Effective MachineryMeasurements usingDynamic Signal Analyzers

Application Note 243-1

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Table of Contents

Chapter 1. Introduction 3

1.1 Benefits of Vibration Analysis 41.2 Using This Application Note 5

Chapter 2. Converting Vibration to an Electrical Signal 7

2.1 Vibration Basics 82.2 Transducers 122.3 Selecting the Right Transducer 162.4 Installation Guidelines 17

Chapter 3. Reducing Vibration to Its Components: The Frequency Domain 19

3.1 The Time Domain 193.2 The Frequency Domain 203.3 Spectral Maps/Waterfalls 223.4 The Phase Spectrum 223.5 Frequency Domain Analyzers 25

Chapter 4. Vibration Characteristics of Common Machinery Faults 27

4.1 Imbalance 274.2 Rolling-Element Bearings 284.3 Oil Whirl in Fluid-Film Bearings 324.4 Misalignment 344.5 Mechanical Looseness 354.6 Gears 364.7 Blades and Vanes 374.8 Resonance 384.9 Electric Motors 394.10 Summary Tables 39

Chapter 5. Advanced Analysis and Documentation 41

5.1 Practical Aspects of Analysis 415.2 Using Phase for Analysis 445.3 Sum and Difference Frequencies 465.4 Speed Normalization 485.5 Baseline Data Collection 50

Chapter 6. Dynamic Signal Analyzers 51

6.1 Types of DSAs 526.2 Measurement Speed 526.3 Frequency Resolution 546.4 Dynamic Range 566.5 Digital Averaging 576.6 HP-IB and HP Instrument Basic 596.7 User Units and Waveform Math 606.8 Synchronous Sample Control and Order Tracking 616.9 Dual/Multi-channel Enhancements 63

Appendix A - Computed Synchronous Resampling and Order Tracking 69

Glossary 75

References 82

Index 84

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Figure 1-1Dynamic SignalAnalysers are(DSAs) are theideal instrumentfor analyzingmachineryvibration.

The analysis of machinery vibra-tion is characterized by a numberof distinct application areas. Inevaluating machinery vibration itsparamount to ask “What is thepurpose of the measurement?”.In general, the analysis will fallintoone of three distinct catego-ries:

1) Product/machine researchand development

2) Production and quality control(this includes rebuilding andoverhaul)

3) In service maintenance andmonitoring

In the cases of these differingapplication categories; the gen-eral principles and measurementsare often the same, but the perfor-mance characteristics, measure-ment flexibility functionality anddata presentation formats canvary.

The implementation of machineryvibration analysis has beenmade practical by the develop-ment of analysis instrumentscalled Dynamic Signal Analyzers(DSAs). Machinery vibration is acomplex combination of signalscaused by a variety of internalsources of vibration. The powerof DSAs lies in their ability toreduce these complex signals totheir component parts. In the ex-ample of Figure 1-2, vibration isproduced by residual imbalanceof the rotor, a bearing defect, andmeshing of the gears — each oc-curring at a unique frequency. Bydisplaying vibration amplitude asa function of frequency (the vibra-tion spectrum), the DSA makes itpossible to identify the individualsources of vibration.

Chapter 1Introduction

Figure 1-2The individualcomponents ofvibration areshown in DSAdisplays ofamplitude versusfrequency.

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Dynamic Signal Analyzers canalso display the vibration ampli-tude as a function of time (Figure1-3), a format that is especiallyuseful for investigating impulsivevibration (e.g. from a chippedgear). The waterfall/spectral mapformat (Figure 1-4) adds a thirddimension to vibration amplitudeversus frequency displays. Thethird dimension can be time, rpmor a count triggered by an exter-nal event (e.g. load, delay fromtop-dead-center, etc.). DSAscome in many shapes, sizes andconfigurations. They range fromstand- alone battery operated por-tables, to bench-top precision in-struments, to rack-mountedcomputer controlled systems.They range from single-channelunits up through multi-channel(~500) systems. Virtually all canbe computer automated and con-trolled, and a wide variety ofpost-processing capabilities andprograms are available.

This application note is a primeron analyzing machinery vibrationwith Dynamic Signal Analyzers.Each of the important steps in theanalysis process from selectingthe right vibration transducer tointerpreting the information dis-played is covered. The tech-niques described provide insightinto the condition of the machin-ery that eliminates much of theguesswork from analysis, trouble-shooting and maintenance.

1.1 Benefits of VibrationAnalysis

The ability to analyze and recordvibration data has existed for aconsiderable time. Its only re-cently with the advent of modernDSAs that the actual detailedanalysis of vibration data has be-come widespread and effective.

Figure 1-3DSA displayof amplitudeversus time areespecially usefulfor analyzingimpulsivevibration thatis characteristicof gear androlling elementdefects.

Figure 1-4DSA map displaysillustrate changesin vibration withrpm, load, ortime. This mapis a collectionof vibrationmeasurementsmade during amachine runup.

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Figure 1.2-1The process of machin-ery vibration analysisconsists of four steps,each critical for success.

The principle objectives in analyz-ing the vibration data are:

1) Simplify and reduce the vibra-tion data into a more compacteasily interpreted form.

2) Associate characteristics ofthe vibration to specific featuresof the machine vibrating.

3) Provide a consistent, repeat-able measurement by which tocharacterize the vibration of amachine.

4) Identify characteristics thatchange with time and operatingconditions, or both.

Figure 1-2 illustrates the princi-ples presented; the vibration datais broken down into its individualfrequency components by theDSA; the analysis can associatethese components to particular

elements in the machine anddepending upon the objective,determine whether an individualcomponent of the vibration isabnormal. The total energy in anysingle component is generallysmall and the ability of a DSA toindividually segregate this compo-nent make it a very sensitive mea-sure of the machine. Often a verylarge change in an individual com-ponent will cause an extremelysmall change in the overallvibration level.

1.2 Using this ApplicationNote

This application note is organizedaround four key steps in theanalysis process shown in Figure1.2-1: (1) converting the vibrationto an electrical signal, (2) reduc-ing it to its components, (3) corre-lating those components with

machine defects, and (4) docu-menting, archiving and analyzingthe results. Each of these steps isvital to analysis, and viewing theprocess in this manner promotesa systematic approach thatincreases the probability ofsuccess. The contents of eachchapter, and their relation tothe steps in Figure 1.2-1 arediscussed below.

Two subjects beyond the scope ofthis note are rotor dynamics andthe vibration characteristics ofspecific types of machinery.Rotor dynamics is required forcomplete analysis of the rotorsused in most turbomachinery (i.e.flexible rotors) although most ofthe information in this note stillapplies (we will note circum-stances when it does not).

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Chapter Overview

Chapter 2Chapter 2Chapter 2Chapter 2Chapter 2: Converting Vibration to an Electrical SignalVibration is converted to an electrical signal with transducers, and effective analysisrequires a signal that accurately represents the vibration. This chapter gives you theinformation needed to select and mount transducers.

Chapter 3:Chapter 3:Chapter 3:Chapter 3:Chapter 3: Reducing Vibration to its Components - The Frequency DomainThe key to successful analysis is reduction of the complex signal to simple components.As shown in Figure 1-2, this is best done with a display of vibration amplitude vs.frequency – a perspective known as the frequency domain. The objective of thischapter is to provide a good working knowledge of the frequency domain.

Chapter 4:Chapter 4:Chapter 4:Chapter 4:Chapter 4: Characteristic Vibration of Common Machinery FaultsEach type of machine fault has distinctive characteristics that can be used foridentification. This chapter describes the characteristics of some of the most commonmachinery faults.

Chapter 5: Chapter 5: Chapter 5: Chapter 5: Chapter 5: Advanced Analysis and DocumentationThis chapter focuses on solving some of the practical problems encountered in machineryvibration analysis, such as identifying spectral relationships, order analysis, orbits, limittesting, automation and other advanced techniques.

Chapter 6:Chapter 6:Chapter 6:Chapter 6:Chapter 6: Dynamic Signal AnalyzersDSAs feature measurement capabilities that make them the ideal instrument formachinery vibration analysis. This chapter explains why these capabilities are important,describes key aspects of each and helps discriminate between the different analyzersranging from single-channel up through large multi-channel systems.

Understanding the vibration char-acteristics of specific types of ma-chinery is important for effectiveanalysis. This information can beobtained from machinerymanufacturers, independenttraining centers, and from welldocumented experience withsimilar machines.

The analysis of machinery vibra-tion is not an easy task, and youwill not fully understand each andevery measurement, nor will youeasily predict the effects ofchanges or an impending failure.What vibration analysis doesprovide is a valuable tool to giveyou additional insight into thedynamics of a rotating machine,the ability to predict most failuresand diagnose the cause ofexcessive vibration.

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Chapter 2Converting Vibration to an

Electrical Signal

Before analysis can begin, vibra-tion must be converted to an elec-trical signal — a task performedby vibration transducers. The keyconsiderations in obtaining a sig-nal that accurately represents thevibration are: (1) selecting theright type of transducer, and (2)locating and installing it correctly.The four types of transducerscommonly used for machinery vi-bration are shown in Figure 2-1.They are differentiated by the pa-rameter measured (i.e. displace-ment, velocity, or acceleration),and by the machine componentmeasured (i.e. shaft or housing).Selection depends on the charac-teristics of the machine and itsexpected faults. Installation re-quires correct placement, securemounting, and proper signalconditioning.

In addition to the motion trans-ducer, for many measurementsthe operating speed of the shaft isof importance. The transducerused for this is called a tachome-ter; and provides a pulse type sig-nal as opposed to the analog datanormally found in motion trans-ducers. The tachometer normallyproduces a fixed number of“pulses” per revolution which is inturn converted to a rotation speedby a frequency counter. Commontypes of tachometers include theuse of the displacement probeand/or optical or magnetic sen-sors.

This chapter begins with a discus-sion of basic vibration conceptsthat are fundamental to under-standing transducers and their in-stallation. This is followed by adescription of each of the threetypes of motion transducers andtwo common tachometer configu-rations. The final section of thechapter provides transducer in-stallation guidelines.

Figure 2.1Four types oftransducerscommonly usedto convert machin-ery vibration toan electricalsignal.

2.1 Vibration Basics

Before starting our discussionof the details of transducers andvibration analysis, it is importantto establish some basic concepts.The three topics we will focuson are:

(a) Vibration Parameters.Using commercially availabletransducers, we can measure thedisplacement, velocity, or acceler-ation of vibration. Selecting theright parameter is critical for ef-fective analysis.

