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Couon of Mcrococ Elcrognc Pror of Sof Mgnc Coo Yuh Io, Igrh, Mbr, IEEE ru School of Inforon Scnc n Tchnolog, oo Unr, 4, h 9, -u, 6-84, Soro, Jn Th r rn nw nurcl ho o cou h crococ lcrognc ror of h of gnc coo SMC In rn ho, SMC u o b coo of hoognou gnc brc wh roc Th crococ lcrognc ror of SMC r obn ung fn ln ho n whch u h h hoognz nrg qul o h or n un on cor h crococ lcrognc ror obn b h rn ho wh ho obn b Ollnorf forul n gnc crcu b on h nongnc grn bounr ol I hown h h hr rul r n goo grn whn ung conn rbl I lo foun h hr r clr crnc ong h u o gnc uron cll whn h gnzon coffcn lrg In Tr Sof gnc coo, Fn ln ho, Ollnorf forul, ongnc grn bounr ol, Inucor S I ITRODUCTIO OFT MAETIC COMPOSITE SMC CORES coo of gnc rcl co b lcrcll nulng n non-gnc rl h ng or ronl ln l u n lcrognc chn uch oor n rcor [], []: h forr h lowr currn lo n qu for forng 3D h [3] I rnll hown h h crococ rbl n currn lo n SMC n on h n, z n h of h gnc rcl Thrfor ncr o oz h rr o rlz rbl ror for SMC uch hgh rbl n low currn lo Th crococ lcrognc ror of SMC cn rol b b h clcl ho b on Mwll- [4], [5], Ollnorf [6] n ruggn forul [7] Th rbl of SMC cn lo b ol ung gnc crcu ho b on h nongnc grn bounr M ol [8] owr h forul woul no b l for ur cor, n h cnno r wh gnc hr n currn lo Th r rn nw nurcl ho b on fn ln ho FEM o cou h crococ lcrognc ror of SMC In h rn ho, u h SMC coo of hoognou gnc brc wh roc Th crococ lcrognc [] - + / [] - - / - z [] + / - - / - ln b -z ln Fg Mol : un on of l cubc lc z [] z + / [] - - / - [] + / - z - / Mnucr rc obr, Corronng uhor: Y Io -l: uo@-nghouc Dgl Obc Infr nr b IEEE - z z ror obn b h rn ho n lnr n nonlnr nl r cor wh h obn b Ollnorf forul n gnc crcu ol Moror w u h ffc of h on n h olu frcon of gnc rcl n SMC on h gnc ror of h nucor on h b of h rn ho A Anl ol II UMERICAL METOD L u conr SMC whch con of gnc rcl co b non-gnc rl wh roc confguron u h brc-h rcl of h z for lc Th unfor gnc nucon l o SMC n z-rcon hown n Fg u h Drchl n unn bounr conon on h n o-boo bounr of h on, rcl Fn ln forulon L u conr c gnc fl whou lcrc currn Th gornng quon A whr, A r h rbl n cor onl, h lr of whch crz ung h cor nrolon funcon fn for ch ln g follow: A whr no h g n Th FE quon for cn b wrn n h for 3 whr Th unnown now no wo r: = + whr n corron o h nuc n rnl cor onl hn w u conn rbl for h 4
