Analysis for time varying torsional stiffness of RV reducer

Rotary vector reducer (RV reducer) serves as a crucial drive train component in industrial robots, and its time varying torsional stiffness significantly impacts the dynamic characteristics, vibration and transmission accuracy. Existing methods for calculating the torsional stiffness suffer from two limitations: (1) considering only the time varying meshing stiffness of the gear pair or the time varying radial stiffness of the bearings as a single factor, and (2) the calculated results according to the traditional initial meshing clearance formula of the cycloid pin gear do not align with the definition of tooth side clearance. To comprehensively and accurately analyze the time varying torsional stiffness, this study proposes a method for the reducer, taking into full consideration the time varying characteristics of gear meshing stiffness and radial stiffness of bearings. To analyze the time varying meshing stiffness of the cycloid pin gear pair, a novel initial meshing clearance formula is derived. Firstly, a new calculation model was constructed to accurately obtain the initial meshing clearance of cycloid pin gear single tooth pair in the low-speed stage. The time varying meshing stiffness of the cycloid pin gear was calculated by determining the number of teeth engaging in meshing simultaneously. Secondly, the time varying meshing stiffness of the involute modified gear in the high-speed stage was simulated employing the weber energy method. Then, time varying radial stiffness of the crankshaft, arm bearings, and supporting bearings was analyzed utilizing finite element method. Finally, by equivalating the time varying meshing stiffness of the two-stage gear mechanism and the time varying radial stiffness of bearings to the output end, the time varying torsional stiffness of the reducer was calculated. The experimental results of the torsional stiffness have only a 3.81% difference compared to the simulated value, which validates the accuracy of this method.