(b) Mechanical Impedance.What we can measure with trans-ducers is the response of the ma-chine to vibration forces causedby machinery characteristics; not

the forces themselves. The me-chanical impedances of the ma-chine shaft/rotor and housingdetermine how they respond tovibration forces and can alter sig-nificantly the characteristics ofthe signal we measure. Thesecharacteristics are oftennon-linear in nature.

(c) Natural Frequencies.When a structure is excited by animpact, it will vibrate at one ormore of its natural frequencies orresonance. These frequencies areimportant because they are oftenassociated with critical speed ofthe machine, where residual im-balance excites the resonance.They can cause large changes inthe vibration response with chang-es in rpm and are often associatedwith critical operation conditions.

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Vibrations Parameters

We will start our discussion ofvibration parameters by examin-ing the vibration produced bysimple imbalance. Referring tothe machine rotor in Figure 2.1-1,note that the heavy spot producesarotating force that appearssinusoidal from any fixed refer-ence position. At points A and C,the force in the direction of thereference is zero. At points B andD it is at positive and negativemaximums, respectively.

The response of the rotor to sucha force is a displacement whichmoves the center of rotation awayfrom the geometric center (Figure2.1-2).1 A displacement measure-ment performed on the rotor re-sults in approximately the samewaveform as the force, with asignal amplitude approximatelyproportional to the magnitude ofthe force. It is not exactly thesame because the dynamics of therotor affect the response. This isan important point in vibrationanalysis, and is discussed in moredetail in the next section.

The velocity and accelerationparameters of the vibration areoffset in phase relative to dis-placement — an important consid-eration when using phase foranalysis. Phase relationships areshown in Figure 2.1-3. Velocity,for example, is offset from dis-placement by 90°. At point B,when the displacement is maxi-mum, the velocity is zero. Atpoint C, when displacement iszero, velocity is maximum.Following the same reasoning, ac-celeration can be shown to be off-set 90° from velocity, and thus180° from displacement.

Figure 2.1-1A heavy spot on amachine rotorresults in arotating forcevector thatappears sinusoidalfrom a fixedreference.

1 Note: This applies to shafts that do notbend in operation (i.e. rigid shafts).Flexible shafts respond somewhatdifferently to imbalance forces.

The amplitude of the vibrationparameters also vary with rotationspeed (rpm) — an important con-sideration in transducer selection.Velocity increases in direct pro-portion to frequency (f), while ac-celeration increases with thesquare of frequency. This varia-tion with frequency, and the phaserelationships shown in Figure2.1-3 , are illustrated in the equa-tions below. In these equations,which apply only to sinusoidalvibration, A is the vibration dis-placement amplitude and f is therotor frequency of rotation (cps orHz).

Displacement = A sin (2p f t)Velocity = 2p f A COS (2p f t)

Acceleration = - (2p f)2 A sin (2p f t)

The three vibration parametersare thus closely related and, infact, can be derived from eachother by a Dynamic Signal Analyz-er (see Section 6.6). However, thevariation in vibration amplitude

with machine speed, and trans-ducer limitations, often mean thatonly one of the parameters willsupply the information necessaryfor analysis.

The impact of variations inamplitude with rotation speed isillustrated in Figure 2.1-4. In thisexample, potentially dangerousvibration levels are present in alow-speed fan and a high-speedgearbox. The two items to noteare: (1) displacement and acceler-ation levels differ widely, and(2) velocity is relatively constant.

From the first, we can concludethat frequency considerations areimportant in selecting a vibrationparameter. Acceleration is not asgood a choice for very low fre-quency analysis, while displace-ment does not work well for highfrequencies. Note that these arelimitations of the vibration param-eter, not the transducer.

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Figure 2.1-2The imbalanceforce produces avibration whosedisplacementhas approximatelythe same wave-form as theforce itself.

Frequency range limitations oftransducers are also an importantconsideration in parameter selec-tion, and are discussed inSection 2.2.

The fact that velocity is a good in-dicator of damage, independent ofmachine speed, implies that it is agood parameter for generalmachine monitoring. That is, avibration limit can be set indepen-dent of frequency. (Velocity re-mains constant with damage levelbecause it is proportional to theenergy content of vibration.) Ve-locity is also a good parameter foranalysis, but the upper frequencylimitation of velocity transducerscan be a problem for gear andhigh-speed bladeanalysis.

Mechanical Impedance

A key point illustrated by Figure2.1-5 is that we are measuring theresponse of the machine to vibra-tion forces, not the forces them-selves. Thus the responsecharacteristics of the machine —its mechanical impedance — havea direct impact on the measuredvibration. The two key results ofthis are: (1) if the response issmall, the vibration will be diffi-cult to analyze, and (2) if responsechanges drastically with frequen-cy, changes in running speed canproduce misleading changes inmeasured vibration level. Theseare important considerationsin selecting and installingtransducers.

Figure 2.1-3Velocity andacceleration ofthe vibration areoffset 90º and 180ºin phase fromdisplacement.

Figure 2.1-4Two cases whichillustrate thevariation ofvibrationparameterswith machinespeed.

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Figure 2.1-7A plot of vibrationresponse versusfrequency for amachine housingshows howmeasuredvibrationlevel can changewith rpm. A defectforce at frequencyB produces a muchlarger vibrationresponse than thesame force level atfrequency A.

The most common example oflow-level response involves ma-chines with relatively light rotorsand fluid-film bearings, mountedin heavy casings. Very little shaftvibration is transmitted to the cas-ing, and shaft vibration must bemeasured directly (see Figure2.1-6). Rolling element bearingsare much stiffer than most fluid-film bearings, and transmit shaft(and their own) vibration to themachine case well.

An example of mechanical imped-ance that changes noticeably withspeed is shown in Figure 2.1-7.This measurement shows how theratio of acceleration response toinput force might vary with fre-quency on a machine. Note thatmeasurements made at speeds Aand B would differ markedly inamplitude, even if the source ofvibration remained the same.This illustrates why simple levelmeasurements made on a machinewhose speed varies can be mis-leading.

Natural Frequencies

In the plot of Figure 2.1-7, theresponse peaks occur at naturalfrequencies. These are the fre-quencies at which a structure willvibrate “naturally” when hit withan impact. A good illustration ofnatural frequency vibration is atuning fork, which is designed tovibrate at a specific frequencywhen impacted (see Figure 2.1-8).When a vibration force occurs at anatural frequency, the structurewill resonate (i.e. respond with alarge amplitude vibration).1

Figure 2.1-5Vibrationmeasuredon a machine isthe response todefect force, notthe force itself.

Figure 2.1-6A relatively lightshaft turning influid-film bearingstransmits littlevibration to themachine housing.Its vibration mustbe measureddirectly with adisplacementtransducer.

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Figure 2.1-8When excited byan impact, atuning forkvibrates at itsnatural frequency.

Natural frequencies relate to ma-chinery vibration analysis in threeimportant areas: (1) resonances ofthe structure can cause changes invibration level with rpm, (2) thedynamics of rotating shaftschange significantly near naturalfrequencies (or critical speeds),and (3) resonances of transducerslimit the operating frequencyrange of velocity transducers andaccelerometers. Changes in vibra-tion response with frequency areshown in Figure 2.1-7. Shaftswhich operate above or near anatural frequency of the shaft areclassified as flexible, and are dis-cussed briefly in Section 3.4. Nat-ural frequency limits on the usefulfrequency range of transducersare described in the next section(2.2).

A relationship worth noting at thispoint is the variation in naturalfrequency with mass and stiffness.The equation for the natural fre-quency of the simple mechanicalsystem in Figure 2.1-9 is given be-low, where k is stiffness and m ismass. Note that natural frequencygoes up with increasing stiffnessand decreasing mass.

Natural frequency (ωn) = (k/m)1/2

If you think of piano wires or gui-tar strings, the tight, lightweightones are higher in frequency thanthe loose, heavy ones. This rela-tionship is important when deter-mining a solution to resonanceproblems.

1 Note: The subject of resonances andstructural vibration is dealt with inmore detail in Hewlett-PackardApplication Note AN243-3. Thoughextremely important to analyzing andunderstanding machine vibration; thefocus of this note is more on analyzingoperating machines than on structuralanalysis.

Figure 2.1-9The naturalfrequency of asimple mechanicalsystem varies withmass and stiffness.

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2.2 Transducers

In this section, each of the trans-ducers shown in Figure 2.1 will bedescribed. We will discuss howeach one works, its importantcharacteristics, and the most com-mon applications. We will alsodiscuss some common tachometertype transducers used to obtainrotation speed information on themachine.

Displacement Transducers

Noncontacting displacementtransducers (also known asproximity probes1), like the one inFigure 2.2-1, are used to measurerelative shaft motion directly. Ahigh frequency oscillation is usedto set up eddy currents in theshaft without actually touching it.As the shaft moves relative to thesensor, the eddy current energychanges, modulating the oscillatorvoltage. This signal is demodulat-ed, providing an output voltageproportional to displacement. Thisis illustrated in Figure 2.2-2.

In practice, noncontacting dis-placement probes are used on vir-tually all turbomachinery becausetheir flexible bearings (fluid film)and heavy housings result in smallexternal responses. Some gasturbines, especially those used onaircraft, use relatively stiff rolling-element bearings, and can thususe housing-mounted transducers(velocity and acceleration) effec-tively.

Key characteristics of displacement transducers

(a) Displacement transducers measure relative motion between the shaft and themount, which is usually the machine housing. Thus, vibration of a stiff shaft/bearingcombination that moves the entire machine is difficult to measure with displacementtransducers alone.

(b) Signal conditioning is included in the electronics. Typical outputs are 200 mV/mil or8mV/micron (1 mil is 0.001 inches; 1 micron is 0.001 millimeters). Technically, the fre-quency response of displacement probes is up to 10,000 Hz (or 600,000 rpm), but as apractical matter the displacement levels at these frequencies is so low that the actualuseful frequency range of proximity probes is about 500 Hz (30,000 rpm).

(c) Shaft surface scratches, out-of-roundness, and variation in electrical propertiesdue to hardness variations, all produce a signal error. Surface treatment and run-outsubtraction can be used to solve these problems [11,12].

(d) Installation is sometimes difficult, often requiring that a hole be drilled in themachine housing.

(e) The output voltage contains a dc offset of 6 – 12 volts, requiring the use of accoupling for sensitive measurements. AC coupling is a feature of all DSAs, and simplymeans that an input capacitor is used to block the dc. The practical disadvantage of accoupling is reduced instrument response below 1Hz (60 rpm).

