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| Analytical Model of Air-Gap Magnetic Field of Slotted Axial Flux Permanent Magnet Motor Based on Improved Complex Relative Permeance Function |
| Tong Wenming1, Du Shaoyu1, Jia Jianguo1, Huang Rui2 |
1. National Engineering Research Center for Rare-Earth Permanent Magnet Machines Shenyang University of Technology Shenyang 110870 China;
2. CloudMinds Robotics Inc. Shanghai 201100 China |
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Abstract The slotting effect has a great influence on the air gap magnetic field. The conformal mapping method is based on the single-slot model to consider the influence of stator slotting, which has good generality. However, it simplifies the stator slot to infinite depth, so the analytical calculation accuracy is low. The exact subdomain method can consider the details of the stator slot with high analytical calculation accuracy. Nevertheless, it needs to be remodeled for different pole-slot combinations, and its generality is poor. This paper proposes a general analytical model of the air gap magnetic field of the slotted axial flux permanent magnet (AFPM) motor, considering the influence of stator slot width, slot depth, and static eccentricity.
Firstly, the topology of the double stator single rotor AFPM motor is introduced, and the analytical expression of the slotless no-load air gap magnetic field is obtained based on the subdomain method. Secondly, the improved complex relative permeance function is used to consider the slotting effect, and then the accurate magnetic field analytical model of the AFPM motor is established. Finally, combined with the variation law of air gap reluctance during static eccentricity, an analytical model of air gap magnetic field considering the influence of static eccentricity is established. The proposed complex relative permeance function calculation method can consider the stator slot width and depth, which has higher analytical calculation accuracy than the traditional complex relative permeance function method.
The calculated air gap flux density, no-load back electromotive force (EMF), and cogging torque are compared with the finite element analysis (FEA) and experimental results. The traditional complex relative permeance function method ignores the stator slot depth, and the calculation accuracy is low at the stator slot opening region. The proposed analytical model agrees with the FEA results, verifying the improved complex relative permeance function method. The air gap flux density, no-load back-EMF, and cogging torque under different eccentricities are calculated. Compared with FEA, the calculation error of the analytical method is within the acceptable range, and the calculation time is reduced by 92.2% under the premise of similar solution accuracy. Compared with the experimental results, no-load back-EMF and cogging torque errors are 4.2% and 11%. The calculation errors meet the actual engineering requirements.
The following conclusions can be drawn. (1) The proposed analytical model considers the slotting effect and improves the analytical calculation accuracy of the static eccentric lower half model. (2) Compared with FEA, the analytical model has the characteristics of fast calculation speed and similar solution accuracy, which improves the calculation efficiency. (3) The analytical model can be further extended to the partly closed slot structure, providing convenience for the fast and accurate calculation of the electromagnetic characteristics of the related motors.
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Received: 30 October 2023
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[1] 鲍晓华, 刘佶炜, 孙跃, 等. 低速大转矩永磁直驱电机研究综述与展望[J]. 电工技术学报, 2019, 34(6): 1148-1160.
Bao Xiaohua, Liu Jiwei, Sun Yue, et al.Review and prospect of low-speed high-torque permanent magnet machines[J]. Transactions of China Electrotechnical Society, 2019, 34(6): 1148-1160.
[2] Shao Lingyun, Navaratne R, Popescu M, et al.Design and construction of axial-flux permanent magnet motors for electric propulsion applications-a review[J]. IEEE Access, 2021, 9: 158998-159017.
[3] 赵纪龙, 逯卓林, 韩青峰, 等. 轴向磁通永磁电机系统及关键技术前沿发展综述[J]. 中国电机工程学报, 2022, 42(7): 2744-2765.
Zhao Jilong, Lu Zhuolin, Han Qingfeng, et al.An overview on development of axial flux permanent magnet motor system and the key technology[J]. Proceedings of the CSEE, 2022, 42(7): 2744-2765.
