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).

31

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.

33

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.

36

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.

37

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.

38

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.

39

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.

40

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

41

Chapter 5

Advanced Analysis

and Documentation

Chapter Overview

5. Advanced Analysis and DocumentationChapters 1 through 4 provide the basic information needed for the analysis of machineryvibration. Chapter 5 contains practical information that will help in determining specificdefects, and in assessing their severity.

5.1 Pracitical Aspects of AnalysisA discussion of 5 practical aspects for successful analysis.

5.2 Using Phase for AnalysisWe have discussed the importance of phase in analyzing imbalance and misalignment.This section is an extension of that discussion, and an introduction to the relatedconcept of time averaging.

5.3 Sum and Difference FrequenciesMultiple defects often produce vibration components that are sums and differences ofcharacteristic frequencies.

5.4 Speed NormalizationA common problem when making direct spectral comparisons is shift in frequency ofvibration components caused by changes in running speed. This section discussessolutions to this problem.

5.5 Baseline Data CollectionRecords of vibration spectra taken when a machine is in good condition or of a similarmachine can provide significant insight into the interpretation of machinery vibrationdata. This section presents guidelines for collecting baseline data.

History records include machinefailures, and vibration spectra be-fore and after significant modifi-cations or repairs. These recordsare often in the form of computerdigital data and organized in aninformation data base. Youshould, for example, be able toimmediately identify the changesin the vibration spectrum of a ma-chine that has had a major modifi-cation. This will immediately

give some insight into the rela-tionship between major machin-ery components and the vibrationspectrum.

Engineering data includes bearingand gear parameters used to cal-culate characteristic frequencies,and machine dynamic modelsused to predict vibration responsecharacteristics (or as an alterna-tive, the results of a structuraltest conducted on the machine).

5.1 Practical Aspects ofAnalysis

In the literature and discussionson the subject of machinery vibra-tion analysis, several factors areregularly mentioned as keys tosuccess. In this section, we willdiscuss five of these factors:(1) documentation, (2) machineryknowledge, (3) severity criteria,(4) instrumentation, and (5)analysis personnel. Its importantto note that a clear objective asto the purpose and scope of themeasurements must be estab-lished. As noted in Chapter 1,there are a number of reasons forundertaking a vibration analysisprogram (for example, new ma-chine development, quality im-provement, maximize service life,maintenance program, and fieldbalancing). It is important at theonset of the program to have aclear understanding of the pur-pose of the measurement; whyand how each measurement is tobe used; and a sound basis formaking the measurement.

Documentation

Thorough documentation oftenprovides the information requiredto successfully analyze a vibra-tion problem. Complete docu-mentation includes baselinevibration spectra, machine main-tenance history, and engineeringdata.

The baseline vibration measure-ments made on a machine providea reference for detecting changesor differences which indicateproblems — and for identifyingsignificant components whenproblems do occur. Without thisinformation, you can easily wastetime determining the source ofa vibration component that isperfectly normal and expected.

Figure 5.1-1Complete documentationconsists of baselinevibration spectra,maintenance history,and engineering data.

MaintenanceHistory

MaintenanceHistory

BaselineVibration

EngineeringSpecifications

42

Vibration Severity Support ClassificationIn./sec. mm/sec Hard Supports Soft Supports.017 .045 good good.028 .071.044 1.12.071 1.8 satisfactory.11 2.8 satisfactory.18 4.5 unsatisfactory.28 7.1 unsatisfactory.44 11.2 impermissible.71 18.0 impermissible1.10 28.02.80 71.0

Also useful are manufacturer’sdata on vibration limits and char-acteristics. This data will notalways be easy to obtain — thekey is to collect the available databefore hand so it is available forcorrelation with measured vibra-tion data.

Computers have become anindispensable tool in organizingrecords and data. A number ofsoftware suppliers offer productsthat organize vibration data,analyze trends (Fig 5.1-1), andprovide detailed correlation ofspectra with known characteristicfrequencies. In some cases suchas ball bearings, they even pro-vide a data base of characteristicfrequencies by product number.

Machinery Knowledge

The design and operating charac-teristics of a machine determineboth the type of defects that arepossible, and the vibration re-sponse to those defects. Vibra-tion analysis is difficult without aworking knowledge of these char-acteristics. Another importantconsideration is the effect ofchanges in operating conditionon measured vibration. By under-standing how vibration changeswith such variables as load andtemperature, you will be betterable to determine whether an in-creased level of vibration is dueto a defect, or to a change inoperating conditions.

The best sources of informationon these characteristics are themanufacturer of the machine, andhistorical records on the same orsimilar machines. In applicationssuch as machinery maintenance,courses from manufacturers canprovide insight into both the pos-sible defects, and the mechanismsof vibration response for specific

severity of the vibration level(amplitude) often arises. Ma-chines will inevitably vibrate andwill also undoubtedly producespectral components at character-istic frequencies given the resolu-tion and sensitivity of modernDSAs. The issue then becomes —what is an acceptable level? It isdifficult to generalize here but anumber of sources are useful.

machines. Several baseline spec-tra taken under different operat-ing conditions are useful fordocumenting the effects of chang-ing operating parameters.

Severity Criteria

Once a vibration spectra is mea-sured and its individual compo-nents identified and correlated,the problem of interpreting the

Figure 5.1-1An example of a"trend analysis"simplified fromvibration spectrumdata over a periodof weeks/monthsby post-testmachineryanalysis software.

Figure 5.1-2Tables of vibra-tion severity,like this onepublished by theISO,* are mostuseful as guide-lines rather thanabsolute limits.

* This material is reproduced withpermission from International Organiza-tion for Standardization Standard 3945-1977, Mechanical Vibration of LargeRotating Machines with Speed Rangefrom 10 to 200 rev/s - Measurement andEvalutation of Vibration Severity in Situ,copyrighted by the American NationalStandards Institute, 1430 Broadway, NewYork, NY 10018.

43

References for severity includepublished vibration standards andhistoric vibration measurements.

The table in Figure 5.1-2 is anexample of a published vibrationstandard. This particular stan-dard is from the InternationalStandards Organization (ISO).To make the standard moreapplicable to a wide range ofmachines, a distinction is made inthe severity criteria between softand hard supports. The essentialproblem with such publishedstandards is that they are toogeneral to allow us to make highaccuracy judgements with thepower and accuracy availablewith modern DSAs. They wereoriginally devised as a tool for in-terpreting severity on the basis ofoverall level measurements. Mod-ern analyzers can identify compo-nents of the vibration whichcontribute negligibly to the over-all spectral energy, but may beindicative of very important localphenomena.

A number of techniques havebeen developed for refining themethod of defining the severitycritera for frequency bands in thevibration spectrum. Figure 5.1-3is an example of one techniquethat breaks the spectrum into 6-frequency bands and specifies theallowable severity level for eachband based on the predominantvibration mechanism present ineach particular band.

Historic vibration measurementsare an excellent reference forseverity measurements, becausethey are specific to the machineor type of machine in question. Inthe case of machine developmentor modification the historical dataon a machine or class of machinescan provide a valuable “yard stick”by which to began the evaluation.

While absolute vibration limitsfor a machine may not be known,there is a high probability thatlarge changes in vibration levelindicate something significantwith respect to the operating con-dition of the machine. The pro-cess of monitoring vibration levelfor changes is referred to as,trend analysis. Since the vibra-tion level in a machine is variable,it isn’t always obvious how muchchange is tolerable. The best ap-proach is to analyze the statisticsof variability for each machine,and base change limits on that.An increase in vibration that ex-ceeds two standard deviations isusually a sign of a problem. Inthe absence of this type of analy-sis, you can use a factor of 2 in-crease as an approximate changelimit threshold.

When significant changes are de-tected, vibration level and otherkey operating parameters shouldbe monitored regularly. The rateof change of these parameters isa good indication of the severityof the problem. The existence ofa consistent pattern of change isindicative of a developing prob-lem and/or changing operatingcondition.

Instrumentation

A wide variety of features andcapabilities are available in in-strumentation ranging from trans-ducers to DSAs to applicationssoftware. Chapter 6 addressesmany of the issues in the selec-tion of DSAs but it's important toput the instrumentation require-ments in the context of the indi-vidual task being addressed. Inmany applications particular per-formance issues or features canbe critical to the measurement,while others are convenience fea-tures or totally superfulous.

For example, in predictivemaintenence or troubleshootingapplications portablility and bat-tery operation could outweighconsiderations of dynamic range,

Figure 5.1-3

A specification

of machine severity

criteria by speci-

fying individual

frequency band

criteria.*

* This material is reproduced with permis-sion from reference [8]: Berry, James E.,Proven Method for Specifying SpectralBand Alarm Levels and FrequenciesUsing Today's Predictive MaintenanceSoftware Systems, Technical Associatesof Charlotte, Inc., 1990).

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real-time bandwidth or program-mability. In the case of produc-tion quality testing of automobileengines; automation and measure-ment time will be more importantthan portability. It would be niceto have an instrument, that is por-table, fast, programmable, etc..But these attributes are not easilyattainable, often not necessaryand undoubtedly expensive.

Though expense is frequently thedriving factor; it is important toput cost in its proper prospective,and access the return on invest-ment. A computer and applicablesoftware that automatically re-trieves vibration data and analyz-es trends can quickly pay foritself. Instrumentation with ageneral purpose feature set, highperformance, a convenient-userinterface, often finds itself beingused in many applications not ini-tially envisioned. Programmabili-ty is another cost factor that willdirecly impact use ability. Instru-ments with built in HP InstrumentBasic can greatly reduce mea-surement automation tasks andcan circumvent the need for anexternal computer to controland automate processes. Easyprogrammability will allowless skilled personnel to collectdata and do preliminary levelseverity checks.

People

The quality and effectiveness ofa vibration analysis program ismost often limited by the avail-ability of capable and skilledpersonel. Successful programsare characterized by people whoare properly trained and given achance to develop analysis exper-tise. In some applications it isneither practical nor desirableto train individual operators asvibration analysts. An example

Table 5.2-1Phase Character-istics of CommonVibration Sources

would be a production assemblyperson. In this case the need fortraining can be aleviated to someextent by built-in automationcapability which can make repeti-tive measurements and accessthe results.

Also consider and experiencedconsultant to help setup and es-tablish your maintenance pro-gram. The consultant can helpovercome the extensive expertiserequired early on in the establish-ment of a machine vibration mon-itoring program. With time, moreand more of the task can be takenover by local personnel.

5.2 Using Phase forAnalysis

The usefulness of the phase spec-trum as a means for differentiat-ing between defects with similaramplitude spectra has alreadybeen discussed. We will presenta more general discussion of thesubject in this section. Time av-eraging, a powerful processingtechnique related to phase, willalso be described.

In general, the phase of vibrationcaused by a defect will either bestable or unstable relative to afixed reference (i.e. keyphasor).The nature of this relationship isshown in Table 5.2-1. Figure 5.2-1is a sequence of vibration spectrathat shows phase for imbalance(1x), and running speed harmon-ics, and unstable phase for power-line related components. Also,the relative phase relationshipbetween vibration at differentpoints on a machine can be usedto differentiate between faults —as in the case of misalignmentand imbalance (see Section 4.4).

Instrumentation required forphase measurements is shown inFigure 5.2-2 and 5.2-3. The key-phasor senses shaft rotation andserves as the phase reference.The phase of vibration that is syn-chronous (i.e. an integer multiple)with rotation is constant, whilethat of nonsynchronous vibrationvaries. Relative phase measure-ments can be made sequentially,as long as the same reference (i.e.

Source Characteristics

Rolling element Unstablebearing effect

Electrical Unstable unless synchronous motor

Gear mesh Unstable

Imbalance Stable, unless caused by uneven loadingor cavitation. Phase follows transducerlocation (4.1)

Looseness Unstable , may be highly directional

Misalignment Stable, relation between axial phase atshaft ends should be approximately 180°

Oil Whirl Unstable

Resonance Unstable, large phase change withchange in speed in rpm.

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keyphasor) is used (see Section6.8 on a dual-channel DSA).Running speed should remainconstant between measurementsto minimize the phase effects ofmechanical impedance. Relativephase measurements on flexiblerotors must include consider-ations of shaft dynamics.

The keyphasor, which is often aproximity sensor that detects akeyway or setscrew, provides arelatively good signal for trigger-ing. Because the gap of the prox-imity probe can vary with speed,there can be some error in thephase measurement as the triggerpoint shifts with the gap causingthe actual position on the shaft ofthe trigger point to vary to somedegree. A better trigger is oftenobtainable with an optical sensorand reflective tape or paint.Sometimes an electrical signalsuch as the spark ignition on agasoline engine is used, thoughhere again, there is a propensityfor this to shift under differingoperating conditions (vacuumadvance).

The actual vibration signal isusually not suitable for triggeringeven though there exists someinstrumentation designed forthis purpose. This method relyson the fact that the imbalance(1x) is often the largest compo-nent; however, noise in the spec-trum adds uncertainty to level,and thus trigger timing. If an in-dependent tachometer referenceis not practical, then it may bepossible to use a band-pass orlow pass filter to reduce the levelof noise and higher frequencycomponents in the vibration

signal to provide a more stabletrigger.

When measuring relative phasebetween two ends of a machine, itis important to mount the trans-ducer with the same orientation.When measuring axial vibration,

for example, if both transducersface the machine, they aremounted 180° out of phase.

Thus vibration due to misalign-ment, which you would expect tobe 180° out of phase, will be mea-sured as in phase. It is likewise

Figure 5.2-1A sequence ofvibration spectrawith phase showsconstant phase forimbalance (1 x andharmonics), andunstable phasefor power-linecomponents(60 Hz harmonics).

Figure 5.2-2Instrumentationsetup for phasemeasurementsand time averaging.

Figure 5.2-3Alternate instru-mentation setup forrelative phasemesurements using2 channel DSA.

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important to remember that phaseresponse of a system is related tothe variable measured; that is,displacement and accelerationmeasurements are 180° out ofphase and if the phase betweenthese is being compared, it is nec-essary to take into account anyphase difference between differ-ent types of motion variables.

