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.
石凡, 王宏华, 李昊, 周潼. 一种计及定转子磁极磁阻的单绕组无轴承开关磁阻电机新型数学模型[J]. 电工技术学报, 2024, 39(24): 7712-7727.
Shi Fan, Wang Honghua, Li Hao, Zhou Tong. A New Mathematical Model for Single-Winding Bearingless Switched Reluctance Motor Considering the Reluctance of Stator and Rotor Poles. Transactions of China Electrotechnical Society, 2024, 39(24): 7712-7727.
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2024, Vol. 39 