[4] 武岳, 张志锋, 平佳齐. 高功率密度轴向磁通永磁电机交流铜耗分析[J]. 电机与控制学报, 2022, 26(5): 65-75.
Wu Yue, Zhang Zhifeng, Ping Jiaqi.Analysis of AC copper loss in high power density axial flux permanent magnet motors[J]. Electric Machines and Control, 2022, 26(5): 65-75.
[5] Khatab M F H, Zhu Z Q, Li H Y, et al. Comparative study of novel axial flux magnetically geared and conventional axial flux permanent magnet machines[J]. CES Transactions on Electrical Machines and Systems, 2018, 2(4): 392-398.
[6] Geng Weiwei, Hou Jining, Li Qiang.Electromagnetic analysis and efficiency improvement of axial-flux permanent magnet motor with yokeless stator by using grain-oriented silicon steel[J]. IEEE Transa-ctions on Magnetics, 2022, 58(2): 8200905.
[7] Zhang Zhuoran, Geng Weiwei, Liu Ye, et al.Feasibility of a new ironless-stator axial flux permanent magnet machine for aircraft electric propulsion application[J]. CES Transactions on Electrical Machines and Systems, 2019, 3(1): 30-38.
[8] 毕云龙, 柴凤, 裴宇龙. 虚拟气隙在轴向磁通永磁电机三维有限元计算中的应用研究[J]. 中国电机工程学报, 2021, 41(6): 1929-1937.
Bi Yunlong, Chai Feng, Pei Yulong.Application and research of virtual air gap in three dimensional finite element analysis of axial flux permanent magnet machines[J]. Proceedings of the CSEE, 2021, 41(6): 1929-1937.
[9] 张志弘, 韩勤锴, 徐学平, 等. 基于保角变换与等效磁路法的永磁直驱发电机气隙磁场计算[J]. 电工技术学报, 2023, 38(3): 703-711.
Zhang Zhihong, Han Qinkai, Xu Xueping, et al.Air gap magnetic field calculation of permanent magnet direct drive generator based on conformal mapping and magnetic equivalent circuit method[J]. Transa-ctions of China Electrotechnical Society, 2023, 38(3): 703-711.
[10] 佟文明, 王萍, 吴胜男, 等. 基于三维等效磁网络模型的混合励磁同步电机电磁特性分析[J]. 电工技术学报, 2023, 38(3): 692-702.
Tong Wenming, Wang Ping, Wu Shengnan, et al.Electromagnetic performance analysis of a hybrid excitation synchronous machine based on 3D equivalent magnetic network[J]. Transactions of China Electrotechnical Society, 2023, 38(3): 692-702.
[11] Huang Rundong, Song Zaixin, Dong Zhiping, et al.An improved magnetic equivalent circuit method for segmented-Halbach axial-flux permanent magnet machines[J]. IEEE Transactions on Transportation Electrification, 2023, 9(2): 3218-3227.
[12] 郭凯凯, 郭有光. 磁通反向直线旋转永磁电机三维非线性等效磁路模型分析[J]. 电工技术学报, 2020, 35(20): 4278-4286.
Guo Kaikai, Guo Youguang.3D nonlinear equivalent magnetic circuit model analysis of a flux reversal linear rotary permanent magnet machine[J]. Transa-ctions of China Electrotechnical Society, 2020, 35(20): 4278-4286.
[13] Peng Bing, Zhuang Xiaoyu.Design and performance analysis of axial flux permanent magnet machines with double-stator dislocation using a combined wye-delta connection[J]. CES Transactions on Electrical Machines and Systems, 2022, 6(1): 53-59.
[14] Guo Baocheng, Du Yunlu, Peng Fei, et al.Magnetic field calculation in axial flux permanent magnet motor with rotor eccentricity[J]. IEEE Transactions on Magnetics, 2022, 58(9): 8206104.
