3-D Analytical Model of Axial-Flux Permanent Magnet Machine With Segmented Multipole-Halbach Array

This paper presents a 3-D analytical model of an axial-flux permanent magnet (AFPM) machine with a segmented multipole-Halbach PM array. Closed-form solutions are self-consistently derived in terms of modified Bessel functions of the first- and the second-kind by solving analytically Laplace and Poisson equations by the method of magnetic scalar potential subject to the appropriate boundary conditions. In the preceding studies, their formulations are based on a 2-D or quasi 3-D geometry, and their discussions are often limited to the magnetic fields with low-poles of the regular PM. The proposed model successfully provides more rigorous and widely applicable expressions for magnetic fields, back-electromotive force, Lorentz torque and torque constant without limitations on the number of poles and the arrangements of the PM. Behavior of the torque constant is then shown against the number of poles ranging widely from low-poles to high-poles of the regular PM, the standard-Halbach PM and the multipole-Halbach PM for changeable geometrical parameters. The obtained results are of much use in understanding intrinsically the performance characteristics of the AFPM.