Time averaging is explained inSection 6.4, and is a powerfultechnique for eliminating nonsyn-chronous components from avibration spectrum. It is mostuseful for reducing the level ofbackground noise, especially vi-bration from other machines. Itmust be used with care, however,since it will reduce the level of allvibration components that arenonsynchronous, including bear-ing and gear frequencies. In theplot of Figure 5.2-4, a time-aver-aged spectrum (dashed line) isoverlaid on a non-averaged spec-trum. The synchronous compo-nents have not changed in level,while the nonsynchronous back-ground noise components aregreatly reduced.

5.3 Sum and DifferenceFrequencies

Vibration spectra often containcomponents that are the resultof interaction between multiplevibration mechanisms. Thesecomponents appear as sum anddifference frequencies of themechanisms involved, and can beuseful as indications of specificproblems, especially in gears andbearings. When the major fre-quency components are closely

spaced, the difference frequencyis often audible. These “beat” fre-quencies are common in rotatingmachinery and are the result of aprocess called “modulation”.

In Figure 5.3-1, the difference be-tween running speed at 144 Hzand the 2nd harmonic of the linefrequency at 120 Hz is 24 Hz.

This component appears at 24 Hzand as sidebands around the har-monics of the rotational speed.

The exact mechanisms whichgenerate sum and difference fre-quencies can be quite complexand a detailed mathematical anal-ysis is beyond the scope of thisnote. However, you can get a feel

Figure 5.2-4Time averagingis effective inreducing the levelof backgroundvibration.

Figure 5.3-1A vibration spectrumwith sum anddifference frequencies.The 24 Hz differencebetween rotationalfrequency and the120 Hz powerlinecomponent appearsboth as a discretesignal, and asside-bands aroundrotational speedharmonics.

Figure 5.3-2The number ofsum and differencecomponents dependson the number ofharmonics in thesignals involved.

1 Phase and frequency modulation arealso present and produce many of thesame sum and difference frequenciesbut their phase relationships differ. Adetailed discussion of this is beyondthe scope of this note.

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for the interactions involved bythinking of them as a form of am-plitude modulation1. In the trigo-nometric identity given below,

cos(f1) * cos(f2) =1/2[cos(f1+f2) + cos(f1-f2)]

it is apparent that the interactionof one frequency with anotherresults in sum and differencefrequencies. If one of the signalscontains a large number of har-monics, then multiple sum anddifference frequencies willappear. This is illustrated inFigure 5.3-2. Phase can be an aidin identifying sum and differencefrequencies, since it will be unsta-ble unless the phase of bothsources is stable.

The most common faults indicat-ed by sum and difference frequen-cies are associated with rollingelement bearings and gears.

A. Rolling element bearings.

Defects in rolling element bear-ings are almost always modulatedby residual imbalance. As thewear progresses, and characteris-tic frequencies are replaced bynoise, these running frequencysidebands may be the only indica-tion of trouble (see Section 4.2).

B. Gears. As pointed out in Sec-tion 4.6, gear defects often appearas gear natural frequencies withsidebands at the running speed ofthe defective gear. These runningspeed sidebands may also appeararound the gearmesh frequency.

Spectral Map and

Waterfall Displays

Waterfalls and spectral maps area useful technique for detectingchanges with time and identifyingspeed related components in avariable-speed machine. Techni-cally, a waterfall differs from amap only in the way in which themap is updated. Waterfalls gener-ally are a continuously updatingdisplay with the newest spectrumappearing at the top of the displayand the oldest scrolling off at thebottom (hence the name water-fall, from the appearance of thedata migrating down the tracelike a waterfall).

Spectral maps on the other handare generally a fixed set of datastarting at a defined time or con-dition (rpm) and ending as somepredetermined time or numberof spectra later. These are some-times referred to as cascade plotsand appear the same once themeasurement has been paused.Many people use the terms inter-changeably causing some confu-sion as to what is meant.

Figure 5.3-3 shows the topologyof this type of three dimensionaldisplay. The third dimension(z-axis) is the number traces, rpmincrements, or time incrementsin the display. This is controlledby the analyzer's trigger- armingcapability which determineswhen a spectrum will be acquiredand displayed. This allows for thevery precise determination ofwhen data will be taken andanalyzed.

Figure 5.3-3The Z axis in a mapor waterfall displaycan be preciselycontrolled by theDSA trigger armingfunction.

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5.4 Speed Normalization

A common problem in machineryvibration analysis is runningspeed variation — both long-termand short-term. Short-term varia-tions in speed make real-timeanalysis difficult. Long-term vari-ations make point-by-point com-parisons between current andbaseline spectra virtually impossi-ble. Synchronous sample control(also known as order tracking)can be used to compensate forboth problems while the measure-ment is in progress.

Traditionally, these systemswhere limited to direct control ofthe analog-to-digital sampler byan external source synchronizedto the machine running speed.Recently however, advances indigital technology have allowedfor the sampling synchronizationto be performed digitally, thusavoiding some of the problemsof the older analog technology.Either scheme seeks to lock thesample rate to the speed of themachine so that speed relatedcomponents appear at a station-ary frequency. This is very usefulin machinery analysis, as was dis-cussed in Chapter 4, since mostmachinery defects are related tosome shaft- rotation frequency.The details of controlling thesample rate and of digital ordertracking are discussed in Section6.7 and Appendix A. A good wayto illustrate the effects of syn-chronous (or external) samplecontrol is with spectral mapsmade in external and normal sam-ple modes, as shown in Figure5.4-1. These maps were madeduring a run-up. Note in thenormal sample-mode map of (a),rotational speed-related compo-nents move to the right as speed

increases, while fixed frequencycomponents (e.g. structural reso-nances and powerline related)move straight up. In the externalsample-control map of (b), rota-tional speed-related componentsmove straight up the map, whilefixed frequency components

move to the left (they are relative-ly lower in frequency as speedincreases).

The main advantage of synchro-nous sample control is that real-time displays of the order relatedspectral components remain fixed

Figure 5.4-1Two spectral mapsof a machine run-upillustrate the effectof external samplerate control.

a)

b)

Figure 5.4-2A "slice marker"function is usedto extract the orderrelated informationfrom the synch-ronously sampledmap display (lower)and and constructsan order track(upper) for the3rd order.

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within the horizontal positionspeed. During individual mea-surements (or especially withaveraging) speed variations donot cause a “smearing” of thefrequency over a range. Anotheradvantage is the extraction of or-der tracks is greatly simplifiedand the accuracy improved. Anorder track is the plot of an indi-vidual order as the rotation speedchanges. Since the frequency ofthese components has been nor-malized to a fixed value, a simplemarker function can be used toextract the order track from themap display (see figure 5.4-2).Frequency can also be normalizedto rotational speed after a mea-surement. In the display of Fig-ure 5.4-3, note that the frequencyaxis and the readout are in termsof orders of rotation (multiplesof running speed), rather than infrequency. This technique simplyamounts to re-scaling the fre-quency axis when the runningspeed is known or can be de-duced, it is not normally usefulwith map/waterfall displays. Thisnormalization does not work inreal time, and resolution is not aconstant percentage of runningspeed (as with synchronous sam-ple control). However, it is usefulwhen no tachometer/keyphasorsignal is readily available.

Short-term speed variation causesa broadening of spectral lines inthe vibration spectrum, as shownin Figure 5.4-4. As speed changesduring the sampling interval forone measurement, the DSA is ef-fectively analyzing several differ-ent spectra. This results in thebroadened spectral componentsof Figure 5.4-4(b).

Figure 5.4-3DSA displayin which thehorizontal(frequency) axisis calibrated inmultiples (orders)of running speed.

a) Constant running speed

b) Changing running speed

Figure 5.4-4Short-term speedvariation resultsin a broadeningof spectralcomponents (b).

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5.5 Baseline DataCollection

Baseline vibration spectra are ref-erence data that represent normalmachine condition, and are essen-tial to effective analysis. In theevent of trouble, they quickly in-dicate the frequency componentsthat have changed. Baseline datais also the basis for trend moni-toring; it is a much more specificindicator of normal vibration thangeneralized vibration severitycharts. To be most useful, theguidelines below should be fol-lowed in collecting baseline data.The key objective of the processis to understand the characteris-tics of the machine.

A. Normalize for Speed.Normalizing the vibration spectrum for speed is required for direct spectrum comparison.Section 5.4 discussed the alternative methods for accomplishing this. Whichever methodis chosen, some provision should be made when taking baseline data.

A spectral map/waterfall of a run-up or coast-down is also useful in dealing withchanges in speed. A spectral map can quickly show how vibration level changes withspeed, and the resonances and other fixed frequencies that are present in the vibrationspectrum.

B. Be CompleteYou can’t take baseline data after the machine has a problem, so it is important to takeall the data you can when it is operating normally. Follow the guidelines in Chapter 2 fortransducer selection and placement. For machines with rolling-element bearings orgears, consider taking high- and low-frequency spectra. The low-frequency spectrum(0-500 Hz) provides good resolution for most analysis, while the high frequency spectrum(0-5 kHz) will provide a baseline for the high frequencies that can indicate problems withbearings and gears.

In addition to vibration data, operating parameters such as oil pressure. temperature,load, bearing and gear parameters should be collected. Also, any information availablefrom the machine manufacturer regarding vibration characteristics and failure mecha-nisms should be included.

Thermal gradient in a machine can cause temporary misalignment; so making severaltemperature readings along the machine may be useful in diagnosing vibration problems.

C. Check Statistical AccuracyThis just means that one measurement may not be representative of normal operation.For example, an adjacent machine may be vibrating excessively when baseline signaturesare taken, or an older machine may already have excessive vibration levels.

The best approach is to take several spectra over time and perform a statistical analysisto yield mean and standard deviation. This results in a representative average level, andalso provides a quantitative basis (e.g. 1 or 2 standard deviations) for determiningwhether a change in level is significant. The accuracy of these statistics can beimproved by updating them with data from regular vibration monitoring data.

D. Document the Effect of Load VibrationThis is not strictly required, but can be invaluable when determining whether a change isdue to a fault, or just a change in load.

E. Update RegularlyBaseline data should be updated after major repairs or changes in operating conditions.

Figure 5.5-1Baseline datashould includefully documentedvibration spectraand engineeringdata, such asbearing and gearparameters, whichcan be invaluablefor analysis.

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Chapter 6

Dynamic Signal Analyzers

Chapter Overview

6.16.16.16.16.1 Types of DSAsDynamic Signal Analyzers are available in a number of different form factors and capabilities.Generally, the “classes” of DSAs can be broken into handheld/portable, benchtop instrumentand computer controlled systems.

6.26.26.26.26.2 Measurement SpeedMachinery vibration is a dynamic phenomenon that can change quickly — so quickly thatslower swept spectrum and some DSAs can completely miss key events. DSAs can capture atypical vibration signal and transform it to the frequency domain within seconds. Anothermethod involves capturing data in a digital form and post- test processing it; thus allowing formuch higher acquisition rates than is possible with on-line processing. Post-test processingalso allows data to be processed and presented in different forms.

6.36.36.36.36.3 Frequency ResolutionClosely spaced machinery vibration signals often must be resolved for accurate analysis.Often industry standards and technical requirements dictate the use of 1/3-octave analysis,especially in the areas of noise control, acoustics and transients.

6.46.46.46.46.4 Dynamic RangeVibration components are often very small relative to vibration from residual imbalance orother machines. The wide dynamic range of DSAs allow them to resolve signals less than1/1000 the level of the background vibration or residual imbalance.

6.56.56.56.56.5 Digital AveragingMachinery vibration signals often contain large amounts of background vibration that canreduce accuracy and obscure small signals. The digital averaging feature of DSAs can beused to reduce both of these effects.

6.66.66.66.66.6 HP-IB and HP I-BASIC1

The Hewlett-Packard Interface Bus is a standardized interface that makes it easy to connect aDSA to a computer, printer or digital plotter. It is important in automating repeated tests andtransferring data to computer data bases and/or analysis programs. The processing power ofmodern DSAs has advanced to the point where HP has implemented a version of the BASICprogramming language resident in the instrument. This allows for extreme flexibility inadapting the instrument to dedicated tasks.

6.7 6.7 6.7 6.7 6.7 User Units and Unit ConversionDSA displays can be calibrated in vibration units such as inches/seconds and rpm. Units ofvibration amplitude can also be converted to other parameters (e.g. acceleration to velocity)using the processing capabilities of DSAs.

6.86.86.86.86.8 Synchronous Sample Rate ControlBy controlling the data-sampling rate with a tachometer pulse, the frequency axis can benormalized to rotational speed. Traditionally, this was done with external analog circuitrydirectly controlling the sampling rate of the analyzer. Increased digital processing power hasallowed this task to be handled digitally, bringing with it increased capability and accuracy.

6.9 6.9 6.9 6.9 6.9 Two-Channel EnhancementWhile single-channel DSAs address most of the needs of machinery analysis, dual- andmulti-channel DSAs provide important enhancements such as real-time phase comparisonsand transfer function measurements.

1 HP-IB: Not just IEEE-488, but the hardware, documentation and support that delivers the shortest path to ameasurement system.

Chapter 6 describes the importantmeasurement capabilities ofDSAs as they relate to machineryvibration analysis. For a moredetailed discussion of DSAsand how they work, refer toHewlett-Packard applicationsnote AN 243.

Figure 6.1-1Hewlett-PackardDSAs representa-tive of the hand-held, benchtopand systemstypes.

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6.1 Types of DSAsThere is a wide variety of DSAson the market; and generally, theycan be broken down into threecategories:

1) Handhelds2) Benchtop Instruments3) Computer Controlled Systems

Though there are variations onthis theme this covers by far themajority of systems on the mar-ket. Obviously, there is a long listof features and trade-offs to con-sider; including speed, portability,number of channels, display reso-lution and price. Figure 6.1-1 is aphotograph of three Hewlett-Packard products representativeof these categories.

The product offerings change rap-idly as technology advances, it ishard to make generalizations, butthe following are some key con-siderations for each DSA type.

