Analytical Model of the Slotless Double-Sided Axial Flux Permanent-Magnet Brushless Machines

Abstract

Analytical approaches, if possible, are suggested for saving the simulation time in the design stage of the electrical machines. This benefit is highlighted when the optimization issues including too many iterations are desired. Hence, this paper presents a 2-D analytical model for magnetic field distribution based on the sub-domain method in a slotless double-sided axial flux permanent-magnet (PM) brushless machines (AFPMBMs) with internal-rotor-external-stators. According to this method, the machine cross-section is divided into the appropriate number of sub-regions and the related partial differential equations (PDEs) extracted from Maxwell equations are formed for magnetic vector potential in each sub-region. Applying curl on the obtained results leads to calculating the magnetic flux density components in each sub-region. Based on the superposition theorem, the analytical procedure is utilized in the two separate steps where in the first step the magnetic flux is originated by only PMs with various magnetization patterns (i.e., parallel, ideal Halbach, 2-segment Halbach and bar magnet in shifting magnetization patterns) and the armature currents are zero. In the second step, all PMs are inactivated and only armature currents affect the magnetic flux distribution. Finally, the obtained analytical results are compared with those of the Finite element method (FEM) to confirm the accuracy of the proposed analytical model. The extracted results reveal the benefit of the analytical model for replacing instead of the FEM to predict the magnetic flux density component in the presented AFPMBMs in a shorter time.