Abstract：Due to their small equivalent airgap length and high flux-focusing capability, spoke-array flux modulation permanent magnet (SA-FMPM) machines offer the advantage of high torque density, thus having great potential in low-speed, direct-drive applications. However, the “flux barrier effect” that exists in SA-FMPM machines becomes an obstacle to enhancing the flux modulation effect and torque capacity. The key is to suppress the additional magnetic-motive-force (MMF). This paper explores the additional MMF in SA-FMPM machines, with a focus on its suppression technologies. Firstly, this paper introduces the generation mechanism of the additional MMF from the magnetic potential drop and the magnetic circuit aspects—the additional MMF results from the fluctuating unequal magnetic potential of each rotor's ferromagnetic poles over time. The defining formulas and mathematical models are developed to quantify the magnetic potential fluctuation, and the detrimental effects of additional MMF on motor performance are analyzed. Secondly, this paper presents three types of effective additional MMF suppression strategies: weakening or eliminating magnetic potential fluctuations, designing flux barriers or flux bridges, and optimizing magnet arrangement. The interrelations and distinctions of these strategies are also analyzed. The existing spoke-array permanent magnet machine topologies and the structural innovations in suppressing additional MMF are overviewed. Their advantages and disadvantages are summarized and evaluated as follows. (1) The principle underlying the weakening/elimination of magnetic potential fluctuations lies in forcing the homopolar rotor ferromagnetic poles to have equal magnetic potential by adding an iron yoke. The other approach is to compensate for the variation in lumped magnetic conductance during rotor rotation. Specifically, the single-bridge, double-bridge, and double-stator topologies are derived. These topologies can significantly weaken the additional MMF, and some can eliminate the magnetic potential fluctuation. However, the machine’s overload capacity is poor due to its easy saturation. (2) The flux barrier/flux bridge design can lead to variations in magnetic reluctance. The core ideal is to achieve the dual change of both “magnetomotive-force unit” and “permeance unit”. The relevant designs include H-, C-, U-, and V-shaped asymmetric flux barrier/bridge structures. These topologies can improve the flux modulation effect, but are limited in suppressing additional MMF. (3) The ideal of magnet arrangement optimization utilizes the “electromagnetic superimposition” theory to improve the flux-focusing ability. Alternatively, the reluctance torque is introduced to compensate for the torque component weakened by additional MMF. The derived topologies are classified into reinforced flux-focusing magnet and spoke-array interior magnet designs. These topologies can reduce flux leakage and enhance primitive PM-excited MMF or synthetic torque, but generate non-working harmonics, thereby increasing losses. This paper discusses the connections between additional MMF and the existing high-performance machine design techniques from rotor-side, stator-side, and harmonic synergetic optimization design perspectives. Moreover, various machine design techniques are further elaborated. The existence of additional MMF is extended to other magnet-inserted machines. Finally, this paper suggests future research directions for additional MMF phenomena.
