Journal of ELECTRICAL ENGINEERING, VOL. 54, NO. 11-12, 2003, 287–292

FAULTS DETECTION OF INDUCTIONMACHINES BY RADIAL FIELD MEASUREMENT

Driss Belkhayat∗∗

— Raphael Romary∗— Mustapha El Adnani

∗∗

— Rodolphe Corton∗— Jean Francois Brudny

∗

In this paper, the authors propose a diagnosis method based on the measurement of the radial magnetic field in the

surrounding area of an induction machine. Considering a star coupled induction machine, the effect of broken rotor bar fault

or a stator phase cutting fault on stator currents and radial field spectrum is analyzed as an illustration of this diagnosis

method. When the saturation is taken into account, the study shows that the fault causes the circulation of a third harmonic

current between the two fed phases. This harmonic current generates new spectrum lines in the air gap flux density linked

to the slotting effect. These high frequency components are easily detectable by the radial field measurement.

K e y w o r d s: Induction machine, diagnosis, radial magnetic field, slotting effect, flux density components

1 INTRODUCTION

In the recent few years much work has been carriedout to investigate the possible fault operations of electri-cal machines. These works have used the acquisition ofan experimental data set. Monitoring and diagnostics ofelectrical machines is a very important topic which cor-responds to the actual industrial requests.

The usual methods for both stator and rotor faultdetection are based on vibrations analysis [1] or on themotor current signature analysis [2] that originated morethan twenty years ago.

For this purpose, these methods need dedicated andfixed equipment for each induction machine under test. Inthe mean time, a new non-invasive technique is proposed.This new method consists in using a voltage sensor basedon an air coil antenna installed outside the machine. Thisantenna measures the voltage proportional to the emittedmagnetic field.

The technique using the measurement of the axial leak-age flux, by setting the antenna in the axis of the shaft,has been widely developed [3].

In this investigation the external coil is placed in aplant containing the axis of the machine (Fig. 1). Theelectric field intensity sensed by the antenna is so propor-tional to the radial magnetic field. Its spectrum analysisshows high frequency components (MHz) due to the fastfront waves voltage when the machine is supplied by aPWM inverter [4], [5]. The mean frequency components(kHz) are due to the slotting effect [6] and appear, evenif the machine is safe and supplied by the network [7].The interference of these components by the fault fieldharmonics is used to diagnose the machine behaviour.

This technique is very practical and can be imple-

mented at low cost, except for very small motors, because

the antenna can be removed from one machine to another

without stopping work.

2 HEALTHY MACHINE

2.1 Magnetic field components

This analytical study is based on the determination of

the air gap flux density expression where the saturation

is neglected. The principle of this determination has been

presented in previous publications [8], [9]. Only the main

results are presented in this paper.

A three phase, p -pole pairs squirrel cage induction

machine with single layer windings and all the conductors

series connected is considered. Using an idealized slot

model with a rectangular profile and taking into account

the teeth, the general expression of the air gap permeance

is

p = P0 + pteeth (1)

where P0 is the mean value of permeance. In a healthy

running, this relationship can be written as [8]

p =∞∑

ks=−∞

∞∑

kr=−∞

Pkskr cos((ksNs+krNr)pαs−krNrpθ)

(2)

where are

∗Laboratoire Systemes Electrotechniques et Environnement, Universite d’Artois, Faculte des Sciences Appliquees, Technoparc Futura,

62400 Bethune, France∗∗

Faculte des Sciences et Techniques, Departement de physique, Marrakech, Morocco, e-mail : belkhayat@fstg-marrakech.ac.ma

ISSN 1335-3632 c© 2003 FEI STU

288 D. Belkhayat et al : FAULTS DETECTION OF INDUCTION MACHINES BY RADIAL FIELD MEASUREMENT

ks, kr — positive, negative or null integer

Ns, Nr — stator and rotor slot number per pair pole

p —pair pole number

αs — angular position of any point in the air-gap

θ — angle between rotor phase 1 and stator phase 1taken as spatial reference

Pkskr — coefficient linked to magnetic circuit geome-try

In order to distinguish the stator and rotor quantities,the upper indexes s and r are used.

