Purpose

In semi-analytical modeling of spoke-type permanent-magnet (PM) machines (STPMM), the saturation effect is usually neglected (i.e. iron parts are considered to be infinitely permeable) and the PM magnetization is assumed tangential (i.e. magnetization pattern is considered to be tangential-parallel). This paper aims to present an improved two-dimensional (2D) subdomain technique for STPMM with the PM magnetization orientation in quasi-Cartesian coordinates by using hyperbolic functions considering non-homogeneous Neumann boundary conditions (BCs) in non-periodic regions and by applying the interfaces conditions (ICs) in both directions (i.e. t- and θ edges ICs).

Design/methodology/approach

The polar coordinate system is transformed into a quasi-Cartesian coordinate system. The rotor and stator regions are divided into primary subdomains, and a partial differential equation (PDE) is assigned to each subdomain. In the PM region, the magnetization orientation is considered in the equations. By applying BCs, the general solution of the equations is determined, and by applying the ICs, the corresponding coefficients are determined.

Findings

Using the proposed coordinate system, the general solution of PDEs and their coefficients can mathematically be simplified. The magnetic field and non-intrinsic unbalanced magnetic forces (UMF) calculations have been performed for three different values of iron core relative permeability (200, 800 and ∞), as well as different magnetization orientation values (135 and 80 degrees). The semi-analytical model based on the subdomain technique is compared with those obtained by the 2D finite-element analysis (FEA). Results disclose that the PM magnetization angle can affect directly the performance characteristics of the STPMM.

Originality/value

A new model for prediction of electromagnetic performances in the STPMM takes into account magnetization direction, and soft magnetic material relative permeability in a pseudo-Cartesian coordinate system by using subdomain technique is presented.

中文翻译：

---

考虑磁化方向和有限软磁材料磁导率的辐条式永磁电机性能计算的改进模型

目的

在辐条式永磁（PM）机器（STPMM）的半分析建模中，通常忽略饱和效应（即，铁部件被认为是无限渗透的），并且PM磁化被假定为切向的（即，考虑了磁化方式）切向平行）。本文旨在通过考虑非周期区域中的非均匀诺伊曼边界条件（BCs）的双曲线函数并通过应用双线性函数，针对准直角坐标系中具有PM磁化取向的STPMM提出一种改进的二维（2D）子域技术在两个方向（即t-和θ边沿IC）上都接触条件（IC）。

设计/方法/方法

极坐标系被转换为准笛卡尔坐标系。转子和定子区域被划分为主子域，并且偏微分方程（PDE）被分配给每个子域。在PM区域中，在等式中考虑了磁化取向。通过应用BC，可以确定方程的一般解，通过应用IC，可以确定相应的系数。

发现

使用所提出的坐标系，可以在数学上简化PDE及其系数的一般解。对于铁芯相对磁导率的三个不同值（200、800和∞）以及不同的磁化取向值（135和80度），已执行了磁场和非固有不平衡磁力（UMF）计算。将基于子域技术的半分析模型与通过2D有限元分析（FEA）获得的模型进行比较。结果表明，PM磁化角会直接影响STPMM的性能特征。

创意/价值

考虑到磁化方向，建立了一种新的STPMM电磁性能预测模型，并通过子域技术给出了伪笛卡尔坐标系中软磁材料的相对磁导率。