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
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.
佟文明, 杜绍雨, 贾建国, 黄芮. 基于改进复相对磁导函数的开槽轴向磁通永磁电机气隙磁场解析模型[J]. 电工技术学报, 2024, 39(24): 7700-7711.
Tong Wenming, Du Shaoyu, Jia Jianguo, Huang Rui. Analytical Model of Air-Gap Magnetic Field of Slotted Axial Flux Permanent Magnet Motor Based on Improved Complex Relative Permeance Function. Transactions of China Electrotechnical Society, 2024, 39(24): 7700-7711.
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