方颖, 梁子漪, 李大伟, 曲荣海. 切向励磁型磁场调制电机的附加磁动势及其抑制技术综述[J]. 电工技术学报, 2025, 40(22): 7107-7126.
Fang Ying, Liang Ziyi, Li Dawei, Qu Ronghai. Overview of Additional Magnetic Motive Force in Spoke-Array Flux Modulation Permanent Magnet Machines and Its Suppression Technologies. Transactions of China Electrotechnical Society, 2025, 40(22): 7107-7126.
[1] Li Dawei, Qu Ronghai, Li Jian.Topologies and analysis of flux-modulation machines[C]//2015 IEEE Energy Conversion Congress and Exposition (ECCE), Montreal, QC, Canada, 2015: 2153-2160. [2] 程明, 马钲洲, 花为, 等. 电机气隙磁场调制统一理论研究进展与展望[J]. 中国电机工程学报, 2025, 45(4): 1220-1237. Cheng Ming, Ma Zhengzhou, Hua Wei, et al.Research progresses and prospects of general airgap field modulation theory for electrical machines[J]. Proceedings of the CSEE, 2025, 45(4): 1220-1237. [3] Zhu Xuhui, Lee C H T, Chan C C, et al. Overview of flux-modulation machines based on flux-modulation principle: topology, theory, and development pro- spects[J]. IEEE Transactions on Transportation Electrification, 2020, 6(2): 612-624. [4] 苏鹏, 申怡, 花为, 等. 轴向模块化磁通反向电机运行机理研究[J]. 中国电机工程学报, 2022, 42(23): 8718-8729. Su Peng, Shen Yi, Hua Wei, et al.Analysis of operation principle for an axial modular flux reversal permanent magnet machine[J]. Proceedings of the CSEE, 2022, 42(23): 8718-8729. [5] 梁子漪, 曲荣海, 陈智, 等. 双机电端口电机系统综述与发展展望[J]. 电工技术学报, 2022, 37(19): 4923-4937. Liang Ziyi, Qu Ronghai, Chen Zhi, et al.Overview of dual-electrical-port dual-mechanical-port machine system and their development[J]. Transactions of China Electrotechnical Society, 2022, 37(19): 4923-4937. [6] 卢浩, 杜怿, 刘新波, 等. 磁场调制型双馈无刷混合励磁电机及其静态性能分析[J]. 电工技术学报, 2020, 35(14): 2969-2978. Lu Hao, Du Yi, Liu Xinbo, et al.Static performance analysis of magnetic field-modulated doubly-fed brushless hybrid excitation motor[J]. Transactions of China Electrotechnical Society, 2020, 35(14): 2969-2978. [7] 于克训, 陈曦, 谢贤飞, 等. 无刷双馈电机研究综述与展望[J]. 电工技术学报, 2024, 39(2): 397-422. Yu Kexun, Chen Xi, Xie Xianfei, et al.Overview and prospect of the brushless doubly-fed machine research[J]. Transactions of China Electrotechnical Society, 2024, 39(2): 397-422. [8] Wu Fan, M El-Refaie A. Permanent magnet vernier machine: a review[J]. IET Electric Power Appli- cations, 2019, 13(2): 127-137. [9] 谢康福. 基于电磁复合的永磁电机理论与拓扑研究[D]. 武汉: 华中科技大学, 2020. Xie Kangfu.Permanent magnet machines theory and topology study based on electromagnetic superimpo- sition[D]. Wuhan: Huazhong University of Science and Technology, 2020. [10] 黄海林, 李大伟, 曲荣海, 等. 磁齿轮复合永磁电机拓扑及应用综述[J]. 电工技术学报, 2022, 37(6): 1381-1397. Huang Hailin, Li Dawei, Qu Ronghai, et al.A review of magnetic geared machines: topologies and appli- cations[J]. Transactions of China Electrotechnical Society, 2022, 37(6): 1381-1397. [11] 曲荣海, 李大伟, 赵钰. 磁场调制电机的由来、发展与挑战[J]. 中国电机工程学报, 2024, 44(18): 7361-7381. Qu Ronghai, Li Dawei, Zhao Yu.The origin, development and challenge of flux modulation machine[J]. Proceedings of the CSEE, 2024, 44(18): 7361-7381. [12] 樊英, 陈秋蒴, 陈俊磊, 等. 基于无人配送车辆运行工况的交替极游标轮毂电机优化设计[J]. 电工技术学报, 2023, 38(19): 5141-5151. Fan Ying, Chen Qiushuo, Chen Junlei, et al.Opti- mization design of consequent pole vernier wheel motor based on operating conditions of unmanned delivery vehicles[J]. Transactions of China Electro- technical Society, 2023, 38(19): 5141-5151. [13] 李亚, 周庆林, 丁石川, 等. 