Back EMF Design of an AFPM Motor using PCB Winding by Quasi 3D Space Harmonic Analysis Method

Transcription

1 73 Jounl of Electicl Engineeing & Technology Vol. 7, No. 5, pp. 73~735, 1 Bck EMF Design of n AFPM Moto using PCB Winding by Qusi 3D Spce Hmonic Anlysis Method De-Kyu Jng*, Jung-Hwn Chng nd Gun-Hee Jng** Abstct This ppe pesents method to design the wvefom of bck electomotive foce (bck EMF) of n xil flux pemnent mgnet (AFPM) moto using pinted cicuit bod (PCB) windings. When the mgnetiztion distibution of pemnent mgnet (PM) is given, the mgnetic field in the i gp egion is clculted by the qusi thee dimensionl (3D) spce hmonic nlysis (SHA) method. Once the flux density distibution in the winding egion is detemined, the equied shpe of the bck EMF cn be obtined by djusting the winding distibution. This cn be done by modifying the distnce between pttens of PCB to contol the hmonics in the winding distibution. The poposed method is veified by finite element nlysis (FEA) esults nd it shows the usefulness of the method in eliminting specific hmonic component in the bck EMF wvefom of moto. Keywods: Axil flux, Bck electomotive foce, PCB winding, Spce hmonic nlysis 1. Intoduction In the design of pemnent mgnet (PM) moto, the shpe nd mplitude of bck electomotive foce (bck EMF) e impotnt fctos influencing moto pefomnces [1, ]. Pticully, the unwnted hmonic components included in the bck EMF genete toque ipples nd losses in the moto [3]. In conventionl xil flux pemnent mgnet (AFPM) motos, the wvefom of the bck EMF is minly detemined by two fctos, the flux density distibution by PM in the i gp egion nd tooth shpe of stto fo confining the field to the coe. Howeve, in the slotless type moto, thee e no mens fo guiding the mgnetic flux to the winding egion nd it is lso not possible to design the shpe of the bck EMF by chnging the tooth shpe fo given PM flux. This ppe pesents method to design the shpe of the bck EMF wvefom of n AFPM moto using pinted cicuit bod (PCB) windings. Fig. 1 shows the pocedue of the poposed method using the qusi thee dimensionl spce hmonic nlysis (3D SHA) method, which is one of nlyticl techniques to pedict the mgnetic field distibution in the moto [4]. When the mgnetiztion distibution of PM is given, the mgnetic field in the i gp egion is clculted by 3D SHA method. This method is deived by combining the two dimensionl spce hmonic nlysis (D SHA) method nd coection function fo mgnetic flux in dil position by consideing the eduction of mgnetic field ne the inne nd oute Coesponding Autho: Deptment of Electicl Engineeing, Dong Univesity, Busn, Koe. (cjhwn@du.c.k) * Deptment of Electicl Engineeing, Dong Univesity, Busn, Koe. (cjhwn@du.c.k) ** PREM, Deptment of Mechnicl Engineeing, Hnyng Univesity, Seoul, Koe. (ghjng@hnyng.c.k) Received: Jnuy 6, 1; Accepted: Mch 7, 1 dius of AFPM [5, 6]. Once the flux density distibution in the winding egion is clculted, the equied shpe of the bck EMF cn be obtined by djusting the winding distibution. It cn be done by modifying the distnce between pttens of the PCB to contol the hmonics in the winding egion. The poposed method is veified by finite element nlysis (FEA) esults nd it shows the usefulness of the method in eliminting specific hmonic components in the bck EMF wvefom of moto. Fig. 1. Pocedue to design bck EMF wvefom. Pinciple of the Method.1 D nlyticl mgnetic-field solution In ode to obtin mgnetic field distibution poduced by PM, the stto nd oto coe e ssumed to hve infinite pemebility. When cuent is bsent in solution egion, mgnetic field intensity, H cn be epesented using mgnetic scl potentil, ϕ.

2 De-Kyu Jng, Jung-Hwn Chng nd Gun-Hee Jng 731 H = ϕ (1) Fo the AFPM moto, mgnetic field cn be descibed by Lplce s eqution nd Poisson s eqution in pol coodintes s follows. the flux density is pidly decesing ne the inne nd oute dius of the AFPM. This effect cn be consideed by fllowing coection function deived fom the 3D FEA [6]. It shows the nomlized xil flux density distibution ccoding to the dil position of moto s shown in Fig.. 1 ϕ ϕ + = θ z 1 ϕm ϕm M + = θ z µ () (3) 1 i o G( ) = tn tn π (9) β1( o i ) = tn( β π / ) (1) whee the subscipts nd m denote the i gp nd PM egions espectively, is dius t which the mgnetic field is computed, µ is the eltive ecoil pemebility of the mgnet, nd M is mgnetiztion distibution of PM. Since the mgnetic field distibution is n even nd peiodic function long cicumfeentil diection, the solutions of Lplce s eqution nd Poisson s eqution in the i gp nd PM egions e s follows. whee i nd o e the inne nd oute dius of the AFPM moto. β 1 nd β e coection fctos. β 1 is used to define the effective dius nd β is used to djust the dop of the xil flux density ne the inne nd oute dius of the AFPM moto. z z ϕ ( θ ) = C1e + Ce cos( nn pθ ) (5) n= 1,3,5 z z ϕm ( θ ) = C3e + C4e + C5 cos( nn pθ ) (6) n= 1,3,5 whee θ is cicumfeentil ngle in mechnicl mesue nd N p is the numbe of pole pis. Specific solutions to the flux density in the i gp egion e obtined by pplying the customy boundy conditions which specify tht the tngentil component of field intensity nd the noml component of the flux density e continuous coss mteil boundies. 1 ϕ B ( θ ) µ H µ B sin( nn θ ) (7) θ = θ = = θ n= 1,3,5 θ n p ϕ B ( θ ) µ H µ B cos( nn θ ) (8) = = = z n= 1,3,5 n p In ode to conside the finite pemebility nd stution chcteistic of the feomgnetic mteils, fcto, C is intoduced. It is defined by the tio of mgnetic flux densities t the i gp egion in the equivlent mgnetic cicuit with nd without consideing eluctnce of the coe [1]. It is constnt slightly gete thn one nd deceses the mgnetic flux density in the winding egion to compenste fo ssumption of infinite pemebility of the coe in the SHA method.. 3D nlyticl mgnetic-field solution In the D SHA, the flux density is ssumed to hve unifom vlue in the dil diection. Howeve, in elity, Fig.. Axil flux density ccoding to dil position.3 Winding distibution With the infomtion on the flux density in the winding egion, PCB pttens cn be designed to hve ppopite winding distibution tht deceses specific hmonic components in the bck EMF wvefom. Unlike the conventionl winding lyouts such s concentic nd distibuted winding, the winding distibution by PCB cn be djusted by modifying the intevls of ech ptten s shown in Fig. 3. Finlly, the windings distibution is descibed by following the Fouie seies. N (, θ ) = N N( ) N( θ ) (11) knc N( ) = Nm cos( m), N( θ ) = N θ k cos θ m= 1,3,5 k= 1,3,5 (1) whee N is the numbe of tuns, N c is the numbe of coils, nd, N( ) nd N( θ ) e nomlized winding distibution in dil nd cicumfeentil diection, espectively. Unlike N( ) hving constnt ptten distnce, N( θ ) hs vible ptten distnce to contol the shpe of the bck EMF.

