This article proposes a new hybrid analytical and numerical finite element (FE) based method for calculating ac eddy current losses in wire windings and demonstrates its applicability for axial flux permanent magnet electric machines. The method takes into account three-dimensional (3-D) field effects in order to achieve accurate results and yet greatly reduce computational efforts. The new 3-D FE-based method is advantageous as it employs minimum simplifications and considers the end turns in the eddy current path, the magnetic flux density variation along the effective length of coils, and the field fringing and leakage, which ultimately increases the accuracy of simulations. This study is one of the first ones to compare meticulous 3-D finite element analysis (FEA) models with more approximate, but faster solution methods, which can be employed in the optimization process. The accuracy of the 3-D FEA calculations has been confirmed through tests on a prototype axial flux permanent magnet machine. The proposed method is applicable for cases with majority of ac copper losses induced due to external magnetic flux sources, such as permanent magnets. Examples of such machines designs are coreless or open slot PM machines with conductors sizes smaller than skin depth.

中文翻译：

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计算永磁电机交流绕组损耗的方法和新 3D FEA 和分析混合技术概述

本文提出了一种新的基于混合分析和数值有限元 (FE) 的方法，用于计算绕组中的交流涡流损耗，并证明其适用于轴向磁通永磁电机。该方法考虑了三维 (3-D) 场效应，以实现准确的结果并大大减少计算工作量。新的基于 3-D FE 的方法具有优势，因为它采用了最小的简化，并考虑了涡流路径中的端匝、沿线圈有效长度的磁通密度变化以及场边缘和泄漏，最终增加了模拟的准确性。这项研究是最早将细致的 3-D 有限元分析 (FEA) 模型与更近似但更快的求解方法进行比较的研究之一，可以在优化过程中使用。3-D FEA 计算的准确性已通过对原型轴向通量永磁电机的测试得到证实。所提出的方法适用于大部分由外部磁通量源（例如永磁体）引起的交流铜损的情况。这种机器设计的例子是导体尺寸小于趋肤深度的无芯或开槽永磁电机。