THREE DIMENSIONAL MAGNETOSTATIC ANALYSIS OF A 3-PHASE, 12/8 POLE 250 W SWITCHED RELUCTANCE MOTOR USED IN A WASHING MACHINE DRIVE

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1 THREE DIMENSIONAL MAGNETOSTATIC ANALYSIS OF A 3-PHASE, /8 POLE 50 W SWITCHED RELUCTANCE MOTOR USED IN A WASHING MACHINE DRIVE Ahmet FENERCİOĞLU Ünl KURT Gziosmnpş University, Turhl Higher Voctionl School, Turhl,Tokt, Turkey, f@gop.edu.tr Amsy University, Amsy Higher Voctionl School, 0589 Amsy, Turkey, ukurt@omu.edu.tr Key Words: SRM design, finite element nlysis, SRM mgnetic nlysis. ABSTRACT In this study, physicl sizes nd geometry of 3-phse, /8 pole, 50 wtts switched reluctnce motor (SRM) which is used in wshing mchine drive hve been determined nd its one-to-one model hs been developed. The model obtined hs been nlyzed through the 3 D mgnetosttic nlysis method nd 3 D finite elements method. As result of the nlyze, phse inductnce, torque ripple, verge nd instnt torque, ir gp power nd mgnetic flux pttern vlues hve been obtined. Besides, nlyticl pproch vlues for these mgnitudes hve been clculted nd simulted. The fct tht the results of the nlyticl pproches nd simultion results re close to the rel size vlues proved tht the pplied simultion method ws correct. I. INTRODUCTION The theory of motor with vrible reluctnce hs been strted to be used since 980 s for the vrible or djusted speed ppliction nd the use of these motors strted to be very populr in engineering pplictions. The dvntges brought by the chep nd powerful switching elements enbled the re-discovery of this motor. SRM is very simple in structure. However its control is complex. For instnce, the process of excittion of the phse windings in pproprite order for torque genertion requires the provision of the position informtion of the rotor. Besides, SRM s hve been enbled to compete with the other DA nd AA motors by the possibility of obtining low cost microprocessor nd power electronic elements [, ]. II. MATERIAL AND METHOD In this study, mgnetosttic nlysis of three-phse, /8 SRM used in the wshing mchine drive through the computer ided three dimensionl finite elements method by determining its rel sizes nd geometry. As result of the simultions, inductnce, torque nd power vlues hve been estimted nd compred with the nlytic results [ 3]. The vlues of physicl chnges of SRM with /8 pole [4] re seen the Tble. The rel picture, simultor cross section nd size vribles nd vlues [4] re given in Figure. Tble. Sizes of the SR Motor studied Symbol Mening nd Unit Vlue R so Sttor outer dimeter (m) 0,06975 R si Sttor inner dimeter (m) 0,0575 R ro Rotor outer dimeter (m) 0,0444 R ri Rotor outer dimeter (m) 0,03050 R sf Shft dimeter (m) 0,0084 l y Sttor yoke (m) 0,050 l g Air gp (m) 0,00046 L stk Stck length (m) 0,04630 β s Sttor pole ngle (rd) 0,66 β r Rotor pole string ngle (rd) 0,704 n s Sttor pole number n r Rotor pole number 8 q Number of phse 3 N Number of winding for pole 00

2 (). In Figure the equivlent vlue for one phse of SRM is shown [3,5]. Figure. Equivlent circuit for one phse of SRM It is expressed s follows: () V dψ ( θ, di' = Ri + M ( () Here the V is the supply voltge, R is the winding resistnce, ψ is the mgnetic flux, i is the phse winding current, M(θ) is the mutul inductnce, θ is the rotor position ngle, i is the winding current excited before the relevnt phse. When sturtion is neglected mgnetic flux is ψ = L(θ, nd there for Eq. () is re rrnged s follows: V dl( di' = Ri + M ( () Here L(θ, shows the phse inductnce. When the differentil expression in Eq. () is divided into pieces, it becomes s follows by neglecting the mutul inductnce; di dl( V = Ri + L( + i (3) When the mutul inductnce vlue is neglected it becomes s Eq. (3) nd Eq. (4) [3,5]. dl ( θ, dl( θ, = ω (4) dt dθ Here we obtin: di di di dl( = ω, V = Ri + L( ω + i ω (5) dt dθ dθ dθ Figure. Model of the /8 SR Motor which is studied. ) Simultor model, b) Rel model c) Size vribles. (c) EQUIVALENT CIRCUIT OF SRM Motor phse inductnce in SRMs vries ccording to rotor position nd the current pssing through the winding. Generl circuit eqution of SRM is given in Eq. Here ω is the ngulr velocity. [3,5] In order to find the phse inductnce in the intermediry rotor positions of SRM, cosine correltions re given in Eq. 6 s Fourier Series by using the mximum nd minimum inductnce vlues. m L( θ, = L ( cos( (6) k= 0 k kn R

