1764 IEEE TRANSACTIONS ON MAGNETICS, VOL. 45, NO. 3, MARCH 2009

Comprehensive Eccentricity Fault Diagnosis in InductionMotors Using Finite Element Method

Jawad Faiz�, Bashir Mahdi Ebrahimi�, Bilal Akin�, and Hamid A. Toliyat�, Fellow, IEEE

School of Electrical and Computer Engineering, University of Tehran, Tehran 1439957131, IranDepartment of Electrical Engineering,Texas A&M University, College Station, TX 77843 USA

Load variation along with static and dynamic eccentricities degrees is one of the major factors directly affecting the dynamic behav-iors of eccentricity signatures as observed in the current spectrum of induction motors. Without taking the effect of load variation intoconsideration precisely, the change in the static and dynamic related fault signature amplitudes provides misleading information wherethe eccentricity degree and the load level exhibit similar effects in the current spectrum. In this paper, we address all these factors in aunified framework by analyzing various combinations both theoretically and experimentally. For this purpose, the time-stepping finiteelement method (TSFEM)-based, load-level-independent method is proposed to determine the static and dynamic eccentricities degreesindividually.

Index Terms—Fault diagnosis, induction motor, load variation, static and dynamic eccentricities, time-stepping finite element (TSFE).

I. INTRODUCTION

M ECHANICAL faults in electrical machines can occurdue to failure of mechanical parts such as gears and

bearings. Mechanical faults are common in electric machines,and represent up to 50%–60% of the faults. Bearing faults andeccentricity between the stator and the rotor are among the crit-ical and severe faults [1]. Conformity of the stator axis, rotoraxis, and rotor rotating axis are disturbed due to bearings fa-tigue and nonuniform air gap. Approximately, 80% of the me-chanical faults lead to the eccentricity [2]. It is to be notedthat eccentricity can result from manufacturing and assemblingprocess. There are three types of eccentricities: static, dynamic,and mixed. Fig. 1 shows the cross sections of the inductionmotor with different types of eccentricities. In the static eccen-tricity [Fig. 1(b)], the symmetrical axis of rotor coincides withthe rotor rotating axis, while the stator symmetrical axis is dis-placed with respect to the aforementioned axis. In this case,air-gap distribution is nonuniform but the minimum air-gap an-gular position is fixed. In the dynamic eccentricity [Fig. 1(c)],only the rotor symmetrical axis is displaced with respect to therotor rotation axis, which coincides with the stator symmetricalaxis. In the mixed eccentricity condition, both symmetrical androtor rotation axes are displaced with respect to the stator rota-tion axis.

Air-gap eccentricity in induction motors is usually detectedby analyzing the stator line current spectrum [3]–[6]. To diag-nose the static eccentricity (SE) and dynamic eccentricity (DE)using frequency spectrum of stator current, two fundamental pa-rameters need to be calculated: 1) frequency of sideband compo-nents due to fault, as a frequency pattern for fault diagnosis and2) sideband components amplitude due to fault, as a fault diag-nosis index [3]–[5]. Although the methods based on lumped pa-rameter models and analytical methods are able to calculate thefirst parameter correctly, the comparison of simulations and ex-perimental results shows large differences between the secondparameter in these methods [5], [6]. The reason for such con-siderable differences is the simplifications and approximationsused in the mentioned modeling methods. It is notable that the

Manuscript received October 07, 2008. Current version published February19, 2009. Corresponding author: J. Faiz (e-mail: jfaiz@ut.ac.ir).

Digital Object Identifier 10.1109/TMAG.2009.2012812

Fig. 1. Cross section of induction motor: (a) healthy, (b) static eccentricity, and(c) dynamic eccentricity.

type of eccentricity and variation of the load does also affectconsiderably the above mentioned parameters. Therefore, com-prehensive diagnosis of eccentricity in motor depends on recog-nition of eccentricity type and precise determination of its per-centage in different loads.

In this paper, in Section II, the induction motor under staticand dynamic eccentricities is modeled with high precisionusing time-stepping finite element method (TSFEM) and thestator current, needed for processing, is accurately calculated.In Sections III and IV, the diagnosis method of the staticeccentricity fault is presented along with determination of thestatic eccentricity percentage in different loads. Sections Vand VI study the diagnosis method of the dynamic eccentricityfault together with determination of its percentage in differentloads. The simulation results for a four-pole, 60-Hz, 230-Vmotor with 36 stator slots and 28 rotor slots are compared withthe experimental results. This comparison shows a very goodagreement between the prediction and test results.

