Analytical Modeling of No-Load Eccentric Slotted Surface-Mounted PM Machines: Cogging Torque and Radial Force

In this paper, the air-gap flux density components in the eccentric surface-mounted phase modulation (SPM) machines are predicted analytically. In the provided model, the slotting effects of the armature are taken into account. In the modeling process, conformal transformations (CTs) are employed to obtain an equivalent concentric slotless machine for the eccentric slotted PM machine. To satisfy the condition of using CTs, i.e., having a Laplace equation, the PMs are replaced with an equivalent current sheet at the surface of the rotor. The approach of finding this current sheet is approved by the basis of the electromagnetic theory. One of the contributions of this paper is that the provided model is capable of modeling the eccentric SPM machines with any PM magnetization pattern by means of CTs. Substituting the predicted air-gap flux density components in the Maxwell stress tensor, the machine unbalanced magnetic force and its cogging torque are computed. Finally, the accuracy of the obtained results is evaluated by means of finite-element analysis.