采用改进子域模型的表贴式永磁游标电机磁场解析计算  

Analytical Calculation of Magnetic Field in Surface-Mounted Permanent Magnet Vernier Machine Based on Improved Subdomain Model

作　　者：常勇[1] 包广清 许瑾[2] 邹明宝 姬伟伟 CHANG Yong;BAO Guangqing;XU Jin;ZOU Mingbao;JI Weiwei(College of Electrical Engineering and Information Engineering,Lanzhou University of Technology,Lanzhou 730050,China;School of Electronics and Information Engineering,Southwest Petroleum University,Chengdu 610500,China;Lanzhou Electric Machinery Co.,Ltd.,Lanzhou 730300,China)

机构地区：[1]兰州理工大学电气工程与信息工程学院,兰州730050 [2]西南石油大学电气信息学院,成都610500 [3]兰州电机股份有限公司,兰州730300

出　　处：《西安交通大学学报》2023年第7期62-73,共12页Journal of Xi'an Jiaotong University

基　　金：国家自然科学基金资助项目(51967012);甘肃省重点研发计划资助项目(20YF8GA055);甘肃省青年科技基金计划资助项目(22JR5RA807)。

摘　　要：针对传统子域解析方法在计算气隙谐波磁场丰富的表贴式永磁游标电机磁场时,出现系数矩阵维数高、计算过程复杂的问题,提出了一种改进的子域解析模型。该模型通过坐标变换,将各子域矢量磁位在二维极坐标系下的拉普拉斯方程或泊松方程变换为准笛卡尔坐标系下的方程形式,利用分离变量法计算各子域矢量磁位方程的通解,根据边界条件计算待定系数,以双曲函数的形式表示各矢量磁位的解析解。计算了空载反电动势、气隙磁密和电磁转矩,与传统子域解析方法、有限元法计算结果进行对比。仿真结果表明:改进子域解析方法与有限元法的相对误差均小于1%;与传统子域解析方法相比,空载反电动势、气隙磁密和电磁转矩计算精度分别提升了1.7%、0.87%和3.66%。实验样机的空载反电动势计算波形和测试波形也基本吻合,验证了该方法的有效性和可行性。An improved subdomain analytical method is proposed to solve the problem that traditional subdomain analytical methods have a high dimension of the coefficient matrix and complex calculation process in the calculation of magnetic field of surface-mounted permanent magnet vernier machines(SPMVMs)rich in airgap harmonic magnetic fields.The proposed method transforms the Laplace equation or Poisson equation of the vector magnetic potential of each subdomain in the two-dimensional polar coordinate system into the equation form in the quasi-Cartesian coordinate system through coordinate transformation and uses the separation variable method to obtain the general solution of the vector magnetic potential equation of each subdomain.According to the boundary conditions,the undetermined coefficients are calculated and the analytical solutions of each vector magnetic potential are expressed in the form of hyperbolic functions.Finally,the no-load back-EMF,airgap magnetic density,and electromagnetic torque are calculated and compared with those obtained using the traditional subdomain analytical method and finite element method(FEM).The results show that the relative error is less than 1%between the improved subdomain analytical method and the FEM.Compared with the traditional subdomain analytical method,the calculation accuracy of no-load back EMF,airgap magnetic density,and electromagnetic torque is improved by 1.7%,0.87%,and 3.66%respectively.The calculated waveforms of the no-load back-EMF for the experimental prototype are consistent with the measured waveforms,which verify the effectiveness and feasibility of the proposed analytical method.

关 键 词：表贴式永磁游标电机 子域解析模型 双曲函数 分离变量法 准笛卡尔坐标系 有限元法 

分 类 号：TM614[电气工程—电力系统及自动化]