Nonlinear dynamic characteristics analysis of double-row planetary gear trains considering the internal and external time-varying meshing stiffness of the ring-planet-sun gear

Abstract

The planetary transmission system constitutes a critical component of the AT automatic transmission. Within this system, the internal time-varying meshing stiffness (TVMS) between the ring gear and planet gears significantly influences the vibration characteristics of the double planetary gear train (PGT). A nonlinear dynamic analysis method for double PGTs, accounting for both internal and external TVMS between the ring gear, planet gear, and sun gear, is proposed. First, a computational model for the internal and external TVMS of helical gear pairs was established. This model calculates the deformation of the outer gear’s root circle to base circle section, alongside the bending and shear deformation of the ring gear’s circumferential section. The influence of tooth width, face pressure angle, and helix angle on both internal and external TVMS was analyzed. Subsequently, a nonlinear dynamic model for a double PGTs with a rotatable ring gear was developed, incorporating TVMS, time-varying meshing damping (TVMD), time-varying backlash (TVB), and comprehensive meshing error. Finally, bifurcation diagrams and the maximum Lyapunov exponent (MLE) were employed to investigate the influence of TVMS on the relative displacement (RD) between the ring-planet gear (RPG) and sun-planet gear (SPG) pair. Time history plots, phase trajectory diagrams, Poincaré sections, and spectra to investigate the nonlinear dynamic characteristics of the double PGTs under TVMS and TVB, as well as the relationship between RDs of the RPG pair and SPG pair. Findings indicate: increasing meshing stiffness suppresses RD amplitudes of both pairs but diminishes periodicity; Increasing backlash amplifies RD between meshing pairs without affecting periodicity; To address the issue of substantial RD in the second row caused by the transmission ratio, modifying parameters of the second PGT reduces this displacement, providing a basis for balanced design of both the first and second row of the PGT.

Keywords

double row PGTs kinematic model internal and external TVMS nonlinear dynamic characteristics backlash

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