Lumped-parameters thermal network of PM synchronous machines for automotive brake-by-wire systems

Thermal analysis represents a key factor in electrical machine design due to the impact of temperature increase on insulation lifetime. In this context, there has been a wide investigation on thermal modeling, particularly for machines used in harsh working conditions. In this perspective, brake-by-wire (BBW) systems represent one of the most challenging applications for electrical machines used for automotive smart actuators. Indeed, electro-actuated braking systems are required to repeatedly operate the electric machine in high overload conditions in order to limit the actuator response time, as well as to enhance gravimetric and volumetric specific performance indexes. Moreover, BBW systems often impose unconventional supply conditions to the electric machine, consisting of dc currents in three-phase windings to keep the rotor fixed during the braking intervals. However, a dc supply leads to uneven temperature distributions in the machine, and simplified thermal models may not accurately represent the temperature variations for the different machine parts. Considering such unconventional supply conditions, this paper initially investigates the applicability of a conventional lumped-parameters thermal network (LPTN) based on symmetry assumptions for the heat paths and suitable for surface-mounted PM synchronous machines used in BBW systems. An extensive test campaign consisting of pulses and load cycle tests representative of the real machine operations was conducted on a prototype equipped with several temperature sensors. The comparison between measurements and predicted average temperatures, together with insights on the unbalanced heat distribution under the dc supply obtained by means of finite element analyses (FEA), paved the way for the proposal of a phase-split LPTN with optimized parameters. The paper also includes a critical analysis of the optimized parameters, proposing a simplified, phase-split lumped-parameters thermal model suitable to predict the temperature variations in the different machine parts for PM synchronous electric machines used in BBW systems.