Systemic design and modelling of a coiled rotor synchronous motor dedicated to electric traction

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mcan Jounal of Elctcal Pow an Engy Sytm 5; 4(-): -7 Publh onln Novmb 5, 4 (htt://www.cncublhnggou.com/j/) o:.648/j...54.

1 mcan Jounal of Elctcal Pow an Engy Sytm 5; 4(-): -7 Publh onln Novmb 5, 4 (htt:// o:.648/j ISSN: 36-9X (Pnt); ISSN: 36-9 (Onln) Sytmc gn an mollng of a col oto ynchonou moto cat to lctc tacton cha Khla, Houcn Maouan, Souh Toun School of Elctonc an Tlcommuncaton of Sfax, Sfax Unvty, Sfax, Tuna Emal a: achakhla@gmal.com (. Khla), Houcn.maouan@c.nu.tn (H. Maouan), ouh.toun@c.nu.tn (S. Toun) To ct th atcl: cha Khla, Houcn Maouan, Souh Toun. Sytmc Dgn an Mollng of a Col oto Synchonou Moto Dcat to Elctc Tacton. mcan Jounal of Elctcal Pow an Engy Sytm. Scal Iu: Dgn, Otmzaton an Contol of Elctc Vhcl: (DOCEV). Vol. 4, No. -, 5,. -7. o:.648/j btact: In th a, w nt a mthoology of gn an molng of th contollng aamt of ynchonou moto wth woun oto, ba on th analytcal mtho. Th mthoology nu a w oatng ang of lctc vhcl. It tak nto account val hycal an tchnologcal contant. Th mol hghly aamtz an quckly hl to ov th mnon an ow tan contollng aamt valu by vayng th mchancal chaacttc of th vhcl. It comatbl wth all ban of lctc vhcl ow wth ngl moto. Th analytcal molng aoach valat ntly by th fnt lmnt mtho. Kywo: Col oto Moto, nalytc Dgn, Contollng Paamt, Sytmc Contol, Elctc Vhcl. Intoucton Th oucton of lctc vhcl n lag gnally uff fom latvly hgh cot coma to ntnal combuton vhcl. Fo th aon, ou choc wa ct to a tuctu of ynchonou woun oto moto wth mooth ol (MSB) to uc th cot of lctc vhcl, bcau th ty of moto wth uc cot coma to oth tuctu of lctc moto. In, th ngn n a tuctu ay to alz, an t wth on an taght lot an concntat wnng ay to achv. Thfo, t ha a gatly uc manufactung cot coma to oth ngn tuctu. It ha no magnt alo lang to a ucton of th cot of vhcl. In th contxt, th a nt a gn mthoology an molng of contol aamt of th tu moto tuctu.. Moto Stuctu Th MSB machn bult wth th am au fo th tato an th oto. Th lot ct towa th moto cnt. Th gn ato fn th moto' tuctu [], [] an [3].. Th ft coffcnt th ato β of th magnt avag angula wth by th ol tch (L=π/). It ajut th magnt wth n vu th ol numb chon. Th con coffcnt (α) th ato of th man tooth avag angula wth by th avag angula wth of a magnt. It ajut th man tooth z an ha a tong nflunc on th lctomotv foc wavfom. Th lat coffcnt ( ) fx th nt tooth z. It th ato of th man tooth avag wth by an nt tooth avag wth. Th avantag of th coffcnt to fn quckly machn ha. Howv, thy a ba on th avag au an t ncay to comut an chck hgh an low angl tth n o to avo any ntcton. Tabl llutat th valu of th coffcnt: Tabl. Valu of th moto aamt Dgnaton β α N Tazoal confguaton. 4 6 Th MSB tuctu llutat by fgu :

takng n account of th coo-lng ytm to ntgat, t l than. Th at cunt can b uc fom th followng latonh: Cm I m = () K Fgu. MSB tuctu. 3.

