Vibration and current monitoring fordetecting airgap eccentricity in large

induction motorsJ.R. Cameron, B.Sc W.T. Thomson, B.Sc, M.Sc, C.Eng., M.I.E.E.,

and A.B. Dow, C.Eng., M.I.E.E.

Indexing terms Motors, Induction motors

Abstract: The paper reports on a study carried out to detect airgap eccentricity in large 3-phase inductionmotors. The philosophy of using a unified online monitoring strategy is presented and the reasons for selectingline current and frame vibration as the monitored parameters are discussed. A theoretical analysis is presentedwhich predicts the presence of unique signature patterns in the current and vibration spectra which are onlycharacteristic of eccentricity. The theoretical predictions are verified by experimental results from a special faultproducing test rig and on-site tests in a power station.

List of principal symbols

ABeF

fsh

J sv

/ l

9'

knriPRSste'

eA

a<DCDr

COl

= area, m= flux density, T= off-centre displacement (absolute eccentricity), m= magnetomotive force, At= frequency of flux density or current slot harmonic,

Hz= frequency of vibration slot harmonic, Hz= supply frequency, Hz= effective mean airgap length in the presence of slot-

ting, m= constant= any integer= sum or difference of any two integers= number of pole pairs= number of rotor slots= number of stator slots= per unit slip= time variable, s= effective relative eccentricity = e/g'= space variable, rad= specific permeance (<S>/AF), Wb/At m2

= permeability of free space, H/m= radial force per unit area, N/m2

= flux, Wb= rotational speed, rad/s= angular supply frequency, rad/s

Subscriptsd,derts, sesastdr6sCO

corcos

= dynamic= rotor= static= saturation= stator= rotor space harmonic= stator space harmonic= time harmonic= rotor time harmonic= stator time harmonic

Paper 4448B, (PI, S6), first received 25th June 1985 and in final form 2nd January1986

Mr. Cameron and Mr. Thomson are with the School of Electronic and ElectricalEngineering, Robert Gordon's Institute of Technology, Schoolhill, AberdeenAB9 1FR, United Kingdom. Mr. Dow is with the South of Scotland ElectricityBoard Technical Services, Research and Development Centre, 45/47 HawbankRoad, College Milton North, East Kilbride, Glasgow, United Kingdom

IEE PROCEEDINGS, Vol. 133, Pt. B, No. 3, MAY 1986

1 Introduction

Large 3-phase induction motors are used in power stationsto drive main auxiliaries such as cooling water pumps, fansand boiler feed pumps. The sudden failure of a main aux-iliary drive can result in loss of prime generating capacityat critical times with consequent substantial cost penalties.It would be beneficial therefore to have some form ofonline monitoring for such motors to detect incipienttrouble and enable planned preventive maintenance orrepair to be carried out. Planned maintenance strategiesand machine condition monitoring have, of course, beenused in power stations for many years to ensure motorfailures are kept to a minimum. In general, this has beensuccessful but there is always the possibility of a failuredue to a fault which is difficult to detect even with existingmonitoring techniques. An example of this is a rubbetween the rotor and stator which can result in seriousdamage to the stator core and windings. The fundamentalcause may be due to overall bearing movement, rotorflexing due to dynamic disturbances, use of narrow airgapsfor high efficiency, or stator core movement. To prevent arub due to such a variety of conditions requires a monitor-ing strategy for the online detection of airgap variationsand other malfunctions such as drive misalignment,dynamic imbalance changes, coupling problems, brokenrotor bars and interturn faults in the stator winding. Inaddition, the transducers should be noninvasive so thatonline measurements can be taken with the minimum ofdisturbance to the normal operation of the power stationplant.

The content of this paper reports on a study carried outto detect airgap eccentricity using noninvasive transducersto monitor stator frame vibration and line current. Thetheoretical predictions are verified by experimental testsusing a special fault producing test rig and from on-sitemeasurements and the results show that unique signaturepatterns occur in the vibration and current spectra whichare characteristic of airgap eccentricity.

2 Previous research

Airgap eccentricity and unbalanced magnetic pull (UMP)have been researched since the beginning of this century;hence there is an abundance of published literature on thesubject. It would be impossible to review all the pub-lications in this paper and the reader is referred to two

