Optimal split ratio in fractional-slot interior permanent magnet machines with non-overlapping windings

The split ratio has been optimized for the maximum torque density when the airgap flux density is fixed in existing papers. However, the airgap flux density can vary with the split ratio significantly in interior permanent magnet (IPM) machines due to flux focusing. Therefore, an optimal airgap flux density may exist, together with the optimal split ratio, for the maximum torque in IPM machines. This paper analytically optimizes the airgap flux density and split ratio individually, as well as the global optimum in terms of the torque density in the fractional-slot IPM machines with non-overlapping windings. In addition, the influence of pole-slot combination and tooth-tips on the optimal split ratio and airgap flux density is discussed. The analytical result is verified by the finite element analysis. It shows that the optimal split ratio reduces with the increase of the airgap flux density, and the preferred airgap flux density is around 0.5-0.7 times of maximum flux density in the stator teeth when the rare earth permanent magnets are employed.