2 cha Khla t al.: Sytmc Dgn an Mollng of a Col oto Synchonou Moto Dcat to Elctc Tacton Wh th au of th whl, M v th ma of th vh-cl, th ucton ato, g th gavty foc, λ th angl btwn th oa an th hozontal an α t a coffcnt takng n account of th coo-lng ytm to ntgat, t l than. Th at cunt can b uc fom th followng latonh: Cm I m = () K Fgu. MSB tuctu. 3. Dmnonng Toqu Th zng toqu calculat at th tm of tatu of th vhcl, wh th cunt awn by th moto maxmum. t th tm, only th momnt of nta an toqu of th vhcl u to gavty foc a gnfcant. Th ctzaton of th movmnt quaton at tatu la to th followng zng toqu: C m M v Vb g n( ) α t + λ t () Wh K th moto contant: D D K n N B (3) 4 Wh n th numb of moto moul, D an D a ctvly th xtnal an ntnal moto amt, N th numb of ha tun an B th flux nty n th a-ga. 4. Moto Szng Th fgu nt th ffnt gomtc aamt of th tato: Fgu. Gomtc aamt of th tato. Th lot wth of th tato gvn by th followng quaton [4] an [5]: D + D π π L ( ) nc = n α β (4) N Wh D an D a ctvly th xtnal an ntnal moto amt, N th numb of man tth an th numb of ol a. Th low angula wth of tato lot gvn by th followng xon: n D nc nc (5) Th uo angula wth of tato lot gvn by th followng xon:

mcan Jounal of Elctcal Pow an Engy Sytm 5; 4(-): -7 3 n D nc nc (6) Th avag angula wth of a man tooth x a follow: ntm π = α β (7) Th avag angula wth of th nt tooth x a follow: ntm = ntm (8) Th avag

3 mcan Jounal of Elctcal Pow an Engy Sytm 5; 4(-): -7 3 n D nc nc (6) Th avag angula wth of a man tooth x a follow: ntm π = α β (7) Th avag angula wth of th nt tooth x a follow: ntm = ntm (8) Th avag angula wth of th lot x a follow: π ncm ntm ntm N Th nfo angula wth of tato man tooth gvn by th followng xon: (9) nt = ntm + ncm nt () Th uo angula wth of tato man tooth gvn by th followng xon: nt = ntm + ncm nt () Fo th confguaton wth tazoal wavfom th hght of a tooth gvn by th followng quaton []: 3 N I m H () N δ K L Wh K f th fllng facto of th lot, δ th allowabl cunt nty n th lot, I m th co conucto zng cunt an N th numb of ha. Th calculaton mtho of th mnonng cunt tal n [4]. Th hght of th tato yok a v by alyng th thom of convaton of flux btwn th man tooth an th tato yok [5]: H c B = B c f ( S,S ) Mn a D D nc (3) Wh B c th nucton n th oto yok, B th flux nty n th a-ga, S cton of a tato tooth, S a th cton of a magnt fo th MSP tuctu o of th oto tooth fo th MSB tuctu an K fu th flux lakag coffcnt Th fgu 3 nt th ffnt gomtc aamt of th oto. Fgu 3. Dffnt gomtc aamt of th oto. Th ml wth of a oto lot a: = γ (4) ncm L a Th lot wth of th tuctu gvn by th followng quaton [4] an [5]: L D + D = n ncm nc (5) π L a β (6) Wth L a th ml angula wth of th magnt an γ a coffcnt ajut by fnt lmnt mulaton wth th hl of th oftwa Maxwll D an can b otmz. Th avag angula wth of th oto man tooth x a follow: π ntm = β ( γ ) (7) Th low angula wth of oto lot gvn by th followng xon: n D nc nc (8) Th uo angula wth of oto lot gvn by th followng xon: n D nc nc (9) Th hght of a oto tooth H mttng to v th ncay ac fo th co: H nc n I = () δ L Wh n th numb of oto col, I th xctaton cunt an δ th ambl cunt nty n th co.