Considering a balanced sine current three phase sys-tem at frequency f (ω angular frequency) flowing throughthe stator windings and the following relationship givingthe magnetic field intensity εs created by the stator

εs =

3∑

q=1

isq

+∞∑

hs=1

Ashs cos

(

phs(αs − (q − 1)2π

3p))

(3)

where

isq — phase “q” stator current (q = 1, 2 or 3)

hs — rank of harmonic component

Ashs — coefficient linked to the winding

The radial air gap flux density components created by thestator are obtained by multiplying the relations (2) and(3)

bs =

3∑

q=1

isq

+∞∑

hs=1

+∞∑

ks=−∞

+∞∑

kr=−∞

AshsPks, kr cos

(

(hs

+ ksNs + krNr)pαs − krNrpθ − hs(q − 1)2π

3

)

(4)

Noting s the slip and Is the RMS value of isq , as

θ = θ0 + (1 − s)ωt/p the relationship (4) becomes

bs =3

2Is√

2

+∞∑

hs=1

+∞∑

ks=−∞

+∞∑

kr=−∞

AshsPks, kr cos

(

(

1+krNr(1

− s))

ωt − (hs + ksNs + krNr)pαs − krNrpθ0

)

(5)

where hs = 6k+1 (k is positive, negative or null integer)In this expression it can be clearly shown that harmonicsat ω + (1 − s)ωkrNr angular frequencies will appear inthe air gap flux density spectrum.

Noting αs = αr + θ , where αr is the angular positionof any point in the air gap relating to the rotor referential,the air gap flux density linked to this rotor referential canbe written as

bs =3

2Is√

2

+∞∑

hs=1

+∞∑

ks=−∞

+∞∑

kr=−∞

AshsPks,kr cos

(

(

1

− (hs + ksNs)(1 − s))

ωt − (hs + ksNs + krNr)pαr

− (hs + ksNs)pθ0

)

(6)

The prime is introduced for quantities which are ex-pressed in a different referential.

These flux density components induce rotor currentharmonics which will be at the origin of rotor flux densitycomponents. In order to show the main effect, only theterms obtained for hs = 1, corresponding to the rotorcurrent harmonics at [1− (1 + ksNs)(1− s)]ω pulsation,will be considered. These harmonics generate magneticfield intensity given by

εr =

+∞∑

hr=1

+∞∑

ks=−∞

εks, hr cos(

(

1 − (1 + ksNs)(1 − s))

ωt

− phrαr − ϕrks

)

(7)

where ϕrks is the rotor current phase lag related to ks .

This magnetic field intensity combined with the perme-ance term P0 , create a rotating field which can be ex-pressed by

br =

+∞∑

hr=1

+∞∑

ks=−∞

brks, hr cos

(

(

1 − (1 + ksNs)(1 − s))

ωt

− phrαr − ϕrks

)

(8)

Other terms are induced by Pks, kr but are neglected inorder to simplify the presentation. For hr = 1, this fluxdensity expression, relating to the stator, can be writtenas

b′r =

+∞∑

ks=−∞

brks,1 cos

(

(

1 − ksNs(1 − s))

ωt − pαs

+ pθ0 − ϕrks

)

(9)

This relationship shows that air gap flux density harmon-ics at

(

1−ksNs(1−s))

ω angular frequencies will appear

in the spectrum. In normal running (s ∼= 0), these har-monics will be at (1 + ksNs)ω angular frequencies.

2.2 Experimental tests

The experimental results concern a 3 kW, 400/230 V,50 Hz, 2-poles pairs, squirrel cage induction machine with36 slots in the stator (N s = 18) and 44 slots in the rotor(Nr = 22). In Fig. 1 we can see the real experimentalsystem with an antenna having a pass-band at 10 MHz.In order to avoid the field produced by the power system,the position of the antenna is carefully chosen to measureonly the radial magnetic field emitted by the workingmachine.

For the following study, the experimental tests andresults are presented for the same machine.

In the spectrum presented in Fig. 1 we can clearlydistinguish the mains flux density components bs createdby the stator and given by the relationship (5) and thoseones created by the rotor and given by the relationship(9). The magnitudes of the spectrum lines are given involts. The corresponding values in tesla can be easilyobtained using the constructor characteristic curve of theantenna.

