SDHLT 02986 electric machines modeling, condition monitoring, and fault diagnosis

AND FAULT DIAGNOSIS HAMID A... ELECTRIC MACHINESMODELING, CONDITION MONITORING, AND FAULT DIAGNOSIS... ELECTRIC MACHINESMODELING, CONDITION MONITORING, AND FAULT DIAGNOSIS HAMID A... 6

AND FAULT DIAGNOSIS

HAMID A TOLIYAT • SUBHASIS NANDI

SEUNGDEOG CHOI • HOMAYOUN MESHGIN-KELK

CRC Press ,

ELECTRIC MACHINES

MODELING, CONDITION MONITORING,

AND FAULT DIAGNOSIS

ELECTRIC MACHINES

MODELING, CONDITION MONITORING,

AND FAULT DIAGNOSIS

HAMID A TOLIYAT SUBHASIS NANDI SEUNGDEOG CHOI HOMAYOUN MESHGIN-KELK

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TÀI LI£llTHL(■VIÊ^

CRC Press

Taylor &i Francis Group

Boca Raton London N e w York

C R C Press is an im p rin t of the Taylor & Francis C ro u p , an in fo r m a business

P r e f a c e xi

1 I n tr o d u c t i o n 1

Seun gdeog Choi R e f e r e n c e s 8

2 F a u lts in I n d u c t i o n a n d S y n c h r o n o u s M o t o r s 9

Bilal A kin an d M ina M Rahim ian 2.1 In tr o d u c tio n of In d u c tio n M otor Favilt 9

2.1.1 B e arin g F a u lts 9

2.1.2 S tator F a u l t s 11

2.1.3 Broken Rotor Bar F a u l t 13

2.1.4 Eccentricity Fault 15

2.2 I n t r o d u c tio n of S y n c h r o n o u s M o to r Fault D i a g n o s i s 16

2.2.1 D a m p e r W i n d i n g F a u l t 17

2.2.2 D e m a g n e tiz a ti o n Fault in P e r m a n e n t M a g n e t S y n c h r o n o u s M a c h in e s (PM SM s) 18

2.2.3 Eccentricity F a u lt 19

2.2.4 Stator Inter-Turn F a u l t 20

2.2.5 Rotor Inter-Turn F a u lt 21

2.2.6 B earin g F ault 22

R e f e r e n c e s 23

3 M o d e l i n g o f E lectric M a c h i n e s U s in g W i n d i n g a n d M o d if ie d W i n d i n g F u n c t i o n A p p r o a c h e s 27

Su bhasis N andi 3.1 I n t r o d u c t i o n 27

3.2 W i n d i n g a n d M odified W i n d i n g F u n c tio n A p p ro a c h e s (WFA a n d M W F A ) 28

3.3 In d u c ta n c e C a lc u la tio n s U sin g WFA a n d M W F A 33

.3.4 Validation of Inductance C alculations U sing WFA a n d M W F A 39

R e f e r e n c e s 45

vi Contents

4 M o d e l i n g o f Ele ctric M a c h i n e s U s i n g M a g n e t i c E q u i v a l e n t

C i r c u i t M e t h o d 47

H om ayoun M eshgin-K elk 4.1 In tro c iu c tio n 47

4.2 In d ire c t A pplication of M a g n e tic E q u i\'a le n t C ircuit for A n a ly sis of Salient Pole S y n c h r o n o u s M a c h i n e s 52

4.2.1 M a g n e tic E q u iv a le n t C ircu it of a Salient Pole S y n c h r o n o u s M a c h i n e 53

4.2.2 In d u c ta n c e Relations of a Salient Pole S y n c h ro n o u s M a c h i n e 55

4.2.3 C alc u la tio n of I n d u c ta n c e s for a Salient Pole S y n c h r o n o u s M a c h i n e 58

4.2.4 E x p e rim e n ta l M e a s u r e m e n t of I n d u c ta n c e s of a Salient Pole S y n c h r o n o u s M a c h i n e 63

4.3 In d ire c t A p p licatio n of M ag n etic E q u iv alen t C ircu it for A n aly sis of In d u c tio n M a c h i n e s 66

4.3.1 A Sim plified M a g n e tic E q u i\’alen t C ircu it of In d u c tio n M a c h i n e s 66

4.3.2 I n d u c ta n c e Relations of In d u c tio n M a c h i n e s 68

4.3.3 C a lc u la tio n of I n d u c ta n c e of a n I n d u c tio n M a c h i n e 70

4.4 D irect A pp licatio n of M a g n e tic E q u iv alen t C ircuit C o n s id e rin g N o n lin e a r M a g n e tic C h a ra c te ristic for M a c h in e A n a l y s i s 73

A p p e n d ix A: In d u ctio n M ach in e P a r a m e t e r s 77

A p p e n d i x B: N o d e P e rm e a n c e M a tric e s 78

R e f e r e n c e s 79

5 A n a l y s i s o f F a u l t y I n d u c t i o n M o t o r s U s i n g F i n i t e E l e m e n t M e t h o d 81

Bashir M alidi Ebrahim i 5.1 I n t r o d u c t i o n 81

5.2 G e o m e tric a l M o d e lin g of Faulty I n d u c tio n M o to rs U sing T im e -S te p p in g Finite E lem en t M e th o d (T S F E M ) 82

5.3 C o u p lin g of Electrical C ircu its a n d Finite E lem ent A r e a 83

5.4 M o d e lin g In te rn a l Faults U sin g Finite Elem ent M e t h o d 85

5.4.1 M o d e lin g Broken Bar F a u lt 85

5.4.2 M o d e lin g Eccentricity F a u l t 87

5.4.2.1 Static E c c e n tr ic it y 87

5.4.2.2 D y n a m i c E c c e n tr ic it y 89

5.4.2.3 M ix ed E c c e n tr ic it y 90

5.5 Im p a c t of M a g n e tic S a tu ra tio n on A ccurate Fault D etection in I n d u c tio n M o t o r s 91

5.5.1 A n a ly sis of A ir-G a p M a g n e tic Flux D en sity in

H e alth y a n d F aulty In d u c tio n M o t o r 94

5.5.1.1 L inear M a g n e tiz a tio n C h a ra c te r is tic 94

5.5.1.2 N o n lin e a r M a g n e tiz a tio n C h a r a c te r is tic 95

R e f e r e n c e s 96

6 Fault D i a g n o s i s of Electric M a c h i n e s U s i n g Te c h n i q u e s Based on F r eque nc y D o m a i n 99

Subhasis N andi 6.1 I n t r o d u c t i o n 99

6.2 Som e D efinitions a n d E xam ples Related to Signal Processing 100

6.2.1 C o n tin u o u s v e rs u s Discrete or D igital or S a m p le d S i g n a l 100

6.2.2 C o n tin u o u s , D iscrete Fou rier T ran sfo rm s, a n d N o n p a r a m e t r i c P ow er S p e c t r u m E s tim a tio n 101

6.2.3 P a ra m e tric P ow er S p e c t r u m E s t i m a t i o n 105

6.2.4 P o w e r S p e c t r u m E s tim a tio n U sing H i g h e r - O r d e r Spectra ( H O S ) 107

6.2.5 Pow'er S p e c t r u m E stim a tio n U sin g S w e p t Sine M e a s u r e m e n ts or Digital F re q u e n c y Locked Loop T e c h n iq u e (D F L L ) 110

6.3 D ia g n o sis of M a c h in e Faults U sin g F re q u e n c y D o m a in -Based T e c h n i q u e s I l l 6.3.1 D etection of M o to r B earin g F a u l t s I l l 6.3.1.1 M ec h a n ic a l V ibration F re q u e n c y A n a ly sis to Detect B earing F a u l t s I l l 6.3.1.2 Line C u r r e n t F re q u e n c y A n a ly s is to D etect B earin g F a u l t s 115

6.3.2 D etection of Stator F a u lts 116

6.3.2.1 D etection of Stator Faults U sin g External Flux S e n s o r s 116

6.3.2.2 D etection of Stator Faults U sin g Line C u r r e n t H a r m o n i c s 117

6.3.2.3 D etection of Stator Faults U sing T erm in al Voltage H a r m o n ic s at S w i t c h - O f f 119

6.3.2.4 D etection of Stator Faults U sing Field C u r r e n t a n d Rotor Search Coil H a r m o n ic s in S y n c h r o n o u s M a c h i n e s 121

6.3.2.5 D etection of Stator Faults U sin g Rotor C u r r e n t a n d S earch Coil Voltages H a r m o n ic s in W o u n d Rotor In d u c tio n M a c h in e s 124

6.3.3 D etection of Rotor F a u l t s 129

v iii C.antcnts

6.3.3.1 D etection of Rotor Faults in Stator l.ine

C u rre n t, Sp eed , Torque, a n d P o w e r 1306.3.3.2 D etection of Rotor Faults in E xternal an d

In te rn a l Search C o i l 1346.3.3.3 D etection of R otor Faults U sing T e rm in a l

Voltage H a r m o n ic s at S w i t c h - O f f 1346.3.3.4 D etection of Rotor Faults at S t a r t - U p 1346.3.3.5 D etectio n of Rotor F aults in P re se n c e of

I n te rb a r C u r r e n t U sing Axial Vibration

S i g n a ls 1356.3.4 D etectio n of Eccentricity F a u l t s 1366.3.4.1 D ete c tio n of Eccentricity Faults U sin g Line

C u r r e n t Signal S p e c t r a 1366.3.4.2 D etectio n of Eccentricity Faults B ased on

N a m e p la te P a r a m e t e r s 1426.3.4.3 D etectio n of Eccentricity Faults U sing

M e c h a n ic a l Vibration Signal S p e c t r a 1476.3.4.4 D etection of In c lin e d Eccentricity F a u lts 1476.3.5 Detection of Faults in Inverter-Fed Induction M a c h i n e s 148