155

ERA reports (Von Kaehne [1] in 1963 and Rai [2] in1974) for comprehensive reviews on the subject. Many ofthe classical papers have concentrated on the calculationof the airgap field as a function of eccentricity [3] andothers have identified the principal factors causing UMP,[4]. The design of rotor assemblies, critical speeds, slotcombinations, windings, vibration problems and the calcu-lation of vibratory forces and acoustic noise have all beenresearched in relation to airgap eccentricity and UMP[5-13]. However, the research has not been directed to thedevelopment of online diagnostics, but it could be arguedthat parameters were identified which were certainly func-tions of airgap eccentricity and UMP and that this shouldsuffice for the development of an online monitor. But it isthe unambiguous identification of airgap eccentricity in theindustrial environment which is required and, to theauthors' knowledge, this has not been satisfactorilyachieved. For example, Rai [2] verified that vibratoryforces at frequencies of 50 Hz, 100 Hz, and 200 Hz canvary due to eccentricity/UMP; however, these componentscan also change due to other malfunctions such as changesin dynamic imbalance, [14]. Leonard and Thomson [15]have verified that the 100 Hz, 200 Hz and 300 Hz com-ponents in the stator frame vibration are functions ofinterturn winding faults, single-phasing and voltage supplyimbalance. Consequently, fault descrimination is not pos-sible by monitoring these components in isolation. Ellisonand Yang [13] verified from tests carried out in ananechoic chamber that slot harmonics in the acoustic noisespectra from a small-power induction motor were func-tions of static eccentricity. However, the application ofnoise measurements in a power station to detect eccentric-ity is not practical due to the number of motors operatingin close proximity and too high background noise levels.Verma and Natarajan [16] have studied the changes in theairgap field as a function of static eccentricity using searchcoils in the stator core, but the installation of airgap searchcoils is neither practical nor economic for monitoring thecondition of auxiliary drive motors which are already inservice in power stations. Binns and Barnard [17] moni-tored the airgap flux and core vibration together and con-cluded that the use of two signals provided usefulinformation for machine analysis, but they did not presentresults for controlled variations in static or dynamic eccen-tricity. Penman et al. [18, 19] have clearly verified thataxial flux monitoring can identify stator winding faults andhave also shown that changes in the axial flux spectrumoccur due to eccentricity [19].

However, from the literature search carried out by theauthors and from numerous discussions with South ofScotland Electricity Board (SSEB) personnel, it was con-cluded that a choice of noninvasive monitoring techniquesfor detecting airgap eccentricity in industrial installationswas necessary. Consideration of methods suitable for thedetection of such eccentricity variations led to the selectionof motor current and stator frame vibration as the appro-priate signals for processing and investigation.

These quantities have the advantage that they can beeasily obtained by noninvasive measurement techniques.The verification of the techniques when applied to theindustrial environment was seen as an essential part of theresearch work.

3 Monitoring philosophy and theoretical principles

3.1 Unified monitoring strategyRotor movement in an induction motor is the result ofelectromagnetic interaction between the airgap flux pro-

156

duced by the 3-phase stator winding and the induced rotorcurrents. Radial magnetic forces are produced between therotor and stator surfaces and are proportional to the fluxdensity squared. These forces result in stator core andwinding vibration. As faults associated with rotor andstator windings and airgap variations alter the normalairgap flux waveform, quantities which are functions of theairgap flux will also change. This means that stator corevibration, line current and stray flux signals can be used tomonitor the condition of the motor. The philosophy of aunified monitoring strategy is that if several interrelatedsignals all indicate a particular fault, the operator is morelikely to believe the information in comparison to informa-tion obtained from one signal source. Previous research byThomson et al. [20, 21] has shown that malfunctions suchas broken rotor bars/high resistance joints, single-phasing,supply imbalance, and short-circuited coils in the statorwinding can be identified by an examination of the signalsmentioned above. However, vibration and current wereselected as the most suitable parameters because of theease with which accelerometers and current transformerscan be installed in an industrial environment.

3.2 EccentricityAirgap eccentricity can occur in the form of static ordynamic eccentricity. In the case of static eccentricity, theposition of minimum radial airgap length is fixed in space.For example, static eccentricity can be caused by statorcore ovality or incorrect positioning of the rotor or statorat the commissioning stage. Provided that the rotor-shaftassembly is sufficiently stiff, then the level of static eccen-tricity should not change. Dynamic eccentricity occurswhen the centre of the rotor is not at the centre of rotationand the minimum airgap revolves with the rotor. Thismeans that dynamic eccentricity is a function of space andtime. Dynamic eccentricity could be caused by a bentshaft, mechanical resonances at critical speeds, or bearingwear and movement. It is also possible that high levels ofstatic eccentricity can produce unacceptable levels of UMPwhich can result in shaft flexing and dynamic eccentricitythus increasing the risk of a rub between the rotor andstator.

3.3 Airgap flux distribution and current signalThe analysis is based on the rotating wave approachwhereby the magnetic flux waves in the airgap are taken asthe product of permeance and magnetomotive force(MMF) waves [22]. This means that the airgap field iscomplex and comprises the following components:

(a) fundamental(b) stator and rotor MMF harmonics(c) stator and rotor slot permeance harmonics(d) airgap eccentricity permeance harmonics(e) permeance harmonics due to saturation.

In the following analysis, the specific permeance A istermed as the permeance.

