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Journal of ZheJiang University (Engineering Science)  2026, Vol. 60 Issue (12): 2571-2580    DOI: 10.3785/j.issn.1008-973X.2026.12.003
    
Torque performance analysis and multi-condition optimization of asymmetric magnetic poles permanent magnet motor
Mingjun XU(),Huihui GENG*(),Wenjing HU,Shilong YAN,Wenyu LI,Shiqiang LIU,Yinuo WANG
School of Transportation and Vehicle Engineering, Shandong University of Technology, Zibo 255000, China
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Abstract  

An asymmetric magnetic pole (AMP) rotor topology was proposed in order to enhance the torque density of interior permanent magnet synchronous motors (IPMSMs). The AMP structure was constructed based on an alternating N/S pole arrangement. An analytical expression for the electromagnetic torque was established by deriving the magnetomotive force distribution function of the AMP rotor and incorporating the energy method. The analytical expression revealed the underlying mechanism by which the AMP design influenced the output torque. A coordinated optimization strategy for multi-operating scenarios was developed in order to improve the comprehensive performance of the asymmetric magnetic pole permanent magnet synchronous motor (AMP-PMSM) under multiple operating conditions. Four representative operating points under typical working conditions were selected. A torque–efficiency coordinated optimization across the entire speed range was achieved for the proposed motor with the dual objective of simultaneously increasing output torque and reducing loss. The optimized motor exhibited a significant improvement in output torque at all operating points. The torque ripple was generally reduced by more than 5%, and the cogging torque decreased by 0.42 N·m. The sum of the core losses and the permanent magnet eddy current losses was reduced by 2.7% and 3% at the corresponding operating point in the medium and high speed operating range, respectively, while the maximum efficiency was improved by 1%. Electromagnetic simulations and prototype experiments were conducted to validate the performance of the proposed AMP-PMSM. Results demonstrated that the optimized motor achieved superior torque capability and operating efficiency.



Key words: permanent magnet motor      asymmetric magnetic pole      multi-objective optimization      multiple operating condition      electromagnetic characteristic     
Received: 18 September 2025      Published: 21 October 2026
CLC:  TM 351  
Fund:  国家自然科学基金资助项目(52275261,52505269);山东省自然科学基金资助项目(ZR2025MS914).
Corresponding Authors: Huihui GENG     E-mail: 20402010115@stumail.sdut.edu.cn;huihuigeng@sdut.edu.cn
Cite this article:

Mingjun XU,Huihui GENG,Wenjing HU,Shilong YAN,Wenyu LI,Shiqiang LIU,Yinuo WANG. Torque performance analysis and multi-condition optimization of asymmetric magnetic poles permanent magnet motor. Journal of ZheJiang University (Engineering Science), 2026, 60(12): 2571-2580.

URL:

https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2026.12.003     OR     https://www.zjujournals.com/eng/Y2026/V60/I12/2571


非对称磁极永磁电机转矩性能分析与多工况优化

为了提升内置式永磁同步电机(IPMSMs)的转矩密度,提出非对称磁极(AMP)转子拓扑结构. 该结构基于N/S极交替排布构建非对称磁极,通过推导非对称磁极转子的磁动势分布函数,结合能量法建立电机输出转矩的解析表达式,揭示非对称磁极设计对输出转矩的作用机理. 为了提升非对称磁极永磁电机在多工况下的综合性能,提出面向多运行工况的协同优化策略. 通过选取4种典型工况下的代表工作点,以同时提升输出转矩和降低损耗为目标,实现了对非对称磁极永磁电机全速域范围内转矩与效率的协同优化. 优化后的电机在各个工作点下的输出转矩均有显著提升,转矩脉动普遍降低5%以上,齿槽转矩减小0.42 N·m,在中高速运行区间,铁芯损耗与永磁体涡流损耗之和在对应工作点下分别降低了2.7%和3%,最高效率提升了1%. 通过电磁仿真与样机试验,对提出的非对称磁极永磁电机的输出性能进行验证. 结果表明,优化后的新型非对称磁极永磁电机具有优良的转矩输出能力与运行效率.


