Analytical prediction of magnetic field distribution in spoke-type permanent-magnet synchronous machines accounting for bridge saturation and magnet shape

This paper presents an analytical model for the prediction of magnetic field distribution in spoke-type permanent-magnet synchronous machines with rectangular magnets and magnetic bridges. The influence of saturation is considered. The magnetic bridges are equivalent to fan-shaped saturation regions. On the basis of the same pole-arc angle and identical magnetic energy, one rectangular magnet is simplified to two fan-shaped regions. The entire field domain is divided into eight types of simple subdomains, i.e., shaft, inner magnetic bridge, inner fan-shaped magnet, outer fan-shaped magnet, outer magnetic bridge, air gap, slot opening, and slot. The effect of magnetic field caused by armature reaction on the saturation of magnetic bridges is considered. The analytical expression of each subdomain is derived and the field solution is obtained by the boundary conditions. The analytical results at the no-load and on-load conditions are verified with the finite-element method.