Journal of ELECTRICAL ENGINEERING VOL. 54, NO. 11-12, 2003 289

Frequency (Hz)

RADIAL FIELD

br(ks=±2)bs(kr=±1)

br(ks=±1)

10-2

10-3

10-4

10-5

10-6

500 1000 1500250 750 17501250

Magnitude (V)Healthy running

Fig. 1. Spectrum of the voltage induced in testing antenna of a

healthy running machine

3 MACHINE FAULTS

3.1 Broken rotor bar fault

Broken rotor bar is one of the most frequent faultsstudied on the squirrel-cage induction motor [10], [11].This type of failure does not cause motor destruction im-mediately. The machine performances do not decrease,but it has been shown [12] that the current increases inthe adjacent bars to the broken one. This anomaly caninduce additional heating which leads to supplementaryfailures. Other studies [13], [14] prove that the broken barfault can be detected by observing the stator current spec-trum where an additional line appears at (1 − 2s)f fre-quency. This spectrum line is not easy to detect becauseit is close to the fundamental current at f frequency. So,a higher frequency band, containing the slot harmonics,is observed to detect the effects of the broken bar fault.

Modification of the rotor mmf

The failure leads to a gap in the rotor mmf wave atthe broken bar position. It can be shown that this gapcan be modelled by introducing a ratio R , function ofαr , between the modified mmf f r and the initial mmf εr

given by (7). Then it comes

fr = R(αr)εr . (10)

This ratio R can be decomposed into Fourier series as

R(αr) = 1 +

+∞∑

hr=1

Rhr cos(hrαr) . (11)

In order to show the preponderant effects of the brokenbar, only the first term of the Fourier series will be con-sidered (hr = 1)

R(αr) = 1 + R1 cosαr . (12)

Equations (10) and (12) show that an additional termR1ε

r cos αr appears. The main term of the corresponding

flux density, taking only P0 into account, is given by

Br1 = P0Rεr . The development leads to

Br1 =

+∞∑

ks=−∞

Bks,1 cos((

1 − (1 − ksNs)(1 − s))

ωt

− (p ± 1)αr − ϕrks

)

(13)

with Bks,1 = P0εks,1R1 .

Relating to the stator referential, it comes

Br1 =

+∞∑

ks=−∞

Bks,1 cos((

1 − ksNs(1 − s))

ωt ± (1 − s)ωt

p

− αs(p ± 1) − (p ± 1)θ0 − ϕrks

)

. (14)

The comparison between (14) and (9) shows off addi-

tional harmonics at ±ωR from the initial ones. For N s =

18, the frequencies of components relative to |ks| = 1

(ranks 17 and 19) are nearly at 850 Hz and 950 Hz.

For |ks| = 2 the frequencies are close to 1750 Hz and

1850 Hz. The broken bar fault brings spectrum lines at

825 Hz, 875 Hz, 925 Hz, 975 Hz ( |ks| = 1) and 1725 Hz,

1775 Hz, 1825 Hz, 1875 Hz ( |ks| = 2).

Frequency (Hz)

850

950

1750

1850

Magnitude (V)

Magnitude (V)0.01

Healthy running

Broken bar fault

Frequency (Hz)

ks=±1

ks=±2

kr=±1

10-2

10-3

10-4

10-5

10-6

10-2

0

500 1000 1500250 750 17501250

500 1000 1500250 750 17501250

Fig. 2. Comparison of the induced voltage spectra of a healthyrunning machine and machine with a broken bar

290 D. Belkhayat et al : FAULTS DETECTION OF INDUCTION MACHINES BY RADIAL FIELD MEASUREMENT

Experimental verifications.

The upper spectrum given in Fig. 2 corresponds to ahealthy running (see Fig. 1). The lower spectrum corre-sponds to a broken bar fault. The results give good confir-mation of the analytical predictions. In the tests the rota-tion speed is practically at synchronism. Lateral spectrumlines in the case of broken bar can be observed. These linescan be easily detected and their frequencies are at ±fR

from the initial harmonics corresponding to the teeth ef-fect in a healthy running. It can be noticed that this phe-nomenon also appears on the spectral lines generated bythe stator currents ( |kr| = 1 1050 Hz, 1150 Hz).

