Abstract The torque ripple of the interior permanent magnet synchronous motor (IPMSM) which affects the driving experience of electric vehicles (EVs), is the most important factor in assessing the quality of driving motors for EVs. Optimizing the rotor structure of the IPMSM is a solution to this drawback that does not significantly increase manufacturing costs. The traditional analytical methods for optimizing the rotor structure are mainly of two kinds: The first method is to make the rotor magnetomotive force (MMF) as close as possible to a sinusoidal waveform by optimizing the magnet distribution; The other method is to make the air gap flux density closer to a sinusoidal waveform by designing an uneven magnetic resistance. However, these methods did not consider the effect of the rotor structure on the air gap relative permeability. This paper proposes an analytical model for calculating the torque ripple of IPMSM, which takes into account the influence of rotor structure on the air gap relative permeability. The optimal design of the rotor structure can be quickly determined by analyzing the analytical model. Firstly, based on the assumption of deep magnetic saturation of the ferromagnetic material at the flux barrier, the flux barrier is abstracted as a rotor virtual slot. Secondly, an air gap relative permeability equation is derived, which takes into account the effect of stator slotting and rotor virtual slotting on the air gap relative permeability. Thirdly, an analytical expression for the torque of IPMSM is obtained, by utilizing the stator MMF equation, rotor MMF equation and the air gap relative permeability equation. The relationship between the position of rotor virtual slot and torque ripple is derived by analyzing the analytical expression, based on which the design principle of IPMSM with low torque ripple is summarized. Finally, an IPMSM for EV with a rated power of 30 kW is optimally designed. The main electromagnetic properties of the original motorand the optimized motor are calculated. The torque ripple is significantly reduced after optimization, without affecting other electromagnetic performance. For torque performance, compared to the original motor, the torque ripple of the optimized motor decreased from 25.5% to 6.8%, a decrease of 18.7%. For the cogging torque performance, compared to the original motor, the cogging torque of the optimized motor decreased from 3.87 Nm to 0.98 Nm. That is to say, optimizing design is beneficial for reducing cogging torque. For inductance performance, the d-axis inductance before and after optimization is 0.243 7 mH, 0.243 9 mH, and the q-axis inductance is 0.838 3 mH and 0.837 1 mH, respectively. The simulation results show that the inductance remains unchanged before and after optimization. Due to the influence of the inductance of IPMSM on its flux weaken ability and reluctance torque utilization, the unchanged inductance means that these properties remain unchanged. For voltage performance, compared to the original motor, the optimized back electromotive force increased from 41.5 V to 43.3 V. For efficiency performance, compared to the original motor, the optimized efficiency increased from 96.55% to 96.66%. The optimization design has little impact on voltage and efficiency performance. Meanwhile, the torque ripple under all operating conditions has been suppressed by optimized design, especially in the flux-weakened region of the maximum current. The following conclusions can be drawn: The rotor virtual slot affects the torque ripple of IPMSM by affecting the air gap relative permeability. By optimizing the position of the rotor virtual slot, it is possible to make the value of the air gap relative permeability 0 for some specific order. For a ZS-slot p-pole IPMSM, the air gap relative permeability with ZS/p order can cause most of the torque ripple. By optimizing the position of the virtual slot, the torque ripple can be reduced without significantly altering the other main electromagnetic performance of the motor. This method is effective for all operating conditions of electric vehicles.
Wang Lixin,Wang Xiaoyuan,Gao Peng等. Torque Ripple Reduction Analysis of Interior Permanent Magnet Synchronous Motor for Electric Vehicle[J]. Transactions of China Electrotechnical Society, 2024, 39(20): 6386-6396.
