High-fidelity thermal modeling and experimental validation of V-shaped PM vernier motors for electric mobility

• Introducing an integrated thermal modeling framework for a V-shaped permanent-magnet Vernier machine with a variable air gap. • A detailed equivalent thermal network approach is used to evaluate precise local temperature gradients and accurate identification of peak-temperature locations • Furthermore, a hybrid analytical–numerical technique is proposed to directly predict end-winding hot-spot temperatures by discretizing the end-winding region into uniform thermal elements with localized resistances and heat sources. • Validation through finite elements (FE) method, CFD, and experimental data demonstrates that the proposed method accurately predicts temperature distribution and hot-spot locations with high precision while significantly shortening computational time compared to full FEA. • The framework provides a powerful tool for the detailed thermal design and optimization of electric machines with complex geometries and variable air gaps. This paper presents an integrated thermal modeling framework for a V-shaped permanent-magnet Vernier machine with a variable air gap. The approach overcomes the limitations of conventional I-shaped equivalent thermal network (ETN) models in predicting average and hot-spot temperatures, particularly in windings, by introducing an Analytical Thermal Mapping (ATM) method. ATM enables accurate evaluation of local temperature gradients and precise identification of peak-temperature locations. A complete thermal model is developed using ETN, with key enhancements including a 3D representation of the end-winding region and increased slot discretization to capture local variations in the convective heat-transfer coefficient (CHTC) caused by the non-uniform air gap. To accurately determine CHTC, the study combines CFD simulations with semi-empirical experimental correlations, providing cross-validation and reliable airflow characterization. Additionally, a hybrid analytical–numerical method is proposed to predict end-winding hot-spot temperatures by discretizing the end-winding into uniform thermal elements with localized heat sources and resistances. Non-uniform boundary conditions on slot surfaces are modeled by dividing them into multiple thermal zones and solving the resulting Poisson equation using Fourier expansion, further improving hot-spot prediction accuracy. Validation against FEA, CFD, and experimental results shows that the proposed framework predicts temperature distributions and hot-spot locations with high accuracy while significantly reducing computational cost. The maximum temperature deviation across all regions is below 10%, and end-winding hot-spot temperatures are predicted with less than 5% error. The framework is therefore well suited for efficient and accurate thermal design and optimization of electric machines with complex geometries and variable air gaps.