Analytical solution of magnetic field in surface-inset permanent magnet machines

Accurate calculation of the airgap magnetic field was the key to design and optimize permanent-magnet machines. An accurate subdomain model for surface-inset permanent magnet machines was set up in 2D polar coordinates, and the solution regions were divided into slot subdomains in the stator, airgap subdomain and slot subdomains in the rotor. The general solution of vector magnetic potential for each subdomain was solved by the variable separation method, and the Fourier coefficients were obtained by the boundary conditions between two adjacent subdomains. The analytical model accounts for the influence of normal/consequent pole rotor structure, radial/parallel magnetization of permanent magnet, fractional-slot concentrated-windings configurations having either all or alternate teeth wound, which can be used to predict the open-circuit, armature reaction and on-load magnetic field distribution. Taking a 40 pole-48 slot surface-inset permanent magnet machine with consequent pole rotor as example, the airgap flux density waveform computed by the analytical method was compared with two-dimensional finite-element method. The comparison results confirm the validity of the analytical prediction. ©2015 Chin. Soc. for Elec. Eng.