A Method for Evaluating the Worst-Case Cogging Torque under Manufacturing Uncertainties

Permanent-magnet (PM) motors have been widely used in industrial applications and automobiles. However, owing to the design tolerances, manufacturing uncertainties, and material inconsistency, deviations from the ideal motor inevitably occur with parasitic effects, such as additional cogging torque and vibration. One of the most significant obstacles for evaluating these uncertainties is the large computational burden caused by the countless uncertain combinations, which must be computed via the finite-element method (FEM). Herein, a worst-uncertain-combination-analyze (WUCA) method is proposed to significantly reduce the computational cost. A widely used analytical method is modified to identify the origin of additional cogging-torque harmonics caused by uncertainties. Different types of uncertainties for the surface-mounted PM machine and interior PM machine can be analyzed simultaneously. With the WUCA method, the worst-case combinations can be confirmed theoretically; thus, FEM calculations for only a few combinations of uncertainties are required, rather than thousands. Compared with the widely adopted design of experiments based uncertain combining methods, the worst-case cogging torque obtained from the WUCA is higher. FEM verification of different pole/slot configurations revealed that the WUCA method was a general and effective method for quickly estimating the worst-case cogging torque under manufacturing uncertainties.