A dynamic rheological model for thin-film lubrication

Abstract

In this study, the effects of the non-Newtonian rheological properties of the lubricant in a thin-film lubrication regime between smooth surfaces were investigated. The thin-film lubrication regime typically appears in Stribeck curves with a clearly observable minimum coefficient of friction (COF) and a low-COF region, which is desired for its lower energy dissipation. A dynamic rheology of the lubricant from the hydrodynamic lubrication regime to the thin-film lubrication regime was proposed based on the convected Maxwell constitutive equation. This rheology model includes the increased relaxation time and the yield stress of the confined lubricant thin film, as well as their dependences on the lubricant film thickness. The Deborah number (De number) was adopted to describe the liquid-solid transition of the confined lubricant thin film under shearing. Then a series of Stribeck curves were calculated based on Tichy's extended lubrication equations with a perturbation of the De number. The results show that the minimum COF points in the Stribeck curve correspond to a critical De number of 1.0, indicating a liquid-to-solid transition of the confined lubricant film. Furthermore, the two proposed parameters in the dynamic rheological model, namely negative slipping length b (indicating the lubricant interfacial effect) and the characteristic relaxation time λ0, were found to determine the minimum COF and the width of the low-COF region, both of which were required to optimize the shape of the Stribeck curve. The developed dynamic rheological model interprets the correlation between the rheological and interfacial properties of lubricant and its lubrication behavior in the thin-film regime.