1 Note: We will limit our discussion toeddy current probes as they are by farthe most commonly used type.

Figure2.2-2Schematicdiagram ofa typicalnoncontactingdisplacmenttransducerinstallation.

Figure 2.2-1Noncontactingdisplacementtransducersinclude a probeand an oscilla-tor module.

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Figure 2.2-3A typical velocitytransducer withextension probeinstalled.

Figure 2.2-4Velocitytransducer outputis a currentgenerated in thecoil as it movesthrough the fieldof the stationarymagnet.

Figure 2.2-5Frequencyresponse of atypical velocitytransducer. Notethat the naturalfrenquency of themagnet-spring-damper system isbelow theoperating range.

Velocity Transducers

Velocity transducers were the firstvibration transducer, and virtuallyall early work in vibration severitywas done using velocity criteria.Velocity transducer constructionis shown in Figure 2.2-4. Thevibrating coil moving through thefield of the magnet produces a rel-atively large output voltage thatdoes not require signal condition-ing. The amplitude of the voltageis directly proportional to the ve-locity of the vibration. As shownin Figure 2.2-5, the spring-mass-damper system is designed for anatural frequency of 8 to 10 Hz,which allows the magnet to stayessentially fixed in space. Thisestablishes a lower frequencylimit of approximately 10 Hz(600 rpm). The upper frequencylimit of 1000 to 2000 Hz is deter-mined by the inertia of the spring-mass-damper system.

Historically, the velocity transduc-er was widely used in machineryvibration measurements; but inrecent years most transducermanufacturers have replaced thistechnology with accelerometersthat have electrically integratedoutputs which provide the samefunctionality as velocity probesbut with wider frequency rangeand better stability. DSAs alsoprovide for internal integrationof acceleration signals; makingaccelerometers the transducer ofchoice — due to its wider frequen-cy response, greater accuracyand more rugged construction.

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Key characteristics of accelerometers

(a) Accelerometers offer the broadest frequency coverage of the three transducer types.Their weakness is at low frequency, where low levels of acceleration result in smalloutput voltages. Their large output at high frequencies also tends to obscure lowerfrequency content when the transducer is used for measuring overall level. This can beovercome by models with built-in integrators giving velocity output, or by added signalprocessing.

(b) The low frequency response of piezoelectric accelerometers is limited toapproximately 5 Hz. This can be improved with special low frequency versions of theaccelerometer. An inherent problem still exists in measuring acceleration at lowfrequency since its level tends to decrease dramatically at low frequencies.

(c) Accelerometers are very sensitive to mounting. Handheld models are available butrepeatability is very dependent upon the individual. This is increasingly true for highfrequencies. When possible, accelerometers should be securely mounted using athreaded stud, high strength magnet, or industrial adhesive. The mounting surfaceshould be flat and smooth — preferably — machined. Frequently, special mountingstuds are bonded or welded in place where repeated measurements are to be made.

Accelerometers

Accelerometers are the mostpopular general purpose vibrationtransducer. They are constructedusing a number of different tech-nologies, but for general purposemeasurements and machinery vi-bration, the most common designis the piezoelectric quartz acceler-ometer. Our discussion will belimited to this type and its deriva-tives. Construction of a simpleaccelerometer is shown in Figure2.2-7. The vibrating mass appliesa force on the piezoelectric crystalthat produces a charge propor-tional to the force (and thus toacceleration).

The frequency response of a typi-cal accelerometer is shown in Fig-ure 2.2-8. Note that the naturalfrequency is above the operatingrange of the transducer (unlikethe velocity transducer). Opera-tion should be limited to about20% of the natural frequency.

Accelerometer sensitivity is large-ly dependent on the size of themass, with a larger mass produc-ing more output. High output isespecially important for increas-ing the usability of accelerometersat low frequencies. However, inour previous discussion of naturalfrequency, we noted that naturalfrequency decreases as massincreases. Thus increased sensi-tivity tends to lead to lower oper-ating frequency range and largerphysical size.

Figure 2.2-6Accelerometersfeature widefrequency rangeand ruggedness.They should besecurely mountedon a flat surfacefor best results.

Figure 2.2-7The outputvoltage of anaccelerometeris produced by theaccelerating masssqueezing thepiezo-electriccrystal stack.The force — andthusthe outputvoltage —isproportional toacceleration.

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Accelerometer output is a low-level, high-impedance signal thatrequires special signal condition-ing. The traditional method is touse a separate charge amplifier,as shown in Figure 2.2-9(a).How-ever, accelerometers areavailable with built-in signal con-ditioning electronics that requireonly a simple current-source sup-ply. The accelerometer can bedirectly connected to most DSAs(Figure 2.2-9(b)). Another advan-tage of this type of accelerometeris that expensive low-noise cablerequired of normal piezoelectricaccelerometers is not required.This can be especially importantwhen long or multiple cablesare required.

Tachometers

Tachometers are devices used tomeasure the rotation speed of amachine shaft. They are useful indetermining accurate operatingspeed and identifying speed relat-ed components of the velocity.The transducer itself normallyprovides a pulse of some fixedamplitude at a rate related to rota-tion speed (typically, once perrevolution). We will discuss twocommon types, the proximityprobe and the optical tachometer.

Figure 2.2-8Accelerometerhigh frequencyresponse islimited by thenatural frequencyof the spring-masssystem.

Figure 2.2-9aTraditionalaccelerometersrequire anexternal chargeamplifier forsignal con-ditioning.

Figure 2.2-9bIntegrated CircuitPiezoelectricaccelerometers,with built-insignal condi-tioning, can beconnected directlyto a compatibleDSA.

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The proximity probe is the sameas previously discussed, however,it is not used to get accuratedisplacement information in thismode. It is commonly used todetect the presence of somethingsuch as a keyway slot (often re-ferred to as a keyphaser) or geartooth. Figure 2.2-10(a) illustratesa proximity probe detecting akeyway to provide a once per rev-olution signal. This transducerhas many of the limitations previ-ously described.

The other common tachometertransducer is the optical tachome-ter. It generally consists of eitheran optical or infrared light sourceand a detector (Figure 2.2-10(b)).Optionally, a lens for focusing thebeam can be provided. The beamis trained on the rotating shaft anddetects the presence of a reflec-tive indicator (usually, a piece oftape or reflective paint).

The output of the tachometer ishandled in one of two ways. Onmulti-channel DSAs the tachome-ter is fed into a channel of theDSA where the once-per-rev pulsetrain will produce a large frequen-cy component at the rotationspeed of the machine. This isuseful in obtaining valuable phaseinformation about the responsechannels. An alternative is tomeasure the rotation speed direct-ly with specialized hardwareinterfaced directly to the DSA’sexternal sample control. It is also

Figure 2.2-10aProximity probeused astachometer toprovide signalwith repetion rateproportional toshaft velocity(rpm).

Figure 2.2-10bOpticaltachometerwhich measuresreflection of lightfrom a rotatingobject to providesignal propor-tional to rotationspeed.

common to connect the tachome-ter signal directly to the triggerinput of the DSA to obtain anaccurate phase reference.

Tachometers differ from motiontransducers in the fundamentalvariable measured. They measurethe timing of an event, i.e. like thepassing of a reference, such as akeyphasor.

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Figure 2.3A vibration nomo-graph shows howthe levels ofdisplacement andaccelerationchange withfrequency,relative to thelevel of velocity.Note that theaccelerationresponse is verylow at 1 Hz (lessthan 100 µ µ µ µ µ V witha 10 m V / g accel-erometer).

2.3 Selecting the RightTransducer

Selecting the right transducer foran application is a straight for-ward process that is described be-low. Table 2.4 in the next sectionis a guide for the application oftransducers to several generaltypes of machinery.

Step 1: Determine the Parameterof Interest.If you are interested in monitoringa critical clearance or relative dis-placement, the only choice is adisplacement transducer. Al-though acceleration and velocitycan be converted to displacement,it will be an absolute measure-ment, rather than the relativemeasurement given by a displace-ment probe. If the parameter is aquantity other than a clearance orrelative displacement, go on tonext step.

Step 2: Mechanical ImpedanceConsiderations.If the vibration is not well trans-mitted to the machine case, youmust use a displacement trans-ducer to measure the shaft runoutdirectly. This will be the casewith a flexible rotor-bearing sys-tem working in a heavy casing. Ifthe shaft is not accessible (as aninternal shaft in a gearbox), or ifthe rotor-bearing system is stiff,you should use a casing mountedvelocity or acceleration transduc-er. In borderline cases, it may be

accelerometer. Choose one de-signed for the frequency range andvibration level anticipated. Thevibration nomograph of Figure 2.3can be used to help determine therequired performance. In manycases for low frequency (<20 Hz)applications or applications wherethe overall level is important foraccessing machinery health avelocity output is required. Thiswill dictate using either a velocitytransducer or more commonly anaccelerometer with integratedoutput proportional to velocity.

appropriate to use both absoluteand relative motion transducers.

If Steps 1 and 2 indicate a dis-placement transducer, it is the onethat will provide the bestresults. If a housing-mounted ac-celeration or velocity transduceris indicated, go on to Step 3.

Step 3: Frequency Considerations.If the frequency of the expectedvibration is greater than 1000 Hz,you must use an accelerometer.(You will have a much better ideaof frequencies to expect afterreading Chapter 4). If the vibra-tion will be in the 10 to 1000 Hzrange, either velocity or accelera-tion transducers can be used. Gen-erally, an accelerometer will bethe choice in these cases. Theimportant thing to consider is theindividual specifications of the

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Table 2.4TransducerApplicationSummary.

Machine DescriptionMachine DescriptionMachine DescriptionMachine DescriptionMachine Description TransducerTransducerTransducerTransducerTransducer LocationLocationLocationLocationLocationVariableVariableVariableVariableVariable

Steam turbine/large pump or compressor Displacement Radial horizontal atA,B,C,D. with fluid-film bearings. Redundant axial at A and D.Gas turbine or medium size pump Displacement Radial horizontal and vertical at

A and B.

Velocity Radial horizontal or vertical atA and B.

Motor/fan both with fluid-film bearings Displacement One radial at each bearing. Oneor Velocity axial displacement to detect thrust

wear.Motor/pump or compressor with rolling Velocity or One radial at each bearing. Oneelement bearings Acceleration axial, usually on motor, to detect

thrust wear.Gear box with rolling element bearings Acceleration Transducers mounted as close to

each bearing as possible.Gearbox shafts with fluid-film bearings Displacement Radial horizontal and vertical at each

bearing. Axial to detect thrust wear.

