调制式永磁齿轮气隙磁场及转矩分析计算

Analytical Calculation of Air-gap Magnetic Field and Torque of Modulated Permanent Magnetic Gears

针对有限元法(Finite element method,FEM)计算调制式永磁齿轮的气隙磁场及转矩时,计算机资源占用率过高且结构参数优化周期较长等缺点,采用'场'、'路'结合的分析方法,建立适于计算机建模的气隙磁场及转矩的数学解析模型。根据恒定磁场中的标量磁位理论,通过求解不同边界条件下的微分方程,获得调制式永磁齿轮中高速永磁圈在无调磁环状况下的气隙磁场数理模型;将引入调磁环后所产生的调制效应表示为等效磁路中的气隙磁导,进而获得调制函数,并以此建立高速永磁圈在有调磁环状况下的气隙磁场数理模型;再将低速永磁圈中的永磁体等效为电流模型,并根据电流在磁场中所受的洛仑兹力进行转矩建模。经算例计算表明,所建模型与FEM计算精度相当,但速度更快,且适于计算机程序化,易于实现调制式永磁齿轮的结构参数分析与优化。

In order to solve the defects that mass computer resource and time for parametric design or optimization in finite element method（FEM） are wasted,based on the analysis method which combined magnetic field with magnetic circuit,a concise and efficient analytical approach is put forward for the calculation of the air-gap magnetic field and torque of modulated permanent magnetic gear.Without ferromagnetic pole-pieces,a magnetic field formula is induced for the air-gap that adjacent to high speed permanent magnetic ring,according to the magnetic scalar potential theory in the static magnetic field;by the equivalent magnetic circuit methods,the ferromagnetic pole-pieces is expressed as air-gap permeance function to improve the formula;magnets of the low speed permanent magnetic ring are reduced to a distribution of equivalent current,which experiences the Lorentz force in external magnetic field for torque calculation.As the calculating results,the formula is accurate but faster than the FEM.The mathematics model is suited for programmable calculation and that will make the structural and parametric design or optimization of modulated permanent magnetic gear simple and time saving.