Handhelds are light-weight, porta-ble and battery operated. Theygenerally have a LCD display thatlimits their resolution and displayupdate rate. The power consump-tion considerations lead to designcompromises, that make thisclass of DSA the lowest perform-ing as a group in terms of speed,dynamic range and accuracy.They tend to be lower in cost buthave a relatively robust set of ca-pabilities. In machinery analysisapplications these are well suitedfor maintenance and trouble-shooting where portability is veryimportant.

The advantage of this type instru-mentation in predictive mainte-nance is the operator receivesimmediate vibration spectralresults and preliminary vibrationseverity analysis.

Benchtop instruments range fromrelatively low-cost, low-perfor-mance instruments to high-perfor-mance instruments. Generally,the benchtop instruments give ex-ceptional performance in a smalleasily operated package. Thetight coupling of the hardwareand software within the instru-ment, leads to very high displayupdates, extremely powerfulanalysis capability and generallyvery high accuracy and dynamicrange. In machinery analysisthese are generally used in trou-bleshooting, research and devel-opment, and in certificationtesting where portability is lessan issue and a small number ofchannels is necessary.

DSA systems consist of an instru-mentation mainframe connectedto a computer. The system is ac-tually a DSA instrument that usesthe computer as the user inter-face and data storage device.Most often, systems are multi-channel in nature having from 2to 500 channels of data acquiredsimultaneously. Systems are alsocapable of being customized byusers or software developers toperform dedicated or high-perfor-mance tasks. They are generallyused when multi-channels are re-quired and the computer interface

is desirable. In machinery analy-sis they are used in manyof the same general areas asbenchtops and in continuous ma-chinery monitoring applications.

6.2 Measurement SpeedSpeed is important in machineryanalysis because vibration char-acteristics can change quickly.This is illustrated in the spectralmap of Figure 6.2-1, where mea-surements of a machine run-upspaced at 0.5 s intervals show sig-nificant variation. Speed is alsoimportant for reducing the timerequired to characterize a ma-chine. The time required to makea measurement with a DSA isdetermined by two factors: (1)measurement resolution, and (2)transform computation time.High resolution measurements re-quire a long data sampling time(frequency resolution spaced at1 Hz intervals requires a 1 s mea-surement time). This is a physi-cal fact, independent of thedesign of the DSA. Computationtime, however, varies widelyamong DSAs, and can make a no-ticeable difference in measure-ment time. Computation time isusually expressed in terms ofreal-time bandwidth — the fre-quency span at which data sam-pling and computation times areequal (higher real-time bandwidthimplies faster computation). Thisis theoretically the maximumbandwidth that data can be col-lected without gaps while simul-taneously computing spectra.

Real-time bandwidth exampleSuppose you were making measurements with a 2000 Hz frequency span. The data samplingtime for this span on DSAs with 400-lines resolution (see Section 6.2) is 0.200 s. If thecomputation time were also 0.200 s, then sampling would never have to stop to let thecomputation catch up. (This computation time would correspond to a real-time bandwidth of2000 Hz). If the computation time were 1 s (a real-time bandwidth of 400 Hz), the analyzerwould miss large amounts of data while waiting for the computation.

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Actual real-time bandwidth andspecified bandwidth can vary con-siderably. Its important to notethat a number of factors influencethe actual real-time bandwidth.Often the processor is required toperform a number of additionalcalculations to display the data;this can have a considerable ef-fect on the real-time bandwidth.Although an increase in the datablock size will increase data sam-pling time the calculation time in-creases at a faster rate for largerblocks; thereby, reducing the real-time bandwidth for larger blocksizes and increasing it for smaller.Obviously, the number of simulta-neous channels will also effectthe rate. For these reasons, thereal-time bandwidth is normallyspecified for a block size of 1024time sample points and with thedisplay update turned off (i.e. fastaveraging). Therefore, if real-time performance (i.e. gap free)is necessary, caution should beexercised in interpreting thespecification.

One way of circumventing theproblem is to buffer up the raw-time- domain digital data in eitherthe analyzer memory (RAM) or ona high-speed data-storage device(normally a hard disk drive).These capabilities are referred toas time capture and throughput,respectively. Figure 6.2-3 illus-trates the concept of time cap-ture. In this manner the analyzercan acquire gap free data, store itin memory, and analyze it laterwithout relying on the processingspeed of the analyzer being ableto keep up with the data acquisi-tion rate. An additional benefit, isthe ability to go back and reana-lyze the data in a number of dif-ferent ways after the fact, withoutreacquiring the data.

Figure 6.2-1Machineryvibration spectracan change veryquickly, as thisspectral map ofa run-up testillustrates.Slower sweptspectrumanalyzers canmiss thesechanges.

Figure 6.2-3Block diagram ofdata flow in a DSAusing time capture.The data is firstacquired andstored in RAM;then analyzedto productspectra, etc.

Figure 6.2-2Total DSAmeasurementtime is the sum ofdata sampling timeand computationtime. Whilesampling time isfixed for a givenresolution,computation timesvary widely amongavailable DSAs.

This mode is similar to taperecording data and then post-processing it. The advantage ofthroughput or time capture is theintegration of the process into theDSA eliminating the extra calibra-tion and setup steps of a separaterecorder. Post-processing isgreatly simplified, saving timeand allowing previewing of theanalyzed data immediately.

One of the shortcomings of this isthat the real-time spectral displayupdate is not available, since thedata isn’t analyzed until after thetest. DSA systems generally havethe capability to monitor inputdata and acquire the throughput/time capture simultaneously. Also,since, all of the data is held inmemory it requires a considerable

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portion of the analyzer memoryresources; especially, if longrecords are required. Many times,what is required is not real-timedata acquisition — the real issueis display update rate. It is possi-ble to keep track of fast changingspectrums and not have real-timeperformance; the gaps do notmaterially effect steady orpseudo-steady state conditions.Generally, real-time performanceis required when transients arepresent and non-real-time analy-sis would risk missing an impor-tant event.

6.3 Frequency ResolutionHigh resolution is required foranalysis when vibration signalsare closely spaced, or when thefrequency of a component mustbe read with high precision. Acommon example of closelyspaced signals are the 1 x andpowerline components of induc-tion motor vibration, which canbe separated by a few Hz. Thesidebands around rolling- elementbearing and gear frequencies areoften closely spaced. High preci-sion is required when the charac-teristic vibration frequencies oftwo possible sources are close to-gether, as in the case of a bearingfrequency and a running speedharmonic.

Frequency resolution in a DSA isdetermined primarily by the num-ber of filters (or lines of resolu-tion), and the ability to zoom.The filters of a DSA are shown inFigure 6.3-1. Signals must lie indifferent filters to be resolved, soresolution depends on the spacingof the filters. If the number of fil-ters is fixed, filter spacing is de-termined by the number of filtersand the analysis span. More fil-ters imply better resolution for agiven span.

Figure 6.3-1Frequencyresolution in aDSA is determinedprimarily by thenumber of filters,and the ability tozoom. In a zoommeasurement, thecomponent ofinterest is madethe center frequencyof the analysis,allowing the use ofan arbitrarilynarrow frequencyspan.

Figure 6.3-2An example gearvibration spec-trum that illus-trates the need forzoom. The side-bands aroundgearmesh oftenindicate the badgear, but are tooclosely spaced toto resolve in (a).The zoommeasurement in (b)centers a nar-rower frequencyspan on the gear-mesh, increasingresolution.

If the span required for the de-sired resolution is too narrow toinclude all the frequencies of in-terest, then the analysis muststart at a frequency above zero.This process is referred to aszooming (because it involveszooming in on an arbitrary centerfrequency), and is a feature ofmost DSAs. Ideally, the zoomfeature should allow frequencyspans down to 1 Hz to be

centered on any frequency in theanalysis range. Typically, imple-mentation of zoom should haveno effect on the real-time band-width of the analyzer, since theprocess is normally handled bydedicated hardware that operatesindependently of the other com-putational hardware.

The gear spectrum in Figure 6.3-2illustrates why the ability to zoom

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Figure 6.3-3A comparison of3 common windowtypes: a) flat top,b) Hanning andc) uniform.

is so important. In the low-reso-lution spectrum of (a), the side-bands around the gearmeshfrequency indicate a problem, butthe exact spacing (which will in-dicate which gear has the defect)is difficult to determine. Sincethe gearmesh is at a relativelyhigh frequency, a span narrowenough to resolve the sidebandscannot cover the entire frequencyrange starting at 0 Hz. Thus wemust zoom on the gearmesh fre-quency to complete the analysis.(See Section 4.6 for more infor-mation on gear analysis.)

Window Functions

Frequency resolution is also af-fected by the shape of the filters— determined in a DSA by thewindow function selected. Thewindow function shapes the inputdata to compensate for disconti-nuities in the sampling process(see application note AN 243).Figure 6.3-3 shows the same vi-bration spectrum measured withthe three windows commonlyavailable on DSAs.

A. The Flat Top window is opti-mized for level accuracy, with aresponse variation with frequencyof 0.1%. This is the window touse unless maximum frequencyresolution is required, or you arecapturing a transient.

B. The Hanning window providesimproved frequency resolution(note the Bandwidth notation atthe bottom of the display), butsacrifices amplitude accuracy.Variation with frequency is upto 15%.

C. The Uniform window providesno weighting, and should be usedonly for totally observed tran-sients, or specialized signals.The wide skirts, known as leak-age, severely restrict frequency

Figure 6.3-4Synthesising1/3 octave datafrom FFT requiresmultilple FFT bandsof analyses. Thelower fre-quenciesof the 1/3 octavehave resolutionrequirements of∆∆∆∆∆f 5Hz while thehigh frequenciesrequire ∆∆∆∆∆f 5kHz.

resolution. (Leakage is whatweighting in the other two win-dow functions minimizes.) Am-plitude variation is up to 36%.

Octave Band Analysis

During most of this note we haveconcentrated on FFT analysis be-cause it is most useful in machin-ery vibration. This is because,many of the vibration componentsare very narrow in bandwidth andrepeat themselves in a uniformlyspaced relationship with respectto frequency (i.e. harmonics andsidebands). Sometimes it is de-sirable to have the frequencyresolution spaced in a logarithmic

or octave fashion, with the fre-quency resolution depicted pro-portionally rather than uniformlyas in FFT analysis. This type ofanalysis is useful when high reso-lution is not required, and for rea-sons beyond the scope of thisnote, is useful in detecting andanalyzing transient behavior.This type analysis is referred toas octave-band analysis.

One method of obtaining this typeof analysis is to resynthesize theoctave analysis data from highresolution FFT data. Figure 6.3-4illustrates the concept of synthe-sis of 1/3-octave data from

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multiple passes of FFT data(1/3-octave refers to a doubling ofthe frequency for every third datapoint). Figure 6.3-5 is a compari-son of comparable 1/3- and 1/12-octave analysis and narrow-bandFFT analysis of the same data.Since the analysis requires mul-tiple “passes” and differing dataacquisition times, the processof synthesis is NOT real-time.Therefore, it is only useful forsteady state analysis.

Real-time octave analysis is a pro-cess of obtaining octave data byprogramming the analyzer to per-form digital filtering on the datarather than FFTs. The digital fil-tering process is inherently pro-portional and logarithmic innature and readily yields the oc-tave spectra. Though this is be-yond the scope of this note, thiscapability is often required fornoise and acoustics problemsassociated with machines. It isspecified in a number of interna-tional standards and the capabil-ity is available in a number ofDSAs.

6.4 Dynamic RangeDynamic range is another aspectof resolution. It is a measure ofthe ability to analyze small sig-nals in the presence of large ones,as shown in Figure 6.4-1. DSAsfeature wide dynamic range, withmost able to display signals thatdiffer in amplitude by factors of1000 or more. Logarithmic displayscales are used to take advantageof this measurement capability.

Wide dynamic range is importantfor analyzing low-level vibrationsignals in the presence of largeresidual imbalance components.

Figure 6.3-5A comparision ofmeasurements ofthe same spec-trum made withnarrowband(FFT), 1/3 octaveand 1/12 octave.

Dynamic range is also importantwhen the component to be ana-lyzed is small compared to the to-tal power level. That is, a largenumber of relatively low-level sig-nals result in a high total powerlevel that limits input sensitivityin the same way a single largesignal would. This is often thecase, for example, when analyz-ing low frequency vibration withan accelerometer.

Dynamic range in an analyzer is acumulative specification of aDSAs ability to distinguish smallsignals in the presence of largersignals. It is effected by a num-ber of components in the data ac-quisition portion of the analyzer:Analog-to-digital converter resolu-tion (number of bits, linearity

etc.), input amplifier noise floor,anti-aliasing filter performance,spurious signals within the ana-lyzer, digital signal processor per-formance, etc.. Generally, thespecification is for the worst casesituations (i.e. max requency spanand lowest input range) and typi-cal performance in the frequencyrange for most machinery mea-surements and reasonable inputranges is significantly higher(20 dB is common). It is impor-tant to understand the differencebetween specified dynamic range(i.e. guaranteed ) and typical(i.e. expected under commonconditions).

Figure 6.4-1Dynamic rangeis defined as theratio betweenthe largest andsmallest signalsthat can beanalyzed at thesame time.

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6.5 Digital AveragingMachinery vibration spectra oftencontain large levels of back-ground noise, vibration fromadjacent machines, or compo-nents that vary in amplitude.Three types of digital averagingare available to reduce the prob-lems that these conditions implyfor analysis.

A. RMS. The result of a RMS av-erage of successive spectra is animproved estimate of the meanlevel of vibration components.RMS averaging should be usedwhen component levels vary sig-nificantly.

B. TIME. While RMS averagingreduces the variance of signal lev-els, it does nothing to reduce un-wanted background noise. Thisbackground noise may mask low-level components, or addunrelated components to thespectrum. Time (or synchronous)averaging effectively reducescomponents that are not relatedto a once per revolution trigger,which is usually a key-phasor.Time averaging can be used whenbackground noise or vibrationfrom adjacent machines inter-feres with analysis. Time averag-ing requires very good speedregulation to be effective. Timeaveraging in the computed ordertracking mode will eliminate thespeed regulation requirement.

