Nonlinear dynamics of planetary gearboxes containing cracks

Gear cracks may occur during the operation of planetary driveline, leading to a huge safety hazard. However, few studies have been conducted to investigate the influence mechanism of planetary driveline vibration with crack extension. In order to simulate the actual working conditions, a damage dynamics model of the planetary gear train is constructed. Firstly, the system dynamics differential equations are established based on the dynamics model and solved to obtain the bifurcation diagram, time-domain diagram, phase diagram, three-dimensional wavelet diagram, three-dimensional spectrogram, and meshing force diagram of the system to investigate the effects of the excitation frequency and the degree of cracking of the gears on the vibration characteristics of the system. Then, the global bifurcation diagram of the system is constructed by using the cell mapping method, and the evolution mechanism of the global vibration characteristics of the system is explored according to the coexisting states of the system. In addition, the proposed dynamics model is verified by planetary gear train failure simulation experiments. The results show that the system has similar global characteristics under healthy operating conditions and cracked faults, and the system instability increases with the gear crack extension. Therefore, it is valuable to predict the planetary gear life by analysing the global vibration characteristics of the system.