4 4 cha Khla t al.: Sytmc Dgn an Mollng of a Col oto Synchonou Moto Dcat to Elctc Tacton Wh K fu < th coffcnt of flux lakag an th a-ga thckn. Wh B c th nucton of magntzaton, B th mannt nucton of magnt an µ th mablty of a. Th hght of th oto yok v by alyng th thom of convaton of flux btwn a magnt o oto tooth an th oto yok [5]: ( S,S ) B Mn a H c B c D D Wh B c th nucton n th oto yok. 5. Back Elctomotv Foc K fu () Th fgu 4 nt th tbuton of th vcto nucton to th lvl of th a-ga fo th functonng at no loa. Th lvl of nucton ach th valu calculat analytcally. Conquntly, th flux va two tm mo quckly. Fnally, th zon ntcal to th zon b. Th two zon xt only f th coffcnt β l than. Tabl. Flux an lctomotv foc n functon of moto aamt. Zon Poton (a) Flux ϕ b (Wb) Emf (V) πβ πβ (D D ) π β αb 8 a ( α ) θ ( α) π β b ( ) θ π β (D α ( + α) D ) π β ( + α) θb π β πβ c ( + α) θ ( + α) 8 (D D ) π ( θ)b 8 π β ( + α ) θ π β (D ( α) D ) π π β ( + α) θb 8 NΩ NΩ NΩ (D D ) B 8 (D D ) B 8 (D D ) B 8 Th fgu 5 nt th voluton of th flux an th lctomotv foc (.m.f.) n functon of lctc angl Fgu 5. Flux an lctomotv foc n functon of lctc angl. L flux nty n th a-ga uc fom m thom: µ n I B = () Wh I th xctaton cunt, th -ga thckn, µ th a mablty an n numb of th oto wnng. 6. nalytcal Molng of Inuctanc an Mutual Inuctanc Fgu 4. Intal oton an nucton n th a-ga. Fom an ntal oton llutat by fgu 4, oto mov wth angula vlocty (Ω = θ/t). Fou tnct ntval aa accong to magnt oton an gomtcal aamt valu fn vouly. Tabl llutat th ffnt ntval a wll a flux vaaton. If α qual to, zon a aa. In th zon b, th flux ca bcau a at of th magnt not n font of th tooth. In th zon c, a magnt of an oot olaty ovla alo th man tooth. 6.. nalytcal Molng of Inuctanc Fo MSB tuctu, ha nuctanc va lghtly n functon of oto oton nc th oto lot a not. Fo th aon, w con that th MSB tuctu wth mooth ol an th ha nuctanc contant n lna gm. Th fgu 6 llutat th tbuton of th fl ln to th lvl of a tato ol whn th tato col ul [] an [].

Th fgu how th nc of a flux lakag ang though th lot onng n a nc of lakag nuctanc n th lot co, an of a man flux ang twc though th a ga an th magnt gvng nc to an nuctanc of ga.

5 mcan Jounal of Elctcal Pow an Engy Sytm 5; 4(-): -7 5 cuv µ D ( L ) nc D H (8) Th mol of th total nuctanc uc fom quaton (6), (7) an (8) [7], [8] an [9]: N N L = Lfut + Lntf = + + cuv ntf (9) Fgu 6. Dtbuton of th fl ln fo a ow col. Th fgu how th nc of a flux lakag ang though th lot onng n a nc of lakag nuctanc n th lot co, an of a man flux ang twc though th a ga an th magnt gvng nc to an nuctanc of ga. W call th quaton to mol an nuctanc fo a lna ytm: L = N Φ (3) Φ = N (4) N L = (5) S D D H N L = µ + ( ) L (3) 4 nc Wh S th ufac of th man tooth, H th hght of th lot, H a th hght of th magnt, L nc th wth of th lot, th thckn of th a-ga an th luctanc. 6.. nalytcal Molng of Mutual Inuctanc Th ncl of th calculaton of th mutual nuctanc t on th uly of a col fo th calculaton of th flux catu by th nghbong col. Th tajctoy of th flux fx th total luctanc of th magntc ccut molng th mutual nuctanc. Th fgu 8 llutat th tajctoy of th flux [8] an [9]. Fgu 8. Dtbuton of th flux gnat by th ow col an catu by ajacnt col. Fgu 7. Ntwok luctanc molng nuctanc. Wh L th nuctanc, th cunt of ngz, N th numb of an Ф th flux gvng bth to th L nuctanc an th éluctanc of th magntc ccut. Th fgu 7 llutat th ntwok of éluctanc molng th nuctanc of total ha of th moto [] an []. ccong to th fac, w can wt: Fom fgu 8 w uct th ntwok of luctanc molng th mutual nuctanc (fgu 9) [8], [9]. Wh th luctanc of th a-ga n font of th tooth wh th col accommoat, a th luctanc of a man tooth, 3 th luctanc of th tato yok, 4 th luctanc of th tooth wh th col accommoat, 5 th luctanc of th a-ga n font of th tooth an 6 th luctanc of th oto yok. N = ( ntf ) Φ ntf = cuv Φ ncoch (6) Wth th luctanc of th a ga an th co a gvn by th followng latonh [9]: = µ ntf ( ) S a (7) Fgu 9. Ntwok luctanc molng mutual nuctanc.

6 6 cha Khla t al.: Sytmc Dgn an Mollng of a Col oto Synchonou Moto Dcat to Elctc Tacton Th xon of th mutual nuctanc gvn by: M = N Φ (3) N M = (3) Wh Φ th flux catu by th col whl ngzng th col, th cculatng cunt n th col an th total luctanc. Th ffnt mutual nuctanc of th moto a qual nc th moto ymmtcal. It com thn [8] an [9]: µ D D µ µ ( ) D + D 4 H µ S ncm ntm D + D + ntm + ntm 4 D D Hc (33) (34) 3 (35) 5 µ D D µ µ H 4 (36) µ S ncm ( ) D + D 4 ntm D + D + ntm + ntm 4 D D Hc (37) 6 (38) Wh ncm th ml wth of th lot, ntm th ml wth of th man tooth, ntm th ml wth of th nt tooth, H c th hght of th oto yok, H c th hght of th tato yok, µ th abolut mablty an µ th latv mablty of th magnt. On uct a gnal xon of th mutual nuctanc of th moto wl nglctng th luctanc of on: M 7. DC Bu Voltag Th moto contant fn by [9]: S N = µ (39) ( ) 4 K n N B B (4) Fo th axal flux tuctu an B a gvn by: g D D = (4) D + D B = (4) Wh D an D a ctvly th xtnal an th ntnal amt of th axal flux moto, N th numb of ha, n th moul numb an B g th flux nty n th a-ga. Th convt contnuou voltag U c calculat o that th vhcl can functon at a maxmum an tablz wth a wak toqu unulaton. Th lctomagntc toqu that th moto mut xt at th oaton ont, va th mchancal ow tanmon ytm T Uc (ucng + ffntal) tmat by th followng xon: T Uc ( T + T + T ) Pf T + Ta + Tc = + T + b vb f + (43) Ω Wh T b th ubbng toqu of th moto, T vb th vcou ubbng toqu of th moto, T f th flu ubbng toqu of th moto, T th toqu u to th fcton ollng tanc, T a th toqu u to th aoynamc foc, T c th toqu u to th clmbng tanc, T th uc lo toqu an P f a th on lo an Ω th moto angula. t th oaton ont, th ha cunt gvn by th followng laton: TUc I = (44) K Th only oblty makng t obl to ach th cunt valu I wth a uc unulaton facto (% fo xaml) to choo th convt contnuou voltag oluton of th followng quaton [7-9]: t = m = % (45) t Wh t th ha cunt mantan tm at vhcl maxmum an t m th boang tm of th ha cunt fom zo to I [7-9]: L I t m = ln (46) U c K Ω max Wh an L a ctvly th ha tanc an nuctanc an Ω max th maxmum angula vlocty of th moto. Th ha cunt mantan tm at maxmum of vhcl (coon to lctc g) gvn by th followng fomula [7-9]: t π (47) 3 Ω max