gnc rcl, 3 rwrn 5 whr h FE r o whch h bounr conon r l hn w conr h gnc uron n h gnc rcl, h won-rhon ho lo o r h lnrz quon gn b 6 whr, 7, 8 n n n 9 Th r of wh rc o n 9 cn b obn fro h cur III COMPUTATIO OF MACROSCOPIC ELECTROMAETIC PROPERTIES A Lnr nl In h rn ho, h crococ rbl obn o h h gnc nrg n h un on, hown n Fg, nclung h rcl n non-gnc lr qul o h hoognz nrg [9] hn ung h conn rbl, h gnc nrg n un on r μ whr,,, n r h olu of h un on, ln n, rbl n olu of ln Th hoognz gnc nrg r n r of h rg fl follow: Fro n, w cn obn h crococ rbl for h lnr c : μ onlnr nl hn w conr gnc uron, h gnc nrg cn b r 3 whr - - - - 4 On h ohr hn, h hoognz gnc nrg cn b r follow: 5 whr, - - - 6 7 Fro 3 n 5, w cn obn h crococ conu rlon for h non-lnr c - - 8 whr I UMERICAL RESULTS A Ollnorf forul n gnc crcu ol To h l of h rn ho, w cor h lnr crococ gnc ror obn b h rn ho wh ho obn b Ollnorf forul n h gnc crcu ol Ollnorf forul [6] 9 h wl bn u o h rbl of hrognou rucur, whr,, n r h rbl of cuu n gnc rcl, olu frcon of gnc rcl n coffcn of gnc
fl whch f In h ho roo n [8], h gnc fl n h un on nlz ung h gnc crcu ho In h ho, for h un on hown n Fg coo of qur fl wh g z n hcn, urroun b g of unfor hcn /, h rbl gn b 4 z Anl of ol : l cubc ol Th gnc ror of SMC nlz b h hr ho ung h coo of h l cubc lc hown n Fg, whch cll ol In h nl, w = = z =5 n =/3 ubu o Ollnorf forul bcu of h oroc nur of h ol In h lnr nl, h rl rbl of gnc rcl In orr o obn h rlonh bwn h crococ rbl n olu frcon, h g lngh chng Fro h rul hown n Fg, w cn h h lu of crococ rbl obn b h hr ho r n goo grn rgrl of w conr h nonlnr gnc ror of SMC, whr h gnc rcl r u o ob h chrcrc of frr Fg 3 how h gnc ror of h hoognou frr cor wll crococ gnc ror of SMC obn b Ollnorf forul, h gnc crcu ol n rn ho whn =9 To cou h crococ rbl fro h Ollnorf forul n gnc crcu ol, h rbl of h frr, whch funcon of, ubu no 9 n On h ohr hn, h chrcrc full conr n h fl couon of h rn ho A hown n Fg 3, h hr ho g lo ncl crococ cur whn =/3 owr, foun n Fg 3b h whn =5, = =, z =54, h ffrnc ong h bco gnfcn In rculr, Ollnorf forul l hghr lu n n coron wh h ohr wo ho Moror, h ffrnc bwn h rul obn b h rn ho n gnc crcu bco lrg ncr Th woul rbu o h fc h h gnc fl wh gnc uron u o low n hgh cnno b wll ro b h gnc crcu C Anl of ol : bo-cnr cubc ol n conr SMC coo of h bo-cnr cubc lc hown n Fg 4, whch cll ol hrfr Th crococ rbl rn b h gnc crcu ol gn b [8], [] z R R R whr R, R gz n R g r h rlucnc of h rcl n g long h z n whch cn b r b z R, Rgz,, 3 4 z gz g - ln b -z ln Fg 4 Mol : un on of bo-cnr cubc lc R Mcrococ rl rbl Dn of flu [T] Dn of flu [T] g 4 35 3 4 35 3 5 35 3 5 5 5 5 oognou Frr 5 Ollnorf Mgnc crcu 5 Prn 5 5 Mgnc fl [A/] oognou Frr 5 Ollnorf Mgnc crcu 5 Prn 4 6 8 Mgnc fl [A/] z 4 [] z [] z Ollnorf Mgnc crcu Prn 8 85 9 95 Frcon Fg Rul n lnr nl of ol b =5 Fg 3 - cur n nonlnr nl of ol whn 9 / =/3 [] / Th lngh on h of gnc rcl n ol o = = z =5 whn =/3, = =, z =54 whn =5 Th chrcrc of frr n SMC ol b h hr ho r hown n Fg 5 I cn b n n Fg 5 h h cou crococ chrcrc r owh lr o ch ohr owr, hown n Fg 5b, h crnc bwn h rul obn b h z [] [] / [] / z
