开关磁阻电机转子径向电磁合力的解析建模
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摘要
由于开关磁阻电机的双凸极结构及磁饱和特性的存在,运转过程中转子径向电磁力的表征缺乏系统有效的方法,造成电机转子振动和噪声分析困难。该文综合等效电路和麦克斯韦应力法,给出了单定子线圈激励下转子所受径向电磁力的表达式。在六对绕组分别采用方波电流和叠合电流激励的工况下,推导了偏心转子运转过程中所受径向电磁合力的解析表达式。在额定转速下,分析了转子所受径向电磁合力的时间历程和频谱分布规律。电磁有限元仿真计算表明该解析模型具有较高的精度,为后续分析开关磁阻电机转子的机电耦合振动奠定了基础。该文建模方法还可用于不同定转子极数的其他开关磁阻电机转子在运转过程中的径向电磁合力建模。
Due to double salient pole structure and magnetic saturation characteristic of switched reluctance motor(SRM), electromagnetic radial force expression of the rotor during the operation has been lack of a systematic and effective method, which makes it difficult to analyze vibration and noise.In this paper, equivalent circuit and Maxwell stress method was integrated to get radial electromagnetic force formula of rotor excited by a single stator coil. When the six pair windings are excited by square wave current or overlap current, the analytical functions of radial electromagnetic resultant in eccentric rotor are deduced, respectively. The time course and spectrum distribution of radical resultants are analyzed at rated speed. Through the simulation of electromagnetic finite element, it is proved that this analytical model has higher accuracy, which lays a foundation for subsequent rotor's electromechanical coupling vibration in SRM. The method could also be used to model the radial electromagnetic resultant of the rotor in other SRM with different numbers of stator and rotor poles.
Due to double salient pole structure and magnetic saturation characteristic of switched reluctance motor(SRM), electromagnetic radial force expression of the rotor during the operation has been lack of a systematic and effective method, which makes it difficult to analyze vibration and noise.In this paper, equivalent circuit and Maxwell stress method was integrated to get radial electromagnetic force formula of rotor excited by a single stator coil. When the six pair windings are excited by square wave current or overlap current, the analytical functions of radial electromagnetic resultant in eccentric rotor are deduced, respectively. The time course and spectrum distribution of radical resultants are analyzed at rated speed. Through the simulation of electromagnetic finite element, it is proved that this analytical model has higher accuracy, which lays a foundation for subsequent rotor's electromechanical coupling vibration in SRM. The method could also be used to model the radial electromagnetic resultant of the rotor in other SRM with different numbers of stator and rotor poles.
引文
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[6]Zhang Jingjun,Long Rong,Zhang Haijun,et al.Analytical and FEM modeling of electromagnetic radial force for switched reluctance motor[J].Applied Mechanics&Materials,2012,121-126(4):3765-3769.
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[8]陈凌,王宏华,谭超.基于麦克斯韦应力法的双绕组无轴承开关磁阻电机新型数学模型[J].电机与控制学报,2017,21(11):9-18.Chen Ling,Wang Honghua,Tan Chao.Innovative mathematical model for dual-winding bearingless switched reluctance motor based on Maxwell stress tensor method[J].Electric Machines and Control,2017,21(11):9-18
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[11]Gan Chun,Wu Jianhua,Shen Mengjie,et al.Investigation of skewing effects on the vibration reduction of three-phase switched reluctance motors[J].IEEE Transactions on Magnetics,2015,51(9):1-9.
[12]Hu Yanfang,Ding Wen,Wang Tao,et al.Investigation on a multi-mode switched reluctance motor:design,optimization,electromagnetic analysis and experiment[J].IEEE Transactions on Industrial Electronics,2017,64(12):9886-9895.
[13]孙玉坤,袁野,黄永红,等.磁悬浮开关磁阻电机及其关键技术发展综述[J].电工技术学报,2015,30(22):1-8.Sun Yukun,Yuan Ye,Huang Yonghong,et al.Development of the bearingless switched reluctance motor and its key technologies[J].Transactions of China Electrotechnical Society,2015,30(22):1-8.
[14]张鑫,王秀和,杨玉波.基于改进磁场分割法的开关磁阻电机径向力波抑制能力解析计算[J].电工技术学报,2015,30(22):9-18.Zhang Xin,Wang Xiuhe,Yang Yubo.The computation of vibration reduction capacity for switched reluctance motor based on improved magnetic field partition method[J].Transactions of China Electrotechnical Society,2015,30(22):9-18.
[15]曹鑫,邓智泉,杨钢,等.无轴承开关磁阻电机麦克斯韦应力法数学模型[J].中国电机工程学报,2009,29(3):78-83.Cao Xin,Deng Zhiquan,Yang Gang,et al.Mathematical model of bearingless switched reluctance motors based on Maxwell stress tensor method[J].Proceedings of the CSEE,2009,29(3):78-83.
[16]Husain I,Radun A,Nairus J.Unbalanced force calculation in switched-reluctance machines[J].IEEETransactions on Magnetics,2000,36(1):330-338.
