Analytical Calculation of Complex Relative Permeance Function and Magnetic Field in Slotted Permanent Magnet Synchronous Machines

In order to analyze accurately the airgap magnetic field of the slotted permanent magnet synchronous machine (PMSM) taking into account the influence of slotting effects, this article proposes an analytical method for calculating the complex relative permeance function. Based on one tooth pitch of the machine as the solution model, the governing Laplace field equation of the airgap region is solved analytically in the polar coordinate system. According to the boundary conditions between the slot and airgap region, the analytical expressions of the radial and tangential components of the complex relative permeance function are derived. With this complex permeance, the no-load radial and tangential airgap magnetic fields of the internal and external slotted PMSM with different slot/pole combinations are obtained. The accuracy of the analytical model is validated by the results of finite element analysis. With good simplicity and generality, this model can be an effective means for further study of motor performance.

Automated summary

This article proposes an analytical method for accurately analyzing the airgap magnetic field of slotted permanent magnet synchronous machines, taking into account the influence of slotting effects by calculating the complex relative permeance function. The analytical model shows good simplicity and generality, providing an effective means for further studying motor performance.