Stator Inter-Turn F au lts 1657.3.1 M odel w i t h o u t S a t u r a t i o n 1657.3.2 M o d el w ith S a t u r a t i o n 1697.4 M odel of S q u irre l-C a g e I n d u c tio n M o to r w ith Incipient

Broken Rotor Bar a n d E n d -R in g F a u lts 1757.5 M o d el of S q u irre l-C a g e I n d u c tio n M o to rs w i t h Eccentricity

F a u lts 1777.6 M o d el of a S y n c h r o n o u s R eluctance M o to r w i t h Stator F a u lt 1797.7 M o d el of a Salient Pole S y n c h r o n o u s M otor w i t h D y n a m ic

Cotiteiits ix

8.4 F eatu re Extraction for O u r Fault D ia g n o sis S y s t e m 190

8.5 Classifier T r a i n i n g 192

8.6 I m p l e m e n t a t i o n 194

R e f e r e n c e s 198

9 I m p l e m e n t a t i o n o f M o t o r C u r r e n t S i g n a t u r e A n a l y s i s F a u lt D i a g n o s i s B ased o n D i g ita l S i g n a l P r o c e s s o r s 199

Seungdeog Choi and Bilal Akin 9.1 I n t r o d u c t i o n 199

9.1.1 C ro ss-C o rre la tio n S ch em e D e riv e d fro m O p tim a l D etector in A d d itiv e W h ite G a u s s ia n N oise (AWGN) C h a n n e l 200

9.2 Reference Fram e T h e o r y 201

9.2.1 Reference F ra m e T h e o r y for C o n d itio n M o n i t o r i n g 202

9.2.2 (Fault) H a r m o n ic A n a ly sis of M u ltip h a s e S y s te m s 202

9.2.3 O n -L in e Fault D etection R e su lts 204

9.2.3.1 v /f C o n tro lle d Inverter-Fed M o to r Line C u r r e n t A n a l y s i s 204

9.2.3.2 F ield -O rien ted C o n tro l Inverter-Fed M otor Line C u r r e n t A n a l y s i s 206

9.2.3.3 I n s t a n t a n e o u s Fault M o n ito rin g in Tim e-F re q u e n c y D o m a in a n d T ransient A n a l y s i s 206

9.3 P hase-S ensitive D etection-B ased Fault D i a g n o s i s 210

9.3.1 I n t r o d u c t i o n 210

9.3.2 Phase-Sensitive D e te c tio n 210

9.3.3 O n -L in e E x p e rim e n ta l R e s u lts 212

R e f e r e n c e s 218

10 I m p l e m e n t a t i o n of F a u lt D i a g n o s i s in H y b r i d Ele ctric V ehicles B ased o n R e fe re n c e F ra m e T h e o r y 221

Bilal Akin 10.1 I n t r o d u c t i o n 221

10.2 O n -B o a rd Fault D ia g n o sis (OBD) for H y b rid Electric Vehicles (H E V s ) 221

10.3 D rive Cycle A n a ly s is for O B D 224

10.4 Rotor A s y m m e t r y D etection at Z e ro S p e e d 226

R e f e r e n c e s 233

11 R o b u s t S ig n a l P r o c e s s i n g T e c h n i q u e s fo r t h e I m p l e m e n t a t i o n of M o to r C u r r e n t S i g n a t u r e A n a l y s i s D i a g n o s i s B a s e d o n D ig ita l S ig n a l P r o c e s s o r s 235

Seungdeog Choi 11.1 I n t r o d u c t i o n 235

11.1.1 C o h e re n t D e t e c t i o n 236

Electric Machines: Fault Diagnosis a n d Condition M ointcring

11.1.2 N o n c o h e r e n t D etection (P h a se A m b i g u i t y

C o m p e n s a t i o n )

11.1.3 Fault F re q u e n c y O ffset C o m p e n s a t i o n

11.2 D e c isio n -M a k in g S c h e m e

11.2.1 A d a p tiv e T h re s h o ld D e sig n (N o is e A m b i g u i t y C o m p e n s a t i o n )

11.2.2 Q - F u n c t i o n

11.2.3 N o ise E s t i m a t i o n

11.3 S im u la tio n a n d E x p e rim e n ta l R e s u l t

11.3.1 M o d e le d MATLAB S im u la tio n R e s u l t

11.3.2 Off-Line E x p e r i m e n t s

11.3.2.1 Off-Line R esults for E c c e n t r i c i t y

11.3.2.2 Off-Line R esults for B ro k e n R otor Bar 11.3.3 O n -L in e E x p e rim e n ta l R e s u lts

R e f e r e n c e s

I n d e x 253

237 237 240

240 242 243 244 244 245 246 247

248 251

P reface

Tilt' d e v e l o p m e n t of th e electric m o to r is o n e of the g reatest a c h ie v e m en ts of

th e m t) d e r n e n e r g y c o n v e rs io n in d u stry C o u n tle s s electric m o to rs are b e in g

u s e d in o u r d aily lives for critical service a p p licatio n s such as tr a n s p o r ta tio n ,

m e d i c a l tre a tm e n t, m i l i t a r y o p eratio n , ancl c o m m u n ic a tio n H ow ever, d u e to

th e f u n d a m e n t a l lim itaticins of m a te ria l lifetime, deterioraticin, c o n t a m i n a ­tion, m a n u f a c t u r i n g d efects, or d a m a g e s in o p eratio n s, an electrical m o to r

w ill e\ e n tu a lly go in to fa ilu re m ode A n u n e x p e c t e d failure m ig h t lead to the loss of v a lu a b le h u m a n life or a costly s ta n d s till in in d u stry , w'hich n e e d s to

b e p r e v e n t e d b y p re c is e ly d e te c tin g or c o n tin u o u s ly m o n ito r in g the w'orking

c o n d itio n of a m otor

T his b o o k w a s w r i t t e n to p rtw id e a full re v ie w of d ia g n o s is te c h n o lo g ies

a n d as a n a p p licatio n g u i d e for g r a d u a te a n d se n io r u n d e r g r a d u a t e s t u d e n t s

in th e p tiw e r e le c tro n ic s d is c ip lin e w'ho w a n t to research , develop, a n d im p le ­

m e n t a fault d i a g n o s i s a n d co n d itio n m o n ito r in g s c h e m e for b e tte r safety

a n d i m p r o v e d re lia b ility in electric m o to r operatio n F u rth e rm o re , electrical

a n d m e c h a n ic a l e n g i n e e r s in the i n d u s t r y are also e n c o u r a g e d to u se por- titins of th is b o o k as a referen ce to u n d e r s t a n d th e f u n d a m e n t a l s of fault

c a u s e a n d effect a n d to fulfill successful im p le m e n ta tio n

T h is b o o k a p p r o a c h e s th e fault d ia g n o s is of electrical moftirs t h r o u g h th e

p r o c e s s of th e o retical a n a ly s is a n d th e n practical application First, the analy- si.s of th e f u n d a m e n t a l s of m a c h in e failure is p re s e n te d t h r o u g h the w i n d ­

in g f u n c t i o n s m e t h o d , th e m a g n e tic e q u iv a le n t circuit m e th o d , a n d finite t'le m e n t analysis Sectind, th e im p le m e n ta tio n of fault d ia g n o s is is review'ed

w i t h t e c h n i q u e s s u c h a s the m o to r c u r r e n t s i g n a t u r e an a ly sis (MCSA)

m e t h o d , fret]uency d o m a i n m ethtid, m o d e l-b a s e d te c h n iq u e s, a n d p a tte rn

r e c o g n i t i o n schem e, hi p a rtic u la r, the MCSA im p le m e n ta tio n m e t h o d is pre- sented in d e ta il in th e last c h a p te r s of the book, w h ic h d is c u s s ro b u s t sig­

n al p r o c e s s i n g t e c h n i q u e s a n d r e fe re n ce -fra m e -th e o ry -b a s ed fault d ia g n o s is

i m p l e m e n t a t i o n fcir h y b r id vehicles as a n exam ple T h e s e theoretical an aly sis

a n d p ra c tic a l im p l e m e n t a t i o n strateg ies a re b a se d on m a n y y e a rs of research

a n d deN-ekipment at th e Electrical M a c h in e s & Ptiwer Electronics (EMPE) i-a b o r a to r y at Texas A & M University

Ha m i d Toliyat

Texas A&M LIniversit}/ College Station, Texas

.VI

2011, w h ic h is a s s u m e d m o re t h a n 507o g r o w t h ju st w i t h i n 5 years [1] Electric

m o to rs h a v e b een a p p lie d to a lm o s t e\'ery place in o u r daily life, s u c h as

m a n u f a c t u r i n g system s, air tra n s p o r ta tio n s , g r o u n d tra n s p o r ta tio n s , b u i l d ­ing air-c o n d itio n e r sy stem s, h o m e e n e r g y co n v ersio n system s, v a r io u s cool­ing systems in electrical devices, a n d even cell p h o n e x'ibration sy stem s

it is also a well-know n fact that the electric m otors co n su m e m ore th an 507o of

w hole electrical energy d e m a n d in the United States The a n n u a l electrical energy

d e m a n d in the United States w a s 3,873 billion kilowatt-hours in 2008, w h ic h is expected to be further increased in e\'ery year d e p e n d in g on population a n d eco­nomic g ro w th [11] This data indicates that m ore th a n 1,900 billion kilowatt-hours

is l o n s u m e d by electric motors annually in the United States, w'hich is the biggest energy con su m p tio n by any single electric device in m o d e rn society

