摘要：现有的磁悬浮开关磁阻电机数学模型推导思路为：先用等效磁路法得到以磁导表示的电感矩阵；再通过有限元辅助分割磁场法得到磁导的解析式，将其代入电感矩阵；最后通过虚位移法得到径向力表达式。该方法计算比较繁琐，并且忽略了正交方向两个径向力的耦合而使计算结果不够精确。本文提出了一种新的气隙磁导计算方法，通过气隙磁场储能推导出了磁悬浮开关磁阻电机的径向力数学模型。该数学模型考虑了相互垂直方向偏移量对径向力的影响，并将每个定子极通过的磁通均考虑在内，准确的描述了电机的径向力特性，为电机的悬浮控制系统设计提供了可靠的理论基础。以一台样机为例，建立有限元仿真模型，仿真结果证明了该数学模型的正确性和有效性。

关键词：磁悬浮开关磁阻电机；数学模型；径向力；有限元分析
Abstract: The derivation idea in most mathematical models of bearingless switched reluctance motor (BSRM) is followed: first, the inductance matrix is constructed based on the magnetic equivalent circuits; then the gap permeance is cut apart on the basis of finiteelement analysis and the mathematical formulas are separately derived; finally, the new mathematical formulas of radial force are derived based on the virtual displacement method. This method is relatively more complicated and inaccurate for ignoring the radial force vertical coupling. A new method was proposed to calculate the airgap permeance. Accordingly, the radial force mathematical model was derived based on the airgap magnetic field energy. Considering the influence of vertical offset on the radial force and every stator flux, it could accurately describe the characteristic of the radial force. It provided reliable theoretical basis for the designing of motor suspension control system. According to a prototype, a finiteelement simulation model was established. Simulation results show the validity of the mathematical model.

Key words: bearingless switched reluctance motors; mathematical model; radial force; finiteelement analysis