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30 IEEE Instrumentation & Measurement Magazine December 2004

Three-phase induction motors are the workhorses of industry because of theirwidespread use. They are used extensively for heating, cooling, refrigeration,pumping, conveyors, and similar applications. They offer users simple,rugged construction, easy maintenance, and cost-effective pricing. These fac-

tors have promoted standardization and development of a manufacturing infrastructurethat has led to a vast installed base of motors; more than 90% of all motors used inindustry worldwide are ac induction motors [1].

Causes of motor failures are bearing faults, insulation faults, and rotor faults [1], [2].Early detection of bearing faults allows replacement of the bearings, rather than replace-ment of the motor. For example, a 100 hp, three-phase ac motor costs approximatelyUS$7500. The replacement ball bearings for the same motor cost approximately US$250.The same type of bearing defects that plague such larger machines as 100 hp are mir-rored in lower hp machines, such as the machine in Figure 1, which has the same type of

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Michael J. Devaney and Levent Eren

© PHOTODISC

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bearings. A cutaway view of a 5 hp, two-pole ac inductionmachine, depicting the bearings and air-gap, is shown inFigure 1.

Even though the replacement of defective bearings is thecheapest fix among the three causes of failure, it is the mostdifficult one to detect. Motors that are in continuous usecannot be stopped for analysis. We have developed a cir-cuit monitor for these motors. Incipient bearing failures aredetectable by the presence of characteristic machine vibra-tion frequencies associated with the various modes of bear-ing failure. We will show that circuit monitors that wedeveloped can detect these frequencies using wavelet pack-et decomposition and a radial basis neural network. Thisdevice monitors an induction motor’s current and defines abearing failure.

Vibration AnalysisMachine vibration analysis is one of the most widely usedcondition monitoring techniques [4]. Vibration monitoring isvery effective in detecting bearing fault, but it requires addi-tional sensors to be fitted to the machines. While some largemotors may already come with vibration transducers, it isnot economically or physically feasible to provide the samefor smaller machines. This means that small- to medium-sizemotors must be checked periodically by portable equipmentthat moves from machine to machine.

Unfortunately, periodic checks by portable equipmentdo not provide continuous monitoring and does not guaran-tee accessibility. Some motors used in critical applications,such as nuclear reactor cooling pump motors, may not beeasily accessible during reactor operation. The Oak RidgeNational Laboratory in the United States directed the initialefforts in motor current signature analysis (MCSA) to pro-vide nonintrusive means for detecting the mechanical andelectrical abnormalities in both motor and driven equip-ment [5]. Schoen and Habetler showed that the relationshipof bearing vibration to the stator current spectrum can bedetermined by an equation based on Kliman’s work fordynamic eccentricity [2], [3]. The bearing fault related vibra-tion frequencies are easily calculated with known bearinggeometry and rotor speed. The vibration frequencies showup in the current spectrum as the modulation frequencies,therefore it is possible to provide continuous monitoringusing motor current data. The circuit monitors detect thesefrequencies using wavelet packet decomposition and a radi-al basis neural network.

Bearing FaultsBearing faults such as outer race, inner race, ball defect, andtrain defect cause machine vibration. These defects havevibration frequency components, fv, that are characteristic ofeach defect type. The mechanical vibration caused by thebearing defect results in air gap eccentricity. Oscillations in airgap length, in turn, cause variations in flux density. The varia-tions in flux density affect the machine inductances, whichproduce harmonics of the stator current. The characteristic

current frequencies, fCF, due to bearing characterist icvibration frequencies are calculate by

fCF = ∣∣ fe ± mfv

∣∣ . (1)

Here, the power system fundamental frequency, fe , becomesthe carrier frequency, and the vibration frequency becomes themodulation frequency.

December 2004 IEEE Instrumentation & Measurement Magazine 31

Fig. 2. Ball bearing geometry.

Pitch Diameter (PD)

Ball Diameter (BD)

Number of Balls (n)

Fig. 1. Cutaway view of a 5-hp, three-phase induction motor. Industry’s heavyreliance on induction machines in critical applications can cause very costlyproduction shut downs due to motor failures. In addition to monetary damageresulting from production loss, machinery replacement, and idled workforce,worker injuries may occur.

Variable Name Definitionfe Power system fundamental

frequencyfCF Characteristic current

frequencyfv Characteristic vibration

frequencyfOD Outer race defect frequencyfID Inner race defect frequencyfBD Ball defect frequencyfCD Cage defect frequencyn Number of ballsm Positive integer multiplier

CO

UR

TE

SY

OF

EM

ER

SO

N E

LEC

TR

IC


The characteristic vibration frequencies due to bearingdefects can be calculated given that the rotor speed and thebearing dimensions are available. The typical ball bearinggeometry is displayed in Figure 2.