[15] 刘蓉晖, 刘锦坤, 章君达, 等. 基于双曲余切变换的Halbach阵列表贴式永磁电机转子偏心气隙磁场解析模型[J]. 电工技术学报, 2023, 38(6): 1433-1446.
Liu Ronghui, Liu Jinkun, Zhang Junda, et al.Analytical model for air-gap magnetic field in halbach arrays surface-mounted permanent magnet motor with rotor eccentricity based on hyperbolic cotangent transformation[J]. Transactions of China Electrotechnical Society, 2023, 38(6): 1433-1446.
[16] 秦伟, 马育华, 张洁龙, 等. 不均匀气隙工况下轴向磁通永磁电动式磁悬浮电机的磁场与力特性分析[J]. 电工技术学报, 2023, 38(4): 889-902.
Qin Wei, Ma Yuhua, Zhang Jielong, et al.Characteristic and magnetic field analysis of an axial flux permanent magnets maglev motor with non-uniform air gap[J]. Transactions of China Elec-trotechnical Society, 2023, 38(4): 889-902.
[17] Zhu Z Q, Howe D.Analytical prediction of the cogging torque in radial-field permanent magnet brushless motors[J]. IEEE Transactions on Magnetics, 1992, 28(2): 1371-1374.
[18] Tong Wenming, Wang Shuai, Wu Shengnan, et al.A complete quasi-3-D analytical model of no-load magnetic field of double-sided slotted AFPMMs considering end effect[J]. IEEE Access, 2018, 6: 59557-59566.
[19] 王明杰, 贾宛英, 张志艳, 等. 永磁直线同步电机空载反电动势和推力的解析计算[J]. 电工技术学报, 2021, 36(5): 954-963.
Wang Mingjie, Jia Wanying, Zhang Zhiyan, et al.Analytical calculation of no-load eletromotive force and thrust in permanent magnet linear synchronous motors[J]. Transactions of China Electrotechnical Society, 2021, 36(5): 954-963.
[20] Zarko D, Ban D, Lipo T A.Analytical calculation of magnetic field distribution in the slotted air gap of a surface permanent-magnet motor using complex relative air-gap permeance[J]. IEEE Transactions on Magnetics, 2006, 42(7): 1828-1837.
[21] Xue Likun, Luo Ling.Semi-analytical calculation of the unsaturated magnetic field distribution of a slotted spoke-type interior permanent magnet machine with conformal mapping method[J]. IEEE Transactions on Magnetics, 2022, 58(5): 8104810.
[22] Ko Y Y, Song J Y, Seo M K, et al.Analytical method for overhang effect of surface-mounted permanent-magnet motor using conformal mapping[J]. IEEE Transactions on Magnetics, 2018, 54(11): 1-5.
[23] Tessarolo A, Olivo M.A new method for the analytical determination of the complex relative permeance function in linear electric machines with slotted air gap[C]//2016 International Symposium on Power Electronics, Electrical Drives, Automation and Motion (SPEEDAM), Capri, Italy, 2016: 1330-1335.
[24] Chan T F, Lai L L, Xie Shuming.Field computation for an axial flux permanent-magnet synchronous generator[J]. IEEE Transactions on Energy Con-version, 2009, 24(1): 1-11.
[25] Zhu Z Q, Howe D, Chan C C.Improved analytical model for predicting the magnetic field distribution in brushless permanent-magnet machines[J]. IEEE Transactions on Magnetics, 2002, 38(1): 229-238.
[26] 冀溥, 王秀和, 王道涵, 等. 转子静态偏心的表面式永磁电机齿槽转矩研究[J]. 中国电机工程学报, 2004, 24(9): 188-191.
Ji Pu, Wang Xiuhe, Wang Daohan, et al.Study of cogging torque in surface-mounted permanent magnet motors with static eccentricity[J]. Proceedings of the CSEE, 2004, 24(9): 188-191. |
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2024, Vol. 39 
