Dynamic Modeling and Analysis of an RV Reducer Considering Tooth Profile Modifications and Errors

Due to their advantages of compact size, high reduction ratio, large stiffness and high load capacity, RV reducers have been widely used in industrial robots. The dynamic characteristics of RV reducers in terms of vibratory response and dynamic transmission error have a significant influence on positioning accuracy and service life. However, the current dynamic studies on RV reducers are not extensive and require deeper study. To bridge this gap, a more effective and realistic lumped parameter dynamic model for RV reducers is developed, considering the tooth profile modification of cycloid gears and system errors. Firstly, for an efficient solution, the equivalent pressure angle and equivalent mesh stiffness of the cycloid-pin gear pair are introduced in the dynamic model based on the loaded tooth contact analysis. Secondly, the differential equations of the system are derived by analyzing the relative displacement relationships between each component, which are solved using the Runge-Kutta method. With this, the effects of errors such as machining errors, assembly errors and bearing clearances on the dynamic behaviors and transmission precision are investigated by comparison to quantify or qualify their influence. This research is helpful in characterizing the multi-tooth mesh and dynamic behavior, and revealing the underlying physics of the RV reducer.