C. PEAK. It is often desirable tohold peak vibration levels duringa run-up or coast-down, or over aperiod of time. The result of peakaveraging is a display of the maxi-mum level at each frequencypoint.

Figure 6.5-1When RMSaveraging isperformed,componentswhich vary inamplitudeconverge totheir mean value,providing abetter statisticalestimate ofamplitude.a) random noiseaverage over10 records.b) un-averagedrandom noise.

RMS Averaging

Because noise can cause spectralcomponents to vary widely in am-plitude, a single measurement isnot statistically accurate. Whilewatching the components vary inamplitude, you could visually av-erage them and determine themean level. This is essentiallywhat RMS averaging does, andthe more averages you take thebetter the accuracy will be. RMSaveraging can be thought of asamplitude averaging, since phaseis ignored. (RMS, or root meansquare, is the square root of themean of the squared spectra.) Theeffect of RMS averagingis shown in Figure 6.5-1.

RMS averaging improves the statistical accuracy of a noisyspectrum, and does not requirea trigger, but it does not actuallyreduce the noise level.

Time Averaging

Time averaging is a techniquethat can be used to reduce thelevel of noise, and thus uncoverlow-level signals that may havebeen obscured by the noise.Sometimes referred to as linearaveraging, this type of averagingrequires a synchronizing trigger— usually a keyphasor.

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Time averaging can be imple-mented in either the time or fre-quency domains, but the timedomain is traditional (thus thename). In this form, the blocksof time data that are transformedby the analyzer to the frequencydomain are averaged before thetransformation. Signals that arefixed in the time record (i.e. syn-chronous with the trigger) willremain, while nonsynchronoussignals eventually average tozero. This is shown in Figures6.5-2(a) and (b), where time aver-aging a noisy square wave hasreduced the noise level, whilekeeping the square wave intact.An example with machinery spec-trum can be found in Section 5.2.

Peak Hold

Peak hold is a function usuallygrouped with averaging in DSAs.By displaying the maximum levelat each frequency over a numberof samples, this feature providesa history of peak levels. Two ap-plications are shown in Figure6.5-3. In (a), peak hold has beenused during a machine coastdown, providing a simple track ofthe maximum level (which is usu-ally 1 x rpm)*. The display in (b)is a peak hold over a relativelylong period that shows the rangeof speed variation of a nominallyconstant speed motor. This couldbe used, for example, as an indi-cation of load variation. Peakhold is also useful for recordingmomentary vibration peaks (e.g.from start-ups or load changes).

* In applications where a tachometer signal isavailable, an order track measurement ispreferable to this method (see sec. 6.8).

Figure 6.5-2The time averageddisplays in (b) showa reduction in thelevel of componentsthat are nonsynch-ronous with thetrigger.

Figure 6.5-3Peak hold used(a) to track peaklevel during a coast-down, and (b) toindicate variation in speed over time.

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6.6 HP-IB andHP Instrument BASICThe Hewlett-Packard InterfaceBus (HP-IB) is a standardizedinterface that can be used toconnect a number of instruments,plotters, printers and computerstogether. Most DSAs come stan-dard with a HP-IB interface anda set of commands that allowsvirtually unlimited possibilitiesfor automatic data storage, pre-sentation, and analysis. Mostcommonly the interface is usedto provide for hardcopy output ofDSA results using a digital printeror plotter that can be connectedand controlled directly.

Computer Data Storage

and Analysis

A common problem encounteredin machinery vibration monitoringis the need to organize, store, plotand archive large amounts ofdata. Often extensive post-testdata processing is required de-pending on the specific applica-tion. It is often convenient to putthe data in a data base type appli-cations program so that trendscan be analyzed and specific dataeasily retrieved.

Though most DSAs have exten-sive data storage capabilities, itis often desirable to transfer thedata to a computer, most com-monly, using HP-IB. It is also de-sirable to place data collected ondifferent DSAs on a common plat-form for comparison and analysis.Hewlett-Packard has standardizedon a common data storage struc-ture for its DSA analyzers allow-ing for easy transfer of databetween instrument types and ap-plication programs using a set ofutility programs and a StandardData Format (SDF). Figure 6.6-1

* MS-DOS and MS Windows are U.S. registeredtrademarks of Microsoft Corporation.

the user customize measure-ments. It is most commonly usedfor automatic and repetitive tests.Not only can I-Basic address thehost DSA, it can communicateover the HP-IB to other instru-ments or peripherals that are at-tached. Figure 6.6-2 illustratesthe advantage of this in a particu-lar application.

Whether through the use of I-Ba-sic or some other programminglanguage the HP-IB capability ontest equipment allows for tyingtogether a number of instrumentsover the HP-IB and controllingthem in concert with each otherto make automated and complexmeasurements using an Instru-ment System concept. The HPDSA Systems are a specific exam-ple of this approach, but the sameconcept can be applied to tradi-tional DSAs.

illustrates the concept of the stan-dardized format and the use ofthe utilities. The utilities consistof a set of MS-DOS® programs forviewing, converting, and transfer-ring data.

Instrument Systems

and I-Basic

Hewlett-Packard has implement-ed a proprietary version of theBASIC programming languagethat allows for many of the capa-bilities of the computer/DSA sys-tem without needing an externalcomputer. HP Instrument Basic(I-Basic) is a version of the HPBasic language which is designedto run inside many HP instru-ments. I-Basic is also available torun in DOS and MS Windows®.

I-Basic is optimized for instru-ment control applications, letting

Figure 6.6-1Use of a StandardData format (SDF)allows data to beeasily interfacedand simplifies theconversion ofnon-SDF DSAsdata to a standardformat.

Figure 6.6-2HP-IB system forscanning a numberof transducers. Sucha system can beconfigured to takeappropriate action(e.g. sound an alarmor remove power)when currentvibration levelexceeds pre-defined limits.

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6.7 User Unitsand Waveform Math

Vibration displays are easier tointerpret if they are presented inunits that are relevant to machin-ery. DSAs provide the capabilityfor user calibration of amplitudeunits, and a selection of units forthe frequency axis. DSAs can alsoconvert spectra from one vibra-tion parameter to another throughintegration and differentiation.

User units calibration is accom-plished by entering a calibrationfactor (such as, 10 mV/g) or usingthe marker function to specify aknown value (such as, markervalue equals 94 dB SPL). TheDSA performs the conversion anddisplays the vibration spectrum inthe desired units, usually referredto as “EU” (Engineering Units).DSAs also provide for customlabeling of user defined units(e.g. g's, in/s, mils, etc.).

The frequency units used for ma-chinery vibration analysis includeHertz, rpm, and orders. Ordersrefer to “orders of rotation”, andare harmonics of the rotationspeed. Orders are handy for anal-ysis because many vibration prob-lems are order-related. By usingexternal-sample control, orderscan be fixed on the display whilespeed changes (see Section 6.8).

Often it is desirable to convertfrom one vibration motion vari-able to another. Referring to theformulas for displacement, veloci-ty, and acceleration in Section2.1, it should be apparent thatthey are related by frequency anda phase shift. For example accel-eration can be converted to veloc-ity through division by jω = j(2πf).This operation is commonly re-ferred to as artificial integration(the “j” term is an operator that

implies a 90° phase shift), and isa feature of most DSAs. Figure6.7-1 shows an integrated accel-eration spectrum overlaid on anactual velocity spectrum mea-sured at the same point.

Table 6.7 summarizes vibrationparameter conversion. Twothings to note about these conver-sions: (1) integrating absolutevelocity will not result in relativedisplacement (i.e. integrated mea-surements from a case-mountedvelocity transducer will not givethe same result as a displacementtransducer that measures theshaft directly),and (2) differentia-tion is usually not recommended,since noise in the spectrum to bedifferentiated tends to give mis-leading results.

A feature of many DSAs which ac-tually implement this capability iswaveform math. It fundamentallyallows you to define mathemati-cal relationships between data

traces within the DSA and calcu-late supplemental data from theresults of measurements; muchthe same way as a calculator canbe used to calculate the results ofstatic measurements. Some DSAsimplement this conversion explic-itly. Order analysis conversion ismore complex but possible.

Historically, these conversionswere made with analog hardwarecircuitry built into the DSA or sig-nal conditioning. This is beinglargely replaced by the math cal-culation which gives good resultsand does not require the costlyadditional circuitry. Thoughthese operations are time provenand straightforward to imple-ment; whenever performing thistype operation it is recommendedthat the operation and units bechecked carefully and tested toinsure that there has not beensome unexpected errorintroduced.

Conversion Operator Description

Acceleration ⇑ velocity /jω Single integration

Acceleration ⇑ displacement 1/ω2 Double integration

Velocity ⇑ displacement 1/jω Single integration

Velocity ⇑ acceleration jω Differentiation

Displacement ⇑ velocity jω Differentiation

Displacement ⇑ acceleration -ω2 Double differentiation

Figure 6.7-1A comparisonbetween an integ-rated accelerationspectrum and anactual velocityspectrum (dashedline).

Table 6.7VibrationParameterConversions

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6.8 SynchronousSample Control andOrder Tracking

One of the complications encoun-tered in analyzing rotating ma-chinery is variation in speed. Formachines that will operate over awide range of speeds, it is desir-able to measure vibration overthe entire range. With a fixed-fre-quency axis, spectral componentsare constantly moving with thechanges in speed. For machinesthat run at a nominally constantspeed, even small changes canmake point-for-point comparisonsdifficult.

The problem of wide-speed varia-tion is sometimes addressed bypost-test manipulation of thedata. The frequency display canbe normalized (i.e. calibrated tofixed location, orders of rotation)through software manipulation.But often what is required is theorder track (i.e. the locus ofpoints characterized by the ampli-tude as a function of rotationspeed for a particular order, seefigure 6.8-1). There are a numberof problems with this approach:(1) it does not provide real-timedisplay update of the data; (2) thenumber of orders measuredchanges with measurement speedand the resolution appears differ-ent at different running speeds;and (3) the scheme assumes thatthe software can calculate or some-how determined the running speed.

To circumvent these problems,external sample control was in-troduced. By controlling the data-sampling-rate with a signal tied torotating speed, the display willhave a fixed calibration in ordersof rotation. (See Section 5.4).This is a result of the analyzer, ineffect, sampling at a constant del-ta angle of rotation.

would be exactly 4 revolutions inone data record). An importantrequirement for the ratio synthe-sizer is anti-aliasing protection.Aliasing occurs when the data-sample rate is too slow, allowinghigh-frequency signals to be mis-represented as low-frequency sig-nals. Aliasing is avoided if a filteris used to limit input signals tofrequencies less than 1/2 the sam-ple rate (See Hewlett-PackardApplication Note AN 243 for moreinformation on aliasing.) Sincethe sampling rate is varying itsnecessary to have a variable (ortracking) filter.

Two problems arise out of thisscheme because of the additionalhardware used. First, the ratiosynthesizer is a phase lock loop

Figure 6.8-2 shows the instrumen-tation required for controlling thesample rate externally. Typically,a once per revolution pulse multi-plied by a ratio synthesizer isused for sample control. The ra-tio synthesizer is required be-cause DSAs typically sample at arate of 2.56 times the frequencyspan. Since it is usually desirableto look at several orders, the onceper revolution tachometer pulsemust be multiplied by 2.56 timesthe number of orders to be ana-lyzed. (If you needed to analyze amachine out to a frequency of 100orders with a once per revolutiontachometer signal the ratio syn-thesizer would be required toproduce 2.56 * 100 = 256 samplepulses per revolution. If theblock size was 1024 points, there

Figure 6.8-1The order trackis the locus ofpoints of a particularorder as a functionof machine speed.Illustrated is theplot of this datasuper-imposed ona waterfall plot.

Figure 6.8-2Instrumentationsetup for con-trolling samplerate externally.

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and it has some inherent time lagand phase error problems. In or-der tracking very small errors infrequency can cause significantamplitude and phase errors. Sec-ond, the tracking filter can be oneof a number of types, the mostpopular is switched capacitancedue to its low cost and ease ofimplementation. Though it is lowcost, it typically has a limiteddynamic range because of theswitching "spurs" (noise spikesthat appear as signals) making itunsuitable. (See appendix A).

To avoid these problems HPdeveloped DIGITAL SYNCHRO-NOUS SAMPLE CONTROLschemes, they use the digitalsignal processing power availableinside the DSA to perform the ra-tio synthesizer functions and todigitally resample the data toproduce conceptually the sameeffect as the external samplecontrol without the addition ofanalog hardware. Additionally,the flexibility and power of digitalprocessing allowed for the elimi-nation of many problems inherentin the older technology. Figure6.8-3 shows a block diagram ofthis digital implementation ofsynchronous- sample control.Appendix A of this note containsa more detailed discussion of theimplementation of this scheme.When the data is synchronouslysampled, producing the ordertrack data is very easy, becauseit's simply the locus of points ata fixed frequency (in the orderdomain) as a function ofrotation speed.

Machine Runup Measurements

An important measurement madeusing the order tacking capabilityof DSA's is the machine runup/down. In many machines theonly time they operate at certainimportant speeds (ie. critical

Figure 6.8-4(a)Bode plot of amachine runup fora simple flexiblerotor systemshowing thecritical speed.The plot representsmagnitude as linearmagnitude and the"X" axis is linear toconform to normalconvention, thoughthe DSA's can alsoscale the data ina Logrithmic format.

speeds, at structural resonances,etc.) is during a runup or run-down. This measurement is animportant indication of machineryhealth and is commonly used toqualify new and overhauled highspeed machinery. The measure-ment uses the residual imbalancein the machine to excite it at

different frequencies as it runs upto operating speed and measuresthe response (magnitude andphase) as a function of speed.This utilizes the basic order track-ing capability of the analyzer cou-pled with special display featuresrequired of this measurement.

Figure 6.8-3Instrumentationfor synchronoussample control forDSA with digitalsynchronousresampling.

