Models of reliability prediction of electric machine taking into account the state of major structural units

POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 13 |NUMBER: 5 |2015 |DECEMBER Models o Reliabili y P edic ion o Elec ic Machine Taking in o Accoun he S a e o Majo S uc u al Uni s Mykhaylo ZAGIRNYAK1, Viachesla PRUS1, Oleksand SOMKA1, I o DOLEZEL2 1Depa men o Elec ic Machines and De ices, Ins i u e o Elec omechanics, Ene gy Sa ing, and Au oma ic Con ol Sys ems, K emenchuk Mykhailo Os oh adskyi Na ional Uni e si y, Pe sho a ne a s ee 20, 39600 K emenchuk, Uk aine 2Depa men o Theo e ical Elec ical Enginee ing, Facul y o Elec ical Enginee ing, Uni e si y o Wes Bohemia, Uni e zi ni 8, 306 14 Pilsen, Czech Republic [email p o ec ed], iachesla[email p o ec ed], [email p o ec ed], [email p o ec ed] DOI: 10.15598/aeee. 13i5.1397 Abs ac . I is shown ha con en ional ma hema i- cal models o calcula ion o he eliabili y o elec ic machine s uc u al uni s, based on he heo y o plan- ning an expe imen , do no ake in o accoun he pecu- lia i ies o hei p ope ies a ia ion du ing he p ocess o manu ac u e and long- e m ope a ion. Taking in o conside a ion he mul iple ac o s o he assigned p ob- lem, he p ospec o he use o uzzy logic pos ula es in he c ea ion o models o calcula ion o eliabili y is subs an ia ed. An app oach o such models building is o med. Keywo ds Elec ic machine, uzzy logic, eliabili y, ib a- ion. 1. In oduc ion In elec ic machines (EM) ope a ion, he main ask is o secu e equi ed eliabili y along wi h highes pos- sible ene gy e iciency. The conside ed p oblem can be sol ed comple ely only unde he condi ion o ak- ing in o accoun eal physical p ocesses aking place in EM in s a ic and dynamic ope a ion modes, which is no always possible. This is explained by inadequacy o heo e ical ideas abou EM pa ame e s change, by change o losses in ce ain uni s, and also by absence o eliable me hods o hei de e mina ion unde un- ce ain y o he condi ions o s uc u al componen s in he p ocess o ope a ion [1], [2], [3]. 2. Mo i a ion Exis ing models o eliabili y o EM s uc u al uni s a e mos ly based on he heo y o planning an expe - imen . They connec eliabili y e alua ion pa ame e s wi h ope a ion modes o EM. Fo example, eliabili y o a di ec cu en elec ic mo o o a powe wheel is de e mined by ela ion o a ailu e a e [4] λm=Vekw·10−60.0011 op a exp [ 0.113ε− −0.019ib+ 0.08εib]+0.062 ·103.77kτ+ 0.951, (1) whe e Ve– a e age ope a ing speed o he au omo- bile; kw– coe icien aking in o conside a ion ope - a ing condi ions a g oups o en e p ises o di e en indus ies; op a– ela ion be ween ime op o ope a ion o an ali e elec ic mo o and o al ime ao anspo cycle; ε– ol age be ween adjacen commu a o ba s; ib– cu en densi y unde he b ush; kτ– ela i e co- e icien o o e hea ing occu ed du ing he ope a ing cycle. Such models a e c ea ed o a ce ain EM ypes and canno be gene alized o o he se ies and e sions. Be- sides, he mechanism o aking in o conside a ion he change o he p ope ies o s uc u al assemblies du - ing hei aging is absen in hem. The mos in o ma i e o he exis ing eliabili y models ake in o accoun he ime o EM ope a ion by in oduc ion o addi ional co- e icien s [4] F( ) = Pn i=1 ciFi( ) = =Pn i=1 ci1−exp − aibi, (2) c 2015 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 447 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 13 |NUMBER: 5 |2015 |DECEMBER whe e n– in e als numbe ; ci– weigh coe icien ; bi,ai– pa ame e s o Weibull dis ibu ion a he i- h in e al. Ob iously, he coe icien ciis o be a iable in his case. Howe e , ecommenda ions as o i s de e mi- na ion a e p ac ically absen , which makes impossible p ac ical use o Eq. (2). Thus, he e occu s a necessi y o de elopmen o new models explici ly aking in o accoun he indices o e- liabili y depending on he s a e o he basic s uc u al uni s. The pu pose o he pape consis ed in he esea ch o a ia ions o he p ope ies o EMs s uc u al uni s and elemen s wi h he ollowing subs an ia ion o hei in luence on he pa ame e s de e mining he indices o EMs eliabili y. As in e ela ion o ac o s, which desc ibe condi- ions o EM s uc u al componen s and hei in e e- la ion wi h eliabili y ac o s, is no unambiguous, he p omising way o sol e his ask is he use o uzzy logic. 3. Theo e ical Pos ula es Du ing he esea ch, he main ypes o s uc u al uni aul s in luencing he eliabili y indices we e singled ou . They include a ious ypes o damages o bea - ing uni , s a o co e, windings, o o (a ma u e) and swi ching poin s. Fac o s showing du ing ope a ion and cha ac e izing he s a e o hese uni s change due o p esence and de- elopmen o ce ain de ec s. So, o collec o and bea - ing uni s hese a e, espec i ely, hei empe a u es θc and θb, ib a ion eloci y νand angula equency ω o o o o a ion, o he winding – empe a u e θW and ib a ion eloci y ν. Vib a ion eloci y νand cu - en densi y Jb unde he b ush a e ypical o con ac ings, e c. As e e y uni o elemen is in luenced by i s own ac o s, and he deg ee o hei a ia ion is no de e mined eliably, hei mu ual in luence and connec- ion wi h de ec s o s uc u al uni s can be aken in o accoun wi h he use o uzzy logic pos ula es [5]. In his case, he mos e icien app oach consis s in di ec ealiza ion o in e connec ion o he s a e o uni s and in luencing ac o s wi h eliabili y indices. I en- ables ob aining a gene alized model o EM eliabili y in a a he simple o m. Howe e , his app oach canno always be applied because o a high deg ee o unce - ain y o in e connec ions be ween pa ame e s o sep- a a e uni s when he e is a ela i ely la ge numbe o in luencing ac o s. So, i is mo e e icien o use uni models ela ing in luencing ac o s o s uc u al de ec s; la e hese models a e ans o med in o EMs eliabili y models wi h he use o he basic pos ula es o eliabili y heo y [6]. Despi e seeming a ie y o di e en de ec s o s uc- u al uni s and elemen s, hei in luence on EM elia- bili y is mainly educed o de e io a ion o he mal and ib a ion p ocesses. As de ec s and damages o elec ic machines s uc- u al uni s a e dis ibu ed in a andom manne and a e o di e en na u e, i was p oposed o inc ease he numbe o he analyzed pa ame e s o he mal and i- b a ion p ocesses. Rela ions used in calcula ion models and connec - ing he pa ame e s o hese p ocesses wi h he s a e o s uc u al uni s a e o be ex emely simpli ied and con- c e ized. I enables singling ou signi ican pa ame e s in luencing ib a ion and empe a u e componen s and ela es all he es o a iable alues. As aul s and damages o EM s uc u al componen s a e andomly dis ibu ed and ha e di e en o igin, in o de o ex end he numbe o analyzed ac o s o i- b a ion i was con i med he necessi y o es ima ion he ac o s o mechanical and elec omagne ic na u e sepa a ely. As a esul , ela ions o ib a ion eloci y compo- nen s, depending on pa ame e s in luencing i ob ained he o m: ν = (ω;δe;kk1),(3) νz= (ω; ∆ ; ∆a;kk2),(4) whe e ν and νz– gene al