Modelling and optimisation of the surface-mounted permanent magnet machine with multi-level array magnets

An analytical and optimisation method is presented to improve the air-gap magnetic field of the surface-mounted permanent magnet machine with multi-level array magnets, which can reduce air-gap magnetic field harmonics and torque ripple. Different from the conventional analytical method (AM) around the entire single-magnet pole, the modelling method of multi-level equal-thickness ferrite magnets with different remanences for improving the air-gap flux density is investigated. Considering the influence of air-gap relative permeability by stator slots and multi-level magnet remanences on the air-gap flux density, the proposed AM for improving air-gap flux density is derived by analysing the slotless air-gap flux density and slotted air-gap relative permeability. The cogging torque is predicted with energy method by analysing the tangential magnetic field distribution at stator slots. Then, the back electromotive force is predicted by analysing the winding distribution and radial air-gap flux density. Based on the proposed AM, the simulated annealing particle swarm optimisation algorithm is used by optimising the widths and thicknesses of the multi-level array magnets to further reduce torque ripple and increase output torque. Finally, the accuracy of the proposed AM is verified by comparing with the finite element method.