[17]刘闯,朱旭勇,卿湘文.开关磁阻电机转子动力学建模与分析[J].中国电机工程学报,2008,28(3):83-89.Liu Chuang,Zhu Xuyong,Qing Xiangwen.Modeling and analysis of switched reluctance machine considering rotor dynamics[J].Proceedings of the CSEE,2008,28(3):83-89.
[18]刘慧娟.Ansoft Maxwell 13电机电磁场实例分析[M].北京:国防工业出版社,2014.
[2]蔡燕,张东学.开关磁阻电机新型转子齿形对转矩脉动抑制的仿真研究[J].电工技术学报,2015,30(增刊2):64-70.Cai Yan,Zhang Dongxue.Simulation study on torque ripple reduction of a switched reluctance motor using new rotor tooth[J].Transactions of China Electrotechnical Society,2015,30(S2):64-70.
[3]Wang Xilian,Ge Baoming,Wang Jin,et al.Radial force analytic modeling for a novel bearingless switched reluctance motor when considering rotor eccentricity[J].Electric Machines&Power Systems,2014,42(6):544-553.
[4]Guo Xiaoqiang,Zhong Rui,Zhao Longpan,et al.Method for radial vibration modeling in switched reluctance motor[J].IET Electric Power Applications,2016,10(9):834-842.
[5]杨艳,邓智泉,曹鑫,等.无轴承开关磁阻电机径向电磁力模型[J].电机与控制学报,2009,13(3):377-382.Yang Yan,Deng Zhiquan,Cao Xin,et al.Magnetic radial force model of bearingless switched reluctance motors[J].Electric Machines and Control,2009,13(3):377-382.
[6]Zhang Jingjun,Long Rong,Zhang Haijun,et al.Analytical and FEM modeling of electromagnetic radial force for switched reluctance motor[J].Applied Mechanics&Materials,2012,121-126(4):3765-3769.
[7]Wang Xilian,Tan Qiuhong,Liu Xiaoyun,et al.Improved radial force modeling and rotor suspension dynamics simulation studies for double-winding bearingless switched reluctance motor[J].Electric Machines&Power Systems,2016,45(1):111-120.
[8]陈凌,王宏华,谭超.基于麦克斯韦应力法的双绕组无轴承开关磁阻电机新型数学模型[J].电机与控制学报,2017,21(11):9-18.Chen Ling,Wang Honghua,Tan Chao.Innovative mathematical model for dual-winding bearingless switched reluctance motor based on Maxwell stress tensor method[J].Electric Machines and Control,2017,21(11):9-18
[9]Weiss C P,Hofmann A,Qi F,et al.Analysis and modelling of rotor eccentricity for switched reluctance machines[C]//7th IET International Conference on Power Electronics,Machines and Drives,Manchester,UK,2014:1-6.
[10]Mao S H,Dorrell D,Tsai M C.Fast analytical determination of aligned and unaligned flux linkage in switched reluctance motors based on a magnetic circuit model[J].IEEE Transactions on Magnetics,2009,45(7):2935-2942.
[11]Gan Chun,Wu Jianhua,Shen Mengjie,et al.Investigation of skewing effects on the vibration reduction of three-phase switched reluctance motors[J].IEEE Transactions on Magnetics,2015,51(9):1-9.
[12]Hu Yanfang,Ding Wen,Wang Tao,et al.Investigation on a multi-mode switched reluctance motor:design,optimization,electromagnetic analysis and experiment[J].IEEE Transactions on Industrial Electronics,2017,64(12):9886-9895.
[13]孙玉坤,袁野,黄永红,等.磁悬浮开关磁阻电机及其关键技术发展综述[J].电工技术学报,2015,30(22):1-8.Sun Yukun,Yuan Ye,Huang Yonghong,et al.Development of the bearingless switched reluctance motor and its key technologies[J].Transactions of China Electrotechnical Society,2015,30(22):1-8.
[14]张鑫,王秀和,杨玉波.基于改进磁场分割法的开关磁阻电机径向力波抑制能力解析计算[J].电工技术学报,2015,30(22):9-18.Zhang Xin,Wang Xiuhe,Yang Yubo.The computation of vibration reduction capacity for switched reluctance motor based on improved magnetic field partition method[J].Transactions of China Electrotechnical Society,2015,30(22):9-18.
[15]曹鑫,邓智泉,杨钢,等.无轴承开关磁阻电机麦克斯韦应力法数学模型[J].中国电机工程学报,2009,29(3):78-83.Cao Xin,Deng Zhiquan,Yang Gang,et al.Mathematical model of bearingless switched reluctance motors based on Maxwell stress tensor method[J].Proceedings of the CSEE,2009,29(3):78-83.
[16]Husain I,Radun A,Nairus J.Unbalanced force calculation in switched-reluctance machines[J].IEEETransactions on Magnetics,2000,36(1):330-338.
[17]刘闯,朱旭勇,卿湘文.开关磁阻电机转子动力学建模与分析[J].中国电机工程学报,2008,28(3):83-89.Liu Chuang,Zhu Xuyong,Qing Xiangwen.Modeling and analysis of switched reluctance machine considering rotor dynamics[J].Proceedings of the CSEE,2008,28(3):83-89.
[18]刘慧娟.Ansoft Maxwell 13电机电磁场实例分析[M].北京:国防工业出版社,2014.