LAUSR

The conventional multi-objective deterministic optimization (MODO) design may be less meaningful or even unacceptable when considering the perturbations of design parameters and reliability of the optimization results. In order to overcome the above-mentioned drawback and improve both the torque capability and permanent magnet (PM) utilization efficiency of dual-flux-modulator coaxial magnetic gear (DFM-CMG) simultaneously, a robust optimization design method is presented. In this method, the sigma criteria with the Monte Carlo simulation (MCS) are adopted to obtain the statistic samples addressing the effects of parametric uncertainties of DFM-CMG on the optimization results. Both 2-D and 3-D finite-element (FE) models of a DFM-CMG are first established, and the 3-D FE model is proven more accurate by the experiment and used for further optimization. Through the parametric study, five parameters are selected as the key design variables to establish the quadratic polynomial regression metamodels. Finally, the multi-objective particle swarm optimization algorithm with MCS is employed to conduct the multi-objective robust optimization (MORO) for DFM-CMG. Although the stall torque per PM consumption achieved by MORO with six sigma ( $6\sigma$ ) is little lower than that achieved by MODO, it still has a 21.4% growth than that of the initial design under the same constraint of the stall torque. Furthermore, the reliability and stability of the MORO results are much higher than those of the MODO results. The MORO method is significantly effective as the torque performance and robustness of DFM-CMG could be improved simultaneously.