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Static Airgap Magnetic Field of Axial Flux Permanent Magnet Disk Motor Xuanfeng Shangguan, Kai Zhang Static Airgap Magnetic Field of Axial Flux Permanent Magnet Disk Motor 1 Xuanfeng Shangguan, 2Kai Zhang School of Electrical Engineering and Automation, Henan Polytechnic University, Jiaozuo, China, [email protected] *2, School of Electrical Engineering and Automation, Henan Polytechnic University, Jiaozuo, China. [email protected] 1, Abstract Due to flat structure of the axial flux permanent magnet disc motor (AFPMDM), the airgap magnetic field distribution is more complex. To study the static airgap magnetic field of AFPMDM, the conventional magnetic circuit method and the method of taking slice in finite element software Magnet are used respectively. Then axial airgap flux density distribution characteristics along circumferential direction and radial direction are analyzed. The accurate three-dimensional airgap magnetic field distribution can be gotten with the above methods. At last, analytical method, finite element method and average radius method are used to calculate the airgap magnetic flux of per pole respectively. Three results are approximate and can reflect per pole magnetic flux of AFPMDM generally. The research for airgap magnetic field of AFPMDM provides theoretical basis for its wide application. Keywords: Airgap Magnetic Field, AFPMDM, Slice, Per Pole Magnetic Flux 1. Introduction The disc axial flux permanent magnet motor, with advantages of axial compact structure, easy to heat dissipation, high efficiency, obviously energy saving effect, high torque - inertia ratio and power density and so on [1, 2], especially the size and weight of which is about 50% of the ordinary permanent magnet motor, is especially suitable for occasions demanding small size, low weight the low-speed drive system [3]. With flat structure, the airgap magnetic field distribution is along the axial direction, so the cross section of this motor can not be selected to create a 2D model simply the same as common radial motor is dealt with [4]. The axial airgap flux density of AFPMDM along the circumferential direction at different radius is different, and the axial airgap flux density along the radius direction in the same electrical degree is also different [5]. Therefore, in order to calculate airgap magnetic field distribution of AFPMM accurately, 3D finite element analysis is asked to use [6, 7]. In this paper, airgap magnetic field distribution only under permanent magnet excitation is studied. In order to save computing time, according to the symmetry of the magnetic field distribution, only a pair of poles 3D motor model [810] is built. 2. No-load airgap magnetic field calculation of AFPMDM by magnetic circuit method The magnetic field analysis of axial flux permanent magnet disc motor is very complex. The main magnetic circuit contains two closed magnetic circuits shown in Figure 1: one magnetic circuit is starting from N pole, passing airgap and the magnetic yoke, through the airgap to reach S pole, at last, through the magnetic yoke returning to N pole; the other one is closed through the airgap, magnetic yoke and end cap [11, 12]. Due to the particularity of the permanent magnet magnetic circuit distribution, the length of the magnetic circuit at different radius is not the same, thus increasing the computational complexity of the magnetic circuit. However, because the airgap length of AFPMDM is longer, and the main magnetic circuit is unsaturated, so for engineering, we often take the magnetic circuit of the average radius as the total magnetic circuit of AFPMDM to calculate. International Journal of Digital Content Technology and its Applications(JDCTA) Volume7,Number7,April 2013 doi:10.4156/jdcta.vol7.issue7.139 1175 Static Airgap Magnetic Field of Axial Flux Permanent Magnet Disk Motor Xuanfeng Shangguan, Kai Zhang (a) (b) Figure 1. Main magnetic circuit of AFPMDM (a) radial direction (b) circumferential direction 1-shaft 2-yoke 3-permanent magnet 4-cover It’s assumed that the magnetic circuit is unsaturated, the magnetic potential drop of iron core and the armature reaction are ignored. Thus, H H m hM (1) 1 2 (2) Where is the total airgap length of motor, 1 is the distance between the surface of the permanent magnet and armature plate surface namely the main airgap length of the motor, 2 is the bond length between the permanent magnet and rotor disk, hM is the length of the magnetization direction of permanent magnet, H is airgap magnetic field strength, H m is the magnetic field strength of PM. According to the magnetic flux continuity principle: (3) Am Bm A B Where A and Am are respectively the effective area of per pole airgap and the area of one pole magnetic flux provided by the PM, B and Bm are the airgap magnetic flux density and the magnetic flux density of the PM at the operating point, is the leakage coefficient. Assuming p is the number of pole pairs, Dmi and Dmo are the inner and outer diameter of PM, p and i are the pole arc coefficient and the calculation pole arc coefficient. Thus, Am 1 2 p ( Dmo Dmi2 ) 8p (4) A 1 2 K F i ( Dmo Dmi2 ) 8p (5) Where K F is the airgap density distribution coefficient, is defined as the ratio of flux density amplitude mean and flux density amplitude maximum in a group of airgap flux density curves distributed along with the circumference. Permanent magnetic material response curve is (6) Bm r 0 H m Br According to the formula (1) ~ (6), assuming i p , the magnetic flux density of the PM at the operating point Bm and the airgap magnetic flux density B can be obtained . Bm K F Br K F r (7) hM 1176 Static Airgap Magnetic Field of Axial Flux Permanent Magnet Disk Motor Xuanfeng Shangguan, Kai Zhang B Where r and Br K F r (8) hM Br are respectively relative magnetic permeability and remnant magnetization. 3. 3D airgap magnetic field analysis of single-side AFPMDM Single-sided axial magnetic flux motor shown in Figure 2a is the simplest disc motor. It has only one rotor side and one stator side. The advantages of this motor are compact structure, short shaft and high torque but existing the great single-sided magnetic force. In this paper, the airgap magnetic field distribution of a pair of poles is analyzed by the 3D static magnetic field solver of Magnet. Figure 2b shows the flux density vector distribution of the motor excited by permanent magnet. (a) (b) Figure 2. Single-sided AFPMDM (a)structure (b)magnetic flux density vector distribution Taking a slice which is perpendicular to the shaft at the center of airgap, the airgap magnetic field is reflected in this slice, and the airgap flux density contour map can be got as shown in Figure 3. Figure 3. Airgap flux density contour map Axial airgap flux density distribution curve of one pole shown in Figure 4 can be obtained through taking the axial airgap flux density values along the circumferential direction respectively in the average radius, inner diameter and outer diameter from the slice as shown in Figure 3. Besides, the axial airgap flux density distribution curve along the radial direction can be got by taking a straight line in the center of the pole (electrical angle is 90°). It’s shown in Figure 5. Comparison analysis between Figure 4 and 5 shows that the amplitudes of airgap flux density in different radius are not the same, that’s because the magnetic path length in different radius is different. Airgap flux density distribution in a certain radius is close to flat-top wave, the flux density amplitude in average radius is maximum, but due to the influence of the edge effect and the end flux leakage, the amplitude of airgap magnetic flux density near the inner and outer diameter of the magnetic poles decreases obviously. 1177 Static Airgap Magnetic Field of Axial Flux Permanent Magnet Disk Motor Xuanfeng Shangguan, Kai Zhang 1 average radius 2 inner diameter 3 outer diameter air gap magnetic flux density Bz(T) 0.8 1 0.7 0.6 0.5 3 0.4 2 0.3 0.2 0.1 0.0 0 20 40 60 80 100 120 140 160 180 electrical degree(°) air gap magnetic flux density Bz(T) Figure 4. Axial airgap flux density distribution curve along the circumferential direction 0.70 0.65 0.60 0.55 0.50 0.45 0.40 30 35 40 45 50 radius(mm) Figure 5. Axial airgap flux density distribution curve along the radial direction According to the above method, the axial airgap flux density is taken from the slice along the circumferential direction and radial direction. The corresponding axial airgap flux density curve will be got. Then the cross-cutting airgap flux density curve nets can be obtained, namely, the accurate 3D airgap flux density space distribution graph in this airgap plane is shown in Figure 6. 0.6 air gap flux desityBz (T) 0.8 0.5 0.6 0.4 0.4 0.3 0.2 0.2 0 240 180 45 120 0.1 40 60 electrical degree( °) 35 0 30 radius( mm) Figure 6. The space distribution diagram of airgap magnetic field Similarly, one slice is taken from the surface of permanent magnet; the airgap magnetic field distribution of permanent magnet surfaces is shown in Figure 7. 