We limit our considerations on length scales for which rubber is rough in contrast to a perfectly smooth ice surface. Thereby we assume that the only source of frictional forces is the viscosity of a sheared intermediate thin liquid layer of melted ice. Rubber hysteresis and adhesion effects are considered to be negligible.

The height of the liquid layer is driven by an equilibrium between the heat built up by viscous friction, energy consumption for phase transition between ice and water and heat flow into the cold underlying ice. Additional microscopic squeeze out phenomena of melted water due to the rubber asperities are also taken into consideration. The size and microscopic real contact area of these asperities are derived from roughness parameters of the free rubber surface using Greenwood-Williamson contact theory and compared with the measured real contact area.

The derived one dimensional differential equation for the height of an averaged liquid layer is solved for stationary sliding by a piecewise analytical approximation. The frictional shear forces are deduced and integrated over the whole macroscopic contact area to result in a global coefficient of friction. The boundary condition at the leading edge of the contact area is prescribed by the height of a “quasi liquid layer” which already exists on the “free” ice surface.

It turns out that this approach meets the measured coefficient of friction in laboratory. More precisely, the calculated dependencies of the friction coefficient on ice temperature, sliding speed and contact pressure are confirmed by measurements of a simple rubber block sample on artificial ice in laboratory.