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

ELECTRIC MACHINES MODELING, CONDITION MONITORING, AND FAULT DIAGNOSIS r- ' ■ ( ^ -— j I ^ E y e W '^ ^ ' ^ Wo u n d s t a t o r r = '" In s u la tio n ^ ^ '' - yCi End Shield f' \ I ' Lam inations S Shaft Slinger Gasket To Fram e Protection To inner HAMID A TOLIYAT •SUBHASIS NANDI SEUNGDEOG CHOI • HOMAYOUN MESHGIN-KELK CRC Press , Taylor & Francis Croup 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 -^-1 hÀ\G HAI V ê \AM 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 C R C Press Taylor & Francis G ro u p 0 B r o k e n S o u n d P a r k w a y N\X', S u i t e 0 B o c a R a t o n , FL 3 48 - © by T a y l o r & F r a n c i s G r o u p , LLC C R C P r e s s is a n i m p r i n t o f T a y l o r & F r a n c i s G r o u p , a n I n t o r m a b u s i n e s s \ ' o c l a i m t o o r i g i n a l U.S G o v e r n m e n t w o r k s \ e r s i o n D at e : 2 I n t e r n a t i o n a l S t a n d a r d Bo o k N u m b e r : 97 - - - 7 - ( H a r d b a c k l T h is bo o k c o n ta in s in fo rm a tio n o b ta in e d from a u th e n tic a n d highly re g a rd e d so u rces R e a so n a b lf efforts h a v e b e e n m a d e t o p u b l i s h r e l ia b l e d a t a a n d i n f o r m a t i o n , b u t t h e a u t h o r a n d p u b l i s h e r c a n n o t a s s u m e r e s p o n s i b i l i t y for t h e v a l i d i t y o f all m a t e r i a l s o r t h e c o n s e q u e n c e s o f t h e i r use T h e a u t h o r s a n d p u b l i s h e r s h a v e a t t e m p t e d t o t r a c e t h e c o p y r i g h t h o l d e r s o f all m a t e r i a l r e p r o d u c e d in t h i s p u b l i c a t i o n a n d a p o l o g i z e to c o p y r i g h t h o l d e r s if p e r m i s s i o n t o p u b l i s h in t h i s f o r m h a s n o t b e e n o b t a i n e d If a n y c o p y r i g h t m a t o r i a l h as n o t b e e n a c k n o w l e d g e d p l e a s e w r i t e a n d let u s k n o w so w e m a y r e c t i f y in a n y f u t u r e r e p r i n t E x c e p t a s p e r m i t t e d u n d e r U.S C o p y r i g h t Law, n o p a r t o f t h i s b o o k m a y be r e p r i n t e d , r e p r o d u c e d , t r a n s m i t ­ t e d , o r u t i l i z e d in a n y f o r m by a n y e l e c t r o n i c , m e c h a n i c a l , o r o t h e r m e a n s , n o w k n o w n o r h e r e a f t e r i n v e n t e d , i n c l u d i n g p h o t o c o p y i n g , m i c r o f i l m i n g , a n d r e c o r d i n g , o r in a n y i n f o r m a t i o n s t o r a g e o r r e t r i e v a l s y s t e m , w ith o u t w ritte n p e rm issio n from the publishers F o r p e r m i s s i o n t o p h o t o c o p y o r u s e m a t e r i a l e l e c t r o n i c a l l y f r o m t h i s w o r k , p le as e ac c e s s w w w c o p y r i g h t c o m ( h t t p : / / w w w c o p y r i g h t c o m / ) o r c o n t a c t t h e C o p y r i g h t C l e a r a n c e C e n t e r , Inc (C C C ) , 2 R o s e w o o d D r iv e , D a n v e r s , M A , - - 0 C C C is a n o t - f o r - p r o f i t o r g a n i z a t i o n t h a t p r o v i d e s l i c e n s e s ind r e g i s t r a t i o n for a v a r i e t y o f u s e r s F or o r g a n i z a t i o n s t h a t h a v e b e e n g r a n t e d a p h o t o c o p y li c e n s e by t h e C C C , a s ep arate system o f p ay m en t has been arranged T r a d e m a r k N o t ic e : P r o d u c t o r c o r p o r a t e n a m e s m a y be t r a d e m a r k s o r r e g i s t e r e d t r a d e m a r k s , a n d a r e u s e d o n l y fo r i d e n t i f i c a t i o n a n d e x p l a n a t i o n w i t h o u t i n t e n t t o in f r i n g e L ib r y o f C o n g r e s s C a t a lo g in g - in - P u b lic a t io n D a ta E l e c t r i c m a c h i n e s : m o d e l i n g , c o n d i t i o n m o n i t o r i n g , a n d f au lt d i a g n o s i s / H a m i d A T o li ya t [et al.] p cm Includes bibliographical references a n d index I S BN - - - 7 - ( h a r d b a c k ) E l e c t r i c m a c h i n e r y - - R e l i a b i l i t y M a c h i n e r y - - M o n i t o r i n g M a c h i n e p a r t S ' - F a i l u r e s I To l iy at , H a m i d A T K 3 E 4 20 12 ’0 - d c V is it t h e T a y lo r & F r a n c is W e b s it e at h t t p : //w w w t a y lo r a n d f r a n c is c o m a n d t h e C R C P r e s s W e b s it e at h t t p : //w w w c r c p r e s s c o m 20i2 t)2 Contents P re fa c e xi In tr o du c ti o n Seun gdeog Choi R e f e re n c e s 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 tro d u c tio