Figure 2.4Transducerlocationsreferenced inTable 2.4

2.4 InstallationGuidelines

After the transducer has been se-lected, it must be properly in-stalled for the best results. Figure2.4 is an example of a machinecombination that is used for theapplication summary in Table 2.4.The machine combination couldbe a small motor and pump, or asteam turbine and generator. Ingeneral, the number of transduc-ers used on a machine combina-tion is determined by the purposeof the measurement. Table 2.4is intended to show typical appli-cations and considerations thatcan be used as a guide in select-ing measurement points andtransducers.

When troubleshooting a vibrationproblem it is critical to get infor-mation on vibration of key compo-nents in the principle directions.The inclusion of phase informa-tion is critical to diagnosing manymachine dynamics problems. Onthe other hand, characterizing anon-critical machine for machin-ery health monitoring purpose; the

goal is often to find a “representa-tive” measurement which cancharacterize the general conditionof the machine with the minimumnumber of measurements. Whenselecting measurement points andtransducers the ultimate goalshould be kept in mind. Carefultransducer selection; bearing inmind manufacturers specification;proper mounting of the transducer

can be critical. One particularcaution: the transducer shouldnever be mounted to a sheet metalcover, since resonances may easi-ly be in the operating speed rangeand can easily mask the realobjective of the measurement.

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difficult. This situation is illustrat-ed in Figure 3.1-2, where two sinewave frequencies are present. Theresult of this combination is atime domain display in which theindividual components are diffi-cult to derive. The time domain isa perspective that feels natural,and provides physical insight intothe vibration. It is especially use-ful in analyzing impulsive signalsfrom bearing and gear defects,and truncated signals from loose-ness. The time domain is also use-ful for analyzing vibration phaserelationships. However, the indi-vidual components of complexsignals are difficult to determine.A perceptive that is much bettersuited to analyzing these compo-nents is the frequency domain.

Chapter 3

Figure 3.1-2Waveform (c) isthe combinationof signals (a) and(b). The nature ofthese componentsis hidden in thetime domain viewof their sum.

Reducing Vibration to its

Components: The Frequency

Domain

The signal obtained from amachinery vibration transducer isa complex combination of re-sponses to multiple internal andexternal forces. The key to effec-tive analysis is to reduce thiscomplex signal to individual com-ponents, each of which can thenbe correlated with its source.Techniques for reducing vibrationto its components are the subjectof this chapter, while the processof correlating these componentswith machinery vibration isdiscussed in Chapters 4 and 5.

Two analysis perspectives areavailable for determining thecomponents of vibration: (1) thetime domain view of vibrationamplitude versus time and (2) thefrequency domain view of vibra-tion amplitude versus frequency.While the time domain providesinsight into the physical nature ofthe vibration, we will see that thefrequency domain is ideally suitedto identifying its components.The advantage of Dynamic SignalAnalyzers for machinery analysisis their ability to work in bothdomains.

This chapter begins with a dis-cussion of the relationshipbetween the time and frequencydomains. Waterfall/spectral maps,which add the dimension ofmachine speed or time to thefrequency domain, are presentednext. The frequency phase spec-trum, an important complement tothe more familiar amplitude spec-trum, is discussed in the followingsection. This chapter closes witha description of the type of instru-ments available for frequencydomain analysis. Information onthe time and frequency domains inthis application note is focused onmachinery vibration. For a moregeneral discussion of the subjectrefer to Hewlett-Packard applica-tion note AN 243.

3.1 The Time Domain

One way to examine vibrationmore closely is to observe how itsamplitude varies with time. Thetime domain display in Figure3.1-1 clearly shows how vibrationdue to an imbalanced rotor varieswith time (we are using a dis-placement transducer to simplifythe phase relationship). The am-plitude of the signal is proportion-al to the amount of imbalance,and the speed of rotation. Thissignal is easy to analyze becausewe are using an idealized examplewith a single source of vibration –real world vibration signals aremuch more complex.

When more than one vibrationcomponent is present, analysis inthe time domain becomes more

Figure 3.1-1 Atime domainrepresenta-tion of vibrationdue to rotorimbalance.

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3.2 The FrequencyDomain

Figure 3.2-1(a) is a three-dimen-sional graph of the signal used inthe last example. Two of the axesare time and amplitude that wesaw in the time domain. The thirdaxis is frequency, which allows usto visually separate the compo-nents of the waveform. When thegraph is viewed along the frequen-cy axis, we see the same timedomain picture we saw in 3.1-2.It is the summation of the twosine waves which are no longereasily recognizable.

However, if we view the graphalong the time axis as in Figure3.2-1(c), the frequency compo-nents are readily apparent. In thisview of amplitude versus frequen-cy, each frequency component ap-pears as a vertical line. Its heightrepresents its amplitude and itsposition represents its frequency.This frequency domain represen-tation of the signal is called thespectrum of the signal.

The power of the frequency do-main lies in the fact that any realworld signal can be generated byadding up sine waves. (This wasshown by Fourier over one hun-dred years ago.) Thus, while theexample we used to illustrate thefrequency domain began as a sum-mation of sine waves, we couldperform a similar reduction tosine wave components for anymachinery vibration signal. It isimportant to understand that thefrequency spectrum of a vibrationsignal completely defines thevibration – no information is lostby converting to the frequency do-main (provided phase informationis included).

A Machinery Example

Figure 3.2-2 should give you betterinsight into frequency domain

analysis applied to machinery.The internal sources of vibrationin this example are rotor imbal-ance, a ball bearing defect, andreduction gear meshing. For pur-poses of illustration in this ex-ample, the sources of vibrationand their resulting frequencycomponents have been somewhatsimplified. (Details of the fre-quency components that each ofthese defects produce are given inChapter 4.)

Imbalance produces a sinusoidalvibration at a frequency of onceper revolution. If we assume a sin-gle defect in the outer race of theball bearing, it will produce an im-pulsive vibration each time a ballpasses over the defect – usuallyaround four times per revolution.To simplify the example, we willassume that this is a sine wave.The two smaller sine waves a-round this frequency are causedby interaction (modulation) of the

Figure 3.2-2Machineryvibrationviewed inthe time andfrequencydomains.

Figure 3.2-1The relationshipbetween the timeand frequencydomains.

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Figure 3.2-3Small signals thatare hidden in thetime domain arereadily apparentin the frequencydomain. By usinga logarithmicamplitude scale,signals whichvary in level bya factor of over1000 can bedisplayed.

bearing defect force with the im-balance force. These signals arecalled sidebands, and occur oftenin machinery vibration. They arespaced at increments of plus andminus the running speed from thedefect frequency. These compo-nents are often referred to as sumand difference frequencies, andare discussed in Section 5.3. Thegear mesh frequency appears atrunning speed multiplied by thenumber of teeth on the main shaftgear, which here we assumed tobe ten. The running speed side-bands around the gear meshingfrequency usually indicate eccen-tricity in the gear. While this is agreatly simplified view of machin-ery vibration, it demonstrates theclarity with which vibration com-ponents can be seen in the fre-quency domain.

Early Warning of Defects

As we pointed out in the introduc-tion, DSAs are used to make ma-chinery vibration measurementsin the frequency domain. This isbecause the low level vibrationproduced by early stages of somedefects cannot be detected by anoverall vibration meter. (In effect,it is “buried” by the relativelylarge residual imbalance compo-nent.) This is especially true ofrolling element bearings, and isone of the reasons this particularproblem is one of the most diffi-cult to detect.

A major advantage of the frequen-cy domain is that low level signalsare easy to see – even in the pres-ence of signals 1000 time larger.This is illustrated in the time andfrequency domain displays of Fig-ure 3.2-3, where the low-level sig-nals that are readily apparent inthe frequency domain cannot beseen in the time domain. A key tothis capability is logarithmicdisplay of amplitude.

22

1 Note: The distinction between maps andwaterfalls is often disputed. For the pur-poses of this note a waterfall is a “live”continuously updating display that con-stantly updates itself with the latest spec-trum while discarding the oldest. A map isa display of multiple spectrums taken atdifferent times/conditions; often requiringcomplete regeneration to add additionalspectra.

While most people prefer themore natural feel of a linear dis-play, logarithmic displays are anaid to displaying the wide dynam-ic range of data present in a DSA.(Dynamic range is discussed insection 6.4). We will presentexamples using both linear andlogrithmic scales in this appli-cation note.

Spectrum Examples

Figure 3.2-6 shows the time andfrequency domain of four signalsthat are common in machineryvibration.

(a) The frequency spectrum of apure sine wave is a single spectralline. For a sine wave of period Tseconds, this line occurs at 1/THz.

(b) A distorted sine wave, produc-ed by “clipping” the signal at someprescribed amount on both thepositive and negative directions.This is much like the truncatedsignal produced by mounting orbearing cap looseness and is madeup of a large number of odd har-monics. Harmonics are compo-nents which occur at frequencymultiples of a fundamental fre-quency. In machinery analysis,we often refer to harmonics as“orders” of the fundamentalrunning speed.

(c) Bearings and gears often pro-duce impulsive signals that aretypified by harmonics in the fre-quency domain. These harmonicsare spaced at the repetition rateof the impulse.

(d) Modulation can result whensome higher characteristic fre-quency interacts with a lowerfrequency, often the residual im-balance. The frequency spectrumof a modulated signal consists ofthe signal being modulated (thecarrier), surrounded by sidebandsspaced at the modulatingfrequency.

Figure 3.2-6Examples offrequencyspectra commonin machineryvibration.

3.3 SpectralMaps/Waterfalls

The vibration characteristics of amachine depend on its dynamicsand the nature of the forces actingupon it. The change of these char-acteristics with machine speedhas two important implicationsfor analysis: (1) the vibration re-sulting from a defect may not ap-pear in all speed ranges, and(2) insight into the nature of themachine may be obtained fromobserving the change in vibrationwith speed. Spectral maps1, suchas the one in Figure 3.3-1 arethree dimensional displays that ef-fectively show variation in the vi-bration spectrum with time. Theseare also called cascade plots.

Rpm spectral maps usually con-sist of a series of vibration spectrameasured at different speeds. Avariety of other parameters, in-cluding time, load, and tempera-ture are also used as the thirddimension for maps and water-falls. A common method for map-ping the variations in the vibrationwith rpm is to measure successivespectra while the machine iscoasting down or running up inspeed. If the machine is instru-mented with a tachometer, thespeed can be monitored and usedto trigger the measurement thusobtaining vibration spectra at uni-formly spaced rpm. Figure 3.3-1illustrates such a map and the

setup used to produce it with aHewlett-Packard DSA with thisbuilt-in capability (Figure 3.3-2).