Figure 6.8-4(b)Polar plot of runupdepicting themagnitude andphase plotted in apolar fashion.Note the rotationintended to compen-sate for positioningof the phasereference and thedisplacementtransducer.

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Two common display formats areused with this measurement; oneis the Bode diagram* and the oth-er is the polar display. The bodeplot depicts the magnitude andthe phase response of the systemto the runup as a function ofspeed (RPM). A benefit of theDSA in this measurement is itsability to simultaneously trackmultiple orders and display themin addition to the fundamental ro-tation speed (1st order); as wellas the overall level and the RPMprofile Figure 6.8-5.

6.9 Dual/Multi-ChannelEnhancements

Most of our discussion has centeraround spectrum measurementswhich can be made with a single-channel DSA, and in some cases areference trigger to obtain phaseinformation. This is not to implythat a single-channel DSA is thebest solution to vibration analysisproblems, it merely points outthat many measurements CAN bemade with a single-channel ana-lyzer. In fact, advances in tech-nology have significantly reducedthe price differential between 1-,2-, and multi-channel DSAs; mak-ing their usage common in ma-chinery vibration analysis.

A multi-channel DSA is muchmore than multiple separate anal-ysis channels, because it canmeasure the amplitude and phaserelationships between two signalsor sets of signals. Another rela-tionship that is commonly mea-sured is called the frequencyresponse function. It is especiallyuseful for performing real-timephase comparisons, and identify-ing the source of vibration or

noise in a machine. The frequen-cy-response function can also beused to determine natural fre-quencies of shafts, gears, and ma-chine housings that can be criticalfor analysis. Multi-channel DSAscan display shaft orbits. Thesedisplays give insight into the pathof the shaft as it rotates, and areespecially useful in high-speedmachinery. For a more generaldiscussion of dual-channel DSAcapabilities, refer to Hewlett-Packard application note AN 243.

Real-Time Comparisons

Comparative phase measure-ments are a powerful tool foranalysis, especially for differenti-ating between similar forms of vi-bration (see Section 4.4 and 5.2).This measurement is made botheasier and more accurate with adual-channel DSA. Referring to

the motor-pump combination inFigure 6.9-1, suppose that you arenot sure whether the high-vibra-tion level is due to imbalance ormisalignment. As pointed out inSection 4.4, the relative phase ofaxial vibration at A and B will be180° if misalignment is the prob-lem (assuming a rigid-rotor).With a single-channel analyzer,you would use a keyphasor as areference, and measure the twoends one at a time. With a dual-channel analyzer, all you have todo is connect an end to eachchannel and measure the transferfunction phase (this connection isdiagrammed in Figure 6.9-1.)Thus, relative phase measure-ments can be made with a single-channel DSA, but are much easier(and less error-prone) with adual- or multi-channel DSA.

* Bode diagram conventions for rotatingmachine applications differ fromelectrical and servo conventions;here the convention common tomachinery vibrations are used.

Figure 6.9-1Misalignment isindicated by a 180°phase relationbetween A and B.For transduceroriented as shown(180° relation),the relative phasewill be 0°.

Figure 6.8-5Runup depiction ofthe 2nd and 3rdorders as well asthe overall leveland the RPM profile.

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Another important place where adual- or multi-channel DSA is use-ful is in two- or multi-plane bal-ancing. The vibration level atmultiple planes can be monitoredsimultaneously, while at the sametime utilizing the external triggerto provide for phase informationfor all channels. This can effectlarge reductions in the number ofmeasurement runs required tobalance a machine.

Cause and Effect Relation-

ships: The Coherence Function

A common problem in machineryvibration analysis is that vibrationfrom one machine in a train iscoupled to the other machines.The coherence function can helpwith these problems by indicatingthe cause and effect relationshipbetween vibration at twolocations.

The coherence display covers arange of 0 to 1, and indicates thepercentage of power in channel 2that is coherent (i.e. linearly relat-ed) with channel 1. Let’s supposethat vibration levels at points Aand D on the motor pump combi-nation of Figure 6.9-1 are similar,and rather high. You would liketo know whether they are inde-pendent or related. A low valueof coherence between vibrationcomponents from A and D indi-cates that they are not related. Ahigh coherence value for a com-ponent implies that there may bea causal relationship. (The highcoherence component could, for

example, be from a third sourceof vibration.) Coherence mea-sured between end points on amotor and pump is shown inFigure 6.9-2. Note that coherenceis high for all the major vibrationcomponents except 240 Hz indi-cating that this vibration is not

from the motor. The techniquewill not work 100% of the time,and you will have to get a feel forwhat constitutes a high level ofcoherence, but it may save in dis-connecting machines to isolatethe source of vibration.

Figure 6.9-2Coherence measuredbetween a pumpand motor clearlyindicates whichcomponents areunrelated.

Figure 6.9-3The transferfunction of agearbox can bemeasured withan instrumentedhammer and atwo-channel DSA.

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Natural Frequency

Measurements

The natural frequencies of a ma-chine housing or foundation canbe easily determined throughwhat is sometimes referred to asa “bump” test. A single impulsivesignal produces a broad spectrumof energy. If the housing is im-pacted with sufficient force (typi-cally with a block of wood), allthe natural frequencies will be ex-cited. The response can be mea-sured with a single-channel DSA,but an imperfect impact mayresult in a misleading spectrum.

A better way to make this mea-surement is with a multi-channelanalyzer and an instrumentedhammer. This is shown diagram-matically in Figure 6.9-3, wherethe natural frequencies of a gear-box are being determined. As wesaw in Section 4.6, gear defectsoften show up at the natural fre-quencies, so this information isvaluable. It can also help identifycritical rotor frequencies inhigh speed machinery. Hewlett-Packard application noteAN 243-3 contains more detailedinformation on measuring the re-sponse of mechanical structures.

Orbits

HP dual-channel DSAs have theability to display orbit diagrams,Figure 6.9-4 shows how an orbitdiagram is generated utilizing twoproximity probes mounted at 90°to each other. Figure 6.9-5 showsdiagramatically a typical orbit di-agram. They are useful for gain-ing insight into rotor motion in

Figure 6.9-4Measurementsetup for orbitmeasurementsusing orthogonalproximity probeand a 2 channelDSA.

Figure 6.9-5The orbit capabil-ity of some two-channel DSAsprovides insightinto rotor motionin machines withfluid-film bearings.

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turbo-machinery. The subject oforbit interpretation is coveredwell in Reference 30. If a multi-channel system (≥4 channels) isused it is possible and often desir-able to make multiple simulta-neous orbit measurements atdifferent shaft locations.

The orbit diagram is fundamental-ly a time domain measurementand it should be emphasized thata DSA will typically low pass fil-ter the data before collection. Insome cases unfiltered time data isdesired, and many DSAs allow forbypassing the filters just for thispurpose.

On the orbit diagram as you moveabout the orbit pattern the inde-pendent variable is time. If themeasurement is triggered by ashaft reference (i.e. keyphasor)then the actual position can bemarked on the diagram and if therpm is known the location of anypoint can be calculated. An alter-native method is to use synchro-nous sample control in orbitmeasurement (see Section 6.8)with an external reference fortrigger (this can be the same sig-nal as the tachometer signal).Now the independent variable isnot time but shaft position andcan be read directly from theDSA's display as shown in Figure6.9-6. Figure 6.9-7

Traditionalmethod formeasuring filteredorbits usingtracking filtersand an oscilloscope.

Figure 6.9-6Orbit diagramusing synchron-ous samplingwill accuratelyrepresent theangular position(note the markerread out).

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Filtered OrbitsNormal orbit diagrams representthe contribution of all frequencieswithin the bandwidth of analysis.These include contributions fromsurface defects and anomolies,higher (or lower) order compo-nents, powerline harmonics, ma-chine noise and the like. Filteredorbits is a technique for focusingthe orbit analysis on a select fre-quency range (or ranges) of inter-est. This was traditionally doneby placing a tracking narrowbandpass filter in the analysisstream (Fig 6.9-7). This allowsthe analysis to focus on contribu-tions to the orbit associated withthat particular frequency or or-der. The traditional techniquerequires special purpose analoghardware and has many of thelimitations associated with theuse of similar techniques dis-cussed elsewhere in this note.

In an FFT analyzer the filteredorbit information is containedwithin the linear spectrum or or-der ratio spectrum measurements(Note: phase information is re-quired, ie. power spectrum mea-surements are not sufficient).The individual frequency compo-nents of the spectrum representprecisely the same sine wave thatwould be extracted by narrowband filtering. The advantagesare the presence of all frequen-cies simultaneously, the precisionand accuracy of the digitalimpementation and in the conve-nient user interface.

Figure 6.9-8 is an example of atraditional orbit diagram and a fil-tered orbit (of the fundementalrotation frequency) for the same

Figure 6.9-8(a)Complex orbitdiagram of arotating shaft atlow speed withsignificant noiseand distortionpresent. Allfrequencycomponents arerepresented.

Figure 6.9-8(b)Filtered orbitof frequencycomponentcorrespondingto first order.Only the singlefrequencycomponent isdisplayed forsame measurementas Figure 6.9-8(a).This data wasextracted fromlinear spectrafrequency domaindata measured ata single rotationspeed.

Figure 6.9-9Filtered orbit ofthe first orderfrequencycomponent takenat the peakresponse of theorder track for thefirst order (noteposition of themarker in theupper trace). Thisdata was extractedfrom measurementof a run-up usingorder trackingmode.

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signal. The higher order informa-tion has been effectively “filteredout”. Both measurements wereactually made simultaneouslyusing the frequency domain mea-surement mode. The measure-ment could also be made in theorder domain using eitherorder tracks or order ratio spec-tra. Figure 6.9-9 is a filtered orbittaken from a run up measurementusing order tracking; in this mea-surement an entire range of fil-tered orbits as a function of RPMbecome part of the measurementset allowing any orbit shape to bereview for any time/rpm in therun-up. A capability of the digitalimplementation is the ability toadd together related componentsto obtain a composite filtered or-bit containing only those frequen-cy (or order) components desire.(Figure 6.9-10).

Figure 6.9-10(a)Filtered orbitconsisting of thecontributions of4 individual ordersto the orbit shape.The markerpositions of theupper trace specifythe components toinclude in therepresentation.

Figure 6.9-10(b)The filtered orbitdiagram for samedata containingonly the contribu-tion of the firstorder.

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Appendix A

Computed Synchronous

Resampling and Order Tracking

Digital Resampling

Digital signal processing (DSP)hardware and software have con-tinually improved, allowing thesubstitution of digital processingin many areas which have tradi-tionally used analog processes.This appendix discusses the im-plementation of DSP techniquesin the processing of time sampleddata to produce rotating machin-ery order domain information.

In DSAs the traditional methodfor order analysis involved vary-ing the actual sample rate (∆t) ofthe data to correspond to somemultiple of machine rotationspeed, so that sampling is lockedto a constant angle of shaft rota-tion. This generally led to a re-quirement for a significantamount of ancillary equipment,making the measurement lesspractical and less commonly used(Figure A-1). The use of ratiosynthesizers (phase locked loops)led to a number of problems, par-ticularly in machines with fastrun-up rates or where high ordernumbers were being analyzed.

A significant improvement ispossible by applying the powerof the DSP and microprocessorsin high-performance dynamic sig-nal analyzers (DSAs) to replaceexternal sampling and low-passtracking filter hardware with adigital implementation. One im-mediate advantage is the use ofexisting general-purpose DSAhardware, since the entire pro-cess is carried out in software

(Figure A-2). Many of the short-comings of older techniques canbe overcome by using digitaltechnology.

There are three basic contribu-tions through digital implementa-tion:

1) Calculation of the resampletimes avoids many of the pitfallsof ratio synthesizers and ap-proaches the “theoretically” per-fect resampling times that wouldbe present from a physical device,such as a shaft encoder.

Figure A-1Traditionalexternal samplingmethod of orderdomain analysis.

Figure A-2Block diagram ofdigital resamplingmethod of orderdomain analysis.

2) Eliminates the need and thelimitations of tracking, low-passanti-aliasing filters by replacingtheir functionality with equivalentdigital filters.

3) Allows the digital data to becaptured in mass memory andpost-test analyzed using tech-niques without extraneous andunwieldy recording, and AD/DAconversions required of the ana-log approach.

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Figure A-3Sample plots ofanalysis done inthe frequency(a) and the order(b) domains.

Figure A-4Deviation of an“ideal” PLL’sestimate of shaftangular positionfrom actual shaftwith constantlyincreasing RPM.

Figure A-5Digital dataprocessing oftachometer anddata for orderdomain process-ing prior to FFT.

External SamplingTechniques

The ideal technique for measuringan order spectrum has long beenconsidered the use of an encoderphysically attached to a shaft togenerate sampling pulses at uni-form angular intervals aroundsome reference shaft. This di-rectly determines the samplingtimes as a function of shaft posi-tion. Then, if various transducersare sampled at these times, theresulting frequency spectrum willshow components that dependupon multiples of the shaft-rota-tion rate as stationary lines, inde-pendent of shaft rpm. This sort ofspectral display is plotted versusorder (multiples of the shaft rota-tion rate), instead of frequency.Thus, if the shaft rotation rate ischanged, any frequency compo-nents that are locked to this rota-tion rate will appear stationaryin the order spectrum, while thespectra of any fixed frequencycomponents will appear to move(Figure A-3).

Unfortunately, the appropriateshaft encoders are not alwayspractical to install and do not, inthemselves, address the problemof aliasing, so other approachesmust often be considered. Theclassical method of bypassing therequirement for a shaft encoder isusing a phase-locked loop (PLL)to generate a sampling frequencythat is a suitable multiple of someshaft rotation rate by synchroniz-ing the loop to a small numberof pulses per revolution. For ex-ample, an optically reflectivestripe might be attached to theshaft, giving one synchronizingpulse per revolution. Then thephase-locked loop might be setto generate exactly 256 sampling

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pulses per shaft revolution, nomatter what the shaft rotationrate might be (Figure A-1). Thiswould yield an analysis typicallyup to 100 orders on an FFT ana-lyzer utilizing external sampling.