le el o ib a ion eloc- i y caused by o o and bea ings imbalance in adial and axial di ec ions; δe– adial clea ance in bea ings; kk1, kk2– s uc u al coe icien s; ∆ and ∆a– axial and ace unou , espec i ely. Elec omagne ic ib a ion is desc ibed by a depen- dence o he o m νm= ( 0;Bµ;Bν;kχ;kd1;kk3),(5) whe e 0– double equency o he ne wo k; Bµ– am- pli ude o he ee h ha monic o s a o ield; Bν– am- pli ude o he non- ee h ha monic o he s a o ield; kχ – coe icien o he o o slo s slan ; kd1– de o ma ion coe icien , kk3– s uc u al coe icien . As he numbe o signi ican pa ame e s in Eq. (3), Eq. (4), Eq. (5) does no exceed h ee, he inal com- pu a ions a e based upon hese pa ame e s o e e y sepa a e case using expe imen al design heo y. Values o ib a ion componen s ob ained by Eq. (3), Eq. (4), Eq. (5) make i possible o calcula e he esul - ing alue o ib a ion eloci y on he basis o ela ion ν=p(νm+ν )2+ν2 z.(6) c 2015 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 448 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 13 |NUMBER: 5 |2015 |DECEMBER When he maximum alue o winding o e hea is cal- cula ed, especially in he case o damaged lamina ed co es, i is necessa y o addi ionally ake in o accoun he i egula i y o i s empe a u e dis ibu ion. I can be aken in o accoun by a dependence o he o m θmax = (∆ϑin, λi,∆pi),(7) whe e ∆ϑin – excess o ai empe a u e inside he ma- chine, λi,∆pi– local alues, espec i ely, o he mal conduc i i y coe icien and speci ic s eel losses. Apa om he desc ibed pa ame e s, he use o spec al componen s o ib a ion eloci y a he sup- ply ol age equency and o a ion equency, as well as measu emen o empe a u e a he poin s o assumed maximum by means o embedded empe a u e indica- o a e also e icien . Solu ion o he p oblem o eliabili y es ima ion in he men ioned o mula ion equi es applica ion o an expe sys em making logic conclusions o wo ypes: •Es ima ion o de ia ion o each pa ame e ( em- pe a u e, ib a ion eloci y, e c.) o he uni in ela ion o no mal alues o his machine in ime and equency domains, aking in o accoun he ope a ing condi ion (cu en load, en i onmen empe a u e, s a ing condi ion, e c.). •De e mina ion o he de ec ype and es ima ion o he emaining ime o ope a ion o he uni ac- co ding o he esul s o calcula ion o he i s s age. In his case combina ion o he classical expe sys- em wi h uzzy logic in assigning specialized ules o Fig. 1: Diag am o an expe sys em o es ima ion o he eli- abili y o EMs wi h unc ions o uzzy conclusion. diagnos ics o he s a e o EMs enables a mo e com- plex app oach o he p oblem o calcula ion o hei eliabili y, which is explained by Fig. 1. As an example he bea ing uni was analyzed (Fig. 2). I can be seen in Fig. 2 ha i consis s o a case cap 1 wi h a bea ing in e ace 3 and he bea ing p ope including olling elemen s 4, an inne ace 5 igidly moun ed on sha 2 and an ou e ace 6. Due o man- u ac u e de ec s and imp ope ins alla ion o he bea - ing, as well as when he case cap is lashed o skewed, such de ec s as c umpling o wo king su aces o aces and olling elemen s (plas ic de o ma ion unde he ac- ion o ib a ion, shock o s a is ical loads), des uc- ion o sepa a o (unde he ac ion o cen i ugal o ce and impac on he sepa a o o a ious-size olling el- emen s), des uc ion o aces, olling elemen s and he body o he machine ( aces skews, shock o e loads) oc- cu in he uni . In his case gaps δappea in in e aces, he e occu shi s o he axis o bea ing moun ing (an- gle α), o ces