Modelling of a punch with a regular base relief sliding along a viscoelastic foundation with a liquid lubricant

A formulation and analytical solution of the problem of the sliding of a rigid three dimensional punch with a periodic structure along a viscoelastic foundation when there is an incompressible liquid in the gap between the contacting surfaces are given. The effect of the liquid on the resistance to the motion of the punch, the pressure distribution in the contact area and the dependence of the resistance on the sliding velocity is studied. The proposed model can be used in different applications such as, for example, when taking account of the phenomenon of aquaplaning when a tyre interacts with wet asphalt. A dimensionless analysis of the model shows that all the characteristics investigated depend on five dimensionless parameters. It follows from a numerical analysis of the model that the existence of a liquid in the gap leads to a decrease in the size of the contact area and of the deformation component of the friction force. If the volume of the liquid does not exceed a certain critical value, the effect is fading with increasing sliding velocity, and if the volume of the liquid exceeds the critical value, the effect occurs at any sliding velocity. In this case, the friction coefficient is a non-monotonic function of the sliding velocity.