II. MODELING AND ANALYZING ECCENTRICITY USING TSFEM

Almost all the reliable fault diagnosis methods are based ontwo items: considering the detailed real-world parameters andpractical conditions. A proper and precise modeling is the firststep in the diagnosis process. Precise modeling methods basedon field computation take the detailed machine structure intoaccount in order to obtain highly accurate results. In this paper,induction motor under static and dynamic eccentricities is mod-eled using TSFEM. In this modeling, the geometrical complex-ities of all parts of the motor such as stator, rotor, and shaft areincluded. Moreover, spatial distribution of the stator windings,permeance of nonuniform air gap, physical conditions of thestator conductors, rotor, shaft, and air gap, and nonlinearity ofthe core materials are taken into account. As input, three-phase

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FAIZ et al.: COMPREHENSIVE ECCENTRICITY FAULT DIAGNOSIS IN INDUCTION MOTORS USING FINITE ELEMENT METHOD 1765

Fig. 2. Flux density distribution in induction motor air gap: (a) healthy and(b) 30% SE.

Fig. 3. Normalized no-load line current spectrum of induction motor:(a) healthy (simulated), (b) healthy (experimental), (c) with 41% SE (simu-lated), and (d) with 41% SE (experimental).

TABLE IAMPLITUDES OF SIDEBAND COMPONENTS AT FREQUENCIES � � ��

IN DECIBELS FOR HEALTHY AND FAULTY MOTOR UNDER

DIFFERENT SE DEGREES (SIMULATION)

sinusoidal voltages are applied to the terminals of the motor.The transient equations of the external circuit and circuit ele-ments are combined with the field equations. In addition, themotion equations are combined with the field equations in thefinite element (FE) method. Also the motion equations are com-bined with these equations in the FE method. Solution of the setof equations gives the stator phase current as a principle vari-able.

When eccentricity occurs, the air-gap field consisting of thefundamental component, stator and rotor mmf harmonics, andstator and rotor slot permeances will have additional harmoniccomponents due to the fault. Meanwhile, the degree of the fun-damental harmonic and ripples vary with the type and eccen-tricity degree. Fig. 2 depicts the magnetic flux density distri-bution of the healthy and faulty motor under static and dynamiceccentricities. As shown in Fig. 2, eccentricity causes asymmet-rical magnetic flux density distribution. Field computation andanalysis shows that there is a particular frequency componentwithin the air-gap flux density waveform, which depends on theposition and number of rotor slots SE and DE as follows [7]:

(1)

where is the frequency component due to the prin-ciple slot harmonic (PSH), is an integer number, is the

Fig. 4. Normalized line current spectrum of induction motor with 41% SE (left:simulated; right: experimental): (a) 33%, (b) 66%, and (c) 100% rated load.

number of rotor slots, is an integer due to dynamic eccen-tricity, is the slip of the motor, is the number of main polepair, is the time harmonics present in the motor supply

, and is the supply fundamental frequency. Therotating flux waves at frequencies induce current sig-natures in the stator at the same frequency. Also, SE and DE in-ject more sideband components at frequencies with the pattern(2) into the stator current, which also can be used to diagnosethe static and mixed eccentricities

(2)

Therefore, considering (1) and (2), all the SE, DE, and mixedeccentricities observed in induction motor can be diagnosed inboth the low-frequency range (around current fundamental har-monic) and high-frequency range (around PSH).

III. STATIC ECCENTRICITY FAULT DIAGNOSIS USING SBCOMPONENTS AROUND FUNDAMENTAL HARMONIC

A. Diagnosis at Fixed Load

Fig. 3 shows the current spectrum of a healthy inductionmotor at no load and a motor with 41% SE around funda-mental harmonic. The SE increases the amplitude of sidebandcomponent at frequency 30.1 Hz, from 79 to 54 dB. Also,the corresponding values at frequency 89.9 Hz increase from

79 to 55 dB. Considerable increase in these amplitudesat frequency is a suitable index for fault diagnosis.Table I tabulates the amplitudes of the sidebands at frequencies

due to different static eccentricity degree (SED) atno load. According to Table I, when the SED is increased, theamplitude of the sideband components is increased as well;however, for a fixed load, the frequency of sideband compo-nents due to the fault at frequencies 31, 89, and118 Hz remain constant.

