Nonlinear torsional vibration modeling and bifurcation characteristic study of a planetary gear train

A nonlinear torsional vibration model of a planetary gear train with errors of transmission, time varying meshing stiffness and gear backlashes is established and dimensionless equations of the system are derived. The solution of the equations is carried out by using the method of numerical integration. By comparing with Poincaré maps and bifurcation diagrams, the bifurcation properties of the system are studied. The influences of some bifurcation parameters such as rotational speed, damping coefficient and gear backlashes on the bifurcation properties of the system are assessed. The study results reveal that the system's motion state will change into chaos in the way of crisis as speed increase and period doubling bifurcation is the way to chaos as backlashes increase. A smaller damping coefficient will make the system's periodic motion state change into complex state. Gear backlashes have a strong impact on the system's bifurcation characteristic when dimensionless the backlashes is bigger than 3.5.