Influence of Airgap Flux Density Waveform on Optimal Split Ratio and Torque Density of SPM Machines

Abstract

This chapter presents an unified analytical model for optimizing the split ratios of surface-mounted permanent magnet (SPM) machines considering various airgap flux density distributions, i.e., square (also referred to as conventional), sinusoidal (sine) and sinusoidal with third harmonic (sine+3rd), considering both overlapping windings and nonoverlapping windings. Besides, torque density under the optimal split ratios are compared for the conventional, sine and sine+3rd. It is found that harmonics in airgap flux density will lower the optimal split ratio and their influence is stronger for nonoverlapping windings compared with overlapping windings. The sine+3rd overlapping windings machines shows competence in torque density with higher value of stator slot Ns especially under high flux density ratio, reaching about 99% of the torque of the conventional one. For sine+3rd nonoverlapping windings machines whose slot number Ns and pole number 2p differed by one, the torque density is larger than the conventional one. The sine+3rd is promising in torque density for both overlapping and nonoverlapping winding machines. Finite element (FE) analysis is carried out on the 12-slot/10-pole SPM machines with conventional, sine-shaped and sine+3rd-shaped PM under different flux density ratio. Finally, a 12-slot/10-pole sine+3rd-shaped machine is prototyped and tested for validation.