Torsional Stiffness Analysis Based on Lagrangian Method for Precision Rotary Vector Reducer with Involute Variable Tooth Thickness

The precision rotary vector reducer with involute variable tooth thickness (PRVT) is a high-performance precision transmission device, which is very suitable for aerospace, medical machinery, industrial robots, automation equipment, and other fields, and its torsional stiffness is an important performance index. This paper establishes a dynamics model of the whole machine based on the Lagrangian method by considering gear meshing stiffness, damping, and machining errors, and the influence of different machining errors on dynamic torsional stiffness is studied. The results show that increasing the distribution circle radius error of the crankshaft, the crank angle error and the distribution circle radius error of the crankshaft bearing hole on the carrier will cause the peak-to-peak torsional stiffness to increase. Therefore, the machining errors should be controlled within a reasonable range to improve the whole machine’s stability. An increase in the crankshaft bearing hole rotation error on the No. 1 beveloid gear has no notable impact on the peak-to-peak value and the average value of the torsional stiffness. Similarly, the rotation angle error of the crankshaft bearing hole on the No. 1 carrier has no significant effect on the torsional stiffness. The research results provide a useful reference for the torsional stiffness analysis of PRVT.