In addition to showing how vibra-tion changes with speed, spectralmaps/waterfalls quickly indicatewhich components are related torotational speed. The componentswill move across the map as thespeed changes, while fixed fre-quency components move straightup the map. This feature is espe-cially useful in recognizingmachine resonances (criticalspeeds), which occur at fixedfrequencies.

3.4 The Phase Spectrum

The complete frequency domainrepresentation of a signal consistsof an amplitude spectrum and aphase spectrum. While the ampli-tude spectrum indicates signallevel as a function of frequency,the phase spectrum shows thephase relation between spectralcomponents. In machinery vibra-tion analysis, phase is requiredfor most balancing techniques.It is also useful in differentiatingbetween faults which produce

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Figure 3.3-1Spectral mapsshow variation inthe vibrationspectrum withtime or rpm.

Figure 3.4-2Two sine waveswith a phaserelationshipof 90º.

Figure 3.4-1The phase of theimbalance signalcorresponds tothe direction ofthe displacement.One 360º rotationof the rotor corre-sponds to one360º cycle of thesignal.

Figure 3.3-2Set-up of DSA toproduce spectralmap.

similar amplitude spectra. DSAsare unique among commonly usedfrequency domain analyzers inproviding both amplitude andphase spectra.

The concept of phase relation-ships is most easily seen in thetime domain. In Figure 3.4-1,phase notation has been added tothe waveform we used in our firsttime-domain example. One 360°cycle of the rotor corresponds toone cycle of the vibration signal.This relationship holds regardlessof where we start on the circle,but absolute phase numbers meannothing without a reference. InFigure 3.4-1, we have defined thereference point as A. This meansthat in effect when the keyphasorpasses point A the time of the firstdata point of the block is definedas t=0. The actual phase is alsodependent upon the orientation(and type) of the transducer. Byconvention for a single-channelmeasurement, a cosine wave (i.e.positive maxima at t=0) is definedas the zero phase reference.

Just as absolute phase can be de-fined relative to a reference point,we can define the relative phaseof two signals of the samefrequency. The signals shown inFigure 3.4-2 are separated by1 quarter of a cycle, or 90°. Wesay that the phase of the trace Aleads that of trace B because itspeak occurs first.

In the frequency domain, eachamplitude component has a corre-sponding phase. Figure 3.4-3 is aDSA display of our imbalanceexample, indicating a 90° phaserelationship between the frequen-cy component and the triggersignal (amplitude is shown as adashed line). The phase is -90°because the peak of the signaloccurs after the trigger.

24

Balancing

The most common application forphase spectrum is in trim balanc-ing. Recall from Figure 3.4-1 thatwe need a reference for absolutephase to be meaningful. In ma-chinery analysis, this reference ismost often provided by a keypha-sor – a displacement or opticaltransducer which detects the pas-sage of a keyway, set screw, orreflecting surface. Figure 3.4-4shows a keyphasor added to ourexample machine. With the trans-ducer 90° behind the keyphasor(in the direction of rotation), andthe keyphasor and heavy spotlined up, the resulting timedomain waveforms are offset inphase by 90°. The correspondingphase spectrum of the vibrationsignal is as shown in Figure 3.4-3.In this case, the keyphasor is usedto trigger the measurement.

Figures 3.4-3 and 3.4-4 indicatethe location of the heavy spot rel-ative to the keyway. This informa-tion can be used in balancing tolocate a compensation weight op-posite the heavy spot. This willreadily give information about thelocation of the imbalance, but lit-tle information about the magni-tude of the imbalance weight.Unless the system has been cali-brated previously on the same orsimilar machines a two-measure-ment scheme which uses trialweights is required to get accuratedata on the magnitude of the im-balance. For balancing, it’s impor-tant to note, that the previousdiscussion assumed a displace-ment transducer; velocity trans-ducers and accelerometers haveadditional 90° and 180° phaseshifts that must be accounted for.

We have also assumed that the ro-tor is rigid. There are two areas ofcaution. First is that a magneticphase detector (i.e. keyphasor)can cause phase shifting errors.This is due to the changing wave-form shape with speed causingthe trigger point to move. Theother area is in balancing speed.It is advisable that balancing notbe done close to resonance fre-quencies as the phase changesvery rapidly with speed nearresonances and this can lead toconsiderable measurement error.

Other Applications of Phase

The phase spectrum is also usefulfor differentiating between de-fects that produce similar ampli-tude spectra. In Section 4.4, wewill describe how axial phasemeasurements can be used todifferentiate between imbalanceand misalignment. Section 5.2explains how the relative stabilityof phase can be used to gaininsight into the nature of defects.

Rigid and Flexible Rotors

We mentioned in the introductionthat flexible rotors required an un-derstanding of the shaft dynamicsfor complete analysis. As thename implies, a flexible rotor isone which bends during opera-tion. This bending occurs at a nat-ural frequency of the rotor, oftenreferred to as a critical speed. Aflexible rotor has several criticalspeeds, each with a specific bend-ing shape (or direction). Theseshapes are called modes, and canbe predicted through structuralmodeling and measured usingorbit analysis. The distinctionbetween rigid and flexible rotorsis important because the dynam-ics of a rotor change significantly

as it approaches and passesthrough a critical speed. Theamplitude of the vibrationresponse peaks, and the phaseresponse shifts by 180°.

This phase shift is shown in theplot of Figure 3.4-5 (commonlyreferred to as a Bode plot). Whenphase is measured at a speed wellabove the critical, the high spotmeasured by the displacementtransducer is at a point oppositethe imbalance – a phase shift of180°. When operating speed isnear the critical speed, the phaseresponse will be shifted between0° and 180°, depending on thedynamics of the rotor.

Accurate interpretation of phasespectra measured on flexible ro-tors requires an understanding ofrotor dynamics that is beyond thecope of this application note.Unless otherwise noted, all state-ments about the use of phase inanalysis refer only to rigid rotors(those which operate well belowthe first critical speed).

25

Figure 3.5-1Parallel filteranalyzers haveinsufficientfrequencyresolution formachineryanalysis.

Figure 3.4-3DSA frequencydomain displayof a 90º phaserelationship.Referring toFigure 3.4-2, thisis the phase oftrace B whentrace A is used totrigger themeasurement.

3.5 Frequency DomainAnalyzers

Instruments which display thefrequency spectrum are generallyreferred to as spectrum analyzers,although DSAs are also commonlyreferred to as real-time or FFTanalyzers. There are three basictypes of spectrum analyzers:(1) parallel filter, (2) swept filter,and (3) DSA. This section will givea short description of each, alongwith advantages and disadvantag-es. For a more detailed discus-sion, refer to Hewlett-Packardapplication note AN 243.

A simple block diagram of a paral-lel-filter analyzer is shown inFigure 3.5-1. These analyzers haveseveral built-in filters that areusually spaced at 1/3- or 1-octaveintervals. This spacing results inresolution that is proportional tofrequency. For a 1/3-octave ana-lyzer, resolution varies fromaround 5 Hz at low frequencies toseveral thousand Hertz (kHz) athigh frequency. A variation of theparallel-filter analyzer that issometimes used in machinerywork has a bank of filters that canbe individually selected.

Parallel-filter analyzers offer agood compromise between resolu-tion and frequency span whenvery large spans are required suchas in acoustics. They tend to beexpensive and do not have theresolution required for manymachinery analysis applications.

Figure 3.4-4Since the heavyspot on the rotorpasses the trans-ducer 90º afterthe keyway passesthe keyphasor,the imbalancesignal lags thekeyphasor pulseby 90º. Thecorrespond-ing frequencydomain phasespectrum isshown inFigure 3.4-3.

Figure 3.4-5The vibrationresponse of aflexible rotorshifts 180º inphase as rpmpasses through acritical speed.

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Figure 3.5-3DSAs digitallysimulate hun-dreds of parallelfilters, providingboth high speedand excellentfrequency resolu-tion. DSAs alsoprovide time andphase displays notavailable on theother frequencydomain analyzers.

Swept-filter analyzers use atuneable filter, much like a radioreceiver. The block diagram forthis type of analyzer is shown inFigure 3.5-2. The frequency reso-lution of these instruments is onthe order of 1 to 5 Hz – betterthan parallel-filter analyzers butnot good enough for many vibra-tion analysis applications. Theyare much slower than the parallel-filter analyzers as they must ana-lyze each individual frequency oneat a time. The slowness of theoperation not only increases themeasurement time; it makes thetechnique unacceptable for situa-tions where non-steady data ispresent.

DSAs use digital techniques toeffectively synthesize a largenumber of parallel-filters. Thelarge number of filters (typically400 or more) provides excellentresolution, and the fact that theyare parallel means that measure-ments can be made quickly.DSAs also provide time- andphase-spectrum displays, andcan be connected directly to com-puters for automated measure-ment. The DSA essentially usesup FFT to create filters of con-stant-bandwidth resolution; unlikethe parallel filters that tend to beproportional bandwidth. Beingdigital in implementation, someDSAs have the ability to analyzethe data in much the same way asthe parallel analyzers in additionto its normal FFT mode; thus al-lowing addition flexibility. Thisis referred to as digital real-timeoctave analysis.

Figure 3.5-2Swept filteranalyzers providebetter frequencyresolution thanparallel filteranalyzers, butare too slow formachineryanalysis.

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Converting a vibration spectrumto a detailed report on machine vi-bration is another challenging as-pect of vibration analysis. Chapter4 and 5 are a starting point, pro-viding a basis for building yourskills through experience.

4.1 Imbalance

Rotor imbalance exists to somedegree in all machines, and ischaracterized by sinusoidal vibra-tion at a frequency of once perrevolution. In the absence of highresolution analysis equipment, im-balance is usually first to get theblame for excessive once per rev-olution vibration – vibration thatcan be caused by several differentfaults. In this section, we will dis-cuss spectral characteristics thatcan be used to differentiate thesefaults from imbalance, eliminatingunnecessary balancing jobs.

Phase plays a key role in detectingand analyzing imbalance, and it isimportant to remember the phaseshifts associated with flexible ro-tors (see Figure 3.4-5). A state of

imbalance occurs when the centerof mass of a rotating system doesnot coincide with the center of ro-tation. It can be caused by a num-ber of things, including incorrectassembly, material build-up/loss,and rotor sag. As shown in Figure4.1-1, the imbalance can be in asingle plane (static imbalance) ormultiple planes (coupled imbal-ance). The combination is refer-red to as dynamic imbalance. Ineither case, the result is a vectorthat rotates with the shaft, pro-ducing the classic once per revo-lution vibration characteristic.

