Nonlinear Model for Halbach Array Axial Flux Permeant Magnet Motor in Stator and Rotor Reference Frames Based on Harmonic Modeling Technique

This article presents nonlinear models based on the harmonic modeling (HM) technique for Halbach array AFPMM in Cartesian coordinate, where the stator winding is a dual three-phase winding. The nonlinear model can consider the saturation effect by embedding the permeability of the stator into the magnetic field solution. Then, a nonlinear model based on the HM technique for the Halbach array AFPMM in the rotor reference frame is derived, it can calculate the magnetic field and electromagnetic force density acting on the rotor surface. The accuracy of the developed nonlinear HM models for the Halbach array AFPMM is verified by the linear model and FEM. The characteristics of the electromagnetic force density acting on the stator and rotor are analyzed. Results show that the spatial order of the electromagnetic force density acting on the stator and rotor are the same, whereas the frequency characteristics are different, so it is necessary to develop the nonlinear model in the rotor reference frame. The nonlinear models developed can quickly and accurately calculate the electromagnetic performance of Halbach array AFPMM in the stator and rotor reference frames, guiding the early design of Halbach array AFPMM, vibration, and noise calculation of AFPMM with the outer rotor.