永磁同步电机转子偏心磁场解析计算

Analytical Calculation for Magnetic Field of Permanent Magnet Synchronous Motors with Rotor Eccentricity

为了快速准确计算两极平行充磁实心圆柱式永磁同步电机(SCPMSM)各种转子偏心参数下的磁场分布,提供研究转子偏心对电机性能影响的有效方法,利用子区域法和摄动法,在二维极坐标平面内建立了考虑定子齿槽效应时的SCPMSM转子偏心磁场解析模型;将求解场域划分为永磁体、气隙和定子槽3类子区域,分别用对应的控制函数来表达,各区域之间用边界条件连接,利用边界条件求出控制方程通解的各个谐波系数。根据摄动理论,将磁场的0阶分量和1阶分量叠加获得相应子域转子偏心磁场分布,利用麦克斯韦应力张量法计算了转子静态偏心以及动态偏心引起的不平衡磁拉力。以一台2极12槽平行充磁SCPMSM为例,将转子偏心磁场以及静态偏心和动态偏心不平衡磁拉力的解析计算结果与有限元计算结果进行对比,验证了解析模型的正确性。

An analytical model for magnetic field of solid cylindrical permanent magnet synchronous motor(SCPMSM)with rotor eccentricity,considering the stator slotting effect,is developed based on subdomain and perturbation methods in 2D polar coordinates to quickly and accurately calculate the magnetic field distribution in two-pole parallel magnetised SCPMSM with rotor eccentricity with various parameters and to provide an effective method of studying the influence of rotor eccentricity on motor performances.The analysis is performed by dividing the solution domain into three subdomains,viz.permanent magnet,air gap and stator slots.Those subdomains are expressed by corresponding governing equations,and are connected by boundary conditions.The harmonic coefficients in the general solutions of these governing equations are determined by the boundary conditions.The magnetic field distributions of corresponding subdomains in the motor with rotor eccentricity are obtained by superposing the first-order component of the magnetic field onto the zeroth-order component according to the perturbation theory.The unbalanced magnetic pulls under both rotor static and dynamic eccentricity modes are calculated using Maxwell stress tensor method.A 2-pole and 12-slot parallel magnetised SCPMSM is taken as an example,and its rotor eccentric magnetic field and unbalanced magnetic pulls under two eccentricity modes are calculated by the proposed model and are compared with those by a finite element method.Result verifies the correctness of the analytical model.