This technique works reasonablywell as long as the shaft speeddoes not change too quickly, andthe phase noise generated by thephase-locked loop is negligible.However, when the shaft is accel-erating rapidly, the phase-lockedloop lags behind, since the loopcannot begin to adjust to a newrpm until after some change inspeed has occurred (Figure A-4).In this situation, the samples arenot spaced uniformly relative tothe shaft angle, and the estimateof rpm can be in error. The re-sponse time of the phased-lockedloop can be reduced by increasingthe bandwidth of the loop, butthis also increases the noise level.At some point, the resulting phasenoise will begin to “smear” thehigher order spectral lines. Smallerrors in the sampling rate withrespect to rotation rate becomemuch more critical at higher or-ders, where the error is effective-ly magnified by the order number.

Digital Resampling Times

Due to improvements in micro-processor performance (fastercomputations at lower cost), andto lower cost memory chips, it isfeasible to design a trackingscheme that is independent ofshaft acceleration and that hasnegligible internal phase noise.The idea is to collect measureddata at some fixed rate, and tostore this data in a large buffer

Figure A-6Processing oftachometersignals to obtainestimates ofresample timesof uniform shaftangle.

Figure A-7Use of resamplingon a fast sine-sweep at afrequency of fiveorders sampled atuniform time (a)and uniform angle(b).

memory. Simultaneously, the ar-rival times of each synchronizingtachometer pulse are measuredand stored (Figure A-5). Then, themicroprocessor can be used todetermine the shaft angle and ve-locity at intermediate points be-tween the tachometer pulses,based upon a model of constantshaft acceleration. The samplingtimes corresponding to the de-sired shaft angular incrementscan be calculated, and the storedmeasurement data can be interpo-lated in some optimum manner toobtain new samples at the desiredtime points (Figure A-6).

Figure A-7a shows a sinusoidchirp having a linear frequencyversus time characteristic,sampled at uniform time inter-vals. Figure A-7b shows this samesignal after resampling at uniformshaft angle increments. The fre-quency spectrum of the sweptsine in Figure A-7a is “smeared”over a band of frequencies, whilethat for Figure A-7b occurs atonly the 5th harmonic of the shaftrotation rate in the order domain(5th order), assuming that theplot is scaled to show exactlyone revolution of the shaft(Figure A-7c).

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Since the data is buffered in mem-ory, it is possible to “look ahead,”and to use data points that occurbefore the desired tachometerpulse times occur. This allowsthe design of a tracking algorithmthat has no inherent time delay,and thus never gets behind, aslong as the shaft is constantlyaccelerating (or running at a con-stant velocity). In addition, theshaft velocity can be correctlycalculated at each instant in time.There is no significant internalphase noise introduced by thisprocedure, although it is impor-tant to measure the arrival timeof each tachometer pulse veryaccurately to reduce the effectsof time jitter.

Though in actual measurementsthe requirement that the shaft ac-celeration be constant is not met,the model can be updated at eachtachometer pulse so errors intro-duced generally are quite small. Itis possible to use a more complexmodel of the shaft acceleration,but this would introduce an addi-tional performance penalty due tothe increased computation time,and the increases in accuracyhave not warranted this step.Generally, the traditional phaselock loop/ratio synthesizer imple-mentation can be thought of asmodeling the shaft position asconstant velocity between ta-chometer pulses. Figure A-4illustrates the problems with thisassumption.

Figure A-8Example of errorsinherent in asimple two pointlinear interpola-tion scheme.

Figure A-9Illustration of theimplementation ofa multi-point FIRinterpolationscheme.

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The computed order tracking ap-proach requires considerably lessin the way of special hardware,compared to the classical tech-nique. For example, in additionto the need for a tracking ratiosynthesizer, the classical ordertracking method requires trackinganti-aliasing filters on each datachannel and often a frequencycounter to determine shaft veloc-ity. With the new approach, afixed analog anti-aliasing filter isused, and the remaining filteringoperations are done digitally (thisis the same hardware used inthe normal FFT analysis mode).There is no need for an analogtracking ratio synthesizer, sincethe shaft position is continuallycalculated from the tachometerpulse arrival times.

Resampling Amplitude

With traditional ratio synthesizer/shaft encoder techniques, oncethe resampling signals have beencreated, the remainder of the or-der analysis can use standardFFT technology with variable A/Dconverter sampling rates to ac-complish the remainder of theprocessing. This assumes thatadequate alias protection is pro-vided by some variable low passfiltering technique.

In the case of digital order track-ing, the situation is not asstraightforward since the data hasalready been anti-alias filteredand digitized at some fixed rate.The digital resampling process ac-tually accomplishes two func-tions; first it provides the variablesample rates. Second, it providesthe variable frequency low passfiltering (in conjunction with thefixed filtering of the DSA’s digitaland analog anti-alias filters)required for adequate alias pro-tection. External sampling imple-mentations must handle theanti-alias filtering as a separatestep; normally adding a separateanalog tracking filter to the input.

As described in the previous sec-tion, the desired sampling timeswere calculated based on thetachometer pulses and a linearacceleration model. In general,these times will lay between twofixed rate samples and an esti-mate must be made of the ampli-tude at the desired time based onexisting data. The fixed sampledata is buffered in computermemory so, again, we can lookboth ahead and back in time atthe data to estimate the newresampled value. The simplestscheme would be to use linearinterpolation between the twoneighboring points. Though thiswould work to some extent, it’sapparent from Figure A-8 that sig-nificant errors can be introduced.

This approach would lead to am-plitude errors and a severe limita-tion on the system’s dynamicrange. In the case of simple linearinterpolation, an amplitude errorof 10% and an effective dynamicrange of only 26 dB would be real-izable. To reduce this error andincrease the dynamic range, it’snecessary to use more data inevaluating our resampled ampli-tude. The current implementationutilizes ten neighboring datapoints (five before and five afterthe resample time) to calculatethe resample data point, formulat-ed as a finite impulse response(FIR) filter (Figure A-9).

Theoretically, this formulationwould lead to amplitude accuracyof .08% and a dynamic range ofapproximately 104 dB. To im-prove speed, the actual filter isimplemented as a look-up tablein memory, which leads to someround-off errors yielding the de-sired 80 dB dynamic range.

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Example Measurements

To demonstrate the digitalimplementation under realisticconditions, run-up tests were per-formed on an automobile utilizingmoderate run-up rates. The datawas actually digitally recordedand analyzed using traditional ex-ternal sampling/ratio synthesistechniques as well as the digitalresampling technique. The follow-ing plots illustrate the differencesbetween the two techniques.

In Figure A-12A the ramp rateswere not particularly fast nor theorder analysis very high, whichare the conditions where the com-puted method would normally beexpected to perform better. Inspite of the low ramp rate, theautomobile engine RPM was notparticularly steady and would“jitter” about its average value.The traditional method’s phaselock loop tended to average thesevariations and consequently re-sulted in some loss of resolution.Figure A-10 is the computed ordertracking measurement and thehalf and odd number orders arequite clear as are the dominanteven order, which would be ex-pected from a four-cylinder, four-cycle engine. Also visible is the60 Hz noise component, which islost in Figure A-11.

Figure A-11 is a similar measure-ment using external samplingand a tracking ratio synthesizerwith a tracking low-pass filter.The conditions have been set togive equivalent resolution andlow-amplitude orders are muchless distinct and the 60 Hz is notdiscernible.

The differences can be attributedto phase lock loop delay. Refer-ence [36] further illustrates thisby examining the ability of a ratiosynthesizer to track a square

Figure A-10Order ratio mapof an automobilerun-up with afour-cylinder,four-cycle engineutilizing comput-ed resampling.

Figure A-11Order ratio maputilizing externalsampling anda PLL ratiosynthesizer.

wave swept at known rates.Figure A-12a and b illustrate theorder tracking capability of thedigital technique which includesphase information. The FIR filter

used in the digital implementationhas essentially no phase shift ortime delay allowing accuratephase measurements.

Figure A-12Order trackmeasurementmade usingdigital resamplingtechniques.(a) Time vs RPM(b) Amplitude oftwo order vs RPMand (c) Phase oftwo order vs RPM.

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Glossary

Acceleration. The time rate ofchange of velocity. Typical unitsare ft/s/s, meters/s/s, and G’s(1G = 32.17 ft/s/s = 9.81 m/s/s).Acceleration measurements areusually made with accelerom-eters.

Accelerometer. Transducerwhose output is directly propor-tional to acceleration. Most com-monly use piezoelectric crystalsto produce output.

Aliasing. A phenomenon whichcan occur whenever a signal isnot sampled at greater than twicethe maximum frequency compo-nent. Causes high frequency sig-nals to appear at low frequencies.Aliasing is avoided by filteringout signals greater than 1/2 thesample rate.

Alignment. A condition wherebythe axes of machine componentsare either coincident, parallel orperpendicular, according to de-sign requirements.

Amplification Factor (Syn-

chronous). A measure of thesusceptibility of a rotor to vibra-tion amplitude when rotationalspeed is equal to the rotor naturalfrequency (implies a flexible ro-tor). For imbalance type excita-tion, synchronous amplificationfactor is calculated by dividingthe amplitude value at the reso-nant peak by the amplitude valueat a speed well above resonance(as determined from a plot of syn-chronous response vs. rpm).

Amplitude. The magnitude ofdynamic motion or vibration. Am-plitude is expressed in terms ofpeak-to- peak, zero-to-peak, orrms. For pure sine waves only,these are related as follows: rms= 0.707 times zero-to-peak; peak-to-peak = 2 times zero-to-peak.DSAs generally display rms forspectral components, and peakfor time domain components.

Anti-Aliasing Filter. A low-pass filter designed to filter outfrequenices higher than 40% thesample rate in order to preventaliasing.

Anti-Friction Bearing. See Roll-ing Element Bearing.

Asymetrical Support. Rotorsupport system that does not pro-vide uniform restraint in all radialdirections. This is typical formost heavy industrial machinerywhere stiffness in one plane maybe substantially different thanstiffness in the perpendicularplane. Occurs in bearings by de-sign, or from preloads such asgravity or misalignment

Asynchronous. Vibration com-ponents that are not related to ro-tating speed (also referred to asnonsynchronous).

Attitude Angle (Steady-State).The angle between the directionof steady-state preload throughthe bearing centerline, and a linedrawn between the shaft center-line and the bearing centerline.(Applies to fluid-film bearings.)

Auto Spectrum (Power Spec-

trum). DSA spectrum displaywhose magnitude represents thepower at each frequency, andwhich has no phase. Rms averag-ing produces an auto spectrum.

Averaging. In a DSA, digitallyaveraging several measurementsto improve accuracy or to reducethe level of asynchronous compo-nents. Refer to definitions of rms,time, and peak-hold averaging.

Axial. In the same direction asthe shaft centerline.

Axial Position. The average po-sition, or change in position, of arotor in the axial direction withrespect to some fixed referenceposition. Ideally the reference is aknown position within the thrustbearing axial clearance or floatzone, and the measurement ismade with a displacement trans-ducer observing the thrust collar.

Balancing Resonance

Speed(s). A rotative speed thatcorresponds to a natural reso-nance frequency.

Balanced Condition. For rotat-ing machinery, a condition wherethe shaft geometric centerline co-incides with the mass centerline.

Balancing. A procedure for ad-justing the radial mass distribu-tion of a rotor so that the masscenterline approaches the rotorgeometric centerline.

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Band-Pass Filter. A filter with asingle transmission band extend-ing from lower to upper cutofffrequencies. The width of theband is determined by the separa-tion of frequencies at whichamplitude is attenuated by3 dB (0.707).

Bandwidth. The spacing be-tween frequencies at which aband-pass filter attenuates thesignal by 3 dB. In a DSA, mea-surement bandwidth is equal to[(frequency span)/(number of fil-ters) x (window factor)]. Windowfactors are: 1 for uniform, 1.5 forHanning, and 3.63 for flat top.

Baseline Spectrum. A vibrationspectrum taken when a machineis in good operating condition;used as a reference for monitor-ing and analysis.

Blade Passing Frequency. Apotential vibration frequency onany bladed machine (turbine,axial compressor, fan, etc.).It is represented by the numberof blades times shaft-rotatingfrequency.

Block Size. The number of sam-ples used in a DSA to computethe Fast Fourier Transform.Also the number of samples ina DSA time display. Most DSAsuse a block size of from 250 to8192. Smaller block size reducesresolution.

Bode Plot. Rectangular coordi-nate plot of 1x component ampli-tude and phase (relative to akeyphasor) vs. running speed.

BPFO, BPFI. Common abbrevia-tions for ball pass frequency ofdefects on outer and inner bear-ing races, respectively.

Bow. A shaft condition such thatthe geometric centerline of theshaft is not straight. Also calledshaft sag.

Brinneling (False). Impres-sions made by bearing rollingelements on the bearing race;typically caused by externalvibration when the shaft isstationary.

Calibration. A test during whichknown values of the measuredvariable are applied to the trans-ducer or readout instrument, andoutput readings varied or ad-justed.

Campbell Diagram. A mathe-matically constructed diagramused to check for coincidence ofvibration sources (i.e. 1 x imbal-ance, 2 x misalignment) with ro-tor natural resonances. The formof the diagram is a rectangularplot of resonant frequency(y-axis) vs excitation frequency(x-axis). Also known as an inter-ference diagram.

Cascade Plot. See Spectral Map.

Cavitation. A condition whichcan occur in liquid-handling ma-chinery (e.g. centrifugal pumps)where a system pressure de-crease in the suction line andpump inlet lowers fluid pressureand vaporization occurs. The re-sult is mixed flow which mayproduce vibration.

Center Frequency. For abandpass filter, the center of thetransmission band.

Charge Amplifier. Amplifierused to convert accelerometeroutput impedance from high tolow, making calibration muchless dependent on cable capaci-tance.

Coherence. The ratio of coher-ent output power between chan-nels in a dual-channel DSA. Aneffective means of determiningthe similarity of vibration at twolocations, giving insight into thepossibility of cause and effect re-lationships.

