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, particularly 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. In addition, the unbalanced magnetic force has been measured on a prototype 3-slot/2-pole machine and shown to be in excellent agreement with predicted results.