3 Here L indictes the phse inductnce (H), θ indictes the rotor position in degrees, n indictes the pole r number. ARM hs low energy rtio. To express this, n energy conversion cycle hs been clculted mgneticlly. SRM is liner model in the first hrmonic of the Fourier Series of the inductnce ccording to the SRM rotor position. Here the inductnce vlue is given in Eq. 7, flux linkge is given in Eq. 8 [3, 6]. L θ, = [( cos( n )] (7) ( 0 Rθ λ θ, i ) = [( cos( n )] R i (8) ( 0 θ Here λ is the flux linkge (wb), i is the phse current. The 0 nd coefficients in Eq. 3 cn be obtined from Eq. 9 [5]. 0 = ( L + Lu ), = ( L u ) L (9) Here n R is the number of rotor, for one phse, L is the mximum inductnce, L u is the minimum inductnce. In the ppliction, this motor is not run in the unligned position. The opertion re of the motor is between the overlp position nd the ligned position of the rotor nd sttor pole. After this position the sme region is vlid for the nd phse nd the excittion is cut nd the nd phse is excited when the st phse overlps. Here β s is the ngle of sttor pole ngle in degrees III. RESULTS AND DISCUSSION Mgnetic devices re trditionlly designed by combining the simplified circuit models nd rules bsed on experimentl evidence. However, since the devices re incresingly vrint nd complex nd the rules re not sufficient, electromgnetic field problems hve been strted to be solved ccording to the nlysis nd design bsed on logicl, detiled solution [,3]. Phse inductnces nd instntneous torque vlues of the SRM model developed re estimted ccording to the position chnge for ech.5 degree of the rotor fter the mgnetosttic nlysis is mde with the 3-dimensionl simultor. Besides these results re lso obtined nlyticlly nd compred in the grphic in Figure 3. Here the rotor position is given between 0-45º. 0º-,5º indictes the genertor opertion region nd,5º-45º indictes the motor opertion region. In both res, the concerned phse is not operted between 5º-30º which is the unligned region. In this region other phse is excited. When the lign of the sttor pole of the phse with the rotor pole finishes, the excittion of tht phse is stopped nd the energy is supplied to the other phse. Tht is, when the rotor pole strts overlpping with the sttor, phse excittion is strted. When there is current pss phse, the torque tends to rotte the rotor in direction to increse the inductnce. The direction of the torque is lwys towrds the closest overlpping position. Therefore positive torque (for instnce motor opertion torque) cn be generted only if the rotor is between the non-overlpping forwrd position nd the next overlpping position. The most generl expression of the instntneous torque cused by phse in ech rotor position is given in Eq. 0 [3,4,6,7]. i W ' T = i di = λ( θ, ) θ θ 0 i= sbit (0) Here T is the instntneous torque (Nm), W is the coenergy (J). Since the instntneous torque chnges ccording to the rotor position, men torque is more pproprite term to express the torque of motor. Considering the liner mgnetic chrcteristic of SRM, men torque or electromgnetic torque is given in Eq.. Figure 3. Chnge of phse inductnce ccording to the rotor position The chrcteristic of the flux linkge between the ligned nd unligned positions is given in Figure 4 () [3,4,7]. dl L Lu = = = L L T e i i i dθ β s β s L u ()

4 () In figure 6, torque ripple of SRM motor is shown. Here, torque ripple cused by the 45º movement of the rotor s result of consecutive triggering of 3 phses. But the speed nd inerti of the rotor hs not been tken into considertion, nd only the sttic conditions re considered. The speed, mss nd inerti of the motor nd the control strtegy of its drive circuit will further reduce the torque ripple [8]. In figure 6, torque ripple is given for the /8 lp of the rotor ccording to the mgnetosttic simultion results. Figure 4. ) Flux Linkge chrcteristics of SRM b) flux distribution of ligned position Figure 4 shows the flux distribution of SRM in ligned position s vectoril nd mgnitude vlues. In the ligned position the locl sturtion in the pole corners is t the minimum levels ccording to the flux distribution. In positions where the rotor pole overlps less with the sttor pole, this sturtion effect is more. The mteril used in the simultor model is the one clled steel 00 nd the BH chrcteristics re given in figure 5. The knee point of this mteril is round.9 T nd sturtion strts fter this vlue. Figure 5. B-H curve of the mteril (steel 00) used s rotor nd sttor core Figure 6. Torque ripple of SRM In this cse, the nlyticlly estimted torque expression nd the vlues obtined by the 3 dimensionl simultors re given in Tble in comprison. Tble. Men torque nd power vlues Solution method Men torque (Nm) Power (W) (for 000 d/d) Motor Power (W) (Lbel Vlue) 50 3B simultor,377 48,78 Anlytic,558 67,78 50 Simultor results in Tble re predicted fter the 3 dimensionl mgnetosttic nlysis. The dynmic operting conditions of the motor, its control strtegy nd the effects of the drive circuit hve not been tken into considertion. Sttor nd rotor hve been tken s whole in the motor design, nd no lmintion hs been mde. Windings hve been drwn s single-coiled nd ech winding hs been excited with 500 mper-tur mmk. It is ssumed tht,5 A flow psses through coil with 00 number of windings. The mgnetic mteril used in the simultion is not the sme with the lminted mteril in the rel motor. BH curve is the mteril clled steel 00 in the 3D FEA simultor softwre librry which is suitble mteril for SRM given in Figure 5. The nlytic results hve been clculted ccording to the equtions given in the mteril nd method section

