Chaos and Impact Characteristics Analysis of a Multistage Planetary Gear System Based on the Energy Method

Abstract

A dynamic modeling method for Multistage Planetary Gear Transmission (MPGT) is proposed based on the concept of integral planetary gearbox modeling. The integrated interaction of multiple nonlinear parameters is considered in the dynamic model. The time-varying mesh stiffness of each gear pair is calculated by the energy method. The effects of input torque, gear backlash, and meshing damping on the chaos and impact characteristics of the system are analyzed in detail. The results show that the dynamic behavior of the system is closely related to the Dynamic Meshing Force (DMF). When the system is in the states of chaos, bifurcation, and jumping, the DMF fluctuates violently, and the stability and reliability of the system are seriously affected. With the increase of input torque and meshing damping, the system exits chaos through the inverse period-doubling bifurcation path, which indicates that increasing the input torque and meshing damping can suppress the chaotic motion and enhance the stability of the system. The backlash has a significant effect on the nonlinear behavior and meshing impact characteristics of the system. When the backlash is small, the system is in bilateral impact, and the meshing impact tends to be stable as the backlash increases. In order to improve the vibration characteristics of the system, a slightly larger backlash is necessary. The results can be used to guide the dynamic characteristics design and vibration control of the MPGT.

Study on Nonlinear Dynamic Characteristics of RV Reducer Transmission System

“…Energies 2024, 17,1178 By projecting the planar displacements δ si and δ pi of the sun gear and planetary gear onto the line of action, the relative displacement δ spi between the sun gear and the i-th planetary gear can be expressed as: (12) where e spi represents the comprehensive meshing error for the i-th involute gear pair, which can be expressed as a sine function [44]:…”

“…Due to manufacturing and installation errors and the need for lubrication, clearances must be present between the gear teeth. To describe the influence of tooth clearances on the relative displacement δ spi between the sun gear and the planetary gear, a piecewise function f (δ spi , t) is employed to depict the relative displacement between the sun gear and the planetary gear, considering the effect of clearances [44].…”

“…Currently, papers on the nonlinear dynamic characteristics of gear transmission systems primarily focus on involute gears [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39], with some scholars researching chaotic and bifurcation characteristics related to cycloidal gears [40][41][42][43][44]. Blankenship and Kahraman [31][32][33] established a single-degree-of-freedom dynamic model for gear pairs with tooth-side clearance.…”

“…Wang et al [43] derived a dynamic model for a multi-stage planetary gear system in a wind turbine gearbox, explaining the bifurcation characteristics of the high-speed stage gear pair. Li et al [44] analyzed the influence of input torque, backlash, and meshing damping on the bifurcation and impact characteristics of a multi-stage planetary gear system. Liu et al [45] proposed a method for modeling the nonlinear dynamics of a multi-stage planetary gear transmission system composed of two-stage planetary gears and one parallel-axis gear.…”