B. Diagnosis at Different Loads

Fig. 4 shows the stator current frequency spectrum for motorwith 41% SE at 33%, 66%, and 100% rated load. The corre-sponding experimental results confirm that the amplitudes ofthe harmonic components reduce due to the increasein the load. Comparison of Fig. 4(a) and (b) shows that a 33%increase in the load leads to a decrease in the amplitude of the

1766 IEEE TRANSACTIONS ON MAGNETICS, VOL. 45, NO. 3, MARCH 2009

TABLE IIAMPLITUDES OF SIDEBAND COMPONENTS OF� � �� FOR HEALTHY

AND FAULTY MOTOR UNDER SE AT DIFFERENT

LOADS IN DECIBELS (EXPERIMENTAL)

Fig. 5. Normalized high-frequency no-load line current spectrum of inductionmotor: (a) healthy and (b) 41% SE.

harmonic components from 54 to 60 dB. The cor-responding values are 55 to 57 dB for harmonic frequency

. However, the increase in the load does not reduce theamplitudes of the harmonics components at to a valuelower than the corresponding values in the healthy motor. Thefrequency spectra of a stator current with a 41% SE and 100%rated load are presented in Fig. 4(c). The decrease in the patternof sideband amplitudes at frequencies is due to the loadincrease, as shown in Fig. 4(c). Table II summarizes this fact forthe healthy and faulty motor under different loads.

IV. STATIC ECCENTRICITY FAULT DIAGNOSIS USING SIDEBAND

COMPONENTS AROUND PSH

A precise fault diagnosis and static SED determination can berealized when the healthy and faulty motors are compared underan identical load. Otherwise, there are some cases as shown inTable II where the amplitudes of sidebands at frequenciesof the healthy motor are larger than those of the faulty motor.Such a case is relevant to the conditions in which the healthymotor load is considerably less than that of the faulty motor.Therefore, the use of the amplitude of the sideband componentsat frequencies as an index is misleading without takingthe operating point into consideration.

A. Diagnosis at Fixed Load

Fig. 5 shows the frequency spectrum of a stator no-loadcurrent for healthy induction motor and motor with 41% SEaround PSH. The SE increases the amplitude of PSH at fre-quency 778 Hz, from 52 to 50 dB. A remarkable increasein this amplitude can be considered as a suitable tool for faultdiagnosis. Table III tabulates the amplitudes of the PSH due todifferent SED at rated load. When the SED is increased, theamplitude of the PSH increases as well; however, since the loadis fixed, the frequency of the PSH remains constant. As shownin Table III, increase of the SE increases the PSH amplitude.

B. Diagnosis at Different Loads

Fig. 6 shows the stator current frequency spectrum for amotor with 41% SE at 33% and 100% rated load. Comparisonof Fig. 6(a) and (b) shows that the increase in the load causesan increase in the PSH amplitude as such that it increases

TABLE IIIAMPLITUDES OF PSH IN DECIBELS FOR HEALTHY AND FAULTY MOTOR AT

RATED LOAD UNDER DIFFERENT STATIC ECCENTRICITY (SIMULATION)

Fig. 6. Normalized high-frequency line current spectrum of induction motorwith 41% SE: (a) 33% rated load, (b) 100% rated load.

TABLE IVAMPLITUDES OF PSH FOR HEALTHY MOTOR AND MOTOR WITH 41% STATIC

ECCENTRICITY FOR DIFFERENT LOADS IN DECIBELS (EXPERIMENTAL)

TABLE VAMPLITUDES OF SIDEBAND COMPONENTS AT FREQUENCIES � � ��

IN DECIBELS FOR HEALTHY AND FAULTY MOTOR UNDER DIFFERENT

DYNAMIC ECCENTRICITY DEGREES (SIMULATION)

from 41 to 30 dB. The increase of the PSH amplitude dueto the load increasing from 0% to 100% rated load has beenpresented in Table IV. Table IV summarizes the amplitude ofPSH amplitude of the healthy and faulty motor from no-load torated load.

V. DYNAMIC ECCENTRICITY FAULT DIAGNOSIS USING SBCOMPONENTS AROUND FUNDAMENTAL HARMONIC

Amplitudes of the sideband components at frequenciescan also be used to diagnose the dynamic eccentricity.

A. Diagnosis at Fixed Load

Amplitudes of the sideband components at frequenciesdue to the DE have been summarized in Table V. A notice-

able point in Table V is that the rate of increase of the sidebandcomponents at frequencies due to the fault and dynamiceccentricity degree (DED) is larger than that of the SE.