With the rap id ly in creased p o p u la tio n a n d h u g e electric e n e r g y c o n s u m p ­tion, s o p h isticated control a n d reliability of m o to r o p e ra tio n s from a h a r s h

in d u s tria l env ir o n m e n t h a s n o w b e e n a m ajor r e q u i r e m e n t in m a n y i n d u s ­trial applications It is especially im p o r t a n t w h e r e a n u n e x p e c te d s h u t d o w n

m ig h t result in the in te r r u p tio n of critical services such as m edical, t r a n s ­

p o rta tio n , o r m ilita ry operatio n s In th o se ap p lic a tio n s w h e r e c o n tin u o u s proc ess is n e e d e d a n d w h e r e d o w n tim e is n o t tolerable, a n u n e x p e c t e d fail­ure« of a m o t o r m ig h t result in costly m a i n t e n a n c e or loss of life

A s s h o w n in Figure 1.1, the electrical m o to r c onsists of m a n y m e c h a n ic a l

a n d electrical parts, such as a ro to r bar, rotor m a g n e t, stato r w i n d i n g , end- ring, b e a rin g , a n d g e a r box D u e to th e c o m m o n ly h a r s h in d u s tria l e m i r o n - mc'nts, each p a r t of electric m o to rs is p o te n tia lly e x p o s e d to the h ig h risk of

u n e x p e c te d m echanical, chem ical, a n d electrical system failures The re a so n s

w h y electric m o to rs fail in i n d u s t r y have b een c o m m o n ly r e p o r te d as follows:

1 Post th e s t a n d a r d lifetim e

2 V\'rong-rated pow er, voltage, a n d c u r r e n t

E lectric M a ch in es: M oileling, C on dition M onitorin g, an d Fault D iag ’osis

5 Electrical stre ss fro m fast s w itc h in g in v erters or u n s ta b le g r o u n d

6 R esidual stress from m a n u f a c t u r i n g

7 M ista k e s d u r i n g r e p a irs

8 H a r s h application e n v i r o n m e n t (dust, w a te r leaks, e n v i r o n m e n t i l

\ ibration, chem ical c o n ta m in a tio n , h ig h te m p e ra tu re )

F ig u re 1.2 show's an e x a m p le of a w'ell know'n electrical m o to r fault such as

b e a r i n g ball d a m a g e T h e b e a r i n g ball is ta k e n from the b e a r i n g m o d u le that

h a d b e e n d i a g n o s e d as faculty for 6 m o n th s The m a i n t y p e s of m o to r fiults are c o m m o n ly ca te g o riz ed as electrical faults, m e c h a n ic a l faults, a n d cuter

d riv e sy stem defects, w h ic h a re as follow's [2-5]:

h A ir-g a p irr e g u la r ity

3 O u te r m o to r d riv e s y ste m failures

a l n \ ’e rte r sy stem failure

b U nstable x’o l t a g e /c u r r e n t so u rce

c S h o rte d o r o p e n e d s u p p ly line

HC;iJRE 1.2

H e.irii'.g b a ll fa u lt a n d s u b s e c iu e n t f a t ig u e d a m a g e V ib r a tio n c o n s u lt a n t , h t t p : / / w w w

Electric Machines: Modeling, Condition Monitoring, and Fault Diagnosis

T h e b e a r i n g fault is k n o w n to m a k e u p a lm o s t 40%, stator related ab o u t 3cS"o,

ro to r related a b o u t 10%, a n d o th e rs m a k e u p 12% of w h o le electrical m o to r fault [2-6],

T h e electric m o to r d e s ig n is c o m m o n ly i n t e n d e d to h ave electrical a n d

m e c h a n ic a l s y m m e t r y in th e stato r a n d the ro to r for b e tte r c o u p lin g a n d

h ig h e r efficiency Fault co n d itio n in a m o to r d e s c rib e d earlier is s u p p o s e d to

d a m a g e the s y m m e tr ic a l p r o p e r t y w'here fa u lt- d e p e n d e n t m o to r o p e ra tio n

M o st a b n o r m a l s y m p t o m s h ave b e e n k n o w n to h ave specific p a tte r n s

p e r t a i n i n g to the m o to r fault c o n d itio n s a n d severity, such as p a r tic u la r fre ­quency, d u ra tio n , a m p litu d e , variance, degree, a n d phase Based on m o n i ­

to rin g a n d a n a ly z in g th e e x p e c te d s y m p t o m s a n d th e ir specific p atterns,

m a n y m o to r fault d ia g n o s e s h a v e b e e n su g g ested , a n d th ere hav'e b een sev ­eral c o m m e rc ia l so lu tio n s in the i n d u s t r y m a r k e t as s h o w n in Figure 1.3 In

p a rtic u la r, the v ib ra tio n s p e c t r u m in F ig u re 1.3a is fro m th e b e a r in g m o d u le

w ith defect ball iii fig u re 1.2 Based on the s p e c t r u m m o n i t o r i n g technique,

th e b e a r i n g m o d u l e is d ia g o n o s e d faculty a n d safely re m o v e d before the s y s ­

te m falls in to c a ta s tro p h ic failure m ode

d A coustic n o ise a n aly sis

e E lec tro m a g n etic field m o n i t o r i n g t h r o u g h i n s e r te d coil

f I n s t a n t a n e o u s o u t p u t p o w e r v a ria tio n analysis

g I n f r a r e d an aly sis

h G as analysis

6 Electric Machines: Modeling, Condition Monitoring, and Fault Diagiu'sis

e Finite-elem ent (FE) m a g n e tic circuit e q u iv a le n ts

f L in e a r-c irc u it-th e o ry -b a se d m a th e m a tic a l m o d e ls

3 M a c h in e -th e o ry -b a s e d fault analysis

a W i n d i n g fu n c tio n a p p r o a c h (WFA)

b M odified w i n d i n g fu n c tio n a p p r o a c h (MWFA)

c M a g n e tic e q u iv a le n t c ircuit (MEC)

4 S im u la tio n s -b a s e d fault analysis

a F inite-elem ent an a ly sis (FEA)

b T im e-step co u p le d finite ele m e n t state space a n aly sis (TSCFE-SS)

The d iffe re n t ty p e s of fault d ia g n o s is m e t h o d s h a v e b e e n s im u lta n e o u s ly

a p p lie d to fin e -tu n e the d e te c tio n in in d u stry The fault d ia g n o s is of electri­cal m o to r s is e x p e c te d to p ro v id e w a r n i n g of i m m i n e n t failures, d i a g n o s i n g

s c h e d u l i n g i n f o r m a tio n for f u tu r e p rev en tiv e m ain te n a n c e

The im p le m e n ta tio n of fault d ia g n o sis h a s b e e n d o n e w ith the following routine:

a D ecide fault existence

b D ecide fault s everity

3 Feed b ack to m o to r co n tro ller o r h u m a n m terface

a L im it m o to r o p e ra tio n b a s e d on fault severity

b S c h e d u le m a in te n a n c e

Fig u re 1.4 s h o w s th e in c re a s e d co n v erg en ce b e t w e e n the e n e r g y system

a n d m o d e r n n e t w o r k s y s te m in m o d e r n ind u stry T h e electrical m o to r s in a car, ship, aircraft, b u ild in g , road, or in a p o w e r sy stem can b e a s s u m e d to be

w a r d e d to a close or re m o te m ic ro c o n tro lle r or digital p ro c e sso r of w h ic h the controller p e r f o r m s in d iv id u a l sy stem control, w h o le sy stem m a n a g e m e n t,

d ia g n o s is s e e m s to be d riv e -in te g ra te d fault d ia g n o s is s y s te m s w ith in m o to r

d riv e DSP w i t h o u t u s in g a n y ex tern al h a r d w a r e [8]

T h is b o o k is i n t e n d e d to p ro v id e f u n d a m e n t a l s of v a rio u s m o to r fault co n ­ditions, adx a n c e d fault m o d e lin g theory, d iv e rse fault d ia g n o s is te c h n iq u e s,

a n d low cost DSP-based fault d ia g n o s is im p le m e n ta tio n strategies

8 Electric Machines: Modeling, Condition Monitoring, and Vault Diagnosis

R e f e r e n c e s

[1] H A T oliyat a n d S.G C a m p b e ll, D SP -B ased E lectrom echan ical M otion Control,

Boca R aton, FL: CRC P ress, 2003

[2] G.B, K lim an, R.A K o e g l,].S te in , R.D E n d ic o tt,a n d M.W M a d d e n , " X o n in v a s iv e

d e te c tio n o f b ro k e n ro to r b a rs in o p e ra tin g in d u c tio n m o to rs," IEEE Trniisiiclioii>

on E nergy C onversion s, vol 3, p p 873-879, D e c e m b e r 1988

[3] S N a n d i, H A T oliyat, a n d X Li, " C o n d itio n m o n ito rin g a n d fau lt d ia g n o s is o f

e lec trical m a c h in e s— A rev iew ," IEEE T ransactions on Encr^^y C onversion , \ ol 20,

no 4, p p 719-729, D e c e m b e r 2005

[4] A Siddic]ue, G.S Y ad a\ a, a n d B S in g h , "A rev iew o f s ta to r fau lt m o n ito rin g

te c h n iq u e s o f in d u c tio n m o to rs," IEEE Trans, on E nergy C onversion , \'o l 20, p p 106-114, M arch 2005

[5] M El H a c h e m i B e n b o u z id , "A rev iew o f in d u c tio n m o to rs s ig n a tu re a n a ly s is as

a m e d iu m for fa u lts d e te c tio n ," IEEE Transactions on Indu strial E lectronics, vol

47, p p 984-993, O c to b e r 2000

[6] Y.E Z h o n g m in g a n d W.L' Bin, "A rev iew o n in d u c tio n m o to r o n lin e fault d ia g ­

n o sis," IEEE IPEM COO, vol 3, p p 1353-1358, 2000

[7] B A k in , U O rg u n e r, H T oliyat, a n d .M R ayner, " P h a s e se n s itiv e d e te c tio n o f

m o to r fau lt s ig n a tu re s in th e p re s e n c e o f n o ise ," IEEE Trniisaclions on Indu strial

