A New Mathematical Model for Single-Winding Bearingless Switched Reluctance Motor Considering the Reluctance of Stator and Rotor Poles
Shi Fan1, Wang Honghua2, Li Hao1, Zhou Tong1
1. School of Electrical and Power Engineering Hohai University Nanjing 211100 China; 2. College of Artificial Intelligence and Automation Hohai University Changzhou 213000 China
Abstract At the center alignment position of the stator and rotor teeth, a large radial suspension force error, discontinuous electromagnetic torque waveform, and concave radial suspension force waveform exist. Moreover, establishing a magnetic saturated model for a single-winding bearingless switched reluctance motor (SWBSRM) is challenging using existing virtual displacement modeling methods. This paper proposes a new mathematical model of SWBSRM considering the reluctance of stator and rotor poles. Firstly, a mathematical model of the overlapping region of stator and rotor teeth of SWBSRM without magnetic saturation is established. A new analytical method for calculating the length of the elliptical edge air gap magnetic circuit in SWBSRM is proposed to solve the problems of discontinuous electromagnetic torque waveform and concave radial suspension force waveform when the centerlines of stator and rotor teeth are aligned, and improve the accuracy of the model. In addition, the air gap’s magnetic pressure is not equal to the magnetic electromotive force of the winding and the reluctance of stator and rotor poles cannot be ignored when magnetic saturation does not occur in the overlapping region of stator and rotor teeth. Therefore, the reluctance of stator and rotor poles should be considered, and the magnetic pressure of the air gap should be represented as a linear function of the magnetic electromotive force. Thus, the error of radial suspension force can be reduced, and the design accuracy of the motor body is improved. Secondly, a mathematical model of the overlapping region of stator and rotor teeth of SWBSRM with magnetic saturation is established. A selection rule of piecewise points is proposed using a piecewise linear function to fit the nonlinear relationship between the magnetic pressure of the air gap and the magnetic electromotive force of the winding. As a result, the radial suspension force and electromagnetic torque can be calculated accurately. Then, a mathematical model of the non-overlapping region of the stator and rotor teeth of SWBSRM is established and applied to multiple working conditions. Thus, A complete mathematical model of SWBSRM within one phase period is formed. Finally, the calculation results of the proposed new mathematical model of SWBSRM are compared with those of the existing virtual displacement method model and the finite element model. The results indicate that the standard error of the calculation results of the radial suspension force combined force of the proposed mathematical model of the overlapping region of stator and rotor teeth of SWBSRM without magnetic saturation is reduced by 90%, and the standard error of the calculation results of its electromagnetic torque is reduced by 78% compared to those of the existing model, verifying the feasibility and effectiveness of the proposed method.
Shi Fan,Wang Honghua,Li Hao等. A New Mathematical Model for Single-Winding Bearingless Switched Reluctance Motor Considering the Reluctance of Stator and Rotor Poles[J]. Transactions of China Electrotechnical Society, 2024, 39(24): 7712-7727.
[1] Schweitzer G, Maslen E H, Buehler P, et al.Magnetic bearings: theory, design, and application to rotating machinery[M]. Berlin: Springer-Verlag Berlin Heidelberg, 2009. [2] Xu Zhenyao, Yu Qingguo, Zhang Fengge.Design and analysis of asymmetric rotor pole type bearingless switched reluctance motor[J]. CES Transactions on Electrical Machines and Systems, 2022, 6(1): 3-10. [3] 孙德博, 胡艳芳, 牛峰, 等. 开关磁阻电机调速系统故障诊断和容错控制方法研究现状及展望[J]. 电工技术学报, 2022, 37(9): 2211-2229. Sun Debo, Hu Yanfang, Niu Feng, et al.Status and prospect of fault diagnosis and tolerant control methods for switched reluctance motor drive system[J]. Transactions of China Electrotechnical Society, 2022, 37(9): 2211-2229. [4] 丁文, 李可, 付海刚. 一种12/10极模块化定子混合励磁开关磁阻电机分析[J]. 电工技术学报, 2022, 37(8): 1948-1958. Ding Wen, Li Ke, Fu Haigang, et al.Analysis of a 12/10-pole modular-stator hybrid-excited switched reluctance machine[J]. Transactions of China Elec-trotechnical Society, 2022, 37(8): 1948-1958. [5] 贲彤, 王进, 陈龙, 等. 考虑磁致伸缩逆效应的非晶合金开关磁阻电机减振方法[J]. 电工技术学报, 2023, 38(10): 2648-2660. Ben Tong, Wang Jin, Chen Long, et al.Vibration reduction method of switched reluctance motor with amorphous alloy cores based on inverse-magnetostriction effect[J]. Transactions of China Electrotechnical Society, 2023, 38(10): 2648-2660. [6] 于丰源, 陈昊, 闫文举, 等. 