Stability of motion state and bifurcation properties of planetary gear train

A nonlinear lateral-torsional coupled vibration model of a planetary gear system was established by taking transmission errors, time varying meshing stiffness and multiple gear backlashes into account. The bifurcation diagram of the system's motion state with rotational speed of sun gear was conducted through four steps. As a bifurcation parameter, the effect of rotational speed on the bifurcation properties of the system was assessed. The study results reveal that periodic motion is the main motion state of planetary gear train in low speed region when ns<2 350 r/min, but chaos motion state is dominant in high speed region when n(s)>2 350 r/min, The way of periodic motion to chaos is doubling bifurcation. There are two kinds of unstable modes and nine unstable regions in the speed region when 1 000 r/min<n(s)<3 000 r/min.