The permeance of an airgap bounded by a slotted statorand a smooth rotor is given by

Asf(0)= Z Ansf cos nstSd (1)

The permeance of an airgap bounded by a slotted rotorand a smooth stator is given by

Art(0, 0 = Z A"rr cos {nrtR(9 - (ort)} (2)

The resultant of these two permeances can be expressed as

IEE PROCEEDINGS, Vol. 133, Pt. B, No. 3, MAY 1986

the product of a constant and the values of the two per-meances [23]. The permeance of a slotted rotor and statorcan therefore be expressed by

oo oo

V JO, 0 = Z Z Anrt» nst COStin = 0 nsi = 0

x {(nrtR±nstS)d-nrtR(ort} (3)

In the presence of static eccentricity, the radial airgaplength is a function of space only. Assuming a smoothstator and rotor the permeance will be

Ase(0)= Z Anscos ns9 (4)

The magnitude of the harmonic permeance waves due tostatic eccentricity are found by Fourier analysis to be

s '(5)

where ns= 1, 2, 3 ...Eqn. 5 shows that as the level of static eccentricity

increases, the magnitude of Ans will also increase.The radial airgap length in the presence of dynamic

eccentricity is a function of space and time. The permeancecan thus be represented as

, t) = COS - 0>r 0 } (6)

Saturation can be represented by a permeance wave withtwice the number of poles and twice the frequency of thefundamental wave [24] because the airgap becomes effec-tively larger in the regions of maximum flux density.Hence, the permeance of a smooth and concentric airgapcombined with the effects of saturation is expressed as

ASfl(0, t) = cos {nsa(2P9 - 2(0, (7)

Combining eqns. 3, 4, 6 and 7 in the way in which thepermeances due to slotting were combined gives the totalpermeance as

OO 00 00 00 00

\0,(o,t)= Z Z Z Z Zn,( = 0 nsi = 0 ns = 0 n<i = O nsa = 0

x Anrt, nst, ns,nd, nsa

x cos {(nrt R ± nst S ± ns ± nd ± 2nsa p)0

-((nrtR±nd)(or±2nsacol)t} (8)

The magnetomotive force produced by the current flowingin the stator and rotor windings consists of a series ofspace and time harmonics. This can be represented by(neglecting phase angle and skew)

oo oorm{9, 0 = Z Z Fnos, "coS cos (n0sp9 -n^ffl j i

ngs = 1 fics = — oo

oo oo

+ Z Z Fn^.n.L^ t-^ vT' cor

f\Qf = 1 n w r = — oo^

x cos (n0rp9 - {n^so), + nOrpwr)t) (9)

The flux density distribution in the airgap is given as theproduct of the permeance and the MMF. Combiningeqns. 8 and 9 gives the resulting expression as:

B(9, t) = Z Bms, ^ s cos (ms9 - Clst) + Z Bmr> ^rms, fis m,, nr

x cos (mr 9 - Qr t) (10)

IEE PROCEEDINGS, Vol. 133, Pt. B, No. 3, MAY 1986

where

ms = nr,R± nstS±ns±nd± 2nsap ± n0sp

Qs = (nrtR ± nd)cor ± 2nMa)1 ±nmsco1

mr = nrtR± nstS ±ns±nd± 2nsap ± nOrp

Qr = (nrtR ±nd± n9rp)oir ± 2nsaco1 ± n^sca.

The flux density distribution varies in both space and timeand the time component gives expressions for predictingthe frequency content of the flux density waveform. Theseexpressions are expressed as follows:

fshl = {(nrt R ± nd) ± 2nsa ±

= {{nrtR ± nd±nerp)

±2nsa±n£Ors}/1

(11)

(12)

As these harmonic fluxes are moving relative to the stator,they should induce corresponding current harmonics inthe stationary stator winding. Hence it should be possibleto detect airgap eccentricity by analysing the stator currentspectrum.

3.4 Stator core vibrationThe radial force waves acting on the stator core structureare proportional to the square of the flux density wave-form [25]. In terms of the force per unit area, the forcewave distribution can be determined from:

o{9, t) =B2(9, t)

(13)

Substituting eqn. 10 into eqn. 13 gives:

o(9, t) = Z ™, O cos (m9 - Qt) (14)m, Q

where

m = n'rtR ± n'stS ± ris ± n'd ± 2n'sap ± n'ep

fi = (n'rtR ± n'd)cor ± 2^^, ± riOia>l

The time component of this expression gives an equationfor predicting the harmonic content of the vibrationforcing function and is expressed as:

fsv = ± ± 2n'sa ± n'Jf, (15)

These harmonic forces acting on the core will cause vibra-tion of the same frequency to be transmitted to the surfaceof the stator core. Hence the surface vibration signal willcontain frequency components characteristic of static anddynamic eccentricity.

A preliminary study by Thomson et al. [26] has shownthat one of the principal slot harmonics in the stator framevibration changed as a function of static eccentricity. Itwas observed that the change in the monitored parameterwas a function of the transducer position around the per-iphery of the frame. The initial results were encouragingand have led to a full investigation into the effectiveness ofstator frame vibration monitoring for detecting static anddynamic eccentricity.

