Chaotic vibration analysis of gear transmission system with stochastic disturbance

In order to study the effects of stochastic disturbance of the input torque on system dynamics, the dynamics equations of a single pair of three degrees of freedom spur gear system are established according to Newton's law, while considering stochastic disturbance of a low frequency external excitation caused by torque fluctuation damping ratio, gear backlash, excitation frequency and meshing stiffness. Using the bifurcation diagram, phase diagram, time history chart, Poincaré map, Lyapunov exponents and power spectrum of the system, the dynamic characteristics of the gear transmission system in gear excitation frequency changing are analyzed, as well as the influence of stochastic disturbance caused by the input torque on the system bifurcation characteristic. Numerical simulation results show that the stochastic non-smooth gear transmission system has a wealth of period-doubling bifurcation. As the gear excitation frequency increases, the gear transmission system turns from periodic motion into chaos via period-doubling bifurcation, then back to periodic motion via inverse period-doubling bifurcation. When the stochastic disturbance caused by the input torque increases, it will affect the stochastic bifurcation area and the dynamic characteristics of the system. ©, 2014, Nanjing University of Aeronautics an Astronautics. All right reserved.