n of Induction M otor Favilt 2.1.1 B earing F au lts 2.1.2 Stator F a u l t s 11 2.1.3 Broken Rotor Bar F a u lt 13 2.1.4 Eccentricity Fault 15 2.2 I n tro d u c tio n of S y n c h ro n o u s M otor Fault D ia g n o s is 16 2.2.1 D a m p e r W in d in g F a u lt 17 2.2.2 D e m a g n e tiz a tio n Fault in P e rm a n e n t M ag n e t S y n c h ro n o u s M a c h in e s (PMSM s) 18 2.2.3 Eccentricity F ault 19 2.2.4 Stator Inter-Turn F a u lt 20 2.2.5 Rotor Inter-Turn F au lt 21 2.2.6 Bearing Fault 22 R e fe r e n c e s 23 M o d e l i n g o f E lectric M a c h in e s U sin 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 tio n A p p r o a c h e s 27 Su bhasis N andi 3.1 3.2 I n t r o d u c t i o n 27 W in d in g a n d M odified W in d in g F un ctio 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 alculatio ns U sing WFA a n d M W F A .33 3.4 Validation of Inductance Calculations U sing WFA a n d M W F A 39 R e f e r e n c e s 45 Contents vi M o d e lin g of Electric M a c h i n e s U s in g M a g n e tic E q u iv a le n t C ir c u it M e t h o d .47 H om ayoun M eshgin-K elk 4.1 4.2 In tro c iu c tio n 47 In direct A pplication of M agnetic E qui\'alent Circuit for A nalysis of Salient Pole S y n c h ro n o u s M a c h i n e s 52 4.2.1 M agnetic Equivalent C ircuit of a Salient Pole S y n c h ro n o u s M a c h in 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 in e 55 4.2.3 C alcu lation of In d u c ta n c e s for a Salient Pole S y n c h ro n o u s M a c h in e 58 4.2.4 E x p e rim en ta l M e a s u r e m e n t of I n d u ctan c e s of a Salient Pole S y n c h ro n o u s M a c h i n e 63 4.3 In direct A pplication of M agnetic E quivalent C ircuit for A nalysis of In d u c tio n M a c h i n e s 66 4.3.1 A Simplified M ag netic E q u i\’alent Circuit of In d u c tio n M a c h in e s 66 4.3.2 In d uctance Relations of Indu ctio n M a c h i n e s 68 4.3.3 C alculation of In d u c ta n c e of an In d u c tio n M a c h i n e 70 4.4 D irect A pplication of M agnetic E quivalent Circuit C o n sid e rin g N o n lin e a r M ag netic C haracteristic for M a c h in e A n a ly s is 73 A p p e n d ix A: Induction M achine P a r a m e t e r s 77 A p p e n d ix B: N o d e Perm e an c e M a trice s 78 R e f e re n c e s 79 A n a l y s i s o f F a u lt y I n d u c t i o n M o t o r s U s in g F i n i te E le m e n t M e t h o d 81 Bashir M alidi Ebrahim i 5.1 5.2 5.3 5.4 5.5 I n tr o d u c t io n .81 G eom e tric a l M o d e lin g of Faulty In d u c tio n M otors U sing T im e-S tep ping Finite E lem ent M e th o d (TSFEM ) 82 C o u p lin g of Electrical C ircuits a n d Finite Elem ent A r e a 83 M o d e lin g Internal Faults U sing Finite Elem ent M e t h o d 85 5.4.1 M o d e lin g Broken Bar F ault .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 tric ity 87 5.4.2.2 D y n a m ic E c c e n tric ity 89 5.4.2.3 M ixed E c c e n tric ity 90 Im p act of M agnetic S a tu tio n on A ccurate Fault D etection in I n d u c tio n M o t o r s 91 Contents 5.5.1 A nalysis of A ir-G ap M agnetic Flux D ensity in H ealthy a n d Faulty Indu ctio n M o to r .94 5.5.1.1 Linear M a g n e tiz a tio n C c te ristic 94 5.5.1.2 N o n lin e a r M a g n e tiz a tio n C h a c te ris tic 95 R e fe re n c e s 96 Fault D i a g n o s i s of Electric M a chi ne s U si ng Techni ques Based on Frequency D o m a i n 99 Subhasis N andi 6.1 6.2 6.3 I n tr o d u c tio n 99 Som e D efinitions a n d Exam ples Related to Signal Processing 100 6.2.1 C o n tin u o u s v e rsu s Discrete or Digital or S am p led S i g n a l 100 6.2.2 C o n tin u o u s, D iscrete Fourier Transform s, a n d N o n p a r a m e tr ic Pow er S p e c tr u m E stim a tio n 101 6.2.3 Param etric Pow er S p e c tr u m E s tim a ti o n 105 6.2.4 Pow er S p e c tr u m E stim a tio n Using H ig h e r-O rd e r Spectra (H O S ) .107 6.2.5 Pow'er S p e c tr u m E stim atio n U sing Sw ept Sine M e a s u re m e n ts or Digital Frequency Locked Loop T echnique (D FLL ) 110 D iag nosis of M a c hine Faults U sing Freq uen cy -D om ainBased T e c h n iq u e s I l l 6.3.1 D etection of M otor B earing F a u l t s I l l 6.3.1.1 M ech anical Vibration Frequency A n alysis to Detect Bearing F a u l t s .I l l 6.3.1.2 Line C u r re n t Frequ en cy A n alysis to D etect Bearing F a u lts 115 6.3.2 D etection of Stator F a u lts 116 6.3.2.1 Detection of Stator Faults U sing External Flux S e n s o r s 116 6.3.2.2 D etection of Stator Faults U sing Line C u rre n t H