E lectronics, \ ol 55, no 6, J u n e 2008

[8] B A kin, U O rg u n e r, H T oliyat, a n d M R ayner, "L o w o rd e r PW.M in v e rte r h.u'-

m o n ic s c o n tr ib u tio n s to th e in v e rte r fed IM fa u lt d ia g n o s is ," IEEE T ransaclions

on Indu strial E lectronics, vol 55, p p 610-619, F e b ru a ry 2008

[9] S C h o i, "R o b u st C o n d itio n M o n ito rin g a n d F au lt D ia g n o sis o f V ariable S p eed

D riv e o f In d u c tio n .Motor," P h D d is s e rta tio n , Texas A & M U n iv ersity , 2010.[10] W.T T h o m so n a n d M Fenger, " C u rr e n t s ig n a tu re a n a ly s is to d e te c t in d u c tio n

m o to r fa u lts," IEEE Industry A pplication s M agazine, vol 7, no 4, 2001

[11] U.S E n erg y In fo rm a tio n A d m in is tra tio n , " A n n u a l E n erg y O u tlo o k 2010: W ith

P ro jectio n s to 2035," W a sh in g to n , DC, A p ril 2010

b a r faults, b e a r i n g faults, a n d stator faults, w h ic h a c c o u n t for m o re t h a n 90%

of o\ erall i n d u c tio n m o to r failures, a re c o n s id e re d [1-3]

2.1.1 Bearing Faults

B e a rin g faults a c c o u n t for m o re t h a n 40°/o of all electric m o to r failures [5-7] Most of the b e a r in g s in in d u s tr ia l facilities r u n u n d e r n o n id e a l c o n d itio n s

a n d a r e subject to fatigue, a m b ie n t m e c h a n ic a l \'ibration, o v e rlo ad in g , m i s ­

a lig n m e n t, c o n ta m in a tio n , c u r r e n t fluting, corrosion, a n d w r o n g lubrica­tion T h e s e n o n id e a l c o n d itio n s s ta r t as m a r g i n a l defects that s p r e a d a n d

p r o p a g a te on the in n e r raceway, o u te r raceways, a n d ro llin g e le m e n ts (see

F ig u re 2.1) A fter a w h ile the defect b e c o m e s significant a n d g e n e ra te s

m e c h a n ic a l v ibration c a u s in g acoustic noise Basically, b e a r i n g faults c a n be classified a s o u te r raceway, in n e r raceway, ball defect, a n d cage defect, w h ic h

a re the m a i n so u rc e s of m a c h i n e vibration T h ese m e c h a n ic a l v ib ra tio n s in the a ir g a p d u e to b e a r in g faults c a n be c o n s id e re d as slight rotor d is p la c e ­

m e n ts, w h ic h re su lt in in s ta n t eccentricities Therefore, the basic fault sig­

n a t u r e f re q u e n c y e q u a tio n of line c u r r e n t d u e to b e a r in g defects is a d o p te d from e c c en tricity lite ra tu re [10]

M e c h a n ic a l v ibration, in f r a r e d or th e rm a l, a n d acoustic a n a ly s e s a re so m e

of th e c o m m o n l y u s e d p re d ic tiv e m a i n t e n a n c e m e t h o d s to m o n i t o r the he.ilth of th e b e a r in g s to p re v e n t m o to r failures

10 Electric Machines: Modeling, Condition Monitoring, and Fault D ia ^icsis

Vibration a n d th e r m a l m o n ito r in g r e q u ir e a d d itio n a l s e n s o rs or t r a n s ­

d u c e rs to be fitted on the m a c h in e s W h ile so m e large m o to rs m ay a lread y

c o m e w ith v ibration a n d th e rm a l tr a n s d u c e rs , it is no t ec o n o m ic a lly or ph\'si- cally feasible to p ro \ ide the s a m e for s m a lle r m a c h in e s Therefore, small- to

m e d iu m - s iz e m o to rs a re ch e c k e d p e rio d ic a lly by m o \'in g p o rta b le e q u i p ­

m e n t fro m m a c h i n e to m a c h i n e in all th r e e m e th o d s S o m e m o to rs used in critical applications, su c h as n u c le a r reactor cooling p u m p m otors, m ay not

b e easily accessible d u r i n g reactor operatio n T he lack of c o n tin u o u s m o n ito r­

in g a n d accessibility are the sh o r tc o m in g s of the a f o r e m e n tio n e d techniques

A n alte rn a te a p p r o a c h b a s e d on line c u r r e n t m o n ito r in g h a s r e c e i\e d m u c h

re s e a rc h a tte n tio n in search of p r o v id in g a practical so lu tio n to co n tin u o u s

m o n i t o r i n g a n d accessibility p roblem s M o to r c u r r e n t m o n i t o r i n g p ro v id es

a n o n i n t r u s i v e w’ay to c o n tin u o u s ly m o n ito r m o to r reliability w i t h m i n im a l

a d d itio n a l cost

B earing faults can b e classified as o u te r raceway, in n e r raceway, ball defect,

a n d cage defect Each fault h a s specific m e c h a n ic a l v ib ra tio n freq u en cy c o m ­

p o n e n t s th a t a re c h aracteristic of each defect ty p e, w'hich is a fun ctio n of

b o t h b e a r i n g g e o m e t r y a n d s p e e d T h e m e c h a n ic a l oscillations d u e to b e a r ­

in g faults c h a n g e th e air-g ap s y m m e t r y a n d m a c h in e i n d u c ta n c e s like eccen ­tricity faults T he m a c h i n e in d u c ta n c e v a ria tio n s a re reflected to the line

c u r r e n t in te r m s of c u r r e n t h a rm o n ic s , w h ic h are th e in d ic a to rs of b e a rin g fault asso ciated w ith m e c h a n ic a l oscillations in th e air-gap

f aults ill Induction and Synchro)wus Motors 11

A gen eric fault d ia g n o s is too! b a s e d on d is c r im in a tiv e e n e rg y f u n c tio n s is

p r o p o s e d by Ilonen et al [12] T h e se e n e r g y f u n c tio n s reveal d is c r im in a tiv e

f r e q u e n c y - d o m a i n re g io n s w h e r e failures are identified S choen [13] im p le ­

m e n t e d a n u n s u p e r v i s e d , on-line sy stem for in d u c tio n m o to r b a s e d on m o to r line c u rre n t A n a m p l i t u d e m o d u l a t i o n (AM) d e te c to r is d e v e lo p e d to d etect

th e b e a r i n g fault w h ile it is still in a n in cip ien t stage of d e v e lo p m e n t in Stack

et al [14] O c a k [15] d e v e lo p e d a h i d d e n M a rk o v m o d e lin g (H M M ) b a se d

b e a r i n g fault d ete c tio n a n d fault d iag n o sis Yazici a n d K lim a n [16] p r o p o s e d

an adaptiv'e statistical tim e -fre q u e n c y m e t h o d for d etectio n of b ro k e n rotor

b a r s a n d b e a r i n g faults in m o to rs u s i n g m o t o r line c u rre n t

2.1.2 Stator Faults

S tc \to r fau lts acco u n t for 30% to 40% of all electric m o to r failures [2,8,9] The

s ta to r fault can be b ro a d ly classified as the l a m in a tio n or f ra m e fault (core defect, c irc u la tio n c u rre n t, or g r o u n d , etc.) a n d th e stator w i n d i n g fault ( w i n d i n g in s u la tio n d a m a g e , d i s p la c e m e n t of c o n d u cto rs, etc.)

T h e m a jo r fu n ctio n of w i n d i n g in s u la tio n m a te ria ls n o r m a lly is to w i t h ­

s t a n d electric stress; how'ever, in m a n y cases it m u s t also e n d u r e o th e r

s tre s s e s s u c h as m e c h a n ic a l a n d e n v i r o n m e n t a l s tre sse s [19] In a motor,

th e to rq u e is the re s u lt of the force created by c u r r e n t in the c o n d u c to r a n d

s u r r o u n d i n g m a g n e tic field T h is s h o w s th a t w i n d i n g in su la tio n m u s t have

e lectrical as well a s m e c h a n ic a l p r o p e r tie s to w i t h s t a n d m e c h a n ic a l stre sse s[20], In a d d itio n , e le c tro m a g n e tic v ib ra tio n at tw ice the p o w e r frequency, dif­ferential e x p a n s io n forces d u e to the te m p e r a tu r e v a ria tio n s follow ing load

c h a n g e s , a n d im pact forces d u e to e le c tric a l/m e c h a n ic a l a s y m m e t r i e s also affect th e a g in g pro cess [21]

N o n u n i f o r m te m p e ra tu re d istrib u tio n in a m o to r will also cause m e ch an ical

d e s tr u c tio n d u e to dilation The m a n u f a c t u r i n g process itself m a y constitute

a t l a m a g i n g or ag in g action The electrical w i n d i n g insulation m u s t be strong

e n o u g h to w i t h s t a n d the m ec h a n ic al ab u se w h ile b ein g w o u n d an d in stalled

in th e motor Thus, the initial m ech an ical stresses are often very severe c o m ­

p a r e d to the s u b s e q u e n t a b u se the w i n d i n g in su latio n gets in service [20]

In c re a s e d te m p e r a t u r e s can cau se a n u m b e r of effects The m a te ria l m ay

be i n h e r e n t l y w e a k e r at elevated t e m p e r a t u r e s a n d a failure m a y o c c u r s im ­ply b e c a u s e of the m e ltin g of the m aterial T h is c a n be a v e r y s h o rt tim e fail­ure, b e c a u s e of the sh o rt le n g th of tim e r e q u ir e d for the t e m p e r a t u r e to rise

to t h e m e ltin g point O n the o th e r h a n d , long-term elevated t e m p e r a t u r e can

c a u s e in te rn a l chem ical effects on m a te ria l [19]