3.2 Stator Cutting phase fault

In order to justify the phenomena in case of statorcutting phase, the saturation has also to be taken intoaccount, so that the expression (4) becomes

p = P0 + pteeth + psat . (15)

Saturation effect

It is known that the saturation effect increases the air-gap equivalent thickness and consequently decreases thepermeance [15], [16]. The permeance saturation term isgiven by

psat = Psat cos(2ωt − 2pαs) . (16)

The permeance expression is linked to the maximum ofmagnetic field intensity which is at the origin of the satu-ration. In order to appreciate the main corresponding ef-fects, only the magnetic field intensity fundamental termis considered.

•Balanced Three phase supply

In that case, after multiplying (16) and the magneticfield intensity (3), the following supplementary term ap-pears in the air gap flux density expression

bssat =

3

4As

1PsatIs cos(3ωt − 3pαs) . (17)

Integration of this term leads to a supplementary linkedflux through the stator phase “q” ϕ3 cos 3ωt and there-fore induces a zero-sequence electric field intensity sys-tem. In the case of machine star coupling without neutral,it is evident that there will not appear any correspondingcurrent flowing.

•Two phase supply

In that case, let us consider the previous current system

with is1 = −is2 = Is√

2 cos ωt and is3 = 0. The magneticfield intensity becomes a pulsating wave instead of a ro-tating one. The maximum of the magnetic field intensityis always located at the same points

εs = As1I

s√

2√

3 cos ωt cos(

pαs +π

6

)

. (18)

The saturation permeance term can be written as

psat = Psat cos 2ωt cos(

2pαs +π

3

)

. (19)

The product of (18) and (19) leads to several terms and

a particular one

bssat =

√6As

1IsPsat cos(3ωt − pαs) . (20)

After integration, the flux linked to “q” stator phase is

ϕssat,s = ϕsat cos

(

3ωt − (q − 1)2π

3

)

. (21)

This flux induces a third harmonic of electric field in-

tensity with RMS value Essat,s = 3ωϕsat/

√2 and there-

fore, the third harmonic current component can flow

through the two fed phases. This current is limited by

the machine and grid impedance Z for the third har-

monic current (Fig. 3).

Issat

Essat,1

Z

ZI

ssat E

ssat,2

Essat,3

Fig. 3. Equivalent scheme for the third harmonic current compo-

nent

To confirm this property, experiments have been made

on a 1.5 kW 400/230 V 50 Hz, 2 pole pair induction ma-

chine with N s = 18 and N r = 12.

In the obtained spectra given in Fig. 4, the observation

of the third harmonic component in the field measured

by the antenna does not allow to appreciate the uncon-

nected phase fault because it is approximately the same

in the both cases. However, it can be easily noticed that

the corresponding current harmonic appears clearly. The

low magnitude original component at 150 Hz figuring in

the three phase supply current spectrum is not due to

the zero-sequence electric field intensity system as em-

phasized in the analytical development. It corresponds to

the third harmonic of the supply system.

Journal of ELECTRICAL ENGINEERING VOL. 54, NO. 11-12, 2003 291

Magnitude (mV)

RADIAL FIELD

CURRENT

Three phase supply

Two phase supply

Magnitude (A)

Magnitude (mV)

RADIAL FIELD

CURRENT

0.5

0.05

0.005

5

Hz

Hz

Hz

Hz

0.5

0.05

0.005

5

0.5

0.05

0.005

5

0.5

0.05

0.005

5

0 50 100 200 250150 300 350

Magnitude (A)

0 50 100 200 250150 300 350

0 50 100 200 250150 300 350

0 50 100 200 250150 300 350

Fig. 4. Comparison of the spectra of a machine with three and two

phase supply respectively — field induced in antenna

Interaction with the teeth effect

In the case of one stator phase cut and considering

third harmonic of the current, the development of the re-

lationship (4) leads to obtain stator field components at

[krNr(1 − s)ω ± 3ω] angular frequencies which are cor-

responding to the interaction of third harmonic current

with the rotor slots. The experiments show that these

harmonics (Fig. 5) appearing clearly in the lower spec-

trum (2 phase supply), for s ∼= 0 additional spectral lines

at 900 ± 150 Hz (kr = 1), 1800 ± 150 Hz (kr = 2) and

2700± 150 Hz (kr = 3) appear. Therefore this technique

gives a good appreciation on the machine diagnosis con-

cerning a stator phase cutting fault.

