DESIGN OF FERRITE MAGNET CFSM TO IMPROVE SPEED RESPONSE OF EPS SYSTEM

Interntionl Journl of Automotive Technology, Vol. 18, No. 3, pp. 499 504 (2017) DOI 10.1007/s12239 017 0049 x Copyright 2017 KSAE/ 096 13 pissn 1229 9138/ eissn 1976 3832 DESIGN OF FERRITE MAGNET CFSM TO IMPROVE SPEED RESPONSE OF EPS SYSTEM Myung-Seop Lim, Dong-Min Kim nd Jung-Pyo Hong * Automotive Engineering, Hngyng University, Seoul 04763, Kore (Received 3 Mrch 2016; Revised 9 November 2016; Accepted 16 November 2016) ABSTRACT This pper dels with the speed response chrcteristic of the concentrted flux synchronous motor (CFSM) using ferrite mgnets for the electric power steering (EPS) system. To nlyze the response chrcteristic of the CFSM, n nlyticl method using the electromechnicl undmped nturl frequency nd dmping rtio bsed on the trnsfer function is proposed. By using the method, the speed response ccording to the vritions of the shpe of the permnent mgnets (PMs) nd rotor core is nlyzed. It ws nlyzed under the conditions of the constnt volume of the PMs s well s the constnt dimeter of the rotor. By using the proposed nlysis method, the improved model is desgined bsed on the initil model fulfilling the required specifictions. Finlly, the torque nd speed response chrcteristics of two motors re simulted through the finite element nlysis (FEA) nd MATLAB Simulink. KEY WORDS : Concentrted Flux Synchronous Motor (CFSM), Dmping rtio, Electric Power Steering (EPS), Electromechnicl undmped nturl frequency, Ferrite mgnet, Speed response chrcteristic, Mss moment of inerti 1. INTRODUCTION Environmentl regultions nd lrge demnds on convenience for drivers ccelerte electrifiction in the vehicle industry. As electrifiction of vehicles hs been progressed, the hydrulic power steering (HPS) systems replced by the electric power steering (EPS) systems. EPS offers severl dvntges over conventionl HPS, such s improved fuel economy nd elimintion of hydrulic fluid (Lee et l., 2014; Jng et l., 2015). As motor for EPS, the permnent mgnet synchronous motor (PMSM) hs been dopted due to its high power density nd efficiency. Prticulrly, rre-erth-free synchronous motor such s ferrite mgnet concentrted flux synchronous motors (CFSMs) is developed s the EPS motors becuse the price instbility of the rre-erth permnent mgnets (PMs). However, the power density of the ferrite mgnet CFSMs is reltively smller thn those of the rre-erth PMSMs. Therefore, the dimeter of the rotor nd sttor should be incresed to chieve the sme performnce of the rre-erth PMSMs. However, the size of the PM nd rotor configurtion hve significntly ffect on the speed response of the EPS system. The speed response chrcteristic of the EPS motors ffects the steering sfety nd drivbility of the drivers. Thus, it is necessry to investigte the speed response chrcteristic of the ferrite mgnet EPS motor. There re some prior works bout the system response or *Corresponding uthor. e-mil: hongjp@hnyng.c.kr control methods of the EPS system from the view point of the controller designers (Chen et l., 2008; Wng et l., 2009; Shriwstv nd Digvne, 2011; Lee et l., 2011, 2012). Some previous ppers only discuss the design method of the EPS motor to reduce cogging torque or torque ripple even though the speed response chrcteristics re very importnt in the EPS system (Kim et l., 2014; Sh et l., 2015; Kim et l., 2010; Ombch nd Junk, 2007). However, there re few prior reserches on the design methods of the EPS motor to chieve fst speed response from the view point of the electric mchine designer. Hence, this pper dels with the nlyticl method to design the ferrite mgnet CFSM to chieve the fst speed response. At first, the nlytic methods to find the CFSM prmeters re presented. Secondly, the method to nlyze the speed response chrcteristic of the motor bsed on the mthemticl model is proposed. Thirdly, bsed on the nlysis results obtined by using the proposed method, the shpe of the PM nd rotor configurtion of the initil model re chnged to propose the improved model. For the improved design, the rotor outer dimeter nd the volume of the ech PM is mintined. Finlly, the torque performnces nd the speed response chrcteristics of the initil model nd improved model re presented nd compred by using finite element nlysis (FEA) nd Mtlb Simulink. 2. CALCULATION OF MOTOR PARAMETERS The motor prmeters which re needed to investigte the 499