F, de e mining he applica ion o he load and ic ion in ensi y, edis ibu e. Fig. 2: Design diag am o a bea ing uni . The inpu pa ame e s o uzzy logic include ib a- ion componen s ν, νm, ν , νz, calcula ed acco ding o Eq. (3), Eq. (4), Eq. (5), Eq. (6) bo h o absence and p esence o damage, wo ha monics o he adial com- ponen o ib a ion eloci y a he supply equency and wo ha monics o he axial componen o ib a ion eloci y a supply ol age equency de e mined by he pa ame e s o he ins alled bea ing, empe a u e θlo he end pa s on he side o he uni damage in acco - dance wi h Eq. (7). The ope a ing p inciple o he model consis s in com- pa a i e analysis o he inpu pa ame e s wi h he ol- lowing ecalcula ion o e o - ee unning ime Tde- c 2015 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 449 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 13 |NUMBER: 5 |2015 |DECEMBER pending on exceeding o one o h ee ins alled le els by one o hem o by some o hem simul aneously. The model was c ea ed wi h he use o he possibil- i ies p o ided by he applica ion package o he wo k wi h uzzy logic [7]. The gene al iew o he model is p esen ed in Fig. 3. Fuzzy condi ions a e o med ac- co ding o he alues o nine inpu a iables and he assignmen o he membe ship unc ion co esponds o hei h ee le els (low, medium and high). Fig. 3: Gene al iew o a uzzy model o a bea ing uni . Unde he condi ion o s uc u al aul lessness o all he o he s uc u al componen s o he EM he de el- oped model enables de e mina ion o : slackening o he bea ing i acco ding o g ow h o he adial compo- nen and winding hea ing; balls de ec s – a addi ional inc ease o spec al componen s a he equencies di- isible by he supply equency; pi o des uc ion – acco ding o g ow h o ib a ion in he axial di ec ion and o he ypes o de ec s. 4. Expe imen al Resea ches Du ing he esea ch he main ypes o s uc u al uni aul s in luencing he eliabili y indices we e singled ou . They include a ious ypes o damages o bea - ing uni , s a o co e, windings, a o o (a ma u e) and cu en collec ion uni s. Theses o e ed in he pape we e es ed du ing expe - imen al esea ch when he e iciency o eliabili y model was being es ima ed o a bea ing uni o AOL12-4 in- duc ion mo o wi h a ed-in aul o he ou e ing. The aul was ob ained by a uni o m dec ease o he ing diame e due o i s g inding o . This de ec e- sul s in he s a ic and dynamic eccen ici y o he ai gap, as well as in pa ial magne ic sa u a ion o he ac i e co e because o he mo o o e load. I becomes appa en in he inc ease o ib a ion componen s a he double equency o powe supply and he basic o a ion equency. Besides, he posi ion o he axis he cap was changed by i s imp ope ins alla ion. Pa ame e s δand α, as well as he equi ed s uc u al pa ame e s we e di ec ly aken in o accoun in he model p ope . Expe imen al da a we e ob ained on he basis o a compu e -aided complex wi h he s uc u e shown in Fig. 4. A measu ing pa o he complex is buil on he basis o a ce i ied measu ing module LCa d E14- 440, including an analog-digi al con e e (ADC) and channels o disc e e inpu /ou pu (DIO) connec ed o a pe sonal compu e (PC). Fig. 4: S uc u e o he measu ing complex. ADC block has 16 di e en ial channels o analog in- pu o which he senso s o measu emen o basic pa- ame e s can be connec ed h ough in e aces schemes (IS 1–4): al e na e cu en senso (CS) wi h ope a - ing ange 0..100 A and educed e o o 1.5 %, al e - na e ol age senso (VS) wi h ope a ing ange 0..750 V and educed e o o 1 %, ib a ion senso s (VBS1, 2) wi h ope a ing ange up o 4000 Hz, and mea- su ing inaccu acy o ib a ion pa ame e a wo king bank no mo e han 1.5 %. Con ol o IS cha ac e is- ics is pe o med h ough DIO channels. Tempe a u e senso s (TS) 700-101BAA-B00 wi h ope a ing ange - 70..