Constant Bandwidth Filter. Aband-pass filter whose bandwidthis independent of center fre-quency. The filters simulateddigitally in a DSA are constantbandwidth.

Constant Percentage Band-

width. A band-pass filter whosebandwidth is a constant percent-age of center frequency. 1/3octave filters, including thosesynthesized in DSAs, are constantpercentage bandwidth.

Critical Machinery. Machineswhich are critical to a major partof the plant process. These ma-chines are usually unspared.

Critical Speeds. In general, anyrotating speed which is associ-ated with high vibration ampli-tude. Often, the rotor speedswhich correspond to naturalfrequencies of the shaft or thesystem.

Critical Speed Map. A rectan-gular plot of system natural fre-quency (y-axis) versus bearing orsupport stiffness (x-axis).

Cross Axis Sensitivity. A mea-sure of off-axis response of veloc-ity and acceleration transducers.

Cycle. One complete sequence ofvalues of a periodic quantity.

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Damping. The quality of a me-chanical system that restrains theamplitude of motion with eachsuccessive cycle. Damping ofshaft motion is provided by oil inbearings, seals, etc. The dampingprocess converts mechanical en-ergy to other forms, usually heat.

Damping, Critical. The smallestamount of damping required to re-turn the system to its equilibriumposition without oscillation.

Decibels (dB). A logarithmicrepresentation of amplitude ratio,defined as 20 times the base tenlogarithm of the ratio of the mea-sured amplitude to a reference.dB readings, for example, are ref-erenced to 1 volt rms. dB or Logamplitude scales are required todisplay the full dynamic range ofa DSA.

Degrees Of Freedom. A phraseused in mechanical vibration todescribe the complexity of thesystem. The number of degreesof freedom is the number of inde-pendent variables describing thestate of a vibrating system.

Digital Filter. A filter whichacts on data after it has beensampled and digitized. Often usedin DSAs to provide anti-aliasingprotection after internal re-sam-pling.

Differentiation. Representationin terms of time rate of change.For example, differentiating ve-locity yields acceleration. In aDSA, differentiation is performedby multiplication by jw, wherew is frequency multiplied by 2p.(Differentiation can also be usedto convert displacement to veloc-ity.)

Discrete Fourier Transform. Aprocedure for calculating discretefrequency components (filters orlines) from sampled time data.Since the frequency domain resultis complex (i.e., real and imagi-nary components), the number ofpoints is equal to half the numberof samples.

Displacement. The change indistance or position of an objectrelative to a reference.

Displacement Transducer. Atransducer whose output is pro-portional to the distance betweenit and the measured object (usu-ally the shaft).

DSA. See Dynamic Signal Ana-lyzer.

Dual Probe. A transducer setconsisting of displacement andvelocity transducers. Combinesmeasurement of shaft motionrelative to the displacement trans-ducer with velocity of the dis-placement transducer to produceabsolute motion of the shaft.

Dual Voting. Concept wheretwo independent inputs are re-quired before action (usually ma-chine shutdown) is taken. Mostoften used with axial positionmeasurements, where failure of asingle transducer might lead to anunnecessary shutdown.

Dynamic Motion. Vibratory mo-tion of a rotor system caused bymechanisms that are active onlywhen the rotor is turning atspeeds above slow roll speed.

Dynamic Signal Analyzer

(DSA). Vibration analyzer thatuses digital signal processing andthe Fast Fourier Transform to dis-play vibration frequency compo-nents. DSAs also display the timedomain and phase spectrum, andcan usually be interfaced to acomputer.

Eccentricity, Mechanical. Thevariation of the outer diameter ofa shaft surface when referencedto the true geometric centerlineof the shaft. Out-of-roundness.

Eccentricity Ratio. The vectordifference between the bearingcenterline and the average steady-state journal centerline.

Eddy Current. Electrical cur-rent which is generated (and dis-sipated) in a conductive materialin the presence of an electromag-netic field.

Electrical Runout. An error sig-nal that occurs in eddy currentdisplacement measurementswhen shaft surface conductivityvaries.

Engineering Units. In a DSA,refers to units that are calibratedby the user (e.g., in/s, g’s).

External Sampling. In a DSA,refers to control of data samplingby a multiplied tachometer signal.Provides a stationary display ofvibration with changing speed.

Fast Fourier Transform (FFT).A computer (or microprocessor)procedure for calculating discretefrequency components from sam-pled time data. A special case ofthe discrete Fourier transformwhere the number of samples isconstrained to a power of 2.

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Filter. Electronic circuitry de-signed to pass or reject a specificfrequency band.

Filtered Orbit. An orbit dia-gram in which the vertical andhorizontal displacement signalshave been filtered. This is nor-mally a bandpass filter centeredat a running speed, however, digi-tal systems are capable of mul-tiple bandpass regions.

Finite Element Modeling. Acomputer aided design techniquefor predicting the dynamic behav-ior of a mechanical system priorto construction. Modeling can beused, for example, to predict thenatural frequencies of a flexiblerotor.

Flat Top Filter. DSA windowfunction which provides the bestamplitude accuracy for measuringdiscrete frequency components.

Fluid-Film Bearing. A bearingwhich supports the shaft on a thinfilm of oil. The fluid-film layermay be generated by journal rota-tion (hydrodynamic bearing), orby externally applied pressure(hydrostatic bearing).

Forced Vibration. The oscilla-tion of a system under the actionof a forcing function. Typicallyforced vibration occurs at the fre-quency of the exciting force.

Free Vibration. Vibration of amechanical system following aninitial force — typically at one ormore natural frequencies.

Frequency. The repetition rateof a periodic event, usually ex-pressed in cycles per second(Hz), revolutions per minute(rpm), or multiples of a rotationalspeed (orders). Orders arecommonly referred to as 1x for

rotational speed, 2x for twicerotational speed, etc.

Frequency Response. Theamplitude and phase responsecharacteristics of a system.

G. The value of acceleration pro-duced by the force of gravity.

Gear Mesh Frequency. A poten-tial vibration frequency on anymachine that contains gears;equal to the number of teeth mul-tiplied by the rotational frequencyof the gear.

Hanning Window. DSA windowfunction that provides better fre-quency resolution than the flattop window, but with reducedamplitude accuracy.

Harmonic. Frequency compo-nent at a frequency that is an inte-ger multiple of the fundamentalfrequency.

Heavy Spot. The angular loca-tion of the imbalance vector at aspecific lateral location on ashaft. The heavy spot typicallydoes not change with rotationalspeed.

Hertz (Hz). The unit of fre-quency represented by cycles persecond.

High Spot. The angular locationon the shaft directly under the vi-bration transducer at the point ofclosest proximity. The high spotcan move with changes in shaftdynamics (e.g., from changes inspeed).

High-Pass Filter. A filter with atransmission band starting at alower cutoff frequency and ex-tending to (theoretically) infinitefrequency.

Hysteresis. Non-uniqueness inthe relationship between twovariables as a parameter in-creases or decreases. Also calleddeadband, or that portion of asystem’s response where achange in input does not producea change in output.

Imbalance. Unequal radialweight distribution on a rotor sys-tem; a shaft condition such thatthe mass and shaft geometriccenterlines do not coincide.

Impact Test. Response testwhere the broad frequency rangeproduced by an impact is used asthe stimulus. Sometimes referredto as a bump test.

Impedance, Mechanical. Themechanical properties of a ma-chine system (mass, stiffness,damping) that determine the re-sponse to periodic forcing func-tions.

Influence Coefficients. Mathe-matical coefficients that describethe influence of system loadingon system deflection.

Integration. A process produc-ing a result that, when differenti-ated, yields the original quantity.Integration of acceleration, forexample, yields velocity. Integra-tion is performed in a DSA by di-viding by jw, where w isfrequency multiplied by 2p. (Inte-gration is also used to convert ve-locity to displacement).

Journal. Specific portions of theshaft surface from which rotor ap-plied loads are transmitted tobearing supports.

Keyphasor. A signal used in ro-tating machinery measurements,generated by a transducer observ-ing a once-per-revolution event.

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The keyphasor signal is used inphase measurements for analysisand balancing.

Lateral Location. The definitionof various points along the shaftaxis of rotation.

Lateral Vibration. See RadialVibration.

Leakage. In DSAs, a result of fi-nite time record length that re-sults in smearing of frequencycomponents. Its effects aregreatly reduced by the use ofweighted window functions suchas flat top and Hanning.

Linearity. The response charac-teristics of a linear system remainconstant with input level. That is,if the response to input a is A, andthe response to input b is B, thenthe response of a linear system toinput (a + b) will be (A + B). Anexample of a non-linear system isone whose response is limited bymechanical stop, such as occurswhen a bearing mount is loose.

Lines. Common term used todescribe the filters of a DSA (e.g.,400 line analyzer).

Linear Averaging. See TimeAveraging.

Low-Pass Filter. A filter whosetransmission band extends fromdc to an upper cutoff frequency.

Mechanical Runout. An error inmeasuring the position of theshaft centerline with a displace-ment probe that is caused byout-of-roundness and surfaceimperfections.

Micrometer (MICRON). Onemillionth (.000001) of a meter.(1 micron = 1 x E-6 meters @0.04 mils.)

MIL. One thousandth (0.001) ofan inch. (1 mil = 25.4 microns.)

Modal Analysis. The process ofbreaking complex vibration intoits component modes of vibration,very much like frequency domainanalysis breaks vibration down tocomponent frequencies.

Mode Shape. The resultant de-flected shape of a rotor at a spe-cific rotational speed to anapplied forcing function. A three-dimensional presentation of rotorlateral deflection along the shaftaxis.

Modulation, Amplitude (AM).The process where the amplitudeof a signal is varied as a functionof the instantaneous value of an-other signal. The first signal iscalled the carrier, and the secondsignal is called the modulatingsignal. Amplitude modulation pro-duces a component at the carrierfrequency, with adjacent compo-nents (sidebands) at the fre-quency of the modulating signal.

Modulation, Frequency (FM).The process where the frequencyof the carrier is determined by theamplitude of the modulating sig-nal. Frequency modulation pro-duces a component at the carrierfrequency, with adjacent compo-nents (sidebands) at the fre-quency of the modulating signal.

Natural Frequency. The fre-quency of free vibration of a sys-tem. The frequency at which anundamped system with a singledegree of freedom will oscillateupon momentary displacementfrom its rest position.

Nodal Point. A point of mini-mum shaft deflection in a specificmode shape. May readily changelocation along the shaft axis dueto changes in residual imbalanceor other forcing function, orchange in restraint such asincreased bearing clearance.

Noise. Any component of atransducer output signal that doesnot represent the variable in-tended to be measured.

Nyquist Criterion. Requirementthat a sampled system sample ata frequency greater than twicethehighest frequency to bemeasured.

Nyquist Plot. A plot of real ver-sus imaginary spectral compo-nents that is often used in servoanalysis. Should not be confusedwith a polar plot of amplitude andphase of 1x vibration.

Octave. The interval betweentwo frequencies with a ratio of2 to 1.

Oil Whirl/Whip. An unstablefree vibration whereby a fluid-film bearing has insufficient unitloading. Under this condition, theshaft centerline dynamic motionis usually circular in the directionof rotation. Oil whirl occurs at theoil flow velocity within the bear-ing, usually 40 to 49% of shaftspeed. Oil whip occurs when thewhirl frequency coincide with(and becomes locked to) a shaftresonant frequency. (Oil whirland whip can occur in any casewhere fluid is between twocylindrical surfaces.)

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Power Spectrum. See AutoSpectrum.

Preload, Bearing. The dimen-sionless quantity that is typicallyexpressed as a number from zeroto one where a preload of zero in-dicates no bearing load upon theshaft, and one indicates the maxi-mum preload (i.e., line contactbetween shaft and bearing).

Preload, External. Any of sev-eral mechanisms that can exter-nally load a bearing. This includes“soft” preloads such as processfluids or gravitational forces aswell as “hard” preloads from gearcontact forces, misalignment,rubs, etc.

Proximitor. See Oscillator/Demodulator.

Radial. Direction perpendicularto the shaft centerline.

Radial Position. The averagelocation, relative to the radialbearing centerline, of the shaftdynamic motion.

Radial Vibration. Shaft dynamicmotion or casing vibration whichis in a direction perpendicular tothe shaft centerline.

Real-Time Analyzer. SeeDynamic Signal Analyzer.

Real-Time Rate. For a DSA, thebroadest frequency span at whichdata is sampled continuously.Real-time rate is mostly depen-dent on FFT processing speed.

Rectangular Window. See Uni-form Window.

Orbit. The path of the shaftcenterline motion during rotation.The orbit is observed with an os-cilloscope connected to x and y-axis displacement transducers.Some dual-channel DSAs alsohave the ability to display orbits.

Oscillator-Demodulator. A sig-nal conditioning device that sendsa radio frequency signal to aneddy-current displacement probe,demodulates the probe output,and provides output signals pro-portional to both the average anddynamic gap distances. (Also re-ferred to as Proximitor, a BentlyNevada trade name.)

Peak Hold. In a DSA, a typeof averaging that holds the peaksignal level for each frequencycomponent.

Period. The time required fora complete oscillation or for asingle cycle of events. The recip-rocal of frequency.

Phase. A measurement of thetiming relationship between twosignals, or between a specific vi-bration event and a keyphasorpulse.

Piezoelectric. Any materialwhich provides a conversion be-tween mechanical and electricalenergy. For a piezoelectric crys-tal, if mechanical stresses areapplied on two opposite faces,electrical charges appear on someother pair of faces.

Polar Plot. Polar coordinate rep-resentation of the locus of the 1xvector at a specific lateral shaftlocation with the shaft rotationalspeed as a parameter.

Relative Motion. Vibration mea-sured relative to a chosen refer-ence. Displacement transducersgenerally measure shaft motionrelative to the transducer mount-ing.

Repeatability. The ability of atransducer or readout instrumentto reproduce readings when thesame input is applied repeatedly.

Resolution. The smallest changein stimulus that will produce a de-tectable change in the instrumentoutput.

