Inductance of Cylindrical Coil
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1 SEBIN JOUN OF EETI ENGINEEING Vol. No. Jue Iductce of ldcl ol G.. vd. Dol N. Păduu stct: Te cldcl coeless d coe cols e used stumet tsfomes d m ote electomgetc devces. I te ppe usg te septo of vles ltcl fomul fo te lekge ductce of t cldcl col wt ustuted coe s deduced ssumg smplfed pt fo te fotl flu. Te esults e comped wt well-kow epemetl dt d dt esultg fom FEM models. ewods: ldcl col. Iductce. Septo of vles. B coe tsfome. oeless cldcl soleod Te fst esult s te. ücle epemetll oted fomul 8 wc cosde te coespodg equvlet gp fo t soleod wt te dmete d d te legt l gve te fomul [] c l δ l α. c. 44. α d Te ect teoetcl soluto fo ts cse s gve te equto [] 4 α c α Φ α α E. Φ α α α Hee d E e te ellptc tegls of fst d secod kd wt te module k e : k. α Te ect vlue of ductce of te coeless cldcl soleod s µ w d Φ [H]. 4 4 Uvest of ov om Bd. Decel 7 O-44 ov om E-ml: gcvd@elt.ucv.o Uvest of ov om Bd. Decel 7 O-44 ov om IMET - Electoputee ov om 4
![G.. vd. Dol N. Păduu Te depedece of te coeffcet c o te soleod dmesos to clculted wt s gve Fg. d gees wt te ücle epemetl esult te specfed [] dom of α. Fg. - oeffcet c fo equvlet gp.](/docs-images/80/81174062/images/2-0.jpg "Te lmts of c fo α equl to d ft c e oted fom. Fo smll k te followg developmet of te ellptc tegls e vlle []:!! k k d!! k E k. 5!")
2 G.. vd. Dol N. Păduu Te depedece of te coeffcet c o te soleod dmesos to clculted wt s gve Fg. d gees wt te ücle epemetl esult te specfed [] dom of α. Fg. - oeffcet c fo equvlet gp. Te lmts of c fo α equl to d ft c e oted fom. Fo smll k te followg developmet of te ellptc tegls e vlle []:!! k k d!! k E k. 5!! osdeg ol two tems sees fo 4 Φ α lm Φ α α Fo α [] α 4 α α 4 α α 44 α we ve te lmts 4 α α 4 c lm α α Φ α 4 4 α α α 4 α Φ α... l α 96 ücle [] poposes to clculte te ductce of coe cldcl col cosdeg te soleod legt equl to eo d te equvlet gp δ c d d toduces te coecto coeffcets k d k wc tke to cosdeto te coe legt le d coe dmete d d e. Fo le l... de te fcto e k. Ts mes d tt ts cse te et fomul 8 te col dmete c e smple susttute coe dmete d e
3 Iductce of ldcl ol µ w d e k k 4c. k.5.6 Hee d s te col dmete d d e s te coe dmete. > k de. 8 d Fg. - Mgetc feld ptte: c - clculted wt FEM clculted wt 8. ekge ductce of coe soleod. Feld polem We wll cosde smmetcl t soleod closel fttg to cldcl steel coe. Te vecto mgetc potetl D [ > ] [ < < ] wll stsf te equto: d dv ot ot µ J J µ δ >. 9 Te mgetc flu le ssug fom te coe edge wll e cosdeed ootl stgt le dsed le Fg. d cosequetl we c ppomte te oud codtos s follows: 45
4 G.. vd. Dol N. Păduu 46 d > < η H B B. Hee w s te col ume of tus d η te to of te tel to etel tgetl mgetc feld o col sufce. Usg te septo of vles metod d cosdeg we wll ot te equtos: s cos 4 I. Hee d I e te modfed Bessel fuctos of fst ode. Tkg to ccout te oud codtos fo d wc gve 4 we wll seek fo te soluto of te ove polem te followg fom wc stsf te oud codto fo µ cos. Usg kow equto fo Bessel fuctos [] d te compoets of flu dest wll e: µ s B d µ cos B. Te oud codto fo detemes te coeffcets. Equtg 9 d fo η we ot: > < H cos. 4
