The lubrication approximation of the friction force for the simulation of measured surfaces

Models of the friction force are assessed by direct comparison with two-dimensional Navier–Stokes results. A three-term formula obtained from asymptotic expansion provides a reasonable estimate of the hydrodynamic friction of rough runners even at sub-micron clearances. Simulations of a measured honed surface are then reported using the conservative time-dependent Elrod–Adams model with spatial resolutions as fine as 0.25 μm per cell (4000×800 mesh). Mesh convergence of the numerical method is observed. Cell sizes between 0.5 μm and 1 μm appear as a reasonable compromise of accuracy and cost for the simulation of honed runners. The significance of each term of the friction formula is discussed, so as to assess the error involved in neglecting terms of the friction formula.