Abstract

Magnetic gears can be divided into two groups: uncontrollable reducers constructed on permanent magnets and controlled ones that contain, in addition to magnets, the stator winding with a frequency converter. The first group has a fixed coefficient of magnetic reduction, while, for the second group, it can be changed by means of a frequency converter. The suggested field analytical calculation method can be used to determine the functional properties of both types of these devices with a use of two Cartesian coordinates x and y. In each active region of the magnetic gear (air gaps, magnets, stator and rotor yokes, a rotor with through teeth and grooves (modulator)), the sought variables, i.e., magnetic potentials and magnetic inductions, are represented as a product of two functions, the first of which is affected by coordinate x and the other by coordinate y. These functions are also multiplied by some unknown constants, the values of which taken are from the boundary conditions of the magnetic field on the interface lines of active regions. The magnetic permeability of ferromagnetic regions (yoke, modulator rods) are assumed to be fixed, with their values being adjusted according to the calculations of magnetic circuit of the reducer. This approach makes it possible to implement the principle of superposition of magnetic fields formed by the rotor and stator sources, respectively. In this case, the calculations of the unknown constants are carried out twice for each source, since the latter have fundamentally different numbers of poles and, hence, have a different spectrum of harmonic components of the magnetomotive forces. The proposed method makes it possible to determine the magnetic inductions in working air gaps of the magnetic gear and the electromagnetic moments that act on the rotors and the stator. The results were confirmed by the experimental data. To implement the method, a set of functions available in the Mathcad mathematical program is enough.

中文翻译：

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傅立叶变量分离法计算电磁齿轮

摘要

电磁齿轮可分为两类：在永磁体上构造的不可控制的减速器，以及除磁体外还包含带变频器的定子绕组的受控齿轮。第一组具有固定的磁减小系数，而第二组可以通过变频器进行更改。建议的现场分析计算方法可通过使用两个笛卡尔坐标x和y来确定这两种类型设备的功能特性。在电磁齿轮的每个有效区域（气隙，磁体，定子和转子磁轭，具有贯通齿和槽的转子（调制器））中，所寻求的变量（即磁势和磁感应强度）表示为两个乘积的乘积函数，其中第一个受坐标x的影响，另一个受坐标y的影响。这些函数还乘以一些未知常数，这些常数的值取自有源区域界面线上的磁场边界条件。假设铁磁区域（磁轭，调制器杆）的导磁率是固定的，其值根据减速器磁路的计算进行调整。这种方法使得可以实现分别由转子和定子源形成的磁场的叠加原理。在这种情况下，对于每个电源，未知常数的计算要进行两次，因为每个电源的极数根本不同，因此，其磁通势的谐波分量的频谱也不同。所提出的方法使得可以确定在磁性齿轮的工作气隙中的磁感应以及作用在转子和定子上的电磁力矩。实验数据证实了该结果。为了实现该方法，在Mathcad数学程序中可用的一组函数就足够了。