A Geartrain Model With Dynamic or Quasi-Static Formulation for Variable Mesh Stiffness

A new model of spur gear contact and gear dynamics was developed for use in studies of dynamic response of mechanical systems involving geartrains. The model is general; in this paper it is applied to geartrain dynamics in valvetrain gear drives. The model dynamically uses a gear contact formulation based on exact involute geometries of gear teeth and can therefore account for varying, non-linear mesh stiffness. It can also account for gear torsional stiffness as well as shaft stiffness at gear centers. The paper further proposes an alternative to dynamic calculation of instantaneous gear tooth contact conditions. The proposed method uses a varying effective mesh stiffness pre-computed through static calculation of contact conditions between teeth of a gear pair, for one mesh, or tooth engagement-disengagement, period. The technique is shown to significantly reduce computational time, while closely matching the predictions of the full model. Since the complex variation of gear mesh stiffness is mainly due to tooth contact kinematics, the model provides a practical and accurate alternative to measuring gear mesh stiffness or calculating it through a detailed FE model of a gear pair.

The model is first exercised in validation examples, in which results for a gear pair are compared to published experimental data and computations. The model is then applied in the context of a realistic valvetrain system of a 6-cylinder in-line diesel engine, in order to investigate the effect of geartrain dynamics on camshaft torsional vibrations and also on the dynamic response of the valvetrain.