Outer Race Defect FrequencyOuter race defect frequency, the ball passing frequency onthe outer race, is given by

fOD = n2

frm

(1 − BD

PDcos φ

). (2)

Rotor speed, frm, is in revolutions per minute. Figure 3shows both vibration and current spectrum of a ball bearingwith an outer race defect. The bearing outer race fundamen-tal defect frequency for the test ball bearing is 107.4 Hz at ano-load speed of 1798 r/min.

Inner Race Defect FrequencyInner race defect frequency, the ball passing frequency onthe inner race, is given by

fID = n2

frm

(1 + BD

PDcos φ

). (3)

Figure 4 shows both vibration and currentspectrum of a ball bearing with an innerrace defect. The bearing inner race funda-mental defect frequency for the test ballbearing is 167.3 Hz at a no-load speed of1798 r/min.

Ball Defective FrequencyBall defective frequency, the ball spin fre-quency, is given by

fBD = PD2BD

frm

(1 −

(BDPD

)2

cos2 φ

). (4)

Figure 5 shows both vibration and currentspectrum of a ball bearing with a ball defect.The bearing ball fundamental defect fre-quency for a 6205 ball bearing is 70.5 Hz at ano-load speed of 1798 r/min.

Cage Defect FrequencyCage defect frequency, caused by irregulari-ty in the train, is given by

fCD = 12

frm

(1 − BD

PDcos φ

). (5)

Figure 6 shows both vibration and currentspectrum of a ball bearing with a cagedefect. The bearing ball fundamental defectfrequency for a 6205 ball bearing is 18 Hz ata no-load speed of 1798 r/min.

Analysis of the Frequency SpectrumIn traditional MCSA, the frequency spec-trum of the steady-state motor current isanalyzed using the Fourier transform (FT).Then, the magnitudes of the characteristicfault frequencies are compared with base-line values to detect any deterioration inbearing health. The major advantage of thisapproach is its low computational com-plexity. However, it does not deal well


Fig. 3. Outer race fault. Frequency spectrums of both current and vibration data for an inductionmotor with a faulty shaft-end bearing.

0.04

0.03

0.02

0.01

0

Vibration and Current Spectrum for Outer Race Defect

500 100 150 200 250 300

Vib

ratio

n A

mpl

itude

0.06

0.05

0.04

0.03

0.02

0.01

0500 100 150 200 250 300

Cur

rent

Am

plitu

de

Frequency (Hz)

Fig. 4. Inner race fault. Frequency spectrums of both captured current and vibration data for aninduction motor with a faulty shaft-end bearing.

Vibration and Current Spectrum for Inner Race Defect

500 100 150 200 250 300

500 100 150 200 250 300

Frequency (Hz)

0.04

0.03

0.02

0.01

0

Vib

ratio

n A

mpl

itude

0.05

0.04

0.03

0.02

0.01

0

Cur

rent

Am

plitu

de


with nonstationary signals. Bearing defect frequencieschange with variations in rotor speed, and the stator cur-rent is nonstationary.

Another analysis tool, wavelet decomposition (WD), isalso available [6]. It provides a better treatment of nonsta-tionary signals, yet it does not have the resolution requiredfor harmonic analysis. The frequency separation achieved byWD is depicted in Figure 7.

Wavelet packet decomposition (WPD) provides a solu-tion to this, but the computational complexi-ty is high [7]. Therefore, it is important toselect filters with a minimal number of coef-ficients. The frequency separation achievedby WPD is depicted in Figure 8.

The WPD of the motor current signal is analternate approach. The wavelet packet trans-form (WPT) analysis permits tailoring of thefrequency bands to cover the range of bear-ing-defect-induced frequencies resulting fromrotor speed variations. Also, wavelet packettechniques provide better analysis of nonsta-tionary signals than Fourier techniques.

WPD of the Motor Current SignalThe basic steps of the algorithm are dis-played in Figure 9. First baseline data for themotor is collected with a healthy set of bear-ings. The motor current data are then cap-tured at user-determined intervals to checkthe status of bearings. The stator current datais notch filtered to suppress both the powersystem harmonics and rotor eccentricity fre-quency components. Then, the signal isdecomposed into 7.5 Hz frequency bandsusing the fast wavelet packet algorithm. Theall-pass implementation of elliptic half-bandfilters is used in the fast wavelet packet filteralgorithm. The resulting wavelet packet coef-ficients are used to calculate the root meansquare (rms) values for defect frequencybands. Finally, rms values for defect frequen-cy bands are compared to baseline data todetect bearing faults and identify the type ofthe fault. Figure 10 plots wavelet packet coef-ficients for a healthy and a faulty (outer racefault) bearing.