a r m o n i c s .117 6.3.2.3 Detection of Stator Faults Using T erm inal Voltage H a rm o n ic s at S w itc h - O f f 119 6.3.2.4 Detection of Stator Faults Using Field C u rr e n t a n d Rotor Search Coil H a rm o n ic s in S y n c h ro n o u s M a c h in e s 121 6.3.2.5 D etection of Stator Faults U sing Rotor C u r r e n t a n d Search Coil Voltages H a rm o n ic s in W o u nd Rotor Ind uction M a c h in e s 124 6.3.3 D etection of Rotor F a u l t s 129 C.antcnts viii 6.3.3.1 Detection of Rotor Faults in Stator l.ine C urrent, Speed, Torque, a n d P o w e r 130 6.3.3.2 D etection of Rotor Faults in E xternal and Internal Search C o i l 134 6.3.3.3 Detection of Rotor Faults Using T erm in al Voltage H a rm o n ic s at S w itc h -O ff 134 6.3.3.4 D etection of Rotor Faults at S t a r t - U p .134 6.3.3.5 D etection of Rotor Faults in Presence of In terbar C u r r e n t U sing Axial Vibration S ig n a ls 135 6.3.4 D etection of Eccentricity F a u lts 136 6.3.4.1 D etectio n of Eccentricity Faults U sin g Line C u rr e n t Signal S p e c t r a 136 6.3.4.2 D etection of Eccentricity Faults Based on N a m e p la te P a r a m e t e r s 142 6.3.4.3 D etection of Eccentricity Faults U sing M e c hanical Vibration Signal S p e c t r a 147 6.3.4.4 D etection of Inclined Eccentricity F a u lts 147 6.3.5 Detection of Faults in Inverter-Fed Induction M a c h i n e s 148 R e f e re n c e s 149 Fa u lt D ia g n o s is of E lectric M a c h i n e s U s in g M o d e l-B a s e d T e c h n i q u e s 155 Siibhasis N andi 7.1 7.2 7.3 I n tr o d u c tio n 155 Model of H ealthy Three-Phase Squirrel-Cage Induction M o to r 158 M odel of T h re e -P h ase S quirrel-C age In duction M otor w ith Stator Inter-Turn Faults 165 7.3.1 M odel w ith o u t S a tu tio n 165 7.3.2 M odel w ith S a t u r a t i o n 169 7.4 M odel of S quirrel-C age Indu c tion M otor w ith Incipient Broken Rotor Bar a n d E nd-R ing F a u lts 175 7.5 M odel of S quirrel-C age In d u c tio n M otors w ith Eccentricity F a u lts 177 7.6 M odel of a S y n c h ro n o u s Reluctance M otor w ith Stator F a u lt 179 7.7 M odel of a Salient Pole S y n c h ro n o u s M otor w ith D y n a m ic Eccentricity F a u lts ]8l R e f e re n c e s 183 A p p lic a tio n o f P a tte r n R e c o g n itio n to F a u lt D i a g n o s i s 185 M asou d H ajiaghajani 8.1 8.2 8.3 I n tr o d u c tio n ] 85 Bayesian T h e o ry a n d Classifier D e s i g n 186 Simplified Form for a N o r m a l D is tr i b u ti o n 189 Electric Machines: Modeling, Condition Monitoring, and Fault Diagnosis 248 40 -42 E < ‘H -4 -0 -4H * -1 100 200 300 400 ~ -SO m) -0,5 Buffer Index Fr equency Offset (a) (b) -O.S \tiip (dB) Ihreshoki 05 i 0.') Frequency Offset FIG URE 11.8 F r e q u e n c y t r a c k i n g fur b r o k e n rotor ba r fault: (a) a v e r a g e d s i g n a l , (b) f r e q u e n c y t r a c k i n g a n d d e c i s i o n m a k i n g (r e so lu ti on: 0.02 F^z), a n d (c) c o h e r e n t d e f e c t i o n w i t h o u t s t r a t e g y for fault fr e ­ q u e n c y o f f s e t c o rr e c tio n need to be smaller than the difference b e tw e e n the supply an d the expected fault frequencies In Fig ure 11.8b, the fault freq uency offset is identified at m a x im u m point w ith 0.46 Hz In Table 11.3, th e fault is d e te r m in e d correctly o n ly after fre ­ q u e n c y tracking a n d d e te c te d a m p litu d e is b o o ste d from -49.8 to -41.32 dB The accu racy of the ML track in g alg o rith m can be c o n firm e d from the a m p l i­ tu d e m o n ito re d th r o u g h the s p e c tr u m an aly zer, w h ic h is -41.8 dB a n d yields only 0.47 dB e rro r from the tracked result Figure 11.8c show's detections th ro u g h one of the o ptim a l schemes, F^D, to com pare the perform ance w ith the algorithm in Figure 11.8b u n d e r error c o n d i­ tions Unlike the zero offset condition in Figure 11.7, the fre q u e n c y /p h ase offsets are completely am b ig u o u s in Figure 11.8 Figure 11.8c show s the serious p erfo r­ m an c e degradation of am p litu d e loss d u e to fre q uency /p hase ambiguity Every detection at Hz, -0.5 Hz, a n d 0.5 H z show's unreliable yalues Meanwhile, th ro u g h the use of phase e rro r-im m u n iz ed detection a n d frequency tracking in F ig u re ll b, the detection p erfo rm ance becom es close to o p tim a l an d ro bu st­ ness of detection is m a in tain ed u n d e r erro r conditions 11.3.3 On-Line Experimental Results T he in d uc tio n m o to r is fed by the inyerter The voltage-to-frequency (y/f) m o to r control a n d on-line fault d iag n o sis service routine are s im u lta n e o u s ly im p le ­ m e n te d on a 32-bit fixed-point, 12-bit ADC, 150-MHz DSP of TMS320F2812 Roluist Sigiiiil Processing Techniques for M C S A Diagnosis 249 FIG URE 11.9 F r e q u e n c y tr a c k in g for e c c e n t r i c i t y s i g n a t u r e w i t h 20"o t o r q u e at 10 s e c o n d s ( s u p p l y fr e q u e n c y : 48.