Modeling polymeric lubricants with non-linear stress constitutive relations

Polymers are added to enhance the tribological performance of lubricating oils so that they can withstand the applied load and resist degradation due to thermal effects and high shear stress. However, their addition can lead to the onset of non-Newtonian effects, in particular viscoelasticity, measured via the Weissenberg number (Wi), i.e. the ratio between the polymer relaxation time and the shear time scale. In this work, we examine the effect of non-linear polymer traits, specifically (i) shear thinning and (ii) the finite polymer extensibility, on the load carrying capacity of the thin lubricating film via the viscoelastic Reynolds approach [Ahmed & Biancofiore, Journal of non-Newtonian Fluid Mechanics, 292, 104524] using constitutive relationships non linear in the stress, such as FENE-CR and FENE-P. We validate our approach by comparisons with direct numerical simulations of viscoelastic films in a parabolic slider bearing. Thereafter, we focus on a journal bearing whose geometry depends on its eccentricity ratio. Our results show that viscoelasticity has a strong impact on the load. