2810                                                                                        IEEE TRANSACTIONS ON MAGNETICS...
2812                                                                                    IEEE TRANSACTIONS ON MAGNETICS, VO...
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  1. 1. 2810 IEEE TRANSACTIONS ON MAGNETICS, VOL. 37, NO. 4, JULY 2001 Magnetization Modeling of a Bonded Magnet for Performance Calculation of Inner-Rotor Type BLDC Motor In-Soung Jung, Member, IEEE, Ha-Gyeong Sung, Yon-Do Chun, and Jin-Hwan Borm Abstract—In many cases, ferrite bonded magnets used in inner-rotor type brushless DC (BLDC) motors do not have rotor core,and the magnetization directions of permanent magnets do nothave only parallel or radial direction. The characteristics of mag-nets are different from cored type ones which have uniform magne-tization direction. In this paper, the magnetization directions andintensities of a ferrite bonded magnet are analyzed by finite ele-ment analysis for magnetization procedure. The characteristics ofan inner-rotor type BLDC motor are analyzed by using the deter-mined magnetization. The analysis results are compared with themeasured ones. Index Terms—BLDC motor, bonded magnet, finite elementmethod, magnetization distribution. Fig. 1. Analysis model. (a) A ferrite bonded magnet type BLDC motor. (b) A I. INTRODUCTION model for determination of magnetization distribution of ferrite bonded magnet.R ECENTLY, bonded permanent magnets are widely used in many applications such as motors, sensors, actuators, etc.[1]. The magnetic materials used for bonded magnets are mainly TABLE I SPECIFICATIONS OF THE ANALYSIS MODELferrite powder and rare earth compound such as NdFeB. In manycases, brushless DC (BLDC) motors with ferrite bonded mag-nets do not have a rotor core in order to reduce manufacturingcost and inertia of the rotating part. So, the magnetization dis-tributions of the bonded magnets do not have only parallel orradial direction, and the characteristics of the magnets are dif-ferent from cored type ones. Many studies on BLDC motors have been performed [2]. But,the studies on the characteristics of a ferrite bonded magnet ina BLDC motor without rotor core are few. In this paper, thecharacteristics of an inner-rotor type BLDC motor without rotorcore are analyzed by using finite element method (FEM). Themagnetization directions and intensities of an anisotropic ferritebonded magnet are pre-determined by analyzing the anisotrop-ically magnetized process in injection molding of the material.By using the determined magnetized information, the perfor- II. METHOD OF ANALYSISmances of a BLDC motor are investigated. The validity of theanalysis method is verified by comparing the analyzed results A. Analysis Modelwith measured ones. Fig. 1(a) shows an inner-rotor type BLDC motor. Its rotor consists of an anisotropic ferrite bonded magnet, and the inner Manuscript received October 13, 2000. part of the magnet is nonmagnetic material. The motor is driven I.-S. Jung and H.-G. Sung are with the Korea Electronics Technology by 120 square wave voltage sources, and three hall sensors areInstitute, JinWi-Myon, PyungTaeck-Si, KyungGi-Do 451-860, Korea (e-mail:isjung@nuri.keti.re.kr; shk@nuri.keti.re.kr). used to detect the rotor position. Table I shows the specifications Y.-D. Chun is with the Department of Electrical Engineering, Hanyang Uni- of the analysis model.versity, Korea. Fig. 1(b) shows the analysis model for anisotropically magne- J.-H. Borm is with the Division of Mechanical and Industrial Engineering,Ajou University, PalDal-Gu, SuWon-Si, KyungGi-Do 442-749, Korea. tized process in injection molding of the ferrite bonded magnet. Publisher Item Identifier S 0018-9464(01)07192-8. In this procedure, Samarium–Cobalt (SmCo) magnets are used 0018–9464/01$10.00 © 2001 IEEE
  2. 2. JUNG et al.: MAGNETIZATION MODELING OF A BONDED MAGNET FOR PERFORMANCE CALCULATION OF INNER-ROTOR TYPE BLDC MOTOR 2811 (a)Fig. 2. Analysis results for magnetization procedure. (a) Flux distributionsof magnetization apparatus. (b) Magnetization vectors of the magnet afteranisotropically magnetized process. (b)Fig. 3. Flux distributions of PM according to magnetization distribution. (a) Incase of radially magnetized PM (conventional modeling method). (b) In case ofmagnetization distributions determined from analysis of magnetization model. Fig. 4. Surface flux density distributions of ferrite bonded magnets in air. (a) Outer surface of the magnet. (b) Inner surface of the magnet.to generate the magnetic fields for anisotropy. The SmCo mag-nets are magnetized in parallel directions. The inner part of the magnetization directions, , of the magnet are determined byPM material is air, whereas the outer part of SmCo magnets con- (2) in each element.sists of ferromagnetic material [3]. (2)B. Analysis Method The magnetization intensities of the magnet cannot exceed For the analysis, 2-D FEM is used. A magneto-static analysis the residual flux density of the material , and if externalis used to determine the magnetization of magnet, and a voltage magnetic fields are not enough to fully magnetize the