The effect of geometrical parameters and materials on the distribution of magnetic field density in a permanent magnet synchronous motor through analytical modeling

Analytical modeling in the early stages of designing electric machines has a significant value in terms of time and accuracy. In this article, an analytical method for modeling the magnetic field distribution in the air gap and magnets of a permanent magnet synchronous motor based on the calculation of the scalar potential vector is presented. In this modeling, which is presented based on the sub-domain modeling method, to reduce the complexity of the problem, the motor under study is divided into two sub-domains, including magnets and air gap, and Maxwell's equations are solved within these sub-domains with specific boundary conditions, and finally, two analytical relationships dependent on the geometrical variables and materials used in the motor under study was presented to estimate the size of the field density in the subdomains. The modeling method is based on the calculation of the scalar potential vector and the estimation of the magnetic field density distribution in each subdomain, which is based on solving the equations of the Laplacian/Poisson field obtained in polar coordinates. The obtained results are important from two points of view, firstly, in the modeling done, the effect of changing the geometrical parameters and materials on the distribution of the magnetic field density in a permanent magnet synchronous motor can be easily investigated, and on the other hand, due to the complex and time-consuming calculations Finite element simulation software in calculating the distribution of magnetic fields in electric machines. The obtained results show that the modeling done is suitable for use in design programs, to avoid long-term calculations by finite element simulations.