关键词: 永磁电机,  非对称磁极,  多目标优化,  多运行工况,  电磁特性 
Fig.1 Structure diagram of asymmetric magnetic poles permanent magnet synchronous motor
参数数值参数数值
相数3定子外径/mm160
极对数4定子内径/mm107.4
定子齿数48转子外径/mm105.8
额定功率/kW5永磁体材料NdFe35
额定转速/(r·min?1)3 000定、转子铁芯材料DW310-35
Tab.1 Main parameter of motor
Fig.2 Magnetic field lines and magnetic flux density cloud map
Fig.3 Rotor magnetomotive force of asymmetric magnetic poles permanent magnet synchronous motor
Fig.4 Fundamental amplitude of rotor magnetomotive force under different pole arc angle
Fig.5 Comparison of rotor magnetomotive force harmonic
Fig.6 Schematic diagram of AMP-PMSM design parameter
设计变量初始值约束范围
第一永磁体充磁方向长度lpm1/mm65~7
第一永磁体宽度wpm1/mm12.512~14
第二永磁体充磁方向长度lpm2/mm65~7
第二永磁体宽度wpm2/mm1514~16
第三永磁体充磁方向长度lpm3/mm43~5
第三永磁体宽度wpm3/mm98~10
第一永磁体夹角η1/(°)4035~55
第三永磁体夹角η3/(°)8070~90
Tab.2 Table of design variable value range
Fig.7 Distribution of drive motor operating condition
Fig.8 Distribution of Pareto front design points at different operating points
权重系数数值权重系数数值
C10.43C60.27
C20.31C70.55
C30.26C80.45
C40.43C90.55
C50.30C100.45
Tab.3 Weight coefficient table
Fig.9 Distribution plot of parameter matching coefficient
参数优化前优化后参数优化前优化后
l1/mm66.8w1/mm12.513
l2/mm65.5w2/mm1514.8
l3/mm44.9w3/mm99.2
η1/(°)4054η3/(°)8089
Tab.4 Comparison table of optimized parameters for AMP-PMSM
状态Tavg1/(N·m)Trip1/%Tcog/(N·m)Tavg2/(N·m)Trip2/%
优化前19.312.40.714.514.7
优化后20.16.90.28157.2
状态Tavg3/(N·m)(Cl3+El3)/WTavg4/(N·m)(Cl4+El4)/W
优化前11.389.38186.3
优化后11.686.98.2180.8
Tab.5 Comparison table of optimization results for AMP-PMSM
Fig.10 Output torque at different operating points
Fig.11 Comparison diagram of output torque
Fig.12 Comparison diagram of cogging torque
Fig.13 Comparison of sum of loss at operating point Op3
Fig.14 Comparison of sum of loss at operating point Op4
Fig.15 Core loss map before optimization
Fig.16 Core loss map after optimization
Fig.17 Efficiency map of AMP-PMSM before optimization
Fig.18 Efficiency map of AMP-PMSM after optimization
Fig.19 Efficiency map of conventional V-type permanent magnet motor
Fig.20 Prototype and back electromotive force test bench
Fig.21 Simulation and experimental result of no-load back electromotive force
Fig.22 Test bench of cogging torque
Fig.23 Test result of cogging torque
Fig.24 Test bench of load characteristic
Fig.25 Output torque at different armature current
Fig.26 Comparison of output torque under rated condition
[1]   史立伟, 刘政委, 乔志伟, 等 基于磁热耦合法的非对称混合磁极永磁电机热分析[J]. 浙江大学学报(工学版), 2024, 58 (1): 207- 218
Shi Liwei, Liu Zhengwei, Qiao Zhiwei, et al Thermal analysis of asymmetric hybrid pole permanent magnet motor based on magneto-thermal coupling method[J]. Journal of Zhejiang University (Engineering Science), 2024, 58 (1): 207- 218
doi: 10.3785/j.issn.1008-973X.2024.01.022
[2]   李烽, 王凯, 高培伟, 等 不同极槽配合交替极永磁电机齿槽转矩和转矩脉动的研究[J]. 中国电机工程学报, 2022, 42 (17): 6491- 6498
Li Feng, Wang Kai, Gao Peiwei, et al Investigation of cogging torque and torque ripple in consequent pole permanent magnet machine with different slot/pole number combinations[J]. Proceedings of the CSEE, 2022, 42 (17): 6491- 6498
doi: 10.13334/j.0258-8013.pcsee.211344
[3]   Zhu X, Xiang Z, Quan L, et al Multimode optimization design methodology for a flux-controllable stator permanent magnet memory motor considering driving cycles[J]. IEEE Transactions on Industrial Electronics, 2018, 65 (7): 5353- 5366
doi: 10.1109/TIE.2017.2777408
[4]   史涔溦, 彭琳, 张振, 等 电压源激励下表贴式永磁同步电机退磁故障建模与分析[J]. 电工技术学报, 2025, 40 (8): 2430- 2440
Shi Cenwei, Peng Lin, Zhang Zhen, et al Modeling and analysis of demagnetization fault in surface mounted permanent magnet synchronous motors with voltage source excitation[J]. Transactions of China Electrotechnical Society, 2025, 40 (8): 2430- 2440
