Abstract: AFMPMGs had serious axial and tangential leakages and low torque density. Based on AFMPMG, an external magnetic ring was introduced to make it a dual-excitation modulation AFMPMG(DEM-AFMPMG) structure. As the DEM-AFMPMG low-speed permanent magnet rotor was clamped between the inner and outer magnetizing rings, the axial and tangential leakage flux of the AFMPMG could be converted into useful harmonics, which increased the output torque and torque density of the DEM-AFMPMG. Although the 3D finite element method taken into account the magnetic leakages at the end of permanent magnet gears and had the advantage of high calculation accuracy, it also maked the occupancy of computer resources too high and the optimization period of structural parameters too long. A mathematical and physical model for calculating DEM-AFMPMG air gap magnetic field and electromagnetic torque was proposed herein based on subdomain method. This method could equate the 3D model to the 2D model, but all factors of the 3D model were included, so that the calculation accuracy was equivalented to that of the 3D finite element. The calculation examples show that the calculation accuracy based on subdomain method is equal to that of 3D finite element method(the calculation errors of air gap magnetic density and electromagnetic torque are less than 5% and the calculation errors of torque density are less than 1.5%), but the calculation speed of subdomain method is faster and it is easy to realize computer programming, which facilitates the analysis and optimization of structural parameters of DEM-AFMPMG. 

Key words: axial field modulation permanent magnet gear(AFMPMG), air-gap magnetic tightness, electromagnetic torque, subdomain method

摘要： 轴向式磁场调制永磁齿轮（AFMPMG）存在轴向及切向漏磁严重及转矩密度偏低等问题。在AFMPMG基础上引入了一个外调磁环，使之构成一种双励磁、双调制的AFMPMG（DEM-AFMPMG）结构，由于DEM-AFMPMG低速永磁转子夹在内、外两个调磁环之间，因此可将AFMPMG轴向及切向漏磁通转化成有用谐波，从而增大DEM-AFMPMG输出转矩及转矩密度。虽然3D有限元法计及了永磁齿轮端部漏磁，具有计算精度高等优点，但同时也使计算机资源占用率过高且结构参数优化周期较长,针对此，提出了一种基于子域法的计算DEM-AFMPMG气隙磁场及电磁转矩数学模型，该方法可将3D模型等效为2D模型，但包括了3D模型的所有因素。算例计算结果表明，基于子域法模型的计算精度与3D有限元法的计算精度相当（气隙磁通密度及电磁转矩的计算误差均不大于5%，转矩密度的计算误差不大于1.5%），但子域法模型计算速度更快，且易于实现计算机程序化，更有利于DEM-AFMPMG的结构参数分析与优化。

关键词: 轴向式磁场调制永磁齿轮, 气隙磁通密度, 电磁转矩, 子域法