Calation of air gap flux density for the surface motor

An analytical method was presented to predict the three-dimensional (3-D) magnetic flux density distribution in the air gap produced by NdFeB permanent magnets of the surface motor. First, the analytical model of the surface motor was established, and Laplace equations of magnetic scalar potential and a series of boundary conditions were given. Then, the analytical expressions of magnet field strength and magnet flux density were obtained in the air gap of produced by NdFeB permanent magnets by the method of separation of variables. Finally, Comparisons the analytical results and finite element results, and the error never exceed five percent. Therefore, high precision has been derived. The analytical field results provide a basis for comparative studies, design optimization, and machine dynamic modeling of the surface motor.