4 Experimental test rig

A special fault producing test rig was designed to investi-gate the following malfunctions:

157

(a) static and dynamic airgap eccentricity(b) broken rotor bars and high resistance joints in cage

rotors(c) slip-ring rotor winding malfunction(d) stator winding faults.

Standard component parts were used to construct the testmachine which is based on a 3-phase, D160M, 50 Hz,11 kW induction motor design. All coil ends of the statorwinding were made accessible for pole changing and adynamometer loading machine was selected to test themotor between no-load and 130% full-load. Static eccen-tricity was introduced by controlled movement of thestator core and dynamic eccentricity achieved by machin-ing the rotor surface eccentric to the centre of rotation.Several rotors were therefore required for studyingdynamic eccentricity variations; however, the differentrotors used in the tests were turned to within ±0.5 thou(12.7 ^m) of the specified eccentricity level, thus keepingthe inherent eccentricity to a minimum. In addition, allrotors were balanced to the same degree after the dynamiceccentricity variations were introduced.

5 Experimental results

5.1 Laboratory testsThe line current was monitored via a clip-on current trans-former and the signal preprocessed using a high pass filterto reduce the magnitude of the dominant 50 Hz com-ponent. An accelerometer was used to sense the vibrationaround the periphery of the motor's outer frame whichwas an interference fit with the stator core assembly. Ahigh resolution spectrum analyser operating in the zoomanalysis mode was used to identify the predicted frequencycomponents. Experimental tests were conducted using 28and 51 slot cage rotors and the current and vibrationsignals examined as a function of static eccentricity from0% to 80%. The upper limit of 80% static eccentricity wasselected to prevent the possibility of an actual rotor-statorrub at this stage of the investigation. At the time ofwriting, variations in dynamic eccentricity between 0%and 50% could be investigated using a selection of 51 slotrotors. However, the results presented on dynamic eccen-tricity concentrate on the upper level of 50% to demon-strate the diagnostic technique. All tests were carried outwith the motor connected in the 4-pole mode and oper-ating at full-load torque and speed as per the manufac-turer's specification.

5.2 Line current: components associatedwith eccentricity

The effects of eccentricity on the current harmonics can beestablished by studying the corresponding flux densitycomponents. Consider the 28 slot rotor machine. With 36stator slots the fundamental slot permeance can beobtained by setting nst = nrt = 1 in eqn. 3, hence:

Art,st(0> 0 = An,, = 1, nst = 1 cos

x {(28±36)0-28wrt} (16)

The fundamental static eccentricity permeance wave isfound, from eqn. 4, to be

Ase(0) = An. = 1 cos 0 (17)

The resultant permeance due to slotting and static eccen-tricity is therefore

\t,st,se(6, t) = kxAnrt = l,nst= \Ans= 1

x cos {(28 ± 36 ± l)0-28corr} (18)

The fundamental MMF produced by the stator winding isgiven as

F(0, t) = Fnes = 1, nws = 1 cos (20 - co.t) (19)

Hence the flux density due to slotting, static eccentricityand the fundamental MMF is

B(6, t) = F(d, t)A(6, t)

B(6, t) = k2 Fngs = 1, nms = 1 Anrt = 1, nst = lAns = 1

x cos {(28 ± 36 ± 1 ± 2)0 - (28wr ± cot)t}

(20)

Eqn. 20 gives flux density waves which result in inducedstator current harmonics at 736 Hz and 636 Hz (full loads = 0.02). It can be seen that the components predicted forstatic eccentricity are in fact the principal slot harmonics.However, the magnitude of these components is pro-portional to the magnitude of the static eccentricity per-meance harmonic. Hence, an increase in static eccentricitywill produce an increase in the flux density and inducedstator current slot harmonics. A similar analysis can becarried out for dynamic eccentricity and the results showthat new frequency components occur in the frequencyspectrum which are unique to dynamic eccentricity.

In general, eqns. 11 and 12 can be used to predict thefrequency content of the current signal. For static eccen-tricity variations nd = 0 and, for dynamic eccentricityvariations, nd = 1, 2, A sample of the predicted fre-quency components due to eccentricity for the 28 and 51slot rotors is given in Table 1.

