Study on the Nonlinear Dynamics of a Single-Stage Gear Vibro-Impact System

A vibro-impact dynamic model of a typical single-stage spur gear train has been proposed in this study. The lumped parameter dynamic model includes the constant meshing stiffnesses, the linear time-invariant viscous damping values and the gear clearance (backlash) non-linearity allowing teeth separations. With taking account of the effect on impact of gear tooth when meshing, the dynamic equations of motion are solved for the steady period response by use of analytical method under given periodic motion conditions. The feasibility of the given periodic motion conditions is demonstrated by comparing the analytical results with that of numeric simulation method. A Poincaré map of the system is established. The stability and bifurcation of the system are studied using analytical methods. Finally, the theoretical analyses are verified using numerical simulation.