Dynamical Analysis of Planetary Gear Transmission System Under Support Stiffness Effects

The transverse-torsional nonlinear model of multistage gear transmission system which is comprised of a planetary gear set and two parallel gear stages is proposed with time-varying meshing stiffness, comprehensive gear errors and gear backlash. The nonlinear dynamic responses are analyzed by applying excitation frequency and support stiffness as the bifurcation parameters. The motions of the system are identified through global bifurcation diagram, largest Lyapunov exponent (LLE) and Poincaré map. The numerical results demonstrate that the support stiffness affects the system, especially on planetary gear set. The motions of the system with the changes of the support stiffness are diverse including some different multiperiodic motions. Also, the state of the system undergoes 2T-periodic motion, chaos, quasi-periodic behavior and multiperiodic motion. For the support stiffness or other nonlinear factors of the gear system, the suitable range of working frequencies could make the system stable. Correspondingly, parameters of the system should be designed properly and controlled for the better operation and enhancing the life of the system.