A Preliminary Investigation of Computer-Aided Schwarz-Christoffel Transformation for Electric Machine Design and Analysis

Abstract

An alternative method to finite element analysis (FEA) for electric machine design and analysis is presented that applies Schwarz-Christoffel (SC) conformal mapping theory using the SC toolbox for MATLABreg that has appeared in the previous literature. In this method, a two-dimensional (2D) developed machine cross-section domain is mapped via SC transformation to a concentric cylinder domain where solutions for the electromagnetic (EM) fields are known. These solutions are mapped back to the original domain, thus solving the original problem. All mapping is done via the SC toolbox. Examples are given in which the procedure is used to calculate the EM field in the air gap of and the force on the rotor of various 2D developed machine cross-sections. The numerical accuracy of the results is verified by comparing the solutions as the air gap gets small with magnetic equivalent circuit (MEC)-derived coenergy solutions