Analytical Solution of a Fractional-Slot Double-Layer-Winding Open-Slot Vernier Permanent Magnet Machine with Tooth Tips

Q1 Engineering Chinese Journal of Electrical Engineering Pub Date : 2024-06-01 DOI:10.23919/CJEE.2024.000057

Weibing Wang;Ming Cheng

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Abstract

An analytical solution (ANA) for a fractional-slot double-layer-winding open-slot vernier permanent magnet (VPM) machine with tooth tips is presented. Magnetic vector potential equations are analytically solved using the technique of variable separation in four subdomains in a two-dimensional polar coordinate system. Based on the solved magnetic vector potential, the flux density distribution, torque, flux linkage, inductance, electromotive force (EMF) and power factor are analytically developed. An 18-slot/32-rotor-pole prototype is analyzed, and the results match well with the finite element analysis (FEA), which validates that the ANA consumes less time than FEA. Therefore, the tooth tips are optimized using the ANA to improve the average torque. Moreover, the ANA can be used to evaluate the demagnetization withstand capabilities of permanent magnets. The material utilization, slot-filling factor, EMF, and torque are compared between the models with three and four subdomains. Finally, an experimental prototype is constructed and tested, and the results validate the ANA.

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带齿尖的分数槽双层绕组开槽游标永磁机的解析解

本文提出了带齿尖的分数槽双层绕组开槽游标永磁（VPM）机器的解析解（ANA）。利用二维极坐标系中四个子域的变量分离技术，对磁矢量势方程进行了分析求解。根据求解的磁矢量势，分析得出了磁通密度分布、扭矩、磁通联结、电感、电动势（EMF）和功率因数。对一个 18 插槽/32 转子-磁极原型进行了分析，结果与有限元分析（FEA）非常吻合，验证了 ANA 比 FEA 耗时更短。因此，使用 ANA 对齿尖进行了优化，以提高平均扭矩。此外，ANA 还可用于评估永磁体的退磁承受能力。比较了三个子域和四个子域模型的材料利用率、槽填充系数、电磁场和扭矩。最后，构建并测试了实验原型，结果验证了 ANA。

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