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

• Published in: Tribology international 2016-05, Vol.97, p.390-399
• Main Authors: Checo, Hugo M., Jaramillo, Alfredo, Ausas, Roberto F., Buscaglia, Gustavo C.
• Format: Article
• Language: English
• Subjects: Asymptotic expansions; Computer simulation; Finite element method; Friction; Friction force; Hydrodynamic lubrication; Mass-conservative model; Mathematical models; Measured-surface simulation; Navier-Stokes equations; Numerical analysis; Time dependence
• ISSN: 0301-679X; 1879-2464
• DOI: 10.1016/j.triboint.2015.12.030

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 0.25μm per cell (4000×800 mesh). Mesh convergence of the numerical method is observed. Cell sizes between 0.5μm and 1μm 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. •A lubrication approximation for the hydrodynamic friction force is obtained.•The approximation is then validated against single-phase Navier–Stokes simulations.•Two friction models extracted from the literature are compared to the lubrication approximation.•The models are compared in realistic measured-surface simulations.•The models found in the literature lead to 30% relative differences for low clearances.