^ 11/, res olu tio n: 0.04 Hz) In Figure 11.9 a n d Figure 11.10, tlie zero fre q ue nc y is the fault sig n a tu r e frequency m e a s u re d by the DSP from the fault equation In Figure 11.9, the DSP m e a su re s th e fault s ig n a tu r e freq uen cy correctly s h o w in g a m a x im u m at zero frequency, that is, -40.2 dB In Figure 11.10, 0.24 H z fault frequ ency offset b e tw e e n the e x p e c te d a n d the ex istin g fault sig n a tu re freq u e n c y is m o n ito re d for the b ro k e n rotor bar signature T he c h a n g es in detected a m p litu d e a n d th re sh o ld s in tim e are s h o w n in Figure 11.11 a n d Figure 11.12 In both figures, th e d etected s ig n a tu r e h a r d ly varies after seconds The th re sh o ld m e a s u r e d is u n sta b le initially a n d b e co m es stabilized after a b o u t seconds A fter b e c o m in g stabilized, it te n ds to d e crease since on e of the threshold p a m e te rs, effecti\’e noise \ ariance 40 -4:i o- Amp (dB) • Threshold '-, -1 Frequency Offset FICLIRE 11.10 F r e q u e n c y tr a c k in g for b r o k e n rotor bar s i g n a t u r e (left s i d e b a n d ) w i t h 100"., t o r q u e at 10 s e c ­ o n d s (-.upplv fr e q u e n c v : "i 11/, r es olut ion: 0.04 Hz) 250 Elcctric Machi)ics: Modeling, Condition Monitoring, nnd Fuitlt Ditignosis Time FIG URE 11.11 D e te c t a b ilit \- v a r ia tio n w i t h t i m e for e cct'ntric itv w i t h 20" t o r q u e ( s u p p l y fr e q u e n c y ; "i I I/) o V N , d ecreases as the n u m b e r of sa m p le s u se d increases, w h ic h co n firm s careful deriv atio n in Equation (11.14) T he latency tim e of abo ut 10 secon ds in fault d ia g n o sis is a s s u m e d to be acceptable b ecause co ndition m o n ito rin g is p e rfo rm e d in a relativ eh ’ long p e rio d of time, especially w ith a m ec h a n ic al ty p e of fault such as b roken rotor b a r or eccentricity In on-line e xperim ents, the threshold applied is de sig n e d to keep false detection errors strictly w ith in 0.097'’/» as sh o w n in Table 11.1 That is v\'hy the sig n a tu re s are u su a lly detected close to threshold w ith in 5-10 dB The th r e s h ­ olds can be fu rth e r d ecreased to detect small sig n a tu re s by re d u cin g the w e ig h tin g factor in Equation (11.14) T his can be d o n e b a s e d on th e relation sh o w n in Figure 11.4 (bottom) from the trade-off of detection p erfo rm an ce T im e FIG URE 11.12 D e t e c t a b i l i t y \ a r ia tio n w i t h t i m e for b r o k e n ro to r b a r w i t h 100% t o r q u e ( s u p p ly f r e q u e n c y : 48.3 Hz) Rol’ust Signal Proccsiing Techiiiqucs for M C S A Diagnosis 231 The resolution of s ig n a tu re a m p litu d e tracking can also be fu rth e r im p rtn ed bv intentionally a d d in g k n o w n frecquency bias, w h ic h lets the detection achie\'ed be m o re precise as th e relati\’ely high frequency signal can be id e n ­ tified in a relati\ ely sh o rte r tim e period The fault d e te c tio n a n d d e c isio n -m a k in g capability of the ro b u st fault d ia g ­ nosis a lg o rith m are d e m o n s t r a t e d in this c h a p te r by m a th e m a tic a l verifica­ tions a n d off-line/on-line e x p e rim en ts It is ob serv ed that am b ig u itie s such as the fault s ig n a tu re freq u e n c y m ism a tc h , the p h a s e of the fault \-ector, a n d c h a n g e s in th e noise le\’el of fault sig n a tu re s can be efficiently h a n d le d u sin g a sim ple a lg o rith m capable of fre q ue nc y tracking, p h a se e lim in a tin g d etec­ tion, a n d a d a p tiv e threshold References |1| S.M Ka_\’, Fuiidiiiuciitals o f Stiitistical Signal P m ccisin g: Estiuintion am i D ctcction Ttieon/, E n g le w o o d Cliffs, NJ: Prentice-Hail, 1993 |2] 15 Akin, H Toliyat, U O rg u n e r, a n d M Rayner, "P h a s e sensiti\ e d etec tio n of m o to r fault s ig n a tu re s in the p resen ce of n oise,” IEEE T ransaction f on ¡ndii>triiil E lectronics, \ ol, 53, pp 2339-2330, Ju