Abstract：The permanent magnet vernier machine (PMVM) is popular for its simple structure and high torque density. It can be modeled as three modules: the PM unit as the excitation source, the tooth-slot structure as the modulator, and the armature winding as the filter. The excitation source generates a magnetic electromotive force, and the modulator converts it into multiple magnetic field harmonics. The winding filter then extracts some of these harmonics to generate back electromotive force. The modulator design is crucial as it determines the magnetic field modulation capability and impacts the output torque. Traditional modulator designs with fixed tooth shapes and limited parameters cannot fully optimize permeance harmonics, limiting torque. Therefore, this paper proposes a multi-degree-of-freedom modulator design method to maximize torque. First, the stator is divided into Region Ⅰ and Region Ⅱ. Region Ⅰ is the part of the tooth slot structure near the stator yoke, which does not directly affect the distribution of airgap permeance. Region Ⅱ is the part of the tooth slot structure adjacent to the airgap, directly affecting the distribution of airgap permeance. Therefore, Region Ⅱ is the key to the design of stator magnetic field modulators. Then, decompose the stator slot into 3 modulation factors and the stator teeth into 15 modulation factors, which can be freely combined to form different modulator structures. Then, the PMVM with different modulation ratios is designed. Although increasing the modulation ratio can enhance magnetic field modulation performance and torque, a higher number of rotor poles increases flux leakage. There is a trade-off between the maximum output torque and the optimal magnetic field modulation ratio. The modulation ratio should be carefully selected. In addition, to further improve optimization efficiency, a modulation tooth structure with continuous modulation factors replaces the original discrete tooth structure. A continuous equivalent split tooth is formed by combining trapezoidal and triangular shapes. The bottom width of the trapezoid is controlled by angles Angle1 and Angle2, while the top width and height of the trapezoid are controlled by angles Angle1_1, Angle2_1, and y1, which also form the bottom of the triangle. The triangle's height is controlled by y2. This approach reduces the original 15 modulation factors to 6, enhancing optimization efficiency. The torques of equivalent split teeth and multi-degree-of-freedom split teeth are almost identical. The slight difference is due to the continuous variation of the split modulation factor of the equivalent split tooth. The multi-degree-of-freedom split modulation factor exhibits discrete variation, whereas the continuous height variation is continuous. Therefore, the equivalent split-tooth structure is more suitable for the design of multi-degree-of-freedom modulators and for applications across a broader range of slot-topology groups. Finally, a 12s34p PMVM is designed using the proposed equivalent teeth. Compared with the conventional uniform split-tooth PMVM, its torque has increased by 37.53%. The prototype has been manufactured, and the experimental results are highly consistent with expectations. This method proposes a new approach to improving torque in PMVM.
王荣鑫, 汪波, 蔡海维, 赵文俊, 程明. 永磁游标电机多自由度磁场调制器设计[J]. 电工技术学报, 2026, 41(4): 1169-1180.
Wang Rongxin, Wang Bo, Cai Haiwei, Zhao Wenjun, Cheng Ming. Design of Multi Degree of Freedom Magnetic Field Modulator for Permanent Magnet Vernier Machine. Transactions of China Electrotechnical Society, 2026, 41(4): 1169-1180.
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