宽窄定子极轴向磁通开关磁阻电机的设计与分析[J]. 电工技术学报, 2023, 38(5): 1261-1274. Yu Fengyuan, Chen Hao, Yan Wenju, et al.Design and characteristic analysis of a wide-narrow stator poles axial flux switched reluctance machine[J]. Transactions of China Electrotechnical Society, 2023, 38(5): 1261-1274. [7] Shimada K, Takemoto M, Chiba A, et al.Radial forces in switched reluctance type bearingless motor[C]//The 9th Symposium on Electromagnetics and Dynamics, 1997: 547-552. [8] Takemoto M, Chiba A, Fukao T.A new control method of bearingless switched reluctance motors using square-wave currents[C]//IEEE Power Engin-eering Society Winter Meeting, Singapore, 2000: 375-380. [9] Wang Zelin, Cao Xin, Deng Zhiquan, et al.Electromagnetic modeling and investigation for bearingless switched reluctance motor considering magnetic saturation[J]. IEEE Transactions on Energy Conversion, 2023, 38(1): 122-133. [10] 孙玉坤, 刘羡飞, 王德明, 等. 基于有限元分析的磁悬浮开关磁阻电机数学模型的全角度拓展[J]. 电工技术学报, 2007, 22(9): 34-39. Sun Yukun, Liu Xianfei, Wang Deming, et al.Extension of mathematical model to full angle for bearingless switched reluctance motors based on finite-element analysis[J]. Transactions of China Electro-technical Society, 2007, 22(9): 34-39. [11] 王喜莲, 崔睿珍, 郝毅, 等. 考虑磁饱和的共悬浮绕组式无轴承开关磁阻电机径向力模型[J]. 电机与控制学报, 2021, 25(6): 46-53. Wang Xilian, Cui Ruizhen, Hao Yi, et al.Radial Force model of a bearingless switched reluctance motor with sharing suspension windings considering magnetic saturation[J]. Electric Machines and Control, 2021, 25(6): 46-53. [12] 杨帆, 袁野, 祝贵, 等. 12/14磁悬浮开关磁阻电机悬浮力全周期模型构建[J]. 电工技术学报, 2023, 38(2): 330-339. Yang Fan, Yuan Ye, Zhu Gui, et al.Suspension force modeling for 12/14 bearingless switched reluctance motor considering flux multi teeth hinge[J]. Transa-ctions of China Electrotechnical Society, 2023, 38(2): 330-339. [13] 李群. 单绕组无轴承开关磁阻电动机控制策略的研究[D]. 南京: 南京航空航天大学, 2013. [14] 朱志莹, 张巍, 朱海浪, 等. 轴向永磁磁悬浮飞轮电机损耗计算与温度场分析[J]. 电气工程学报, 2022, 17(4): 174-180. Zhu Zhiying, Zhang Wei, Zhu Hailang, et al.Analysis of loss and temperature field of axial permanent magnet magnetic bearingless flywheel machine[J]. Journal of Electrical Engineering, 2022, 17(4): 174-180. [15] 赵丽丹, 邓智泉, 曹鑫, 等. 12/8极单绕组无轴承开关磁阻电机绕组开路故障有限元分析[J]. 电工技术学报, 2013, 28(7): 131-137. Zhao Lidan, Deng Zhiquan, Cao Xin, et al.Finite element analysis of open circuit fault in a 12/8 single winding bearingless switched reluctance motor[J]. Transactions of China Electrotechnical Society, 2013, 28(7): 131-137. [16] 曹鑫, 刘从宇, 邓智泉, 等. 单绕组12/4极无轴承开关磁阻电机转矩和悬浮力的解耦机理与实现[J].电工技术学报, 2018, 33(15): 3527-3534. Cao Xin, Liu Congyu, Deng Zhiquan, et al.Decoupling mechanism and implementation of torque and levitation force in single-winding 12/4 bearing-less switched reluctance motor[J]. Transactions of China Electrotechnical Society, 2018, 33(15): 3527-3534. [17] 曹鑫. 12/8极无轴承开关磁阻电机的研究[D]. 南京: 南京航空航天大学, 2010. Cao Xin.Research on 12/8 bearingless switched reluctance machine[D]. Nanjing: Nanjing University of Aeronautics and Astronautics, 2010. [18] Takemoto M, Shimada K, Chiba A, et al.A design and characteristics of switched reluctance type bearingless motors[C]//Proceedings of the 4th International Symposium on Magnetic Suspension Technology, NASA, Gifu, Japan, 1998: 49-63. [19] Takemoto M, Suzuki H, Chiba A, et al.Improved analysis of a bearingless switched reluctance motor[J]. IEEE Transactions on Industry Applications, 2001, 37(1): 26-34. [20] 邓智泉, 杨钢, 张媛, 等. 一种新型的无轴承开关磁阻电机数学模型[J]. 中国电机工程学报, 2005, 25(9): 139-146. Deng Zhiquan, Yang Gang, Zhang Yuan, et al.An innovative mathematical model for a bearingless switched reluctance motor[J]. Proceedings of the CSEE, 2005, 25(9): 139-146. [21] 孙玉坤, 吴建兵, 项倩雯. 基于有限元法的磁悬浮开关磁阻电机数学模型[J]. 中国电机工程学报, 2007, 27(12): 33-40. Sun Yukun, Wu Jianbing, Xiang Qianwen.The mathematic model of bearingless switched reluctance motor based on the finite-element analysis[J]. Proceedings of the CSEE, 2007, 27(12): 33-40. [22] Takemoto M, Chiba A, Akagi H, et al.Radial force and torque of a bearingless switched reluctance motor operation in a region of magnetic saturation[J]. IEEE Transactions on Industry Applications, 2004, 40(1): 103-112. [23] Takemoto M, Chiba A, Akagi H, et al.Torque and suspension force in a bearingless switched reluctance motor[J]. Electrical Engineering in Japan, 2006, 157(2): 72-82. [24] 项倩雯. 飞轮电池用五自由度单绕组磁悬浮开关磁阻电机参数设计及运行控制[D]. 镇江: 江苏大学, 2013. Xiang Qianwen.Parameter design and operation control of 5-DOF single-winding bearingless switched reluctance motor for flywheel batteries[D]. Zhenjiang: Jiangsu University, 2013.
2024, Vol. 39 
