

Table of Contents


Summary

101 Introduction

























1031 Introduction

1032 Wind Speed










1037 Dampers



























106 Impact Loading



107 Floor Vibration

1071 Introduction


10721 Walking







10733 Damping

10734 Resonance




10751 Harmonics



Bibliography

Related Titles

53191ch11

Table of Contents


Summary

111 Introduction

















11244 Other Systems





























112911 Buildings

112912 Bridges


112921 Buildings

112922 Bridges
















































113714 Test Results








Bibliography

Related Titles

53191ch12

Table of Contents


Summary

121 Introduction





















12231 Kaul Method


































126 Conclusions

References

Related Titles

53191ch13

Table of Contents


Summary

131 Introduction











Bibliography

Related Titles

53191ch14

Table of Contents


Summary

141 Introduction












Bibliography

Related Titles

Preface




































v






efforts


Vancouver Canada

Prefacevi



Acknowledgments






vii



Editor-in-Chief
































ix



Contributors

xi








Singapore


Kyoto Japan


Science



Jalles France


Singapore


Technology

Singapore


Technology

Singapore




Technology

Singapore








Kyoto Japan




Singapore


Singapore





Contents


11 Introduction 1-1









21 Introduction 2-2

22 Amplifiers 2-2









31 Introduction 3-1






41 Introduction 4-1






xiii




51 Definitions 5-2



54 Pyroshocks 5-17


56 Standards 5-24







61 Introduction 6-2












71 Introduction 7-1





76 Conclusion 7-20


81 Introduction 8-1





86 Conclusion 8-23



91 Introduction 9-1




Contentsxiv




96 Conclusions 9-35


and Tuan Ngo 10-1





























Contents xv



1Vibration

Instrumentation


11 Introduction 1-1



Equipment












Summary


11 Introduction








1-1



















the object













6 Control devices


AnalogDigital

Interface

DigitalSignal


FilterAmplifier

FilterAmplifier

SignalGenerator



PowerAmplifier

MountingFixtures

TestObject

ResponseSensor

ControlSensor

Exciter

SwivelBase

















1 Test object

2 Excitation system

3 Control system




























SignalModification

System

TestObject

ControlSystem


System








and


Box 11







Exciters

Shakers


excitations)


excitations)





3 Drop (impulsive)

Signal Conditioning


Sensors








(Stroke)

Maximum

Velocity

Maximum

Acceleration

Maximum

Force

Excitation

Waveform

Hydraulic

(electrohydraulic)

Low

(01ndash500 Hz)


(50 insec

125 cmsec)

Intermediate

(20 g)

High (100000 lbf

450000 N)



Inertial


Intermediate

(2ndash50 Hz)


(50 insec

125 cmsec)

Intermediate

(20 g)

Intermediate

(1000 lbf 4500 N)

Sinusoidal only

Electromagnetic

(electrodynamic)

High

(2ndash10000 Hz)


(50 insec

125 cmsec)


(450 lbf 2000 N)



random)

VibrationInstru

mentation

1-5



CRCndashpp1ndash112

























20 dbdecade)

























Stroke

Limit M

ax

Acceleration

MaxVelocity

Peak

Vel

ocity

(cm

s)

01 1 10 100

FullLoad

NoLoad

Frequency (Hz)(a)

Peak

Vel

ocity

(cm

s)

100

10

1

100

10

1

01 1 10 100

FullLoad

NoLoad

Frequency (Hz)(b)



typical




1211 Force Rating









21p


















for acceleration

1212 Power Rating

















1213 Stroke Rating







Example 11








for the test

Solution







rating as






Acc

eler

atio

n(g

)

Con

stan

t Dis

plac

emen

t

Constant Velo

city

Frequency (Hz)

S

FP

0101

10 10 100

10

10























motors


























































m m

2mw2r cos wt

wtw w

wt



















































Denmark







Electrical Lediedt












d=dt as








Rev2

k2bs

Reye eth124THORN


given by

yevfrac14 kb

Re







eth127THORN

where

bo frac14 k2bRe

eth128THORN



yevfrac14 kb

Rb







effectiveness















100

10


Antiresonance

Resonance

Shak

erD

ispl

acem

entM

agni

tude

Resonance

1000




























13 Control System
















ExcitationInput

(Reference)

Feedback Paths

DriveSignal

ShakerResponse

TestTable

TestObject

Test ObjectResponse


(Shaker)(Ram)

Controllerand

Amplifier



















































1311 Compressor
























desired spectrum









































1321 Oscillators








oscillator
















DC Voltage

Oscillator


FrequencyConverter

FilterAmplifier


FrequencyCounter


Variable-GainOutput

Amplifier

SignalSpecification

LevelSpecification





53191fm


Preface

Acknowledgments

Editor-in-Chief

Contributors

Contents

Related Titles

53191ch1

Table of Contents


Summary

11 Introduction



1211 Force Rating

1212 Power Rating

1213 Stroke Rating






13 Control System


1311 Compressor





1321 Oscillators


1323 Tape Players






142 Linearity





151 Potentiometer


















15101 Sensitivity


















1621 Stroboscope






References


Summary


1A1 Dynamic Signals


1A111 Aliasing





1A212 Gain










1A222 Attenuation











1A5 Integration



























1A724 Zoom Settings






1A822 Overlapping




1A832 STFT vs RPM














Bibliography

Related Titles

53191ch2

Table of Contents


Summary

21 Introduction

22 Amplifiers







2242 Common Mode







23 Analog Filters















243 Demodulation










255 Digital Filters


26 Bridge Circuits






2641 Owen Bridge










281 Phase Shifters







292 Oscilloscopes

2921 Triggering



Bibliography

Related Titles

53191ch3

Table of Contents


Summary

31 Introduction


321 Test Signals




3222 Sine Sweep

3223 Sine Dwell

3224 Decaying Sine

3225 Sine Beat












































3432 Pluck Test

3433 Shaker Tests






















Bibliography

Related Titles

53191ch4

Table of Contents


Summary

41 Introduction



























Bibliography

Related Titles

53191ch5

Table of Contents


Summary

51 Definitions

511 Shock


513 Half-Sine Shock







531 Need





534 Definitions












5351 Definition












54 Pyroshocks







5524 Amplitude

5525 Duration

5526 Difficulties

56 Standards




564 Bump Test


571 Definition


58 Shock Machines

581 Main Types



58211 Impact Mode

58212 Impulse Mode














584 Limitations










592 Main Advantages


5931 Requirements

5932 Solutions





59411 Abacuses




5101 Principle



51022 ZERD Function









References

Related Titles

53191ch6

Table of Contents


Summary

61 Introduction




















682 Data Collectors





691 Time Domain





6915 Orbits









6926 Masks


693 Modal Domain


610 Fault Detection

6101 Standards











61111 Unbalance

61112 Misalignment


61114 Soft Foot

61115 Rubs

61116 Resonances

61117 Oil Whirl

61118 Oil Whip







61131 Pumps

61132 Fans



61135 Compressors



References

Related Titles

53191ch7

Table of Contents


Summary

71 Introduction


721 General Terms


723 Tool Wear



















7411 Time Domain







752 Neural Networks



753 Fuzzy Logic

754 Other Methods

76 Conclusion

References

Related Titles

53191ch8

Table of Contents


Summary

81 Introduction




841 Coverage Index

842 Overlap Index


85 A Case Study









86 Conclusion

References

Related Titles

53191ch9

Table of Contents


Summary

91 Introduction









941 Learning Mode

942 Monitoring Mode

943 Diagnostic Mode

944 Experiments







9443 Tests




96 Conclusions

References

Related Titles

53191ch10

Table of Contents


Summary

101 Introduction

























1031 Introduction

1032 Wind Speed










1037 Dampers



























106 Impact Loading



107 Floor Vibration

1071 Introduction


10721 Walking







10733 Damping

10734 Resonance




10751 Harmonics



Bibliography

Related Titles

53191ch11

Table of Contents


Summary

111 Introduction

















11244 Other Systems





























112911 Buildings

112912 Bridges


112921 Buildings

112922 Bridges
















































113714 Test Results








Bibliography

Related Titles

53191ch12

Table of Contents


Summary

121 Introduction





















12231 Kaul Method


































126 Conclusions

References

Related Titles

53191ch13

Table of Contents


Summary

131 Introduction











Bibliography

Related Titles

53191ch14

Table of Contents


Summary

141 Introduction












Bibliography

Related Titles




efforts


Vancouver Canada

Prefacevi



Acknowledgments






vii



Editor-in-Chief
































ix



Contributors

xi








Singapore


Kyoto Japan


Science



Jalles France


Singapore


Technology

Singapore


Technology

Singapore




Technology

Singapore








Kyoto Japan




Singapore


Singapore





Contents


11 Introduction 1-1









21 Introduction 2-2

22 Amplifiers 2-2









31 Introduction 3-1






41 Introduction 4-1






xiii




51 Definitions 5-2



54 Pyroshocks 5-17


56 Standards 5-24







61 Introduction 6-2












71 Introduction 7-1





76 Conclusion 7-20


81 Introduction 8-1





86 Conclusion 8-23



91 Introduction 9-1




Contentsxiv




96 Conclusions 9-35


and Tuan Ngo 10-1





























Contents xv



1Vibration

Instrumentation


11 Introduction 1-1



Equipment












Summary


11 Introduction








1-1



















the object













6 Control devices


AnalogDigital

Interface

DigitalSignal


FilterAmplifier

FilterAmplifier

SignalGenerator



PowerAmplifier

MountingFixtures

TestObject

ResponseSensor

ControlSensor

Exciter

SwivelBase

















1 Test object

2 Excitation system

3 Control system




























SignalModification

System

TestObject

ControlSystem


System








and


Box 11







Exciters

Shakers


excitations)


excitations)





3 Drop (impulsive)

Signal Conditioning


Sensors








(Stroke)

Maximum

Velocity

Maximum

Acceleration

Maximum

Force

Excitation

Waveform

Hydraulic

(electrohydraulic)

Low

(01ndash500 Hz)


(50 insec

125 cmsec)

Intermediate

(20 g)

High (100000 lbf

450000 N)



Inertial


Intermediate

(2ndash50 Hz)


(50 insec

125 cmsec)

Intermediate

(20 g)

Intermediate

(1000 lbf 4500 N)

Sinusoidal only

Electromagnetic

(electrodynamic)

High

(2ndash10000 Hz)


(50 insec

125 cmsec)


(450 lbf 2000 N)



random)

VibrationInstru

mentation

1-5



CRCndashpp1ndash112

























20 dbdecade)

























Stroke

Limit M

ax

Acceleration

MaxVelocity

Peak

Vel

ocity

(cm

s)

01 1 10 100

FullLoad

NoLoad

Frequency (Hz)(a)

Peak

Vel

ocity

(cm

s)

100

10

1

100

10

1

01 1 10 100

FullLoad

NoLoad

Frequency (Hz)(b)



typical




1211 Force Rating









21p


















for acceleration

1212 Power Rating

















1213 Stroke Rating







Example 11








for the test

Solution







rating as






Acc

eler

atio

n(g

)

Con

stan

t Dis

plac

emen

t

Constant Velo

city

Frequency (Hz)

S

FP

0101

10 10 100

10

10























motors


























































m m

2mw2r cos wt

wtw w

wt



















































Denmark







Electrical Lediedt












d=dt as








Rev2

k2bs

Reye eth124THORN


given by

yevfrac14 kb

Re







eth127THORN

where

bo frac14 k2bRe

eth128THORN



yevfrac14 kb

Rb







effectiveness















100

10


Antiresonance

Resonance

Shak

erD

ispl

acem

entM

agni

tude

Resonance

1000




























13 Control System
















ExcitationInput

(Reference)

Feedback Paths

DriveSignal

ShakerResponse

TestTable

TestObject

Test ObjectResponse


(Shaker)(Ram)

Controllerand

Amplifier



















































1311 Compressor
























desired spectrum









































1321 Oscillators








oscillator
















DC Voltage

Oscillator


FrequencyConverter

FilterAmplifier


FrequencyCounter


Variable-GainOutput

Amplifier

SignalSpecification

LevelSpecification





53191fm


Preface

Acknowledgments

Editor-in-Chief

Contributors

Contents

Related Titles

53191ch1

Table of Contents


Summary

11 Introduction



1211 Force Rating

1212 Power Rating

1213 Stroke Rating






13 Control System


1311 Compressor





1321 Oscillators


1323 Tape Players






142 Linearity





151 Potentiometer


















15101 Sensitivity


















1621 Stroboscope






References


Summary


1A1 Dynamic Signals


1A111 Aliasing





1A212 Gain










1A222 Attenuation











1A5 Integration



























1A724 Zoom Settings






1A822 Overlapping




1A832 STFT vs RPM














Bibliography

Related Titles

53191ch2

Table of Contents


Summary

21 Introduction

22 Amplifiers







2242 Common Mode







23 Analog Filters















243 Demodulation










255 Digital Filters


26 Bridge Circuits






2641 Owen Bridge










281 Phase Shifters







292 Oscilloscopes

2921 Triggering



Bibliography

Related Titles

53191ch3

Table of Contents


Summary

31 Introduction


321 Test Signals




3222 Sine Sweep

3223 Sine Dwell

3224 Decaying Sine

3225 Sine Beat












































3432 Pluck Test

3433 Shaker Tests






















Bibliography

Related Titles

53191ch4

Table of Contents


Summary

41 Introduction



























Bibliography

Related Titles

53191ch5

Table of Contents


Summary

51 Definitions

511 Shock


513 Half-Sine Shock







531 Need





534 Definitions












5351 Definition












54 Pyroshocks







5524 Amplitude

5525 Duration

5526 Difficulties

56 Standards




564 Bump Test


571 Definition


58 Shock Machines

581 Main Types



58211 Impact Mode

58212 Impulse Mode














584 Limitations










592 Main Advantages


5931 Requirements

5932 Solutions





59411 Abacuses




5101 Principle



51022 ZERD Function









References

Related Titles

53191ch6

Table of Contents


Summary

61 Introduction




















682 Data Collectors





691 Time Domain





6915 Orbits









6926 Masks


693 Modal Domain


610 Fault Detection

6101 Standards











61111 Unbalance

61112 Misalignment


61114 Soft Foot

61115 Rubs

61116 Resonances

61117 Oil Whirl

61118 Oil Whip







61131 Pumps

61132 Fans



61135 Compressors



References

Related Titles

53191ch7

Table of Contents


Summary

71 Introduction


721 General Terms


723 Tool Wear



















7411 Time Domain







752 Neural Networks



753 Fuzzy Logic

754 Other Methods

76 Conclusion

References

Related Titles

53191ch8

Table of Contents


Summary

81 Introduction




841 Coverage Index

842 Overlap Index


85 A Case Study









86 Conclusion

References

Related Titles

53191ch9

Table of Contents


Summary

91 Introduction









941 Learning Mode

942 Monitoring Mode

943 Diagnostic Mode

944 Experiments







9443 Tests




96 Conclusions

References

Related Titles

53191ch10

Table of Contents


Summary

101 Introduction

























1031 Introduction

1032 Wind Speed










1037 Dampers



























106 Impact Loading



107 Floor Vibration

1071 Introduction


10721 Walking







10733 Damping

10734 Resonance




10751 Harmonics



Bibliography

Related Titles

53191ch11

Table of Contents


Summary

111 Introduction

















11244 Other Systems





























112911 Buildings

112912 Bridges


112921 Buildings

112922 Bridges
















































113714 Test Results








Bibliography

Related Titles

53191ch12

Table of Contents


Summary

121 Introduction





















12231 Kaul Method


































126 Conclusions

References

Related Titles

53191ch13

Table of Contents


Summary

131 Introduction











Bibliography

Related Titles

53191ch14

Table of Contents


Summary

141 Introduction












Bibliography

Related Titles

Acknowledgments






vii



Editor-in-Chief
































ix



Contributors

xi








Singapore


Kyoto Japan


Science



Jalles France


Singapore


Technology

Singapore


Technology

Singapore




Technology

Singapore








Kyoto Japan




Singapore


Singapore





Contents


11 Introduction 1-1









21 Introduction 2-2

22 Amplifiers 2-2









31 Introduction 3-1






41 Introduction 4-1






xiii




51 Definitions 5-2



54 Pyroshocks 5-17


56 Standards 5-24







61 Introduction 6-2












71 Introduction 7-1





76 Conclusion 7-20


81 Introduction 8-1





86 Conclusion 8-23



91 Introduction 9-1




Contentsxiv




96 Conclusions 9-35


and Tuan Ngo 10-1





























Contents xv



1Vibration

Instrumentation


11 Introduction 1-1



Equipment












Summary


11 Introduction








1-1



















the object













6 Control devices


AnalogDigital

Interface

DigitalSignal


FilterAmplifier

FilterAmplifier

SignalGenerator



PowerAmplifier

MountingFixtures

TestObject

ResponseSensor

ControlSensor

Exciter

SwivelBase

















1 Test object

2 Excitation system

3 Control system




























SignalModification

System

TestObject

ControlSystem


System








and


Box 11







Exciters

Shakers


excitations)


excitations)





3 Drop (impulsive)

Signal Conditioning


Sensors








(Stroke)

Maximum

Velocity

Maximum

Acceleration

Maximum

Force

Excitation

Waveform

Hydraulic

(electrohydraulic)

Low

(01ndash500 Hz)


(50 insec

125 cmsec)

Intermediate

(20 g)

High (100000 lbf

450000 N)



Inertial


Intermediate

(2ndash50 Hz)


(50 insec

125 cmsec)

Intermediate

(20 g)

Intermediate

(1000 lbf 4500 N)

Sinusoidal only

Electromagnetic

(electrodynamic)

High

(2ndash10000 Hz)


(50 insec

125 cmsec)


(450 lbf 2000 N)



random)

VibrationInstru

mentation

1-5



CRCndashpp1ndash112

























20 dbdecade)

























Stroke

Limit M

ax

Acceleration

MaxVelocity

Peak

Vel

ocity

(cm

s)

01 1 10 100

FullLoad

NoLoad

Frequency (Hz)(a)

Peak

Vel

ocity

(cm

s)

