Non-linear dynamic simulation of gear response under the idling condition

A dynamic lumped-parameter gear model incorporating the effects of a time-varying and asymmetric mesh stiffness and a backlash nonlinearity is formulated to analyze the spur gear rattle response under the idling condition. The proposed theory assumes a rectangular time-varying mesh stiffness function. The phase shift between the mesh stiffness for forward and backward contacts is examined. Numerical studies are employed to examine the effects of engine torque fluctuations and tooth surface friction on the gear rattle response and the corresponding tooth impact behavior. Comparisons between the results from the time-invariant mesh stiffness model and the proposed time-varying mesh stiffness model reveal differences in the gear responses, especially when the mean rotational speed of the fluctuating gear pair is non-zero. The analysis reveals significant effects on the high frequency response components. However, the idling gear dynamics are relatively insensitive to tooth surface friction.