+500 ◦C and sensibili y ±0.06 %, and a o a ion equency senso (RFS) based on op ical achome e BE-5H wi h z= 1000 o −1and equency measu e- men uni , a e connec ed o PC sepa a ely h ough an in e ace con e e (IC). Inpu pa ame e s o he uzzy model we e de e - mined by means o i e old measu emen wi h he ol- lowing s a is ic p ocessing o he esul s. Magne ic c 2015 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 450 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 13 |NUMBER: 5 |2015 |DECEMBER ib a ion was sepa a ed om he o e all one due o swi ching o he EM supply ol age. The ob ained alues o ib a ion eloci y: νe 1= 0.74 mm ·s−1;νe 2= 1.16 mm ·s−1; νez1= 0.8 mm ·s−1;νez2= 0.95 mm ·s−1, whe e νe 1, νe 2;νez1, νez2– espec i ely adial and ax- ial oo -mean-squa e alues o ib a ion eloci y o EM wi hou damages (1) and wi h damaged (2) bea ing uni (Fig. 5). Co esponding alues o empe a u e θla e espec- i ely 67 and 70 ◦C (Fig. 5). Fig. 5: Resul s o he change o he EM winding slo empe a- u e: 1 – undamaged EM; 2 – EM wi h a damage. In his case admissible alue νe o es ed EMs, ac- co ding o S anda d 20815-93 is 1.12 MM/C, and alue o he excessi e empe a u e o he winding o he p e- sc ibed insula ion class B in EM – 80 ◦C. To inc ease he eliabili y o iden i ica ion o he con- side ed de ec s he esul s o spec al analysis o adial componen o ib a ion o kha monics in ela ion o ol age supply equency ( he 3 d and he 17 h ha - monics in Fig. 6, which change unde damage p esen shows appea ance o unbalance and elec ical asymme- y o EM s uc u e) we e used. Resul s o de e mina ion o e o - ee unning ime, acco ding o simula ion da a using uzzy logic, di e om expe imen al alues ob ained h ough mean al- ues o ib a ion eloci y and empe a u e using expe i- men al design heo y wi hin 17 %. Taking in o consid- e a ion he ambigui y o he condi ion o o he s uc- u al componen s, such an e o is admissible in his case. Fig. 6: Resul s o spec al analysis o a adial componen o ib a ion: 1 – undamaged EM; 2 – EM wi h a damage. Besides, he modeling esul s enable e alua ion o he mu ual in luence o he inpu pa ame e s and, hus, iden i ica ion o mani es a ion o basic de ec s. I p o- ides he possibili y o accu a e de e mina ion o he damage ype and he s a e o he conside ed uni a e ele an imp o emen o he model. 5. Conclusion The e iciency o he use o uzzy logic pos ula es in he c ea ion o elec ic machine eliabili y p edic ion models has been p o ed. I p o ides he possibili y o aking in o accoun he a ia ion o he s a e o majo s uc u al uni s and elemen s by es ima ion o hei he mal and ib a ion pa ame e s. Re e ences [1] MAKUC, D., K. DROBNIC, V. AMBROZIC, M. LEBLANC, D. MILJAVEC, R. FISER and M. NEMEC. Pa ame e s es ima ion o induc ion mo- o wi h aul y o o . P zeglad Elek o echniczny. 2012, ol. 88, iss. 1a, pp. 41–46. ISSN 0033-2097. [2] PRUS, V. V., M. V. ZAGIRNYAK, I. A. KOLOTYLO and D. MILJAVEC. Es ima e and aking in o accoun change o s eel losses in in- duc ion mo o s in p ocess o hei aging. In: IEEE EUROCON. Sain Pe e sbu g: IEEE, 2009, pp. 777–782. ISBN 978-1-4244-3861-7. DOI: 10.1109/EURCON.2009.5167722. [3] ZAGIRNYAK, M. V., V. V. PRUS, I. A. KOLOTYLO and D. MILJAVEC. Taking s a- o co es in o accoun when induc ion mo o s i- b a ion pa ame e s a e calcula ed. P zeglad Elek- c 2015 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 451 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 13 |NUMBER: 5 |2015 |DECEMBER o echniczny. 