T h e r m a l stress is probably the m o st re c o g n iz e d cause of w i n d i n g in s u la ­tion d e g ra d a tio n an d u ltim ate failure The m a in sources of th erm al stress in electric m a c h i n e r y are c o p p e r losses, e d d y current, a n d stray load losses in the

c o p p e r conductors, plus additional h e a tin g d u e to core los.ses, w in d ag e, a n d so foi th [22] H ig h te m p e ra tu re causes a chemical reaction that m a k e s w 'inding

in s u la tio n m aterial brittle A n o th e r problem is that d u e to s u d d e n te m p e ra tu re

12 Electric Machiues: Modeling, Condition Monitoring, and Fault Diagiicsis

increase, c o p p e r co n d u c to r an d c o p p e r ba rs e x p a n d faster th a n w i n d i n g imsii- iation m aterial, w h ich causes stress on g r o u n d wall insulation [19],

A n o th e r significant effect on w i n d i n g in s u la tio n ag in g is p a rtia l d'is-

c h a rg e s (PD) Partial d is c h a r g e s are sm all electric s p a rk s th at o c c u r w itf iin

a ir b u b b le s in th e w i n d i n g in s u la tio n m aterial d u e to n o n u n i f o r m e lectric field d is trib u tio n O n c e b e g u n , PD c a u s e s p r o g r e s s i\’e d e te rio ra tio n of in^su- lating m aterials, u ltim a te ly le a d in g to electrical b r e a k d o w n O n the o t h e r

h a n d , m o to r w i n d i n g in su la tio n ex p e rie n c es h ig h e r voltage s tre sse s u h i e n

u s e d w i t h a n in v e rte r th a n w h e n c o n n e c te d directly to the a lte r n a tin g c u r ­ren t (AC) u tility grid T h e h ig h e r stre sse s a re d e p e n d e n t on th e m o to r c a b le

le n g th a n d a re c a u s e d by th e in teractio n of the fast rising voltage p u ls e s of

th e d riv e a n d tr a n s m is s io n line effects in the cable [23,24]

In a d d itio n to th e a fo re m e n tio n e d \ ’a rio u s causes, d e l a m i n a t i n g d is-

ch arg es, e n w i n d i n g d isc h a rg e s, m o i s t u r e attacks, abrasive m a te ria l attac.ks,

c h em ical d eco m p o sitio n , a n d ra d ia tio n can also be c o u n te d as accelerati ng effects o n a g in g of w i n d i n g in s u la tio n [25]

M o to r a n d g e n e ra to r w i n d i n g in s u la tio n failures d u r i n g m a c h i n e ope-ra- tion c a n lead to a cata stro p h ic m a c h i n e failure re s u ltin g in a costly outa.ige

P re v e n tio n of su c h a n o u ta g e is a m ajor c o n cern for b o th the m a c h in e m a n u ­

fa c tu re r a n d user, since it can re su lt in significant loss of re v e n u e d u r i n g t he

o u ta g e as well as r e p a ir o r r e p la c e m en t cost In the literatu re [19,25], PD is

ta k e n as a s ig n a tu r e of isolation agin g , w h ic h b e g in s w ith in voids, cracks, or

in clu sio n s w i t h i n a solid dielectric, at c o n d u c to r - d ie le c tr ic interfaces vvithiin solid o r liq u id dielectrics, o r in b u b b le s w i t h i n liquid dielectrics O n c e b e g u n ,

PD c a u se s p ro g re s s iv e d e te rio ra tio n of in s u la tin g m aterials, u ltim a te ly l e a d ­ing to electrical b re a k d o w n

W h e n a p a rtia l d is c h a r g e occurs, the e v e n t m a y be d e te c te d as a v ery sm.all

c h a n g e in the c u r r e n t d r a w n b y the sa m p le u n d e r test PD c u r r e n t s a re dlif- ficult to m e a s u r e b e c a u s e of th e ir sm all m a g n i t u d e a n d sh o rt d u r a t i o n [2!5] Therefore, PD in a m o t o r /g e n e r a to r before a b r e a k d o w n does n o t h a v e a siig- nificant effect on th e p o w e r system

T h e m o s t serio u s result of a m ajor fault m a y n o t o n ly d e s tro y the m ach im -

e ry b u t m a y s p r e a d in the sy stem a n d c a u se total failure T h e m o st coim-

m o n t y p e of fault, w h ic h is also th e m o s t d a n g e r o u s one, is the b r e a k d o w ns

th a t m a y h a v e several c o n seq u en ces A g re a t r e d u c tio n of the line voltaige

ov er a m a jo r p a r t of the p o w e r s y ste m w ill b e o b se rv e d If a n a lte r n a to r is

d a m a g e d , th is m i g h t affect th e w h o le system For exam ple, w h e n a toleer- able i n t e r - t u r n or i n -p h a s e fault occurs, th e p o w e r g e n e ra tio n w ill b e u n b a l ­

a n c e d a n d th e p o w e r q u a lity w ill d ra s tic a lly decrease Extra h a r m o n i c s w i l l

b e injected to th e w h o le system If th e a lte rn a to r fault is n o t tolerable o r it is

a p h a s e - to - p h a s e fault, th e n th e s u r g e w ill d a m a g e th e m a c h in e itself a n d

so m e p a r t s of the system U n lik e a m o t o r c o n n e c te d to t h e utility f o l l o w i n g a few s t e p - d o w n tra n s fo rm e rs , th e g e n e ra to r faults a re m o r e risk y in t e r m s of

p e r m a n e n t d a m a g e s a n d costly s h u t d o w n s d e p e n d i n g o n the g r id structuire

A m o to r w ith a tolerable i n te r - tu r n s h o r t b e h a v e s like a n u n b a la n c e d lo;ad

laiilts in Induction and Synchronous Motors 13

a n d d is tu r b s the n e ig h b o r in g utility However, a n a lte rn a to r failure affects

th e whole system , w h e r e a m o to r failure h a s lim ite d d is tre s s on the p o w e r system In b o th of th e se cases the p o w e r q u a lity of th e p o w e r sy ste m w ill be

d egraded

In the literature, th ere are several m e t h o d s for c o n d itio n m o n ito r in g a n d protection of m o to rs a n d generators T h e s u p e rio rity of th e se m e t h o d s

d e p e n d s on the t y p e of application, p o w e r ra tin g of the m a c h in e ry , location

of the m ach in ery , cost of m a c h i n e itself a n d sensors, a n d so on [24-25]

M o n ito rin g the t e m p e r a t u r e of th e h ig h p o w e r m o to r a n d g e n e ra to r stator w'indings, it is possible to d e t e r m i n e if the w i n d i n g is at risk of t h e r m a l d e t e ­rioration T h is can be d o n e e ith e r b y e m b e d d e d th e r m o c o u p le s or t h e r m a l cameras In a d d itio n , by m o n ito r in g th e te m p e r a tu r e , a n in c re a se in th e s ta ­tor t e m p e r a tu r e over tim e u n d e r the s a m e o p e r a tin g c o n d itio n s (load, a m b i ­ent te m p e ra tu re, a n d voltage) can be indicative of th e cooling s y s te m failure.Ozone g a s g en e ra tio n o c c u rs as a c o n s e q u e n c e of PD o n th e stato r coil Surface p a r tia l d is c h a r g e s are the cau se of d e te rio ra tio n fro m defective slot

a n d e n d - w i n d i n g stre ss relief c o a tin g s as w ell as co n d u c tiv e pollution By

m o n ito rin g th e o z o n e g as co n cen tratio n over time, failure m e c h a n i s m s th at give rise to the surface p a r tia l d is c h a r g e c a n be d e te c te d [26] T h u s o zo n e

m o n ito rin g d o e s n o t find p r o b le m s in the very early stag es of d e t e r io r a ­tion O zo n e m o n ito r in g can be d o n e p erio d ic a lly w i t h in e x p e n siv e c h em ical detectors th a t are t h r o w n a w a y after each use O th e r w is e , c o n tin u o u s o zo n e

m o n ito rin g is n o w feasible w i t h electronic detectors

In add itio n , p h a s e a n d g r o u n d fault relays a re in sta lle d in a m a c h i n e to

p r e \ e n t s ev ere m a c h in e d a m a g e c a u s e d by w i n d i n g in s u la tio n failure [20]

A n o th e r effective solution is on-line m o n ito r in g of p a rtia l d is c h a r g e that

w a r n s the u s e r before c a ta stro p h ic d a m a g e T h is can be d o n e e ith e r b y m o n i ­

to rin g differential line c u r r e n t or u s in g so m e special s e n s o r s s u c h as a n te n n a ,

h ig h voltage capacitors o n the m a c h in e te rm in a ls, or ra d io f re q u e n c y (RF)

c u r r e n t t r a n s f o r m e r s at the m a c h in e n e u tra l or on s u rg e capacitor g r o u n d s

T h ese sensors are sensitive to the h ig h fre q u e n c y sig n a ls from th e PD, yet are insensitive to the p o w e r fre q u e n c y voltage a n d its h a r m o n i c s [25]

Broken Rotor Bar Fault

T h e b ro k e n r o to r b a r fault c o n d i t i o n is sh o w 'n in F ig u r e 2.2, w h ic h

a c c o u n ts for m o r e t h a n 5% of all th e e lectric m o t o r f a ilu r e s in i n d u s t r y

C a g e rotors a r e b a s ic a lly of t w o ty p e s : cast a n d fa b ric a ted P re v io u sly ,

14 Electric Machines: Modeling, Condition Monitoring, and Fault Diagnosis

FIG U RE 2.2

B ro k en r o to r b a r in a n in d u c t io n m otor.