100

10

1

100

10

1

01 1 10 100

FullLoad

NoLoad

Frequency (Hz)(b)



typical




1211 Force Rating









21p


















for acceleration

1212 Power Rating

















1213 Stroke Rating







Example 11








for the test

Solution







rating as






Acc

eler

atio

n(g

)

Con

stan

t Dis

plac

emen

t

Constant Velo

city

Frequency (Hz)

S

FP

0101

10 10 100

10

10























motors


























































m m

2mw2r cos wt

wtw w

wt



















































Denmark







Electrical Lediedt












d=dt as








Rev2

k2bs

Reye eth124THORN


given by

yevfrac14 kb

Re







eth127THORN

where

bo frac14 k2bRe

eth128THORN



yevfrac14 kb

Rb







effectiveness















100

10


Antiresonance

Resonance

Shak

erD

ispl

acem

entM

agni

tude

Resonance

1000




























13 Control System
















ExcitationInput

(Reference)

Feedback Paths

DriveSignal

ShakerResponse

TestTable

TestObject

Test ObjectResponse


(Shaker)(Ram)

Controllerand

Amplifier



















































1311 Compressor
























desired spectrum









































1321 Oscillators








oscillator
















DC Voltage

Oscillator


FrequencyConverter

FilterAmplifier


FrequencyCounter


Variable-GainOutput

Amplifier

SignalSpecification

LevelSpecification





53191fm


Preface

Acknowledgments

Editor-in-Chief

Contributors

Contents

Related Titles

53191ch1

Table of Contents


Summary

11 Introduction



1211 Force Rating

1212 Power Rating

1213 Stroke Rating






13 Control System


1311 Compressor





1321 Oscillators


1323 Tape Players






142 Linearity





151 Potentiometer


















15101 Sensitivity


















1621 Stroboscope






References


Summary


1A1 Dynamic Signals


1A111 Aliasing





1A212 Gain










1A222 Attenuation











1A5 Integration



























1A724 Zoom Settings






1A822 Overlapping




1A832 STFT vs RPM














Bibliography

Related Titles

53191ch2

Table of Contents


Summary

21 Introduction

22 Amplifiers







2242 Common Mode







23 Analog Filters















243 Demodulation










255 Digital Filters


26 Bridge Circuits






2641 Owen Bridge










281 Phase Shifters







292 Oscilloscopes

2921 Triggering



Bibliography

Related Titles

53191ch3

Table of Contents


Summary

31 Introduction


321 Test Signals




3222 Sine Sweep

3223 Sine Dwell

3224 Decaying Sine

3225 Sine Beat












































3432 Pluck Test

3433 Shaker Tests






















Bibliography

Related Titles

53191ch4

Table of Contents


Summary

41 Introduction



























Bibliography

Related Titles

53191ch5

Table of Contents


Summary

51 Definitions

511 Shock


513 Half-Sine Shock







531 Need





534 Definitions












5351 Definition












54 Pyroshocks







5524 Amplitude

5525 Duration

5526 Difficulties

56 Standards




564 Bump Test


571 Definition


58 Shock Machines

581 Main Types



58211 Impact Mode

58212 Impulse Mode














584 Limitations










592 Main Advantages


5931 Requirements

5932 Solutions





59411 Abacuses




5101 Principle



51022 ZERD Function









References

Related Titles

53191ch6

Table of Contents


Summary

61 Introduction




















682 Data Collectors





691 Time Domain





6915 Orbits









6926 Masks


693 Modal Domain


610 Fault Detection

6101 Standards











61111 Unbalance

61112 Misalignment


61114 Soft Foot

61115 Rubs

61116 Resonances

61117 Oil Whirl

61118 Oil Whip







61131 Pumps

61132 Fans



61135 Compressors



References

Related Titles

53191ch7

Table of Contents


Summary

71 Introduction


721 General Terms


723 Tool Wear



















7411 Time Domain







752 Neural Networks



753 Fuzzy Logic

754 Other Methods

76 Conclusion

References

Related Titles

53191ch8

Table of Contents


Summary

81 Introduction




841 Coverage Index

842 Overlap Index


85 A Case Study









86 Conclusion

References

Related Titles

53191ch9

Table of Contents


Summary

91 Introduction









941 Learning Mode

942 Monitoring Mode

943 Diagnostic Mode

944 Experiments







9443 Tests




96 Conclusions

References

Related Titles

53191ch10

Table of Contents


Summary

101 Introduction

























1031 Introduction

1032 Wind Speed










1037 Dampers



























106 Impact Loading



107 Floor Vibration

1071 Introduction


10721 Walking







10733 Damping

10734 Resonance




10751 Harmonics



Bibliography

Related Titles

53191ch11

Table of Contents


Summary

111 Introduction

















11244 Other Systems





























112911 Buildings

112912 Bridges


112921 Buildings

112922 Bridges
















































113714 Test Results








Bibliography

Related Titles

53191ch12

Table of Contents


Summary

121 Introduction





















12231 Kaul Method


































126 Conclusions

References

Related Titles

53191ch13

Table of Contents


Summary

131 Introduction











Bibliography

Related Titles

53191ch14

Table of Contents


Summary

141 Introduction












Bibliography

Related Titles

Editor-in-Chief
































ix



Contributors

xi








Singapore


Kyoto Japan


Science



Jalles France


Singapore


Technology

Singapore


Technology

Singapore




Technology

Singapore








Kyoto Japan




Singapore


Singapore





Contents


11 Introduction 1-1









21 Introduction 2-2

22 Amplifiers 2-2









31 Introduction 3-1






41 Introduction 4-1






xiii




51 Definitions 5-2



54 Pyroshocks 5-17


56 Standards 5-24







61 Introduction 6-2












71 Introduction 7-1





76 Conclusion 7-20


81 Introduction 8-1





86 Conclusion 8-23



91 Introduction 9-1




Contentsxiv




96 Conclusions 9-35


and Tuan Ngo 10-1





























Contents xv



1Vibration

Instrumentation


11 Introduction 1-1



Equipment












Summary


11 Introduction








1-1



















the object













6 Control devices


AnalogDigital

Interface

DigitalSignal


FilterAmplifier

FilterAmplifier

SignalGenerator



PowerAmplifier

MountingFixtures

TestObject

ResponseSensor

ControlSensor

Exciter

SwivelBase

















1 Test object

2 Excitation system

3 Control system




























SignalModification

System

TestObject

ControlSystem


System








and


Box 11







Exciters

Shakers


excitations)


excitations)





3 Drop (impulsive)

Signal Conditioning


Sensors








(Stroke)

Maximum

Velocity

Maximum

Acceleration

Maximum

Force

Excitation

Waveform

Hydraulic

(electrohydraulic)

Low

(01ndash500 Hz)


(50 insec

125 cmsec)

Intermediate

(20 g)

High (100000 lbf

450000 N)



Inertial


Intermediate

(2ndash50 Hz)


(50 insec

125 cmsec)

Intermediate

(20 g)

Intermediate

(1000 lbf 4500 N)

Sinusoidal only

Electromagnetic

(electrodynamic)

High

(2ndash10000 Hz)


(50 insec

125 cmsec)


(450 lbf 2000 N)



random)

VibrationInstru

mentation

1-5



CRCndashpp1ndash112

























20 dbdecade)

























Stroke

Limit M

ax

Acceleration

MaxVelocity

Peak

Vel

ocity

(cm

s)

01 1 10 100

FullLoad

NoLoad

Frequency (Hz)(a)

Peak

Vel

ocity

(cm

s)

100

10

1

100

10

1

01 1 10 100

FullLoad

NoLoad

Frequency (Hz)(b)



typical




1211 Force Rating









21p


















for acceleration

1212 Power Rating

















1213 Stroke Rating







Example 11








for the test

Solution







rating as






Acc

eler

atio

n(g

)

Con

stan

t Dis

plac

emen

t

Constant Velo

city

Frequency (Hz)

S

FP

0101

10 10 100

10

10























motors


























































m m

2mw2r cos wt

wtw w

wt



















































Denmark







Electrical Lediedt












d=dt as








Rev2

k2bs

Reye eth124THORN


given by

yevfrac14 kb

Re







eth127THORN

where

bo frac14 k2bRe

eth128THORN



yevfrac14 kb

Rb







effectiveness















100

10


Antiresonance

Resonance

Shak

erD

ispl

acem

entM

agni

tude

Resonance

1000




























13 Control System
















ExcitationInput

(Reference)

Feedback Paths

DriveSignal

ShakerResponse

TestTable

TestObject

Test ObjectResponse


(Shaker)(Ram)

Controllerand

Amplifier



















































1311 Compressor
























desired spectrum









































1321 Oscillators








oscillator
















DC Voltage

Oscillator


FrequencyConverter

FilterAmplifier


FrequencyCounter


Variable-GainOutput

Amplifier

SignalSpecification

LevelSpecification





53191fm


Preface

Acknowledgments

Editor-in-Chief

Contributors

Contents

Related Titles

53191ch1

Table of Contents


Summary

11 Introduction



1211 Force Rating

1212 Power Rating

1213 Stroke Rating






13 Control System


1311 Compressor





1321 Oscillators


1323 Tape Players






142 Linearity





151 Potentiometer


















15101 Sensitivity


















1621 Stroboscope






References


Summary


1A1 Dynamic Signals


1A111 Aliasing





1A212 Gain










1A222 Attenuation











1A5 Integration



























1A724 Zoom Settings






1A822 Overlapping




1A832 STFT vs RPM














Bibliography

Related Titles

53191ch2

Table of Contents


Summary

21 Introduction

22 Amplifiers







2242 Common Mode







23 Analog Filters















243 Demodulation










255 Digital Filters


26 Bridge Circuits






2641 Owen Bridge










281 Phase Shifters







292 Oscilloscopes

2921 Triggering



Bibliography

Related Titles

53191ch3

Table of Contents


Summary

31 Introduction


321 Test Signals




3222 Sine Sweep

3223 Sine Dwell

3224 Decaying Sine

3225 Sine Beat












































3432 Pluck Test

3433 Shaker Tests






















Bibliography

Related Titles

53191ch4

Table of Contents


Summary

41 Introduction



























Bibliography

Related Titles

53191ch5

Table of Contents


Summary

51 Definitions

511 Shock


513 Half-Sine Shock







531 Need





534 Definitions












5351 Definition












54 Pyroshocks







5524 Amplitude

5525 Duration

5526 Difficulties

56 Standards




564 Bump Test


571 Definition


58 Shock Machines

581 Main Types



58211 Impact Mode

58212 Impulse Mode














584 Limitations










592 Main Advantages


5931 Requirements

5932 Solutions





59411 Abacuses




5101 Principle



51022 ZERD Function









References

Related Titles

53191ch6

Table of Contents


Summary

61 Introduction




















682 Data Collectors





691 Time Domain





6915 Orbits









6926 Masks


693 Modal Domain


610 Fault Detection

6101 Standards











61111 Unbalance

61112 Misalignment


61114 Soft Foot

61115 Rubs

61116 Resonances

61117 Oil Whirl

61118 Oil Whip







61131 Pumps

61132 Fans



61135 Compressors



References

Related Titles

53191ch7

Table of Contents


Summary

71 Introduction


721 General Terms


723 Tool Wear



















7411 Time Domain







752 Neural Networks



753 Fuzzy Logic

754 Other Methods

76 Conclusion

References

Related Titles

53191ch8

Table of Contents


Summary

81 Introduction




841 Coverage Index

842 Overlap Index


85 A Case Study









86 Conclusion

References

Related Titles

53191ch9

Table of Contents


Summary

91 Introduction









941 Learning Mode

942 Monitoring Mode

943 Diagnostic Mode

944 Experiments







9443 Tests




96 Conclusions

References

Related Titles

53191ch10

Table of Contents


Summary

101 Introduction

























1031 Introduction

1032 Wind Speed










1037 Dampers



























106 Impact Loading



107 Floor Vibration

1071 Introduction


10721 Walking







10733 Damping

10734 Resonance




10751 Harmonics



Bibliography

Related Titles

53191ch11

Table of Contents


Summary

111 Introduction

















11244 Other Systems





























112911 Buildings

112912 Bridges


112921 Buildings

112922 Bridges
















































113714 Test Results








Bibliography

Related Titles

53191ch12

Table of Contents


Summary

121 Introduction





















12231 Kaul Method


































126 Conclusions

References

Related Titles

53191ch13

Table of Contents


Summary

131 Introduction











Bibliography

Related Titles

53191ch14

Table of Contents


Summary

141 Introduction












Bibliography

Related Titles

Contributors

xi








Singapore


Kyoto Japan


Science



Jalles France


Singapore


Technology

Singapore


Technology

Singapore




Technology

Singapore








Kyoto Japan




Singapore


Singapore





Contents


11 Introduction 1-1









21 Introduction 2-2

22 Amplifiers 2-2









31 Introduction 3-1






41 Introduction 4-1






xiii




51 Definitions 5-2



54 Pyroshocks 5-17


56 Standards 5-24







61 Introduction 6-2












71 Introduction 7-1





76 Conclusion 7-20


81 Introduction 8-1





86 Conclusion 8-23



91 Introduction 9-1




Contentsxiv




96 Conclusions 9-35


and Tuan Ngo 10-1





























Contents xv



1Vibration

Instrumentation


11 Introduction 1-1



Equipment












Summary


11 Introduction








1-1



















the object













6 Control devices


AnalogDigital

Interface

DigitalSignal


FilterAmplifier

FilterAmplifier

SignalGenerator



PowerAmplifier

MountingFixtures

TestObject

ResponseSensor

ControlSensor

Exciter

SwivelBase

















1 Test object

2 Excitation system

3 Control system




























SignalModification

System

TestObject

ControlSystem


System








and


Box 11







Exciters

Shakers


excitations)


excitations)





3 Drop (impulsive)

Signal Conditioning


Sensors








(Stroke)

Maximum

Velocity

Maximum

Acceleration

Maximum

Force

Excitation

Waveform

Hydraulic

(electrohydraulic)

Low

(01ndash500 Hz)


(50 insec

125 cmsec)

Intermediate

(20 g)

High (100000 lbf

450000 N)



Inertial


Intermediate

(2ndash50 Hz)


(50 insec

125 cmsec)

Intermediate

(20 g)

Intermediate

(1000 lbf 4500 N)

Sinusoidal only

Electromagnetic

(electrodynamic)

High

(2ndash10000 Hz)


(50 insec

125 cmsec)


(450 lbf 2000 N)



random)

VibrationInstru

mentation

1-5



CRCndashpp1ndash112

























20 dbdecade)

























Stroke

Limit M

ax

Acceleration

MaxVelocity

Peak

Vel

ocity

(cm

s)

01 1 10 100

FullLoad

NoLoad

Frequency (Hz)(a)

Peak

Vel

ocity

(cm

s)

100

10

1

100

10

1

01 1 10 100

FullLoad

NoLoad

Frequency (Hz)(b)



typical




1211 Force Rating









21p


















for acceleration

1212 Power Rating

















1213 Stroke Rating







Example 11








for the test

Solution







rating as






Acc

eler

atio

n(g

)

Con

stan

t Dis

plac

emen

t

Constant Velo

city

Frequency (Hz)

S

FP

0101

10 10 100

10

10























motors


























































m m

2mw2r cos wt

wtw w

wt



















































Denmark







Electrical Lediedt












d=dt as








Rev2

k2bs

Reye eth124THORN


given by

yevfrac14 kb

Re







eth127THORN

where

bo frac14 k2bRe

eth128THORN



yevfrac14 kb

Rb







effectiveness















100

10


Antiresonance

Resonance

Shak

erD

ispl

acem

entM

agni

tude

Resonance

1000




























13 Control System
















ExcitationInput

(Reference)

Feedback Paths

DriveSignal

ShakerResponse

TestTable

TestObject

Test ObjectResponse


(Shaker)(Ram)

