An analysis method for the 3-D open-circuit air-gap magnetic field of the slotted axial flux motor

The three-dimensional (3-D) open-circuit air gap magnetic field (OCAGMF) distribution is fundamental to the design of the slotted axial flux permanent magnet motor (AFPMM). However, its calculation presents significant challenges due to geometric complexity, slotting effects, end effects, magnetic leakage, and saturation. The 3-D finite element method (FEM) is an accurate method, but it is computationally expensive. This paper proposes a high-efficiency analytical method for the 3-D OCAGMF of the AFPMM. First, the 3-D slotless OCAGMF of the slotted AFPMM, considering the curvature effect, is derived by solving the 3-D Maxwell equation in cylindrical coordinates. Next, the influence of slotting and end effects on the 3-D OCAGMF of the AFPMM is evaluated based on the 3-D relative permeance function (RPF) in the z-θ plane and the z-r plane. Then, a nonlinear magnetic equivalent circuit model (MECM) is formulated to account for magnetic leakage and saturation. Finally, the validity of the proposed analytical method is verified through the direct measurement experiment of the OCAGMF. Compared with the 3-D FEM, the analytical method presents fast calculation speed and high calculation accuracy. This work provides an effective tool for rapid optimization of the slotted AFPMM, balancing fidelity and speed for industrial applications.