电工技术学报  2024, Vol. 39 Issue (24): 7712-7727    DOI: 10.19595/j.cnki.1000-6753.tces.232201
电机及其系统 |
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
石凡1, 王宏华2, 李昊1, 周潼1
1.河海大学电气与动力工程学院 南京 211100;
2.河海大学人工智能与自动化学院 常州 213000
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
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摘要 该文提出一种计及定转子磁极磁阻的单绕组无轴承开关磁阻电机(SWBSRM)新型数学模型,以解决此电机现有虚位移法建模中存在的径向悬浮力误差较大、定转子齿极中线对齐位置处电磁转矩波形不连续和径向悬浮力波形凹陷以及不便于建立磁饱和模型问题。首先,建立SWBSRM定转子极交叠区线性数学模型:提出一种高精度的计算椭圆形边缘气隙磁路长度的解析方法,解决定转子齿极中线对齐位置处存在的转矩波形不连续和悬浮力波形凹陷问题;此外,提出在建立定转子极交叠区无磁饱和数学模型时计及定转子磁极磁阻,并将气隙磁压表示为关于绕组磁动势的线性函数以更精确地计算气隙磁压,可显著减小悬浮力误差。其次,建立计及磁饱和的SWBSRM定转子极交叠区数学模型:采用分段线性函数拟合气隙磁压和绕组磁动势之间的非线性关系,提出具有高拟合精度的分段点选取规律,可较精确地计算悬浮力和转矩。然后,建立适用于多工况的SWBSRM定转子极非交叠区数学模型,从而与定转子极交叠区数学模型构成一个相周期内的完整数学模型。最后,通过与SWBSRM现有虚位移法模型和有限元模型的计算结果对比,验证了所建模型的优良性能。
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石凡
王宏华
李昊
周潼
关键词 单绕组无轴承开关磁阻电机边缘气隙磁路磁极磁阻磁饱和数学模型    
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.
Key wordsSingle-winding bearingless switched reluctance motor    edge gap magnetic circuit    magnetic pole reluctance    magnetic saturation    mathematical model   
收稿日期: 2024-01-02     
PACS: TM352  
基金资助:国家自然科学基金资助项目(51477042)
通讯作者: 王宏华 男,1963年生,教授,博士生导师,研究方向为电力电子与运动控制系统、先进控制理论及应用。E-mail: wanghonghua@263.net   
作者简介: 石 凡 女,1994年生,博士研究生,研究方向为无轴承开关磁阻电机优化设计及振动抑制技术。E-mail: 18751809142@163.com
引用本文:   
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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