500 Myung-Seop Lim, Dong-Min Kim nd Jung-Pyo Hong L q = 3 π -- μ ---------------- 0DL stk k --------- wn 2 g P n where μ 0 nd μ r re the permebility of free spce nd the reltive permebility of core in H/m, respectively. D is the rotor outer dimeter in mm. L stk is the stck length of the sttor, nd g is the ir-gp length. k w is the winding fctor, nd P n is the number of pole-pir. t m nd h m re the thickness nd height of the PM in mm, respectively. (3) Figure 1. Geometry define of the CFSM used in the nlyticl pproch: () Front view of the CFSM for one pole; (b) Top vew of the sttor tooth nd coil. Tble 1. Densities of mterils used in the motor. Items Mgnet Core Shft Density (kg/m 3 ) 5000 7850 2712 speed response chrcteristic were obtined by the nlyticl pproches. Therefore, the mthemticl models to find the prmeters re orgnized in this pper. The prmeters re phse resistnce, inductnce, bck electromotive force (BEMF), nd mss moment of inerti of the rotor. The geometry of the 14 pole-18 slot CFSM used in this study is shown in Figure 1. 2.1. Resistnce The phse resistnce in the rmture is dependent on the length of the coil, the cross-sectionl re of the conductor, nd the operting temperture. The 14 pole-18 slot CFSM hs the concentrted winding in the sttor, nd the spce fctor of the slot is 43 %. The operting temperture of the coil in the EPS motor is ssumed s 60 o C. l R = --------------- coil ( = 4 + 2b + 2l c)n ------------------------------------ σs copper σs copper where l coil is the length of the coil, nd σ is the conductivity of the conductor. S copper is cross-sectionl re of the conductor, nd N is the coil turn number. 2.2. Inductnce The d, q-xis inductnces re clculted by considering the PM shpe s well s the configurtion of the rotor (Hendershot nd Miller, 2010). Slot lekge nd hrmonic inductnces re neglected. d-xis inductnce L d is L d = 3 π -- ----------------- μ 0DL k -- 4 stk --------- wn 2 π 1 g P n ------------------------------- π gμ -- 4P r n -------- h m + ---- 2 D nd, q-xis inductnce L q is t m (1) (2) 2.3. Bck Electromotive Force The ir-gp flux density B gm is obtined through the Guss lw nd Ampere s lw. Eqution (4) is derived s the result. In this process, the sturtion of the core nd irreversible demgnetiztion of the PM re not considered. B rem B gm = ------------------------------- (4) πd 2μ ----------- rec g + ------------- 4ph m t m where B rem is the residul induction in T. p nd μ rec re pole number nd the recoil permebility of PM, respectively. Bsed on (4), the BEMF E of the CFSM is clculted by considering the winding fctor, turn number, stck length, nd geometric dimensions. The derived eqution is shown in (5). E = ωψ m = ω --- 4 k -------- wn DL stk ----------- B gm π 2 p where ω is the electricl ngulr speed in rd/s, nd Ψ m is the linkge flux in Wb. 2.4. Mss Moment of Inerti For the CFSM in this study, electricl steel S60 is used s the core mteril, nd NMF-12G ferrite mgnet is used. For the shft mteril, luminum, non-mgnetic mteril, is used to void lekge of flux. The densities of the mterils re orgnized in Tble 1. The mss moment of inerti of the rotor J cn be clculted from the definition of the mss moment of inerti nd the prllel-xis theorem. J = J core + J PM J core = r i 2dm i m core 2 J PM = p r j dm j + m PM d 2 m PM where m i,j is the mss of ech smll prticles in the rotor core nd PM. r i,j is the distnce between ech smll prticles nd the center of mss in the rotor core nd PM. m core nd m PM re the entire mss of the rotor core nd PM, respectively. d is the distnce between the center of PM mss nd the center of rottion. 3. SPEED RESPONSE CHARACTERISTIC The proposed method to nlyze the speed response (5) (6)

