Static Modeling of the Stiffness and Contact Forces of Rolling Element Eccentric Drives for Use in Robotic Drive Systems

Rolling element eccentric drives promise to be an easy-to-manufacture and performant gear system for robotic actuators. They share characteristics with other eccentric drives, such as strain wave and cycloidal drives, but use rolling elements instead of an eccentric gear. They offer reduced manufacturing complexity and costs by using readily available standard parts. Little research into rolling element eccentric drives is available, and their characteristics are still underexplored. This work uses a contact-based model to investigate the previously unknown stiffness of rolling element eccentric drives. Such calculation methods are well established for structurally similar components, such as cycloidal drives and roller bearings, and provide a high-level and computationally efficient model. Good stiffness models are critical for accurately predicting robotic actuator behavior and enabling better control of robotic systems. Additionally, the proposed model is used to calculate the contact forces under load occurring in rolling element eccentric drives. Contact forces are critical to calculating a drive's load capacity, lifetime, and efficiency and serve as the foundation for further research. The mathematical description of the proposed model is derived, and the stiffness of a representative rolling element eccentric drive is calculated. Different manufacturing techniques, characterized by tolerance levels and material choices, are compared. Irrespective of manufacturing precision, similar stiffness curves result for drives made of steel, but higher contact forces result from less precise manufacturing. The stiffness of drives made from 3D printed plastic is considerably lower than that of drives made from steel. Additionally, the stiffness of rolling element eccentric drives is compared to similar eccentric drives, and a comparable twist-over-torque curve is shown.