Dn of flu [T] Dn of flu [T] 4 35 3 5 oognou Frr 5 Ollnorf Mgnc crcu 5 Prn 5 5 Mgnc fl [A/] 4 35 3 5 oognou Frr 5 Ollnorf Mgnc crcu 5 Prn 4 6 8 Mgnc fl [A/] rn ho n h ohr bco gnfcn whn ncr Th woul b u o h fc h h ur gnc fl cnno b ccurl ol b Ollnorf roch n gnc crcu ho Moror, h ffrnc n h rul obn b h hr ho n ol r lrgr hn ho n ol Th woul b u o h fc h gnc r n ol lowr hn h n ol o h gnc uron l occur n h forr D Anl of nucor =/3 b =5 Fg 5 - cur n nonlnr nl of ol whn =9 I nown h hr non-unfor n h olu frcon of gnc rcl n SMC bcu of h r n h roucon roc r w nlz h ffc of nonunfor n on h gnc ror of h nucor ung h rn ho n whch ol lo Th nucnc of ol nucor of SMC hown n Fg 6 cou In h nl, h lu of n r of h ur gnc l chng fro 9 o 7 Th urn of col n o A fn n Tbl h h nucnc bco clrl ll whn hr non-unfor n COCLUSIO In h r, w h rn nw nurcl ho o cou h crococ lcrognc ror of SMC In h rn ho, h r obn o h h gnc nrg n h un on nclung gnc rcl n non-gnc lr qul o h hoognz nrg Th crococ gnc ror obn b h rn ho h bn cor wh h obn b Ollnorf forul n h gnc crcu ol I h bn foun h h hr ho g lo ncl rul for crococ rbl whn h rl u o h lnr ror On h ohr hn, hr r gnfcn ffrnc ong h cll whn h gnzon coffcn lrg or h l gnc fl rong Th ron for h crnc woul b u o h fc h h ur gnc fl cnno b wll r b Ollnorf roch n gnc crcu olng ln o l h rn ho o nl of hr n currn lo n SMC n fuur Moror, w wll l h rn ho o or colc l 4 [] 5 5 z [] SMC cor of frr gh Col 5 5 4 Low [] z [] - ln b -z ln Fg 6 Mol nucor of SMC Tbl urcl rul of h nucnc gh frcon Low frcon Inucnc[] Frr Frr 75 9 9 798 9 8 698 9 7 63 ACOLEDMET Dr wno of To Yun Co n Dr A Furu, Y Uhr of Fuu L g u hlful con for h u REFERECES [] Y uo, J Zhu, Z Ln n J J Zhong, Murn n Molng of Cor Lo of Sof Mgnc Coo Unr 3-D Mgnc Econ n Rong Moor, IEEE Trn Mgn, ol 4, no, 395-397, 5 [] M Przbl, Ślur, J ro, ruhl DC Moor wh on Prnn Mgn n Powr Mgnc Cor, XIX Inrnonl Confrnc on Elcrcl Mchn, -4, [3] Shorollh, Jnghorbn, Sof gnc coo rl SMC, J Mr Proc Tchnol, 89, -, 7 [4] J C M rn, Color n Mrl l n Ml Fl, Trn Ro Soc, ol 53, 385-4, 94 [5] A Shol, Elcrognc Mng Forul n Alcon, IEE ELECTROMAETIC AES SERIES 47, 999 [6] F Ollnorf, Mgno r Mrn, Arch f Elrochn, 5, 436-447, 93 [7] D A ruggn, rchnung rchnr hlchr onnn on hrognn Subnzn, I Dlrzonnn un Lfhgn r Mchorr u oron Subnzn, Annln r Ph, 5 Folg, n 4, 636-664, 935 [8] F Mzlr, Lgr, R Lbourgo, n R rru, Prbl of Sof Mgnc Coo Fro Fl of nocrlln Rbbon, IEEE Trn Mgn, ol 38, no 5, 33-334, [9], Igrh n T on, Eon of Effc Prbl of Mgnc Coo Mrl, IEEE Trn Mgn, ol 4, no 5, 5-53, 5 [] S n, Y Oh n Aw, Effc of Prcl Sh on DC- Pror of Powr Cor n Molng, J Mgn Soc Jn, 35, 436-44, 3 [] gh SMC cor of frr Col 5 5 4 Low []