Desirability-Based Multi-Response Robust Design Optimization of IPMSM Considering Manufacturing Uncertainty

Manufacturing uncertainties such as variations in material properties, dimensional tolerances, and assembly deviations of permanent magnets (PMs) significantly affect the mean and variance of key motor performances, including back electromotive force (back-EMF) and cogging torque. This study proposes a multi-response robust design optimization method that simultaneously improves the mean and variance of the back-EMF and cogging torque, thereby mitigating the performance variations caused by manufacturing tolerances in an integrated starter generator (ISG) type electric oil pump (EOP) motor. First, significant design variables were identified through a first-order Taylor series-based approximated variance and analysis of variance (ANOVA), to reduce dimensionality. Sampling points were generated using a combination of Latin hypercube design (LHD) and sequential maximin distance design (SMDD), and a Kriging surrogate model was constructed and validated through normalized root mean square error (NRMSE). The Derringer–Suich desirability function and relevant constraints were then applied, and robust solutions were obtained using sequential quadratic programming (SQP). To set desirability targets, 10,000 LHD samples were used to explore feasible designs satisfying the voltage constraint, and the knee region of the resulting mean–variance trade-off distribution was utilized. Finally, the robust design was validated using 106 Monte Carlo simulation (MCS) runs, confirming improved robustness compared with the present design while substantially reducing the number of expensive finite element analysis (FEA) evaluations required for robust optimization. The proposed framework provides a practical and robust design pathway for improving the quality consistency under permanent magnet (PM) manufacturing tolerances.