Resonance. The condition ofvibration amplitude and phasechange response caused by acorresponding system sensitivityto a particular forcing frequency.A resonance is typically identifiedby a substantial amplitude in-crease, and related phase shift.

Rolling Element Bearing. Bear-ing whose low friction qualitiesderive from rolling elements(balls or rollers), with littlelubrication.

Root Mean Square (rms).Square root of the arithmetical av-erage of a set of squared instanta-neous values. DSAs perform rmsaveraging digitally on successivevibration spectra.

Rotor, Flexible. A rotor whichoperates close enough to, or be-yond its first bending criticalspeed for dynamic effects to influ-ence rotor deformations. Rotorswhich cannot be classified asrigid rotors are considered tobe flexible rotors.

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Rotor, Rigid. A rotor which op-erates substantially below its firstbending critical speed. A rigid ro-tor can be brought into, and willremain in, a state of satisfactorybalance at all operating speedswhen balanced on any two arbi-trarily selected correction planes.

RPM Spectral Map. A spectralmap of vibration spectra versusrpm.

Runout Compensation. Elec-tronic correction of a transduceroutput signal for the error result-ing from slow roll runout.

Seismic. Refers to an inertiallyreferenced measurement or ameasurement relative to freespace.

Seismic Transducer. A trans-ducer that is mounted on the caseor housing of a machine and mea-sures casing vibration relative tofree space. Accelerometers andvelocity transducers are seismic.

Signal Conditioner. A deviceplaced between a signal sourceand a readout instrument tochange the signal. Examples: at-tenuators, preamplifiers, chargeamplifiers.

Signature. Term usually appliedto the vibration frequency spec-trum which is distinctive and spe-cial to a machine or component,system or subsystem at a specificpoint in time, under specific ma-chine operating conditions, etc.Used for historical comparison ofmechanical condition over the op-erating life of the machine.

Slow Roll Speed. Low rotativespeed at which dynamic motioneffects from forces such as imbal-ance are negligible.

Spectral Map. A three-dimen-sional plot of the vibration ampli-tude spectrum versus anothervariable, usually time or rpm.

Spectrum Analyzer. An instru-ment which displays the fre-quency spectrum of an inputsignal.

Stiffness. The spring-like qualityof mechanical and hydraulic ele-ments to elasticity deform underload.

Strain. The physical deforma-tion, deflection, or change inlength resulting from stress(force per unit area).

Subharmonic. Sinusoidal quanti-ty of a frequency that is an inte-gral submultiple of a fundamentalfrequency.

Subsynchronous.Component(s) of a vibration sig-nal which has a frequency lessthan shaft rotative frequency.

Synchronous Sampling. In aDSA, it refers to the control ofthe effective sampling rate ofdata; which includes the pro-cesses of external sampling andcomputed resampling used inorder tracking.

Time Averaging. In a DSA, aver-aging of time records that resultsin reduction of asynchronouscomponents.

Time Record. In a DSA, the sam-pled time data converted to thefrequency domain by the FFT.Most DSAs use a time record of1024 samples.

Torsional Vibration. Amplitudemodulation of torque measured indegrees peak-to-peak referencedto the axis of shaft rotation.

Tracking Filter. A low-pass orband-pass filter which automati-cally tracks the input signal. Atracking filter is usually requiredfor aliasing protection when datasampling is controlled externally.

Transducer. A device for trans-lating the magnitude of one quan-tity into another quantity.

Transient Vibration. Tempo-rarily sustained vibration of a me-chanical system. It may consist offorced or free vibration or both.Typically this is associated withchanges in machine operatingcondition such as speed, load,etc.

Transverse Sensitivity. SeeCross-Axis Sensitivity.

Trigger. Any event which can beused as a timing reference. In aDSA, a trigger can be used to ini-tiate a measurement.

Unbalance. See Imbalance.

Uniform Window. In a DSA, awindow function with uniformweighting across the time record.This window does not protectagainst leakage, and should beused only with transient signalscontained completely within thetime record.

Vector. A quantity which hasboth magnitude and direction(phase).

Waterfall Plot. See SpectralMap.

82

Application Notes:

243 The Fundamentals of Signal

Analysis. The time, frequency,and modal domains are explainedwithout rigorous mathematics.Provides a block-diagram levelunderstanding of DSAs.

243-3 The Fundamentals of

Modal Testing. The basics ofstructural analysis presentedat a block diagram level ofunderstanding.

Machinery Monitoring:

1) Dodd, V.R. and East, J.R., The

Third Generation of Vibration

Surveillance, Minicourse notes,Machinery Monitoring and Analy-sis Meeting, Vibration Institute,Clarendon Hills, IL 1983.

2) Dodd, V.R., Machinery

Monitoring Update, SixthTurbomachinery SymposiumProceedings, Texas A&MUniversity, 1977.

3) Mitchell, John S., Machinery

Analysis and Monitoring, Sec-ond Edition, Penn Well Books,Tulsa, OK, 1993.

References:

4) Myrick, S.T., Survey Results

on Condition Monitoring of

Turbomachinery in the Petro-

chemical Industry; I. Protection

and Diagnostic Monitoring of

‘Critical’ Machinery, VibrationInstitute, 1982.

5) Tiedt, Brain, Economic

Justification for Machinery

Monitoring, Bently NevadaPublication L0377-00.

6) Wett, Ted, Compressor Moni-

toring Protects Olefins Plant’s

Reliability. Bently Nevada Publi-cation L0339-00.

7) Steward, R.M., The Specifica-

tion and Development of a Stan-

dard for Gearbox Monitoring,

Vibrations in Rotating Machinery,Mechanical Engineering Publica-tions Limited, Inc. London, 1980.

8) Berry, James E., Proven

Method for Specifing Spectral

Band Alarm Levels and Frequen-

cies Using Todays Predictive

Maintenance Software Systems,Technical Associates of Char-lotte, Inc., 1990.

Transducers:

9) Bently, Donald, Shaft Vibra-

tion Measurement and Analysis

Techniques, Noise and VibrationControl International, April, 1983.

10) Dranetz, Abraham I. andOrlacchio, Anthony W., Piezoel

electric and Piezoresistive Pick-

ups, in Shock and Vibration Hand-book, C.M. Harris and C.E. Crede,eds., McGraw-Hill, 1976.

11) Glitch: Definition of and

Methods for Correction, includ-

ing Shaft Burnishing to Remove

Electrical Runout, Bently NevadaApplication Note L0195-00,August 1978.

12) How to Minimize Electrical

Runout During Rotor Manufac-

turing, Bently Nevada Applica-tion Note L0197-00, July 1969.

13) Judd John, Noise in Vibra-

tion Monitoring, Measurementsand Control, June 1983.

14) REBAM (TM) - A Technical

Review, Bently Nevada Publica-tion, 5/83.

15) Stuart, John W., Retrofitting

Gas Turbines and Centrifugal

Compressors with Proximity

Vibration Probes, Bently NevadaPublication L0357-00, June 1981.

16) Wilson, Jon, Noise Suppres-

sion and Prevention in Piezo-

electric Transducer Systems,

Sound and Vibration, April 1979.

83

Vibration Analysis:

17) Ehrich, F.F., Sum and Differ-

ence Frequencies in Vibration of

High Speed Rotating Machinery,

Journal of Engineering for Indus-try, February 1972.

18) Eshleman, Ronald L., The

Role of Sum and Difference Fre-

quencies in Rotating Machinery

Fault Analysis, Vibrations inRotating Machinery, MechanicalEngineering Publications Limited,Inc., London, 1980.

19) Jackson, Charles, The Practi-

cal Vibration Primer, Gulf Pub-lishing Company, Houston, Texas,1979.

20) Steward, R.M., Vibration

Analysis As an Aid to the Detec-

tion and Diagnosis of Faults in

Rotating Machinery, I Mech E,C192/76, 1976.

21) Maxwell, J. Howard,Introduction Motor Magnetic

Vibration, Proceedings of theVibration Institute Machinery Vi-bration Monitoring and AnalysisMeeting, Houston, Texas, April1983, Vibration Institute,Clarendon Hills, IL.

22) Taylor, James I., An Update

of Determination of Antifriction

Bearing Condition by Spectral

Analysis, Vibration Institute,1981.

23) Taylor, James I., Identifica-

tion of Gear Defects by Vibration

Analysis, Vibration Institute,1979.

Fluid Film Bearings andRotor Dynamics:

24) Rieger, N.F. and Crofoot, J.F.,Vibrations of Rotating Machin-

ery, Vibration Institute, 1977.

25) Bently, Donald E., Oil Whirl

Resonance, Bently NevadaPublication L0324-01, July, 1981.

26) Ehrich, E.F., Indentification

and Avoidance of Instabilities

and Self-Excited Vibrations in

Rotating Machinery, ASMEPaper 72-DE-21.

27) Gunter, E.J., Rotor Bearing

Stability, Vibration Institute,1983.

28) Loewy, R.G. and Piarulli, V.J.,Dynamics of Rotating Shafts,The Shock and VibrationInformation Center, 1969.

29) McHugh, J.D., Principles

of Turbomachinery Bearings,

Proceedings of the 8thTurbomachinery Symposium,Texas A&M University.

30) Orbits, Bently NevadaApplications Notes.

Vibration Control:

31) Beranek, L.L., Noise and

Vibration Control, McGraw-HillBook Co., New York, NY, 1971.

32) Fundamentals of Balancing,

Schenck Trebel Corporation, DeerPark, NY, 1983.

33) Dodd, V.R., Total Alignment,Penn Well Books, Tulsa, OK,1975.

34) Gunter, E.J., Ed., Field

Balancing of Rotating Equip-

ment, Vibration Institute, 1983.

35) Hagler, R., Schwerdin, H., andEshleman, R., Effects of Shaft

Misalignment on Machinery

Vibration, Design News,January, 1979.

Digital Order Tracking:

36) Potter, Ron and Gibler, Mike,Computer Order Tracking

Obsoletes Older Methods, "SAENoise and Vibration Conference,May 16-18, 1989, pp 63-67.

37)Potter, Ron, A New Order

Tracking Method for Rotating

Machinery, Sound & VibrationSept 1990, pp30-34.

84

Index

Gears 22, 36, 47gearmesh frequency 34, 47, 55natural frequency 31, 36, 47, 63

Hanning Window (DSA) 55Heavy Spot (balancing) 8, 24High Spot 24Hewlett-Packard Interface Bus

(HP-IB) 51, 59

IEEE-488 Interface (HP-IB) 51Imbalance 27, 28, 33, 34, 35, 41, 44,

51, 56, 63Impulsive Signal Spectrum 19, 22,65Inner Race Defect 29Integration 13, 60

Keyphasor 15, 23, 24, 44, 63

Leakage (DSA) 55Looseness 22, 32, 35

Measurement Speed (DSA) 52Mechanical Impedance 8, 10, 17Misalignment 32, 34, 44, 45, 63Missing Blade Spectrum 38Multiple Rolling Element Bearing

Defects 32

Natural Frequencies 36, 38effect of mass and stiffness 11measurement of 65

1/3 Octave Analyzers 25, 56Oil Whirl 32, 33Oil Whip 33Orbits 62Order Tracking 48, 61, 62Outer Race Defect Frequency 20,

29, 30

Parallel Filter Analyzer 25Peak Average 57Phase 22, 23, 38

detecting misalignment 34measurement with

dual-channel DSA 63use in analysis 44

Pitch Diameter 29Predictive Maintenance 43

Proximity Probe (DisplacementTransducer) 12

Ratio Synthesizer 61, 66Real-Time Bandwidth 53Real-Time Comparisons 63Resonance 38Rigid Rotor 24Rotor Dynamics 5, 24Rotor, Cracked

(Induction Motor) 39RMS Averaging 57Runup Measurements 62Runup Tests 50, 52, 57

Severity Criteria 41, 42, 43Sidebands 21, 22, 30, 32, 36, 37, 38Speed Variation 27, 48, 49, 57, 58, 61Spectral Maps 19, 22, 47, 50Spectrum 3, 20, 22, 24Statistical Accuracy 50, 55, 57Sum and Difference Frequencies

19, 41, 46Swept Filter Analyzers 26Synchronous (Time) Averaging 57Synchronous Sample Control 48,

61, 62

Time Domain 19Transducer Installation Guidelines7Transfer Function Measurement 51Trend Analysis 43Truncation 35

Uniform Window (DSA) 55Units Calibration 60Units Conversion 51

Vane Passing Frequency 37Velocity Transducers 9, 11, 13Vibration Parameters 8, 9, 60

phase relationships 8variation in level with rpm 11

Waterfall 22, 47Window Function (DSA) 55

Zoom Analysis (DSA) 7, 54

Accelerometers 13, 14, 15Aliasing 56, 59, 61Anti-Friction Bearings 28Averaging 51, 53, 57

rms 57time 5, 46, 52, 53, 60, 62, 66peak hold 57

Balancing 24, 27Ball Spin Frequency 29Baseline Data 41, 50Bearing (rolling element)

Characteristic Frequencies 29BASIC program to calculate 29factors modifying 30example spectra 30

Blade Passing Frequency 37Bode Plot 62Bump Test 65

Cascade Plots (Spectral Maps,Waterfalls) 22, 47

Coastdown Tests 50, 55, 57, 58Coherence Function 64Computer Data Storage

and Analysis 59Contact Angle 30Critical Speed 24, 32, 33, 62

Differentiation 60Digital Plotters 51, 59Displacement Transducers 12Documentation 6, 41, 51Dual-Channel DSA 34, 45, 63, 65Dynamic Range 22, 28, 43, 51, 52,56

Eddy Current Probe 12Electrical Defects 39Engineering Units Calibration 60External Sample Control

(Synchronous Sample) 48, 60,61

Filtered Orbits 66, 67Flat Top Window (DSA) 55Flexible Rotor 17, 23, 32Fluid-Film Bearings 10, 32, 33, 38Frequency Domain 19, 20, 25Frequency Resolution 26, 54, 55Fundamental Train Frequency 30

85

Data subject to change.

Copyright © 1994, 1997

Hewlett-Packard Co.

12/97

5962-7276E

H

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