Halbach阵列同心式磁力齿轮磁场分析与优化设计

Magnetic Field Computation and Optimization Design for a Concentric Magnetic Gear With Halbach Permanent-magnet Arrays

采用二维全局解析法计算Halbach阵列同心式磁力齿轮气隙磁场。求解场域划分为内外转子永磁体、内外两层气隙和调磁定子的槽形区域,3类子区域的拉普拉斯方程和泊松方程通过边界连续条件建立联系。得到内外两层气隙区域的矢量磁位磁通密度解析表达式,有利于方便、快速、精确地计算任意转子位置的电磁转矩。气隙磁场波形与二维有限元法计算波形较吻合。与径向充磁相比,Halbach阵列充磁方式所得转矩更大,且更接近正弦。运用Matlab优化工具箱中的遗传算法对Halbach阵列同心式磁力齿轮某些参数进行优化,试验结果表明计算值与测量值较为一致,证明了所提方法的正确性和有效性。

In this paper,exact 2-D analytical method is proposed to calculate the magnetic field distribution in a concentric magnetic gear with Halbach permanent-magnet arrays.The analytical method is based on the resolution of Laplace’s and Poisson’s equations for each sub-domain,i.e.,inner and outer permanent magnet rotors,inner and outer air-gaps,and slots.The globe solution is obtained using boundary and continuity conditions.Owing to obtaining the analytical expressions of air-gap flux density,any rotor position of electromagnetic torque is calculated precisely,quickly and easily.Compared air-gap magnetic field distributions computed by the analytical method with those obtained from the 2-D finite element method（FEM）,the waveform shows good agreement with the measured waveform.The torque of Halbach arrays is greater than the radial magnetization’s,and more nearly sinusoidal.The genetic algorithm optimization toolbox of Matlab（GAOT） provides a good tool for the concentric Halbach array magnetic gear’s optimization design.The calculated and measured values are more consistent,which proves the proposed method is correct and effective.