Distinguishing Characteristics

of Imbalance

The key characteristics of vibra-tion caused by imbalance are:

(1) it is sinusoidal at a frequencyof once per revolution (1x),

(2) it is a rotating vector, and

(3) amplitude increases withspeed (i.e. F=mw2). These charac-teristics are very useful in differ-entiating imbalance from faultsthat produce similar vibration.

Figure 4.1-1Imbalance,whether staticor coupled,results in aspectral peakat a frequencyof once perrevolution (1 x).

Chapter 4

Vibration Characteristics of

Common Machinery Faults

In the last chapter, we saw how acomplicated time domain vibra-tion signal can be reduced to sim-ple spectral components using thefrequency domain. In Chapters 4and 5, we will take the next stepin analysis – correlating thesecomponents with specific ma-chine characteristics or faults.This chapter provides the basictheory, while Chapter 5 addressessome of the common analysisproblems and techniques.

Each machine defect produces aunique set of vibration compo-nents that can be used for identifi-cation. This chapter describesthese vibration patterns or “signa-tures” for the most commonmachinery defects. Where appro-priate, frequency calculation for-mulas and details of spectrumgeneration are also included. Thedescriptions will give you the ba-sic information needed to corre-late vibration components withdefects; the details provide in-sights that will improve your abili-ty to analyze unusual situations.

The table in Section 4.10 summa-rizes the vibration pattern descrip-tions of Chapter 4. It is importantto understand, however, that cor-relation is rarely as easy as match-ing vibration components on aDSA display with those in a table.Machinery dynamics, operatingconditions (e.g. load and tempera-ture), multiple faults, and speedvariation all affect vibration, com-plicating the correlation process.Methods of dealing with theseproblems are the subject ofChapter 5.

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Figure 4.1-2The rotating natureof the imbalance forceresults in a phasereading (relative toa key phasor) thatfollows transducerlocation. This is use-ful in differentiatingimbalance from faultswhich produce direc-tional vibration.

The driving force in imbalance isthe centrifugal forces caused by amass rotating about a centerpoint; as such, the vibrationcaused by pure imbalance is aonce-per-revolution sine wave,sometimes accompanied by low-level harmonics. The faults com-monly mistaken for imbalanceusually produce high-level har-monics, or occur at a higher fre-quency. In general, if the signalhas high harmonics above onceper revolution, the fault is not asimple imbalance. However, high-level harmonics can occur withlarge imbalance forces, or whenhorizontal and vertical supportstiffnesses differ by a largeamount (see Section 4.4).

Because the imbalance force is arotating vector, the phase of vibra-tion relative to a keyphasor fol-lows transducer location, whilethe amplitude changes are gener-ally small. As shown in Figure4.1-2, moving the transducer 90°results in a 90° change in phasereading with approximately thesame amplitude1. It is also com-mon for the stiffness to varyto some extent from verticalto horizontal; this can undersome circumstances cause widevariations in phase readings withflexible rotors.

4.2 Rolling-ElementBearings

Rolling-element (anti-friction)bearings are the most commoncause of small machinery failure,and overall vibration level chang-es are virtually undetectable inthe early stages of deterioration.However, the unique vibrationcharacteristics of rolling elementbearing defects make vibrationanalysis an effective tool for bothearly detection and analysis offaults.

The specific frequencies that re-sult from bearing defects dependon the defect, the bearing geome-try, and the speed of rotation. Therequired bearing dimensions areshown in Figure 4.2-1, and areusually available from the bearingmanufacturer. Included in thissection is an HP Instrument Basic2

program that computes the ex-pected frequencies given bearingparameters and rotation speed.One caution: parameters of the

same model-number bearing canchange with manufacturer.

The major problem in detectingthe early stages of failure in roll-ing-element bearings is that theresulting vibration is very low inlevel and often masked by higherlevel vibration. If monitoring isperformed with a simple vibrationmeter (or in the time domain),these low levels will not be de-tected and unpredicted failuresare inevitable (see Figure 3.2-3).The advantage of a DSA is thatwith the high resolution and dy-namic range available, vibrationcomponents as small as 1/1000ththe amplitude of higher levelvibrations can be measured anddetected.

Interestingly, some early indica-tions of a bearing failure can laterbe obliterated in the later stagesas the failure develops. For exam-ple, often in the early stages offailure a very succinct vibration

1 The amplitudes obtained from these tworeadings can vary with support stiffnessand running speed. With flexible rotors,small speed variations between the twomeasurements will result in a phase rela-tion very different from the one pictured.

2 Instrument Basic is an HP implementationof the Basic programming language thatruns resident in many DSA analyzers.

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Figure 4.2-1Using the parametersshown, the basicfrequencies resultingfrom rolling elementbearing defects canbe completed.

Table 4.2BearingCharacteristicFrequencies.

Figure 4.2-2The I-BASIC programto compute bearingcharacteristic frequen-cies. The specific unitused in lines 230 and240 is not critical, aslong as it is the samefor both.

component will be present. As thefailure develops, the overall ener-gy of the fault will increase, butoften become more broad band innature and difficult to detect inthe presence of the other vibrationcomponents of the machine (Fig4.2-3). This appearance of “heal-ing” can be misleading. Theexample also illustrates a charac-teristic of frequency-spectrumanalysis: it’s usually easier to de-tect a distinct low-level narrow-band tone than a wide-band signalof high levels in the presence ofother signals or noise.

Frequencies Generated by

Rolling-Element Bearing

Defects

Formulas for calculating the fre-quencies resulting from bearingdefects are given in Table 4.2. Theformulas assume a single defect,rolling contact, and a rotating in-ner race with fixed outer race.The results can be expressed inorders of rotation by leaving outthe (RPM/60) term. The I-Basicprogram listing in Figure 4.2-2 willcompute the bearing frequenciesautomatically.

If bearing dimensions are notavailable, inner- and outer-racedefect frequencies can be approxi-mated as 60% and 40% of the num-ber of balls multiplied by therunning speed, respectively. Thisapproximation is possible becausethe ratio of ball diameter to pitchdiameter is relatively constant forrolling-element bearings.

While it isn’t necessary to under-stand the derivation of these for-mulas, two points of explanationmay give you a better feel forthem. (1) Since the balls contactboth the shaft-speed inner raceand the fixed speed outer race,the rate of rotation relative to theshaft center is the average, or 1/2

30

the shaft speed. This is the reasonfor the factor of 1/2 in the formu-las. (2) The term in parentheses isan adjustment for the diameter ofthe component in question. Forexample, a ball passes over de-fects on the inner race more oftenthat those on the outer race, be-cause the linear distance is short-er. Vibration components at thefundamental-train frequency,which occurs at a frequency lowerthat running speed, is usuallycaused by a severely worn cage.

Rolling-element bearing frequen-cies are transmitted well to themachine case (because the bear-ings are stiff), and are best mea-sured with accelerometers. Forbearings which provide axial sup-port, axial measurements oftenprovide the best sensitivity to de-fect vibration (because machinesare usually more flexible in thisdirection).

Example Spectra

The example spectrum of Figure4.2-4 is the result of a defect inthe outer race. A printout of thebearing data and characteristicfrequencies, computed with theprogram given in Figure 4.2-2, ap-pears below the spectrum. Notethe sidebands at running speedwhich are characteristic of mostbeginning spectra.

The spectrum in Figure 4.2-5 isalso the result of a defect in theouter race. In this case, the char-acteristic ball-pass frequency hasdisappeared, but its harmonicsremain. The component around200 Hz is the gearmesh vibration.

Some Details of

Spectrum Generation

To give you better insight intohow bearing spectra are generat-ed, we’ll take a look at some sim-ulated bearing signals and their

resulting spectra. The characteris-tics we will focus on are:

(1) the impulsive nature of bear-ing vibration (which produceshigh frequency components),

(2) the effect of multiple defects,and

(3) modulation of the bearingcharacteristic frequencies byrunning speed.

In contrast to the sinusoidal vibra-tion produced by imbalance,vibration produced by bearingdefects is impulsive, with muchsharper edges. The effect of thesesharp edges is a large number ofhigher frequency harmonics.In Figure 4.2-6, the lower trace isa time display of a simulateddefect and the upper trace is thecorresponding frequency spec-trum. The defects are spaced at10 ms intervals, resulting in a har-monic spacing of 100 Hz (1/10 ms)in the frequency spectrum.

Factors That Modify FrequencyFactors That Modify FrequencyFactors That Modify FrequencyFactors That Modify FrequencyFactors That Modify FrequencyCharacteristicsCharacteristicsCharacteristicsCharacteristicsCharacteristics

While the computation of characteristicbearing frequencies is straightforward,several factors can modify the vibrationspectrum that results from bearingdefects.

A. Bearing frequencies are usuallymodulated by residual imbalance, whichwill produce sidebands at runningfrequency (see Figure 4.2-9). Othervibration can also modulate (or bemodulated by) bearing frequencies, andbearing spectra often contain componentsthat are sums or differences of thesefrequencies (see Section 5.3).

B. As bearing wear continues and defectsappear around the entire surface of therace, the vibration will become much morelike random noise, and discrete spectralpeaks will be reduced, or disappear. Thiswill also be the case with roughnesscaused by abrasive wear or lack oflubrication. Another variation that occursin advanced stages is concentration of thedefect energy in higher harmonics of thebearing characteristic frequency (seeFigure 4.2-6).

C. Some of these frequencies will appearin the vibration spectrum of a goodbearing. This is usually due to productiontolerances, and does not imply incipientfailure.

D. To modify the formulas for a stationaryshaft and rotating outer race, change thesigns in equations (1) and (2) of table 4.2.

E. Contact angle can change with axialload, causing small deviations fromcalculated frequencies.

F. Small defects in stationary races whichare out of the load zone will often onlyproduce noticeable vibration when loadedby imbalance forces (ie. once perrevolution).

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Figure 4.2-6The impulsivenature of bear-ing defects pro-duces a largenumber ofharmonicsspaced at thecharacteristicfrequency.

Figure 4.2-3As bearing defectsprogress, the vib-ration becomesmore like randomnoise, and spec-tral peaks tendto disappear.

Figure 4.2-4HP InstrumentBasic print out ofbearing data andcharacteristicfrequencies withcorrespondingspectra. Theresult of a singledefect on outerrace is evident.

Figure 4.2-5In this exampleof an outer racedefect, the com-ponent at the ballpass (outer race)frequency hasdisappeared, butits harmonicsremain. This ischaracteristic ofadvanced stagesof a defect.