Controllerand

Amplifier



















































1311 Compressor
























desired spectrum









































1321 Oscillators








oscillator
















DC Voltage

Oscillator


FrequencyConverter

FilterAmplifier


FrequencyCounter


Variable-GainOutput

Amplifier

SignalSpecification

LevelSpecification





53191fm


Preface

Acknowledgments

Editor-in-Chief

Contributors

Contents

Related Titles

53191ch1

Table of Contents


Summary

11 Introduction



1211 Force Rating

1212 Power Rating

1213 Stroke Rating






13 Control System


1311 Compressor





1321 Oscillators


1323 Tape Players






142 Linearity





151 Potentiometer


















15101 Sensitivity


















1621 Stroboscope






References


Summary


1A1 Dynamic Signals


1A111 Aliasing





1A212 Gain










1A222 Attenuation











1A5 Integration



























1A724 Zoom Settings






1A822 Overlapping




1A832 STFT vs RPM














Bibliography

Related Titles

53191ch2

Table of Contents


Summary

21 Introduction

22 Amplifiers







2242 Common Mode







23 Analog Filters















243 Demodulation










255 Digital Filters


26 Bridge Circuits






2641 Owen Bridge










281 Phase Shifters







292 Oscilloscopes

2921 Triggering



Bibliography

Related Titles

53191ch3

Table of Contents


Summary

31 Introduction


321 Test Signals




3222 Sine Sweep

3223 Sine Dwell

3224 Decaying Sine

3225 Sine Beat












































3432 Pluck Test

3433 Shaker Tests






















Bibliography

Related Titles

53191ch4

Table of Contents


Summary

41 Introduction



























Bibliography

Related Titles

53191ch5

Table of Contents


Summary

51 Definitions

511 Shock


513 Half-Sine Shock







531 Need





534 Definitions












5351 Definition












54 Pyroshocks







5524 Amplitude

5525 Duration

5526 Difficulties

56 Standards




564 Bump Test


571 Definition


58 Shock Machines

581 Main Types



58211 Impact Mode

58212 Impulse Mode














584 Limitations










592 Main Advantages


5931 Requirements

5932 Solutions





59411 Abacuses




5101 Principle



51022 ZERD Function









References

Related Titles

53191ch6

Table of Contents


Summary

61 Introduction




















682 Data Collectors





691 Time Domain





6915 Orbits









6926 Masks


693 Modal Domain


610 Fault Detection

6101 Standards











61111 Unbalance

61112 Misalignment


61114 Soft Foot

61115 Rubs

61116 Resonances

61117 Oil Whirl

61118 Oil Whip







61131 Pumps

61132 Fans



61135 Compressors



References

Related Titles

53191ch7

Table of Contents


Summary

71 Introduction


721 General Terms


723 Tool Wear



















7411 Time Domain







752 Neural Networks



753 Fuzzy Logic

754 Other Methods

76 Conclusion

References

Related Titles

53191ch8

Table of Contents


Summary

81 Introduction




841 Coverage Index

842 Overlap Index


85 A Case Study









86 Conclusion

References

Related Titles

53191ch9

Table of Contents


Summary

91 Introduction









941 Learning Mode

942 Monitoring Mode

943 Diagnostic Mode

944 Experiments







9443 Tests




96 Conclusions

References

Related Titles

53191ch10

Table of Contents


Summary

101 Introduction

























1031 Introduction

1032 Wind Speed










1037 Dampers



























106 Impact Loading



107 Floor Vibration

1071 Introduction


10721 Walking







10733 Damping

10734 Resonance




10751 Harmonics



Bibliography

Related Titles

53191ch11

Table of Contents


Summary

111 Introduction

















11244 Other Systems





























112911 Buildings

112912 Bridges


112921 Buildings

112922 Bridges
















































113714 Test Results








Bibliography

Related Titles

53191ch12

Table of Contents


Summary

121 Introduction





















12231 Kaul Method


































126 Conclusions

References

Related Titles

53191ch13

Table of Contents


Summary

131 Introduction











Bibliography

Related Titles

53191ch14

Table of Contents


Summary

141 Introduction












Bibliography

Related Titles

Contents


11 Introduction 1-1









21 Introduction 2-2

22 Amplifiers 2-2









31 Introduction 3-1






41 Introduction 4-1






xiii




51 Definitions 5-2



54 Pyroshocks 5-17


56 Standards 5-24







61 Introduction 6-2












71 Introduction 7-1





76 Conclusion 7-20


81 Introduction 8-1





86 Conclusion 8-23



91 Introduction 9-1




Contentsxiv




96 Conclusions 9-35


and Tuan Ngo 10-1





























Contents xv



1Vibration

Instrumentation


11 Introduction 1-1



Equipment












Summary


11 Introduction








1-1



















the object













6 Control devices


AnalogDigital

Interface

DigitalSignal


FilterAmplifier

FilterAmplifier

SignalGenerator



PowerAmplifier

MountingFixtures

TestObject

ResponseSensor

ControlSensor

Exciter

SwivelBase

















1 Test object

2 Excitation system

3 Control system




























SignalModification

System

TestObject

ControlSystem


System








and


Box 11







Exciters

Shakers


excitations)


excitations)





3 Drop (impulsive)

Signal Conditioning


Sensors








(Stroke)

Maximum

Velocity

Maximum

Acceleration

Maximum

Force

Excitation

Waveform

Hydraulic

(electrohydraulic)

Low

(01ndash500 Hz)


(50 insec

125 cmsec)

Intermediate

(20 g)

High (100000 lbf

450000 N)



Inertial


Intermediate

(2ndash50 Hz)


(50 insec

125 cmsec)

Intermediate

(20 g)

Intermediate

(1000 lbf 4500 N)

Sinusoidal only

Electromagnetic

(electrodynamic)

High

(2ndash10000 Hz)


(50 insec

125 cmsec)


(450 lbf 2000 N)



random)

VibrationInstru

mentation

1-5



CRCndashpp1ndash112

























20 dbdecade)

























Stroke

Limit M

ax

Acceleration

MaxVelocity

Peak

Vel

ocity

(cm

s)

01 1 10 100

FullLoad

NoLoad

Frequency (Hz)(a)

Peak

Vel

ocity

(cm

s)

100

10

1

100

10

1

01 1 10 100

FullLoad

NoLoad

Frequency (Hz)(b)



typical




1211 Force Rating









21p


















for acceleration

1212 Power Rating

















1213 Stroke Rating







Example 11








for the test

Solution







rating as






Acc

eler

atio

n(g

)

Con

stan

t Dis

plac

emen

t

Constant Velo

city

Frequency (Hz)

S

FP

0101

10 10 100

10

10























motors


























































m m

2mw2r cos wt

wtw w

wt



















































Denmark







Electrical Lediedt












d=dt as








Rev2

k2bs

Reye eth124THORN


given by

yevfrac14 kb

Re







eth127THORN

where

bo frac14 k2bRe

eth128THORN



yevfrac14 kb

Rb







effectiveness















100

10


Antiresonance

Resonance

Shak

erD

ispl

acem

entM

agni

tude

Resonance

1000




























13 Control System
















ExcitationInput

(Reference)

Feedback Paths

DriveSignal

ShakerResponse

TestTable

TestObject

Test ObjectResponse


(Shaker)(Ram)

Controllerand

Amplifier



















































1311 Compressor
























desired spectrum









































1321 Oscillators








oscillator
















DC Voltage

Oscillator


FrequencyConverter

FilterAmplifier


FrequencyCounter


Variable-GainOutput

Amplifier

SignalSpecification

LevelSpecification





53191fm


Preface

Acknowledgments

Editor-in-Chief

Contributors

Contents

Related Titles

53191ch1

Table of Contents


Summary

11 Introduction



1211 Force Rating

1212 Power Rating

1213 Stroke Rating






13 Control System


1311 Compressor





1321 Oscillators


1323 Tape Players






142 Linearity





151 Potentiometer


















15101 Sensitivity


















1621 Stroboscope






References


Summary


1A1 Dynamic Signals


1A111 Aliasing





1A212 Gain










1A222 Attenuation











1A5 Integration



























1A724 Zoom Settings






1A822 Overlapping




1A832 STFT vs RPM














Bibliography

Related Titles

53191ch2

Table of Contents


Summary

21 Introduction

22 Amplifiers







2242 Common Mode







23 Analog Filters















243 Demodulation










255 Digital Filters


26 Bridge Circuits






2641 Owen Bridge










281 Phase Shifters







292 Oscilloscopes

2921 Triggering



Bibliography

Related Titles

53191ch3

Table of Contents


Summary

31 Introduction


321 Test Signals




3222 Sine Sweep

3223 Sine Dwell

3224 Decaying Sine

3225 Sine Beat












































3432 Pluck Test

3433 Shaker Tests






















Bibliography

Related Titles

53191ch4

Table of Contents


Summary

41 Introduction



























Bibliography

Related Titles

53191ch5

Table of Contents


Summary

51 Definitions

511 Shock


513 Half-Sine Shock







531 Need





534 Definitions












5351 Definition












54 Pyroshocks







5524 Amplitude

5525 Duration

5526 Difficulties

56 Standards




564 Bump Test


571 Definition


58 Shock Machines

581 Main Types



58211 Impact Mode

58212 Impulse Mode














584 Limitations










592 Main Advantages


5931 Requirements

5932 Solutions





59411 Abacuses




5101 Principle



51022 ZERD Function









References

Related Titles

53191ch6

Table of Contents


Summary

61 Introduction




















682 Data Collectors





691 Time Domain





6915 Orbits









6926 Masks


693 Modal Domain


610 Fault Detection

6101 Standards











61111 Unbalance

61112 Misalignment


61114 Soft Foot

61115 Rubs

61116 Resonances

61117 Oil Whirl

61118 Oil Whip







61131 Pumps

61132 Fans



61135 Compressors



References

Related Titles

53191ch7

Table of Contents


Summary

71 Introduction


721 General Terms


723 Tool Wear



















7411 Time Domain







752 Neural Networks



753 Fuzzy Logic

754 Other Methods

76 Conclusion

References

Related Titles

53191ch8

Table of Contents


Summary

81 Introduction




841 Coverage Index

842 Overlap Index


85 A Case Study









86 Conclusion

References

Related Titles

53191ch9

Table of Contents


Summary

91 Introduction









941 Learning Mode

942 Monitoring Mode

943 Diagnostic Mode

944 Experiments







9443 Tests




96 Conclusions

References

Related Titles

53191ch10

Table of Contents


Summary

101 Introduction

























1031 Introduction

1032 Wind Speed










1037 Dampers



























106 Impact Loading



107 Floor Vibration

1071 Introduction


10721 Walking







10733 Damping

10734 Resonance




10751 Harmonics



Bibliography

Related Titles

53191ch11

Table of Contents


Summary

111 Introduction

















11244 Other Systems





























112911 Buildings

112912 Bridges


112921 Buildings

112922 Bridges
















































113714 Test Results








Bibliography

Related Titles

53191ch12

Table of Contents


Summary

121 Introduction





















12231 Kaul Method


































126 Conclusions

References

Related Titles

53191ch13

Table of Contents


Summary

131 Introduction











Bibliography

Related Titles

53191ch14

Table of Contents


Summary

141 Introduction












Bibliography

Related Titles


51 Definitions 5-2



54 Pyroshocks 5-17


56 Standards 5-24







61 Introduction 6-2












71 Introduction 7-1





76 Conclusion 7-20


81 Introduction 8-1





86 Conclusion 8-23



91 Introduction 9-1




Contentsxiv




96 Conclusions 9-35


and Tuan Ngo 10-1





























Contents xv



1Vibration

Instrumentation


11 Introduction 1-1



Equipment












Summary


11 Introduction








1-1



















the object













6 Control devices


AnalogDigital

Interface

DigitalSignal


FilterAmplifier

FilterAmplifier

SignalGenerator



PowerAmplifier

MountingFixtures

TestObject

ResponseSensor

ControlSensor

Exciter

SwivelBase

















1 Test object

2 Excitation system

3 Control system




























SignalModification

System

TestObject

ControlSystem


System








and


Box 11







Exciters

Shakers


excitations)


excitations)





3 Drop (impulsive)

Signal Conditioning


Sensors








(Stroke)

Maximum

Velocity

Maximum

Acceleration

Maximum

Force

Excitation

Waveform

Hydraulic

(electrohydraulic)

Low

(01ndash500 Hz)


(50 insec

125 cmsec)

Intermediate

(20 g)

High (100000 lbf

450000 N)



Inertial


Intermediate

(2ndash50 Hz)


(50 insec

125 cmsec)

Intermediate

(20 g)

Intermediate

(1000 lbf 4500 N)

Sinusoidal only

Electromagnetic

(electrodynamic)

High

(2ndash10000 Hz)


(50 insec

125 cmsec)


(450 lbf 2000 N)



random)

VibrationInstru

mentation

1-5



CRCndashpp1ndash112

























20 dbdecade)

























Stroke

Limit M

ax

Acceleration

MaxVelocity

Peak

Vel

ocity

(cm

s)

01 1 10 100

FullLoad

NoLoad

Frequency (Hz)(a)

Peak

Vel

ocity

(cm

s)

100

10

1

100

10

1

01 1 10 100

FullLoad

NoLoad

Frequency (Hz)(b)



typical




1211 Force Rating









21p


















for acceleration

1212 Power Rating

















1213 Stroke Rating







Example 11








for the test

Solution







rating as






Acc

eler

atio

n(g

)

Con

stan

t Dis

plac

emen

t

Constant Velo

city

Frequency (Hz)

S

FP

0101

10 10 100

10

10























motors


























































m m

2mw2r cos wt

wtw w

wt



















































Denmark







Electrical Lediedt












d=dt as








Rev2

k2bs

Reye eth124THORN


given by

yevfrac14 kb

Re







eth127THORN

where

bo frac14 k2bRe

eth128THORN



yevfrac14 kb

Rb







effectiveness















100

10


Antiresonance

Resonance

Shak

erD

ispl

acem

entM

agni

tude

Resonance

1000




























13 Control System
















ExcitationInput

(Reference)

Feedback Paths

DriveSignal

ShakerResponse

TestTable

TestObject

Test ObjectResponse


(Shaker)(Ram)

Controllerand

Amplifier



















































1311 Compressor
























desired spectrum









































1321 Oscillators








oscillator
















DC Voltage

Oscillator


FrequencyConverter

FilterAmplifier


FrequencyCounter


Variable-GainOutput

Amplifier

SignalSpecification

LevelSpecification





53191fm


Preface

Acknowledgments

Editor-in-Chief

Contributors

Contents

Related Titles

53191ch1

Table of Contents


Summary

11 Introduction



1211 Force Rating

1212 Power Rating

1213 Stroke Rating






13 Control System


1311 Compressor





1321 Oscillators


1323 Tape Players






142 Linearity





151 Potentiometer


















15101 Sensitivity


















1621 Stroboscope






References


Summary


1A1 Dynamic Signals


1A111 Aliasing





1A212 Gain










1A222 Attenuation











1A5 Integration



























1A724 Zoom Settings






1A822 Overlapping




1A832 STFT vs RPM














Bibliography

Related Titles

53191ch2

Table of Contents


Summary

21 Introduction

22 Amplifiers







2242 Common Mode







23 Analog Filters















243 Demodulation










255 Digital Filters


26 Bridge Circuits






2641 Owen Bridge










281 Phase Shifters







292 Oscilloscopes

2921 Triggering



Bibliography

Related Titles

53191ch3

Table of Contents


Summary

31 Introduction


321 Test Signals




3222 Sine Sweep

3223 Sine Dwell

3224 Decaying Sine

3225 Sine Beat












































3432 Pluck Test

3433 Shaker Tests






















Bibliography

Related Titles

53191ch4

Table of Contents


Summary

41 Introduction



























Bibliography

Related Titles

53191ch5

Table of Contents


Summary

51 Definitions

511 Shock


513 Half-Sine Shock







531 Need





534 Definitions












5351 Definition












54 Pyroshocks







5524 Amplitude

5525 Duration

5526 Difficulties

56 Standards




564 Bump Test


571 Definition


58 Shock Machines

581 Main Types



58211 Impact Mode

58212 Impulse Mode














584 Limitations










592 Main Advantages


5931 Requirements

5932 Solutions





59411 Abacuses




5101 Principle



51022 ZERD Function









References

Related Titles

53191ch6

Table of Contents


Summary

61 Introduction




















682 Data Collectors





691 Time Domain





6915 Orbits









6926 Masks


693 Modal Domain


610 Fault Detection

6101 Standards











61111 Unbalance

61112 Misalignment


61114 Soft Foot

61115 Rubs

61116 Resonances

61117 Oil Whirl

61118 Oil Whip







61131 Pumps

61132 Fans



61135 Compressors



References

Related Titles

53191ch7

Table of Contents


Summary

71 Introduction


721 General Terms


723 Tool Wear



















7411 Time Domain







752 Neural Networks



753 Fuzzy Logic

754 Other Methods

76 Conclusion

References

Related Titles

53191ch8

Table of Contents


Summary

81 Introduction




841 Coverage Index

842 Overlap Index


85 A Case Study









86 Conclusion

References

Related Titles

53191ch9

Table of Contents


Summary

91 Introduction









941 Learning Mode

942 Monitoring Mode

943 Diagnostic Mode

944 Experiments







9443 Tests




96 Conclusions

References

Related Titles

53191ch10

Table of Contents


Summary

101 Introduction

























1031 Introduction

1032 Wind Speed










1037 Dampers



























106 Impact Loading



107 Floor Vibration

1071 Introduction


10721 Walking







10733 Damping

10734 Resonance




10751 Harmonics



Bibliography

Related Titles

53191ch11

Table of Contents


Summary

111 Introduction

















11244 Other Systems





























112911 Buildings

112912 Bridges


112921 Buildings

112922 Bridges
















































113714 Test Results








Bibliography

Related Titles

53191ch12

Table of Contents


Summary

121 Introduction





















12231 Kaul Method


































126 Conclusions

References

Related Titles

53191ch13

Table of Contents


Summary

131 Introduction











Bibliography

Related Titles

53191ch14

Table of Contents


Summary

141 Introduction












Bibliography

Related Titles


96 Conclusions 9-35


and Tuan Ngo 10-1





























Contents xv



1Vibration

Instrumentation


11 Introduction 1-1



Equipment












Summary


11 Introduction








1-1



















the object













6 Control devices


AnalogDigital

Interface

DigitalSignal


FilterAmplifier

FilterAmplifier

SignalGenerator



PowerAmplifier

MountingFixtures

TestObject

ResponseSensor

ControlSensor

Exciter

SwivelBase

















1 Test object

2 Excitation system

3 Control system




























SignalModification

System

TestObject

ControlSystem


System








and


Box 11







Exciters

Shakers


excitations)


excitations)





3 Drop (impulsive)

Signal Conditioning


Sensors








(Stroke)

Maximum

Velocity

Maximum

Acceleration

Maximum

Force

Excitation

Waveform

Hydraulic

(electrohydraulic)

Low

(01ndash500 Hz)


(50 insec

125 cmsec)

Intermediate

(20 g)

High (100000 lbf

450000 N)



Inertial


Intermediate

(2ndash50 Hz)


(50 insec

125 cmsec)

Intermediate

(20 g)

Intermediate

(1000 lbf 4500 N)

Sinusoidal only

Electromagnetic

(electrodynamic)

High

(2ndash10000 Hz)


(50 insec

125 cmsec)


(450 lbf 2000 N)



random)

VibrationInstru

mentation

1-5



CRCndashpp1ndash112

























20 dbdecade)

























Stroke

Limit M

ax

Acceleration

MaxVelocity

Peak

Vel

ocity

(cm

s)

01 1 10 100

FullLoad

NoLoad

Frequency (Hz)(a)

Peak

Vel

ocity

(cm

s)

100

10

1

100

10

1

01 1 10 100

FullLoad

NoLoad

Frequency (Hz)(b)



typical




1211 Force Rating









21p


















for acceleration

1212 Power Rating

















1213 Stroke Rating







Example 11








for the test

Solution







rating as






Acc

eler

atio

n(g

)

Con

stan

t Dis

plac

emen

t

Constant Velo

city

Frequency (Hz)