表嵌式交替极永磁电机拓扑演化及气隙磁场调制效应研究[J]. 电工技术学报, 2023, 38(12): 3188-3198. Li Ya, Zhou Qinglin, Ding Shichuan, et al.Investi- gation of topologies evolution and air-gap field modulation effect on surface-inset consequent-pole PM machines[J]. Transactions of China Electro- technical Society, 2023, 38(12): 3188-3198. [14] Xie Kangfu, Li Dawei, Qu Ronghai, et al.A novel permanent magnet vernier machine with halbach array magnets in stator slot opening[J]. IEEE Transactions on Magnetics, 2017, 53(6): 7207005. [15] Kim B, Lipo T A.Analysis of a PM vernier motor with spoke structure[C]//2014 IEEE Energy Con- version Congress and Exposition (ECCE), Pittsburgh, PA, USA, 2014: 2358-2365. [16] Pu Yun, Xiang Zixuan, Jiang Min, et al.Investigation on electromagnetic torque of a flux-switching per- manent magnet motor from perspective of flux density harmonic reduction ratio[J]. IEEE Transa- ctions on Magnetics, 2022, 58(2): 8101706. [17] Mushenya J, Khan A.Performance analysis and mechanical assembly considerations for a spoke-type permanent magnet vernier machine with an inner salient pole core on the rotor[C]//2022 IEEE Energy Conversion Congress and Exposition (ECCE), Detroit, MI, USA, 2022: 1-8. [18] 梁子漪, 曲荣海, 李大伟, 等. 一种交替极切向励磁游标永磁电机的分析与设计[J]. 电工技术学报, 2020, 35(15): 3173-3181. Liang Ziyi, Qu Ronghai, Li Dawei, et al.Analysis of a consequent-pole spoke-array vernier permanent mag- net machine[J]. Transactions of China Electro- technical Society, 2020, 35(15): 3173-3181. [19] 曲荣海, 李大伟, 任翔. 磁场调制电机[M]. 北京: 科学出版社, 2022. [20] Zou Tianjie, Li Dawei, Qu Ronghai, et al.Per- formance comparison of surface and spoke-type flux-modulation machines with different pole ratios[J]. IEEE Transactions on Magnetics, 2017, 53(6): 7402605. [21] Liu Yang, Song Bao, Tang Xiaoqi.Additional magneto motive force of spoke-type vernier permanent-magnet machines[J]. IEEE Transactions on Magnetics, 2023, 59(11): 8104006. [22] 徐高红, 陈健, 陈前. 一种新型倒T型连续极高转矩密度永磁游标电机[J]. 电气工程学报, 2025, 20(2): 157-164. Xu Gaohong, Chen Jian, Chen Qian.A novel inverted T-type consequent high torque density permanent magnet vernier motor[J]. Journal of Electrical Engineering, 2025, 20(2): 157-164. [23] 张远志. 切向励磁型游标永磁直驱风力发电机技术研究[D]. 武汉: 华中科技大学, 2022. Zhang Yuanzhi.Research on spoke-type vernier permanent magnet direct-drive wind turbine gen- erator[D]. Wuhan: Huazhong University of Science and Technology, 2022. [24] 刘洋, 宋宝, 周向东, 等. 轮辐式游标永磁电机分析与多目标优化设计[J]. 电机与控制学报, 2023, 27(9): 1-9. Liu Yang, Song Bao, Zhou Xiangdong, et al.Analysis and multi-objective optimization of spoke type vernier permanent-magnet machine[J]. Electric Machines and Control, 2023, 27(9): 1-9. [25] Wu Shuang, Guo Liyan, Wang Huimin, et al.Analytical calculation for magnetic field in spoke- type permanent magnet machines based on a rotor magnetic potential model[J]. IEEE Transactions on Magnetics, 2022, 58(2): 8103605. [26] Chen Hong, Li Dawei, Qu Ronghai, et al.An improved analytical model for inductance calculation of interior permanent magnet machines[J]. IEEE Transactions on Magnetics, 2014, 50(6): 7027108. [27] Wu Shuang, Guo Liyan, Wang Huimin, et al.Inductance calculation of interior permanent magnet machines considering asymmetrical saturation of the bridge[J]. IEEE Transactions on Magnetics, 2019, 55(11): 8107511. [28] Zhao W, Lipo T A, Kwon