1178 Static Airgap Magnetic Field of Axial Flux Permanent Magnet Disk Motor Xuanfeng Shangguan, Kai Zhang 0.7 0.6 air gap flux densityBz(T) 0.8 0.5 0.6 0.4 0.4 0.2 0.3 0 0.2 -0.2 240 0.1 180 45 120 40 60 electrical degree( °) 0 0 35 radius ( mm) 30 Figure 7. The space distribution diagram of airgap magnetic field of critical the PM surface Figure 7 shows that the magnetic field distribution of PM surface is flat-top shape. It’s impacted by the shape of PM, and the permanent magnet is magnetized along the axis, therefore, the flux leakage is relatively small when the slice is taken from the PM surface. 4. Study for the variation regular of axial airgap flux density amplitude In order to research the relationship between flux density amplitude and pole arc coefficient, the motor model is built by selecting the pole arc coefficient p =0.8,0.7,0.6,0.5, respectively. And the slice is taken from the center plane of airgap to solve the 3D static magnetic field, and then the axial airgap flux density distribution curve of one pole along the circumferential direction at the average radius corresponding to different pole arc coefficient can be got that is shown in Figure 8. pole arc coefficient 0.8 pole arc coefficient 0.7 pole arc coefficient 0.6 pole arc coefficient 0.5 0.8 air gap flux density Bz(T) 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0 20 40 60 80 100 120 140 160 180 200 electrical degree(°) Figure 8. Airgap flux density change curves corresponding to different pole arc coefficient It can be seen from Figure 8 that the airgap flux density amplitude at the average radius keeps a constant. It is nothing to do with the pole arc coefficient. Next, the factors that affect the airgap flux density amplitude at the average radius will be studied. Firstly, the magnetization length of the permanent magnet is changed while keeping the airgap length that is 4mm unchanged. Secondly, the length of the airgap is changed while keeping the magnetization 1179 Static Airgap Magnetic Field of Axial Flux Permanent Magnet Disk Motor Xuanfeng Shangguan, Kai Zhang length of the PM a constant hM 6mm . According to the above two methods, the airgap flux density amplitude curve at the average radius is shown in Figure 9. =4mm hM=6mm air gap flux density amplitudeB(T) 0.8 0.7 0.6 0.5 0.4 0.3 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 hM/ Figure 9. The change curve of airgap flux density amplitude at the average radius It can be seen from the above figure that the airgap flux density amplitude is related to the size of hM , but the flux density amplitude corresponding to the same value of hM in different situations is not the same. As can be seen from the formula (8), considering the flux leakage, magnetic saturation and so on, the flux leakage will become larger with the increase of airgap length when the value of hM is a constant. That is to say, the flux leakage coefficient becomes larger and the amplitude of airgap flux density will decrease. Overall, the amplitude of airgap flux density is mainly determined by the size of hM . 5. Calculation of per pole airgap magnetic flux with different methods Whether static characteristic or dynamic characteristic is considered, the airgap magnetic flux is an important parameter for motor, and it affects electromagnetic torque and back electromotive force directly. So it is very necessary to calculate per pole airgap magnetic flux. Firstly, using the analytical method to calculate the per pole airgap magnetic flux. For nonsinusoidal magnetic flux density waveforms, the per pole airgap magnetic flux formula is as follows [9]: Rout 2 2 f i Bmg rdr i Bmg Rin2 ) (9) ( Rout Rin 2p 2p Where, Bmg is the amplitude of airgap flux density, Rout is the outer radius of PM, Rin is the inner radius of PM. Per pole airgap magnetic flux can be calculated combining the equations (8) and (9) with motor parameters, and K F are respectively approach to 1.4 and 0.88 according to their characteristic curves. Secondly, the magnetic field integrator of finite element software is used to calculate per pole airgap magnetic flux. Taking a slice at the airgap center of one pole and completing the static simulation of 3D magnetic field, airgap flux density distribution of one pole can be got as shown in Figure 10. Then the airgap magnetic flux of per pole can be calculated by magnetic field integrator on this slice. 