S

FP

0101

10 10 100

10

10























motors


























































m m

2mw2r cos wt

wtw w

wt



















































Denmark







Electrical Lediedt












d=dt as








Rev2

k2bs

Reye eth124THORN


given by

yevfrac14 kb

Re







eth127THORN

where

bo frac14 k2bRe

eth128THORN



yevfrac14 kb

Rb







effectiveness















100

10


Antiresonance

Resonance

Shak

erD

ispl

acem

entM

agni

tude

Resonance

1000




























13 Control System
















ExcitationInput

(Reference)

Feedback Paths

DriveSignal

ShakerResponse

TestTable

TestObject

Test ObjectResponse


(Shaker)(Ram)

Controllerand

Amplifier



















































1311 Compressor
























desired spectrum









































1321 Oscillators








oscillator
















DC Voltage

Oscillator


FrequencyConverter

FilterAmplifier


FrequencyCounter


Variable-GainOutput

Amplifier

SignalSpecification

LevelSpecification





53191fm


Preface

Acknowledgments

Editor-in-Chief

Contributors

Contents

Related Titles

53191ch1

Table of Contents


Summary

11 Introduction



1211 Force Rating

1212 Power Rating

1213 Stroke Rating






13 Control System


1311 Compressor





1321 Oscillators


1323 Tape Players






142 Linearity





151 Potentiometer


















15101 Sensitivity


















1621 Stroboscope






References


Summary


1A1 Dynamic Signals


1A111 Aliasing





1A212 Gain










1A222 Attenuation











1A5 Integration



























1A724 Zoom Settings






1A822 Overlapping




1A832 STFT vs RPM














Bibliography

Related Titles

53191ch2

Table of Contents


Summary

21 Introduction

22 Amplifiers







2242 Common Mode







23 Analog Filters















243 Demodulation










255 Digital Filters


26 Bridge Circuits






2641 Owen Bridge










281 Phase Shifters







292 Oscilloscopes

2921 Triggering



Bibliography

Related Titles

53191ch3

Table of Contents


Summary

31 Introduction


321 Test Signals




3222 Sine Sweep

3223 Sine Dwell

3224 Decaying Sine

3225 Sine Beat












































3432 Pluck Test

3433 Shaker Tests






















Bibliography

Related Titles

53191ch4

Table of Contents


Summary

41 Introduction



























Bibliography

Related Titles

53191ch5

Table of Contents


Summary

51 Definitions

511 Shock


513 Half-Sine Shock







531 Need





534 Definitions












5351 Definition












54 Pyroshocks







5524 Amplitude

5525 Duration

5526 Difficulties

56 Standards




564 Bump Test


571 Definition


58 Shock Machines

581 Main Types



58211 Impact Mode

58212 Impulse Mode














584 Limitations










592 Main Advantages


5931 Requirements

5932 Solutions





59411 Abacuses




5101 Principle



51022 ZERD Function









References

Related Titles

53191ch6

Table of Contents


Summary

61 Introduction




















682 Data Collectors





691 Time Domain





6915 Orbits









6926 Masks


693 Modal Domain


610 Fault Detection

6101 Standards











61111 Unbalance

61112 Misalignment


61114 Soft Foot

61115 Rubs

61116 Resonances

61117 Oil Whirl

61118 Oil Whip







61131 Pumps

61132 Fans



61135 Compressors



References

Related Titles

53191ch7

Table of Contents


Summary

71 Introduction


721 General Terms


723 Tool Wear



















7411 Time Domain







752 Neural Networks



753 Fuzzy Logic

754 Other Methods

76 Conclusion

References

Related Titles

53191ch8

Table of Contents


Summary

81 Introduction




841 Coverage Index

842 Overlap Index


85 A Case Study









86 Conclusion

References

Related Titles

53191ch9

Table of Contents


Summary

91 Introduction









941 Learning Mode

942 Monitoring Mode

943 Diagnostic Mode

944 Experiments







9443 Tests




96 Conclusions

References

Related Titles

53191ch10

Table of Contents


Summary

101 Introduction

























1031 Introduction

1032 Wind Speed










1037 Dampers



























106 Impact Loading



107 Floor Vibration

1071 Introduction


10721 Walking







10733 Damping

10734 Resonance




10751 Harmonics



Bibliography

Related Titles

53191ch11

Table of Contents


Summary

111 Introduction

















11244 Other Systems





























112911 Buildings

112912 Bridges


112921 Buildings

112922 Bridges
















































113714 Test Results








Bibliography

Related Titles

53191ch12

Table of Contents


Summary

121 Introduction





















12231 Kaul Method


































126 Conclusions

References

Related Titles

53191ch13

Table of Contents


Summary

131 Introduction











Bibliography

Related Titles

53191ch14

Table of Contents


Summary

141 Introduction












Bibliography

Related Titles

1Vibration

Instrumentation


11 Introduction 1-1



Equipment












Summary


11 Introduction








1-1



















the object













6 Control devices


AnalogDigital

Interface

DigitalSignal


FilterAmplifier

FilterAmplifier

SignalGenerator



PowerAmplifier

MountingFixtures

TestObject

ResponseSensor

ControlSensor

Exciter

SwivelBase

















1 Test object

2 Excitation system

3 Control system




























SignalModification

System

TestObject

ControlSystem


System








and


Box 11







Exciters

Shakers


excitations)


excitations)





3 Drop (impulsive)

Signal Conditioning


Sensors








(Stroke)

Maximum

Velocity

Maximum

Acceleration

Maximum

Force

Excitation

Waveform

Hydraulic

(electrohydraulic)

Low

(01ndash500 Hz)


(50 insec

125 cmsec)

Intermediate

(20 g)

High (100000 lbf

450000 N)



Inertial


Intermediate

(2ndash50 Hz)


(50 insec

125 cmsec)

Intermediate

(20 g)

Intermediate

(1000 lbf 4500 N)

Sinusoidal only

Electromagnetic

(electrodynamic)

High

(2ndash10000 Hz)


(50 insec

125 cmsec)


(450 lbf 2000 N)



random)

VibrationInstru

mentation

1-5



CRCndashpp1ndash112

























20 dbdecade)

























Stroke

Limit M

ax

Acceleration

MaxVelocity

Peak

Vel

ocity

(cm

s)

01 1 10 100

FullLoad

NoLoad

Frequency (Hz)(a)

Peak

Vel

ocity

(cm

s)

100

10

1

100

10

1

01 1 10 100

FullLoad

NoLoad

Frequency (Hz)(b)



typical




1211 Force Rating









21p


















for acceleration

1212 Power Rating

















1213 Stroke Rating







Example 11








for the test

Solution







rating as






Acc

eler

atio

n(g

)

Con

stan

t Dis

plac

emen

t

Constant Velo

city

Frequency (Hz)

S

FP

0101

10 10 100

10

10























motors


























































m m

2mw2r cos wt

wtw w

wt



















































Denmark







Electrical Lediedt












d=dt as








Rev2

k2bs

Reye eth124THORN


given by

yevfrac14 kb

Re







eth127THORN

where

bo frac14 k2bRe

eth128THORN



yevfrac14 kb

Rb







effectiveness















100

10


Antiresonance

Resonance

Shak

erD

ispl

acem

entM

agni

tude

Resonance

1000




























13 Control System
















ExcitationInput

(Reference)

Feedback Paths

DriveSignal

ShakerResponse

TestTable

TestObject

Test ObjectResponse


(Shaker)(Ram)

Controllerand

Amplifier



















































1311 Compressor
























desired spectrum









































1321 Oscillators








oscillator
















DC Voltage

Oscillator


FrequencyConverter

FilterAmplifier


FrequencyCounter


Variable-GainOutput

Amplifier

SignalSpecification

LevelSpecification





53191fm


Preface

Acknowledgments

Editor-in-Chief

Contributors

Contents

Related Titles

53191ch1

Table of Contents


Summary

11 Introduction



1211 Force Rating

1212 Power Rating

1213 Stroke Rating






13 Control System


1311 Compressor





1321 Oscillators


1323 Tape Players






142 Linearity





151 Potentiometer


















15101 Sensitivity


















1621 Stroboscope






References


Summary


1A1 Dynamic Signals


1A111 Aliasing





1A212 Gain










1A222 Attenuation











1A5 Integration



























1A724 Zoom Settings






1A822 Overlapping




1A832 STFT vs RPM














Bibliography

Related Titles

53191ch2

Table of Contents


Summary

21 Introduction

22 Amplifiers







2242 Common Mode







23 Analog Filters















243 Demodulation










255 Digital Filters


26 Bridge Circuits






2641 Owen Bridge










281 Phase Shifters







292 Oscilloscopes

2921 Triggering



Bibliography

Related Titles

53191ch3

Table of Contents


Summary

31 Introduction


321 Test Signals




3222 Sine Sweep

3223 Sine Dwell

3224 Decaying Sine

3225 Sine Beat












































3432 Pluck Test

3433 Shaker Tests






















Bibliography

Related Titles

53191ch4

Table of Contents


Summary

41 Introduction



























Bibliography

Related Titles

53191ch5

Table of Contents


Summary

51 Definitions

511 Shock


513 Half-Sine Shock







531 Need





534 Definitions












5351 Definition












54 Pyroshocks







5524 Amplitude

5525 Duration

5526 Difficulties

56 Standards




564 Bump Test


571 Definition


58 Shock Machines

581 Main Types



58211 Impact Mode

58212 Impulse Mode














584 Limitations










592 Main Advantages


5931 Requirements

5932 Solutions





59411 Abacuses




5101 Principle



51022 ZERD Function









References

Related Titles

53191ch6

Table of Contents


Summary

61 Introduction




















682 Data Collectors





691 Time Domain





6915 Orbits









6926 Masks


693 Modal Domain


610 Fault Detection

6101 Standards











61111 Unbalance

61112 Misalignment


61114 Soft Foot

61115 Rubs

61116 Resonances

61117 Oil Whirl

61118 Oil Whip







61131 Pumps

61132 Fans



61135 Compressors



References

Related Titles

53191ch7

Table of Contents


Summary

71 Introduction


721 General Terms


723 Tool Wear



















7411 Time Domain







752 Neural Networks



753 Fuzzy Logic

754 Other Methods

76 Conclusion

References

Related Titles

53191ch8

Table of Contents


Summary

81 Introduction




841 Coverage Index

842 Overlap Index


85 A Case Study









86 Conclusion

References

Related Titles

53191ch9

Table of Contents


Summary

91 Introduction









941 Learning Mode

942 Monitoring Mode

943 Diagnostic Mode

944 Experiments







9443 Tests




96 Conclusions

References

Related Titles

53191ch10

Table of Contents


Summary

101 Introduction

























1031 Introduction

1032 Wind Speed










1037 Dampers



























106 Impact Loading



107 Floor Vibration

1071 Introduction


10721 Walking







10733 Damping

10734 Resonance




10751 Harmonics



Bibliography

Related Titles

53191ch11

Table of Contents


Summary

111 Introduction

















11244 Other Systems





























112911 Buildings

112912 Bridges


112921 Buildings

112922 Bridges
















































113714 Test Results








Bibliography

Related Titles

53191ch12

Table of Contents


Summary

121 Introduction





















12231 Kaul Method


































126 Conclusions

References

Related Titles

53191ch13

Table of Contents


Summary

131 Introduction











Bibliography

Related Titles

53191ch14

Table of Contents


Summary

141 Introduction












Bibliography

Related Titles

















the object













6 Control devices


AnalogDigital

Interface

DigitalSignal


FilterAmplifier

FilterAmplifier

SignalGenerator



PowerAmplifier

MountingFixtures

TestObject

ResponseSensor

ControlSensor

Exciter

SwivelBase

















1 Test object

2 Excitation system

3 Control system




























SignalModification

System

TestObject

ControlSystem


System








and


Box 11







Exciters

Shakers


excitations)


excitations)





3 Drop (impulsive)

Signal Conditioning


Sensors








(Stroke)

Maximum

Velocity

Maximum

Acceleration

Maximum

Force

Excitation

Waveform

Hydraulic

(electrohydraulic)

Low

(01ndash500 Hz)


(50 insec

125 cmsec)

Intermediate

(20 g)

High (100000 lbf

450000 N)



Inertial


Intermediate

(2ndash50 Hz)


(50 insec

125 cmsec)

Intermediate

(20 g)

Intermediate

(1000 lbf 4500 N)

Sinusoidal only

Electromagnetic

(electrodynamic)

High

(2ndash10000 Hz)


(50 insec

125 cmsec)


(450 lbf 2000 N)



random)

VibrationInstru

mentation

1-5



CRCndashpp1ndash112

























20 dbdecade)

























Stroke

Limit M

ax

Acceleration

MaxVelocity

Peak

Vel

ocity

(cm

s)

01 1 10 100

FullLoad

NoLoad

Frequency (Hz)(a)

Peak

Vel

ocity

(cm

s)

100

10

1

100

10

1

01 1 10 100

FullLoad

NoLoad

Frequency (Hz)(b)



typical




1211 Force Rating









21p


















for acceleration

1212 Power Rating

















1213 Stroke Rating







Example 11








for the test

Solution







rating as






Acc

eler

atio

n(g

)

Con

stan

t Dis

plac

emen

t

Constant Velo

city

Frequency (Hz)

S

FP

0101

10 10 100

10

10























motors


























































m m

2mw2r cos wt

wtw w

wt



















































Denmark







Electrical Lediedt












d=dt as








Rev2

k2bs

Reye eth124THORN


given by

yevfrac14 kb

Re







eth127THORN

where

bo frac14 k2bRe

eth128THORN



yevfrac14 kb

Rb







effectiveness















100

10


Antiresonance

Resonance

Shak

erD

ispl

acem

entM

agni

tude

Resonance

1000




























13 Control System
















ExcitationInput

(Reference)

Feedback Paths

DriveSignal

ShakerResponse

TestTable

TestObject

Test ObjectResponse


(Shaker)(Ram)

Controllerand

Amplifier



















































1311 Compressor
























desired spectrum









































1321 Oscillators








oscillator
















DC Voltage

Oscillator


FrequencyConverter

FilterAmplifier


FrequencyCounter


Variable-GainOutput

Amplifier

SignalSpecification

LevelSpecification





53191fm


Preface

Acknowledgments

Editor-in-Chief

Contributors

Contents

Related Titles

53191ch1

Table of Contents


Summary

11 Introduction



1211 Force Rating

1212 Power Rating

1213 Stroke Rating






13 Control System


1311 Compressor





1321 Oscillators


1323 Tape Players






142 Linearity





151 Potentiometer


















15101 Sensitivity


















1621 Stroboscope






References


Summary


1A1 Dynamic Signals


1A111 Aliasing





1A212 Gain










1A222 Attenuation











1A5 Integration



























1A724 Zoom Settings






1A822 Overlapping




1A832 STFT vs RPM














Bibliography

Related Titles

53191ch2

Table of Contents


Summary

21 Introduction

22 Amplifiers







2242 Common Mode







23 Analog Filters















243 Demodulation










255 Digital Filters


26 Bridge Circuits






2641 Owen Bridge










281 Phase Shifters







292 Oscilloscopes

2921 Triggering



Bibliography

Related Titles

53191ch3

Table of Contents


Summary

31 Introduction


321 Test Signals




3222 Sine Sweep

3223 Sine Dwell

3224 Decaying Sine

3225 Sine Beat












































3432 Pluck Test

3433 Shaker Tests






















Bibliography

Related Titles

53191ch4

Table of Contents


Summary

41 Introduction



























Bibliography

Related Titles

53191ch5

Table of Contents


Summary

51 Definitions

511 Shock


513 Half-Sine Shock







531 Need





534 Definitions












5351 Definition












54 Pyroshocks







5524 Amplitude

5525 Duration

5526 Difficulties

56 Standards




564 Bump Test


571 Definition


58 Shock Machines

581 Main Types



58211 Impact Mode

58212 Impulse Mode














584 Limitations










592 Main Advantages


5931 Requirements

5932 Solutions





59411 Abacuses




5101 Principle



51022 ZERD Function









References

Related Titles

53191ch6

Table of Contents


Summary

61 Introduction




















682 Data Collectors





691 Time Domain





6915 Orbits









6926 Masks


693 Modal Domain


610 Fault Detection

6101 Standards











61111 Unbalance

61112 Misalignment


61114 Soft Foot

61115 Rubs

61116 Resonances

61117 Oil Whirl

61118 Oil Whip







61131 Pumps

61132 Fans



61135 Compressors



References

Related Titles

53191ch7

Table of Contents


Summary

71 Introduction


721 General Terms


723 Tool Wear



















7411 Time Domain







752 Neural Networks



753 Fuzzy Logic

754 Other Methods

76 Conclusion

References

Related Titles

53191ch8

Table of Contents


Summary

81 Introduction




841 Coverage Index

842 Overlap Index


85 A Case Study









86 Conclusion

References

Related Titles

53191ch9

Table of Contents


Summary

91 Introduction









941 Learning Mode

942 Monitoring Mode

943 Diagnostic Mode

944 Experiments







9443 Tests




96 Conclusions

References

Related Titles

53191ch10

Table of Contents


Summary

101 Introduction

























1031 Introduction

1032 Wind Speed










1037 Dampers



























106 Impact Loading



107 Floor Vibration

1071 Introduction


10721 Walking







10733 Damping

10734 Resonance




10751 Harmonics



Bibliography

Related Titles

53191ch11

Table of Contents


Summary

111 Introduction

















11244 Other Systems





























112911 Buildings

112912 Bridges


112921 Buildings

112922 Bridges
















































113714 Test Results








Bibliography

Related Titles

53191ch12

Table of Contents


Summary

121 Introduction





















12231 Kaul Method


































126 Conclusions

References

Related Titles

53191ch13

Table of Contents


Summary

131 Introduction











Bibliography

Related Titles

53191ch14

Table of Contents


Summary

141 Introduction












Bibliography

Related Titles













1 Test object

2 Excitation system

3 Control system




























SignalModification

System

TestObject

ControlSystem


System








and


Box 11







Exciters

Shakers


excitations)


excitations)





3 Drop (impulsive)

Signal Conditioning


Sensors








(Stroke)

Maximum

Velocity

Maximum

Acceleration

Maximum

Force

Excitation

Waveform

Hydraulic

(electrohydraulic)

