Dynamic Model and Load Sharing Analysis of Planetary Transmission

Abstract

In this paper, a torsional-translational coupled nonlinear dynamic model for planetary gear train with three planet gears is developed, which includes manufacture and assembly errors. The motion equations of the dynamic model are built in consideration of gear elastic deformation and errors. To describe the relationship between displacements, elastic deformation and errors, the gear elastic compatibility equations are presented, in which manufacture and assembly errors are equivalent to the line of action of gear pairs. By means of Ishikawa formula, time-varying mesh stiffness of the gear pair is determined. Thus, dynamic equations of the gear train consisted of motion equations and gear elastic compatibility equations can be found, Runge-Kutta numerical integral method can be applied to solve the dynamic equations. Dynamic load sharing coefficient is adopted to evaluate the load sharing characteristic among planet gears. A planetary gear train is exercised as the example to analyze the load sharing among the planet gears, the effect of system stiffness, manufacture and assembly errors are quantified. The results indicate that floating sun gear and adding flexible planet pin have significantly superior load sharing characteristics. The study provides a theoretical guideline for design planetary gear train.