Isomorphic Node Mapping Method for Magnetic–Thermal Coupled Network Modeling of PM Vernier Machine

This paper proposes a magnetic-thermal coupled network modeling approach based on novel isomorphic node mapping of a permanent magnet vernier machine (PMVM). The key is to achieve dynamic coupling between electromagnetic and thermal domains by constructing a consistent node topology sharing across both network models in the radial cross-sectional plane. First, a high-resolution equivalent magnetic network (EMN) is constructed using mesh-based segmentation of core components, capturing local saturation and flux modulation effects. Second, an isomorphic equivalent thermal network (ETN) is established by mapping thermal nodes from the magnetic topology, enabling spatially aligned power loss injection and temperature computation. Then, bidirectional data transfers between domains are established, and critical losses are dynamically assigned to thermal nodes. Meanwhile, temperature feedback is correspondingly achieved with material property adjustments in the EMN. Finally, the effectiveness of the proposed coupling model is verified by finite element analysis and experimental results, including both magnetic and thermal performance, demonstrating high accuracy and structural consistency for multi-physics modeling.