7 mcan Jounal of Elctcal Pow an Engy Sytm 5; 4(-): -7 7 Th convt contnuou voltag tak th followng fom [7-9]: U c 8. Ga ato I = x π 3 Ωmax L + K Ω max (48) Th lctc moto contoll by a low fquncy lctomagntc convt [-6]. Fo th aon th nton of a ga amlf wth ato n th am to nabl th vhcl to ach th maxmum of 8 km / h n ou alcaton. Th ato alo hl nu o ntolaton of fnc voltag n o to hav a goo qualty of lctomagntc toqu. π F = (49) n V n qt Wh n T th fnc voltag ntolaton coffcnt, th numb of a ol, n qt th coffcnt of qualty of th uly voltag, F th wtchng fquncy an V max th maxmum of th vhcl. max 9. Fnt Elmnt Valaton Th moto tu n -D by FEM fnt lmnt oftwa wth gomtc ov by th analytcal mol. Th fnt lmnt mol ba on cylncal cut lan gomtc ntaton at th avag contou. Valu of back lctomotv foc, lctomagntc toqu, nuctanc an mutual nuctanc a vy clo to tho foun by th analytcal mtho. In concluon, th analytcal molng aoach valat ntly by th fnt lmnt mtho.. Concluon Th a cb a mthoology of analytcal zng an molng of a ynchonou axal flux moto wth woun oto. Th mol hghly aamtz. It cov thaft a w ow ang by cfcaton ata changng accong to th T vhcl to z. Th aoach valat by th fnt lmnt mtho. It thn nt an ffctv gn ogam of th ty of moto. fnc [] S. TOUNSI «Lo mollng of th lctomagntc an IGBT convt», Intnatonal Int. J. Elctc an Hyb Vhcl (IJEHV), Vol. 5, No., 3, : [] S. TOUNSI «Comaatv tuy of tazoïal an nuoïal contol of lctc vhcl ow tan», Intnatonal Jounal of Scntfc & Tchnology ach (IJST), Vol., Iu, Nov. [3] [M. HDJ KCEM, S. TOUNSI,. NEJI «Sytmc Dgn an Contol of Elctc Vhcl Pow Chan», Intnatonal Jounal of Scntfc & Tchnology ach (IJST), Vol., Iu, Nov. [4] S. TOUNSI «Contol of th Elctc Vhcl Pow Chan wth Elctomagntc Swtch ucng th Engy Conumton», Jounal of Elctomagntc naly an lcaton (JEM) Vol.3 No., Dcmb. [5] S. TOUNSI, M. HDJ KCEM t. NEJI «Dgn of Statc Convt fo Elctc Tacton», Intnatonal vw on Mollng an Smlaton (IEMOS) Volum 3, N. 6, Dcmb, [6] S. TOUNSI t. NEJI: Dgn of an xal Flux Buhl DC Moto wth Concntat Wnng fo Elctc Vhcl, Jounal of Elctcal Engnng (JEE), Volum, - Eton:, [7] S. TOUNSI,. NEJI, an F. SELLMI: Dgn Mthoology of Pmannt Magnt Moto Imovng Pfomanc of Elctc Vhcl, Intnatonal Jounal of Mollng an Smulaton (IJMS), Volum 9, N, 9. [8]. Moalla, S. TOUNSI t. Nj: Dtmnaton of axal flux moto lctc aamt by th analytc-fnt lmnt mtho, n Intnatonal Confnc on Elctcal Sytm Dgn & Tchnolog (ICEEDT 7), 4-6 Novmb, Hammamt, TUNISI. [9] N. Mlloul, S. TOUNSI t. Nj: Mollng by th fnt lmnt mtho of a col oto ynchonou moto quvalnt to a mannt magnt axal flux moto, n Intnatonal Confnc on Elctcal Sytm Dgn & Tchnolog (ICEEDT 7), 4-6 Novmb, Hammamt, TUNISI.

Applications of Lagrange Equations

Applications of Lagrange Equations Applcaton of agang Euaton Ca Stuy : Elctc Ccut ng th agang uaton of oton, vlop th athatcal ol fo th ccut hown n Fgu.Sulat th ult by SIMI. Th ccuty paat a: 0.0 H, 0.00 H, 0.00 H, C 0.0 F, C 0. F, 0 Ω, Ω