5 ccording to the liner operting conditions. The torque estimted through simultion nd nlytic method is the electromgnetic torque s it is clculted ccording to the co-energy. Therefore the power vlues estimted in Tble re the ir gp power nd the losses hve been neglected. IV. CONCLUSION It is more difficult to estimte the electricl nd mgnetic chrcteristics of SRM thn the other methods. Becuse, inductnce, power nd energy mounts vry ccording to the rotor position in SRM. SRM doesn t hve the stble condition where ll stte vribles re fixed. The prmeters chnging ccording to the rotor position, locl mgnetic sturtion effects nd vrint mgnetic permebility ffect the chrcteristics of SRM nd therefore the behviour of SRM is ttempted to be incresed through the simultion works rther thn the nlyticl methods. The bsic electricl prmeters of the 3 phse, /8 pole SRM which is exmined in this study hve been predicted by mking mgnetosttic nlysis through the three dimensionl finite elements method s well s the nlytic solutions. The results obtined re the nlytic estimtes, simultion results nd motor lbel vlues nd it is seen tht these vlues re close when compred to ech other. In this cse, the results provided by the study proves the correctness of the simultion method, becuse in order to conclude correct design nd nlysis it is necessry tht the computer bsed simultion methods for everything except bsic sizing clcultions re prt of the design process. In prticulr, it is strongly recommended to use the three dimensionl simultors in mgnetic system design s the mchine geometry cnnot be fully defined in two dimensionl simultors nd effects like coil end-fields, xil flux, fringing flux nd skewing cnnot be tken into ccount [3,9]. REFERENCES. Gürdl, O., Elektrik Mkinlrının Tsrımı, Atls Yyın Dğıtım, İstnbul, 0-40, 00.. Krishnn, R., Switched Reluctnce Motor Drives, CRC Press, Florid, -69, Fenercioğlu, A., Anhtrlmlı Relüktns Motorun (HY-ARM) Tsrımı ve Anlizi, Doktor Tezi, Gzi Üniversitesi Fen Bilimleri Enstitüsü, Ankr Trımer, İ., Redüktörsüz Meknik Sistemler İçin Düşük Devirli Ve Yüksek Torklu Elektrik Motor Tsrımlrı, Doktor Tezi, Gzi Üniversitesi Fen Bilimleri Enstitüsü, Ankr Dursun, M., Sygın, A., Güneş Enerjisi İle Çlışn Bir Sulm Sistemi İçin Boost Konvertörlü Anhtrlmlı Relüktns Motor Sürücüsü, Erciyes Üniversitesi Fen Bilimleri Ens. Dergisi, (-) 57-65, Gürdl,O., Fenercioglu, A., Computer Aided Three Dimensionl Mgnetosttic Anlysis of Heliclly Structured Switched Reluctnce Motor (HS-SRM), Journl of The Fculty of Engineering nd Architecture of Gzi University, Omç, Z., Kürüm, H., Anhtrlmlı Reluktns Motorun TMS30LF407A Syısl Sinyl İşlemcisi ile PWM Akım Kontrolü, Elektrik-Elektronik ve Bilgisyr Mühendisliği Sempozyumu, Burs - 6, Şhin, F., Ertn, H.B., Leblebicioğlu, K., Optimum Geometry for Torque Ripple Minimiztion of Switched Reluctnce Motors, IEEE Trnsctions on Energy Conversion, 5():30-39, Fenercioglu, A., Trımer, "Anhtrlmlı Relüktns Motorlrd Fz Endüktnsın Etki Eden Fktörlerin İncelenmesi", Pmukkle Üniversitesi, Mühendislik Bilimleri Dergisi, 3.cilt,.syı, 007.