Multi-Objective Optimization of a PMSM Helical Cooling Channel Based on Bidirectional Magneto-Thermal Coupling and Experimentally Validated Thermal-Hydraulic Modeling

Permanent magnet synchronous motors (PMSMs) are increasingly used in electric vehicles, where rising power density and compact packaging impose greater demands on motor thermal management. However, cooling-channel design involves a coupled trade-off between heat removal and hydraulic resistance, while temperature-dependent electromagnetic losses are often not fully considered in optimization studies. To address this issue, this study investigates the multi-objective optimization and verification of a helical cooling channel for a liquid-cooled PMSM based on bidirectional magneto-thermal coupling. A three-dimensional transient electromagnetic model was coupled with a conjugate heat-transfer model to account for the feedback between winding temperature, copper resistivity, electromagnetic loss, and motor temperature. An experimental temperature-rise test bench was established for model validation, and an optimal Latin hypercube design, Universal Kriging surrogate models, and the non-dominated sorting genetic algorithm II (NSGA-II) were integrated in Isight (v2022, Dassault Systèmes, Vélizy-Villacoublay, France) to optimize the channel height, width, and fillet radius with the maximum motor temperature and coolant pressure drop as the objectives. Results show that the numerical model reproduced the measured thermal-hydraulic responses over the investigated coolant-flow-rate range, with maximum deviations of 1.16% for the end-winding temperature and 5.54% for the coolant pressure drop. Under the investigated peak-power condition, the total electromagnetic loss was 3864 W, of which the stator winding and stator core accounted for 66.2% and 30.5%, respectively, confirming that they are the dominant heat sources. The Universal Kriging model achieved training coefficients of determination of 0.97 and 0.98, with corresponding 10-fold cross-validated values of 0.953 and 0.968, for the maximum motor temperature and coolant pressure drop, respectively, and was therefore selected for NSGA-II optimization. For the selected compromise solution, the independently calculated pressure drop decreased from 12,312.97 to 8318.54 Pa, corresponding to a reduction of 32.45%, while the maximum motor temperature decreased from approximately 375.18 to 371.80 K, or by 3.38 K. The deviations between the surrogate predictions and independent computational fluid dynamics (CFD) results were 1.47% for pressure drop and 0.20% for maximum temperature. The proposed framework provides a physically consistent and experimentally supported method for the thermal-hydraulic design of PMSM cooling channels and offers a basis for further optimization of high-power-density motor thermal management systems.