volume | PIER Journals

Abstract

To address the trade-off between increasing output torque and reducing torque ripple and cogging torque in interior permanent magnet synchronous motors (IPMSMs), this study proposes a structure incorporating stator-rotor auxiliary slots and rotor damping holes. Additionally, a hybrid permanent magnet configuration combining N35 and N30 grades was adopted to maintain high performance while further reducing costs. First, an analytical expression for the cogging torque was derived, and a finite element model of the motor was established. Subsequently, a parametric sweep and optimization of the stator and rotor auxiliary slots were conducted to obtain the optimal combination of auxiliary slot dimensions. Furthermore, a multi-objective optimization algorithm was proposed to optimize the motor parameters. Finally, radial electromagnetic force analysis was performed on the optimized motor model. The results demonstrate that the proposed structure effectively suppresses the torque ripple, cogging torque, and amplitude of the radial electromagnetic force, thereby reducing motor vibration amplitude while ensuring that the electromagnetic torque remains unaffected. The proposed design achieves a favorable balance between output torque enhancement and torque ripple/cogging torque reduction, with cost control through hybrid permanent magnets, demonstrating comprehensive performance improvements for IPMSMs.

1. Chen, Hao, Nabeel A. O. Demerdash, Ayman M. El-Refaie, Youguang Guo, Wei Hua, and Christopher H. T. Lee, "Investigation of a 3D-magnetic flux PMSM with high torque density for electric vehicles," IEEE Transactions on Energy Conversion, Vol. 37, No. 2, 1442-1454, 2022.
doi:10.1109/tec.2021.3137803 Google Scholar

2. Monadi, Mehdi, Mohammad Nabipour, Fatemeh Akbari-Behbahani, and Edris Pouresmaeil, "Speed control techniques for permanent magnet synchronous motors in electric vehicle applications toward sustainable energy mobility: A review," IEEE Access, Vol. 12, 119615-119632, 2024.
doi:10.1109/access.2024.3450199 Google Scholar

3. Choi, Gilsu and Gerd Bramerdorfer, "Comprehensive design and analysis of an interior permanent magnet synchronous machine for light-duty passenger EVs," IEEE Access, Vol. 10, 819-831, 2022.
doi:10.1109/access.2021.3137897 Google Scholar

4. Sun, Ke and Shaopeng Tian, "Multiobjective optimization of IPMSM with FSCW applying rotor notch design for torque performance improvement," IEEE Transactions on Magnetics, Vol. 58, No. 5, 1-9, 2022.
doi:10.1109/tmag.2022.3155269 Google Scholar

5. Zou, Tianjie, David Gerada, Antonino La Rocca, Mohsen Moslemin, Alasdair Cairns, Mengmeng Cui, Anuvav Bardalai, Fengyu Zhang, and Chris Gerada, "A comprehensive design guideline of hairpin windings for high power density electric vehicle traction motors," IEEE Transactions on Transportation Electrification, Vol. 8, No. 3, 3578-3593, 2022.
doi:10.1109/tte.2022.3149786 Google Scholar

6. Kim, Jihun, Changhyeon Kim, Young-Dae Shim, and Eun-Ho Lee, "Investigation of plastic deformation and electromagnetic interaction for copper losses caused by hairpin motor manufacturing," IEEE Transactions on Transportation Electrification, Vol. 11, No. 4, 10583-10592, 2025.
doi:10.1109/tte.2025.3549447 Google Scholar

7. Jansson, Elisabet, Torbjörn Thiringer, and Emma Arfa Grunditz, "Influence of flux barrier shape and mechanical constraints on field-weakening performance in double-layer interior permanent magnet machines," IEEE Transactions on Energy Conversion, Vol. 40, No. 1, 30-42, 2025.
doi:10.1109/tec.2024.3421954 Google Scholar

8. Dai, Litao, Jian Gao, Shuangxia Niu, and Shoudao Huang, "Multi-electromagnetic performance optimization of double-layer interior permanent magnet synchronous machine," IEEE Transactions on Industrial Electronics, Vol. 71, No. 11, 14535-14545, 2024.
doi:10.1109/tie.2024.3379651 Google Scholar

9. Xie, Ying, Hou-yu Li, Wei Cai, and Zi-hao He, "Design and research of hairpin winding double-layer interior permanent magnet synchronous motor," Electric Machines and Control, Vol. 26, No. 4, 47-56, 2022.
doi:10.15938/j.emc.2022.04.006 Google Scholar

10. Zhou, Han, Xiuhe Wang, Wenliang Zhao, Zezhi Xing, and Jinpeng Liu, "Research on magnetic field prediction of synchronous reluctance motor considering structure of multilayer flux barrier and saturation of rotor core," IEEE Transactions on Transportation Electrification, Vol. 11, No. 2, 5983-5998, 2025.
doi:10.1109/tte.2024.3496442 Google Scholar

11. Liu, Chang, Shuguang Zuo, Xudong Wu, Bin Yin, Haijun Zhuang, and Shichen Wang, "Torque ripple reduction of permanent magnet-assisted synchronous reluctance motors based on equivalent slotting effect and auxiliary flux barriers," IEEE Transactions on Transportation Electrification, Vol. 11, No. 2, 7054-7065, 2025.
doi:10.1109/tte.2024.3523436 Google Scholar

12. Zhang, Youguo, Yanbo Yang, Z. Y. Gu, Liangzi Li, and Tiancai Ma, "Multi-objective optimization for noise reduction of IPMSM based on non-uniform air gap," IEEE Access, Vol. 12, 48819-48829, 2024.
doi:10.1109/access.2024.3381776 Google Scholar

