Comparative Study between the Synchronous Motor to Permanent Magnets and Axial Flux (MSAP) and its Equivalent to Coiled Rotor (MSRB)

Transcription

1 Intrnational Journal of Elctrical Componnts and Enrgy Convrsion 2015; 1(3: Publishd onlin MM DD, 2015 ( doi: /j.ijcc Comparativ Study btwn th Synchronous Motor to Prmannt Magnts and Axial Flux (MSAP and its Equivalnt to Coild Rotor (MSRB Souhir Tounsi National School of Elctronics and Tlcommunications of Sfax, SETIT-Rsarch Unit, Sfax Univrsity, Sfax, Tunisia addrss: To cit this articl: Souhir Tounsi. Comparativ Study btwn th Synchronous Motor to Prmannt Magnts and Axial Flux (MSAP and its Equivalnt to Coild Rotor (MSRB. Intrnational Journal of Elctrical Componnts and Enrgy Convrsion. Vol. 1, No. 3, 2015, pp doi: /j.ijcc Abstract: This work consists in conciving of a coild rotor synchronous motor quivalnt to a prmannt magnt axial-flux motor for lctric vhicl by th jo mthod analytical / finit lmnts. An analytical modl sizing motor is dvlopd by th finit lmnt mthod. A comparison btwn a 4 pairs of pols 6 tth structur of a prmannt magnt axial-flux motor and th studid motor is mad in th goal to slct th most ffctiv structur for th sam strngth and sam lctric constant. Kywords: Dsign, Elctric Motor, Finit Elmnt, Slction, Modularity 1. Introduction This papr prsnt a dsign mthodology of a synchronous motor structur to coild rotor (MSRB quivalnt to th motor with prmannt magnts and axial flux (MSAP studid in [1], [2] and [3], by th finit lmnt mthod using th softwar MAXWELL 2D. Th gait followd during th dsign of this motor is similar to th on stablishd for th MSAP [1], [2] and [3]. Indd th whol basis calculation maks itslf for th MSAP thn w study hlp in th softwar MAXWELL 2D th rotor paramtrs alrady concivd whil rplacing vry magnt by a coil prmitting to com closr to th maximum of th rsults gottn for th MSAP in ordr to assur th quivalnc of two structur. Th scond cofficint (α is th ratio of th main tooth avrag angular width by th avrag angular width of a magnt. It adjusts th main tooth siz and has a strong influnc on th lctromotiv forc wavform. Hr, it is fixd at on. Th last cofficint fixs th insrtd tooth siz. It s th ratio of th main tooth avrag width by an insrtd tooth avrag width. Th advantag of ths cofficints is to dfin quickly machin shap. Howvr, thy ar basd on th avrag radius and it is ncssary to comput and chck highr and lowr angls tth in ordr to avoid any rsction. Th MSAP and MSRB quivalnts structurs ar illustratd by figur 1: 2. Gomtric Paramtrs of th Motor 2.1. Motor Structur Th gomtric paramtrs of th MSRB ar alrady calculatd from thos calculatd for th MSAP [1], [2] and [3]. Th MSAP machin is built with th sam radius for th stator and th rotor. Th slots dirctd towards th motor s cntr. Th magnts shap is th sam than th main tth. Thr dsign ratios dfin th motor's structur. Th first cofficint is th ratio β of th magnt avrag angular width by th pol pitch (L=π/p. It adjusts th magnt width in vrsus th pols numbr chosn. Figur 1. MSAP and MSRB quivalnts structurs.