B.Torque pulsation mini- mization in spoke-type interior permanent magnet motors with skewing and sinusoidal permanent magnet configurations[J]. IEEE Transactions on Mag- netics, 2015, 51(11): 1-4. [29] Evans S A.Salient pole shoe shapes of interior permanent magnet synchronous machines[C]//The XIX International Conference on Electrical Machines- ICEM 2010, Rome, Italy, 2010: 1-6. [30] Pang Yong, Zhu Z Q, Feng Z J.Cogging torque in cost-effective surface-mounted permanent-magnet machines[J]. IEEE Transactions on Magnetics, 2011, 47(9): 2269-2276. [31] Muteba M.Effect of combination between stator-slot and rotor-pole numbers on the performance of multi- phase spoke-type PM motors for vehicle traction applications[C]//2021 7th International Conference on Electrical, Electronics and Information Engineering (ICEEIE), Malang, Indonesia, 2021: 90-95. [32] Ren Xiang, Li Dawei, Qu Ronghai, et al.Investigation of spoke array permanent magnet vernier machine with alternate flux bridges[J]. IEEE Transactions on Energy Conversion, 2018, 33(4): 2112-2121. [33] Ge Xiao, Zhu Z Q, Li Jiebao, et al.A spoke-type IPM machine with novel alternate airspace barriers and reduction of unipolar leakage flux by step-staggered rotor[J]. IEEE Transactions on Industry Applications, 2016, 52(6): 4789-4797. [34] Liang Ziyi, Gao Yuting, Li Dawei, et al.Design of a novel dual flux modulation machine with consequent- pole spoke-array permanent magnets in both stator and rotor[J]. CES Transactions on Electrical Machines and Systems, 2018, 2(1): 73-81. [35] Liu Wenbo, Lipo T A.Analysis of consequent pole spoke type vernier permanent magnet machine with alternating flux barrier design[J]. IEEE Transactions on Industry Applications, 2018, 54(6): 5918-5929. [36] Zhang Yuanzhi, Li Dawei, Yan Peng, et al.A high torque density claw-pole permanent-magnets vernier machine[J]. IEEE Journal of Emerging and Selected Topics in Power Electronics, 2022, 10(2): 1756-1765. [37] Zhang Yuanzhi, Li Dawei, Fang Li, et al.Design and manufacture of a high-torque-density permanent magnet traction motor for light-duty electric vehicles[J]. IEEE Transactions on Transportation Electrification, 2024, 10(1): 379-391. [38] Li Dawei, Qu Ronghai, Lipo T A.High-power-factor vernier permanent-magnet machines[J]. IEEE Transa- ctions on Industry Applications, 2014, 50(6): 3664-3674. [39] Li Dawei, Qu Ronghai, Xu Wei, et al.Design pro- cedure of dual-stator spoke-array vernier permanent- magnet machines[J]. IEEE Transactions on Industry Applications, 2015, 51(4): 2972-2983. [40] Cheng Yi, Zhang Yuanzhi, Qu Ronghai, et al.Design and analysis of 10 MW HTS double-stator flux- modulation generator for wind turbine[J]. IEEE Transactions on Applied Superconductivity, 2021, 31(5): 5201408. [41] Cheng Yi, Qu Ronghai, Gao Yuting, et al.Com- parison of electromagnetic performance of 10-MW HTS double-stator flux modulation wind generators with different topologies[J]. IEEE Transactions on Applied Superconductivity, 2020, 30(4): 5202307. [42] Gao Yuting, Li Dawei, Qu Ronghai, et al.Analysis of a novel consequent-pole flux switching permanent magnet machine with flux bridges in stator core[J]. IEEE Transactions on Energy Conversion, 2018, 33(4): 2153-2162. [43] Qiao Zhenyang, Zhang Yunpeng, Luo Jian, et al.Design and analysis of a consequent-pole flux switching permanent magnet machine with