Linearity analysis of a brushed DC machine thermal system in response to speed input using transfer function

Abstract

This study represents a preliminary step toward developing a real-time condition monitoring system for brushed DC machines by analyzing the linearity of their thermal behavior. The temperature response of an MY1016 DC motor was collected under no-load conditions at five different speed levels, ranging from 20% to 100% of the rated speed, until the motor reached steady-state conditions to emphasize the temperature increase due to speed variability. A transfer function model was identified using MATLAB’s System Identification Toolbox, and the system’s linearity was evaluated by analyzing the spread of pole values across different speeds. Results showed significant variability in the coefficient of variation (CV) for key components, with values ranging from 0.18 for the casing to 0.84 for the brush. These findings reveal significant deviations from linear thermal behavior, indicating that a single linear transfer function may be insufficient to model the system. This research highlights the need to validate linearity assumptions in thermal modeling and introduces a framework for assessing thermal variability under varying speed conditions.