fa b ric a te d ty p e , c a n h a r d l y b e r e p a i r e d o n c e fa u lts lik e c r a c k e d o r breiken

r o t o r b a r s d e v e l o p in th e m

T here are a n u m b e r of reaso n s for ro to r b ar a n d e n d -rin g breakage T h e y can

b e ca u se d b y th erm al, m agnetic, d y n a m ic , en v iro n m e n ta l, m e c h a n ic al, a n d resid u al stresses Normally, the stresses re m a in w ith in the tolerance b a n d - w'idth a n d the m o to r op erates p ro p erly for years A n incipient b r o k e n rotor

b a r condition agg rav ates itself a lm o s t e x p o n e n tia lly in tim e as excessive c u r ­ren t flow' is e x p e c te d to b e co n cen trated o n adjacent b a r s in ste a d of th e b ro k e n one, W'hich p ro v id e s p ro p a g a te d electrical stress to adjacent areas W h e n any

of these stresses are above allowable levels, the lifetim e of the m o to r shortens

A b ro k e n ro to r b a r can be c o n sid e re d as ro to r a s y m m e t r y [17] th a t causes

u n b a l a n c e d line c u rre n ts , to rq u e p u lsa tio n , a n d d e c re a s e d a v e ra g e torc[ue[12] T h e electric a n d m a g n e tic a s y m m e t r y in in d u c tio n m a c h i n e rotors

b o o s ts u p the left sid e b a n d of s u p p ly fre q u e n c y [17]

E lk a s a b g y et al [29] show' th at b r o k e n ro to r b a r fault can be d e te c te d by tim e a n d f re q u e n c y d o m a i n an a ly sis of i n d u c e d voltages in s e a r c h coils

p laced in the motor D u r i n g r e g u l a r o p eratio n s, a s y m m e tr ic a l s ta to r w 'ind­

in g excited at fre q u e n c y / , in d u c e s ro to r b a r c u r r e n ts at s/, fre q u e n c ies [27],

W h e n a n a s y m m e t r y is i n t r o d u c e d in the rotor s tru c tu r e , the backw 'a rd

ro ta tin g n e g ativ e se q u e n c e -s/, c o m p o n e n t sta rts the c h a in electrical a n d

m e c h a n ic a l in tera c tio n s b e t w e e n th e ro to r a n d stato r of the m otor Initially, sta to r e le ctro m o tiv e force (EMF) at f re q u e n c y (1 - 2s)/, is i n d u c e d t h a t c a u s e s

to rq u e a n d s p e e d ripples A f te r w a r d , to rq u e a n d s p e e d ripples a re reflected

to th e stato r as line c u r r e n t o scillations at fre q u e n c y (1 + 2s)/, N ex t, (1 -f 2s) / , c o m p o n e n t in d u c e s ro to r c u r r e n t s at ±3s/, a n d th is c h a in rea c tio n g o e s on

u n t i l co m p letely b e in g filtered b y th e ro to r in ertia A p a r a m e te r- e s tim a tio n -

b a s e d b r o k e n ro to r b a r d e te c tio n is r e p o r t e d in [30] T h e h a r m o n i c s at the stato r te r m i n a l voltages i m m e d ia te ly after s w itc h in g off the m o t o r c a n be

u s e d as a d ia g n o stic m e t h o d [31]

¡units in Induction and Si/nclironous Motors 15

c o n s ta n t offset fro m the center of th e stator or the rotor is m is a lig n e d along the stator bore O n the o th e r h a n d w h e n d y n a m i c eccentricity occurs, the c e n ­terline of the s h a ft is at a \'a riable offset from the cen ter of the stato r o r m in i- mLim air-g ap revolves w ith the rotor If the d is ta n c e b e t u ’een the stator bore

an d ro to r is not ec^ual t h r o u g h o u t the e n tire m achine, v a r y i n g m a g n e tic flux

u 'ith in the air-g a p creates im b a la n c e s in the c u r r e n t flow, w h ic h can be iden- tilied in the c u r r e n t s p e c tr u m I m p r o p e r m o u n tin g , a loose or m is s in g bolt,

m is a lig n m e n t, o r ro to r u n b a la n c e m ig h t be cau ses of air-g a p eccentricity.Eccentricity is a c'juite w e ll- k n o w n p ro b le m a n d a n a ly tic a l resu lts s u p ­

p o rte d b)- e x p e r i m e n t s h ave a lre a d y b een re p o rte d In the literature, there are sexeral successful w o rk s r e p o r tin g fault d ia g n o s is of eccentricity based

on line c u r r e n t m e a s u r e m e n t U n lik e b e a r i n g faults, it is easier to d ia g n o s e ecci'ntricity ev'en for in\-erter-fed m a c h i n e cases d u e to th e ir h ig h a m p l i t u d e

I K iU R E 2.4

I

16 Electric Machines: Modeling, Condition Monitoring, and Fault Diagnosis

of fault s ig n a tu r e s w ith re sp e c t to th e noise floor in the line c u r r e n t s p e c ­

tr u m Because b o t h static anci d y n a m i c eccentricities tend to co ex ist in p r a c ­tice, on ly m ix e d eccentricity is c o n s id e re d to sh o w th e effects of i m e r t e r

h a rm o n ic s M a g n e tic field in th e a ir-g ap of a n eccentric m o to r is alw'ays n o n -

u n if o r m Since th e flux lin k a g e s in the air-g a p oscillate w i t h s y n c h r o n o u s frecjuency, a n y a d d itio n a l h a r m o n ic s oscillatin g at the s p e e d d u e to n o n u n i ­

fo rm s t r u c t u r e a re e x p e c te d to take place at ro ta tin g f re q u e n c y s i d e b a n d s of the s y n c h r o n o u s frequency

H ow ever, so m e faults like ro to r w i n d i n g faults, b ro k e n d a m p e r bars, or

en d -rin g s, are specific to w o u n d ro to r s y n c h r o n o u s m a c h in e s , a n d d e m a g ­

n e tiz a tio n faults are lim ite d to p e r m a n e n t m a g n e t s y n c h r o n o u s m a c h in e s (PMSMs)

Like in d u c tio n m a c h in e s, s y n c h r o n o u s m a c h in e s are subject to m a n y d if ­ferent t y p e s of m e c h a n ic a l a n d electrical faults, w h ic h c a n b r o a d ly be c la s ­sified in to the following: (1) o p e n or s h o rt circuit in o n e or m o r e t u r n s of

a stator w in d in g ; (2) o p e n o r s h o rt circu ited rotor w i n d i n g in w o u n d ro to r

s y n c h r o n o u s m ach in es; (3) b ro k e n d a m p e r b a r s or en d -rin g s; (4) ecce n trici­ties; (5) ro to r m e c h a n ic al faults su c h as b e a r i n g d a m a g e , b e n t s haft, a n d m i s ­

a lig n m e n t; a n d (6) d e m a g n e tiz a t io n fault in PMSMs

Each of th e se fault c o n d itio n s p r o d u c e s specific s y m p t o m s d u r i n g m o to r

S o m e of the fault c o n d itio n s in s y n c h r o n o u s m a c h in e s h ave s i m i l a r c a u s e s

a n d s y m p t o m s of the s a m e faults in th e in d u c tio n m a c h in e s , w h ic h h a v e

b e e n d i s c u s s e d in Section 2.1

faults in Induction and Si/Iĩcliroiìoiis Motors 17

2.2.1 Dam per W inding Fault

To p r o d u c e to rq u e in s y n c h r o n o u s m a c h in e s, the ro to r m u s t be t u r n i n g at

s y n c h r o n o u s s p e e d , w h ic h is th e s p e e d of th e stator field At an y o th e r s p e e d , thi' ro ta tin g field of stato r poles w ill n o t be s y n c h r o n i z e d w ith rotor poles,

b u t first attracts, a n d th e n rep els them T h is co n d itio n p ro d u c e s n o average

to rq u e a n d the m a c h in e w ill n o t start U sin g a d ire c t c u r r e n t (DC) m o to r or

a d a m p e r w i n d i n g , the m a c h i n e c a n be b r o u g h t n e a r to the s y n c h r o n o u s speed D a m p e r w in d in g s , as s h o w n in F ig u re 2.5, consist of h e a v y c o p p e r bars, w i t h th e tw'o e n d s s h o r te d together, in s ta lle d in ro to r slots T h e c u r ­ren ts i n d u c e d in the b a rs interact by th e ro ta tin g air-g a p field a n d p r o d u c e s torque In o t h e r w o rd s, the m a c h i n e is s ta r te d as an in d u c tio n m o to r [33]

T h e field w i n d i n g is excited b y a d ire c t c u r r e n t w'hen the m a c h i n e is b r o u g h t

u p to th e s y n c h r o n o u s s p eed W h e n th e load is s u d d e n l y c h a n g e d , a n oscil­latory m o tio n w ill be s u p e r i m p o s e d o n th e n o r m a l s y n c h r o n o u s ro ta tio n of

th e shaft T h e d a m p e r w i n d i n g h e lp s d a m p o u t these oscillations

D iag n o stic s of b ro k e n d a m p e r b a rs in s y n c h r o n o u s m a c h in e s h a s n o t b e e n

c o v e re d as w id e ly as the o th e r faults like eccentricity a n d i n te r - tu r n faults [34-37], D u r i n g transience, the e le c tro m a g n e tic b e h a v io r of a s y n c h r o n o u s

m a c h i n e s w i t h d a m p e r w i n d i n g is s im ila r to th at of a n in d u c tio n m ach in e

D u r i n g tra n s ie n t time, w h e n the m a c h in e accelerates fro m zero s p e e d to s y n ­

c h r o n o u s s p e e d , a significant c u r r e n t flow's in the d a m p e r w in d in g Excessive

FIG U RE 2.5

A s a lie n t pi>le s y n c h r o n o u s m a c h in e w it h

(( (H ỉĩtesN ’ o f T H C O -W e st in g lio iise )