flux- concentrated magnet for torque enhancement[J]. IEEE Transactions on Energy Conversion, 2024, 39(4): 2468-2479. [44] Liang Ziyi, Gao Yuting, Li Dawei, et al.Investigate of a flux switching permanent magnet machine with alternative flux bridges[C]//2019 IEEE Energy Con- version Congress and Exposition (ECCE), Baltimore, MD, USA, 2019: 6548-6554. [45] Zhang Yuwei, Zhao Yu, Li Dawei, et al.A novel high torque density spoke-array permanent magnets vernier machine with magnets bridge[C]//2023 26th Inter- national Conference on Electrical Machines and Systems (ICEMS), Zhuhai, China, 2023: 1746-1751. [46] Yang Hui, Li Ya, Lin Heyun, et al.Principle investi- gation and performance comparison of consequent- pole switched flux PM machines[J]. IEEE Transa- ctions on Transportation Electrification, 2021, 7(2): 766-778. [47] 隋嘉庆, 冯桂宏, 张炳义. 基于不等磁极组合的外转子内置式永磁同步电机转矩脉动抑制研究[J]. 电机与控制应用, 2022, 49(3): 61-67. Sui Jiaqing, Feng Guihong, Zhang Bingyi.Research on torque ripple suppression of interior permanent magnet synchronous motor with outer rotor based on unequal magnetic pole combination[J]. Electric Machines & Control Application, 2022, 49(3): 61-67. [48] Cao Chi, Zhao Wenliang, Liu Yan, et al.Performance improvement of spoke-type interior permanent mag- net motors with asymmetric rotor structures[C]//2021 24th International Conference on Electrical Machines and Systems (ICEMS), Gyeongju, South Korea, 2021: 1326-1330. [49] 项子旋, 卢子润, 朱孝勇, 等. 轮辐式永磁轮毂电机高效轻质设计与优化研究[J]. 中国电机工程学报, 2021, 41(24): 8283-8295. Xiang Zixuan, Lu Zirun, Zhu Xiaoyong, et al.High- efficiency and lightweight design and optimization of spoke-type permanent magnet in-wheel motor[J]. Proceedings of the CSEE, 2021, 41(24): 8283-8295. [50] Zhao Yu, Li Dawei, Lin Mengxuan, et al.Investi- gation of line-start permanent magnet vernier machine with different rotor topologies[J]. IEEE Journal of Emerging and Selected Topics in Power Electronics, 2022, 10(3): 2859-2870. [51] Chen Yiqiang, Zhu Xiaoyong, Quan Li, et al.A V-shaped PM vernier motor with enhanced flux- modulated effect and low torque ripple[J]. IEEE Transactions on Magnetics, 2018, 54(11): 8203804. [52] 周健荣, 樊德阳, 项子旋, 等. V型游标永磁电机功率因数内在机理及其提升方法[J]. 电工技术学报, 2023, 38(14): 3789-3799. Zhou Jianrong, Fan Deyang, Xiang Zixuan, et al.Production mechanism of power factor of V-type vernier permanent magnet machine and improvement method[J]. Transactions of China Electrotechnical Society, 2023, 38(14): 3789-3799. [53] Liang Peixin, Chai Feng, Yu Yanjun, et al.Analytical model of a spoke-type permanent magnet synchronous in-wheel motor with trapezoid magnet accounting for tooth saturation[J]. IEEE Transactions on Industrial Electronics, 2019, 66(2): 1162-1171. [54] Huang Hailin, Li Dawei, Qu Ronghai, et al.Design and analysis of T-shaped consequent pole dual PM vernier machines with differential magnetic network method[J]. IEEE Journal of Emerging and Selected Topics in Power Electronics, 2022, 10(4): 4546-4555. [55] Wang Jing, Geng Weiwei, Li Qiang, et al.A new flux-concentrating rotor of permanent magnet motor for electric vehicle application[J]. IEEE Transactions on Industrial Electronics, 2022, 69(11): 10882-10892. [56] Chen Canruo, Ren Xiang, Li Dawei, et al.Torque performance enhancement of flux-switching permanent magnet machines with dual sets of magnet arrange- ments[J]. IEEE Transactions on Transportation Elec- trification, 