Magnitude(mV)

5

0.5

0.05

0.005

Magnitude(mV)

Three phase supply

5

0.5

0.05

0.005

0 0.5k 1k 2k 2.5k1.5k 3k

0 0.5k 1k 2k 2.5k1.5k 3k Hz

Hz

Two phase supply

Fig. 5. Comparison of the induced voltage spectra of a machine

with three and two phase supply respectively

4 CONCLUSION

In this paper, the authors have presented a new diag-nosis method consisting in the use of an antenna posi-tioned in the surrounding area of the induction machinefor the measurement of the radial magnetic field. It hasbeen shown that the spectrum of this field contains highrank lines due to the slotting effect giving informationconcerning broken rotor bar and stator cutting phase ma-chine faults. This result is particularly important to dis-criminate the induction machine faults from the powersystem fault. So, the proposed approach is very interest-ing for manufacturers to detect machines faults withoutany mechanical link and using low cost non-invasive sen-sor. Other studies are now undertaken to extract moreinformation from the magnetic field emitted in view toidentify other machine faults.

References

[1] BOULENGER, A.—PACHAUD, C. : Surveillance des machines

par analyse des vibrations, AFNOR, Paris, Mai 1995.

[2] CALIS, H.—UNSWORTH, P.J. : Fault Diagnosis in Induction

Motors by Motor Current Signal Analysis, International Work-

shop SDEMPED’99, Gijon, Spain, 1–3 Sept. 1999, 237–241.

[3] HENAO, H.—ASSAF, T.—CAPOLINO, G.A. : Detection of

Voltage Source Dissymmetry in an Induction Motor Using the

Measurement of Axial Leakage Flux, ICEM 2000, Finland,

1110–1114.

[4] HENNETON, A.—ROGER, D.—BRUDNY, J.F. : Electromag-

netic Signature of Electrical Machines Fed by PMW Inverter,

MARELEC, Marine and Electromagnetic Conference and Exhi-

bition 2001, Stockholm, Sweden, July 2001, CD ROM.

292 D. Belkhayat et al : FAULTS DETECTION OF INDUCTION MACHINES BY RADIAL FIELD MEASUREMENT

[5] HENNETON, A.—ROGER, D.—NAPIERALSKA, E. : Study

of Electromagnetic Phenomena, Contribution to External Radi-

ation of Machines, ICEM 2000, Finland, 1125–1129.

[6] BRUDNY, J.F.—ROGER, D. : Induction Machine Speed Sen-

sor Based on Stator Current Measurement, Sixth international

conference on Power Electronic and Variable Speed Drives, IEE

PEVD96, UK, 322–327.

[7] PANKOW, Y.—CORTON, R.—ROMARY, R.—AUTIER, V.—

BRUDNY, J.F. : Effets de la denture des moteurs asynchrones

dans le cadre du diagnostic par mesure de champ radial, COM-

PIEGNE, France, octobre 2001, 283–292.

[8] BELKHAYAT, D. : ”Reduction active du bruit magnetique des

machines asynchrones alimentees en tension sous frequence vari-

able, No. 1293, 1994, Lille, France.

[9] BELKHAYAT, D.—ROGER, D.—BRUDNY, J.F. : Active Re-

duction of Magnetic Noise in Asynchronous Machine Controlled

by Stator Current Harmonics, IEE, Eighth international confer-

ence on electrical machine and drives, Cambridge, U.K., Sept.

1997, 400–405.

[10] FISER, R.;FERKOLJ, S. : Development of Steady-State Mathe-

matical Model of Induction Motor with Rotor Cage Fault, ICEM

2000, Finland, 2188-2191.

[11] KRAL, C.—PIRKER, F.—PASCOLI, G. : Detection of Rotor

Faults in Squirrel-Cage Induction Machines at Standstill Bor

Batch Tests by Means of the Vienna Monitoring Method, IEEE

Transactions on Industry Applications, Vol. 38, No. 3, May/Jun.

2002, 618–624.

