1. MOE Key Lab of Nondestructive Testing, Nanchang Hangkong University, Nanchang 330063, China;
2. College of Information Engineering, Nanchang Hangkong University, Nanchang 330063, China;
3. Power Supply Service Management Center, Jiangxi Provincial Electric Power Co., Ltd., Nanchang 330077, China;
4. College of Electrical Engineering, Zhejiang University, Hangzhou 310027, China
As for the problem of rotor strength analysis of the surface-mounted high speed permanent magnet machine with a non-magnetic alloy sleeve, the analytical solution of rotor strength was proposed based on the plane stress model of elastic mechanics. The displacement method in polar coordinate was employed to deduce the analytical solution, and the influences of the static interference fit, rotational speed and temperature gradient of rotor were taken into account in the analytical solution proposed. Then the effectiveness of the analytical solution was validated by finite element simulations and experiments, respectively. Finally, the influences of design parameters including sleeve thickness, static interference fit, rotational speed and rotor temperature on rotor stress were further investigated based on the analytical solution proposed. The simulations and experiments show that the analytical solution proposed can accurately calculate the radial stress, hoop stress and equivalent Mises stress of the rotor of surface-mounted high speed permanent magnet machine, considering the influence of temperature gradient. High speed centrifugal force and rotor heating result in significant increasing of the tensile stress in permanent magnets, meanwhile, the equivalent Mises stress of non-magnetic alloy sleeve also increases. The pre-pressure of the permanent magnet can be improved by appropriately increasing the static interference fit and sleeve thickness, so as to protect permanent magnets from the tensile stress produced by high speed centrifugal force and rotor heating.
[1] 懂剑宁,黄允凯,金龙,等. 高速永磁电机设计与分析技术综述[J].中国电机工程学报,2014, 34(27):4640-4653.
DONG Jian-ning, HUANG Yun-kai, JIN Long, et al. Review on high speed permanent magnet machine including design and analysis technologies[J]. Proceedings of the CSEE, 2014,34(27):4640-4653.
[2] 郝龙,杨金福,唐长亮,等. 变负载工况下高速永磁电机转子动力学特性试验研究[J]. 振动与冲击,2018, 37(15):1-5.
HAO Long, YANG Jin-fu, TANG Chang-liang, et al. Tests for dynamic characteristics of a high speed permanent magnet motor’s rotor under different loads [J].Journal of Vibration and Shock, 2018, 37(15): 1-5.
[3] 郑大伟,朱明刚,郑立允,等. 稀土永磁材料在永磁电机中的应用[J]. 微特电机,2015,43(4):81-84.
ZHENG Da-wei, ZHU Ming-gang, ZHENG Li-yun, et al. Application of rare earth permanent magnetic materials for permanent magnet machines[J]. Small and Special Electrical Machines, 2015, 43(4):81-84.
[4] 张昆, 汤文辉, 冉宪文. 正交各向异性CFRP 材料的本构关系及其在平板撞击模拟中的应用[J].振动与冲击, 2019, 38(22):101-106.
ZHANG Kun, TANG Wen-hui, RAN Xian-wen. Constitutive relationship of anisotropic CFRP material and its application in planar plate impact simulation[J]. Journal of Vibration and Shock, 2019, 38(22):101 -106.
[5] 邓云飞, 张 永, 安静丹, 等. TC4 钛合金力学性能测试及其本构关系研究[J].振动与冲击, 2020, 39(18):70-77.
DENG Yun-fei, ZHANG Yong, AN Jing-dan, et al. Mechanical properties and constitutive relationship of TC4 titanium alloy[J]. Journal of Vibration and Shock, 2020, 39(18):70-77.
[6] Kolondzovski Z, Arkkio A, Larjola J, et al. Power limits of high-speed permanent-magnet electrical machines for compressor applications [J]. IEEE Transactions on Energy Conversion, 2011, 26(1): 73-82.
[7] 万援,催淑梅,吴绍朋,等.扁平大功率高速永磁同步电机的护套设计及其强度优化[J].电工技术学报, 2018,33(1):55-63.
WAN Yuan, CUI Shu-mei, WU Shao-peng, et al. Design and strength optimization of the carbon fiber sleeve of high-power high-speed PMSM with flat structure[J].Transactions of China Electrotechnical Society, 2018, 33(1):55-63.
[8] Chen L, Zhu C. Rotor strength analysis for high speed permanent magnet machines [C]// Proc. Of 17th International Conference on Electrical Machines and Systems (ICEMS), Hangzhou, China, 2014, pp:65-69.
[9] 张超,朱建国,佟文明,等.高速内置式永磁转子强度分析与设计[J]. 电机与控制学报,2017,21(12):43-50.
ZHANG Chao, ZHU Jian-guo, TONG Wen-ming, et al. Strength analysis and design of high speed interior permanent magnet rotor[J]. Electric Machines and Control, 2017,21(12):43-50.
[10] Zhang F, Du G, Wang T. Rotor retaining sleeve design for a 1.12-MW high-speed PM machine [J]. IEEE Transactions on Industry Applications, 2015, 51(5): 3675-3685.
[11] Shao Y, Wang X, Gao Q, et al. Rotor strength analysis of Ultra-high speed permanent magnet synchronous motor [C]// Proc. of 22th International Conference on Electrical Machines and Systems (ICEMS), Harbin, China, 2019, pp:1-4.
[12] 王保俊,毕刘新,陈亮亮,等. 碳纤维绑扎表贴式高速永磁电机转子强度分析[J]. 浙江大学学报:工学版,2013, 47(12):2101-2110
WANG Bao-jun, BI Liu-xin, CHEN Liang-liang, et al. Strength analysis of a surface mounted high speed permanent magnetic machine rotor with cancan fiber bandage[J]. Journal of Zhejiang University: Engineering Science, 2013, 47(12):2101-2110
[13] Binder A, Schneider T, Klohr M. Fixation of buried and surface-mounted magnets in high-speed permanent-magnet synchronous machines [J]. IEEE Transactions on Industrial Electronics, 2006, 42(4): 1031-1037.
[14] 陈亮亮,祝长生,王萌. 碳纤维护套高速永磁电机热态转子强度[J]. 浙江大学学报:工学版, 2015, 49(01): 162-172.
CHEN Liang-liang, ZHU Chang-sheng, WANG Meng. Strength analysis for thermal carbon-fiber retaining rotor in high-speed permanent magnet machine [J]. Journal of Zhejiang University: Engineering Science, 2015, 49(01): 162-172.
[15] 刘威,陈进华,张驰,等. 考虑轴间填充物的高速永磁电机转子强度分析[J].电工技术学报,2018,33(5):1024-1031.
LIU Wei, CHEN Jin-hua, ZHANG Chi, et al. Strength analysis of high speed permanent magnet machine rotor with inter-shaft filling[J].Transactions of China Electrotechnical Society, 2018,33(5):1024-1031.
[16] Borisavljevic A, Polinder H, Ferreira J A. On the speed limits of permanent-magnet machines [J]. IEEE Transactions on Industrial Electronics, 2010, 57(1): 220-227.
[17] 王继强,王凤翔,鲍文博, 等. 高速永磁电机转子设计与强度分析[J]. 中国电机工程学报, 2005, 25(15): 140-145.
WANG Ji-qiang, WANG Feng-xiang, BAO Wen-bo, et al. Rotor design and strength analysis of high speed permanent magnet machine [J]. Proceedings of the CSEE, 2005, 25(15): 140-145.
[18] 程文杰,耿海鹏,冯圣, 等. 高速永磁同步电机转子强度分析[J]. 中国电机工程学报, 2012, 32(27): 87-94.
CHENG Wen-jie, GENG Hai-peng, FENG Sheng,et al. Rotor strength analysis of high-speed permanent magnet synchronous motors [J]. Proceedings of the CSEE, 2012, 32(27): 87-94.
[19] 张超,朱建国,韩雪岩. 高速表贴式永磁电机转子强度分析[J]. 中国电机工程学报, 2016, 36(17): 4719-4728.
ZHANG Chao, ZHU Jian-guo, HAN Xue-yan. Rotor strength analysis of high-speed surface mounted permanent magnet motors [J]. Proceedings of the CSEE, 2016, 36(17): 4719-4728.
[20] 陈亮亮,祝长生,蒋科坚. 含极间填充块的高速表贴式永磁同步电机转子强度分析[J]. 浙江大学学报:工学版, 2015, 49(09): 1738-1748.
CHEN Liang-liang, ZHU Chang-sheng, JIANG Ke-jian. Rotor strength analysis for high-speed surface-mounted permanent magnet synchronous motor with filled blocks between magnetic poles [J]. Journal of Zhejiang University:Engineering Science, 2015, 49(09): 1738-1748.
[21] 张凤阁,杜光辉,王天煜. 高速永磁电机转子不同保护措施的强度分析[J]. 中国电机工程学报, 2013, 33(Supplement): 195-202.
ZHANG Feng-ge, DU Guang-hui, WANG Tian-yu. Rotor strength analysis of high-speed permanent magnet under different protection measures [J]. Proceedings of the CSEE, 2013, 33(Supplement): 195-202.
[22] Chen L, Zhu C, Zhong Z, Liu B. Rotor strength analysis for high-speed segmented surface-mounted permanent magnet synchronous machines [J]. IET Electric Power Applications, 2018,12(7): 979-990.
[23] Du G, Xu W, Zhu J, et al. Rotor stress analysis for high-speed permanent magnet machines considering assembly gap and temperature gradient[J]. IEEE Transactions on Energy Conversion, 2019, 34(4): 2276-2285