An Analytical Method for Determining Flux Density in Surface-Mounted Permanent Magnet Machines with Unequal Magnetic Poles

An analytical method was proposed for obtaining the magnetic field distribution for surface-mounted permanent magnet machines with the structure of unequal magnetic poles. Firstly, the Laplace equation and Poisson equation were solved using the method of the separation of variables, and then the mathematical model of the motor structure with unequal magnetic poles was obtained. Secondly, according to the design parameters of the two types of prototypes motors, the flux density in the air gap region of the two types of prototypes motors was calculated, respectively. Thirdly, by comparing the results calculated using the analytical method with the results obtained using the finite element method, the analytical method proposed in this paper was proven to be effective. Moreover, the armature reaction field and the effect of the stator slotting were considered in the mathematical model as well. Overall, the analytical method presented in this paper provides a theoretical basis for the analytical calculation of motors with the structure of unequal magnetic poles.