Low

(01ndash500 Hz)


(50 insec

125 cmsec)

Intermediate

(20 g)

High (100000 lbf

450000 N)



Inertial


Intermediate

(2ndash50 Hz)


(50 insec

125 cmsec)

Intermediate

(20 g)

Intermediate

(1000 lbf 4500 N)

Sinusoidal only

Electromagnetic

(electrodynamic)

High

(2ndash10000 Hz)


(50 insec

125 cmsec)


(450 lbf 2000 N)



random)

VibrationInstru

mentation

1-5



CRCndashpp1ndash112

























20 dbdecade)

























Stroke

Limit M

ax

Acceleration

MaxVelocity

Peak

Vel

ocity

(cm

s)

01 1 10 100

FullLoad

NoLoad

Frequency (Hz)(a)

Peak

Vel

ocity

(cm

s)

100

10

1

100

10

1

01 1 10 100

FullLoad

NoLoad

Frequency (Hz)(b)



typical




1211 Force Rating









21p


















for acceleration

1212 Power Rating

















1213 Stroke Rating







Example 11








for the test

Solution







rating as






Acc

eler

atio

n(g

)

Con

stan

t Dis

plac

emen

t

Constant Velo

city

Frequency (Hz)

S

FP

0101

10 10 100

10

10























motors


























































m m

2mw2r cos wt

wtw w

wt



















































Denmark







Electrical Lediedt












d=dt as








Rev2

k2bs

Reye eth124THORN


given by

yevfrac14 kb

Re







eth127THORN

where

bo frac14 k2bRe

eth128THORN



yevfrac14 kb

Rb







effectiveness















100

10


Antiresonance

Resonance

Shak

erD

ispl

acem

entM

agni

tude

Resonance

1000




























13 Control System
















ExcitationInput

(Reference)

Feedback Paths

DriveSignal

ShakerResponse

TestTable

TestObject

Test ObjectResponse


(Shaker)(Ram)

Controllerand

Amplifier



















































1311 Compressor
























desired spectrum









































1321 Oscillators








oscillator
















DC Voltage

Oscillator


FrequencyConverter

FilterAmplifier


FrequencyCounter


Variable-GainOutput

Amplifier

SignalSpecification

LevelSpecification





53191fm


Preface

Acknowledgments

Editor-in-Chief

Contributors

Contents

Related Titles

53191ch1

Table of Contents


Summary

11 Introduction



1211 Force Rating

1212 Power Rating

1213 Stroke Rating






13 Control System


1311 Compressor





1321 Oscillators


1323 Tape Players






142 Linearity





151 Potentiometer


















15101 Sensitivity


















1621 Stroboscope






References


Summary


1A1 Dynamic Signals


1A111 Aliasing





1A212 Gain










1A222 Attenuation











1A5 Integration



























1A724 Zoom Settings






1A822 Overlapping




1A832 STFT vs RPM














Bibliography

Related Titles

53191ch2

Table of Contents


Summary

21 Introduction

22 Amplifiers







2242 Common Mode







23 Analog Filters















243 Demodulation










255 Digital Filters


26 Bridge Circuits






2641 Owen Bridge










281 Phase Shifters







292 Oscilloscopes

2921 Triggering



Bibliography

Related Titles

53191ch3

Table of Contents


Summary

31 Introduction


321 Test Signals




3222 Sine Sweep

3223 Sine Dwell

3224 Decaying Sine

3225 Sine Beat












































3432 Pluck Test

3433 Shaker Tests






















Bibliography

Related Titles

53191ch4

Table of Contents


Summary

41 Introduction



























Bibliography

Related Titles

53191ch5

Table of Contents


Summary

51 Definitions

511 Shock


513 Half-Sine Shock







531 Need





534 Definitions












5351 Definition












54 Pyroshocks







5524 Amplitude

5525 Duration

5526 Difficulties

56 Standards




564 Bump Test


571 Definition


58 Shock Machines

581 Main Types



58211 Impact Mode

58212 Impulse Mode














584 Limitations










592 Main Advantages


5931 Requirements

5932 Solutions





59411 Abacuses




5101 Principle



51022 ZERD Function









References

Related Titles

53191ch6

Table of Contents


Summary

61 Introduction




















682 Data Collectors





691 Time Domain





6915 Orbits









6926 Masks


693 Modal Domain


610 Fault Detection

6101 Standards











61111 Unbalance

61112 Misalignment


61114 Soft Foot

61115 Rubs

61116 Resonances

61117 Oil Whirl

61118 Oil Whip







61131 Pumps

61132 Fans



61135 Compressors



References

Related Titles

53191ch7

Table of Contents


Summary

71 Introduction


721 General Terms


723 Tool Wear



















7411 Time Domain







752 Neural Networks



753 Fuzzy Logic

754 Other Methods

76 Conclusion

References

Related Titles

53191ch8

Table of Contents


Summary

81 Introduction




841 Coverage Index

842 Overlap Index


85 A Case Study









86 Conclusion

References

Related Titles

53191ch9

Table of Contents


Summary

91 Introduction









941 Learning Mode

942 Monitoring Mode

943 Diagnostic Mode

944 Experiments







9443 Tests




96 Conclusions

References

Related Titles

53191ch10

Table of Contents


Summary

101 Introduction

























1031 Introduction

1032 Wind Speed










1037 Dampers



























106 Impact Loading



107 Floor Vibration

1071 Introduction


10721 Walking







10733 Damping

10734 Resonance




10751 Harmonics



Bibliography

Related Titles

53191ch11

Table of Contents


Summary

111 Introduction

















11244 Other Systems





























112911 Buildings

112912 Bridges


112921 Buildings

112922 Bridges
















































113714 Test Results








Bibliography

Related Titles

53191ch12

Table of Contents


Summary

121 Introduction





















12231 Kaul Method


































126 Conclusions

References

Related Titles

53191ch13

Table of Contents


Summary

131 Introduction











Bibliography

Related Titles

53191ch14

Table of Contents


Summary

141 Introduction












Bibliography

Related Titles



and


Box 11







Exciters

Shakers


excitations)


excitations)





3 Drop (impulsive)

Signal Conditioning


Sensors








(Stroke)

Maximum

Velocity

Maximum

Acceleration

Maximum

Force

Excitation

Waveform

Hydraulic

(electrohydraulic)

Low

(01ndash500 Hz)


(50 insec

125 cmsec)

Intermediate

(20 g)

High (100000 lbf

450000 N)



Inertial


Intermediate

(2ndash50 Hz)


(50 insec

125 cmsec)

Intermediate

(20 g)

Intermediate

(1000 lbf 4500 N)

Sinusoidal only

Electromagnetic

(electrodynamic)

High

(2ndash10000 Hz)


(50 insec

125 cmsec)


(450 lbf 2000 N)



random)

VibrationInstru

mentation

1-5



CRCndashpp1ndash112

























20 dbdecade)

























Stroke

Limit M

ax

Acceleration

MaxVelocity

Peak

Vel

ocity

(cm

s)

01 1 10 100

FullLoad

NoLoad

Frequency (Hz)(a)

Peak

Vel

ocity

(cm

s)

100

10

1

100

10

1

01 1 10 100

FullLoad

NoLoad

Frequency (Hz)(b)



typical




1211 Force Rating









21p


















for acceleration

1212 Power Rating

















1213 Stroke Rating







Example 11








for the test

Solution







rating as






Acc

eler

atio

n(g

)

Con

stan

t Dis

plac

emen

t

Constant Velo

city

Frequency (Hz)

S

FP

0101

10 10 100

10

10























motors


























































m m

2mw2r cos wt

wtw w

wt



















































Denmark







Electrical Lediedt












d=dt as








Rev2

k2bs

Reye eth124THORN


given by

yevfrac14 kb

Re







eth127THORN

where

bo frac14 k2bRe

eth128THORN



yevfrac14 kb

Rb







effectiveness















100

10


Antiresonance

Resonance

Shak

erD

ispl

acem

entM

agni

tude

Resonance

1000




























13 Control System
















ExcitationInput

(Reference)

Feedback Paths

DriveSignal

ShakerResponse

TestTable

TestObject

Test ObjectResponse


(Shaker)(Ram)

Controllerand

Amplifier



















































1311 Compressor
























desired spectrum









































1321 Oscillators








oscillator
















DC Voltage

Oscillator


FrequencyConverter

FilterAmplifier


FrequencyCounter


Variable-GainOutput

Amplifier

SignalSpecification

LevelSpecification





53191fm


Preface

Acknowledgments

Editor-in-Chief

Contributors

Contents

Related Titles

53191ch1

Table of Contents


Summary

11 Introduction



1211 Force Rating

1212 Power Rating

1213 Stroke Rating






13 Control System


1311 Compressor





1321 Oscillators


1323 Tape Players






142 Linearity





151 Potentiometer


















15101 Sensitivity


















1621 Stroboscope






References


Summary


1A1 Dynamic Signals


1A111 Aliasing





1A212 Gain










1A222 Attenuation











1A5 Integration



























1A724 Zoom Settings






1A822 Overlapping




1A832 STFT vs RPM














Bibliography

Related Titles

53191ch2

Table of Contents


Summary

21 Introduction

22 Amplifiers







2242 Common Mode







23 Analog Filters















243 Demodulation










255 Digital Filters


26 Bridge Circuits






2641 Owen Bridge










281 Phase Shifters







292 Oscilloscopes

2921 Triggering



Bibliography

Related Titles

53191ch3

Table of Contents


Summary

31 Introduction


321 Test Signals




3222 Sine Sweep

3223 Sine Dwell

3224 Decaying Sine

3225 Sine Beat












































3432 Pluck Test

3433 Shaker Tests






















Bibliography

Related Titles

53191ch4

Table of Contents


Summary

41 Introduction



























Bibliography

Related Titles

53191ch5

Table of Contents


Summary

51 Definitions

511 Shock


513 Half-Sine Shock







531 Need





534 Definitions












5351 Definition












54 Pyroshocks







5524 Amplitude

5525 Duration

5526 Difficulties

56 Standards




564 Bump Test


571 Definition


58 Shock Machines

581 Main Types



58211 Impact Mode

58212 Impulse Mode














584 Limitations










592 Main Advantages


5931 Requirements

5932 Solutions





59411 Abacuses




5101 Principle



51022 ZERD Function









References

Related Titles

53191ch6

Table of Contents


Summary

61 Introduction




















682 Data Collectors





691 Time Domain





6915 Orbits









6926 Masks


693 Modal Domain


610 Fault Detection

6101 Standards











61111 Unbalance

61112 Misalignment


61114 Soft Foot

61115 Rubs

61116 Resonances

61117 Oil Whirl

61118 Oil Whip







61131 Pumps

61132 Fans



61135 Compressors



References

Related Titles

53191ch7

Table of Contents


Summary

71 Introduction


721 General Terms


723 Tool Wear



















7411 Time Domain







752 Neural Networks



753 Fuzzy Logic

754 Other Methods

76 Conclusion

References

Related Titles

53191ch8

Table of Contents


Summary

81 Introduction




841 Coverage Index

842 Overlap Index


85 A Case Study









86 Conclusion

References

Related Titles

53191ch9

Table of Contents


Summary

91 Introduction









941 Learning Mode

942 Monitoring Mode

943 Diagnostic Mode

944 Experiments







9443 Tests




96 Conclusions

References

Related Titles

53191ch10

Table of Contents


Summary

101 Introduction

























1031 Introduction

1032 Wind Speed










1037 Dampers



























106 Impact Loading



107 Floor Vibration

1071 Introduction


10721 Walking







10733 Damping

10734 Resonance




10751 Harmonics



Bibliography

Related Titles

53191ch11

Table of Contents


Summary

111 Introduction

















11244 Other Systems





























112911 Buildings

112912 Bridges


112921 Buildings

112922 Bridges
















































113714 Test Results








Bibliography

Related Titles

53191ch12

Table of Contents


Summary

121 Introduction





















12231 Kaul Method


































126 Conclusions

References

Related Titles

53191ch13

Table of Contents


Summary

131 Introduction











Bibliography

Related Titles

53191ch14

Table of Contents


Summary

141 Introduction












Bibliography

Related Titles




(Stroke)

Maximum

Velocity

Maximum

Acceleration

Maximum

Force

Excitation

Waveform

Hydraulic

(electrohydraulic)

Low

(01ndash500 Hz)


(50 insec

125 cmsec)

Intermediate

(20 g)

High (100000 lbf

450000 N)



Inertial


Intermediate

(2ndash50 Hz)


(50 insec

125 cmsec)

Intermediate

(20 g)

Intermediate

(1000 lbf 4500 N)

Sinusoidal only

Electromagnetic

(electrodynamic)

High

(2ndash10000 Hz)


(50 insec

125 cmsec)


(450 lbf 2000 N)



random)

VibrationInstru

mentation

1-5



CRCndashpp1ndash112

























20 dbdecade)

























Stroke

Limit M

ax

Acceleration

MaxVelocity

Peak

Vel

ocity

(cm

s)

01 1 10 100

FullLoad

NoLoad

Frequency (Hz)(a)

Peak

Vel

ocity

(cm

s)

100

10

1

100

10

1

01 1 10 100

FullLoad

NoLoad

Frequency (Hz)(b)



typical




1211 Force Rating









21p


















for acceleration

1212 Power Rating

















1213 Stroke Rating







Example 11








for the test

Solution







rating as






Acc

eler

atio

n(g

)

Con

stan

t Dis

plac

emen

t

Constant Velo

city

Frequency (Hz)

S

FP

0101

10 10 100

10

10























motors


























































m m

2mw2r cos wt

wtw w

wt



















































Denmark







Electrical Lediedt












d=dt as








Rev2

k2bs

Reye eth124THORN


given by

yevfrac14 kb

Re







eth127THORN

where

bo frac14 k2bRe

eth128THORN



yevfrac14 kb

Rb







effectiveness















100

10


Antiresonance

Resonance

Shak

erD

ispl

acem

entM

agni

tude

Resonance

1000




























13 Control System
















ExcitationInput

(Reference)

Feedback Paths

DriveSignal

ShakerResponse

TestTable

TestObject

Test ObjectResponse


(Shaker)(Ram)

Controllerand

Amplifier



















































1311 Compressor
























desired spectrum









































1321 Oscillators








oscillator
















DC Voltage

Oscillator


FrequencyConverter

FilterAmplifier


FrequencyCounter


Variable-GainOutput

Amplifier

SignalSpecification

LevelSpecification





53191fm


Preface

Acknowledgments

Editor-in-Chief

Contributors

Contents

Related Titles

53191ch1

Table of Contents


Summary

11 Introduction



1211 Force Rating

1212 Power Rating

1213 Stroke Rating






13 Control System


1311 Compressor





1321 Oscillators


1323 Tape Players






142 Linearity





151 Potentiometer


















15101 Sensitivity


















1621 Stroboscope






References


Summary


1A1 Dynamic Signals


1A111 Aliasing





1A212 Gain










1A222 Attenuation











1A5 Integration



























1A724 Zoom Settings






1A822 Overlapping




1A832 STFT vs RPM














Bibliography

Related Titles

53191ch2

Table of Contents


Summary

21 Introduction

22 Amplifiers







2242 Common Mode







23 Analog Filters















243 Demodulation










255 Digital Filters


26 Bridge Circuits






2641 Owen Bridge










281 Phase Shifters







292 Oscilloscopes

2921 Triggering



Bibliography

Related Titles

53191ch3

Table of Contents


Summary

31 Introduction


321 Test Signals




3222 Sine Sweep

3223 Sine Dwell

3224 Decaying Sine

3225 Sine Beat












































3432 Pluck Test

3433 Shaker Tests






















Bibliography

Related Titles

53191ch4

Table of Contents


Summary

41 Introduction



























Bibliography

Related Titles

53191ch5

Table of Contents


Summary

51 Definitions

511 Shock


513 Half-Sine Shock







531 Need





534 Definitions












5351 Definition












54 Pyroshocks







5524 Amplitude

5525 Duration

5526 Difficulties

56 Standards




564 Bump Test


571 Definition


58 Shock Machines

581 Main Types



58211 Impact Mode

58212 Impulse Mode














584 Limitations










592 Main Advantages


5931 Requirements

5932 Solutions





59411 Abacuses




5101 Principle



51022 ZERD Function









References

Related Titles

53191ch6

Table of Contents


Summary

61 Introduction




















682 Data Collectors





691 Time Domain





6915 Orbits









6926 Masks


693 Modal Domain


610 Fault Detection

6101 Standards











61111 Unbalance

61112 Misalignment


61114 Soft Foot

61115 Rubs

61116 Resonances

61117 Oil Whirl

61118 Oil Whip







61131 Pumps

61132 Fans



61135 Compressors



References

Related Titles

53191ch7

Table of Contents


Summary

71 Introduction


721 General Terms


723 Tool Wear



















7411 Time Domain







752 Neural Networks



753 Fuzzy Logic

754 Other Methods

76 Conclusion

References

Related Titles

53191ch8

Table of Contents


Summary

81 Introduction




841 Coverage Index

842 Overlap Index


85 A Case Study









86 Conclusion

References

Related Titles

53191ch9

Table of Contents


Summary

91 Introduction









941 Learning Mode

942 Monitoring Mode

943 Diagnostic Mode

944 Experiments







9443 Tests




96 Conclusions

References

Related Titles

53191ch10

Table of Contents


Summary

101 Introduction

























1031 Introduction

1032 Wind Speed










1037 Dampers



























106 Impact Loading



107 Floor Vibration

1071 Introduction


10721 Walking







10733 Damping

10734 Resonance




10751 Harmonics



Bibliography

Related Titles

53191ch11

Table of Contents


Summary

111 Introduction

















11244 Other Systems





























112911 Buildings

112912 Bridges


112921 Buildings

112922 Bridges
















































113714 Test Results








Bibliography

Related Titles

53191ch12

Table of Contents


Summary

121 Introduction





















12231 Kaul Method


































126 Conclusions

References

Related Titles

53191ch13

Table of Contents


Summary

131 Introduction











Bibliography

Related Titles

53191ch14

Table of Contents


Summary

141 Introduction












Bibliography

Related Titles
























20 dbdecade)

























