基于精确子域模型的永磁直线同步电机空载磁场解析计算

Analytical Calculation of No-Load Magnetic Field in Permanent Magnet Linear Synchronous Motors Based on an Accurate Subdomain Model

准确计算永磁直线同步电机(PMLSM)磁场分布是得到电机参数及性能的前提,而建立精确的数学模型则是求解电机磁场问题的关键。鉴于PMLSM传统解析理论在齿槽效应对气隙磁场影响的求解上存在局限性,提出PMLSM精确子域模型以得到精确磁场分布。计及永磁体相对磁导率、电机槽深、所有槽与槽之间对磁场分布的相互影响,采用标量磁位分别建立PMLSM永磁体、气隙、槽子域拉普拉斯方程。根据各子域交界面边界条件,基于傅里叶级数法,列出所有边界条件方程组,并建立端部等效模型,求解得到各子域标量磁位和空载磁通密度分布,进而探讨各个齿槽、端部区域对气隙磁场空间分布的影响。有限元结果证明了所用解析方法的准确性。

Accurate calculation of the magnetic field distribution in permanent magnet linear synchronous motor(PMLSM)is required to obtain the parameters and performance,and the establishment of an accurate mathematical model is the key to solving the magnetic field problem.To avoid the limitations of the traditional analytical theory of PMLSM in solving the slot effect on air gap magnetic field,an accurate subdomain model of PMLSM is proposed to obtain the accurate magnetic field distribution.By taking into account the relative magnetic permeability of the permanent magnet(PM),slot depth and mutual influence of all slots on the magnetic field distribution,the Laplace equation of permanent magnet subdomain,airgap subdomain and slot subdomain are established in the scalar magnetic potential.According to the boundary conditions of each subdomain interface,all boundary condition equations are set up based on the Fourier series method,and the equivalent model of end area is established.The scalar magnetic potential and no-load flux density distribution of each subdomain are then solved.The slot and end effects on the spatial distribution of air gap magnetic field are discussed.The accuracy of analytical model is validated by the finite element method(FEM)results.