TRƯƠNG 'DH f-A \G

w iiiiJ iiig a n d in t pr r iip ti‘i1 e n d - r in g

TAI LIỆU THƯ VIEN

18 Electric Machines: Modeling, Condition Monitoring, and f a u l t Diagnosis

s t a r t - s t o p cycles o r fre q u e n t load or s p e e d c h a n g e s can c a u s e the b re a k a g e

of the d a m p e r bars

A n on-line fault d ia g n o s is m e t h o d for d e te c tio n of b r o k e n r o to r b a rs h as

b e e n p r o p o s e d b y K r a m e r [38] u s in g flux p ro b e a n d finite e le m e n t (FE) niod- eling For the sq u irre l-c a g e in d u c tio n m a c h in e s , several m e t h o d s of d e te c ­tion of b ro k e n ro to r b a r s h a v e b e e n r e p o r t e d in the literatu re It h a s b e e n

f o u n d th a t in s q u irrel-cag e in d u c tio n m a c h in e s w h e n a b a r b r e a k s so m e of the c u r r e n t th at w o u l d have flowed in th a t b a r w ill flow in to th e tu-o adjacont

b a rs on e ith e r side T h is co u ld result in b r e a k a g e of several b a r s [39] Sim ilar effects h a v e b e e n r e p o r t e d for the con\'e rter-fed s y n c h r o n o u s m a c h i n e s w ith

b ro k e n d a m p e r b a rs [40] W i n d i n g fu n c tio n an aly sis a n d ti m e - s t e p p i n g FE

a n aly sis h ave b e e n u s e d to s t u d y th e b ro k e n d a m p e r b a r s a n d e n d - r in g s [38,41],

For d e te c tin g the b r o k e n d a m p e r bars, flux p ro b e s c a n be a tta c h e d to the stator b o re surface for m e a s u r e m e n t of air-g a p flux w a v e f o r m d u r i n g accel­eration from s ta n d s till to rated sp e e d [38], A n o th e r m e t h o d is th e s e p a ra tio n

of pole voltages of th e field w i n d i n g a c c o rd in g to its polarity T h is way, the

d ifference of the pole voltages c a n be d e te r m in e d T he m a i n field of a s y m ­

m e tric a l b u ilt m a c h i n e d i s a p p e a r s in the differen ce voltage, b u t the d iffe r­ence voltage, w h ic h is c a u s e d b y p e r t u r b e d field of the m i s s i n g d a m p e r bar,

h ig h efficiency, low noise, h ig h to rq u e to c u r r e n t ratio, h i g h p o w e r to w e ig h t ratio, a n d ro b u stn ess

D u r i n g the n o r m a l o p e ra tio n of th e PMSM, th e in v e rs e m a g n e tic field

p r o d u c e d by the stato r c u r r e n t o p p o s e s the p e r m a n e n t m a g n e t s ' r e m a n e n t

in d u c tio n W h e n th is p h e n o m e n o n is re p e a te d , the p e r m a n e n t m a g n e t s will

b e d e m a g n e tiz e d T h is d e m a g n e t i z a t i o n c a n be all ov er th e p o le (complete

d e m a g n e tiz atio n ), or o n a p a r t of the pole (partial d e m a g n e tiz a tio n ) H ig h

t e m p e r a t u r e c a n also d e m a g n e t i z e the m a g n e t Stator w i n d i n g sh o rt-circu it fault m a y p a r tia lly d e m a g n e t i z e a su rfa c e m o u n t m a g n e t P a r tia l d e m a g n e ­tiza tio n c au ses m a g n e tic force h a r m o n ic s , noise, a n d m e c h a n i c a l vib ratio n ,

c a u s in g u n b a l a n c e d m a g n e tic p u l l in th e m achine

T h e d e m a g n e t i z a t i o n effects o n the p a r a m e te rs of the m o to r, su c h a s cog­

g in g torque, to rq u e ripple, back-EMF, a n d load an g le c u rv e , w e r e in v e s ti­

g a te d b y R uiz e t al.[43] For steady-state a n aly sis u n d e r d e m a g n e t i z a t i o n

c o n d itio n s, fast Fou rier tr a n s f o r m (FFT) of the s ta to r c u r r e n t is u s e d for

faults in Induction a n d Si/nchwnoHS Motors 19

freq u en cy analysis T im e -fre q u en c y an a ly sis methcids have b e e n u s e d for

n o n s ta tio n a r y con d itio n s T hese te c h n iq u e s, such as sh o rt-tim e F ourier tra n sfo rm (STFT), c o n t i n u o u s u ’avelet tr a n s f o r m (CVVT), a n d d isc re te w a v e ­let tra n sfo rm (DWT), r e q u ir e the p r o p e r selection of the p a r a m e te rs s u c h as

w 'in d o w size a n d coefficients

Field r e c o n s tru c tio n m e th o d (FRM) can also be u s e d to d etect th e d e m a g ­

n e tiz a tio n fault in PM SM s The flux lin k a g e s of the stato r ph a se s, w h ic h are calcu lated by FRM, a r e u s e d to m o n ito r the faults [44]

T h e re a re tw o t y p e s of eccentricity in the s y n c h r o n o u s m o to r as in the

i n d u c tio n m otor: static a n d d y n a m ic In the case of static eccentricity, the

c enterline of the s h a f t is at a c o n s ta n t offset from the cen ter of the stator Therefore, th e n o n u n i f o r m air-g a p d o e s no t v a r y in time O n the o th e r h a n d , v\'hen d y n a m i c eccentricity occurs, the cen terlin e of the sh a ft is at a variable offset from the c e n te r of the stator a n d the air-g a p le n g th c h a n g e s as th e ro tor rotates d y n a m ic a lly In reality, b o th static a n d d y n a m i c eccentricities tend

to coexist I m p r o p e r m o u n t i n g , the n o n c ir c u la r ity of the stato r core, a loose

or m is s in g bolt, a b e n t ro to r sh a ft o r m is a lig n m e n t, b e a r in g wear, a n d rotor

u n b a la n c e m ig h t be c a u s e s of air-g a p eccentricity

V arious fault d ia g n o s i s m e t h o d s for eccentricity fault d e te c tio n in s y n ­

c h r o n o u s m a c h i n e s h a \ e been p r o p o s e d in literature The m o d ifie d w i n d i n g

fu n ctio n a p p r o a c h (MWFA) a c c o u n tin g for all space h a rm o n ic s , a n d th e FE

m e th o d h a v e been u s e d to m o d e l th e salien t pole s y n c h r o n o u s m a c h in e s

T h e s e m o d e ls s h o w th e effect of d y n a m i c air-g a p eccentricity on the p e r f o r ­

m a n c e of a salient p o le s y n c h r o n o u s m a c h i n e [45]

E b ra h im i et al p r e s e n t a m e t h o d of d e te c tin g static eccentricity (SE),

d ) ’n a m ic eccentricity (DE), a n d m ix e d eccentricity (ME) in t h r e e - p h a s e i’MSVls [46] The n o m i n a t e d in dex is the a m p l i t u d e of sid e b a n d c o m p o ­

n e n t s w ith a p a r t i c u l a r fre q u e n c y p a tte r n in th e stato r c u r r e n t s p e c t r u m

T h e occu rren ce, as well as the t y p e a n d percentage, of eccentricity c a n be

i l e te r m in e d u sin g t h is index A fter d e t e r m i n a t i o n of the co rrelatio n b e tw e e n

th e in dex a n d the SE a n d DE, the t y p e of the eccentricity is d e t e r m i n e d by a A-nearest n e ig h b o r classifier T h e n a th ree-lay er artificial n e u ra l n e tw o r k is

e n ip lo v e d to e s tim a te the eccentricity d e g r e e a n d its type

20 Electric Machines: Modeling, Condition Monitoring, and Fault D iapiosis

Le R oux et al in v estig ate im p le m e n ta tio n a n d d e te c tio n of ro to r faults

u ltim a te failure is th e r m a l stress T h e dielectric, c orona, tra c k in g , an d t r a n ­sient voltage c o n d itio n s a re so m e of th e electrical stre sse s le a d in g to in te r­

t u r n s h o r t circuit failures [48]

In th e case of a n in te r - tu r n fault in stato r w i n d i n g , th e s y m m e t r y of the

m a c h in e is d e stro y e d T h is p r o d u c e s a r e \’erse ro ta tin g field th a t decreases

th e o u t p u t to rq u e a n d in c re a se s losses p e r a m p e r e of fu n d a m e n t a l frequency

of the positive s e q u e n c e c u rre n t T h e stator faults in s y n c h r o n o u s reluctance

m o to rs (SynRM) u n d e r steady-state o p e r a tin g c o n d itio n s h a v e b e e n s tu d ie d

in [49] T h e d e ta ile d m o d e lin g of the faulted m a c h in e h a s b e e n carried o u t

u s i n g a m o d ifie d w i n d i n g fu n c tio n a p p r o a c h (MWFA) M o n ito r in g the stator

c u r r e n t in th e p re se n c e of su c h faults s h o w s th at o d d triple h a rm o n ic s a re

in c re a s e d in the line c u r r e n t of S ynR M w ith in te r - tu r n fault The line c u r r e n t

of th e faulty p h a s e in creases f u r th e r w h e n the n u m b e r of sh o r te d t u r n s g o e s

up T h e in c re a se of the 9 th h a r m o n i c se e m s to be a g o o d in d icatio n of th e

c o m p o n e n ts clearly in c re a s e d w ith stato r in te r - tu r n fault T h e fin d in g s a r e

h e lp fu l to d etect faults in v o lv in g few t u r n s w ith o u t a m b ig u ity , in spite of

s u p p ly u n b a la n c e a n d tim e harm cm ics [35]

For a n a ly z in g in te rn a l p h a s e a n d g r o u n d faults in stator w in d in g , a

m a th e m a tic a l m o d e l for a s y n c h r o n o u s m a c h in e h a s b e e n p re s e n te d b y

