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
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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
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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-
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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
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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
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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-
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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
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