Nonlinear Dynamics of a Multistage Gear Transmission System with Multi-Clearance

The nonlinear torsional model of a multistage gear transmission system which consists of a planetary gear and two parallel gear stages is established with time-varying meshing stiffness, comprehensive gear error and multi-clearance. The nonlinear dynamic responses are analyzed by applying the reference of backlash bifurcation parameters. The motions of the system on the change of backlash are identified through global bifurcation diagram, largest Lyapunov exponent (LLE), FFT spectra, Poincaré maps, the phase diagrams and time series. The numerical results demonstrate that the system exhibits rich features of nonlinear dynamics such as the periodic motion, nonperiodic states and chaotic states. It is found that the sun-planet backlash has more complex effect on the system than the ring-planet backlash. The motions of the system with backlash of parallel gear are diverse including some different multi-periodic motions. Furthermore, the state of the system can change from chaos into quasi-periodic behavior, which means that the dynamic behavior of the system is composed of more stable components with the increase of the backlash. Correspondingly, the parameters of the system should be designed properly and controlled timely for better operation and enhancing the life of the system.