R e ic h m e id e r et al [50] T h is m e t h o d e m p lo y s a d ir e c t p h a s e represer.tation,

u s i n g a tra d itio n a l c o u p le d circuit a p p ro a c h

A specific fre q u e n c y p a t t e r n of th e s ta to r c u r r e n t is d e r iv e d for short-circuit fault d e te c tio n in PM SM s [51] T h e a m p l i t u d e of th e s i d e - b a n d c o m p o n e n ts at

th e se fre q u e n c ies is u s e d to d e t e r m i n e th e n u m b e r of sh o rt-c irc u ite d t u r n s

U sin g th e m u t u a l in f o r m a tio n index, th e relation b e t w e e n the n o m in a te d c r i ­terio n a n d the n u m b e r of sh o rt-c irc u ite d t u r n s is specified T h e o c c u rre n ce

/ aults ill Induction and S}/nchronous Motors 21

a n d the n u m b e r of sh o rt-c irc u ite d t u r n s a re p re d ic te d u s in g s u p p o r t x’ector

m a c h in e (SVM) as a classifier

The tw o -reactio n th e o ry is well su ite d for c o m p u te r m o d e lin g s y n c h r o n o u s

m achines How ever, in the d eriv a tio n of th e dqO m o d e l of a s y n c h r o n o u s

m achine, th e m a c h i n e w i n d i n g s a re a s s u m e d to b e s in u s o id a lly d is trib u te d

T his im plies th at all h i g h e r space h a r m o n ic s p r o d u c e d in the case of an

in tern al fault, the s ta to r w i n d i n g s n o longer h a v e th e ch aracteristics of s i n u ­soidally d is tr ib u te d w i n d i n g s The faulted w i n d i n g s w ill p r o d u c e s tro n g e r space h a rm o n ic s M oreover, the s y m m e t r y b e t w e e n the m a c h i n e w i n d i n g s W’ill no lo n g er be presen t Therefore, the co n v e n tio n a l dqO m o d e l is n o t su ite d

to an a ly z e in te rn a l faults

In ter-tu rn faults of a s y n c h r o n o u s m a c h in e can be m o d e le d b a s e d on the actual w i n d i n g a r ra n g e m e n ts T his m e th o d , w h ic h is k n o w n as w i n d i n g function a p p ro a c h , calculates the m a c h in e in d u c ta n c e s directly fro m the

m a c h in e w i n d i n g d istrib u tio n U sin g th is m odel, th e space h a r m o n ic s p r o ­

d u ced by th e m a c h in e w i n d i n g s are ta k e n into acco u n t [52] A b d a lla h et al

u s e a w i n d i n g fu n c tio n a p p r o a c h to sim u la te in te r-tu rn faults in stator w i n d ­ings of the p e r m a n e n t m a g n e t s y n c h r o n o u s m a c h in e s [53]

The ti m e - s t e p p i n g finite e le m e n t m e t h o d (FEM) is a n o t h e r a n a ly s is

m i'th o d to s t u d y a s y n c h r o n o u s m a c h i n e w ith in te r - tu r n fault V aseghi et

al e m p lo y FEM for in te r n a l fault a n a ly s is of a s u r f a c e - m o u n te d p e r m a n e n t -

m a g n e t s y n c h r o n o u s m a c h i n e [54] It is u s e d for m a g n e tic field s t u d y a n d

d e t e r m i n i n g th e m a c h i n e p a r a m e t e r s u n d e r \'a r io u s fault c o n d itio n s a n d

th e effect of m a c h i n e p ole n u m b e r a n d n u m b e r of faulted t u r n s on m a c h in e

p a ra m e te rs

2.2.5 Rotor Inter-Turn Fault

Kotor w i n d i n g in te r - tu r n fault is a c o m m o n electrical fault in s y n c h r o n o u s

m a c h in e s Its existence m a y result in s e rio u s p ro b le m s su c h as h i g h rotor

c u rre n t, h ig h w i n d i n g te m p e r a tu r e , low reactive o u t p u t pow'er, d is to rte d

\ o l t a g e w a v e fo rm , a n d m e c h a n ic a l vibration T he rotor w i n d i n g in te r - tu r n fault is m a in ly c a u s e d by p o o r m a n u f a c t u r i n g o r o p e r a tin g c o n d itio n s such

as loose ro to r end w i n d i n g , loose s p acer block, p o o r t r i m m i n g of s o ld ered joint, d e fo rm a tio n of h i g h - s p e e d rotor w i n d i n g d u e to cen trifu g a l force, o v e r­heating, a n d p o o r in su la tio n

T h e re a re m a n y s t u d ie s a b o u t fault d ia g n o s is of ro to r w i n d i n g tu rn -to -

t u r n faults O n e m e t h o d is b a s e d on in d ire c t m e a s u r e m e n t of the i m p e d a n c e

of the rotor field w i n d i n g d u r i n g o p e ra tio n [55] T h is m e th o d is u se fu l vs'hen thi' n i u n b e r of s h o rte d t u r n s is significant

S o m e m e t h o d s a re b a s e d on d e te c tio n of flux a s y m m e t r y c re a te d by

s h o rte d t u r n s by a p p ly in g a l te r n a tin g c u r r e n t to the field [56] T h is m e t h o d

is a c c u ra te b u t n ot e a sy to i m p le m e n t b e cau se it r e q u ire s r e m o v in g the rotor from the bore

22 Electric Machines: Modeling, Condition Monitoring, and Fault D iapiosis

So m e reliable m e t h o d s b a s e d on d ir e c t m e a s u r e m e n t of the air-g ap m a g ­netic flux can b e a p p lie d to the m a c h i n e in o p e ra tio n [57] T h e flux i> m e a ­

s u r e d b y a s earch coil in stalled in the a ir gap

The n e u r a l n e tw o r k m o d e ls of m a c h in e s can b e u s e d to d e te c t th t rotor

t u r n faults T h is m e t h o d re q u ire s tr a i n i n g d a ta t h r o u g h s im u la tio n o r exper­iment A m a th e m a tic a l m o d e l of the m a c h in e is n e e d e d for s im u la to c data The e x p e r im e n ta l t r a in in g d a ta can b e acc^uired u s in g a m a c h i n e in w hich

th e ro to r t u r n s can be sh o rted , Streifel et al p r o p o s e a m e t h o d b a s e d on tra\ - elin g w a v e [58] T h is m e t h o d alo n g w i t h n e u r a l n e tw o r k fe a tu re ex tr.u tio n

a n d n o v e lty d etectio n a lg o rith m is u s e d for fault d ia g n o s is of short-circuited

w i n d i n g s in an y ro ta tin g m a c h in e r y a n d o th e r e q u i p m e n t c o n t a in in g s y m ­

m etrical w in d in g s

T he t e r m in a l p a r a m e te rs a re affected by the fault c o n d itio n of the rotor

w i n d i n g , b u t it is difficult to relate th e m to g e th e r b y ac c u ra te m a th e m a ti­cal exp ressio n s A n artificial n e u ra l n e tw o r k m e t h o d is in\'e stigated by

H o n g z h o n g et al for ro to r s h o r te d w i n d i n g fault d ia g n o s is [59] Since it is difficult to find the faulty sa m p le s in practical applications, th e se sam ples are g a in e d t h r o u g h calculation U sing th is m e th o d , the se\ erity of the fault

c an b e d e te c te d , b u t the location of the fault c a n n o t be d e t e r m in e d

2.2.6 Bearing Fault

Even u n d e r n o r m a l o p e r a tin g c o n d itio n s w ith b a la n c e d load a n d good

a l ig n m e n t, b e a r i n g failu res m a y tak e place F la k in g of b e a r i n g s m i g h t occur

w h e n fatig u e c a u se s sm a ll pieces to s e p a r a te fro m th e b e a rin g S o m e tim e s

b e a r i n g faults a re c o n s id e r e d as r o to r a s y m m e t r y faults, w h i c h a re u sually

c o v ered u n d e r the eccentricity-related faults T h e b e a r i n g fa ilu re s have been

r e p o r t e d fre q u e n tly in in d u stry D ifferent t e c h n iq u e s for a jo int tim e fre­

q u e n c y a n a ly s is a n d a n e x p e r i m e n t a l s t u d y of d e te c tio n a n d fault d ia g n o sis

of d a m a g e d b e a r i n g s o n a PM SM w e r e in v estig a te d by R o sero et al [60(

W h e n th e m o to r is r u n n i n g u n d e r n o n s t a t i o n a r y co n d itio n s, c o n \ e n t i o n a l sig n a l p ro c e s s in g m e t h o d s su c h as FFT in m o to r c u r r e n t s i g n a t u r e analysis (MCSA) d o n o t w o r k w'ell In s u c h co n d itio n s, th e s ta to r c u r r e n t can be a n a ­

ly zed b y m e a n s of STFT a n d G a b o r s p e c t r o g r a m for d e te c tin g th e b e a r in g

d a m a g e

A n o t h e r fault d ia g n o s is m e t h o d for d e te c tin g b e a r i n g fault in PMSM b a se d

o n f re q u e n c y r e s p o n s e an aly sis is p r o p o s e d by Pacas et al [61] The torque

a n d velocity sig n als of th e m a c h i n e w ill b e p erio d ic a lly d i s t u r b e d w h e n the

b e a r i n g is d a m a g e d T h e se d i s t u r b a n c e s cau se the f re q u e n c y r e s p o n s e of the

m e c h a n ic a l s y ste m to c h a n g e at specific frequencies U tiliz in g th e velocity of

th e m o to r a n d th e t o r q u e - g e n e r a tin g c o m p o n e n t of th e stato r c u r r e n t (/,,), the fre q u e n c y re s p o n s e of th e m a c h i n e in th e closed lo o p s p e e d control can be

d e riv e d T h e fre q u e n c y re s p o n s e an a ly sis p r o p o s e d in th is s t u d y yields more reliable fault d e te c tio n resu lts t h a n th e FFT analysis

ỉ íìiilts in Induction and Synchronous Motors 23

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