2021, 7(4): 2623-2634. [57] Bi Yanding, Fu Weinong, Niu Shuangxia, et al.Torque enhancement of a dual-PM flux-switching machine with improved multiple high-order working harmonics[J]. IEEE Transactions on Transportation Electrification, 2024, 10(2): 2830-2843. [58] Hua Yuntao, Wang Chen, Liu Ye, et al.Comparative study of high torque density spoke-type PM in-wheel motors for special vehicle traction applications[J]. IEEE Transactions on Industry Applications, 2022, 58(2): 1952-1962. [59] 刘细平, 刘章麒, 李亚, 等. 电动汽车用双层永磁体IPMSM优化分析[J]. 电机与控制学报, 2017, 21(10): 30-39. Liu Xiping, Liu Zhangqi, Li Ya, et al.Optimization and analysis of IPMSM with double-layer permanent magnet used in electric vehicle[J]. Electric Machines and Control, 2017, 21(10): 30-39. [60] 李吉程, 王爱元, 王成敏, 等. 内置式永磁同步电机不同转子拓扑结构对电机性能的影响分析[J]. 电机与控制应用, 2024, 51(2): 103-112. Li Jicheng, Wang Aiyuan, Wang Chengmin, et al.Analysis of the influence of different rotor topology structures on the performance of interior permanent magnet synchronous motors[J]. Electric Machines & Control Application, 2024, 51(2): 103-112. [61] Zhu Ziqiang, Xiao Yang.Novel magnetic-field- shifting techniques in asymmetric rotor pole interior PM machines with enhanced torque density[J]. IEEE Transactions on Magnetics, 2022, 58(2): 8100610. [62] 王力新, 王晓远, 高鹏, 等. 电动汽车用内置式永磁同步电机转矩脉动分析及抑制[J]. 电工技术学报, 2024, 39(20): 6386-6396. Wang Lixin, Wang Xiaoyuan, Gao Peng, et al.Torque ripple reduction analysis of interior permanent magnet synchronous motor for electric vehicle[J]. Transa- ctions of China Electrotechnical Society, 2024, 39(20): 6386-6396. [63] Li Ya, Zhou Qinglin, Ding Shichuan, et al.Influences of rotor design on air-gap field modulation effect in spoke-type permanent magnet machine for traction applications[J]. IEEE Transactions on Industry Appli- cations, 2023, 59(6): 6674-6684. [64] Liu Ye, Ma Kang, Xu Jiulong.Design optimization of rotor bridge and fixing hole for spoke-type PMSM[J]. IEEE Transactions on Magnetics, 2023, 59(11): 8102105. [65] Zhang Hengliang, Hua Wei.The influence of mag- netization on modular spoke-type permanent-magnet machine for in-wheel traction applications[J]. IEEE Transactions on Magnetics, 2018, 54(11): 8105105. [66] Chen Qian, Xu Gaohong, Zhai Fangfang, et al.A novel spoke-type PM motor with auxiliary salient poles for low torque pulsation[J]. IEEE Transactions on Industrial Electronics, 2020, 67(6): 4762-4773. [67] Xu Meimei, Zhao Wenxiang, Ji Jinghua, et al.Auxiliary notching rotor design to minimize torque ripple for interior permanent magnet machines[J]. IEEE Transactions on Industrial Electronics, 2024, 71(10): 12051-12062. [68] Wang Daohan, Wang Xiuhe, Jung S Y.Reduction on cogging torque in flux-switching permanent magnet machine by teeth notching schemes[J]. IEEE Transactions on Magnetics, 2012, 48(11): 4228-4231. [69] Wang Bingdong, Wang Daohan, Peng Chen, et al.Interior permanent magnet synchronous machines with composed T-shaped notching rotor[J]. IEEE Transactions on Industrial Electronics, 2024, 71(6): 5519-5529. [70] Li Ya, Zhou Qinglin, Ding Shichuan, et al.A novel flux concentrated stator consequent-pole permanent magnet machine with non-uniform stator modulation teeth[C]//2023 IEEE International Magnetic Conference- Short Papers (INTERMAG Short Papers), Sendai, Japan, 2023: 1-2. [71] Zhao Guishu, Hua Wei.Comparative study between