n e 2008 13| S.H Kia, H H e n a o , a n d G C ap olin o, "A h ig h -re so lu tio n freq uen cy e stim atio n m e th o d for th r e e -p h a se in d u c tio n niaciiine fault detectio n," IEEE T ransactions on Indu strial E lectronics, vol 34, no 4, A u g u s t 2007 |4] ,A Ik'llini, G Franceschini, an d C Tassoni, "M o n ito r in g of in d u ctio n m a c h in e s li\' m a x i m u m cox’arian ce nietho d for frequency tracking," IEEE Tra}isactions on Indu strial A pplication s, vol 42, no 1, pp 69-78, J a n u a r y / F e b r u a r y 2006 |5| Viterbi, P rinciples o f C oherent C on m m n icalion , N e w York: M cG raw -H ill, 1966 [6| S.VI.A C ru z , H.A Toliyat, a n d A.J.M C a rd o so , "DSP im p le m e n ta tio n of the m ultiple reference fram es theo ry for the d ia g n o s is of sta to r faults in a DTC in d u c tio n mc)tor dri\-e," IEEE T ransactions on E nergy C o n iv rsio n , \'ol 20, no 2, pp 329-333, Jun e 2003 [7] M B e n b o u /i d , M Vieira, a n d C T heys, " i n d u c ti o n m o to rs' faults detectio n an d localization u sin g stato r c u rre n t adv an ced signal processin g tech n iq u e s," IEEE T ransaclions on P o w e r Electronics, \ ’oi 14, pp 14-22, J a n u a r y 1999 ¡8] S Ciw i, B Akin, M R ahim ian, a n d H.A lo iiy a t, " i m p l e m e n t a ti o n of a fault d ia g n o s is a lg o r ith m for in d u c tio n m a c h in e s b a se d o n adv ance d digital signal pi'ocessing tech n iq u e s," IEEE T ransactions on Indn strial E lectronics, vol 38, no 3, pp 937-948, M arch 2011 In d ex A coustic an a ly s es, 4, A coustic noise, m ec h a n ic a l \ ibration, c a u s e d bv, 9, 137 A d a p t i \ e th r e s h o ld d esig n , 240-241 A d d itiv e w h ite G a u s s i a n no ise (AVVGX), 200, 201, 242 A ir-g a p flux tu b e s , 50-51 A ir-gap s, 15 S ee »¡so E ccentricity faults d v n a m i c eccentricity, 19-20 f u n c tio n s of, 177 inverse, 177, 182 len g th of, 70, 89 m a g n e tic fields in, 16 n ia g n etic flux in, 19 n ia g n e to m to iv e force in, 120-121 p erm ea b ility , 28-29 p e rn ie a n a c e , 68 s y m m e t r y , 31, 37 A lgebraic m a c h i n e ee]uations, 73 A liasing , 100 A lternatt)rs, fa ilu re of, 13 A m p e r e 's law, 29 A m p li tu d e m o d u l a t i o n (AM) detectors, 11 A n a lo g u e -t o -d i g ita l c o n v e rte rs (ADC), 206 A n aU sis e q u a tio n s , 101 A n g u l a r velocity, 112 A n so ft C o rp o t io n , 39 A p p lic atio n env ir o n m e n t, electric m otors, Artificial intelligence, 156 A rtificial n e u l n e t w o r k m e th o d , 22 Axial tlux, 117 A xial x’ibration sig n als, 135-136 B B artlett w indow , 103 Bayes m i n i m u m e r r o r classifier, 189-190,197 Bayesian d ecisio n theory, 185-186 See also Classifier d e sig n d efin in g, 186 fault d ete c tio n using , 197 p ro b a b ility d e n s ity in, 187 stru c tu r e , 189 Bearing balls, d a m a g e d , Bearing faults, classifications, 10 defin in g , d iag n o s is, 4, 11 eccentricity faults, zvrsus, 15-16 m o d e lin g , 85 o verview , p re v a len ce of, B isp e ctru m , 99 Blackm an-T ukey w in d o w , 103 Drinelling, 115 Broken ro tor b a r faults, 13-14 d etec tion, 148 field a s y m m e t r y c a u se d by, 226, 230 m o d e lin g , 5-8 on -fau lt d ia g n o s is of, 18 o n li n e fault detec tion , 212 p a tte rn recogn itio n, u se in, 191, 194 s q u irre l cage in d u c tio n m otors, in, 175, 177 C a rte r 's coefficients, 41 Classifier desig n, 186 Sec also Bayesian d ecisio n th e o ry C o d e of Federal R e g u la tio n s (CFR), 222 C o n d it io n -b a s e d m a i n te n a n c e (CBM), 156 C o n t i n u o u s F o urier tr a n sfo r m s, 101 C o n t i n u o u s signal, 100 C o p p e r rotors, 13 C PU utiliz atio n, 199 253 254 C u r r e n t m o n ito rin g , motor, 10 D D a m p e r w i n d i n g faults, 17-18 D a m p e r w in d in g s , 17 D ecision rule, 187 D igital fre q u e n c y locked loop te c h n iq u e (DFLL), 99 D igital fre q u e n c y locked loop te c h n iq u e (DFLL), 110 D igital signal p ro c e s s o rs (DSP), 199, 200 a d a p t i \ ’e th r e s h o ld desig n, 240-241 tro l signals, 216 d a ta p ro c e s sin g w ith, 237 e m b e d d e d , 201 fault codes, 210 fault fre q u e n c y offset c o m p e n s a tio n , 237-239 fault-detectio n p ro c e d u r e s, 235-236, 241 o n li n e fault d etectio n, 204, 206 p h a se -se n siti\'e m o to r fault s ig n a tu r e d etec tio n, 210-212, 2Í7, 241, 249 re al-tim e analysis, 210, 239 