Computationally Efficient Tolerance Analysis of the Cogging Torque of Brushless PMSMs

This paper investigates the impact of tolerances related to permanent magnets on the cogging torque performance of Permanent magnet synchronous machines (PMSMs). These machines usually show a considerable sensitivity regarding tolerances for geometric dimensions and material characteristics. A consistent approach is presented in order to minimize the computational effort for evaluating the sensitivity, robustness, or reliability. Thereby, design of experiments is used to minimize the required number of finite element simulations. In this work, a Box-Behnken-based approach is considered. Subsequently, a surrogate modeling technique based on a second-order equation is applied. As a consequence, a reduction of the computational cost by 96% is achieved. The obtained results are compared with outcomes solely derived by means of finite element computations and very good agreement is observed. This is illustrated by providing the probability distribution of the cogging torque for the considered machine design. In addition, the cumulative distribution is presented, which usually is applied for analyzing the reliability. Considering the analysis of the impact of tolerances as part of optimization scenarios increases the number of designs to be analyzed by at least one degree of magnitude. The obtained results look promising for achieving this at feasible computational cost.