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