referen ce signals, 214 D iscrete F o urier tr a n s f o r m (DPT), 101-102 D iscrete signal, 100 D isc re te-tim e F o urier tr a n s fo r m , 101 D o ub ly fed in d u c t io n g e n e to r (DFIG), 125 Drive cycle analysis, 224-226 D y n a m ic eccentricity, 15, 19, 41, 59, 60, 147 d e fin in g , 90 i n d u c t a n c e values, re la tio n sh ip b e tw e e n , 73 m o d e l in g , 178,182 E ccentricity faults, 15-16 causes, 87,136 d etec tio n, 19-20,136 d y n a m i c eccentricity; see D y n a m ic eccentricity inclin e d , 147-148 Index line ciu'rent signal spectra, im pact on, 136-138 m e c h a n ic a l \ ihration sign al spectra, d e te c tio n b ased on, 147 m ixed ; see M ixed eccentricity n a m e p l a te p a m e te r s , d etec tio n baseci on, 142-144 s q u irre l-c a se in d u c tio n motiir, in, 177-179 static eccentricity; srt’ Static eccentricity E d d y c u rr e n ts , 28, 54, 158 Electric m a c h in e s, rotatin g, 27 Electric m o to rs defects in, 2-3 d e s i g n of, e n e r g y d e m a n d s of, failures of, 1-2 g r o w t h in use, s y m p t o m s of a b n o rm a lity , Electrical M a c h in e s & Pow er E lectronics (EMPE) lab, 197 Electrical sca lar p o ten tial, -4 E n d -rin g faults, 175,177 Euler's identity, 102 Fast E ourier tr a n s f o r m s (FFT), 99,102, 109 s p e c t r u m a n a ly z e r o u u t s , 206, 212, 246 Fault a m p litu d e , 236 Fault detection, See also specific detection methods: specific faults d iagn osis, e x te rn a l flux senso rs, 116-117 m e c h a n ical v ib ratio n f r e q u e n c y analysis, 111-114 overview, 155-156 p a m e te rs, 91 p a tte rn re c o g n itio n in; see P a tte rn re c o g n itio n in fault d ia g n o s is stator faults, of; see Stator faults tools for, 11 Fault h arm o nics, 15 Faults, bearing See B earing faults Faults, stator See S tato r faults Field re c o n s tru c tio n m e t h o d (FRM), 19 253 Itulcx Finili' elem o n t m e t h o d (FEM), 21, 39 ciirre n t-te d ap p ro a c h , 81-82 electrical circu it c ou pling , -8 i n f o rm a tio n received from , 156 o\ervievs-, 81 th r e e -d im e n s io n a l, 81, 82, 83 tim e-step ping finite elem en t m e th o d (TSFEM); see Tim e-stepp ing finite c lem en t m eth o d (TSFEM) t w o -d i m e n s i o n a l, 81, 82, 83 \'oltage-fed ap p ro a c h , 81, 82 Fin ite-elem ent (FE) m a g n e tic circu it eq u iv alen ts , F inite -ele m en t a n a ly s is (FEA), Flux a s y m m e t r y , 22 Flux density, 8Z 92, 94-95, 118 F o r w a r d eq u a tio n s, 101 F o urier series, 101 F u n d a m e n t a l fre q u e n c y voltage u n b a la n c e , 118 Fuz-/y logic analysis, G a b o r s p e c t r o g r a m , 22 G a u ss's law, 29, 30 G a u s s i a n noise c h a n n e l, 242 t i e n e r a l i / e d r o u g h n e s s See R o ug hn ess, g e n e liz e d C iro u n d in g unstab le, H H a iin i n g w in d o w , 109 H i d d e n Vlarko\' m o d e l in g (HMM), 11 H ig her-()rd er sp e c tra (HOS) b ased sp ectral analysis, 107 H y b rid electric vehicles (HEV), fault d ia g n o s is u sin g reference fram e th e o ry c a ta s tr o p h ic failures, 222 d ia g n o s tic criteria, 222 driv e cvcle analysis, 224-226 m a l f u n c t io n in dicato r lights (Mil.), 222 m e c h a n ic a l v ibrations, 223 on-b(iard d ia g n o s is ((^BD), 221-222, 224-226 overview, 221 real-tim e fault s i g n a tu r e tracks, 228 to rq u e v alues, 226, 227 vector ro tation d irec tio n , 227 z ero s p e e d tests, 226-229 H ysteresis, 158 I In d u c ta n c e values, ca lc u latin g , 73, 77 In d u c tio n m a c h in e s, 68-70, 72-73 In d u c tio n m o to rs faulty, tim e - s te p p i n g finite ele m e n t m e t h o d (TSFEM) m o d e l in g of, 82-83 s q u irre l cage; ic e S q u irre l cage in d u c tio n m o to rs h if r a r e d a n a ly s e s o f b e a r i n g faults, In tern al faults (I.M) b ro k e n rotor b a r fault; see Broken ro to r b a r fault eccentricity faults; f e e Eccentricity faults o verview , 85 Inverter-fed indu ctio n m achines, 148-149 J Jacobian, 76 L e akag e in d u c ta n c e s, 163 L e akag e p a th reluctances, 70 L east-sq u are e stim ates, 171 Line c u r r e n t f r e q u e n c y analv sis, 115 Line c u r r e n t h a rm o n ic s , 117-llH L in ear velocity, 112 L in ea r-circu it-th e o ry -b ase d m a th e m a tic a l m o dels, Load to rque, 193 M M a c h in e -th e o ry -b a s e d fault analy sis, M agnetic e q u iv alen t circuit (MFC) m e th o d accuracy, 47 e d d y c u rr e n t, 54 256 