DESIGN OF FERRITE MAGNET CFSM TO IMPROVE SPEED RESPONSE OF EPS SYSTEM 501 chrcteristic is bsed on the mthemticl model of n electric motor. For the method, the trnsfer function of the mchine ws deduced, nd the two objective functions representing for the speed response chrcteristic were derived. Finlly, the vlues of the design prmeters were determined bsed on the derived objective functions. 3.1. Motor Model in Lplce Domin To nlyze the speed response chrcteristic of electric motors, mthemticl model ws used. The motors cn be expressed simply by using both electricl nd mechnicl equtions. They re voltge eqution nd torque eqution, respectively. The voltge eqution of the electric motor is di V = R i + L ----- + E dt di = R i + L ----- + k E φ f ω m dt where V nd i re the rmture voltge nd current; R nd L re the rmture coil resistnce nd the phse inductnce; L is the verge vlue of the L d nd L q obtined from (2) nd (3). E is BEMF in rms. k E nd φ f re the BEMF constnt nd field flux. ω m is the mechnicl speeds in rd/s. The torque eqution is (7) Figure 2. Block digrm of the electric motor trnsfer function. Figure 3. Tendency of the speed response chrcteristics ccording to the PM shpes in the CFSM. T e = J dω m --------- + Bω m + T L dt (8) = k T φ f i where J nd B re the mss moment of inerti nd friction coefficient; T e nd k t re the electric torque nd torque constnt. ω m nd T L re the mechnicl speeds in rd/s nd lod torque. In this study, it ws ssumed tht lod torque T L is zero, nd it cn be neglected in the follow equtions. Lplce trnsformtion of (7) nd (8) ws conducted to find the trnsfer function of the mchine in Lplce domin. As the results, the voltge eqution is V () s = ( R + sl )i () s + E () s (9) = ( R + sl )i () s + k E φ f ω m () s nd the torque eqution is T e () s = ( sj+ B)ω m () s (10) = k T φ f i () s Bsed on the (9) nd (10), block digrm nd trnsfer function cn be deducted. 3.2. Trnsfer Function The block digrm of n electric motor is shown in Figure 2. From the digrm, the trnsfer function in Lplce domin cn be obtined. ω ------ m = V ---------------- 1 1 k T φ f ------------ sl + R sj+ B ----------------------------------------------------------------------- 1 1 1+ ---------------- k T φ f ------------ k sl + R sj+ B E φ f (11) Figure 4. Proposed models: () Initil model; (b) Improved model. Eqution (11) cn be orgnized by 2nd order stndrd form s below. ω ------ m = V where ------ K JL ------------------------------------------------------------------- R s 2 ----- B + -- R s ----- B L J L -- K 2 + + + -------- J JL k E φ f = k T φ f = K (12) (13) From (12), the electromechnicl undmped nturl frequency ω n nd dmping rtio ζ cn be obtined s (14) nd (15). ω n = B -- R K 2 ---- + ------- J L JL (14)

502 Myung-Seop Lim, Dong-Min Kim nd Jung-Pyo Hong Tble 2. Densities of mterils used in the motor. Items Initil model Improved model Pole / Slot 14 / 18 L stk (mm) 39 D (mm) 48 h m (mm) 15 10 t m (mm) 3.2 4.8 R (mω) 16.6 L (mh) 0.045 0.041 J (kg m 2 ) 1.686 10 3 1.512 10 3 B (kg m 2 /s) 1.0 10 4 ω n (rd/s) 241.4 316.7 ζ 0.77 0.64 R B -- + ---- J L ζ = ------------------------------- 2 B -- R K 2 ---- + ------- J L JL (15) The high electromechnicl undmped nturl frequency ω n nd low dmping rtio ζ cn led to the fst response speed of the electric mchines (Dorf nd Bishop, 2010). Therefore, in this study, ω n nd ζ were used s the objective functions to estimte the speed response chrcteristic of the EPS motors. Figure 5. BEMF of the proposed models. nd increse in t m of 4.8 mm cuse tht the designed mchine cnnot fulfill the required torque nd power. This is due to the fct tht the mgnitude of the BEMF should be 2.25 V rms t lest to chieve the required torque nd power considering the input current limittion. Therefore, the t m nd h m for the improved model were determined s 4.8 mm nd 10 mm, respectively. The configurtions nd prmeters of the motors re shown in Figure 4 nd Tble 2. Lstly, by using the FEA nd Mtlb Simulink, the torque performnce nd speed response re simulted nd compred to verify the vlidity of the proposed nlysis method. 