Analytical optimisation of external rotor permanent magnet machines

This study presents an analytical model for optimising the maximum torque per volume in external rotor permanent magnet (PM) machines, in which the maximum achievable airgap flux density depends on the split ratio of airgap diameter to outer diameter and the stator slot area is a function of split ratio, airgap flux density, and stator split ratio of stator diameter at slot bottom to airgap diameter. The optimal split ratio, stator split ratio and airgap flux density are derived analytically with/without considering that the maximum achievable airgap flux density is limited by the split ratio. In addition, the influence of airgap flux density distributions, slot and pole numbers, slot shapes, tooth-tips, end-windings, rotor yoke and inner diameter on the optima is discussed. The analytical analyses are validated by both finite element and experimental results. It is shown that the torque density of external rotor PM machines is maximum when the average airgap flux density is slightly lower than half of the maximum flux density in the stator.