Abstract：The accurate analysis and calculation of the electromagnetic field distribution characteristics are the basis for the performance optimization of active magnetic bearing (AMB). At present, the influence of eddy current and the nonlinearity of material permeability were rarely both considered in the magnetic field analysis of AMB. Therefore, the exponential equation was used to fit the magnetization curve of the silicon steel sheet to consider the nonlinearity of magnetic permeability f the material, the dynamic relative magnetic permeability was introduced to account for the influence of the eddy current. Then a nonlinear equivalent magnetic circuit model (NEMC) of radial AMB was established with the edge effect, stator and rotor core reluctance, nonlinear magnetic permeability, eddy current influence and real-time control current. Using this model, the magnetic field distribution in the air-gap was calculated when the rotor had a static displacement of 0.1mm. The results are in good agreement with the finite element simulation (FEM) results, and the relative error in the opposite of magnetic poles is basically less than 3%. In addition, the influence of eddy current caused by rotor period vibration on magnetic flux and electromagnetic force was analyzed. After considering the eddy current, the magnetic flux and the electromagnetic force decrease, and the higher the vibration frequency, the greater the attenuation.
叶品州, 李红伟, 于文涛, 仲慧. 考虑材料非线性及涡流影响的径向电磁轴承等效磁路建模[J]. 电工技术学报, 2020, 35(9): 1858-1867.
Ye Pinzhou, Li Hongwei, Yu Wentao, Zhong Hui. Equivalent Magnetic Circuit Modeling of Radial Active Magnetic Bearing Considering Material Nonlinearity and Eddy Current Effects. Transactions of China Electrotechnical Society, 2020, 35(9): 1858-1867.
[1] Schweitzer G, Maslen E H.Magnetic bearings: theory, design, and application to rotating machinery[M]. BeHin: Springer-Verlag Berlin and Heidelberg, 2009. [2] 张维煜, 朱熀秋, 袁野. 磁悬浮轴承应用发展及关键技术综述[J]. 电工技术学报, 2015, 30(12): 12-20. Zhang Weiyu, Zhu Huangqiu, Yuan Ye.Study on key technologies and applications of magnetic bearings[J]. Transactions of China Electrotechnical Society, 2015, 30(12): 12-20. [3] Le Yun, Fang Jiancheng.Design and optimization of a radial magnetic bearing for high-speed motor with flexible rotor[J]. IEEE Transactions on Magnetics, 2015, 51(6): 1-13. [4] Wang Dongxiong, Wang Nianxian, Ye Chun, et al.Research on analytical bearing capacity model of active magnetic bearings based on magnetic satur- ation[J]. IET Electric Power Applications, 2017, 11(9): 1548-1557. [5] 张云鹏, 薛博文, 刘淑琴, 等. 基于气隙磁通边缘效应的轴向混合磁轴承承载力解析计算[J]. 电机与控制学报, 2014, 18(9): 54-59, 67. Zhang Yunpeng, Xue Bowen, Liu Shuqin, et al.Calculation of electromagnetic force of axial hybrid magnetic bearing based on fringe effect of magnetic flux[J]. Electric Machines and Control, 2014, 18(9): 54-59, 67. [6] 张云鹏, 刘淑琴, 李红伟, 等. 基于磁路分析的周向混合磁轴承径向承载力解析计算[J]. 电工技术学报, 2012, 27(5): 137-142. Zhang Yunpeng, Liu Shuqin, Li Hongwei, et al.Calculation of radial electromagnetic force of axial hybrid magnetic bearing based on magnetic circuit analysis[J]. Transactions of China Electrotechnical Society, 2012, 27(5): 137-142. [7] 赵旭升, 邓智泉. 永磁偏置径向磁轴承的原理分析与参数设计[J]. 电工技术学报, 2011, 26(11): 127-134. Zhao Xusheng, Deng Zhiquan.Principle analysis and parameter design of permanent magnet[J]. Transa- ctions of China Electrotechnical Society, 2011, 26(11): 127-134. [8] 吴磊涛, 王东, 苏振中, 等. 异极式永磁偏置径向磁轴承的建模与实验[J].电工技术学报, 2018, 33(5): 1051-1057. Wu Leitao, Wang Dong, Su Zhenzhong, et al.Modeling and experiment of permanent magnetic biased radial heter-polar magnetic bearing[J]. Transactions of China Electrotechnical Society, 2018, 33(5): 1051-1057. [9] 朱熀秋, 丁书玲. 计及边缘效应的交流混合磁轴承建模[J]. 中国电机工程学报, 2016, 36(23): 6528-6535. Zhu Huangqiu, Ding Shuling.Modeling for AC hybrid magnetic bearings considering edge effect[J]. Proceedings of the CSEE, 2016, 36(23): 6528-6535. [10] Fariba S, Akbar R, Mohammad M.2D analytical model for heteropolar active magnetic bearings considering eccentricity[J]. IET Electric Power Applications, 2018, 12(5): 614-626. [11] Aleksei R, Alexander S.Losses estimation and modelling in active magnetic bearings[C]//IEEE Sixteenth European conference on Power Electronics and Applications, Lappeenranta, Finland, 2014: 1-8. [12] Sun Yanhua, Yick-Sing Ho.Dynamic stiffnesses of active magnetic thrust bearing including eddy- current effects[J]. IEEE Transaction on Magnetics, 2009, 45(1): 139-149. [13] 董宏林, 闫颖鑫, 王科俊, 等. 径向电磁轴承气隙磁阻近似计算方法分析[J]. 机械工程学报, 2007, 43(8): 43-47. Dong Honglin, Yan Yingxin, Wang Kejun, et al.Analysis of approximate calculation method for air gap reluctance of radial magnetic bearings[J]. Chinese Journal of Mechanical Engineering, 2007, 43(8): 43-47. [14] 林其壬, 赵佑民. 磁路设计原理[M]. 北京: 机械工业出版社, 1987. [15] Kang K, Palazzolo A.Homopolar magnetic bearing saturation effects on rotating machinery vibration[J]. IEEE Transactiions on Magnetics, 2012, 48(6): 984-1994. [16] Jalal N.A generalized dynamical model for trans- formers with saturation and hysteresis effects[J]. Mathematical and Computer Modelling of Dynamical Systems, 2013, 19(1): 51-66. [17] Meeker D C, Maslen E H.An augmented circuit model for magnetic bearings including eddy currents, fringing, and leakage[J]. IEEE Transactions on Magnetics, 1996, 32(4): 3219-3227. [18] Le Yun, Fang Jiancheng.Dynamic circuit model of a radial magnetic bearing with permanent magnet bias and laminated cores[J]. International Journal of Applied Electromagnetics and Mechanics, 2014, 46(1): 43-60. [19] 高辉, 徐龙祥. 主动磁悬浮轴承系统拍振现象分析[J]. 机械工程学报, 2011, 47(13): 104-112. Gao Hui, Xu Longxiang.Analysis of beat vibration for active magnetic bearing system[J]. Journal of Mechanical Engineering, 2011, 47(13): 104-112.
2020, Vol. 35 