flux o rientation , 34 i n d u c t a n c e coefficients, 38 m a c h in e geom etry, ex plo ratio n of, 47 m a g n e t ic flux lines, 47-48 o verview , 47 p e r m e a n c e co m p u ta tio n , 49, 51 ro to r slots, 30-31, 34 salie n t pole s y n c h r o n o u s m a c h in e , of, 3 - l s sim plified MEC of in d u c ta n c e m ach in es, 66-68 sk e w in g , 31 stato r slots, 30-31, 34 M a g n e tic field w av efo rm s, 94 M a g n e tic flux lines, 47-48 M a g n e to m o tiv e force (MMF), 29, 33, 49 h a rm o n ic s, effect on, 138 no des, levels of, 34 p e r m e a n c e h a rm o n ic s, re la tio n sh ip b e tw e e n , 170-171 stato rs a n d rotors, \ ecto rs of, 33 tr a n s f o r m m atrix, 33 M a x i m u m lik elih oo d detection, 238-239 M ax w ell eq u atio n s, 39 M e a n m u vector, 189 M e a n sp e ctral d e v iatio n (MSD), 113 M e a n s q u a r e d e r r o r estim a tio n , 243 M ech a n ic a l v ib ratio n fre q u en cy analysis, 111-114 M ix ed eccentricity, 39, 62 d e fin in g , 90 m o d e lin g , 90-91 M od ified w i n d i n g fu n c tio n a p p r o a c h (MWFA) See W i n d i n g a n d 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 (W FA /M W F A ) M o to r b e a r i n g faults de te c tin g 111 lin e c u r r e n t f r e q u e n c y an alysis, 115 m e a n sp e c tra l d e v ia tio n (MSD), 115 m e c h a n ic a l v ib ratio n fr e q u e n c y analy sis, 111-114 o verv iew 111 M o to r c u r r e n t s i g n a tu r e an aly sis (MCSA), 5, 3, 99, 99 See also R eference fr a m e th e o ry Index b e a r i n g fault co n d itio n s , 22 fault s i g n a tu re s , 202, 210-212, 235 im p le m e n ta tio n , 199 lo w -cost p ro te c tio n ap plication s, noise s u p p r e s s i o n , 200-201 o verv iew , 199-200 p h a s e tra n sfo rm a tio iis, 202-203 M ultiple sig n a l classification (MUSIC), 99, 107 N X e u l n e tw o rk s , 6, 22 N e w to n 's m e t h o d , 73 N oise v arian ce, 243-244 O Oil analysis, O verlo ad, electrical, O z o n e m o n ito r in g , 13 P a m e tric p o w e r s p e c t r u m estimafi(.)n, 105-107 Particle d is c h a rg e s , 12 P a ttern r e c o g n itio n in fault d i a g n o s is classification issues, 189 decision ru les, 189 err o r rate, 189 featu re ex tra c tio n in, 190-194 h arm o n ics, 190-191 im p le m e n ta tio n , 194-197 overv’iew, 185-186 P e rio d o g m , 103 Perm anent m ag n et syn ch ro n o u s m a c h i n e s (PMSMs), 16 d e m a g n e tiz a t io n faults of, 18-19 fault d e te c tio n in, 20-21 p o pu la rity, 18 P e rm ean ce h a rm o n ic s , 170-171 Pole pairs, 143 P o w er s p ectral d e n s i ty (PSD), 103, 105', 193, 247 Principle slot h a r m o n i c s (PSH), 137 257 Index Q -fu n ctio n , 242-243 saliency effects, 59 self-inductance, 61, 65 s p e e d of, 92 R o u g h n ess, g e n e liz e d 111, 115 R Radio f r e q u e n c y (RF) c u r r e n t tr a n s fo r m e rs , 13 R ad io -fre q u e n c y (RF) e m issio n m o n i to r in g , Real-tim e fault s i g n a t u r e tracks, 217, 228, 230 Reciprocity th e o r e m , 163 R e c ta n g u la r w in d o w , 103 Reference fr a m e theory, 201-202 c o n dition m o n ito r in g , u se in, 202 hvbrid cars, u s e d on, fault d ia g n o s is u s i n g referen ce fr a m e theory, h y b rid electric vehicles (FIEV) m icro tro llers, u tilizin g, 204 usage, 202 Reference s ig n als, 211 ROOT MUSIC, 99 Rotor faults axial \ ib ratio n signals, im p a c t on, 135-136 brciken ro to r b a r faults; sec Broken ro to r b a r faults c u r r e n t d is trib u tio n , affect on, 130, 131 ex tern al a n d in te rn a l coils, de tec tio n by p re s e n c e of, 134 in te r-tu rn faults, 21-22 o \ i ' r \ i e w , 129-130 start-up, d e te c tio n at, 134-135 te r m in a l v oltag e h a rm o n ic s, d e te c tio n usin g, 134 Rotor search coils, 121, 123-124 Rotors a l u m i n u m , 13 b rt'k cn ro to r b a r faults; srt’ Rotor faults cast, 13 copper, 13 d e p t h b e t w e e n poles, 61 in to r-tu rn faults; see Rotor faults m i s a l i g n m e n t of, 15 relu cta n ce s of, 73 S alient pole s y n c h r o n o u s m a c h in e, 19, 41 in d u c ta n c e c alc ulation s, 8-6 in d u c ta n c e re latio n s of, 55-58, 64 m a g n e tic e q u iv a l e n t circu it of, 3-55 S a m p le d signal, 100 S a tu r a tio n ch aracteristics, 75, 117, 118, 120 S calar m a g n e tic po tential, 48 S h a n n o n s a m p l i n g th e o r e m , 101 S h o rt tim e Fo u rie r tr a n s f o r m s (STFT), 99 S ignal p ro ces sin g , 99 c o