Coexisting periodic solutions and their stability of a nonlinear planetary gear train

Coexisting Periodic solutions and their stability of a nonlinear torsional vibration model for a planetary gear train with gear backlashes are studied by using the method of PNF. Some adaptations are made for the PNF method so as to make it suitable for the non-smooth and nonlinear planetary gear train. The coexisting periodic solutions of the system under certain dimensionless rotational speed are studied by using the method of modified PNF, with the stability of each periodic solution investigated at the same time. The bifurcation characteristics of the periodic trajectories are studied as well by using PNF at different speeds. The results show that a nonlinear planetary gear train with certain parameters may have several coexisting stable or unstable periodic trajectories Moreover, the motion of the system could also evolve into chaos by way of period-doubling bifurcation as the speed increases.