2 70 Souhir Tounsi: Comparativ Study btwn th Synchronous Motor to Prmannt Magnts and Axial Flux (MSAP and its Equivalnt to Coild Rotor (MSRB 2.2. Gomtric Paramtrs of th Stator Th gomtric paramtrs of th MSRB stator rmain unaltrd sinc w kpt th on of th MSAP. Th figur 2 prsnts th diffrnt gomtric paramtrs of th stator: Figur 4. Diffrnt gomtric paramtrs of th rotor. 3. Analytical Computation Figur 2. Gomtric paramtrs of th MSRB stator Gomtric Paramtrs of th Rotor Th rotor of th MSRB is gottn whil rplacing vry magnt by a vry dtrmind winding so that it is quivalnt to th rotor of th MSAP (figur Modularity For applications to lvatd currnt, w collcts svral floors on th motor axis to rduc th rotor flux and thraftr w rmdy to th distortion of th stator flux and consquntly back lctromotiv forc Flux and Back Elctromotiv Forc By analogy with th analytic calculation mad for th MSAP [1-3], back lctromotiv forc capturd by th winding coms from th drivativ of th flux, it s ncssary to b thrfor capabl to xprss th flux according to th position of th magnts. As th shows in th figur 5, th magntic induction is supposd prfctly rctangular to th lvl of th air-gap. Th lakags btwn th air-gap and th stator ar disrgardd. With ths hypothss, th flux capturd by a coil can xprssd as follow: Figur 3. Rplacmnt of th magnts of th MSAP by a winding for th MSRB. This quivalnc is assurd by: - Consrvation of th rotor yok thicknss calculatd for th MSAP. So Hcr dosn't chang. - Th middl width of a rotor slot is as: A ncmr = γ L (1 With La is th middl width of th magnt and γ is a cofficint adjustd by finit lmnt simulations with th hlp of th softwar Maxwll 2D and can b optimizd. - Th hight of a rotor tooth Hdr prmitting to rsrv th ncssary spac for th coppr: H a n I s dr = (2 δ Lncr Whr ns is th numbr of spir of th rotor coil, I is th currnt of xcitation and δ is th admissibl currnt dnsity in th coppr. Th figur 4 prsnts th diffrnt gomtric paramtrs of th rotor. b B ( θds (3 Sbobin Tooth sction φ = Th figur 5- (b rprsnts th distribution of th vctor induction to th lvl of th air-gap for th functioning at no load of th two typs of motor. Th lvl of induction is idntical for th two cass and rachs th valu calculatd analytically. For th MSRB, th xcitation currnt is qual to 7A driving to th quivalnc of th MSRB and MSAP. From an initial position illustratd by figur 5-(a, rotor movs with angular vlocity (Ω = dθ/dt. Four distinct rvals appar according to magnts positions and gomtrical paramtrs valus dfind prviously. Tabl 1 illustrats ths diffrnt rvals as wll as flux variation for ach position. In th zon a th flux is constant bcaus magnt and tooth lngth ar diffrnt. If α is qual to 1, zon a disappars. In th zon b, th flux dcrass bcaus a part of th magnt is not in front of th tooth. In th zon c, a magnt of an opposit polarity ovrlaps also th main tooth. Consquntly, th flux varis 2 tims mor quickly. Finally, th zon d is idntical to th zon b. Ths two zons xist only if th cofficint β is lss than 1.

3 Intrnational Journal of Elctrical Componnts and Enrgy Convrsion 2015; 1(3: Figur 5. Initial position and induction in th air-gap. Th global phas back lctromotiv forc is wll proportional to th angular spd, to th numbr of spirs by phas Nsph and to th drivativ of th flux in rlation to th mchanical angl. It s givn by th following quation [4-12]: width of th landing of th f.c..m. largst possibl [4-12]. dφ E N d θ b = sph Ω (4 Th figur 6 prsnts th volution of th flux and th lctromotiv forc (f.c..m. on on lctric priod. W not that strongst variation of flux happns in th zon c. In practic th zons b' and 'd ar gnrally wak and ar smoothd by th flux lakags. hav a trapzoidal shap or sinusoidal of th f.c..m., is it ncssary to fix th appropriatd valus of β and α. For xampl, for a BDC machin (Brushlss DC motor, it is ncssary that β and α ar nar of th unit in ordr to hav th Tabl 1. Flux and lctromotiv forc in function of motor paramtrs. Figur 6. Flux and lctromotiv forc in function of lctric angl. Zon Position (rad Flux ϕ b (Wb Emf (V a πβ πβ ( 1 α θ ( 1 α π 0 β α B 2p 2p 8 p b πβ π β ( 1 α θ 1 ( 1+ α πβ 2p p 2 ( 1 +α θ B NsphΩ m B 8 2p 8 c π β πβ 1 ( 1+ α θ ( 1+ α π p 2 ( 2 θ B 2N Ω B 2p 8 p 8 d πβ π β ( 1+ α θ 1 ( 1 α π πβ 2p p 2 ( 1+ α θ B 8 p 2p N sphω m B 8 sph m So all calculation maks for th MSAP rmains valid whil rplacing B by th following xprssion for th MSRB:

4 72 Souhir Tounsi: Comparativ Study btwn th Synchronous Motor to Prmannt Magnts and Axial Flux (MSAP and its Equivalnt to Coild Rotor (MSRB B 3.3. Elctromagntic Torqu µ ni 0 = (5 Th instantanous lctromagntic powr dvlopd by th motor P(t is xprssd by th following quation: P t = t i t (6 m ( ( ( i i i = 1 Whr i(t and i(t ar rspctivly back th lctromotiv forc and th currnt of th i phas according to th tim. For a powring with rctangular currnts in phas with th lctromotiv forc, th instantanous powr is qual to its middl valu P: Figur 7. Schma of th motor whil spcifying th cut plan. P=2EI (7 Whr E and I ar rspctivly th maximal valu of lctromotiv forc and th maximal valu of th currnt. Th lctromagntic torqu dvlopd by th motor is givn by th following xprssion: EI C = 2 (8 Ω Th landing of th f.c..m. dducts from th analytic modl is givn by th following rlation: ( D D i E= 2Nsph Ω µ 0nI (9 8 Whr Nsph is th numbr of spirs by phas, D and Di ar rspctivly th rnal and rnal diamtr of th motor and I is th currnt of xcitation. From th 9 quations and 10, w dduct th xprssion of th torqu: ( D D i C = Nsph Iµ 0nI (10 4 Whil noting by K th lctric constant of th motor ( D D dfind by ( i N torqu bcoms: sph 0 2 µ ni, th xprssion of th Figur 8. 2D modl of th motor D Finit Elmnt Modling Th finit lmnt modling of th MSRB rquirs as th MSAP a gomtric rprsntation of th motor so long as of th msh, this last must b thinnr in th air-gap bcaus th calculation ssntially taks plac in this zon and in ordr to hav a good prcision of th rsults and a rducd tim of th simulation (Figur 9 [8-12]. Figur 9. Gomtric rprsntation of th motor providd with th msh Comparison of th Simulation Rsults Trapzoidal Cas Figur 10 illustrats th flux at load of MSAP and MSRB. 4. Finit Elmnt Modlling C=KI ( Study in Cylindrical Cut Plan of th MSRB Th motor is studid on a cylindrical cut plan. Th plan of cut maks itslf according to th middl diamtr of th motor (Figur 7, Whn w sprads th cylindrical cut plan, w gts th modl 2 D of th motor (Figur 8 [4-12]. Figur 10. Flux at load of MSAP (AP and MSRB (RB. Figur 11 illustrats th Back lctromotiv forc at load of MSAP and MSRB.

5 Intrnational Journal of Elctrical Componnts and Enrgy Convrsion 2015; 1(3: Figur 15 illustrats th torqu at load of MSAP and MSRB. Figur 11. Back lctromotiv forc at load of MSAP (AP and MSRB (RB. Figur 12 illustrats th torqu at load of MSAP and MSRB. Figur 15. Torqu at load of MSAP (AP and MSRB (RB. W not in th sam that th curvs of th flux, th back lctromotiv forc and th torqu gottn in th sinusoidal cas at load for th MSRB ar nar of thos gottn for th MSAP [8-12]. 5. Slction of th Most Effctiv Structur Figur 12. Torqu at load of MSAP (AP and MSRB (RB. W nots that th curvs of th flux, th back lctromotiv forc and th torqu gottn in th trapzoidal cas at load for th MSRB ar nar of thos gottn for th MSAP Sinusoidal Cas Figur 13 illustrats th flux at load of MSAP and MSRB. Figur 13. Flux at load of MSAP (AP and MSRB (RB. Figur 14 illustrats th Back lctromotiv forc at load of MSAP and MSRB. Th critria s of slction ar: th fficincy, th cost and th powr to wight ratio. Th following tabl prsnts th diffrnt valus gottn for th MSAP and th MSRB. Tabl 2. Th diffrnt valus gottn for th MSAP and th MSRB. MSAP MSRB Efficincy_trap 97,793 % 98 % Powr to wight ratio _trap 58,3345 (W/Kg 55,311 (W/Kg Cost_trap 2459 $ 2117 $ Efficincy_sin 87,970 % 92 % Powr to wight ratio _sin 78,541 (W/Kg 56,077 (W/Kg Cost_sin 1518,3 $ 1279 $ According to th gottn rsults, w nots that th MSRB is lss xpnsiv than th MSAP, in mor it prsnts fficincy slightly suprior to th on gottn for th MSAP. On th othr hand th MSRB prsnts a powr to wight ratio lowr to th on of th MSAP. Thus, th MSRB can b th most ffctiv structur if th usr is contnt with its wll dvlopd powr to wight ratio. 6. Conclusion Figur 14. Back lctromotiv forc at load of MSAP (AP and MSRB (RB. Th comparison btwn th two motors allowd us to conclud that th MSRB concivd prsnt thus a wakr cost than th on of th MSAP; W got a rduction ncouraging of th pric qual to 300 $. Bsids, th MSAP has fficincy and a powr to wight ratio lvatd. Thus, with ths promising proprtis, th MSRB concivd can b an attractiv solution in th world of th lctric vhicls sinc it's spcially to wak cost in rlation to it's quivalnc to th MSAP.

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