Table 1: Predicted frequency components in the line currentwith 28 and 51 slot rotors using eqn. 11

Rrotorslots

2851

= 50H;

sfull-loadslip

0.020.037

z.p = 2,nr

de

711.51254

t = ^ . n ( O S = ^ , n d

Frequency, Hz

psh

»s "rf = 0 , +naS

7361278

de

760.51302

de = dynamic eccentricity componentpsh = principal slot harmonic

The frequency spectra shown in Fig. 1 shows that thepredicted frequency component due to static eccentricity(736 Hz) increased by 12.9 dB with an introduction of80% eccentricity. This verifies the prediction that the prin-cipal slot harmonic should increase in magnitude with anincrease in static eccentricity. However, the componentswhich are functions of dynamic eccentricity also increased.For example, the 760.5 Hz component increased by 34 dB.This is an interesting result in that it suggests that dynamiceccentricity is associated with static eccentricity. Furthertests were conducted with lower levels of static eccentricity(0% to 60%) and the results shown in Fig. 2a indicate thatthe principal slot harmonics do not change significantly.However, the results shown in Fig. 2b indicate that thechange in a number of the dynamic eccentricity com-ponents is pronounced. For example, between 0% and60% static eccentricity the components at 811.5 Hz and911.5 Hz increased by a factor of 6 and 4.6, respectively.Hence, these particular tests have shown that static eccen-tricity variations result in significant increases in thedynamic eccentricity components. The same levels of staticeccentricity were introduced with a 51-slot rotor and theresults followed a similar pattern. A 51-slot rotor with

158 IEE PROCEEDINGS, Vol. 133, Pt. B, No. 3, MAY 1986

50% purely dynamic eccentricity was tested and theresulting spectra are shown in Fig. 3. Both the predicted

Combining the static eccentricity permeance wave(eqn. 17) with the fundamental stator MMF (eqn. 19) gives

70r

690 730 770frequency, Hz

a

850

650 690 730 770frequency.Hz

850

Fig. 1 Current zoom spectrum, with a 28-slot rotor and 4 poles

a Uniform airgapb 80% static airgap eccentricity

(i) psh: 736 Hz, 38.2 dB (ii) de: 711.5 Hz, 4.7 dB(iii) de: 760.5 Hz, -0 .6 dB (iv) psh: 736 Hz, 51.1 dB(v) de: 711.5 Hz, 26.6 dB (vi) de: 760.5 Hz, 34.1 dB

dynamic components increased substantially (for example,the one at 1302 Hz by 16.7 dB) whereas the principal slotharmonic increased by only 1.8 dB. Hence, a unique signa-ture pattern occurred in the current spectrum which wascharacteristic of only dynamic eccentricity.

5.3 Frame vibration: components associatedwith eccentricity

The vibratory forces which induce the largest surfacevibrations are those of low pole number. To determinethese forcing functions and establish which ones areaffected by eccentricity, the appropriate flux density wavesmust be multiplied in pairs in accordance with eqn. 13.

The flux density wave due to slotting, static eccentricity,saturation and the fundamental stator MMF (produced ina similar way as eqn. 20) is expressed as:

B,(6, t) = k3 FnQs = 1, nM = lAnr, = 1,

nst = lAns = lAnsa = 1 cos {(28 ± 36 ± 1 ± 4 ± 2)0

- (2Scor ± 2(ol ± cojt} (21)

From eqn. 21, with the motor operating at a full loadslip = 0.02, two important flux density waves of the samemagnitude are obtained. These are:

B2(6, t) = Bt cos (6 + 2nS36t) (22)

B3(6, t) = Bt cos {3d + 2nS36t) (23)

IEE PROCEEDINGS, Vol. 133, Pt. B, No. 3, MAY 1986

40 60°/o, static eccentricity

0 20 40 60 80•/•.static eccentricity

b

Fig. 2 Current eccentricity components against static eccentricity with28-slot rotor and 4 polesa Principal slot harmonicsb Dynamic eccentricity components

another set of flux density waves.

B4(0, t) = k4 Fngs = 1, nms = 1 Ans = 1

x cos {(2+ 1)6-(OS)

Therefore

B5{6, t) = B4 cos {36 - 2n50t}

B6(6, t) = B4 cos {6 - 2n50t}

(24)

(25)

(26)

Multiplying flux density waves B2 and B5 gives a forcewave with two pole pairs at 886 Hz rotating in the forwarddirection, i.e.

ai=o cos (26 - 2TT8860 (27)

Multiplying the flux density waves B3 and B6 in a similarway gives another two pole pair force wave at 886 Hz withthe same magnitude rotating in the opposite direction.

a2 = a cos (26 + 2TI8860 (28)

The addition of these two force waves, a1 and a2, pro-duces a pulsating force wave with 2-pole pairs at a fre-quency of 886 Hz. The magnitude of the forcing function isproportional to the square of the static eccentricity per-meance wave and will thus increase with an increase instatic eccentricity. These changes due to static eccentricityvariations will be reflected in the surface vibration mea-surements which should show positions of nodes and anti-nodes.

159

The general expression given by eqn. 15 was used topredict the frequency content of the frame vibration signal.