material,source transient analysis using time-stepping FEM is used to the intensities remain lower than . So, the intensities of theanalyze the performances of the BLDC motor. The governing magnet are determined by (3) and (4) in each element.equation for 2-D FE analysis is given by (1). in case of (3) in case of (4) (1) The - and -components of magnetization of the bonded magnet are calculated by (5) and (6).where, is the -component of magnetic vector potential, (5) is the input current density, and (6) , are the - and -component of magnetization of permanent magnets. To analyze a BLDC motor, a circuit equation expressed byFrom the analysis of the magnetization model, the flux density (7) is added to (1).vectors of each element in bonded magnet region are ob-tained. The magnetization directions of the anisotropic ferritematerial are arranged to same directions as external flux. So, the (7)
  3. 3. 2812 IEEE TRANSACTIONS ON MAGNETICS, VOL. 37, NO. 4, JULY 2001(a) Fig. 6. Variation of line to line back EMF of the BLDC motor according to radial thickness of the bonded magnet.(b)Fig. 5. Line to line back EMF waveforms in case of 750 rpm. (a) Analysisresults. (b) Experimental results. Fig. 7. Speed and current according to torque (lines: analysis results, symbols:where measured results). subscript means each phase of windings, is the input voltage, of inner distributions, the values are greatly different from each is the winding resistance, other. The measured results show the validity of the proposed is an end-winding leakage inductance calculated analysis method. from a conventional equation [4], and Fig. 5 shows the analysis and measured results for line to is the flux linkage. line back EMF waveforms of the BLDC motor at the speed of In transient FE analysis of BLDC motor, the mesh should be 750 rpm. The profiles of analyzed and measured results are verychanged according to the rotation of the rotor. A moving mesh close, but the measured voltage value is 39% greater than thetechnique is used to model the rotation of the rotor [5]. analyzed one. It is due to the overhang effect of the magnet [6]. Fig. 6 shows the line to line back EMF values according to III. ANALYSIS RESULTS AND DISCUSSIONS the radial thickness of the bonded magnet. As the thickness in- creases, the value of back EMF rises. But, the rate of rise de- Fig. 2(a) shows flux distributions of the magnetization appa- creases because the inner part of the magnet less contributes toratus. The fluxes do not pass radially but arc with near poles. the performance. So, in consideration of manufacturing cost, theSo, magnetization directions of the bonded magnet are fixed as magnet thickness of mm is proper for this motor.shown in Fig. 2(b). Fig. 7 shows the torque and current curves according to speed, Fig. 3 shows the flux distributions of the magnet according and the analyzed results have good agreement with measuredto magnetization distributions, that is, one is the case of radial ones. In this analysis, the effective stack width is set to 39%magnetization with constant intensity (conventional modeling increase to consider the overhang effect of the magnet.method) and the other is the case that have analyzed magneti-zation distributions. We can see that the flux patterns are verydifferent. IV. CONCLUSION Fig. 4 shows the surface flux density distributions in air for In this paper, we analyzed an inner-rotor type BLDC motoreach case of Fig. 3. In case of outer distributions, the values at that does not have a rotor core. For the analysis, the magnetiza-the center of the magnet pole are different about 2 times. In case tion distributions of the anisotropic ferrite bonded magnet were
  4. 4. JUNG et al.: MAGNETIZATION MODELING OF A BONDED MAGNET FOR PERFORMANCE CALCULATION OF INNER-ROTOR TYPE BLDC MOTOR 2813determined by analyzing the magnetization process in injection [2] W.-B. Tsai and T.-Y. Chang, “Analysis of flux leakage in a brushless per-molding of the magnet. The validity of the analysis method was manent magnet motor with embedded magnets,” IEEE Trans on Magn., vol. 35, no. 1, pp. 543–547, 1999.verified by comparing the analyzed results with measured ones. [3] T. Sakai, K. Nakamura, and A. Morii, “Plastics magnet injection We confirm that our analysis method is useful for analysis molding process: Mixing/kneading and injection molding,” inand design of many electromagnetic machines and devices using ANTEC’89, 1989, pp. 244–252. [4] J. R. Hendershot and T. J. E. Miller, Design of Brushless Permanent-air-cored bonded magnets. Magnet Motors: Oxford, 1994. [5] S. B. Yoon, I. S. Jung, K. C. Kim, and D. S. Hyun, “Dynamic analysis of REFERENCES a reciprocating linear actuator for gas compression using finite element method,” IEEE Trans. on Magn., vol. 33, no. 5, pp. 4113–4115, 1997. [1] J. Ormerod and S. Constantinides, “Bonded permanent magnets: Cur- [6] J. P. Wang, D. K. Lieu, W. L. Lorimer, and A. Hartman, “Influence of rent status and future opportunities,” J. Appl. Phys., vol. 81, no. 8, pp. the permanent magnet overhang on the performance of the brushless dc 4816–4820, 1997. motor,” J. of Applied Physics, vol. 83, no. 11, pp. 6362–6364, 1998.