Effect of sliding friction on the dynamics of spur gear pair with realistic time-varying stiffness

The chief objective of this article is to propose a new method of incorporating the sliding friction and realistic time-varying stiffness into an analytical (multi-degree-of-freedom) spur gear model and to evaluate their effects. An accurate finite element/contact mechanics analysis code is employed, in the “static” mode, to compute the mesh stiffness at every time instant under a range of loading conditions. Here, the time-varying stiffness is calculated as an effective function which may also include the effect of profile modifications. The realistic mesh stiffness is then incorporated into the linear time-varying spur gear model with the contributions of sliding friction. Proposed methods are illustrated via two spur gear examples and validated by using the finite element in the “dynamic” mode as experimental results. A key question whether the sliding friction is indeed the source of the off-line-of-action forces and motions is then answered by our analytical model. Finally, the effect of the profile modification on the dynamic transmission error has been analytically examined under the influence of sliding friction. For instance, the linear tip relief introduces an amplification in the off-line-of-action forces and motions due to an out of phase relationship between the normal load and friction forces.