Two important consequences of the highTwo important consequences of the highTwo important consequences of the highTwo important consequences of the highTwo important consequences of the highfrequency content are:frequency content are:frequency content are:frequency content are:frequency content are:

A. High-frequency resonances in thebearing and machine structure may beexcited, resulting in non-order relatedcomponents not produced by other defects(except gears). One type of vibration meterdesigned for early detection of bearingdefects de-pends on these highfrequencies (20-50 kHz) to excite thenatural frequency of a specialaccelerometer. (With no excitingfrequency in this range, the output ofthe transducer is very low.) This typeof instrument can pro-duce misleadingresults if the accelerometer is notcarefully mounted or if the defect issuch that little high frequency energyis produced.

B. High-frequency content tends toindicate the seriousness of the flaw,since shallow defects will tend to bemore sinusoidal, producing fewerhigh-frequency defects.

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Every machine has some residualimbalance which will amplitudemodulate the bearing frequencies.In Figure 4.2-8, a bearing defectpulse is being modulated by im-balance. The imbalance compo-nent appears at the 21 Hz runningspeed, and as sidebands aroundthe bearing frequency harmonics.This type of spectrum is commonwith bearing defects. Note thatother defects, such as loosenessor misalignment, will also modu-late the bearing frequencies.

4.3 Oil Whirl inFluid-Film Bearings

Rotors supported by fluid-filmbearings are subject to instabili-ties not experienced with rollingelement bearings. When the insta-bility occurs in a flexible rotorat a critical speed, the resultingvibration can be catastrophic.Several mechanisms exist for pro-ducing instabilities, includinghysteresis, trapped fluid, and shaftvibration interacting with bear-ings. In this section we willdiscuss only fluid-bearing instabil-ities, which are the most common.

Figure 4.2-7Two simulatedexamples ofmultiple defects.Note that theharmonic spacingremains at thecharacteristicfrequency.

Figure 4.2-8Bearing frequen-cies are almostalways modulatedby residual imbal-ance at runningspeed.

Multiple Defects and Running

Speed Sidebands

The characteristic spectrum ofmultiple bearing defects is diffi-cult to predict, depending heavilyon the nature of the defects,Figures 4.2-7(a) and (b) show twosimulated multiple defects andtheir resulting spectra. Note thatas long as the sequence repeatsitself at the appropriate character-istic frequency, the spacing of theharmonics will be at that frequen-cy. in this case, only the harmonicamplitudes will change.

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twice critical speed. At this speed,the whirl (which is approximately1/2 running speed) will be at thecritical speed, resulting in a largevibration response that the fluidfilm may no longer be able to sup-port. The spectral map displayof Figure 4.3-2 illustrates how oilwhirl becomes unstable oil whipwhen shaft speed reaches twicecritical and the oil whirl coincideswith a rotor-natural frequency.Whirl must be suppressed if themachine is to be run at greaterthan twice the critical speed.

Changes in oil viscosity or pres-sure, and external preloads areamong the conditions that canlead to a reduction in the abilityof the fluid to support the shaft.In some cases, the speed of themachine can be reduced to elimi-nate instability until a permanentremedy can be found. Stabilitysometimes involves a delicate bal-ance of conditions, and changesin the operating environment mayrequire a bearing redesign (e.g.with tilting pad or pressure damdesigns). Whirl may also causeinstability when the shaft reaches

A basic difference exists betweenvibration due to instability, andvibration due to other faults suchas imbalance. Consider the caseof a shaft imbalance. Vibration ofthe shaft is a forced response tothe imbalance force, occurs at thesame frequency, and is propor-tional to the size of the force.Instability, on the other hand, is aself-excited vibration that drawsenergy into vibratory motion thatis relatively independent of therotational frequency. The differ-ence is subtle, but has a profoundeffect on measures taken toaddress the problem.

Oil Whirl and Whip

Deviation from normal operatingconditions (attitude angle andeccentricity ratio) are the mostcommon cause of instability influid-film bearing supportedrotors. As shown in Figure 4.3-1,the rotor is supported by a thinfilm of oil. The entrained fluidcirculates at about 1/2 the speedof the rotor (the average of shaftand housing speeds). Because ofviscous losses in the fluid, thepressure ahead of the point ofminimum clearance is lower thanbehind it. This pressure differen-tial causes a tangential destabiliz-ing force in the direction of therotation that results in a whirl – orprecession – of the rotor at slight-ly less than 1/2 rotational speed(usually 0.43 - 0.48).

Whirl is inherently unstable,since it increases centrifugal forc-es which in turn increase whirlforces. Stability is normally main-tained through damping in therotor-bearing system. The systemwill become unstable when thefluid can no longer support theshaft, or when the whirl frequencycoincides with a shaft-naturalfrequency.

Figure 4.3-2A spectral mapshowing oilwhirl becomingoil whip insta-bility as shaftspeed reachestwice critical.

Figure 4.3-1A pressuredifferentialin fluid-filmbearings pro-duces a tan-gential forcethat resultsin whirl.

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Vibration due to misalignmentoften also contains a large numberof harmonics, much like thecharacteristic spectra of loose-ness and excessive clearance. Thekey distinguishing feature is ahigh 2x component, especially inthe axial direction.

Using Phase to Detect

Misalignment

As shown in Figure 4.4-2, theaxial vibration at each end of themachine (or across the coupling)is 180º out of phase. This relation-ship can be used to differentiatemisalignment from imbalance,which produces in-phase axialvibration. This test cannot be usedin the radial direction, sinceimbalance phase varies with thetype of imbalance. Relative phasecan be measured with a single-channel DSA using a keyphaserreference, or directly with a dual-channel DSA (see Section 6.8).

4.4 Misalignment

Vibration due to misalignment isusually characterized by a 2xrunning speed component andhigh axial vibration levels. Whena misaligned shaft is supported byrolling-element bearing, thesecharacteristic frequencies mayalso appear. Phase, both end toend on the machine and acrossthe coupling, is a useful tool fordifferentiating misalignment fromimbalance.

Misalignment takes two basicforms: (1) preload from a bentshaft or improperly seated bear-ing, (2) offset of the shaft centerlines of machines in the sametrain and (3) angular misalign-ment. Flexible couplings increasethe ability of the train to toleratemisalignment; however, they arenot a cure for serious alignmentproblems. The axial component ofthe force due to misalignmentis shown in Figure 4.4-2. Machinesare often more flexible in the axialdirection, with the result that highlevels of axial vibration usuallyaccompany misalignment. Thehigh axial levels are a key indica-tor of misalignment.

High second harmonic vibrationlevels are also a common resultof misalignment. The ratio of 1xto 2x component levels can beused as an indicator of severity.Second harmonics are caused bystiffness asymmetry in the ma-chine and its supports, or in thecoupling. This asymmetry causesa sinusiodal variation in responselevel – a form of rotating imped-ance vector. The vibration thatresults from the rotating forceand impedance vectors containsa component at twice therotating frequency, as shownin Figure 4.4-1.

Figure 4.4-1Alignmentproblems areusually char-acterized bya large 2 xrunning speedcomponent, anda high level ofaxial vibration.

Several notes of caution relative to phaseSeveral notes of caution relative to phaseSeveral notes of caution relative to phaseSeveral notes of caution relative to phaseSeveral notes of caution relative to phasemeasurements are appropriate at thismeasurements are appropriate at thismeasurements are appropriate at thismeasurements are appropriate at thismeasurements are appropriate at thispoint:point:point:point:point:

A. Machine dynamics will affect phaseread-ings, so that the axial phaserelationship may be 150° or 200° ratherthan precisely 180°.

B. Transducer orientation is important.stages of gear defects are often difficultto analyze. Transducers mounted axially tothe outside of the machine will most oftenbe oriented in opposite directions. If this isthe case, a 180° phase relationship will bemeasured as 0°.

C. Great care must be exercised whenmeas-uring relative phase with a single-channel DSA. Two measurements arerequired, each referenced to the shaftwith a keyphasor (or similar reference).These measurements should be made atthe same speed. In gen-eral, you shouldmake more than one meas-urement ateach point to insure that phase readingsare repeatable.

Figure 4.4-2A bent or mis-aligned shaftresults in ahigh level ofaxial vibration.

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4.5 Mechancial Looseness

Mechanical looseness usuallyinvolves mounts or bearing caps,and almost always results in alarge number of harmonics in thevibration spectrum. Componentsat integer fractions of runningspeed may also occur. Loosenesstends to produce vibration thatis directional, a characteristic thatis useful in differentiating loose-ness from rotational defects suchas imbalance. A technique thatworks well for detecting andanalyzing looseness, is to makevibration measurements at severalpoints on the machine. Measuredvibration level will be highest inthe direction and vicinity of thelooseness. Also measuring vibra-tion level on a bolt and comparingthe level measured on the housingcan pinpoint where to shim andtorque.

The harmonics that characterizelooseness are a result of impulsesand distortion (limiting) in themachine response. Also, measur-ing vibration level on a bolt andcomparing the level measuredon the housing can pinpoint whereto shim and troque. Consider thebearing shell in Figure 4.5. Whenit is tight, the response to imbal-ance at the transducer is sinusoi-dally varying. When the mountingbolt is loose, there will be trunca-tions when the looseness is taken

belt and the resulting vibration islargely once per revolution. Thedirectionality that usually accom-panies looseness results in vibra-tion levels that vary significantlywith transducer direction. In otherwords, while imbalance responseis usually about the same in hori-zontal and vertical directions,looseness in a mount that produc-es a large vertical component mayproduce a much smaller horizon-tal component.

up. While these waveforms areidealized, the mechanism forproducing harmonics should beclear. The general term fordeviation from expected behavior,as when the sinusoidal vibrationis interrupted by a mechanicallimit, is non-linearity.

Belt drives present one situationwhere looseness does not result ina large number of harmonics. Inthis case, the impacts and sharptruncations are damped by the

Figure 4.5Looseness usuallyresults in a trun-cated waveformthat produces aspectrum with alarge number ofboth odd and evenharmonics.

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Figure 4.6-1The character-istic spectrumof a gearset ingood conditioncontains com-ponents due torunning speedof both shafts,and gear-mesh-ing frequency.

4.6 Gears

Gear problems are characterizedby vibration spectra that aretypically easy to recognize, butdifficult to interpret. The difficultyis due to two factors: (1) it isoften difficult to mount thetransducer close to the problem,and (2), the number of vibrationsources in a muilti-gear driveresult in a complex assortmentof gear mesh, modulation, andrunning frequencies. Because ofthe complex array of componentsthat must be identified, the highresolution provided by a DSA is avirtual necessity. It is helpful todetect problems early throughregular monitoring, since theadvanced stages of gear defectsare often difficult to analyze.Baseline vibration spectra arehelpful in analysis because high-level components are commoneven in new gear boxes. Baselinespectra taken when the gearboxis in good condition make it easierto identify new components,or components that changesignificantly in level.