3 73 Bck EMF Design of n AFPM Moto using PCB Winding by Qusi 3D Spce Hmonic Anlysis Method kw n nd B n, Fouie coefficient of the xil component of the mgnetic flux density in the winding egion. When the i gp flux density hs hmonic components, it is tue in genel, the bck EMF wvefom hs hmonics even though the winding distibution is ssumed to hve pue sine wve. Thus, ech hmonic component of the bck EMF cn be eliminted only when the winding distibutions stisfy the following condition. kw = N k = ( N k + N k + N k + ) = (19) n θ k kn θ1 1n θ 3 3n θ 5 5n k= 1,3,5 Fig. 3. Winding distibution in dil nd cicumfeentil diection.4 Bck EMF Fom the flux density nd winding distibution, the flux linkge in coil is given s θc o ( ) θ (, ) ( ) ( ) c i (13) λ α = N θ G B θ + α ddθ whee θc nd α e the ngul coil pitch nd the otting ngle of oto in mechnicl mesue, espectively. Substituting (8), (9) nd (11) into (13), the flux linkge expession cn be nged s θc o ( ) = ( ) ( ) ( ) ( ) θ c + i λ α N N G d N θ B θ α dθ whee = N k N k B nn θ cos( α) (14) k kn n p n= 1,3,5 k= 1,3,5 o k = N( ) G( ) d (15) c i θc knc kkn = cos θ cos( nn pθ) dθ θ (16) The ssocited bck EMF is the deivtive of the flux linkge s follows. whee ( ) e( α ) = NN ω k n kw B sin nn α (17) p m n n p n= 1,3,5 kw = N k (18) n θ k kn k= 1,3,5 In (17), it is found tht the mplitude of the n th hmonic component in the bck EMF is detemined by coefficients, When the numbes of pole pis nd coils e detemined, the k kn hs constnt vlues. Theefoe, the kw n cn be zeo by finding the combintions of the hmonic components in the winding distibution bsed on (19)..5 Winding design method In ode to eliminte specific hmonic in the bck EMF, ech hmonic of the winding distibution could be djusted to stisfy (19). Although thee e mny combintions of the hmonics mking kw n to be zeo, the PCB winding could not expess ll of them due to the sptil hmonic distotion. To find fesible solutions stisfying (19), the genel winding distibution hving the sme intevl between the pttens is good stting point in designing PCB pttens In this ppe, two methods e pesented bsed on the given genel winding distibution. The fist method consides one winding hmonic multiplied by the biggest vlue of k kn s design vible. With this selection, we cn eliminte cetin hmonic in bck EMF by the smllest chnge in the genel winding distibution. Fo limited spce nd the numbe of tuns, it is difficult to expess high hmonics in winding distibution. The second method conside the thid winding hmonic, the lowest one, s design vible. Howeve, one moe thing should be conside in this method. If the thid hmonic hs too high vlue to stisfy (19), distotion of the winding distibution would be sevee nd the designed winding could not be implemented by PCB. Thus, in ode to minimize the chnge of the thid winding hmonic, the hmonic of the genel winding distibution multiplied by biggest vlue of k is mde to zeo in the second method. kn 3. Appliction of the method The poposed method is pplied to slotless AFPM moto hving specifictions s shown in Tble. With the xil mgnetiztion by Hlbch y of PM, coil hs 5 lyes nd ech lye hs 8 tuns. In ode to vlidte the poposed method, the wvefoms of the bck EMF nd its hmonic components e comped with FEA s well s SHA esults. In the genel 3D FEA,