[1] 佟文明, 姚颖聪, 李世奇, 等. 考虑磁桥不均匀饱和的内置式永磁同步电机等效磁网络模型[J]. 电工技术学报, 2022, 37(12): 2961-2970. Tong Wenming, Yao Yingcong, Li Shiqi, et al.Equivalent magnetic network model for interior permanent magnet machines considering non-uniform saturation of magnetic bridges[J]. Transactions of China Electrotechnical Society, 2022, 37(12): 2961-2970. [2] Peng Chen, Wang Daohan, Feng Zhenkang, et al.A new segmented rotor to mitigate torque ripple and electromagnetic vibration of interior permanent magnet machine[J]. IEEE Transactions on Industrial Electronics, 2022, 69(2): 1367-1377. [3] 王道涵, 彭晨, 王柄东, 等. 电动汽车新型转子内置式永磁同步电动机转矩脉动与电磁振动抑制研究[J]. 中国电机工程学报, 2022, 42(14): 5289-5300. Wang Daohan, Peng Chen, Wang Bingdong, et al.Research on a novel interior permanent magnet machine with segmented rotor to mitigate torque ripple and electromagnetic vibration[J]. Proceedings of the CSEE, 2022, 42(14): 5289-5300. [4] 王群京, 郑耀达, 刘先增. 基于结构参数优化的电机振动噪声的抑制研究[J]. 电气工程学报, 2023, 18(2): 16-25. Wang Qunjing, Zheng Yaoda, Liu Xianzeng.Research on suppression of motor vibration and noise based on structural parameter optimization[J]. Journal of Electrical Engineering, 2023, 18(2): 16-25. [5] 高锋阳, 齐晓东, 李晓峰, 等. 不等宽不等厚Halbach部分分段永磁同步电机电磁性能解析计算与优化分析[J]. 电工技术学报, 2022, 37(6): 1398-1414. Gao Fengyang, Qi Xiaodong, Li Xiaofeng, et al.Analytical calculation and optimization analysis of electromagnetic performance of Halbach partially- segmented permanent magnet synchronous motors with unequal width and thickness[J]. Transactions of China Electrotechnical Society, 2022, 37(6): 1398-1414. [6] 高锋阳, 齐晓东, 李晓峰, 等. 部分分段Halbach永磁同步电机优化设计[J]. 电工技术学报, 2021, 36(4): 787-800. Gao Fengyang, Qi Xiaodong, Li Xiaofeng, et al.Optimization design of partially-segmented Halbach permanent magnet synchronous motor[J]. Transactions of China Electrotechnical Society, 2021, 36(4): 787-800. [7] Zhao Wenliang, Lipo T A, Kwon B.Torque pulsation minimization in spoke-type interior permanent magnet motors with skewing and sinusoidal permanent magnet configurations[C]//2015 IEEE International Magnetics Conference (INTERMAG), Beijing, China, 2015, doi: 10. 1109/INTMAG. 2015. 7156886. [8] Shi Zhou, Sun Xiaodong, Cai Yingfeng, et al.Torque analysis and dynamic performance improvement of a PMSM for EVs by skew angle optimization[J]. IEEE Transactions on Applied Superconductivity, 2019, 29(2):0600305. [9] Song C H, Kim D H, Kim K C.Design of a novel IPMSM bridge for torque ripple reduction[J]. IEEE Transactions on Magnetics, 2021, 57(2): 8201004. [10] Liu Chengcheng, Huang Xiaorui, Zhang Wenfeng, et al.Shape optimization and demagnetization analysis of interior permanent magnet synchronous machine with hybrid cores[J]. AIP Advances, 2023, 13(3): 035215. [11] Im Y H, Hwang S I, Jang S M, et al.Analysis of torque pulsation considering interior permanent magnet rotor rib shape using response surface methodology[J]. IEEE Transactions on Magnetics, 2012, 48(2): 979-982. [12] Pan Zhicheng, Yang Kai, Wang Xiaojie.Optimal design of flux-barrier to improve torque performance of IPMSM for electric spindle[C]//2015 18 th International Conference on Electrical Machines