a novel multi-tooth and a V-shaped flux-switching permanent magnet machines[J]. IEEE Transactions on Magnetics, 2019, 55(7): 8104908. [72] Huang Jiahui, Fu Weinong, Niu Shuangxia, et al.A novel stator dual-PM flux-switching machine with improved utilization of high-order harmonics and reduced flux leakage[C]//2023 26th International Conference on Electrical Machines and Systems (ICEMS), Zhuhai, China, 2023: 5114-5118. [73] Fang Li, Li Dawei, Ren Xiang, et al.A quantitative air-gap construction method to maximize torque of vernier PM machines[J]. IEEE Transactions on Transportation Electrification, 2023, 9(1): 463-473. [74] 程明, 文宏辉, 曾煜, 等. 电机气隙磁场调制行为及其转矩分析[J]. 电工技术学报, 2020, 35(5): 921-930. Cheng Ming, Wen Honghui, Zeng Yu, et al.Analysis of airgap field modulation behavior and torque component in electric machines[J]. Transactions of China Electrotechnical Society, 2020, 35(5): 921-930. [75] Chen Hong, Li Dawei, Qu Ronghai, et al.Torque capacity improvement of flux-switching PM machines based on directional stator permeance design[J]. IEEE Transactions on Industrial Electronics, 2024, 71(5): 4551-4561. [76] Xu Liang, Wu Wenjie, Zhao Wenxiang.Airgap magnetic field harmonic synergetic optimization approach for power factor improvement of PM vernier machines[J]. IEEE Transactions on Industrial Elec- tronics, 2022, 69(12): 12281-12291. [77] Chen Qian, Liao Jihong, Qian Wei, et al.Design and optimization a new spoke-type flux-modulation machine with inverted T-shape permanent magnets[J]. IEEE Transactions on Energy Conversion, 2023, 38(1): 203-217. [78] Zhu Xiaofeng, Hua Wei, Wu Zhongze, et al.Analytical approach for cogging torque reduction in flux-switching permanent magnet machines based on magnetomotive force-permeance model[J]. IEEE Transactions on Industrial Electronics, 2018, 65(3): 1965-1979. [79] Zhang Zhiheng, Wang Peixin, Hua Wei, et al.Comprehensive investigation and evaluation of cogging torque suppression techniques of flux- switching permanent magnet machines[J]. IEEE Transactions on Transportation Electrification, 2023, 9(3): 3894-3907. [80] Fang Li, Li Dawei, Zhang Yuanzhi.Analysis of consequent pole vernier PM machine based on advanced MMF-permeance model[C]//2022 IEEE 3rd China International Youth Conference on Electrical Engineering (CIYCEE), Wuhan, China, 2022: 1-6. [81] Chen Hong.Comparative analysis of consequent-pole permanent magnet vernier machines with different rotor-types[C]//2022 IEEE 3rd China International Youth Conference on Electrical Engineering (CIYCEE), Wuhan, China, 2022: 1-7. [82] Liao Jihong, Chen Qian, Xu Gaohong.Back-EMF optimization of a rotor permanent magnet flux- switching machine through air-gap harmonic design[C]// 2023 26th International Conference on Electrical Machines and Systems (ICEMS), Zhuhai, China, 2023: 767-772. [83] Liu Guohai, Wang Yanyang, Chen Qian, et al.Multiobjective deterministic and robust optimization design of a new spoke-type permanent magnet machine for the improvement of torque perfor- mance[J]. IEEE Transactions on Industrial Electronics, 2020, 67(12): 10202-10212. [84] Onsal M, Cumhur B, Demir Y, et al.Rotor design optimization of a new flux-assisted consequent pole spoke-type permanent magnet torque motor for low- speed applications[J]. IEEE Transactions on Mag- netics, 2018, 54(11): 8206005.
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