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 . (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)
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 , 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 . analyzed one. It is due to the overhang effect of the magnet . 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
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