2013, ol. 89, iss. 12, pp. 286–289. ISSN 0033-2097. [4] KUZNETSOV N. L. and N. F. KOTELENETS. Tes ing and eliabili y o elec ic machines. – M. Moscow: Vysshaia shkola, 1988. ISBN 5-06- 001233-6. [5] TANAKA, K. An In oduc ion o Fuzzy Logic o P ac ical Applica ions. 1s ed. New Yo k: Sp inge , 1997. ISBN 978-0-387-94807-2. [6] BILLINTON, R. and R. N. ALLAN. Reliabil- i y E alua ion o Enginee ing Sys ems: Concep s and Techniques. Be lin: Sp inge -Ve lag, 2008. ISBN 978-1-4899-0685-4. [7] Ma lab: Ge ing S a ed Guide R2011b. Ma h- wo ks [online]. A ailable a : h ps://www.ma. u exas.edu/use s/haack/ge s a .pd . Abou Au ho s Mykhaylo V. ZAGIRNYAK was bo n in 1947. He g adua ed om Lugansk Machine-Cons uc ion Ins i u e in 1970 and was quali ied as an Elec ical Enginee , Lugansk, Uk aine. He ecei ed he deg ee o Can.Sc. (Ph.D.) om Kha ko Poly echnical Ins i u e in 1977, and he deg ee o DSc. om Kha ko S a e Poly echnical Uni e si y in 1996, bo h in Elec ical Enginee ing. He was isi ing esea che wi h he Depa men o Elec ical Enginee ing, Uni e si y o Ken ucky, Lexing on, USA unde IREX P og am (1983–1984) and Fulb igh P og am (1997–1998). His esea ch in e es s a e in he a ea o calcula ion o magne ic ields o elec omagne ic sepa a o s, elec ic machines and o he elec omagne ic de ices. P esen ly he is ec o o K emenchuk Mykhailo Os oh adskyi Na ional Uni e si y and Chai man and P o esso o Elec ic Machines and De ices Depa men (K e- menchuk, Uk aine). Viachesla V. PRUS was bo n in 1973. He g ad- ua ed om Kha ko S a e Poly echnical Uni e si y in 1996 and was quali ied as an Elec ical Enginee . He ecei ed he deg ee o Can.Sc. (Ph.D.) om Ins i u e o Elec odynamics o Na ional Academy o Science o Uk aine in 2004. His esea ch in e es s a e in he a ea o elec ic machines and elec omagne ic de ices. P esen ly he is Associa e P o esso o Elec ic Machines and De ices Depa men o K emenchuk Mykhailo Os oh adskyi Na ional Uni e si y (K e- menchuk, Uk aine). Oleksand O. SOMKA was bo n in 1989. He ecei ed his M.Sc. deg ee om K emenchuk Mykhailo Os oh adskyi Na ional Uni e si y in 2012. His esea ch in e es s a e in he a ea o eliabili y o elec ic machines. P esen ly he is a pos -g adua e s uden o Elec ic Machines and De ices Depa men o K emenchuk Mykhailo Os oh adskyi Na ional Uni e si y (K emenchuk, Uk aine). I o DOLEZEL was bo n in 1949. He ob ained his M.Sc. deg ee om he Facul y o Elec ical Enginee ing a he Czech Technical Uni e si y in P ague in 1973. His in e es s a e aimed mainly a ma hema ical and compu e modeling o elec omag- ne ic ields and coupled p oblems in hea y cu en and powe applica ions. He is an au ho o co-au ho o wo monog aphs (USA), abou 450 esea ch pa- pe s (o e 50 in jou nals wi h impac ac o s) and se e al la ge codes. Membe o Scien i ic boa ds o nume ous in e na ional con e ences, edi o ial boa ds and o he bodies. P esen ly he wo ks wi h he Czech Technical Uni e si y in P ague (Facul y o Elec ical Enginee ing), Academy o Sciences o he Czech Republic (Ins i u e o The momechanics) in P ague and Uni e si y o Wes Bohemia (Facul y o Elec ical Enginee ing) in Pilsen. c 2015 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 452