Multi-Objective Optimization on Heat Transfer and Pumping Power of Combined Direct–Indirect Cooling System for PMSM Electric Motor

Efficient thermal management is essential for maintaining the reliability, durability, and power density of permanent magnet synchronous motors (PMSMs) used in electric vehicles (EVs). In this study, a combined direct–indirect cooling system (CDICS) was evaluated using multi-objective optimization to identify a constrained compromise between maximum component temperatures and ideal hydraulic pumping power. A three-dimensional CFD model was established to resolve conjugate heat transfer and oil–air two-phase flow within the proposed cooling configuration. The model was compared with winding temperature measurements obtained from motor dynamometer tests under two operating conditions, showing absolute CFD-measurement differences of 0.37 K and 0.50 K, respectively. Nozzle diameter (Dn), coolant volume flow rate (Qin), and inlet oil temperature (Tin) were selected as the primary design and operating variables for optimizing the thermo-hydraulic performance of the proposed cooling system. Discrete-grid maximin space-filling design was used to generate 30 CFD design cases, which were used to develop artificial neural network (ANN) surrogate models for bounded interpolation within the investigated design space. The models showed close agreement with the available CFD data, with R2 values of 0.9976–0.9994 for the six holdout cases. These values are interpreted as indicators of interpolation performance rather than evidence of universal generalization. The trained surrogate models were coupled with NSGA-II and TOPSIS to identify the optimal thermo-hydraulic compromise. The selected constrained compromise design within the investigated design space was Dn = 1.7 mm, Qin = 16.59 LPM, and Tin = 15.0 °C. The selected condition yielded CFD-predicted maximum stator, winding, and housing temperatures of 107.5 °C, 109.8 °C, and 65.0 °C, respectively, with an ideal hydraulic pumping power of 20.0 W. Relative to the reconciled reference baseline, the maximum stator, winding, and housing temperatures differed nominally by <0.1 K, 0.3 K, and 1.5 K, respectively. Because these differences were smaller than the corresponding 1.98–2.29 K variations observed in the single-point laminar-SST comparison, all three temperature predictions were considered numerically comparable within the assessed model sensitivity rather than established thermal improvements. The CFD-estimated ideal hydraulic pumping power decreased by 9.0 W (31.0%). Because the baseline and selected conditions differed in both coolant flow rate and inlet temperature, and chiller and other auxiliary energy requirements were excluded, this value does not represent total cooling system energy savings.