and Systems (ICEMS), Pattaya, Thailand, 2015: 773-778. [13] Sarani E, Vaez-Zadeh S.Line start permanent magnet motors with double-barrier configuration for magnet conservation and performance improvement[J]. IET Electric Power Applications, 2017, 11(9): 1656-1663. [14] Alotto P, Barcaro M, Bianchi N, et al.Optimization of interior PM motors with machaon rotor flux barriers[J]. IEEE Transactions on Magnetics, 2011, 47(5): 958-961. [15] Fang Liang, Kim S I, Kwon S O, et al.Novel double-barrier rotor designs in interior-PM motor for reducing torque pulsation[J]. IEEE Transactions on Magnetics, 2010, 46(6): 2183-2186. [16] Zhu Shushu, Hu Yaohua, Liu Chuang, et al.Shaping of the air gap in a V-typed IPMSM for compressed-air system applications[J]. IEEE Transactions on Magnetics, 2021, 57(2): 8103705. [17] 孙毅, 蔡顺, 林迎前, 等. 永磁辅助同步磁阻电机顶层优化设计[J]. 电工技术学报, 2022, 37(9): 2306-2318. Sun Yi, Cai Shun, Lin Yingqian, et al.Top-level design pattern of PM-assisted synchronous reluctance machines[J]. Transactions of China Electrotechnical Society, 2022, 37(9): 2306-2318. [18] 刘成成, 刘乾宇, 王韶鹏, 等. 低转矩脉动同步磁阻电机磁障形状分析与优化设计[J]. 电机与控制学报, 2022, 26(12): 38-47. Liu Chengcheng, Liu Qianyu, Wang Shaopeng, et al.Flux barrier shape analysis and optimal design for low torque ripple synchronous reluctance machine[J]. Electric Machines and Control, 2022, 26(12): 38-47. [19] Chen Yunyun, Cai Tongle, Zhu Xiaoyong, et al.Optimization of a new asymmetric-hybrid-PM machine with high torque density and low torque ripple considering the difference of magnetic materials[J]. IEEE Transactions on Magnetics, 2022, 58(2): 8103505. [20] 张玉峰, 高文韬, 史乔宁, 等. 基于改进迭代田口法的双余度永磁同步电机优化设计[J]. 电工技术学报, 2023, 38(10): 2637-2647, 2685. Zhang Yufeng, Gao Wentao, Shi Qiaoning, et al.Optimization design of dual-redundancy permanent magnet synchronous motor based on improved iterations taguchi method[J]. Transactions of China Electrotechnical Society, 2023, 38(10): 2637-2647, 2685. [21] Barcaro M, Bianchi N.Torque ripple reduction in fractional-slot interior PM machines optimizing the flux-barrier geometries[C]//International Conference on Electrical Machines, Marseille, France, 2012: 1496-1502. [22] Hu Yaohua, Zhu Shushu, Liu Chuang, et al.Electromagnetic performance analysis of interior PM machines for electric vehicle applications[J]. IEEE Transactions on Energy Conversion, 2018, 33(1): 199-208. [23] Han S H, Jahns T M, Zhu Z Q.Design tradeoffs between stator core loss and torque ripple in IPM machines[C]//2008 IEEE Industry Applications Society Annual Meeting, Edmonton, AB, Canada, 2008: 1-8. [24] Han S H, Jahns T M, Soong W L.Torque ripple reduction in interior permanent magnet synchronous machines using the principle of mutual harmonics exclusion[C]//2007 IEEE Industry Applications Annual Meeting, New Orleans, LA, USA, 2007: 558-565. [25] 徐广人, 唐任远, 安忠良. 永磁同步电动机气隙磁场分析[J]. 沈阳电力高等专科学校学报, 2001(2): 1-4. Xu Guangren, Tang Renyuan, An Zhongliang.The analysis of airgap magnetic field of permanent magnet synchronous motor[J]. Journal of Shenyang Electric Power Institute, 2001(2): 1-4.
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