[12] MILIMONFARED, J.—KELK, H.M.—NANDI, S.—MINAS-

SIANS, A.D.—TOLIYAT, H.A. : A Novel Approach for Broken

Rotor Bar Detection in Cage Induction Motor, IEEE Transac-

tions on Industry Applications, Vol. 35, No. 5, Sept./Oct.1999,

1000–1006.

[13] DORRELL, D.G.—PATERSON, N.C.—WATSON, J.F. : The

Causes and Quantification of Sideband Currents for Use in Rotor

Fault Detection Systems for Cage Induction Motors, ICEM 1996,

Vigo, Spain, 414–419..

[14] ELKASABGY, N.M.—EASTMAN, A.R.—DAWSON, G.E. :

Detection of Broken Bars in the Cage Rotor on an Induction

Machine, IEEE Transactions on Industry Applications, Vol. 28,

No. 1, Jan./Feb. 1992, 165–171.

[15] MOREIRA, J.C.—LIPO, T.A. : Modelling of Saturated AC Ma-

chines Including Air Gap Flux Components, 1990 IEEE Industry

Application Society Annual Meeting, 37–44.

[16] IVANOV, A.—MOLENSKI, S. : Machines electriques, Tech-

nique Sovietique Edition de Moscou 1983.

Received 16 June 2003

Driss Belkhayat (PhD), studies — 1985 Baccalaurat,Morocco 1985-1989 Licence & Matrise, Gnie Electrique PhD,Universit des sciences et technologie de Lile (France). Researchfield — electromagnetic noise reduction (induction machines).Since 1994 Professor at the University CADI AYAD of Mar-rakech LSEE Member (France).

Raphael Romary (PhD), Rodolphe Corton (PhD), Jean

Francois Brudny (Prof, DSc, Member IEEE) Mustapha

El Adnani (Prof, DSc). Biographies not supplied.

ELEKTRO 2004

5th

International

Conference

University of ZilinaFaculty of Electrical Engineering

v

connected with

5th International Conference

NEW TRENDS IN DIAGNOSTICS

AND REPAIRS OF ELECTRICAL

MACHINES AND EQUIPMENTS

25–26 May 2004

Zilina, Slovak Republicsupported by

Rector of University of ZilinaProf. Jan Bujnak

and Dean ofFaculty of Electrical Engineering

University of ZilinaAssoc. Prof. Jan Michalık

The Conference is the fifth of series of con-ferences, which began in 1995 ELEKTRO

and 1996 DIAGNOSTIC, respectively ini-

tially as national conference with interna-

tional participation. The purpose of the

Conference is to provide an internationalforum for researches, professionals and ed-

ucationists interested in electrical and elec-

tronic engineering as well as boundary areaswith main attention to the following topics:

A: Telecommunication Systems and

Services • Digital Signal Processing • Mob-ile and Satellite Radio Networks • Broad-band Networks • Optoelectronic Systems

and Networks • Next Generation Networks• Learning

B: Electric Drives and Mechatron-

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• Electric Traction • Mechatronics • App-lications

C: Power Electrical Systems • Power

Electronic • Power Engineering • Power

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of Intelligent Buildings and their Control• Communication Systems in Transport and

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of Experimental Electrical Engineering, Mea-surement of Electrical and Nonelectrical

Values, Processing of Measurement Results

in Electrical and Electronic Engineering• Diagnostic Methods and New Technolo-

gies Used at Fabrication, Revisions and Re-

pairs of Electric Machines and Equipments

F: Trends in Theoretical and Applied

Electrical Engineering • Analysis of Elec-tromagnetic Field and Electrical Circuits us-

ing Analytical Methods, Numerical Compu-tations and Simulations • ElectromagneticFields in Various Materials and Coupled

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G: Materials and Technologies for Elec-

trical Engineering • New and ForwardMaterials • New Experimental Methods and

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Dielectrics), Thin Layers and Heterostruc-

tures • Microelectronic and Optoelectronic

Devices • Optical Fibers and Cables

Contributions presented on the Conference

can be published in special issue of jour-nal ADVANCES IN ELECTRICAL AND

ELECTRONIC ENGINEERING.

Preliminary registration • 15.1.2004 Ab-stract submission • 15.1.2004 Contribution

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