4 De-Kyu Jng, Jung-Hwn Chng nd Gun-Hee Jng 733 ech coil is modeled s single tube not distinguishing conductos fo convenience. Howeve, with this method, it is not possible to nlyze the effect of the winding lyout hving diffeent intevl between conductos on the wvefom of the bck EMF. In this ppe, the PCB pttens e modeled by diffeent tubes coesponding to ech tun. Fig. 4 shows the FEA model fo 3D mgnetic field nlysis with commecil softwe, FLUX3D. Fig. 4. Anlysis model of Model II fo FEA method Fo the genel winding, 3 d nd 5 th hmonic components of the bck EMF e geneted s shown in Fig. 5 nd Fig. 6. In the esults of the SHA, the mplitudes Bck EMF (V) D FEA 3-D SHA of the bck-emf hve slightly highe vlue thn those of the FEA. This is due to the lekge flux in the i gp egion nd ptil stution of coe in the FEA nlysis. When input cuent hs pue sinusoidl wve, the 3 d hmonic component of the bck EMF in ech phse does not influence on the toque ipple in blnced thee-phse system. Thus the 3 d hmonic component cn be ignoed in the design of the bck EMF wvefom. In this ppe, the winding pttens e designed to emove the 5 th hmonic of the bck EMF wvefom. Fig. 7 shows the pocedue of the winding design fo Coil I nd Coil II coesponding to ech method pesented in the pevious section. In ode to emove the 5 th hmonic component in the bck EMF, the vlue of kw 5 is mde zeo by consideing up to the 11 th ode of hmonics in the winding distibution bsed on (). 11 kw = N k = ( N k + N k + + N k ) = () 5 θ k k 5 θ1 1,5 θ 3 3,5 θ11 5,11 k= 1,3,5 Tble. Specifictions of n nlysis AFPM moto Symbol Content Vlue Nl numbe of winding lyes 5 N numbe of tuns pe lye 8 B emnence [T] 1. i inne dius of PM [mm] 5. o oute dius of PM [mm] 9.45 lm mgnet length [mm]. g i gp length [mm] Electicl ngle (degee) Fig. 5. Compison of the bck EMF wvefoms fo the genel winding lyout (@ 7, pm) Amplitude (V) Hmonic ode 3-D FEA 3-D SHA Fig. 6. FFT nlysis of the bck EMF wvefoms fo genel winding lyout (@7, pm) Fig. 7. Pocedue of winding design () Fo Coil I (b) Fo Coil II Fo Coil I, it cn be done esily by djusting the 7 th hmonic component, Nθ 7 of the genel winding distibution wvefom, becuse the k 75 hve biggest vlue of the k k 5 s shown in Tble 3. Unlike Coil I, in Coil II, the vlue of 7 th hmonic is mde to be zeo nd then the 3 d hmonic of the winding distibution is chnged to stisfy (). Fig. 8 nd Fig. 9 show the winding distibution nd the winding ptten of genel winding, Coil I nd Coil II.

5 734 Bck EMF Design of n AFPM Moto using PCB Winding by Qusi 3D Spce Hmonic Anlysis Method Tble 3. The vlue of k kn n k Bck EMF (V) D FEA with Genel winding 3-D SHA with Genel winding 3-D FEA with Coil I 3-D SHA with Coil I Numbe of tuns pe lye Genel winding Coil I Coil II Mechnicl ngle (degee) Fig. 8. Winding distibutions pe lye Fig. 9. Winding pttens: () Genel winding; (b) Coil I; (c) Coil II Fig. 1 nd Fig. 11 show the compison of the bck EMF wvefoms in SHA nd FEA fo the Coil I nd Coil II espectively. Fig. 1 compes the tio of the 3 d nd 5 th hmonic components to fundmentl mplitude fo the winding distibution. The 5 th hmonic component fo Coil I nd Coil II educed espectively by 99% nd 99% in SHA, nd 33% nd 8% in FEA s shown in Fig. 1(). Although the 3 d hmonic component does not hve effect on the toque ipple in the blnced thee-phse cse, it is lso decesed in the Coil I nd Coil II by 69% nd 88% in SHA, nd 43% nd 6% in FEA espectively s shown in Fig. 1(b). The diffeence between the SHA nd FEA esults in tht the PCB winding lyout could not ccutely expess the designed winding distibution. Pticully, the 7 th hmonic component of the winding distibution is moe difficult to expess thn the 3 d hmonic. So, the Coil I hs much moe diffeence between the nlyses esults thn the Coil II. If the numbe of tuns pe lye is enough to Electicl ngle (degee) Fig. 1. Compison of bck EMF fo