Closed-Form Solution for Axial Flux Permanent-Magnet Machines With a Traction Application Study

This research attempts to find a new closed-form solution for axial flux permanent-magnet (AFPM) machines and applies it in a traction application example. The machine types considered are with toroid and overlapping windings. The proposed closed-form solution includes analytical derivations for winding lengths, resistances, and inductances as functions of fundamental air-gap flux density and inner-to-outer diameter ratio. Finite-element analysis is used to verify the accuracy of the proposed analytical calculations. Furthermore, a parametric analysis is performed on inductances, resistances, phase back-EMFs, phase terminal voltages, efficiencies, and torque speed capability to compare for both winding types. The proposed solution should assist traction machine designers to ascertain benefits and limitations of the toroid and overlapping winding types in traction application as well as to achieve faster design results.