[5]   Qiao Z, Shi L, Li F, et al Characteristics analysis of magnetic-pole-shift in an asymmetric hybrid pole-permanent magnet-assisted synchronous reluctance motor[J]. IEEE Journal of Emerging and Selected Topics in Power Electronics, 2025, 13 (2): 1394- 1405
doi: 10.1109/JESTPE.2024.3466168
[6]   Zhu Z Q, Xiao Y 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
doi: 10.1109/tmag.2021.3076418
[7]   Xiao Y, Zhu Z Q, Wang S S, et al A novel asymmetric interior permanent magnet machine for electric vehicles[J]. IEEE Transactions on Energy Conversion, 2021, 36 (3): 2404- 2415
doi: 10.1109/TEC.2021.3055260
[8]   王冰洁, 朱孝勇, 郑诗玥, 等 一种非对称混合永磁拓扑的电机转矩特性分析[J]. 微电机, 2022, 55 (3): 21- 25
Wang Bingjie, Zhu Xiaoyong, Zheng Shiyue, et al Torque characteristics analysis of a hybrid permanent magnet motor with asymmetric topology design[J]. Micromotors, 2022, 55 (3): 21- 25
doi: 10.3969/j.issn.1001-6848.2022.03.005
[9]   杨明磊, 钟再敏, 邵仲书, 等 三段式Halbach阵列永磁电机解析建模与研究[J]. 西安交通大学学报, 2023, 57 (11): 130- 141
Yang Minglei, Zhong Zaimin, Shao Zhongshu, et al Analytical modeling and research of three-segment Halbach array permanent magnet motor[J]. Journal of Xi’an Jiaotong University, 2023, 57 (11): 130- 141
[10]   吕品, 马浩天, 苏勋文, 等 非均匀Halbach阵列外转子永磁同步电机分析与优化[J]. 哈尔滨理工大学学报, 2025, 30 (4): 58- 70
Lv Pin, Ma Haotian, Su Xunwen, et al Analysis and optimization of outer-rotor permanent magnet synchronous motor with non-uniform halbach array[J]. Journal of Harbin University of Science and Technology, 2025, 30 (4): 58- 70
[11]   吕品, 王宁, 商泽华, 等. 三段式双层Halbach混合极永磁直线电机优化设计[J/OL]. 哈尔滨理工大学学报, [2025-07-08]. https://link.cnki.net/urlid/23.1404.n.20250708.0837.002.
[12]   贾晨, 吉敬华, 凌志健, 等 基于非气隙侧调制的永磁电机绕组因数提升机理[J]. 中国电机工程学报, 2025, 45 (4): 1260- 1270
Jia Chen, Ji Jinghua, Ling Zhijian, et al Mechanism of winding factor enhancement permanent magnet motor based on non-air-gap side modulation[J]. Proceedings of the CSEE, 2025, 45 (4): 1260- 1270
doi: 10.13334/j.0258-8013.pcsee.241497
[13]   Zhao Y, Li D, Liang Z, et al A high power factor PM vernier machine with segmented stator[J]. IEEE Transactions on Transportation Electrification, 2024, 10 (4): 9294- 9303
doi: 10.1109/TTE.2024.3353925
[14]   徐磊, 朱孝勇, 张超, 等 磁极径向组合轴向磁场永磁电机转矩品质分析与优化设计[J]. 中国电机工程学报, 2021, 41 (6): 1971- 1982
Xu Lei, Zhu Xiaoyong, Zhang Chao, et al Torque quality analysis and optimization design of axial field machine with radial combined permanent magnet poles[J]. Proceedings of the CSEE, 2021, 41 (6): 1971- 1982
doi: 10.13334/j.0258-8013.pcsee.202252
[15]   曹永娟, 冯亮亮, 毛瑞, 等 轴向磁场永磁记忆电机多目标分层优化设计[J]. 中国电机工程学报, 2021, 41 (6): 1983- 1991
Cao Yongjuan, Feng Liangliang, Mao Rui, et al Multi-objective stratified optimization design of axial-flux permanent magnet memory motor[J]. Proceedings of the Chinese Society for Electrical Engineering, 2021, 41 (6): 1983- 1991
[16]   谢颖, 肖志博, 蔡蔚, 等 新型调制齿结构内置式轮毂电机设计分析与转矩脉动优化[J]. 电机与控制学报, 2025, 29 (7): 142- 151
Xie Ying, Xiao Zhibo, Cai Wei, et al Design analysis and torque ripple optimization of novel modulated tooth structure internal hub motor[J]. Electric Machines and Control, 2025, 29 (7): 142- 151
doi: 10.15938/j.emc.2025.07.014
[17]   Zhu X, Bai J, Xiang Z, et al Low-vibration design and investigation of a consequent-pole PM motor utilizing composite MMF and subarea permeance[J]. IEEE Transactions on Transportation Electrification, 2025, 11 (1): 3568- 3579
doi: 10.1109/TTE.2024.3439406
[18]   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- 1236
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- 1236
doi: 10.13334/j.0258-8013.pcsee.241164
[19]   Zhou X, Zhu X, Wu W, et al Multi-objective optimization design of variable-saliency-ratio PM motor considering driving cycles[J]. IEEE Transactions on Industrial Electronics, 2021, 68 (8): 6516- 6526
doi: 10.1109/TIE.2020.3007106
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