Coil I (@7 pm) Bck EMF (V) D FEA with Genel winding 3-D SHA with Genel winding 3-D FEA with Coil II 3-D SHA with Coil II Electicl ngle (degee) Fig. 11. Compison of bck EMF fo Coil II (@7 pm) Amplitude of 5th hmonic (%) Amplitude of 3th hmonic (%) Genel winding Genel winding 3-D FEA with Coil I 3-D FEA with Coil II 3-D SHA with Coil I & II Winding model () Winding model (b) Designed Winding 3-D FEA with Coil I 3-D FEA with Coil II 3-D SHA with Coil I 3-D SHA with Coil II Designed Winding Fig. 1. Compison of the mplitude of the hmonics: () mplitude of 5 th hmonic; (b) mplitude of 3 d hmonic

6 De-Kyu Jng, Jung-Hwn Chng nd Gun-Hee Jng 735 expess the designed winding distibution, it will be moe effective to eliminte cetin hmonics in the bck EMF. 4. Conclusion This ppe dels with method to contol the wvefom of the bck EMF using PCB windings. Fo the given PM flux in the i gp egion, ppopite winding distibution cn be designed to eliminte specific hmonic components in the bck EMF by consideing the effect of ech hmonic in the winding distibution. The poposed method is veified by FEA esults nd evels tht it cn be used to contol the shpe of the bck EMF fo bette pefomnce of moto. Acknowledgements This wok ws suppoted by gnt fom the Intentionl Coopetion of the Koe Institute of Enegy Technology Evlution nd Plnning (No. 1311), funded by the Ministy of Knowledge Economy, Republic of Koe. Refeences [1] D. Dune Hnselmn, Bushless Pemnent Mgnet Moto Design, nd ed., The Wites s Collective, 3, pp , [] M. Mkovic nd Y. Peid, Simplified Design Methodology fo Slotless Bushless DC Moto, IEEE Tns. Mgn., vol 4, no 1, 6, pp [3] A.J.A. Vndenput nd J. C. Compte, Design nd development of high-speed xil flux pemnentmgnet mchine, Fund Shin, 1, pp [4] Z. Q. Zhu, D. Howe nd C. C. Chn, Impoved nlyticl model fo pedicting the mgnetic field distibution in bushless pemnent mgnet mchines, IEEE Tns. Mgn., vol. 38, no. 1, pp.9-38, Jn.. [5] T. F. Chn, Field computtion fo n Axil Flux pemnent-mgnet Synchonous Geneto, IEEE Tns. Mgn., vol 4, no 1, 9, pp [6] J. Azzouzi, G. Bkt nd B. Dkyo, Qusi-3D Anlyticl Modeling of the Mgnetic Field of n Axil Flux Pemnent Mgnets Synchonous Mchine, IEEE Tns. Mgn., vol. no. 4, 5, pp De-Kyu Jng He eceived B.S. degee in electicl engineeing fom Dong-A Univesity, Busn, Rep. of Koe in 11. Since 11, he hs been studying fo M.S. degee in electicl engineeing fom Dong-A Univesity. His esech inteests e design nd nlysis of electo-mechnicl systems including diving cicuits. Jung-Hwn Chng He eceived B.S. nd M.S. degees in electicl engineeing nd Ph.D. degee in pecision mechnicl engineeing fom Hnyng Univesity, Seoul, Rep. of Koe in 1994, 1997 nd 1, espectively. Fom 1 to, he woked t Institute of Bin Koe 1 t Hnyng Univesity, whee he developed mico dive nd high-speed spindle moto. Fom to 3, he woked s esech fellow t Univesity of Clifoni t Bekeley with the suppot of Koe Science nd Engineeing Foundtion, nd nlyzed nd developed electiclly contolled engine vlve system. Fom 3 to 9, he woked in Koe Electotechnology Resech Institute (KERI) s senio eseche, nd engged in the developments of specil pupose mchines. Since 9, he hs been with the deptment of electicl engineeing, Dong-A Univesity, Busn Rep. of Koe, s ssistnt pofesso. His inteests e the design nd nlysis of electo-mechnicl systems including diving cicuits. Gun-Hee Jng He eceived Ph. D. degee in Mechnicl Engineeing fom Univesity of Clifoni, Bekeley. His esech inteests e Vibtion Anlysis of Rotting System, Anlysis of Hydodynmic Being nd Anlysis of Electomechnicl Coupled Field in BLDC Moto.