Stroke

Limit M

ax

Acceleration

MaxVelocity

Peak

Vel

ocity

(cm

s)

01 1 10 100

FullLoad

NoLoad

Frequency (Hz)(a)

Peak

Vel

ocity

(cm

s)

100

10

1

100

10

1

01 1 10 100

FullLoad

NoLoad

Frequency (Hz)(b)



typical




1211 Force Rating









21p


















for acceleration

1212 Power Rating

















1213 Stroke Rating







Example 11








for the test

Solution







rating as






Acc

eler

atio

n(g

)

Con

stan

t Dis

plac

emen

t

Constant Velo

city

Frequency (Hz)

S

FP

0101

10 10 100

10

10























motors


























































m m

2mw2r cos wt

wtw w

wt



















































Denmark







Electrical Lediedt












d=dt as








Rev2

k2bs

Reye eth124THORN


given by

yevfrac14 kb

Re







eth127THORN

where

bo frac14 k2bRe

eth128THORN



yevfrac14 kb

Rb







effectiveness















100

10


Antiresonance

Resonance

Shak

erD

ispl

acem

entM

agni

tude

Resonance

1000




























13 Control System
















ExcitationInput

(Reference)

Feedback Paths

DriveSignal

ShakerResponse

TestTable

TestObject

Test ObjectResponse


(Shaker)(Ram)

Controllerand

Amplifier



















































1311 Compressor
























desired spectrum









































1321 Oscillators








oscillator
















DC Voltage

Oscillator


FrequencyConverter

FilterAmplifier


FrequencyCounter


Variable-GainOutput

Amplifier

SignalSpecification

LevelSpecification





53191fm


Preface

Acknowledgments

Editor-in-Chief

Contributors

Contents

Related Titles

53191ch1

Table of Contents


Summary

11 Introduction



1211 Force Rating

1212 Power Rating

1213 Stroke Rating






13 Control System


1311 Compressor





1321 Oscillators


1323 Tape Players






142 Linearity





151 Potentiometer


















15101 Sensitivity


















1621 Stroboscope






References


Summary


1A1 Dynamic Signals


1A111 Aliasing





1A212 Gain










1A222 Attenuation











1A5 Integration



























1A724 Zoom Settings






1A822 Overlapping




1A832 STFT vs RPM














Bibliography

Related Titles

53191ch2

Table of Contents


Summary

21 Introduction

22 Amplifiers







2242 Common Mode







23 Analog Filters















243 Demodulation










255 Digital Filters


26 Bridge Circuits






2641 Owen Bridge










281 Phase Shifters







292 Oscilloscopes

2921 Triggering



Bibliography

Related Titles

53191ch3

Table of Contents


Summary

31 Introduction


321 Test Signals




3222 Sine Sweep

3223 Sine Dwell

3224 Decaying Sine

3225 Sine Beat












































3432 Pluck Test

3433 Shaker Tests






















Bibliography

Related Titles

53191ch4

Table of Contents


Summary

41 Introduction



























Bibliography

Related Titles

53191ch5

Table of Contents


Summary

51 Definitions

511 Shock


513 Half-Sine Shock







531 Need





534 Definitions












5351 Definition












54 Pyroshocks







5524 Amplitude

5525 Duration

5526 Difficulties

56 Standards




564 Bump Test


571 Definition


58 Shock Machines

581 Main Types



58211 Impact Mode

58212 Impulse Mode














584 Limitations










592 Main Advantages


5931 Requirements

5932 Solutions





59411 Abacuses




5101 Principle



51022 ZERD Function









References

Related Titles

53191ch6

Table of Contents


Summary

61 Introduction




















682 Data Collectors





691 Time Domain





6915 Orbits









6926 Masks


693 Modal Domain


610 Fault Detection

6101 Standards











61111 Unbalance

61112 Misalignment


61114 Soft Foot

61115 Rubs

61116 Resonances

61117 Oil Whirl

61118 Oil Whip







61131 Pumps

61132 Fans



61135 Compressors



References

Related Titles

53191ch7

Table of Contents


Summary

71 Introduction


721 General Terms


723 Tool Wear



















7411 Time Domain







752 Neural Networks



753 Fuzzy Logic

754 Other Methods

76 Conclusion

References

Related Titles

53191ch8

Table of Contents


Summary

81 Introduction




841 Coverage Index

842 Overlap Index


85 A Case Study









86 Conclusion

References

Related Titles

53191ch9

Table of Contents


Summary

91 Introduction









941 Learning Mode

942 Monitoring Mode

943 Diagnostic Mode

944 Experiments







9443 Tests




96 Conclusions

References

Related Titles

53191ch10

Table of Contents


Summary

101 Introduction

























1031 Introduction

1032 Wind Speed










1037 Dampers



























106 Impact Loading



107 Floor Vibration

1071 Introduction


10721 Walking







10733 Damping

10734 Resonance




10751 Harmonics



Bibliography

Related Titles

53191ch11

Table of Contents


Summary

111 Introduction

















11244 Other Systems





























112911 Buildings

112912 Bridges


112921 Buildings

112922 Bridges
















































113714 Test Results








Bibliography

Related Titles

53191ch12

Table of Contents


Summary

121 Introduction





















12231 Kaul Method


































126 Conclusions

References

Related Titles

53191ch13

Table of Contents


Summary

131 Introduction











Bibliography

Related Titles

53191ch14

Table of Contents


Summary

141 Introduction












Bibliography

Related Titles

1211 Force Rating









21p


















for acceleration

1212 Power Rating

















1213 Stroke Rating







Example 11








for the test

Solution







rating as






Acc

eler

atio

n(g

)

Con

stan

t Dis

plac

emen

t

Constant Velo

city

Frequency (Hz)

S

FP

0101

10 10 100

10

10























motors


























































m m

2mw2r cos wt

wtw w

wt



















































Denmark







Electrical Lediedt












d=dt as








Rev2

k2bs

Reye eth124THORN


given by

yevfrac14 kb

Re







eth127THORN

where

bo frac14 k2bRe

eth128THORN



yevfrac14 kb

Rb







effectiveness















100

10


Antiresonance

Resonance

Shak

erD

ispl

acem

entM

agni

tude

Resonance

1000




























13 Control System
















ExcitationInput

(Reference)

Feedback Paths

DriveSignal

ShakerResponse

TestTable

TestObject

Test ObjectResponse


(Shaker)(Ram)

Controllerand

Amplifier



















































1311 Compressor
























desired spectrum









































1321 Oscillators








oscillator
















DC Voltage

Oscillator


FrequencyConverter

FilterAmplifier


FrequencyCounter


Variable-GainOutput

Amplifier

SignalSpecification

LevelSpecification





53191fm


Preface

Acknowledgments

Editor-in-Chief

Contributors

Contents

Related Titles

53191ch1

Table of Contents


Summary

11 Introduction



1211 Force Rating

1212 Power Rating

1213 Stroke Rating






13 Control System


1311 Compressor





1321 Oscillators


1323 Tape Players






142 Linearity





151 Potentiometer


















15101 Sensitivity


















1621 Stroboscope






References


Summary


1A1 Dynamic Signals


1A111 Aliasing





1A212 Gain










1A222 Attenuation











1A5 Integration



























1A724 Zoom Settings






1A822 Overlapping




1A832 STFT vs RPM














Bibliography

Related Titles

53191ch2

Table of Contents


Summary

21 Introduction

22 Amplifiers







2242 Common Mode







23 Analog Filters















243 Demodulation










255 Digital Filters


26 Bridge Circuits






2641 Owen Bridge










281 Phase Shifters







292 Oscilloscopes

2921 Triggering



Bibliography

Related Titles

53191ch3

Table of Contents


Summary

31 Introduction


321 Test Signals




3222 Sine Sweep

3223 Sine Dwell

3224 Decaying Sine

3225 Sine Beat












































3432 Pluck Test

3433 Shaker Tests






















Bibliography

Related Titles

53191ch4

Table of Contents


Summary

41 Introduction



























Bibliography

Related Titles

53191ch5

Table of Contents


Summary

51 Definitions

511 Shock


513 Half-Sine Shock







531 Need





534 Definitions












5351 Definition












54 Pyroshocks







5524 Amplitude

5525 Duration

5526 Difficulties

56 Standards




564 Bump Test


571 Definition


58 Shock Machines

581 Main Types



58211 Impact Mode

58212 Impulse Mode














584 Limitations










592 Main Advantages


5931 Requirements

5932 Solutions





59411 Abacuses




5101 Principle



51022 ZERD Function









References

Related Titles

53191ch6

Table of Contents


Summary

61 Introduction




















682 Data Collectors





691 Time Domain





6915 Orbits









6926 Masks


693 Modal Domain


610 Fault Detection

6101 Standards











61111 Unbalance

61112 Misalignment


61114 Soft Foot

61115 Rubs

61116 Resonances

61117 Oil Whirl

61118 Oil Whip







61131 Pumps

61132 Fans



61135 Compressors



References

Related Titles

53191ch7

Table of Contents


Summary

71 Introduction


721 General Terms


723 Tool Wear



















7411 Time Domain







752 Neural Networks



753 Fuzzy Logic

754 Other Methods

76 Conclusion

References

Related Titles

53191ch8

Table of Contents


Summary

81 Introduction




841 Coverage Index

842 Overlap Index


85 A Case Study









86 Conclusion

References

Related Titles

53191ch9

Table of Contents


Summary

91 Introduction









941 Learning Mode

942 Monitoring Mode

943 Diagnostic Mode

944 Experiments







9443 Tests




96 Conclusions

References

Related Titles

53191ch10

Table of Contents


Summary

101 Introduction

























1031 Introduction

1032 Wind Speed










1037 Dampers



























106 Impact Loading



107 Floor Vibration

1071 Introduction


10721 Walking







10733 Damping

10734 Resonance




10751 Harmonics



Bibliography

Related Titles

53191ch11

Table of Contents


Summary

111 Introduction

















11244 Other Systems





























112911 Buildings

112912 Bridges


112921 Buildings

112922 Bridges
















































113714 Test Results








Bibliography

Related Titles

53191ch12

Table of Contents


Summary

121 Introduction





















12231 Kaul Method


































126 Conclusions

References

Related Titles

53191ch13

Table of Contents


Summary

131 Introduction











Bibliography

Related Titles

53191ch14

Table of Contents


Summary

141 Introduction












Bibliography

Related Titles








1213 Stroke Rating







Example 11








for the test

Solution







rating as






Acc

eler

atio

n(g

)

Con

stan

t Dis

plac

emen

t

Constant Velo

city

Frequency (Hz)

S

FP

0101

10 10 100

10

10























motors


























































m m

2mw2r cos wt

wtw w

wt



















































Denmark







Electrical Lediedt












d=dt as








Rev2

k2bs

Reye eth124THORN


given by

yevfrac14 kb

Re







eth127THORN

where

bo frac14 k2bRe

eth128THORN



yevfrac14 kb

Rb







effectiveness















100

10


Antiresonance

Resonance

Shak

erD

ispl

acem

entM

agni

tude

Resonance

1000




























13 Control System
















ExcitationInput

(Reference)

Feedback Paths

DriveSignal

ShakerResponse

TestTable

TestObject

Test ObjectResponse


(Shaker)(Ram)

Controllerand

Amplifier



















































1311 Compressor
























desired spectrum









































1321 Oscillators








oscillator
















DC Voltage

Oscillator


FrequencyConverter

FilterAmplifier


FrequencyCounter


Variable-GainOutput

Amplifier

SignalSpecification

LevelSpecification





53191fm


Preface

Acknowledgments

Editor-in-Chief

Contributors

Contents

Related Titles

53191ch1

Table of Contents


Summary

11 Introduction



1211 Force Rating

1212 Power Rating

1213 Stroke Rating






13 Control System


1311 Compressor





1321 Oscillators


1323 Tape Players






142 Linearity





151 Potentiometer


















15101 Sensitivity


















1621 Stroboscope






References


Summary


1A1 Dynamic Signals


1A111 Aliasing





1A212 Gain










1A222 Attenuation











1A5 Integration



























1A724 Zoom Settings






1A822 Overlapping




1A832 STFT vs RPM














Bibliography

Related Titles

53191ch2

Table of Contents


Summary

21 Introduction

22 Amplifiers







2242 Common Mode







23 Analog Filters















243 Demodulation










255 Digital Filters


26 Bridge Circuits






2641 Owen Bridge










281 Phase Shifters







292 Oscilloscopes

2921 Triggering



Bibliography

Related Titles

53191ch3

Table of Contents


Summary

31 Introduction


321 Test Signals




3222 Sine Sweep

3223 Sine Dwell

3224 Decaying Sine

3225 Sine Beat












































3432 Pluck Test

3433 Shaker Tests






















Bibliography

Related Titles

53191ch4

Table of Contents


Summary

41 Introduction



























Bibliography

Related Titles

53191ch5

Table of Contents


Summary

51 Definitions

511 Shock


513 Half-Sine Shock







531 Need





534 Definitions












5351 Definition












54 Pyroshocks







5524 Amplitude

5525 Duration

5526 Difficulties

56 Standards




564 Bump Test


571 Definition


58 Shock Machines

581 Main Types



58211 Impact Mode

58212 Impulse Mode














584 Limitations










592 Main Advantages


5931 Requirements

5932 Solutions





59411 Abacuses




5101 Principle



51022 ZERD Function









References

Related Titles

53191ch6

Table of Contents


Summary

61 Introduction




















682 Data Collectors





691 Time Domain





6915 Orbits









6926 Masks


693 Modal Domain


610 Fault Detection

6101 Standards











61111 Unbalance

61112 Misalignment


61114 Soft Foot

61115 Rubs

61116 Resonances

61117 Oil Whirl

61118 Oil Whip







61131 Pumps

61132 Fans



61135 Compressors



References

Related Titles

53191ch7

Table of Contents


Summary

71 Introduction


721 General Terms


723 Tool Wear



















7411 Time Domain







752 Neural Networks



753 Fuzzy Logic

754 Other Methods

76 Conclusion

References

Related Titles

53191ch8

Table of Contents


Summary

81 Introduction




841 Coverage Index

842 Overlap Index


85 A Case Study









86 Conclusion

References

Related Titles

53191ch9

Table of Contents


Summary

91 Introduction









941 Learning Mode

942 Monitoring Mode

943 Diagnostic Mode

944 Experiments







9443 Tests




96 Conclusions

References

Related Titles

53191ch10

Table of Contents


Summary

101 Introduction

























1031 Introduction

1032 Wind Speed










1037 Dampers



























106 Impact Loading



107 Floor Vibration

1071 Introduction


10721 Walking







10733 Damping

10734 Resonance




10751 Harmonics



Bibliography

Related Titles

53191ch11

Table of Contents


Summary

111 Introduction

















11244 Other Systems





























112911 Buildings

112912 Bridges


112921 Buildings

112922 Bridges
















































113714 Test Results








Bibliography

Related Titles

53191ch12

Table of Contents


Summary

121 Introduction





















12231 Kaul Method


































126 Conclusions

References

Related Titles

53191ch13

Table of Contents


Summary

131 Introduction











Bibliography

Related Titles

53191ch14

Table of Contents


Summary

141 Introduction












Bibliography

Related Titles


















motors


























































m m

2mw2r cos wt

wtw w

wt



















































Denmark







Electrical Lediedt












d=dt as








Rev2

k2bs

Reye eth124THORN


given by

yevfrac14 kb

Re







eth127THORN

where

bo frac14 k2bRe

eth128THORN



yevfrac14 kb

Rb







effectiveness















100

10


Antiresonance

Resonance

Shak

erD

ispl

acem

entM

agni

tude

Resonance

1000




























13 Control System
















ExcitationInput

(Reference)

Feedback Paths

DriveSignal

ShakerResponse

TestTable

TestObject

Test ObjectResponse


(Shaker)(Ram)

