Effect of transmission errors on the dynamic behavior of planetary gear train

A nonlinear dynamic model of planetary gear train with backlashes, time-varying stiffness and transmission errors, was developed to simulate the dynamics of the system. The motion equations of the system were deduced. The specific effect of the transmission errors on the dynamic behavior of the planetary gear system was investigated using digital simulation technique. The bifurcation diagrams of displacement of the mesh gear pair to the amplitude of transmissions errors E_r were obtained. The maximal Lyapunov exponents with respect to E_r were also given in this paper. Results indicated that the vibrations amplitude of the system increased with the increasing of E_r. The originally stable periodic motions lost its regular characteristics immediately at given E_r and turned quickly into a chaotic motion which possessed much higher amplitude. The conclusions are helpful to dynamical design of precision planetary gears trains.