Influence of tooth surface morphological characteristics on dynamic characteristics of a two-row planetary gear train

The planetary gear train is an essential part of the automatic transmission drive system, and its tooth surface morphological characteristics affect the dynamic characteristics of the planetary gear train through mesh stiffness and backlash. This paper introduces a method for analyzing the effect of tooth surface morphological characteristics on the dynamic characteristics of a two-row planetary gear train. The torsional dynamics model of a two-row planetary gear train is established by considering a variety of nonlinear factors, in which a time-varying meshing stiffness model considering fractal features is constructed using the potential energy method and fractal contact theory, and a backlash model considering fractal features is constructed using fractal theory and the involute tooth profile equation. The influence of tooth surface morphology on time-varying meshing stiffness and backlash is examined, and the influence of tooth surface morphology on the dynamic characteristics of the planetary gear train is analyzed based on bifurcation diagrams under different operating conditions. The findings reveal that: an increase in fractal dimension D or a decrease in characteristic scale factor G results in a smoother tooth surface, leading to enhanced meshing stiffness and reduced backlash; as D decreases and G increases, the relative displacement amplitude of meshing pairs of two rows of planetary gear train increases, and the most stable operating speed range of planetary gear train gradually moves to the direction of the low rotational speed; the vibration response of two rows of planetary gear train at Ra = 1.25 has a big difference, the relative displacement of the first row is smaller than that of the second row in the low and medium speed zones, but the opposite is true in the high speed zone.