1225 1265 1305 1345frequency, Hz

a

1385 1425

1225 1265 1305 1345frequency, Hz

b

1385 1425

Fig. 3 Current zoom spectrum with a 51-slot rotor and 4 polesa Uniform airgapb 50% dynamic airgap eccentricity

(i) psh: 1278 Hz, 23.4 dB (ii) de: 1254 Hz, 10.2 dB(iii) de: 1302 Hz, 12.3 dB (iv) psh: 1278 Hz, 25.2 dB(v) de: 1254 Hz, 20.4 dB (vi) de: 1302 Hz, 29 dB

For static eccentricity variations n'd = 0, hence the predic-ted slot harmonics should change in magnitude and in thecase of the component at 886 Hz a 2-pole pair vibrationpattern around the frame should occur. With dynamiceccentricity variations n'd — 1, 2 , . . . , new componentsshould appear which are only characteristic of dynamiceccentricity. A sample of the expected components due toeccentricity is presented in Table 2.

The variation of the predicted principal slot harmonicsaround the periphery of the frame as a function of staticeccentricity with 28 and 51 slot rotors is presented inFig. 4. The variation of the 886 Hz component withchanges in static eccentricity shows that a 2-pole pairstanding wave pattern with optimum sensing positions for

Table 2: Predicted frequency components in the frame vibra-tion with 28 and 51 slot rotors using eqn. 15

R

rotorslots

"'** =28n'sa =51"'** =51

s

full-loadslip

10.02

00.037

00.037

f, = 50 Hz, p =

de

-nld.ria> = 2

861.5-n'd,n'm = 01204-n'd,n'a= -21104

2, n'r, = 1,n;

Frequency,

psh

n'd = 0, ria =886

n'd = 0.n'a =1228n'a = 0- n'o =1128

Hz

2

0

- 2

de

+n'd, n'm910.5

+n'a.n'a1252+n'd, n'm1152

= 2

= 0

= - 2

detecting the largest changes is produced. This agrees withthe theoretical predictions given by eqns. 27 and 28. A

807.

0.5

J2 0.4

to,0.2

0.1

-100 -50 9 *50 *100 *15Oangular position on core.degree

aa.

80°/.

-150 -100 -50 0 *50 *100 *15Oangular position on core,degree

bFig. 4 Acceleration level against transducer position as a function ofstatic eccentricitya 886 Hz component, 28 slot rotorb 1228 Hz component, 51 slot rotor

similar pattern is observed in the 1228 Hz component ofthe 51-slot rotor and confirms that static eccentricity canbe identified by monitoring the principal slot harmonics inthe vibration spectrum. Fig. 5 shows the resulting spectrafor the 28-slot rotor with a uniform airgap and 80% staticeccentricity at one of the optimum sensing positions. Thedynamic eccentricity components (861.5 Hz, 910.5 Hz)have increased by 25.8 dB and 15.9 dB, respectively, andthis further confirms the presence of dynamic eccentricityas a similar pattern appeared in the current spectra, Fig. 1.A 51-slot rotor with 50% purely dynamic eccentricity wastested and the results are presented in Fig. 6. Examinationof the spectra shows that the predicted dynamic com-ponents increased, for example, at 1104 Hz and 1152 Hzthe magnitudes increased by 25.3 dB and 17.3 dB, respec-tively. This confirms that dynamic eccentricity can be iden-tified by monitoring the stator frame vibration.

6 On-site tests

The main objective of the on-site tests was to assess theeffectiveness of the diagnostic techniques developed in thelaboratory, when applied to large 3-phase inductionmotors operating in a power station. Two nominally iden-tical 3-phase induction motors (A and B) with differentamounts of airgap eccentricity were selected for the tests.

The motor specifications are as follows: 3-phase, PAM,50 Hz, 11 kV, 1.2 MW, 12/14-poles.

It was known that ovality of the stator core was presentin motor B. All tests were conducted during no-load oper-

160 IEE PROCEEDINGS, Vol. 133, Pt. B, No. 3, MA Y 1986

120

COT>

leve

lio

nac

cele

i

104

88

72

56

Table 3: Predicted frequency components in the line current

(ii)

850

120

104

GO•oZ 88

.1 72

56

930 970frequency, Hz

1010

(v)

1050

850 890 930 970frequency,Hz

b

1010 1050

Stator frame vibration zoom spectrum with a 28-slot rotor and 4Fig. 5poles

a Uniform airgapb 80% static airgap eccentricity

(i) psh: 886 Hz, 88.8 dB (ii) de: 861.5 Hz, 63.2 dB(iii) de: 910.5 Hz, 71.2 dB (iv) psh: 886 Hz, 112.3 dB(v) de: 861.5 Hz, 89 dB (vi) de: 910.5 Hz, 87.1 dB

120r

1115

12 Or

104

^ 88co

1 72vuua

56

40

1155 1195frequency, Hz

1235 1275

(vii)(x)

1075 1115 1155 1195

freauency Hz

1235 1275

Motor

AB

A? = 1

No-load

slip

s

0.0020.003

12.p = 6./i,,

Supplyfrequency,Hz

49.8550.2

de

-nd. +n (

969.5977

1, nms = 1 . nsa =

Frequency, Hz

psh

978.5985

Table 4 : Predicted frequency components in thet ion signal

Motor

AB

R =

No-loadslip

s

0.00240.0024

= 112, p = 6, i

Supplyfrequency,Hz

50.0550.075

de

~n'd- nw

924924.5

f = 1,/7'm = 0 , n ; a =

Frequency,

ps/)

= 0 n'd = 0.n'^

932932.5

0

987993.5

i f rame vibra-

= 0

Hz

de

0 +n'a.n'm = 0

940.5941

ation (operating condition provided at time of testing) andthe predicted frequency components in the current andframe vibration spectra are presented in Tables 3 and 4.

