Analytical Method for Overhang Effect of Surface-Mounted Permanent-Magnet Motor Using Conformal Mapping

In this paper, an analytical method for predicting the rotor overhang (OH) effect is presented using two types of conformal mappings (CMs), which are the r-θ and zr plane CMs. First, the no-load air-gap flux density (AFD) of a slotted air gap without OH is determined using the rθ plane CM. Second, the complex relative air-gap permeance (CRAP) in the zr plane is obtained by the zr plane CM. This helps in taking the OH effect into account. Finally, the no-load AFD of the slotted and OH air gaps in cylindrical coordinates is derived from the no-load AFD in the rθ plane with CRAP along the z-axis. The accuracy of the presented method is verified by comparing the results of no-load analysis with those of 3-D finite-element analysis.