Characteristic Gear

Frequencies

A. Gear Mesh: This is the frequen-cy most commonly associatedwith gears, and is equal to thenumber of teeth multiplied by therotational frequency. Figure 4.6-2is a simulated vibration spectrumof a gearbox with a 15-toothgear running at 3000 rpm (50 Hz).The gear-mesh frequency is 15 x15 = 750 Hz. This component willappear in the vibration spectrumwhether the gear is bad or not.Low-level-running-speed side-bands around the gearmeshfrequency are also common.These are usually caused bysmall amounts of eccentricity orbacklash.

The amplitude of the gearmeshcomponent can change signifi-cantly with operating conditions,implying that gearmesh level isnot a reliable indication of condi-tion. On the other hand, high-levelsidebands or large amounts ofenergy under the gearmesh orgear-natural-frequency compo-nents (Figure 4.6-2), are a goodindication that a problem exits.

B. Natural Frequencies: The im-pulse that results from large geardefects usually excites the naturalfrequencies of one or more gearsin a set. Often this is the key indi-cation of a fault, since the ampli-tude of the gearmesh frequencydoes not always change. In thesimulated vibration spectrumof Figure 4.6-2, the gearmeshfrequency is 1272 Hz. The broad-band response around 600 Hz iscentered on a gear-natural fre-quency, with sidebands at therunning speed of the bad gear.The high-resolution-zoomed spec-trum of 4.6-2(b) shows this detail.

C. Sidebands: Frequencies gener-ated in a gearbox can be modulat-ed by backlash, eccentricity,loading, bottoming, and pulsesproduced by defects. The side-bands produced are often valuablein determining which gear is bad.In the spectrum of Figure 4.6-2(b),for example, the sidebandsaround the natural frequencyindicate that the bad gear has arunning speed of 12.5 Hz. In thecase of eccentricity, the gearmeshfrequency will usually havesidebands at running speed.

Hints On Gear AnalysisHints On Gear AnalysisHints On Gear AnalysisHints On Gear AnalysisHints On Gear AnalysisA. Select And Mount TransducersCarefully. If gearmesh or naturalfrequencies above 2000 Hz are expected,use an accelerometer. Mounting should bein the radial direction for spur gears, axialfor gears that take a thrust load, and asclose to the bearings as possible.B. Determine Natural Frequencies. Sincerecognition of natural frequencies is soimportant for analysis, take every oppor-tunity to determine what they are. Thiscan be done by impacting the shaft of theas-sembled gearbox, and measuring thevibration response of the housing. Thismeasurement should be done with a two-channel DSA for best results (Section 6.8),but a single-channel measurement willgive you an idea of the frequencies toexpect.C. Identify Frequencies. Take the time todiagram the gearbox, and identify gear-mesh and shaft speed frequencies. Even ifyou don’t know the natural frequencies,shaft speed sidebands will often indicatethe bad gear.

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Figure 4.6-2Gear natural fre-quencies, excitedby impulses fromlarge defects, areoften the onlyindication ofproblems. Thezoom spectrumin (b) shows thenatural frequency,with sidebandsthat correspondto running speedof the bad gear.

Figure 4.7A space in thevibration sig-nal caused bya missing bladeresults in alarge numberof harmonics.A missingblade usuallyalso causesenough im-balance tosignificantlyincrease the1 x level.

4.7 Blades and Vanes

Problems with blades and vanesare usually characterized by highfundamental vibration or a largenumber of harmonics near theblade or vane passing frequency.Some components of passingfrequency (number of bladesor vanes x speed) are alwayspresent, and levels can vary mark-edly with load. This is especiallytrue for high speed machinery,and makes the recording of oper-ating parameters critical. It is veryhelpful in the analysis stage tohave baseline spectra for severaloperating levels.

If a blade or vane is missing, theresult will typically be imbalance,resulting in high 1x vibration. Formore subtle problems such ascracked blades, changes in thevibration are both difficult todetect and difficult to quantify.Detection is a problem, especiallyin high- speed machinery, becauseblade vibration can’t be measureddirectly. Strain gauges can beused, but the signal must be eithertele-metered or transferredthrough slip rings. Indirect detec-tion produces a spectrum thatis the result of complex interac-tions that may be difficult toexplain. This, combined withthe large variation of levelswith load, make spectra difficultto interpret quantitatively.

One characteristic that oftenappears in missing- or cracked-blade spectra is a large number ofharmonics around the blade pass-ing frequency. Figure 4.7 showshow a space in the vibration sig-nal greatly increases the numberof harmonics without changingthe fundamental frequency.

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4.8 Resonance

Problems with resonance occurwhen natural frequencies of theshaft, machine housing, or attach-ed structures are excited byrunning speed (or harmonics ofrunning speed). These problemsare usually easy to identifybecause levels drop appreciablywhen running speed is raisedor lowered. Spectral maps areespecially useful for detectingresonance vibration because thestrong dependence on rotationalspeed is readily apparent (seeFigure 4.8). Phase is also a usefultool for differentiating resonancesfrom rotationally related compo-nents. Say, for example, that youencounter a high level of vibrationat 16-times running speed. If thevibration is rotationally related(e.g. a blade passing frequency),the phase relative to a keyphasorsignal or residual imbalance willbe constant. If the vibration is a

resonance, the phase will not beconstant. This is a useful tech-nique when it is not practical tovary the speed of the machine.

Piping is one of the most commonsources of resonance problems.When running speed coincideswith a natural frequency of thepipe, the resulting vibration willbe excessive, and strain on boththe pipe and the machine can leadto early failure. The most logicalapproach is to change the naturalfrequency of the pipe. It can beraised by making the pipe shorteror stiffer (e.g. by adding a sup-port), or lowered by making thepipe longer (see Figure 2.1-9). Thesame rules apply to any attachedstructure. Structural analysis ofthe structure by measuing operat-ing mode shapes is useful indetermining optimal positioningof supports and braces.

Shaft resonance problems in high-speed machinery are sometimescaused by changes in the stiffnessprovided by fluid-film bearings,load changes, or by the effectsof machines added to the train.Bearing wear, for example, canreduce the stiffness of the shaft/bearing system, and lower the res-onant frequency to running speedmultiples. Coupling changes canraise or lower torsional naturalfrequencies to running speed. Thedynamics of these situations canbe quite complex, and are beyondthe scope of this note. Hewlett-Packard application note AN 243-3deals with the topic of measuringthe resonance and structural prop-erties of machines in some detail.The key is to understand thatmaintenance and installation re-lated factors can alter assump-tions made in the rotor design.

Figure 4.8Spectral Maps areespecially usefulfor analyzing vi-bration due toresonances.

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4.9 Electric Motors

Excessive vibration in electricmotors can be caused by eithermechanical, or electromagneticdefects. The latter can oftenbe isolated by removing power:vibration caused by electrical ormagnetic defects will disappear.The high frequency resolutionof DSAs is key for analyzingelectrical problems in inductionmotors, since running speed andpower-line related componentsare often very closely spaced (seeSection 6.3 on resolution).

Vibration caused by electricalproblems in induction motors canbe analyzed to determine thenature of the defect. In general, astationary defect such as a short-ed stator produces a 2 x powerlinefrequency component. A rotatingdefect, such as a broken rotor bar,produces 1 x running speed with2 x slip frequency sidebands. (Slipfrequency = line synchronousfrequency – running frequency).

The vibration spectrum of induc-tion motors always containssignificant components at power-line frequency times the numberof poles. A great deal of researchhas been done on the subject ofrelating the spectrum of the elec-tric supply current to specificproblems. A number of commer-cially available software productswhich can readily identify elec-tric-motor faults from frequencyspectra of the current taken witha DSA and a current probe.

Table 4.10-1Phase Characteristics ofCommon Vibration Sources

SourceSourceSourceSourceSource Characteristics*Characteristics*Characteristics*Characteristics*Characteristics*Rolling element Unstablebearing defectElectrical Unstable unless synchronous motorGear mesh UnstableImbalance Stable unless caused by uneven loading or cavitation.

Phase follows transducer location (4.1)Looseness Unstable; may be highly directionalMisalignment Stable; relation between axial phase at shaft

ends should be approximately 180°Oil whirl UnstableResonance Unstable; large phase change with change in

speed in rpm.

4.10 Summary Tables

Tables 4.10-1 (below) and 4.10-2(next page) summarize the vibra-tion characteristics informationin this chapter. This informationshould be used as a guide only,since the vibration resulting fromspecific defects can be modifiedby machinery dynamics.

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FrequencyFrequencyFrequencyFrequencyFrequency Possible CausePossible CausePossible CausePossible CausePossible Cause CommentsCommentsCommentsCommentsComments1 x rpm Imbalance Steady phase that follows transducer. Can

be caused by load variation, materialbuildup, or pump cavitation.

Misalignment or Bent Shaft High axial levels, ~180° axial phaserelation at the shaft ends. Usuallycharacterized by high 2x level.

Strain Caused by casing or foundation distortion,or from attached structures (e.g. piping).

Looseness Directional – changes with transducerlocation. Usually high harmonic content andrandom phase.

Resonance Drops off sharply with changes in speed.From attached structures or changes inattitude angle or eccentricity ratio.

Electrical Broken rotor bar in induction motor. 2x slipfrequencies sidebands often produced.

2 x rpm Misalignment or Bent Shaft High levels of axial vibration.Harmonics Looseness Impulsive or truncated time waveform;

large number of harmonics.Rubs Shaft contacting machine housing.

Sub-rpm Oil whirl Typically 0.43 - 0.48 rpm; unstable phaseBearing cage See formula in Table 4-2.2

N x rpm Rolling element bearings See formulas in Table 4-2.2 Usuallymodulated by running speed.

Gears Gearmesh (teeth x rpm); usually modulatedby running speed of bad gear.

Belts Belt x running speed and x 2 running.Blades/Vanes Number of blades/vanes x rpm; usually

present in normal machine. Harmonicsusually indicate that a problem exists.

N x powerline Electrical Shorted stator; broken or eccentric rotor.Resonance Several sources, including shaft, casing,

foundation and attached structrues.Frequency is proportional to stiffness andinversly proportional to mass.

Table 4.10-2Vibration FrequenciesRelated To MachineryFaults