Bifurcation and chaos of gear transmission system with clearance subjected to internal and external excitation

In order to investigate the effect of bearing stiffness and gear side clearance on the bifurcation and chaos of gear-rotor system, and with the consideration of the actions of the clearance, internal and external excitation, a non-linear dynamic model of gear-rotor system is built. In the process of numerical simulation of dynamics equation, in order to judge whether the vibration of gear rotor system is chaos or not, the chaotic time series method is used to calculate the maximum Lyapunov exponent of high dimension nonlinear equation of gear rotor system. The results show that with the increase of bearing stiffness, the lateral-torsional critical speed of system increases, the region where bifurcation and chaos appear also changes. The vibration of first order bending critical speed of gear rotor system is affected by clearance greatly. When clearance is relatively small, the vibration of the first order bending critical speed is relatively preferable. When clearance increases to a certain value, the vibration of the first order bending critical speed is double period motion. When clearance continue to increase, the vibration of the first order bending critical speed changes to chaos from double period motion. When clearance increases to a large value, the vibration of the first order bending critical speed turns into chaos rapidly. The maximum Lyapunov exponent of high dimension nonlinear equation can be calculated by chaotic time series analysis method effectively.