5 Iductce of ldcl ol Multplg te lst equto cos d tegtg etwee d t esults s cos d. 5. Fotl flu We wll ppomte te mgetc feld ptte fo > wt te cuet les pot cotct. Ude suc ssumptos te mgetc flu pssg toug te ed of te dmete cldcl coe d te coespodg ductce c e evluted s [4] wφ Φ µ µ w. 6 I Ts ssumpto detemes te vlue of te vecto mgetc potetl d te costt : µ Φ. 7 Fo > te vecto mgetc potetl wll e µ cos > <. 8 Te equtos of mgetc flu les e cost. I Fg. d c we c see te eoug good smlt of te tus clculted feld pttes wt te oted FEM.. tel flu Te mgetc flu emeget fom te cldcl pt of te coe ove te col d te coespodg ductce wll e d [ ] µ Φ cos µ w cos. 9 Te telkge toug te col d coespodg ductce wll e: Ψ d w B d µ s 47
6 G.. vd. Dol N. Păduu 48 d µ cos s w..4 Totl ductce Te totl ductce of cldcl col closel fttg to cldcl coe wll e µ s w. Fg. - oeffcet k fom fomul 8 clculted wt 4. Te ücle coeffcet k fom 8 defed s to of te coe col ductce to te eo legt coeless col ductce s ow α α Φ 4 l k s. Tkg to ccout te equtos d 5 we ot fo k coeffcet te equtos:
7 Iductce of ldcl ol s 4 T T T k < Φ >. 4 Te vlues of k clculted wt te tems <.7 fo. > sees 4 e gve Fg. e. ompso wt epemetl d FEM esults Te compso wt ücle s fomul 8 d te esults oted FEM cosdeg smptotc oud codtos o te oute dus of te ego. m fo cm s gve Fg. 4. ette geemet of teoetcl esults t of gve [] wt oted FEM c e oseved Fg. 4 especll fo sot soleod d log coe. Fg. 4 - ompso of te clculted wt 4 k vlues wt te gve [] d detemed usg FEM. 4 ocluso. Te ductce of coeless cldcl col c e lws clculted wt fomul 4 wt te coeffcet c clculted wt o gve Fg. fo wde ge of α.
8 G.. vd. Dol N. Păduu. Te ductce of cldcl col c e clculted fo smll dmetes usg te ücle s epemetl fomul 8 d te gve [] cuves fo k. Fo lge dmetes te gve [5] cuves lso c e used.. Fo ll te dmetes d fo log o sot coe te ductce of t cldcl col closel fttg to cldcl ustuted steel coe c evluted usg te poposed fomul o te ücle s epemetl fomul 8 d te cuves fom Fg. fo k. 4. Te ductces oted wt te poposed fomul o wt ücle s fomul 8 wt k fom Fg. e ette geemet wt te FEM esults wt smptotc oud codtos. 5 ckowledgemet Te utos would lke to tk Pofesso.. ledov Teccl Uvest of Sof Bulg fo useful commets d offeed efeeces. e Ellptc t m k k k! 5 E k! k m.7596m.5.478m.8879m l m.465m.778m.4577m.4496m l m f m < M m m E m f m < M E m E m m m E m M.99 e. Fo >. ests te followg eqult: eplcg 4 we ot: 5 5 < > T < 5..5 Fom wc esults te est evluto gve 4. d..
9 Iductce of ldcl ol 6 efeeces []. ücle: Iuktvtät ud stomkft ee ldespule mt Stke Juc de EG- Foscug 6 99 pp. 8-. [] П. Л. Калантаров Л. А. Цейтлин: Расчет индуктивностей Энергоатомиздат 986. [] E. Jke F. Emde F. ősc: Tlfe őee fuktoe Teue Stuttgt 96. [4] Л.Б. Ганзбург А. И. Федотов: Проектирование электромагнитных и магнитных механизмов Машиностроение 98. [5] А. К. Александров П. Р. Пенчев: Магнитни проводимости ВМЕИ София 985. [6] N. Pduu G.. vd: Voltge coe tsfome SIE' te XII - t It. Smp. o Electcl pptus d Tecologes M - Jue Plovdv Bulg pp
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