A Semi-Analytical Method for the Analysis of Electrical Machines with Complex 3D Salient Geometries

This research proposes the novel Schwarz-Christoffel harmonic analysis (SCHA) method based on three main steps: slicing the geometry to reduce the problem from 3-D to 2-D, applying Schwarz-Christoffel (SC) conformal mapping to transform the air gap domain to a simpler rectangular domain, and finally computing the field distribution with harmonic analysis (HA). It is further shown how to apply the proposed method to an axial variable flux reluctance motor (AVFRM) to show how it handles 3-D topologies with complex salient geometries. This semi-analytical (SA) method demonstrates less than 4% discrepancy in average output torque calculation compared to the traditional 3-D finite element method (FEM), with 1050 times fewer degrees of freedom (DoFs), and 20 times fewer DoFs than 2-D FEM, all while still accounting for the exact representation of the tooth and slot shapes. Thus, tasks such as tooth-shape optimization can be accelerated.