Analytical Modeling of Slotless Eccentric Surface-Mounted PM Machines Using a Conformal Transformation

In this work, an analytical technique is developed for modeling of the air gap flux density in the slotless eccentric surface-mounted permanent magnet (PM) machines. In the developed model, a 2-D solution for the Poisson equation is provided. In the modeling process, the eccentric stator is replaced with an equivalent current sheet at the stator bore. This current sheet is selected such that the overall tangential flux density caused by the PMs and the current sheet at the removed stator bore is zero. To find the contribution of current sheet on the air gap flux density, a conformal transformation is applied. The obtained exact values of the instantaneous air gap flux density components are used to compute the variables of the eccentric machine such as the back-EMF, the electromagnetic torque, and the unbalanced magnetic force. The provided model is valid for static, dynamic, and even mixed rotor eccentricity conditions. Finally, finite-element analysis is applied to verify the proposed model.