Modeling of Ball Bearings for Accurate Force and Torque Transmission in Dynamic Robotic Systems

Abstract This paper presents a high-fidelity methodology for the dynamic modeling of robotic systems with revolute joints that incorporate ball bearings. To bridge the gap between simulation and physical hardware, the bearing is modeled not as an ideal revolute joint but by decomposing it into its constituent components: the inner race, outer race, and rolling elements. The interactions between these components are governed by a nonlinear constraint system, with contact forces evaluated using Hertzian contact theory. When applied to the dynamics of a mobile robot, the model reveals that geometric parameters such as bearing clearance, raceway curvature, and eccentricity are critical factors that significantly alter the transmission of forces and moments between links. Experimental validation confirms that this detailed component-level approach is essential for enhancing simulation fidelity and accurately predicting the dynamic behavior of the complete robotic system.