B. Diagnosis at Different Loads

Fig. 7(a) presents a 3-D diagram of the amplitude variationsof a sideband component at , for a healthy and faultymotor, under different DED, at different loads. Referring toFig. 7(a), it can be seen that a lower load and higher DEDincrease the harmonic component amplitude. Mean-while, the minimum amplitudes of harmonic components

FAIZ et al.: COMPREHENSIVE ECCENTRICITY FAULT DIAGNOSIS IN INDUCTION MOTORS USING FINITE ELEMENT METHOD 1767

Fig. 7. Amplitude variation of harmonic components versus DED and differentloads: (a) � � � and (b) the first dominant harmonic component around PSH�� �.

occur at the rated load and the minimum DED. Avery important point in Fig. 7(a) is that the minimum load andminimum DED have larger harmonic amplitude compared withthe rated load and maximum DED. It is obvious that at a fixedload, increase of the DED leads to the increase of the harmoniccomponents amplitude of . Also Fig. 7(a) indicatesthat increasing the load at a fixed DED adds to the harmoniccomponents amplitude of . Comparison of two lattercases in Fig. 7(a) indicates that there is a larger incremental rateof harmonic components amplitude of when the loadincreases while DED is fixed compared with the case in whichDED increases while the load is fixed. Regarding Fig. 7(a), itis noteworthy that commonly observed inherent eccentricity ininduction motors produces harmonic components with largeamplitudes. Neglecting this point will result in an error whenanalyzing and diagnosing the faulty motor. Although, thissection and Section IV confirm that the use of the amplitudeof the sideband components around the fundamental harmonicas the fault diagnosis index makes it possible to diagnose theeccentricity, the reason is that both eccentricities increase theamplitude of the sideband components around the fundamentalharmonic and knowing that both eccentricities have an identicaleffect upon the amplitudes of the sideband components atfrequencies , it is impossible to diagnose the type ofeccentricity.

VI. DYNAMIC ECCENTRICITY FAULT DIAGNOSIS USING

SIDEBAND COMPONENTS AROUND PSH

A. Diagnosis at Fixed Load

Referring to (1), the DE can also be diagnosed through ampli-tude of sideband components around PSH. Therefore, the fre-quencies used to diagnose the fault in a 28-bars, 60-Hz, four-poles motor with the no-load at arethe order of dynamic off centrality. In Table VI, the sidebandcomponents with frequencies to are obtained forabove mentioned . According to Table VI, the DE increasesthe amplitude of sideband components around PSH which canbe used for dynamic eccentricity. It is necessary to note that theSE and its degree cannot influence the amplitude of sidebandcomponents around PSH. So, the use of amplitude of sideband

TABLE VIAMPLITUDE OF SIDEBAND COMPONENTS AT FREQUENCIES AROUND PSH FOR

DIFFERENT DYNAMIC ECCENTRICITY DEGREES IN DECIBELS (SIMULATION)

components around PSH as a fault diagnosis index not only di-agnoses the eccentricity but also can determine the eccentricitytype. In spite of this, noise can affect this index and fault diag-nosis has error.

B. Diagnosis at Different Loads

Fig. 7(b) shows the amplitude of the first dominant harmoniccomponent around PSH for different loads and different DED.The peak of the harmonic amplitude is seen at the highest DEDand the rated load. On the other hand, the minimum harmonicamplitude is seen at the lowest DED and no-load. As shownin Fig. 6, an increase in the eccentricity degree and load con-sequently increase the amplitude of the sideband componentsaround PSH. The difference is that the rate of this increase withincrease of the eccentricity degree and fixed load is higher thanthe case in which the load increases and eccentricity degree isfixed.

VII. CONCLUSION

In this paper, the dynamic and static eccentricities were mod-eled and analyzed using TSFEM. The amplitude of sidebandcomponents around fundamental harmonic and PSH were usedto diagnose the fault. Use of the amplitude of sideband compo-nents around fundamental harmonic could be a fault diagnosisindex, however they have no use to detect the type of eccen-tricity. The use of the amplitude of the sideband components inPSH and around can not only diagnose the fault but also detectthe eccentricity type. However, the latter index is under influ-ence of noise, and therefore, the simultaneous use of the am-plitude of the sideband components at frequency andincrease of the corresponding value at PSH and around PSH canbe considered as a certain solution.

REFERENCES

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