Nonlinear modeling of non-Newtonian hydrodynamic lubrication

Lubrication is essential to improve the performance of sliding surfaces. Power transmission in mechanical and biological systems rely on proper lubrication to minimize wear and energy losses. However, most practical applications involve conditions that cause or require the lubricant to exhibit non-Newtonian behavior, namely shear thinning and viscoelasticity. In this study a novel non-linear 1D Reynolds equation is proposed for modeling shear thinning and a 1D viscoelastic Reynolds equation is proposed to model viscoelastic effects. The models are compared with the direct numerical simulation (DNS) of thin films for different geometries. The results are in good qualitative and quantitative agreement indicating the simplified models are valid. The pressure presents strong variations as lubricant elasticity becomes significant, but stagnates as the polymer relaxation time becomes slow compared to the characteristic ow time. The net film pressure is shown to be a superposition of a Newtonian and viscoelastic component. The viscoelastic pressure varies as contact geometry changes. Surfaces with constant slope (plane slider) exhibit a constant decrease in film pressure whereas parabolic surfaces can enhance pressure for low relaxation times.