13. Han, Jichao, Yutian Sun, Ping Zheng, Haiming Qi, Jiechen Dong, Yufei Liu, Chunli Zhang, Baojun Ge, and Weili Li, "Influence of complex fluid flow on temperature distribution in the rotor region of large hydrogenerator under the rotor rotation," IEEE Access, Vol. 10, 3252-3262, 2022.
doi:10.1109/access.2021.3132280 Google Scholar

14. Wan, Xiaobo, Sen Yang, Yingchun Li, Yong Shi, and Jianyong Lou, "Minimization of cogging torque for V-type IPMSM by the asymmetric auxiliary slots on the rotor," IEEE Access, Vol. 10, 89428-89436, 2022.
doi:10.1109/access.2022.3201246 Google Scholar

15. Huang, Chao, Rongsheng Jia, Binbin Chen, Minglong Zhang, Hongjin Chen, Yuchen Wang, and Jianfeng Mao, "Research on cogging torque reduction based on multi-parameter optimization of auxiliary slots and pole-arc coefficient," Journal of Electrical Engineering & Technology, Vol. 20, No. 3, 1439-1449, 2025.
doi:10.1007/s42835-024-02058-5 Google Scholar

16. Kazemisangdehi, Seyedmilad, Zi Qiang Zhu, Liang Chen, Lei Yang, and Yanjian Zhou, "A mixed hybrid rare-earth and ferrite magnet asymmetric V-shape IPMSM," IEEE Transactions on Transportation Electrification, Vol. 11, No. 4, 8742-8755, 2025.
doi:10.1109/tte.2025.3554499 Google Scholar

17. Ajamloo, Akbar Mohammadi, Aghil Ghaheri, Mohamed N. Ibrahim, and Peter Sergeant, "A new hybrid permanent magnet-assisted synchronous reluctance motor with efficient utilization of rare-earth permanent magnets," IEEE Transactions on Energy Conversion, Vol. 40, No. 2, 1325-1338, 2025.
doi:10.1109/tec.2024.3486933 Google Scholar

18. Diao, Chengwu, Wenliang Zhao, Longxuan Li, Cong Liu, Mengmeng Tian, and Xiuhe Wang, "Analytical modeling and optimization of permanent magnet synchronous machine with hybrid magnets," IEEE Transactions on Industry Applications, Vol. 61, No. 1, 243-254, 2025.
doi:10.1109/tia.2024.3481390 Google Scholar

19. Xia, Jiakuan, Meijun Qi, Ting Dong, and Menglin Song, "Parameter sensitivity analysis and optimization of electromagnetic force waves of fractional slot surface-mounted PM motor with external rotor," IEEE Access, Vol. 11, 91756-91766, 2023.
doi:10.1109/access.2023.3308491 Google Scholar

20. Gu, Yuxi, Xiaoyuan Wang, Peng Gao, and Xiaoning Li, "Mechanical parametric sensitivity analysis of high-speed permanent magnet synchronous machine," IEEE Transactions on Applied Superconductivity, Vol. 31, No. 8, 1-4, 2021.
doi:10.1109/tasc.2021.3094436 Google Scholar

21. Xu, Ran and Wenming Tong, "Multi-objective hierarchical optimization of interior permanent magnet synchronous machines based on rotor surface modification," CES Transactions on Electrical Machines and Systems, Vol. 6, No. 4, 352-358, 2022.
doi:10.30941/cestems.2022.00046 Google Scholar

22. Chu, Jinlong, He Cheng, Junhang Sun, Cheng Peng, and Yihua Hu, "Multi-objective optimization design of hybrid excitation double stator permanent magnet synchronous machine," IEEE Transactions on Energy Conversion, Vol. 38, No. 4, 2364-2375, 2023.
doi:10.1109/tec.2023.3279934 Google Scholar

23. Wu, Zhipeng, Chenglin Song, and Wenzhe Deng, "Radial electromagnetic force and vibroacoustic mechanism analysis of integer slot permanent magnet synchronous motors," IEEE Transactions on Transportation Electrification, Vol. 11, No. 6, 13568-13578, 2025.
doi:10.1109/tte.2025.3597692 Google Scholar

24. Hong, Jianfeng, Lin Gui, and Junci Cao, "Analysis and experimental verification of the tangential force effect on electromagnetic vibration of PM motor," IEEE Transactions on Energy Conversion, Vol. 38, No. 3, 1893-1902, 2023.
doi:10.1109/tec.2023.3241082 Google Scholar

25. Zhao, Chenchen, Ming Cheng, Yubin Wang, Siyu De, Suixiang Shi, Chuntong Song, and Zheng Wang, "Analytical method of stator modal analysis for stator-permanent magnet machines," IEEE Transactions on Transportation Electrification, Vol. 11, No. 1, 2088-2096, 2025.
doi:10.1109/tte.2024.3416187 Google Scholar

26. Srikhumphun, Phuson, Pattasad Seangwong, Jonggrist Jongudomkarn, Apirat Siritaratiwat, Nuwantha Fernando, Sakda Somkun, and Pirat Khunkitti, "Design optimization and comparative study of skewed halbach-array magnets torus axial-flux permanent magnet motors for electric vehicles," IEEE Access, Vol. 12, 99912-99920, 2024.
doi:10.1109/access.2024.3429552 Google Scholar

Professor Han Lin

Dr. Huawei Liu

Professor Zhonggen Wang