Purpose

The purpose of this paper is to propose a two-dimensional (2-D) hybrid analytical model (HAM) in polar coordinates, combining a 2-D exact subdomain (SD) technique and magnetic equivalent circuit (MEC), for the magnetic field calculation in electrical machines at no-load and on-load conditions.

Design/methodology/approach

In this paper, the proposed technique is applied to dual-rotor permanent magnet (PM) synchronous machines. The magnetic field is computed by coupling an exact analytical model (AM), based on the formal resolution of Maxwell’s equations applied in subdomains, in regions at unitary relative permeability with a MEC, using a nodal-mesh formulation (i.e. Kirchhoff's current law), in ferromagnetic regions. The AM and MEC are connected in both directions (i.e. r- and theta-edges) of the (non-)periodicity direction (i.e. in the interface between teeth regions and all its adjacent regions as slots and/or air-gap). To provide accurate solutions, the current density distribution in slot regions is modeled by using Maxwell’s equations instead to MEC and characterized by an equivalent magnetomotive force (MMF) located in the slots, teeth and yoke.

Findings

It is found that whatever the iron core relative permeability, the developed HAM gives accurate results for both no-load and on-load conditions. Finite element analysis demonstrates the excellent results of the developed technique.

Originality/value

The main objective of this paper is to achieve a direct coupling between the AM and MEC in both directions (i.e. r- and theta-edges). The current density distribution is modeled by using Maxwell’s equations instead to MEC and characterized by an MMF.

中文翻译：

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电机磁场计算的二维混合模型：精确子域技术和磁等效电路

目的

本文的目的是提出一种极坐标中的二维 (2-D) 混合分析模型 (HAM)，结合二维精确子域 (SD) 技术和磁等效电路 (MEC)，用于磁场电机在空载和负载条件下的计算。

设计/方法/方法

在本文中，所提出的技术应用于双转子永磁 (PM) 同步电机。磁场是通过耦合精确分析模型 (AM) 来计算的，该模型基于应用在子域中的麦克斯韦方程组的形式分辨率，在具有 MEC 的单一相对磁导率区域中，使用节点网格公式（即基尔霍夫电流定律），在铁磁区。AM 和 MEC 在（非）周期性方向的两个方向（即 r 和 theta 边缘）上（即，在齿区域与其所有相邻区域之间的界面中作为槽和/或气隙）连接。为了提供准确的解决方案，槽区域中的电流密度分布通过使用麦克斯韦方程代替 MEC 进行建模，并以位于槽、齿和轭中的等效磁动势 (MMF) 为特征。

发现

发现无论铁芯的相对磁导率如何，开发的 HAM 都能为空载和负载条件提供准确的结果。有限元分析证明了所开发技术的优异结果。

原创性/价值

本文的主要目标是在两个方向（即 r 和 theta 边缘）上实现 AM 和 MEC 之间的直接耦合。电流密度分布是通过使用麦克斯韦方程而不是 MEC 来建模的，并以 MMF 为特征。