针对无轴承开关磁阻电机现有的基于无磁饱和假设的数学模型只适用于未磁饱和工况的缺点，为宽转子单绕组无轴承开关磁阻电机建立了一种可以计及磁饱和影响的全周期径向力数学模型。首先依据该电机的磁场有限元分析结果，基于麦克斯韦应力法求出了径向力关于气隙磁密的表达式；然后对铁心材料的非线性磁化特性进行拟合，再根据该电机的等效磁路计算了计及磁饱和影响的气隙磁密；之后建立了该电机的径向力模型，并在对比分析了边缘气隙磁密和主气隙磁密对径向力的影响后，对所建径向力模型进行简化，以减小计算量和复杂度。最后利用三维有限元分析进行验证，结果表明所建径向力模型对该电机未磁饱和、部分磁饱和以及完全磁饱和工况均适用。计及磁饱和的全周期径向力模型的建立，可以为电机运行特性分析、本体优化设计以及控制策略研究提供更准确的理论参考。

The existing mathematical models based on the assumption of magnetic unsaturation for bearingless switched reluctance motors have limitations, as they are only suitable for non-magnetically saturated conditions. A comprehensive radial force mathematical model is developed for a wide rotor single-winding bearingless switched reluctance motor, taking into account the effects of magnetic saturation. Firstly, based on the finite element analysis of the motor’s magnetic field, the expression for the radial force in terms of the air gap magnetic density is derived using the Maxwell stress method. Next, the nonlinear magnetization characteristics of the iron core material are fitted, and the air gap magnetic density, accounting for the effects of magnetic saturation, is calculated using the motor’s equivalent magnetic circuit. Subsequently, the radial force model of the motor is established. After comparing and analyzing the influence of edge air gap magnetic density and main air gap flux density on the radial force, the developed radial force model is simplified to reduce computational complexity. Finally, the model is validated through finite element analysis. The results indicate that the established radial mathematic model is applicable to the motor under conditions of magnetic unsaturation, partial magnetic saturation, and complete magnetic saturation. The development of a full-period radial force model considering magnetic saturation provides a more accurate theoretical reference for the analysis of motor operating characteristics, structural optimization design, and control strategy research.

国家自然科学基金项目(51977103)；江苏省重点研发计划项目(BE2021094)；南京工程学院科技创新基金项目(YKJ202208)