6.1 Line currentThe current spectra for motors A and B are presented inFig. 7. Examination of the spectra shows that the differ-ence in magnitude between the principal slot harmonics isonly 2.1 dB but the dynamic eccentricity components inmotor B are 7-13 dB higher than the corresponding onesfor motor A. The results indicate that the signature pat-terns obtained from the on-site tests are of the same formas the ones obtained in the laboratory, Fig. 1. It is impor-tant to note that the tests were carried out at differenttimes of the day with corresponding different supply fre-quencies. This is reflected in the changes to the measuredspectra. For example, one of the dynamic componentsfrom motor A was at 969.5 Hz, whereas with motor B thecorresponding component appeared at 977 Hz. Thismeans an online monitoring strategy must accuratelydetermine the supply frequency as part of the signal pro-cessing to predict the expected frequency componentswhich are functions of eccentricity.

6.2 Frame vibrationThe vibration was sensed at numerous positions on theouter frame enclosure and on the bearing housing. It wasfound that an optimum sensing position for detecting thefrequency components due to airgap eccentricity was inline with a core support plate opposite one of the corebars.

The vibration spectra are presented in Fig. 8 and theresults show that the principal slot harmonic in motor B is10 dB higher than in motor A, which suggests a higherstatic eccentricity. In addition, the dynamic component at941 Hz is 6.4 dB higher in motor B. Hence the resultsshow that airgap eccentricity can be identified in the indus-trial environment

Fig. 6 Stator frame vibration zoom spectrum with a 51-slot rotor and 4poles

a Uniform airgapb 50% dynamic airgap eccentricity

(i) de: 1104 Hz, 58.4 dB(iii) de: 1152 Hz, 50.8 dB(v) psh: 1228 Hz, 69.8 dB

(vii) de: 1104 Hz, 83.6 dB(ix) de: 1152 Hz, 68.1 dB(xi) psh: 1228 Hz, 75.2 dB

(ii) psh: 1128 Hz, 71.4 dBfiv) de: 1204 Hz, 73.7 dB(vi) de: 1252 Hz, 57.6 dB

(viii) psh: 1128 Hz, 64.1 dB(x) de: 1204 Hz, 87.7 dB

(xii) de: 1252 Hz, 61.6 dB

1EE PROCEEDINGS, Vol. 133, Pt. B, No. 3, MAY 1986 161

Conclusions 8 Acknowledgments

The laboratory and on-site tests have demonstrated thatstatic and dynamic eccentricity can be detected by moni-toring the current and frame vibration signals. Static

The authors wish to thank the South of Scotland Elec-tricity Board for providing the financial support for thisproject and for their permission to publish this paper.

110

78

5 62

46

30935

110r

935

955 975 995frequency, H z

a

1015 1035

955 975 995 1015frequency, z

b

1035

Fig. 7polesa Motor Ab Motor B

(i) psh: 978.5 Hz, 90.9 dB(iii) de:987 Hz, 43.1 dB(v) de: 977 Hz, 51.5 dB

On-site test current zoom spectrum with a 112-slot rotor and 12

(ii) de: 969.5 Hz, 44.5 dB(iv) psh: 9S5 Hz, 88.8 dB(vi) de: 993.5 Hz, 56.4 dB

!20r

104

88

r. 72

561

40l

830

1 1830 870 910 950 990

frequency, Hz1030

870 910 950frequency, Hz

b

990 1030

Fig. 8 On-site test outer frame vibration zoom spectrum with a 112-slotrotor and 12 polesa Motor Ab Motor B

(i) psh: 932 Hz, 83.9 dB (ii) de: 924 Hz, 58.5 dB(iii) de: 940.5 Hz, 51.9 dB (iv) psh: 932.5 Hz, 94.9 dB(v) de: 924.5 Hz, 62.2 dB (vi) de: 941 Hz, 58.3 dB

eccentricity can be identified by changes in the vibrationprincipal slot harmonics, and dynamic eccentricity is char-acterised by the appearance of unique frequency com-ponents in both signals. In addition, static eccentricityvariations result in the introduction of dynamic eccentric-ity components in the current and vibration thus indicat-ing that dynamic eccentricity is a by-product of staticeccentricity. The motors tested in the laboratory and in thepower station had different pole numbers, rotor slots, andwere operating at different loads; however, in each case thepredicted frequency components were identified. To enablethe industrial user to make decisions on the running condi-tion of the motor, the degree of severity of eccentricity hasto be quantified. Further work is currently in progress topredict the magnitudes of fhe frequency components in themeasured parameters as a function of eccentricity. Thiswill mean that limit levels can then be set and an accept-able background noise level determined. Further evalu-ation tests have to be done in the industrial environmentbefore a dedicated diagnostic instrument can be developed.This evaluation phase is essential to ensure that the diag-nostic technique obtains credibility with the industrialoperator.

