Bifurcation and Chaos Analysis of Gear System With Clearance Under Different Load Conditions

Abstract

In the transmission process of gear system, the change of load will make the system in different states of motion, which affects the transmission efficiency of gear system. It is important to investigate the nonlinear dynamic characteristics of gear system under different load states. Using straight cylindrical gears as the object of study, the concentrated mass method is used to establish a dynamic model that takes into account nonlinear factors such as tooth side clearance, time-varying meshing stiffness and transmission errors. The differential equations of the system are solved by the Longe-Kutta method to obtain the bifurcation diagram, the maximum Lyapunov exponent diagram and the phase plane diagram of the gear system to analyze the effect of the meshing damping ratio on the dynamic characteristics of the system under different load states. The results show that the influence of the engagement damping ratio on the dynamic characteristics of the system is greater under light load conditions, showing different states of motion as the engagement damping ratio gradually increases. Under heavy load conditions, the effect of the engagement damping ratio on the dynamic characteristics of the system is small. Appropriately increasing the mesh damping ratio is beneficial to the gear system to avoid the chaotic zone and maintain a stable cyclic motion state. The results of the study provide a reference for the design of gear systems with variable loads.