4. COMPARISON OF INITIAL AND IMPROVED MODES In this study, two CFSMs which hs different rotor shpe re proposed. They re the initil model nd the improved model. The initil model is determined to fulfill the required specifictions. The thickness t m nd height h m of the PMs re 3.2 mm nd 15 mm, respectively. Bsed on the initil model, the improved model is designed through the proposed nlysis method to chieve the fst speed response. The tendency of the speed response chrcteristics such s the ω n nd ζ s well s mgnitude of the BEMF ccording to the vritions of the PMs shpes is presented in Figure 3. t m nd h m should not need to be integers, theoreticlly, becuse they re vribles bout the dimensions of PM. Therefore, there is n infinite number of combintions of t m nd h m. Consequently, the numbers of ω n nd ζ is no limited, theoreticlly. They were nlyzed under the conditions of the constnt volume of the PMs s well s the constnt dimeter of the rotor. Given the ω n nd ζ of the nlysis results, incresing thickness t m nd decresing height h m of the PMs mke improvement of the speed response of the CFSM. However, given the mgnitude of the BEMF in Figure 3, further decrese in h m under 10 mm Figure 6. Cogging torque of the proposed models. Figure 7. Torque ripple of the proposed models.

DESIGN OF FERRITE MAGNET CFSM TO IMPROVE SPEED RESPONSE OF EPS SYSTEM 503 Tble 3. Lod conditions nd FEA results of models. Items Initil model Improved model DC link voltge (V) 12 Current limit (A rms ) 60 Phse BEMF (V) 2.44 2.25 Torque (Nm) 4.19 4.10 Torque ripple (%) 3.8 2.9 Cogging torque (mnm) 2.88 2.58 4.1. Performnce BEMF t 1,000 rpm nd cogging torque of the proposed motors under no-lod condition re shown in Figure 5 nd Figure 6. Also, Figure 7 presents the torque ripple of the motors under the 60 A rms lod condition. Given the results, the BEMF nd cogging torque re decresed bout 7.8 % nd 10.4 %, respectively. The torque ripple is reduced by 0.9 %. Thus, it cn be concluded tht the torque chrcteristics of the improved model re excellent rther thn those of the initil model. All of the results re obtined vi the nonliner FEA. The lod conditions nd nonliner FEA results re orgnized in Tble 3. 4.2. Speed Response Aprt from the torque performnce, the rise time is nlyzed to compre the speed response chrcteristics of the motors. The nlysis results re obtined by using the Mtlb Simulink. Figures 8 nd 9 present the response chrcteristic to the unit step input without nd with PI controller, respectively. Figure 10 shows the speed response of the mchines with PI controller considering the ctul voltge nd current limittions. Assuming tht there re no limittions of the current nd voltge of the controllers, fst rise time cn be chieved since the high voltge nd current cn be pplied to the mchines in n instnt. However, there re limittions of the voltge nd current for the ctul controllers. Therefore, speed response nd rise time Figure 9. Speed reponse of ech model with controller. Figure 10. Speed reponse of ech model with controller considering the ctul voltge nd current limittions. Tble 4. Speed response chrcteristics of ech model. Rise time (msec) Items Initil model Improved model Motor 11.9 7.8 Motor with PI controller 1.54 0.32 Motor with PI controller considering limittions 40.2 36.1 Figure 8. Speed response of ech model. of the mchines considering the ctul voltge nd current limittions of the controllers re belted nd delyed compring to those of the unlimited voltge nd current conditions of the controllers. Consequently, limittions mens tht the mximum input voltge nd current tht the controller cn pply to the electric mchine. Given the results, the rise time decresed by 4.10 msec, 1.22 msec, nd 4.10 msec ccording to the simultion conditions. The rise times of the motors re orgnized in Tble 4. Consequently, it is verified tht the speed responses of the mchine cn be improved due to the proposed method.