Since the motor current amplitude willincrease with increased load, the bearingbaseline data should be collected with ahealthy set of bearings under varying loadconditions. The baseline data can then becategorized under various load condi-tions. As a result, the possibility of misde-tection due to an increase in load currentcan be minimized.

In the succeeding data analysis, the baseline data cate-gory to be used can be chosen by determining the rotorspeed from the captured data. The rotor speed sidebandsshow up in the current spectrum due to rotor eccentrici-ties. All motors have some degree of rotor eccentricity,permitting possible speed detection. The speed resolutiondepends on the length of the current data. Once the speedis determined, the torque can be estimated from the curveof torque versus speed with reasonable accuracy.


Fig. 5. Ball fault. Frequency spectrums of both captured current and vibration data for aninduction motor with a faulty shaft-end bearing.

0.04

0.03

0.02

0.01

0

Vibration and Current Spectrum for Ball Defect

500 100 150 200 250 300

Vib

ratio

n A

mpl

itude

0.06

0.05

0.04

0.03

0.02

0.01

0500 100 150 200 250 300

Cur

rent

Am

plitu

de

Frequency (Hz)

Fig. 6. Cage fault. Frequency spectrums of both current and vibration data for an induction motorwith a faulty shaft-end bearing.

0.04

0.03

0.02

0.01

0

Vibration and Current Spectrum for Cage Defect

500 100 150 200 250 300

Vib

ratio

n A

mpl

itude

0.06

0.05

0.04

0.03

0.02

0.01

0500 100 150 200 250 300

Cur

rent

Am

plitu

de

Frequency (Hz)



The sampled current data containspower system harmonics, as well asfrequency components resulting fromrotor eccentricity. The induced fre-quency components in the stator cur-rent spectrum from a bearing fault aresignificantly smaller than the powersystem harmonics. Therefore, prepro-cessing the current signal suppressesthe power system harmonics before thesignal is decomposed into 7.5 Hz pack-ets using the fast wavelet packet algo-rithms. A second-order notch filter suppresses the powersystem harmonics.

An all-pass implementation of an elliptic half-band infi-nite impulse response (IIR) filter decomposes the notch-fil-tered current data into 7.5 Hz wavelet packets. After thesignal is decomposed into 7.5 Hz packets, wavelet packet

coefficients are used to calculate therms values. The wavelet packet coeffi-cients, dp

j,k, can be used to calculate therms value of any node (p, j)

xrms( j, p) =√∑

k

(dp

j,k

)2. (6)

The new readings are comparedwith baseline readings to determineany degradat ion in the bear ing

health. Usually, readings may be flagged as defectivethat are two standard deviations higher than the base-line readings.

The use of frequency bands minimizes the number of rmsvalues to be determined and provides better detection in caseof slight frequency variations that can be caused by changes inslippage. The reduced number of coefficients leads to simplersystems if detection algorithms are used. The use of frequencybands also overcomes the leakage problem that is caused bythe lack of resolution in fast FT (FFT) analysis.

Fig. 7. Wavelet decomposition.

2

2H(z)

G(z)

x(n)

y0(n)

y1(n)

y2(n)

H(z)

G(z)

Constant Relative Bandwith (WT)

f0 2f0 3f0 4f0 5f0 6f0 7f0 8f0

Frequency

Fig. 8. Wavelet packet decomposition.

2H(z)

G(z)

x(n)

H(z)

G(z)

y2(n)

y3(n)

y1(n)

y0(n)

H(z)

G(z)

f0 2f0 3f0 4f0 5f0 6f0 7f0 8f0

Frequency

Constant Bandwith (WPT)

2

Fig. 9. Basic steps of the algorithm.

Collect Current Data

Notch Filter PowerHarmonics

Wavelet PacketDecomposition

Calculate rms fromWP Coefficients

Collect Baseline Data

Compare with BaselineData

Significant Change

NoChange

Bearing faults

are the primary

cause of

three-phase

induction motor

failure.


Neural NetworksA neural network can improvethe fault detection rate. In addi-tion to improved accuracy, it isalso possible to detect and clas-sify different types of faultsusing neural networks, whichmay be useful in determiningthe cause of bearing failure.

