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The split ratio has been optimized for the maximum torque density when the air-gap flux density is fixed in existing papers. However, the air-gap flux density can vary with the split ratio significantly in interior permanent-magnet (IPM) machines due to flux focusing. Therefore, an optimal air-gap flux density may exist, together with the optimal split ratio, for the maximum torque in IPM machines. This paper analytically optimizes the air-gap 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 air-gap 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 air-gap flux density, and the preferred air-gap 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.