Controllerand

Amplifier



















































1311 Compressor
























desired spectrum









































1321 Oscillators








oscillator
















DC Voltage

Oscillator


FrequencyConverter

FilterAmplifier


FrequencyCounter


Variable-GainOutput

Amplifier

SignalSpecification

LevelSpecification





53191fm


Preface

Acknowledgments

Editor-in-Chief

Contributors

Contents

Related Titles

53191ch1

Table of Contents


Summary

11 Introduction



1211 Force Rating

1212 Power Rating

1213 Stroke Rating






13 Control System


1311 Compressor





1321 Oscillators


1323 Tape Players






142 Linearity





151 Potentiometer


















15101 Sensitivity


















1621 Stroboscope






References


Summary


1A1 Dynamic Signals


1A111 Aliasing





1A212 Gain










1A222 Attenuation











1A5 Integration



























1A724 Zoom Settings






1A822 Overlapping




1A832 STFT vs RPM














Bibliography

Related Titles

53191ch2

Table of Contents


Summary

21 Introduction

22 Amplifiers







2242 Common Mode







23 Analog Filters















243 Demodulation










255 Digital Filters


26 Bridge Circuits






2641 Owen Bridge










281 Phase Shifters







292 Oscilloscopes

2921 Triggering



Bibliography

Related Titles

53191ch3

Table of Contents


Summary

31 Introduction


321 Test Signals




3222 Sine Sweep

3223 Sine Dwell

3224 Decaying Sine

3225 Sine Beat












































3432 Pluck Test

3433 Shaker Tests






















Bibliography

Related Titles

53191ch4

Table of Contents


Summary

41 Introduction



























Bibliography

Related Titles

53191ch5

Table of Contents


Summary

51 Definitions

511 Shock


513 Half-Sine Shock







531 Need





534 Definitions












5351 Definition












54 Pyroshocks







5524 Amplitude

5525 Duration

5526 Difficulties

56 Standards




564 Bump Test


571 Definition


58 Shock Machines

581 Main Types



58211 Impact Mode

58212 Impulse Mode














584 Limitations










592 Main Advantages


5931 Requirements

5932 Solutions





59411 Abacuses




5101 Principle



51022 ZERD Function









References

Related Titles

53191ch6

Table of Contents


Summary

61 Introduction




















682 Data Collectors





691 Time Domain





6915 Orbits









6926 Masks


693 Modal Domain


610 Fault Detection

6101 Standards











61111 Unbalance

61112 Misalignment


61114 Soft Foot

61115 Rubs

61116 Resonances

61117 Oil Whirl

61118 Oil Whip







61131 Pumps

61132 Fans



61135 Compressors



References

Related Titles

53191ch7

Table of Contents


Summary

71 Introduction


721 General Terms


723 Tool Wear



















7411 Time Domain







752 Neural Networks



753 Fuzzy Logic

754 Other Methods

76 Conclusion

References

Related Titles

53191ch8

Table of Contents


Summary

81 Introduction




841 Coverage Index

842 Overlap Index


85 A Case Study









86 Conclusion

References

Related Titles

53191ch9

Table of Contents


Summary

91 Introduction









941 Learning Mode

942 Monitoring Mode

943 Diagnostic Mode

944 Experiments







9443 Tests




96 Conclusions

References

Related Titles

53191ch10

Table of Contents


Summary

101 Introduction

























1031 Introduction

1032 Wind Speed










1037 Dampers



























106 Impact Loading



107 Floor Vibration

1071 Introduction


10721 Walking







10733 Damping

10734 Resonance




10751 Harmonics



Bibliography

Related Titles

53191ch11

Table of Contents


Summary

111 Introduction

















11244 Other Systems





























112911 Buildings

112912 Bridges


112921 Buildings

112922 Bridges
















































113714 Test Results








Bibliography

Related Titles

53191ch12

Table of Contents


Summary

121 Introduction





















12231 Kaul Method


































126 Conclusions

References

Related Titles

53191ch13

Table of Contents


Summary

131 Introduction











Bibliography

Related Titles

53191ch14

Table of Contents


Summary

141 Introduction












Bibliography

Related Titles























m m

2mw2r cos wt

wtw w

wt



















































Denmark







Electrical Lediedt












d=dt as








Rev2

k2bs

Reye eth124THORN


given by

yevfrac14 kb

Re







eth127THORN

where

bo frac14 k2bRe

eth128THORN



yevfrac14 kb

Rb







effectiveness















100

10


Antiresonance

Resonance

Shak

erD

ispl

acem

entM

agni

tude

Resonance

1000




























13 Control System
















ExcitationInput

(Reference)

Feedback Paths

DriveSignal

ShakerResponse

TestTable

TestObject

Test ObjectResponse


(Shaker)(Ram)

Controllerand

Amplifier



















































1311 Compressor
























desired spectrum









































1321 Oscillators








oscillator
















DC Voltage

Oscillator


FrequencyConverter

FilterAmplifier


FrequencyCounter


Variable-GainOutput

Amplifier

SignalSpecification

LevelSpecification





53191fm


Preface

Acknowledgments

Editor-in-Chief

Contributors

Contents

Related Titles

53191ch1

Table of Contents


Summary

11 Introduction



1211 Force Rating

1212 Power Rating

1213 Stroke Rating






13 Control System


1311 Compressor





1321 Oscillators


1323 Tape Players






142 Linearity





151 Potentiometer


















15101 Sensitivity


















1621 Stroboscope






References


Summary


1A1 Dynamic Signals


1A111 Aliasing





1A212 Gain










1A222 Attenuation











1A5 Integration



























1A724 Zoom Settings






1A822 Overlapping




1A832 STFT vs RPM














Bibliography

Related Titles

53191ch2

Table of Contents


Summary

21 Introduction

22 Amplifiers







2242 Common Mode







23 Analog Filters















243 Demodulation










255 Digital Filters


26 Bridge Circuits






2641 Owen Bridge










281 Phase Shifters







292 Oscilloscopes

2921 Triggering



Bibliography

Related Titles

53191ch3

Table of Contents


Summary

31 Introduction


321 Test Signals




3222 Sine Sweep

3223 Sine Dwell

3224 Decaying Sine

3225 Sine Beat












































3432 Pluck Test

3433 Shaker Tests






















Bibliography

Related Titles

53191ch4

Table of Contents


Summary

41 Introduction



























Bibliography

Related Titles

53191ch5

Table of Contents


Summary

51 Definitions

511 Shock


513 Half-Sine Shock







531 Need





534 Definitions












5351 Definition












54 Pyroshocks







5524 Amplitude

5525 Duration

5526 Difficulties

56 Standards




564 Bump Test


571 Definition


58 Shock Machines

581 Main Types



58211 Impact Mode

58212 Impulse Mode














584 Limitations










592 Main Advantages


5931 Requirements

5932 Solutions





59411 Abacuses




5101 Principle



51022 ZERD Function









References

Related Titles

53191ch6

Table of Contents


Summary

61 Introduction




















682 Data Collectors





691 Time Domain





6915 Orbits









6926 Masks


693 Modal Domain


610 Fault Detection

6101 Standards











61111 Unbalance

61112 Misalignment


61114 Soft Foot

61115 Rubs

61116 Resonances

61117 Oil Whirl

61118 Oil Whip







61131 Pumps

61132 Fans



61135 Compressors



References

Related Titles

53191ch7

Table of Contents


Summary

71 Introduction


721 General Terms


723 Tool Wear



















7411 Time Domain







752 Neural Networks



753 Fuzzy Logic

754 Other Methods

76 Conclusion

References

Related Titles

53191ch8

Table of Contents


Summary

81 Introduction




841 Coverage Index

842 Overlap Index


85 A Case Study









86 Conclusion

References

Related Titles

53191ch9

Table of Contents


Summary

91 Introduction









941 Learning Mode

942 Monitoring Mode

943 Diagnostic Mode

944 Experiments







9443 Tests




96 Conclusions

References

Related Titles

53191ch10

Table of Contents


Summary

101 Introduction

























1031 Introduction

1032 Wind Speed










1037 Dampers



























106 Impact Loading



107 Floor Vibration

1071 Introduction


10721 Walking







10733 Damping

10734 Resonance




10751 Harmonics



Bibliography

Related Titles

53191ch11

Table of Contents


Summary

111 Introduction

















11244 Other Systems





























112911 Buildings

112912 Bridges


112921 Buildings

112922 Bridges
















































113714 Test Results








Bibliography

Related Titles

53191ch12

Table of Contents


Summary

121 Introduction





















12231 Kaul Method


































126 Conclusions

References

Related Titles

53191ch13

Table of Contents


Summary

131 Introduction











Bibliography

Related Titles

53191ch14

Table of Contents


Summary

141 Introduction












Bibliography

Related Titles














































Denmark







Electrical Lediedt












d=dt as








Rev2

k2bs

Reye eth124THORN


given by

yevfrac14 kb

Re







eth127THORN

where

bo frac14 k2bRe

eth128THORN



yevfrac14 kb

Rb







effectiveness















100

10


Antiresonance

Resonance

Shak

erD

ispl

acem

entM

agni

tude

Resonance

1000




























13 Control System
















ExcitationInput

(Reference)

Feedback Paths

DriveSignal

ShakerResponse

TestTable

TestObject

Test ObjectResponse


(Shaker)(Ram)

Controllerand

Amplifier



















































1311 Compressor
























desired spectrum









































1321 Oscillators








oscillator
















DC Voltage

Oscillator


FrequencyConverter

FilterAmplifier


FrequencyCounter


Variable-GainOutput

Amplifier

SignalSpecification

LevelSpecification





53191fm


Preface

Acknowledgments

Editor-in-Chief

Contributors

Contents

Related Titles

53191ch1

Table of Contents


Summary

11 Introduction



1211 Force Rating

1212 Power Rating

1213 Stroke Rating






13 Control System


1311 Compressor





1321 Oscillators


1323 Tape Players






142 Linearity





151 Potentiometer


















15101 Sensitivity


















1621 Stroboscope






References


Summary


1A1 Dynamic Signals


1A111 Aliasing





1A212 Gain










1A222 Attenuation











1A5 Integration



























1A724 Zoom Settings






1A822 Overlapping




1A832 STFT vs RPM














Bibliography

Related Titles

53191ch2

Table of Contents


Summary

21 Introduction

22 Amplifiers







2242 Common Mode







23 Analog Filters















243 Demodulation










255 Digital Filters


26 Bridge Circuits






2641 Owen Bridge










281 Phase Shifters







292 Oscilloscopes

2921 Triggering



Bibliography

Related Titles

53191ch3

Table of Contents


Summary

31 Introduction


321 Test Signals




3222 Sine Sweep

3223 Sine Dwell

3224 Decaying Sine

3225 Sine Beat












































3432 Pluck Test

3433 Shaker Tests






















Bibliography

Related Titles

53191ch4

Table of Contents


Summary

41 Introduction



























Bibliography

Related Titles

53191ch5

Table of Contents


Summary

51 Definitions

511 Shock


513 Half-Sine Shock







531 Need





534 Definitions












5351 Definition












54 Pyroshocks







5524 Amplitude

5525 Duration

5526 Difficulties

56 Standards




564 Bump Test


571 Definition


58 Shock Machines

581 Main Types



58211 Impact Mode

58212 Impulse Mode














584 Limitations










592 Main Advantages


5931 Requirements

5932 Solutions





59411 Abacuses




5101 Principle



51022 ZERD Function









References

Related Titles

53191ch6

Table of Contents


Summary

61 Introduction




















682 Data Collectors





691 Time Domain





6915 Orbits









6926 Masks


693 Modal Domain


610 Fault Detection

6101 Standards











61111 Unbalance

61112 Misalignment


61114 Soft Foot

61115 Rubs

61116 Resonances

61117 Oil Whirl

61118 Oil Whip







61131 Pumps

61132 Fans



61135 Compressors



References

Related Titles

53191ch7

Table of Contents


Summary

71 Introduction


721 General Terms


723 Tool Wear



















7411 Time Domain







752 Neural Networks



753 Fuzzy Logic

754 Other Methods

76 Conclusion

References

Related Titles

53191ch8

Table of Contents


Summary

81 Introduction




841 Coverage Index

842 Overlap Index


85 A Case Study









86 Conclusion

References

Related Titles

53191ch9

Table of Contents


Summary

91 Introduction









941 Learning Mode

942 Monitoring Mode

943 Diagnostic Mode

944 Experiments







9443 Tests




96 Conclusions

References

Related Titles

53191ch10

Table of Contents


Summary

101 Introduction

























1031 Introduction

1032 Wind Speed










1037 Dampers



























106 Impact Loading



107 Floor Vibration

1071 Introduction


10721 Walking







10733 Damping

10734 Resonance




10751 Harmonics



Bibliography

Related Titles

53191ch11

Table of Contents


Summary

111 Introduction

















11244 Other Systems





























112911 Buildings

112912 Bridges


112921 Buildings

112922 Bridges
















































113714 Test Results








Bibliography

Related Titles

53191ch12

Table of Contents


Summary

121 Introduction





















12231 Kaul Method


































126 Conclusions

References

Related Titles

53191ch13

Table of Contents


Summary

131 Introduction











Bibliography

Related Titles

53191ch14

Table of Contents


Summary

141 Introduction












Bibliography

Related Titles




Electrical Lediedt












d=dt as








Rev2

k2bs

Reye eth124THORN


given by

yevfrac14 kb

Re







eth127THORN

where

bo frac14 k2bRe

eth128THORN



yevfrac14 kb

Rb







effectiveness















100

10


Antiresonance

Resonance

Shak

erD

ispl

acem

entM

agni

tude

Resonance

1000




























13 Control System
















ExcitationInput

(Reference)

Feedback Paths

DriveSignal

ShakerResponse

TestTable

TestObject

Test ObjectResponse


(Shaker)(Ram)

Controllerand

Amplifier



















































1311 Compressor
























desired spectrum









































1321 Oscillators








oscillator
















DC Voltage

Oscillator


FrequencyConverter

FilterAmplifier


FrequencyCounter


Variable-GainOutput

Amplifier

SignalSpecification

LevelSpecification





53191fm


Preface

Acknowledgments

Editor-in-Chief

Contributors

Contents

Related Titles

53191ch1

Table of Contents


Summary

11 Introduction



1211 Force Rating

1212 Power Rating

1213 Stroke Rating






13 Control System


1311 Compressor





1321 Oscillators


1323 Tape Players






142 Linearity





151 Potentiometer


















15101 Sensitivity


















1621 Stroboscope






References


Summary


1A1 Dynamic Signals


1A111 Aliasing





1A212 Gain










1A222 Attenuation











1A5 Integration



























1A724 Zoom Settings






1A822 Overlapping




1A832 STFT vs RPM














Bibliography

Related Titles

53191ch2

Table of Contents


Summary

21 Introduction

22 Amplifiers







2242 Common Mode







23 Analog Filters















243 Demodulation










255 Digital Filters


26 Bridge Circuits






2641 Owen Bridge










281 Phase Shifters







292 Oscilloscopes

2921 Triggering



Bibliography

Related Titles

53191ch3

Table of Contents


Summary

31 Introduction


321 Test Signals




3222 Sine Sweep

3223 Sine Dwell

3224 Decaying Sine

3225 Sine Beat












































3432 Pluck Test

3433 Shaker Tests






















Bibliography

Related Titles

53191ch4

Table of Contents


Summary

41 Introduction



























Bibliography

Related Titles

53191ch5

Table of Contents


Summary

51 Definitions

511 Shock


513 Half-Sine Shock







531 Need





534 Definitions












5351 Definition












54 Pyroshocks







5524 Amplitude

5525 Duration

5526 Difficulties

56 Standards




564 Bump Test


571 Definition


58 Shock Machines

581 Main Types



58211 Impact Mode

58212 Impulse Mode














584 Limitations










592 Main Advantages


5931 Requirements

5932 Solutions





59411 Abacuses




5101 Principle



51022 ZERD Function









References

Related Titles

53191ch6

Table of Contents


Summary

61 Introduction




















682 Data Collectors





691 Time Domain





6915 Orbits









6926 Masks


693 Modal Domain


610 Fault Detection

6101 Standards











61111 Unbalance

61112 Misalignment


61114 Soft Foot

61115 Rubs

61116 Resonances

61117 Oil Whirl

61118 Oil Whip







61131 Pumps

61132 Fans



61135 Compressors



References

Related Titles

53191ch7

Table of Contents


Summary

71 Introduction


721 General Terms


723 Tool Wear



















7411 Time Domain







752 Neural Networks



753 Fuzzy Logic

754 Other Methods

76 Conclusion

References

Related Titles

53191ch8

Table of Contents


Summary

81 Introduction




841 Coverage Index

842 Overlap Index


85 A Case Study









86 Conclusion

References

Related Titles

53191ch9

Table of Contents


Summary

91 Introduction









941 Learning Mode

942 Monitoring Mode

943 Diagnostic Mode

944 Experiments







9443 Tests




96 Conclusions

References

Related Titles

53191ch10

Table of Contents


Summary

101 Introduction

























1031 Introduction

1032 Wind Speed










1037 Dampers



























106 Impact Loading



107 Floor Vibration

1071 Introduction


10721 Walking







10733 Damping

10734 Resonance




10751 Harmonics



Bibliography

Related Titles

53191ch11

Table of Contents


Summary

111 Introduction

















11244 Other Systems





























112911 Buildings

112912 Bridges


112921 Buildings

112922 Bridges
















































113714 Test Results








Bibliography

Related Titles

53191ch12

Table of Contents


Summary

121 Introduction





















12231 Kaul Method


































126 Conclusions

References

Related Titles

53191ch13

Table of Contents


Summary

131 Introduction











Bibliography

Related Titles

53191ch14

Table of Contents


Summary

141 Introduction












Bibliography

Related Titles


Rev2

k2bs

Reye eth124THORN


given by

yevfrac14 kb

Re







eth127THORN

where

bo frac14 k2bRe

eth128THORN



yevfrac14 kb

Rb







effectiveness















100

10


Antiresonance

Resonance

Shak

erD

ispl

acem

entM

agni

tude

Resonance

1000




























13 Control System
















ExcitationInput

(Reference)

Feedback Paths

DriveSignal

ShakerResponse

TestTable

TestObject

Test ObjectResponse


(Shaker)(Ram)