Thanks are also expressed to J.S. Grant, Technical ServicesManager, SSEB, R&D Centre for his advice and co-operation and for the assistance given by power stationpersonnel during the on-site testing.

9 References

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2 RAI, G.B.: 'Airgap eccentricity in induction motors'. ERA Report 74-1188, ERA Technology Ltd., Leatherhead, Surrey, UK, 1974

3 SWANN, S.A.: 'Effect of rotor eccentricity on the magnetic field inairgap of a nonsalient pole machine', Proc. IEE, 1963, 110, (5), pp.903-915

4 BINNS, K.J., and DYE, M.: 'Identification of principal factorscausing unbalanced magnetic pull in cage induction motors', Proc.IEE, 1973,120, (3), pp. 349-354

5 CRAWFORD, W.G.: 'Unbalanced magnetic pull and the mechanicalstability of rotating electrical machines', Eng., 1951, 171, pp. 504-505

6 BRADFORD, M.: 'Unbalanced magnetic pull in a 6-pole inductionmotor', Proc. IEE, 1968, 115, (11), pp. 1619-1627

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8 KOVACS, K.P.: 'Two-pole induction motor vibrations caused by

162 IEE PROCEEDINGS, Vol. 133, Pt. B, No. 3, MAY 1986

homopolar alternating fluxes', IEEE Trans., 1977, PAS-96, (4), pp.1105-1108

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14 ERSKINE, J.B.: 'A users view of noise and vibration aspects of ACinductin motors'. IEE Colloquium Digest 1978, pp. 52-64

15 LEONARD, R.A., and THOMSON, W.T.: 'Vibration and stray fluxmonitoring for unbalanced supply and interturn winding fault diag-nosis in induction motors'. Proceedings of 1st UK International Con-ference on Condition monitoring, University College of Swansea,Swansea, UK, April 1984, pp. 340-354

16 VERM A, S.P., and NATARAJAN, R.: 'Effects of eccentricity ininduction motors'. Proceedings of International Conference on Elec-trical machines, 3, Budapest, Hungary, Sept. 1982, pp. 930-933

17 BINNS, K.J., and BARNARD, W.T.: 'Some aspects of the use of fluxand vibration spectra in electrical machines'. Proceedings of Con-

ference on Applications on time-series analysis, University ofSouthampton, Southampton, UK, 1977, pp. 71.1-71.12

18 PENMAN, J., HAD WICK, J.G., and BARKER, B.: 'Detection offaults in electrical machines by examination of the axially directedfluxes'. Proceedings of 3rd International Conference on Electricalmachines, Brussels, Belgium, 1978, pp. R/5-1-R/5-1O

19 PENMAN, J., HADWICK, J.G., and STRONACH, A.F.: 'Protectionstrategy against the occurrence of faults in electrical machines'. IEEConf. Publ 185, 1980, pp. 54-58

20 THOMSON, W.T., LEONARD, R.A., DEANS, N.D., and MILNE,A.J.: 'Condition monitoring of induction motors for availabilityassessment in offshore installations'. Proceedings of 4th EuredataConference, Venice, Italy, 1983

21 THOMSON, W.T., LEONARD, R.A., DEANS, N.D., and MILNE,A.J.: 'Monitoring strategy for discriminating between different typesof rotor defects in induction motors', 18th UPEC Proceedings, Uni-versity of Surrey, Guildford, Surrey, UK, 1983, pp. 241-246

22 YANG, S.J.: 'Low noise electric motors' (IEE Monographs in Electri-cal and Electronic Engineering, Oxford Science Publications, 1981)

23 HELLER, B., and JOKL, A.L.: 'Tangential forces in squirrel cageinduction motors', IEEE, Trans, 1969, PAS-88, (4), pp. 484-492

24 HELLER, B., and HAM AT A, V.: 'Harmonic field effects in inductionmachines' (Elsevier Scientific Publishing Company, 1977)

25 CARTER, G.W.: 'The electromagnetic field in its engineering aspects'(Longmans, 1967)

26 THOMSON, W.T, LEONARD, R.A., MILNE, A.J., and PENMAN,J.: 'Failure identification of offshore induction motor systems usingonline condition monitoring'. Proceedings of 4th National ReliabilityConference, Birmingham, UK, 1983, pp. 2C/3/1-2C/3/11

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