h e re n t d etec tio n , 236-237 fault a m p litu d e , 236 n o n c o h e r e n t dete c tio n, 236, 237 S ig n a l-b a se d fault de tec tio n, S in g le-p o in t defects 111, 114 Skew effect, 72 S lo ttin g p e r f o r m a n c e effect, 138 Space h a rm o n ic s, 70 S p e c to g r a m s, 99 S p e c tra l leakage, 103 S p e c t r u m m o n i to r in g tech n iq u e, S q u ir re l cage in d u c tio n m otors, IIZ 134 b ro k e n roto r b a r or e n d - r in g faults in, 175, 177 d esc r ip tio n , 158 eccentricity faults in, 177-179 FE m e t h o d of c o m p u t in g , 163 m o d e lin g , a s s u m p t i o n s m ad e, 158 s ta r jun ctio n voltage, 158, 159 stato r fault d ete c tio n, 169 WFA m e t h o d of c o m p u t in g , 163 S q u ir re l cage rotor bars, 13 S tar ju n c tio n voltage, 158, 159 Static eccentricity, 15, 19, 59, 60,142, 143, 144, 147 in d u c t a n c e \ ’alues, rela tio n sh ip b e tw e e n , 73 258 m o d e l i n g , 87, 89, 178 S ta tistica l m o t o r a n a ly s is in real tim e (SMART), 107 S ta to r faults coils, s h o r te d , 119 e x t e r n a l tlux sen s o rs, 116-117 field c u r r e n t a n d roto r s e a r c h coil h a r m o n ic s , d e te c tio n u sin g , 121, 123-124 i n t e r - t u r n , 20-21, 165, 169 o\-er\ievv, 11, 116 p a r t ic l e d is c h a r g e s , 12 pre v a le n c e , 11 re s u l t s of, 12-13 ro t o r c u r r e n t a n d se a r c h coil v o lta g e s h a r m o n i c s in w o u n d r o t o r i n d u c t io n m a c h i n e s , d e te c tio n u sin g , 124-125 s q u i r r e l cage in d u c t a n c e m o to rs, d e t e c t i n g in, 169-170 s y n c h r o n o u s re lu c ta n c e m a c h i n e , in; ÍCC S y n c h r o n o u s r e l u c ta n c e m achine t e m p e r a t u r e , effects of, 11-12, 13 t e r m i n a l v o lta g e at sw itch-off, d e te c tio n u sin g , 119-121 v oltage, d e c a y i n g , 119 S ta t o r-r o to r in d u c t a n c e s , 165 S ta to r-s ta to r in d u c t a n c e s , 165 S ta to rs b a c k ir o n relu c tan ces, 69 e le c t r o m o t i v e force (EMF) of, 14 faults; se e S ta to r faults h a r m o n i c s of, 14 i n t e r - t u r n faults, 117 p h a s e c u r r e n t s , 68 r e l u c ta n c e s of, 73 s k e w of, 72 slot o p e n i n g s , size of, 72, 73 w i n d i n g of, 20 S u p p o r t v e c to r m a c h i n e (SVM), 21 S y n c h r o n o u s r e l u c ta n c e m a c h i n e , 43 d e f i n in g , 179 o v e r v i e w , 179 s t a t o r fau lt in, 179, 182 S y n th e s is e q u a t i o n s , 101 Index T erm inal voltage h a rm o n ic s, 134 T h e r m a l a n a ly s e s b e a r i n g faults, of, s e n s o r s n e e d e d for, 10 T h e r m a l stress, effect on stators, 11-12 T h r e e - p h a s e in d u c tio n motor, 63, 74 T im e -fr e q u e n c y analysis, 99, 206, 208 T im e -ste p co u p le d finite e le m e n t state space a n a lv s is (TSCFE-SS), T im e -s t e p p in g finite ele m e n t c o u p le d state sp ace (TSFEM-SS), 82 T im e -s t e p p in g finite ele m e n t m e t h o d (TSFEM), 82-83 Torque ripples, 92, 118 Total h a r m o n i c d istrib u tio n , 244 Triplen h a rm o n ic s, 119, 120-121, 144 T r is p e c tr u m , 99 U U n b a la n c e d m a g n e tic pull (L'MP), 137, 144 Vector ro tatio na l frequency, 202-203 Vibration s p e c t r u m analysis, 4, 9, 10 V ibration, m e c h a n ic a l, Voltage h a rm o n ic s, 143 W W a \’elet d e c o m p o s itio n a lg o r it h m , 156 Welch w in d o w , 103 W ig ne r-V ille tr a n s fo r m s , 99 W in d a g e losses, 28,158,167 W in d i n g a n d 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 (W F A / MWFA), 19, 20 accuracy, 38 air-gap a s y m m e t r y , 37 air-gap fu n ctio n , 30, 31, 33, 36 air-gap, p e r m e a b il it y of, 28-29 case ex am ples, 31-33, 38 Index d e fin in g , 30-31 in d u c tn n c e profiles, 41 in\ i'rse a ir -g a p fun ction , 33, 35 m a g n e tic field intensity, 29 m a g n e tic tlux density, 30, 3-3 m a g n e t o m o t iv e force (M MF) d is trib u tio n s , 33 s a tu tio n , 28 slot effects, 28, 35, 41 t h r e e - d i m e n s i o n a l (3D) effects, 41 259 t u r n s f u n c t io n , 29, 37 u sag e, 27-28 W i n d i n g f u n c t i o n a p p r o a c h (WFA), 163 W ind ow ' f u n c t io n , 102-103 Z e r o fr e q u e n c y , 244 Z o o m fast F o u r i e r t r a n s f o r m s (FFT), 105 An environmentally fnendly book printed and bound in England by www.printondemand-worldwide.co-n PEFCCertified MIX TMi product II •fom Mtuixkblr m>A