Analysis the influence of mesh damping ratio on the bifurcation characteristic of herringbone planetary gear systems

In order to investigate the influence of meshing damping ratio on bifurcation behavior of the herringbone planetary gear system, pure torsional dynamics model is constructed, taking into account a range of dynamic driving factors, including time-varying meshing stiffness, tooth backlash, tooth friction and transmission error. The Runge-Kutta method is employed for the solution of system's dynamic equations. Bifurcation diagram, time history diagram, phase diagram, Poincaré section diagram and FFT are used to analyze the effects of bifurcation behavior and damping ratio on the bifurcation characteristics of system. The results show that system is transformed into chaotic motion by jump bifurcation and doubling bifurcation. As the meshing damping ratio is augmented, the jump bifurcation position lags, and the motion state gradually degenerates from chaotic motion to period-doubling motion. In order to guarantee the optimal functioning of transmission system, it is essential to enhance the meshing damping ratio in a manner that effectively restrains the occurrence of chaotic motion and enhances overall stability.