Magnet Shape Modeling in Slotless Axial Flux Permanent Magnet Machines Under No-Load Conditions

Abstract

This paper presents a new 3D analytical model based on the Fourier–Bessel series for electromagnetic modeling of the performance of slotless axial flux permanent magnet (AFPM) machines under no-load conditions. The machine geometry is divided into different domains including the permanent magnet (PM) domain, the air-gap domain, and so on. The Laplace equation in terms of scalar magnetic potential is solved in each domain, and their solutions are expressed based on the Fourier–Bessel series to accurately consider the radial variation of the air-gap magnetic field. A 2D geometry function based on the Fourier–Bessel series is introduced to accurately consider the different PM shaping in the magnet domain. The boundary condition is then used to determine the unknown constants in the general solutions. This 3D analytical model is prepared to calculate the no-load flux linkage of stator phases while considering different PM shapes and skewing effects. Two indexes including the amplitude of the fundamental component and the total harmonic distortion (THD) of no-load phase flux linkage are considered to investigate the effect of skewed PMs and other PM shapes. The capability of the proposed 3D analytical model is also presented to calculate the air-gap magnetic field due to the stator phases for determining the inductance matrix. Finally, the accuracy of the proposed 3D analytical model is verified by comparing it with the corresponding results obtained through the finite element method (FEM) and the experiment setup.