504 Myung-Seop Lim, Dong-Min Kim nd Jung-Pyo Hong 5. CONCLUSION The nlyticl method to improve the speed response of the CFSM by redesigning the shpe of the rotor ws presented in this study. Bsed on the proposed method, the improved motor fulfilling both the required specifictions nd fst speed response ws proposed. The BEMF of the improved motor ws decresed by 7.8 %, but the cogging torque nd torque ripple of the improved motor ws decresed by 10.4 % nd 0.9 %, respectively, compring to those of the initil motor. Also, the rise time ws reduced bout 10.2 % ~ 79.2 %. Consequently, the proposed nlyticl method ws useful to design the CFSM to chieve the fst speed response. ACKNOWLEDGEMENT This reserch ws supported by the MSIP (Ministry of Science, ICT nd Future Plnning), Kore, under the ITRC (Informtion Technology Reserch Center) (IITP-2016-H8601-16-1005) supervised by the IITP (Institute for Informtion & Communiction Technology Promotion). REFERENCES Chen, X., Yng, T., Chen, X. nd Zhou, K. (2008). A generic model-bsed dvnced control of electric powerssisted steering systems. IEEE Trns. Control Systems Technology 16, 6, 1289 1300. Dorf, R. C. nd Bishop, R. H. (2010). Modern Control Systems. 12th edn. Prentice Hll. New Jersey, USA. Hendershot, J. R. nd Miller, T. J. E. (2010). Design of Brushless Permnent Mgnet Mchine. 2nd edn. Motor Design Books LLC. Florid, USA. Jng, J. Y., Cho, S. G., Lee, S. J., Kim, K. S., Kim, J. M., Hong, J. P. nd Lee, T. H. (2015). Relibility-bsed robust design optimiztion with kernl density estimtion for electric power steering motor considering mnufcturing uncertinties. IEEE Trns. Mgnetics 51, 3, 8001904. Kim, Y. B., Kim, H. J., Jung, K. T. nd Hong, J. P. (2014). Influence of mnufcturing tolernces on cogging torque of IPMSM for EPS ppliction. IEEE Int. Conf. Electric Mchines nd Systems, 382 386. Kim, Y. K., Rhyu, S. H. nd Jung, I. S. (2010). Shpe optimiztion for reduction the cogging torque of BLAC motor for EPS ppliction. IEEE Int. Conf. Electric Mchines nd Systems, 1163 1167. Lee, G. H., Choi, W. C., Kim, S. I., Kwon, S. O. nd Hong, J. P. (2011). Torque ripple minimiztion control of permnent mgnet synchronous motors for EPS pplictions. Int. J. Automotive Technology 12, 2, 291 297. Lee, J. H., Moon, H. T. nd Yoo, J. Y. (2012). Current sensorelss drive method for electric power steering. Int. J. Automotive Technology 13, 7, 1141 1147. Lee, S. J., Kim, S. I. nd Hong, J. P. (2014). Chrcteristics of PM synchronous motors ccording to pole-slot combintions for EPS pplictions. Int. J. Automotive Technology 15, 7, 1183 1187. Ombch, G. nd Junk, J. (2007). Two rotors design s comprison of permnent mgnet brushless synchronous motor for nd electric power steering ppliction. Europen Conf. Power Electronics nd Applictions, 1 9. Sh, S., Kim, S. A. nd Cho, Y. H. (2015). Optiml rotor shpe design for minimizing cogging torque of spoke type BLAC motor for EPS. IEEE Int. Conf. Industril Electronics nd Applictions, 1313 1318. Shriwstv, R. G. nd Digvne, M. B. (2011). Electric power steering with permnent mgnet synchronous motor drive used in utomotive ppliction. Int. Conf. Electricl Energy Systems, 145 148. Wng, S., Yin, C. nd Zho, J. (2009). Design nd fullvehicle tests of EPS control system. Int. Forum on Computer Science-Technology nd Applictions, 101 104.