Numerical Simulation of Surface Contact and Mixed Lubrication — Deterministic Approach vs. Stochastic Approach

Surface contact and lubrication analysis as well as surface failure prediction through computer simulation are important research subjects, because power and motion are transmitted through surface contact (dry or lubricated) in mechanical systems, 80–90% of machine element failures, such as pitting due to contact fatigue, wear and scuffing, originate on the surfaces, and more than 1/3 of energy produced globally is dissipated through frictional loss. Engineering surfaces in various machineries are finished typically by machining processes, and surface roughness is usually in a range of 0.02–2 micron. When conducting contact mechanics and lubrication analyses, effects of surface roughness and texture/topography have to be taken into account. Conventional approaches, however, were based on either a smooth surface assumption, or simplified models with a few stochastic parameters, such as mean roughness height, root mean square (RMS), maximum peak to valley, etc. Today those conventional models do not seem to be satisfactory, as they were developed in the past when advanced computers were not available. For example, the famous Hertzian contact theory was developed in 1882 based on the smooth surface assumption. It often greatly underestimates contact stress when the surfaces are rough. Unfortunately, today most industrial standards for predicting surface failures in gears, bearings, and many other components are still based on the Hertzian theory. Advanced computer technologies have recently made deterministic simulations possible. This paper reviews recent development of deterministic approaches by the present author and his research partners, in comparison with conventional stochastic models. Focus is given to mixed lubrication modeling, which is a difficult task, as it must simulate both solid-to-solid contact and hydrodynamic lubrication simultaneously. Actually, dry contact and full-film hydrodynamic lubrication are two extreme conditions of mixed lubrication. Analyzed sample cases and result comparison between different models presented in this paper have shown that deterministic models based on the Reynolds equation, which was originally derived from Navier-Stokes equation for fluid lubrication, can be used to simulate mixed lubrication and dry contact. This enables us to employ a unified equation system to simulate the entire transition from fully lubricated condition down to dry contact. Also, developed computer programs based on the deterministic approach take digitized rough surface topography as input data, so that approximation due to simplified stochastic surface models can be avoided.