A neurocomputing approachto information processinginvolves a learning process with-in an artificial neural networkthat adaptively responds toinputs according to a learningrule. A neural network must fol-low important topics that areuseful for complex problemsolving: nonlinearity, input-out-put mapping, adaptivity, evi-dential response, and imageprocessing.

This study used radial basisfunction neural networks(RBFNNs) to improve the proce-dure for detecting bearing fault.Figure 11 depicts the architectureof the RBFNN. The network consists of three layers: an inputlayer, a single layer of nonlinear processing neurons, and anoutput layer.

The RBFNN is a multilayer, feedforward network withthe hidden units containing the radial basis function, a statis-tical transformation based on a Gaussian distribution. Fewerhidden layers, one set of weights requirement, and fasterconvergence are advantages of RBFNNs over commonlyused multilayer perceptron neural networks.

The implementation of RBFNN to the bearing fault detec-tion resulted in 97% accuracy in the fault detection rate. Thetraining and testing of the neural network was based on actu-al field data from two types of faults: outer race and cagefaults. Outer race fault was introduced by drilling various sizeholes on the outer race of the shaft-end bearing, while thecage defect was created by causing deformation in the cage.

SummaryBearing faults are the primary cause of three-phase induc-tion motor failure. Incipient bearing failures are detectableby the presence of characteristic machine vibration frequen-cies associated with the various bearing failure modes. Thesevibrations modify the machine’s air-gap flux and thus serveto amplitude modulate its stator current. Current monitoringcan detect these vibrations.

Monitoring the induced current frequencies to detect thecharacteristic bearing failure involves suppressing the moredominant power system harmonics and then analyzing theremaining current spectrum. WPD provides a means to

assess this spectrum, which is less sensitive than the FT tovariations in the motor speed, which may result fromchanges in mechanical load or line voltage. A radial basisneural network then provides an effective means of detect-ing two common sources of bearing failure.

The migration of circuit monitors from the mains tobranch circuits for purposes of assessing power and powerquality has increased the likelihood that such a device ismonitoring an induction motor’s current. The ability tomonitor the motor bearing health via such a monitor thenbecomes a value added benefit.


Fig. 10. Outer race fault. WPC plots for race defect and no defect. WPCs for two different frequency bands;nodes, are plotted: 157.5–165 Hz and 165–172.5 Hz. Increased amplitude in node 23 for the bottom chart indicatesthe outer race fault.

23

22

0 50 100 150

No Defect

Outer Race Defect

21

23

22

21100500 150

Coefficient Number

Nod

e N

umbe

r

Fig. 11. Radial basis function neural network architecture.

wT∈Rm×n

y

y

Σ

Φ

Φ

ΦΣ

X

X

X

X

(continued on page 50)



ConclusionsUncertainty is a pervasive and persistent quality of real-timesystems. The total elimination of uncertainty is often impossi-ble, however, because of the complex nature of the systemsunder control. But rather than admit defeat, a proactiveapproach to mitigating uncertainty is needed. This approachstarts with acknowledging uncertainty’s existence and thenidentifying its possible causes so that the mitigation strategycan be designed.

Each mitigation strategy is a custom engineered solution.But whatever the solution, one thing is for certain; in real-time systems you will need to deal with uncertainty in itsmany forms.

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[4] M.G. Hinchey and J.P. Bowen, Industrial-Strength Formal Methods

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Phillip A. Laplante ([email protected]) received hisB.S., M.Eng.,A. and Ph.D. in computer science, electricalengineering, and computer science, respectively, fromStevens Institute of Technology and an M.B.A. from theUniversity of Colorado. He is an associate professor of soft-ware engineering at Penn State Great Valley GraduateCenter and codirector of the software engineering laborato-ry. His research interests span real-time and embedded sys-tems, software engineering, and image processing. He hasauthored numerous papers and 20 books, including Real-Time Systems Design and Analysis (IEEE/John Wiley). Hecofounded the journal Real-Time Imaging and serves on theeditorial boards of several journals and is editor-in-chief ofthe CRC Press Series on Image Processing. He is a memberof SPIE, IS&T, and ACM and a Senior Member of the IEEE.He is a registered professional engineer in the Common-wealth of Pennsylvania.

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Michael J. Devaney ([email protected]) is a professorof electrical and computer engineering at the University ofMissouri-Columbia. He is a member of IEEE Instrumentationand Measurement Society.

Levent Eren is an assistant professor of electrical and elec-tronics engineering at the University of Bahcesehir inIstanbul, Turkey. He is a member of IEEE Instrumentationand Measurement Society.

Detecting Faults continued from page 35
