Analytical and FE Modeling for the Design of Coreless Axial Flux Machines with Halbach Array and Surface PM Rotors

This paper introduces a rapid analytical modeling approach for coreless axial flux permanent magnet (AFPM) machines featuring surface-mounted and Halbach PM array rotors. The methodology employs a 2D model at an arbitrary diameter of the machine and converts AFPM machines into an equivalent linear machine. Initially, equations for PM flux density, accounting for harmonic content, are developed for both rotor types. Subsequently, a force equation is derived for the 2D equivalent machine based on the Lorentz force equation and the stator winding factor. In the final step, a torque equation at an arbitrary diameter - specifically, the average diameter in this paper - is formulated using matching boundary conditions. The developed analytical model is validated through 2D/3D finite element analysis (FEA) and experimental measurements. This analytical framework is then applied to conduct a parametric study, aiming to assess the impact of Halbach array PM rotor dimensions on the performance of a coreless AFPM machine for electric aircraft propulsion. The results of this study provide a sizing methodology for Halbach array rotors, enabling the achievement of maximum specific power density and efficiency in coreless stator AFPM machines.