Unbalanced magnetic forces in permanent magnet brushless machines with diametrically asymmetric phase windings

A general analytical model, formulated in 2-D polar coordinates, is developed to predict the unbalanced magnetic force which results in permanent magnet brushless AC and DC machines having a diametrically asymmetric disposition of slots and phase windings. It is shown that the unbalanced magnetic force can be significant in machines having a fractional ratio of slot number to pole number, especially when the electric loading is high. The developed model is validated by finite element calculations on 9-slot/8-pole and 3-slot/2-pole machines.