Optimization of Magnetic Pole Geometry for Field Harmonic Control in Electric Motors

Abstract

A principal source of vibration in permanent magnet motors and generators is the induced stress from the rotating permanent magnets. The harmonic content of this forcing function may excite resonant modes of vibration in the motor or surrounding structure. Thus attenuation of specific harmonics is of considerable interest. This paper describes a method for optimal shaping of the permanent magnets to eliminate one or more of these harmonics. The analytical model for an optimized 4-pole motor consisted of segmented PMs and a solid ring stator. The permanent magnets were modeled as a number of thin radially cut annular layers with specific sector angles. Changing the shape of the PMs resulted in a different flux density field and thus a different frequency spectrum of the forcing function. Attenuation of specified higher harmonics could be achieved at the expense of increasing other harmonics. For a 4-pole motor, the optimization algorithm was fairly successful at eliminating any one of the 8th, 12th or 16th harmonics. The algorithm used was developed to solve combinatorial optimization problems, and drew heavily upon principles from statistical mechanics. The final pole geometry is dependent upon the choice of the cost function used in the optimization algorithm.