1180 Static Airgap Magnetic Field of Axial Flux Permanent Magnet Disk Motor Xuanfeng Shangguan, Kai Zhang Figure 10. Magnetic flux density distribution of one pole Finally, using the average radius method to calculate the per pole airgap magnetic flux. Taking the axial flux density values of one pole in the average radius along the circumferential direction from the slice in Figure 10 and the default interpolation in the software is 1001 points, so per pole magnetic flux can be calculated by putting these flux density values into formula (10). f Rout 1001 Rin 1001 B ldr B l ( R i 1 i i 1 i out Rin ) (10) The calculation results of the above three methods are listed in Table 1: Table 1. The calculation results of the above three methods Calculation method Analytic method FEM Average radius method 4.83×10-4Wb Per pole magnetic flux 5.21×10-4Wb 5.35×10-4Wb It can be seen that calculation results of per pole magnetic flux are close to each other with the above three methods. The result calculated by the finite element method is the most accurate in the three methods, because the 3D static solver of Magnet is used. This method will take long computing time. Besides, the calculation gap between analytic method and FEM is 0.38×10-4Wb. So the error of analytic method is relatively large because the leakage flux coefficient is from experience curve. However, the gap between average radius method and FEM is only 0.14×10-4Wb, the error of average radius method is very small. Therefore the AFPMDM can be equivalent to linear motor to model and analyzed by using the average radius method. 6. The main parameters of the motor in this paper Motor parameters Table 2. The main parameters of the motor Value Motor parameters Rated voltage Rated power Number of phases Number of pole pairs PM material Remnant magnetization density one pole angle 48V 168W 3 3 NdFeB 1.2T 48° Inner diameter of PM Outer diameter of PM Thickness of PM thickness of stator core air gap length Thickness of magnetic yoke Value 60mm 105mm 6mm 15mm 4mm 5mm 7. Conclusion By taking slice in airgap center, airgap magnetic field spatial distribution of AFPMDM is obtained. In this way, the complex axial airgap magnetic field distribution can be displayed simply, conveniently, and accurately. Axial airgap magnetic field distribution is close to flat-top wave. Due to the influence of the edge effect and the end flux leakage, the airgap flux density decrease gradually near the inner and outer diameter of the magnetic poles. The airgap flux density amplitude is maximum at average 1181 Static Airgap Magnetic Field of Axial Flux Permanent Magnet Disk Motor Xuanfeng Shangguan, Kai Zhang radius and it is determined by the size of hM . Then, the analytic method, finite element method and average radius method are adopted to calculate per pole magnetic flux of AFPMDM. In general, the above three methods can calculate per pole magnetic flux of AFPMDM with certain accuracy. The above research has achieved anticipated effect and provided a basis for the research of AFPMDM airgap magnetic field. 8. References [1] Zhao Rubin, Feng Lingling, “Design of Disk Type Coreless Permanent Magnet Synchronous Generator”, Electrical Machinery Technology, vol. 33, no. 3, pp.1-4, 2012. [2] Yongjuan Cao, Weifeng Chen, Li Yu, “Control and Simulation of a Novel Permanent Magnet Brushless DC Wheel Motor based on Finite Element Method”, IJACT, AICIT, vol. 4, no. 13, pp. 279-286, 2012. [3] De Donata G., Giulii Capponi F., Caricchi F., “Fractional-Slot Concentrated-Winding Axial-Flux Permanent-Magnet machine with Core-wound Coils”, Industry Applications, IEEE Transactions on, vol.48, no.2, pp.630-641, 2012. [4] Mei Ying, Pan Zaiping, “Research on a Novel Axial Field Disk Type Switched Reluctance Motor”, Micromotors, vol. 44, no. 1, pp.4-6, 2011. [5] Zhang Dilin, “The Calculation of the Performance of Axial Flux PM Synchronous Generator Based on ANSOFT”, Marine Electric & Electronic Engineering, vol. 28, no. 4, pp.222-224, 2008. [6] Xia Bing, Jin Mengjia, Shen Jianxin, “Design of Axial Flux Permanent Magnet Machines with Segmental 2D Finite Element Method”, Small & Special Electrical Machines, vol. 39, no. 4, pp.13, 2011. [7] Wang Yan-fang, Su Yan-ping, “Simulation and Analysis of Electromagnetic Field for Moving-coil Permanent Magnet Motor”, JDCTA, AICIT, vol. 6, no. 13, pp.185-191, 2012. [8] Tang Renyuan, “Theory and Design of Modern Permanent Magnet Machines”, China Machine Press, Beijing, 2011. [9] J. F. Gieras, R. J. Wang and M. J. Kamper, “Axial Fulx Permanent Magnet Brushless Machines”, Springer Science + Business Media B.V., Norwell, 2008. [10] Tze-Yee Ho, Mu-Song Chen, Lung-Hsian Yang, Jia-Shen, Lin, Po-Hung Chen, “The Design of a High Power Factor Brushless DC Motor Drive”, IJACT, AICIT, vol. 4, no. 18, pp.141-149, 2012. [11] Shoucheng Ding, Wenhui Li, Shizhou Yang, Jianhai Li, Guici Yuan, “The Motor Virtual Experimental System Based on Matlab Web Technology”, Journal of Networks, vol. 5, no. 12, pp.1490-1495, 2010. [12] Longxin Zhen, Xiaogang Wei, “Structure and Performance Analysis of Regenerative Electromagnetic Shock Absorber”, Journal of Networks, vol. 5, no. 12, pp.1467-1474, 2010. 1182