Controllerand

Amplifier



















































1311 Compressor
























desired spectrum









































1321 Oscillators








oscillator
















DC Voltage

Oscillator


FrequencyConverter

FilterAmplifier


FrequencyCounter


Variable-GainOutput

Amplifier

SignalSpecification

LevelSpecification





53191fm


Preface

Acknowledgments

Editor-in-Chief

Contributors

Contents

Related Titles

53191ch1

Table of Contents


Summary

11 Introduction



1211 Force Rating

1212 Power Rating

1213 Stroke Rating






13 Control System


1311 Compressor





1321 Oscillators


1323 Tape Players






142 Linearity





151 Potentiometer


















15101 Sensitivity


















1621 Stroboscope






References


Summary


1A1 Dynamic Signals


1A111 Aliasing





1A212 Gain










1A222 Attenuation











1A5 Integration



























1A724 Zoom Settings






1A822 Overlapping




1A832 STFT vs RPM














Bibliography

Related Titles

53191ch2

Table of Contents


Summary

21 Introduction

22 Amplifiers







2242 Common Mode







23 Analog Filters















243 Demodulation










255 Digital Filters


26 Bridge Circuits






2641 Owen Bridge










281 Phase Shifters







292 Oscilloscopes

2921 Triggering



Bibliography

Related Titles

53191ch3

Table of Contents


Summary

31 Introduction


321 Test Signals




3222 Sine Sweep

3223 Sine Dwell

3224 Decaying Sine

3225 Sine Beat












































3432 Pluck Test

3433 Shaker Tests






















Bibliography

Related Titles

53191ch4

Table of Contents


Summary

41 Introduction



























Bibliography

Related Titles

53191ch5

Table of Contents


Summary

51 Definitions

511 Shock


513 Half-Sine Shock







531 Need





534 Definitions












5351 Definition












54 Pyroshocks







5524 Amplitude

5525 Duration

5526 Difficulties

56 Standards




564 Bump Test


571 Definition


58 Shock Machines

581 Main Types



58211 Impact Mode

58212 Impulse Mode














584 Limitations










592 Main Advantages


5931 Requirements

5932 Solutions





59411 Abacuses




5101 Principle



51022 ZERD Function









References

Related Titles

53191ch6

Table of Contents


Summary

61 Introduction




















682 Data Collectors





691 Time Domain





6915 Orbits









6926 Masks


693 Modal Domain


610 Fault Detection

6101 Standards











61111 Unbalance

61112 Misalignment


61114 Soft Foot

61115 Rubs

61116 Resonances

61117 Oil Whirl

61118 Oil Whip







61131 Pumps

61132 Fans



61135 Compressors



References

Related Titles

53191ch7

Table of Contents


Summary

71 Introduction


721 General Terms


723 Tool Wear



















7411 Time Domain







752 Neural Networks



753 Fuzzy Logic

754 Other Methods

76 Conclusion

References

Related Titles

53191ch8

Table of Contents


Summary

81 Introduction




841 Coverage Index

842 Overlap Index


85 A Case Study









86 Conclusion

References

Related Titles

53191ch9

Table of Contents


Summary

91 Introduction









941 Learning Mode

942 Monitoring Mode

943 Diagnostic Mode

944 Experiments







9443 Tests




96 Conclusions

References

Related Titles

53191ch10

Table of Contents


Summary

101 Introduction

























1031 Introduction

1032 Wind Speed










1037 Dampers



























106 Impact Loading



107 Floor Vibration

1071 Introduction


10721 Walking







10733 Damping

10734 Resonance




10751 Harmonics



Bibliography

Related Titles

53191ch11

Table of Contents


Summary

111 Introduction

















11244 Other Systems





























112911 Buildings

112912 Bridges


112921 Buildings

112922 Bridges
















































113714 Test Results








Bibliography

Related Titles

53191ch12

Table of Contents


Summary

121 Introduction





















12231 Kaul Method


































126 Conclusions

References

Related Titles

53191ch13

Table of Contents


Summary

131 Introduction











Bibliography

Related Titles

53191ch14

Table of Contents


Summary

141 Introduction












Bibliography

Related Titles























13 Control System
















ExcitationInput

(Reference)

Feedback Paths

DriveSignal

ShakerResponse

TestTable

TestObject

Test ObjectResponse


(Shaker)(Ram)

Controllerand

Amplifier



















































1311 Compressor
























desired spectrum









































1321 Oscillators








oscillator
















DC Voltage

Oscillator


FrequencyConverter

FilterAmplifier


FrequencyCounter


Variable-GainOutput

Amplifier

SignalSpecification

LevelSpecification





53191fm


Preface

Acknowledgments

Editor-in-Chief

Contributors

Contents

Related Titles

53191ch1

Table of Contents


Summary

11 Introduction



1211 Force Rating

1212 Power Rating

1213 Stroke Rating






13 Control System


1311 Compressor





1321 Oscillators


1323 Tape Players






142 Linearity





151 Potentiometer


















15101 Sensitivity


















1621 Stroboscope






References


Summary


1A1 Dynamic Signals


1A111 Aliasing





1A212 Gain










1A222 Attenuation











1A5 Integration



























1A724 Zoom Settings






1A822 Overlapping




1A832 STFT vs RPM














Bibliography

Related Titles

53191ch2

Table of Contents


Summary

21 Introduction

22 Amplifiers







2242 Common Mode







23 Analog Filters















243 Demodulation










255 Digital Filters


26 Bridge Circuits






2641 Owen Bridge










281 Phase Shifters







292 Oscilloscopes

2921 Triggering



Bibliography

Related Titles

53191ch3

Table of Contents


Summary

31 Introduction


321 Test Signals




3222 Sine Sweep

3223 Sine Dwell

3224 Decaying Sine

3225 Sine Beat












































3432 Pluck Test

3433 Shaker Tests






















Bibliography

Related Titles

53191ch4

Table of Contents


Summary

41 Introduction



























Bibliography

Related Titles

53191ch5

Table of Contents


Summary

51 Definitions

511 Shock


513 Half-Sine Shock







531 Need





534 Definitions












5351 Definition












54 Pyroshocks







5524 Amplitude

5525 Duration

5526 Difficulties

56 Standards




564 Bump Test


571 Definition


58 Shock Machines

581 Main Types



58211 Impact Mode

58212 Impulse Mode














584 Limitations










592 Main Advantages


5931 Requirements

5932 Solutions





59411 Abacuses




5101 Principle



51022 ZERD Function









References

Related Titles

53191ch6

Table of Contents


Summary

61 Introduction




















682 Data Collectors





691 Time Domain





6915 Orbits









6926 Masks


693 Modal Domain


610 Fault Detection

6101 Standards











61111 Unbalance

61112 Misalignment


61114 Soft Foot

61115 Rubs

61116 Resonances

61117 Oil Whirl

61118 Oil Whip







61131 Pumps

61132 Fans



61135 Compressors



References

Related Titles

53191ch7

Table of Contents


Summary

71 Introduction


721 General Terms


723 Tool Wear



















7411 Time Domain







752 Neural Networks



753 Fuzzy Logic

754 Other Methods

76 Conclusion

References

Related Titles

53191ch8

Table of Contents


Summary

81 Introduction




841 Coverage Index

842 Overlap Index


85 A Case Study









86 Conclusion

References

Related Titles

53191ch9

Table of Contents


Summary

91 Introduction









941 Learning Mode

942 Monitoring Mode

943 Diagnostic Mode

944 Experiments







9443 Tests




96 Conclusions

References

Related Titles

53191ch10

Table of Contents


Summary

101 Introduction

























1031 Introduction

1032 Wind Speed










1037 Dampers



























106 Impact Loading



107 Floor Vibration

1071 Introduction


10721 Walking







10733 Damping

10734 Resonance




10751 Harmonics



Bibliography

Related Titles

53191ch11

Table of Contents


Summary

111 Introduction

















11244 Other Systems





























112911 Buildings

112912 Bridges


112921 Buildings

112922 Bridges
















































113714 Test Results








Bibliography

Related Titles

53191ch12

Table of Contents


Summary

121 Introduction





















12231 Kaul Method


































126 Conclusions

References

Related Titles

53191ch13

Table of Contents


Summary

131 Introduction











Bibliography

Related Titles

53191ch14

Table of Contents


Summary

141 Introduction












Bibliography

Related Titles















































1311 Compressor
























desired spectrum









































1321 Oscillators








oscillator
















DC Voltage

Oscillator


FrequencyConverter

FilterAmplifier


FrequencyCounter


Variable-GainOutput

Amplifier

SignalSpecification

LevelSpecification





53191fm


Preface

Acknowledgments

Editor-in-Chief

Contributors

Contents

Related Titles

53191ch1

Table of Contents


Summary

11 Introduction



1211 Force Rating

1212 Power Rating

1213 Stroke Rating






13 Control System


1311 Compressor





1321 Oscillators


1323 Tape Players






142 Linearity





151 Potentiometer


















15101 Sensitivity


















1621 Stroboscope






References


Summary


1A1 Dynamic Signals


1A111 Aliasing





1A212 Gain










1A222 Attenuation











1A5 Integration



























1A724 Zoom Settings






1A822 Overlapping




1A832 STFT vs RPM














Bibliography

Related Titles

53191ch2

Table of Contents


Summary

21 Introduction

22 Amplifiers







2242 Common Mode







23 Analog Filters















243 Demodulation










255 Digital Filters


26 Bridge Circuits






2641 Owen Bridge










281 Phase Shifters







292 Oscilloscopes

2921 Triggering



Bibliography

Related Titles

53191ch3

Table of Contents


Summary

31 Introduction


321 Test Signals




3222 Sine Sweep

3223 Sine Dwell

3224 Decaying Sine

3225 Sine Beat












































3432 Pluck Test

3433 Shaker Tests






















Bibliography

Related Titles

53191ch4

Table of Contents


Summary

41 Introduction



























Bibliography

Related Titles

53191ch5

Table of Contents


Summary

51 Definitions

511 Shock


513 Half-Sine Shock







531 Need





534 Definitions












5351 Definition












54 Pyroshocks







5524 Amplitude

5525 Duration

5526 Difficulties

56 Standards




564 Bump Test


571 Definition


58 Shock Machines

581 Main Types



58211 Impact Mode

58212 Impulse Mode














584 Limitations










592 Main Advantages


5931 Requirements

5932 Solutions





59411 Abacuses




5101 Principle



51022 ZERD Function









References

Related Titles

53191ch6

Table of Contents


Summary

61 Introduction




















682 Data Collectors





691 Time Domain





6915 Orbits









6926 Masks


693 Modal Domain


610 Fault Detection

6101 Standards











61111 Unbalance

61112 Misalignment


61114 Soft Foot

61115 Rubs

61116 Resonances

61117 Oil Whirl

61118 Oil Whip







61131 Pumps

61132 Fans



61135 Compressors



References

Related Titles

53191ch7

Table of Contents


Summary

71 Introduction


721 General Terms


723 Tool Wear



















7411 Time Domain







752 Neural Networks



753 Fuzzy Logic

754 Other Methods

76 Conclusion

References

Related Titles

53191ch8

Table of Contents


Summary

81 Introduction




841 Coverage Index

842 Overlap Index


85 A Case Study









86 Conclusion

References

Related Titles

53191ch9

Table of Contents


Summary

91 Introduction









941 Learning Mode

942 Monitoring Mode

943 Diagnostic Mode

944 Experiments







9443 Tests




96 Conclusions

References

Related Titles

53191ch10

Table of Contents


Summary

101 Introduction

























1031 Introduction

1032 Wind Speed










1037 Dampers



























106 Impact Loading



107 Floor Vibration

1071 Introduction


10721 Walking







10733 Damping

10734 Resonance




10751 Harmonics



Bibliography

Related Titles

53191ch11

Table of Contents


Summary

111 Introduction

















11244 Other Systems





























112911 Buildings

112912 Bridges


112921 Buildings

112922 Bridges
















































113714 Test Results








Bibliography

Related Titles

53191ch12

Table of Contents


Summary

121 Introduction





















12231 Kaul Method


































126 Conclusions

References

Related Titles

53191ch13

Table of Contents


Summary

131 Introduction











Bibliography

Related Titles

53191ch14

Table of Contents


Summary

141 Introduction












Bibliography

Related Titles



















desired spectrum









































1321 Oscillators








oscillator
















DC Voltage

Oscillator


FrequencyConverter

FilterAmplifier


FrequencyCounter


Variable-GainOutput

Amplifier

SignalSpecification

LevelSpecification





53191fm


Preface

Acknowledgments

Editor-in-Chief

Contributors

Contents

Related Titles

53191ch1

Table of Contents


Summary

11 Introduction



1211 Force Rating

1212 Power Rating

1213 Stroke Rating






13 Control System


1311 Compressor





1321 Oscillators


1323 Tape Players






142 Linearity





151 Potentiometer


















15101 Sensitivity


















1621 Stroboscope






References


Summary


1A1 Dynamic Signals


1A111 Aliasing





1A212 Gain










1A222 Attenuation











1A5 Integration



























1A724 Zoom Settings






1A822 Overlapping




1A832 STFT vs RPM














Bibliography

Related Titles

53191ch2

Table of Contents


Summary

21 Introduction

22 Amplifiers







2242 Common Mode







23 Analog Filters















243 Demodulation










255 Digital Filters


26 Bridge Circuits






2641 Owen Bridge










281 Phase Shifters







292 Oscilloscopes

2921 Triggering



Bibliography

Related Titles

53191ch3

Table of Contents


Summary

31 Introduction


321 Test Signals




3222 Sine Sweep

3223 Sine Dwell

3224 Decaying Sine

3225 Sine Beat












































3432 Pluck Test

3433 Shaker Tests






















Bibliography

Related Titles

53191ch4

Table of Contents


Summary

41 Introduction



























Bibliography

Related Titles

53191ch5

Table of Contents


Summary

51 Definitions

511 Shock


513 Half-Sine Shock







531 Need





534 Definitions












5351 Definition












54 Pyroshocks







5524 Amplitude

5525 Duration

5526 Difficulties

56 Standards




564 Bump Test


571 Definition


58 Shock Machines

581 Main Types



58211 Impact Mode

58212 Impulse Mode














584 Limitations










592 Main Advantages


5931 Requirements

5932 Solutions





59411 Abacuses




5101 Principle



51022 ZERD Function









References

Related Titles

53191ch6

Table of Contents


Summary

61 Introduction




















682 Data Collectors





691 Time Domain





6915 Orbits









6926 Masks


693 Modal Domain


610 Fault Detection

6101 Standards











61111 Unbalance

61112 Misalignment


61114 Soft Foot

61115 Rubs

61116 Resonances

61117 Oil Whirl

61118 Oil Whip







61131 Pumps

61132 Fans



61135 Compressors



References

Related Titles

53191ch7

Table of Contents


Summary

71 Introduction


721 General Terms


723 Tool Wear



















7411 Time Domain







752 Neural Networks



753 Fuzzy Logic

754 Other Methods

76 Conclusion

References

Related Titles

53191ch8

Table of Contents


Summary

81 Introduction




841 Coverage Index

842 Overlap Index


85 A Case Study









86 Conclusion

References

Related Titles

53191ch9

Table of Contents


Summary

91 Introduction









941 Learning Mode

942 Monitoring Mode

943 Diagnostic Mode

944 Experiments







9443 Tests




96 Conclusions

References

Related Titles

53191ch10

Table of Contents


Summary

101 Introduction

























1031 Introduction

1032 Wind Speed










1037 Dampers



























106 Impact Loading



107 Floor Vibration

1071 Introduction


10721 Walking







10733 Damping

10734 Resonance




10751 Harmonics



Bibliography

Related Titles

53191ch11

Table of Contents


Summary

111 Introduction

















11244 Other Systems





























112911 Buildings

112912 Bridges


112921 Buildings

112922 Bridges
















































113714 Test Results








Bibliography

Related Titles

53191ch12

Table of Contents


Summary

121 Introduction





















12231 Kaul Method


































126 Conclusions

References

Related Titles

53191ch13

Table of Contents


Summary

131 Introduction











Bibliography

Related Titles

53191ch14

Table of Contents


Summary

141 Introduction












Bibliography

Related Titles










1321 Oscillators








oscillator
















DC Voltage

Oscillator


FrequencyConverter

FilterAmplifier


FrequencyCounter


Variable-GainOutput

Amplifier

SignalSpecification

LevelSpecification





53191fm


Preface

Acknowledgments

Editor-in-Chief

Contributors

Contents

Related Titles

53191ch1

Table of Contents


Summary

11 Introduction



1211 Force Rating

1212 Power Rating

1213 Stroke Rating






13 Control System


1311 Compressor





1321 Oscillators


1323 Tape Players






142 Linearity





151 Potentiometer


















15101 Sensitivity


















1621 Stroboscope






References


Summary


1A1 Dynamic Signals


1A111 Aliasing





1A212 Gain










1A222 Attenuation











1A5 Integration



























1A724 Zoom Settings






1A822 Overlapping




1A832 STFT vs RPM














Bibliography

Related Titles

53191ch2

Table of Contents


Summary

21 Introduction

22 Amplifiers







2242 Common Mode







23 Analog Filters















243 Demodulation










255 Digital Filters


26 Bridge Circuits






2641 Owen Bridge










281 Phase Shifters







292 Oscilloscopes

2921 Triggering



Bibliography

Related Titles

53191ch3

Table of Contents


Summary

31 Introduction


321 Test Signals




3222 Sine Sweep

3223 Sine Dwell

3224 Decaying Sine

3225 Sine Beat












































3432 Pluck Test

3433 Shaker Tests






















Bibliography

Related Titles

53191ch4

Table of Contents


Summary

41 Introduction



























Bibliography

Related Titles

53191ch5

Table of Contents


Summary

51 Definitions

511 Shock


513 Half-Sine Shock







531 Need





534 Definitions












5351 Definition












54 Pyroshocks







5524 Amplitude

5525 Duration

5526 Difficulties

56 Standards




564 Bump Test


571 Definition


58 Shock Machines

581 Main Types



58211 Impact Mode

58212 Impulse Mode














584 Limitations










592 Main Advantages


5931 Requirements

5932 Solutions





59411 Abacuses




5101 Principle



51022 ZERD Function









References

Related Titles

53191ch6

Table of Contents


Summary

61 Introduction




















682 Data Collectors





691 Time Domain





6915 Orbits









6926 Masks


693 Modal Domain


610 Fault Detection

6101 Standards











61111 Unbalance

61112 Misalignment


61114 Soft Foot

61115 Rubs

61116 Resonances

61117 Oil Whirl

61118 Oil Whip







61131 Pumps

61132 Fans



61135 Compressors



References

Related Titles

53191ch7

Table of Contents


Summary

71 Introduction


721 General Terms


723 Tool Wear



















7411 Time Domain







752 Neural Networks



753 Fuzzy Logic

754 Other Methods

76 Conclusion

References

Related Titles

53191ch8

Table of Contents


Summary

81 Introduction




841 Coverage Index

842 Overlap Index


85 A Case Study









86 Conclusion

References

Related Titles

53191ch9

Table of Contents


Summary

91 Introduction









941 Learning Mode

942 Monitoring Mode

943 Diagnostic Mode

944 Experiments







9443 Tests




96 Conclusions

References

Related Titles

53191ch10

Table of Contents


Summary

101 Introduction

























1031 Introduction

1032 Wind Speed










1037 Dampers



























106 Impact Loading



107 Floor Vibration

1071 Introduction


10721 Walking







10733 Damping

10734 Resonance




10751 Harmonics



Bibliography

Related Titles

53191ch11

Table of Contents


Summary

111 Introduction

















11244 Other Systems





























112911 Buildings

112912 Bridges


112921 Buildings

112922 Bridges
















































113714 Test Results








Bibliography

Related Titles

53191ch12

Table of Contents


Summary

121 Introduction





















12231 Kaul Method


































126 Conclusions

References

Related Titles

53191ch13

Table of Contents


Summary

131 Introduction











Bibliography

Related Titles

53191ch14

Table of Contents


Summary

141 Introduction












Bibliography

Related Titles

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