偏心式谐波磁力齿轮气隙磁场分式线性变换解析模型  

Analytical Model of Magnetic Field of Eccentric Harmonic Magnetic Gear Using Fractional Linear Transformation Method

作　　者：章跃进[1] 章君达 Zhang Yuejin;Zhang Junda(School of Mechatronics Engineering and Automation Shanghai University Shanghai 200072 Chin)

机构地区：[1]上海大学机电工程与自动化学院,上海200072

出　　处：《电工技术学报》2018年第15期3572-3577,共6页Transactions of China Electrotechnical Society

摘　　要：采用分式线性变换法解析计算偏心式谐波磁力齿轮气隙磁场。将z平面的两个非同心圆变换成w平面的两个同心圆,给定两同心圆磁位差为1的边界条件,并求解两同心圆环形区域内的拉普拉斯方程。经反变换得到转子偏心时的气隙相对磁导函数,修正无偏心时定转子永磁产生的气隙磁场。根据叠加原理合成偏心情况下的定转子气隙磁场,从而获得气隙磁场径向和切向分量。利用麦克斯韦应力张量法计算谐波磁力齿轮的电磁转矩。通过与有限元法计算结果进行比较,验证了该文解析方法的正确性。The air-gap magnetic field distribution of an eccentric harmonic magnetic gear is analyzed by applying the fractional linear transformation method. Two eccentric circles in the z-plane are mapped on two concentric circles in the w-plane. The Laplace field equation in the concentric annular is easily solved by assuming unit difference in magnetic potential between two circles. After the field expressions are mapped back into the z-plane the relative permeance functions due to the rotor eccentricity can then be obtained. The magnetic field distribution can be estimated by modulating the field distribution in the air gap without rotor eccentricity by the relative permeance function. The resultant air-gap magnetic fields can be obtained by superposition of the stator and rotor field components with rotor eccentricity. When the radial and tangential components of flux densities are calculated, the electromagnetic torque of the magnetic harmonic gear is determined by the Maxwell stress tensor. Finite element results confirm the validity of the analytical prediction.

关 键 词：谐波磁力齿轮 转子偏心 分式线性变换 相对磁导函数 电磁转矩 

分 类 号：TM153[电气工程—电工理论与新技术]