Space-harmonics modeling of an axial-flux permanent-magnet machine

The content of space harmonics in axial-flux permanent-magnet machines (AFPMMs) is an important concern to the machine designer due to its impact on the performance. In AFPMMs, the harmonics are related to the flux-density and the MMF distributions in the air gap, which are mainly determined by the permanent- magnet excitation. This paper proposes two different approaches to study the flux density in the air gap. The finite-element and analytical method are jointly developed in order to model, compare and optimize the flux density waveforms. Many optimization methods have been proposed in order to optimize the design of permanent magnet machines. In this paper, the authors investigate the optimal permanent-magnet design in order to minimize the space-harmonics distribution using the sequential quadratic programming (SQP) optimization algorithm. By selecting the appropriate PM shape and size, it is possible to remove the undesirable harmonics. Using the SQP, the permanent-magnet shape is optimized, and the harmonics content is notably reduced. The optimal solutions given by the analytical and finite element model are then validated.