Design and identification of lumped-parameter thermal network model for real-time temperature estimation of permanent-magnet spherical motors

The permanent-magnet spherical motor (PMSphM) is a kind of intriguing multi-degree of freedom motor with promising applications in future robotics. However, its compact design can lead to inefficient heat dissipation, resulting in coil overheating. This necessitates real-time prediction and monitoring of hotspot temperature increases. This study presents a lumped-parameter thermal network (LPTN) model for a PMSphM to track its temperature transients. Capitalizing on the PMSphM's symmetric structure, a simplified heat path diagram is used to facilitate a two-dimensional (2-D) LPTN model with T-nodes, which lump the distributed heat generation in the coil and present it as external heat source input to the average-temperature node that connects to the body-centroid node through a negative-valued thermal resistance. The present LPTN model achieves an average deviation of less than 5% when compared to numerical simulations and experimental measurements. It provides a computationally efficient alternative, reducing calculation time by over 90% even compared to significantly simplified numerical simulations. The validation study underscores the model's precision and its practical applicability for real-time temperature estimation.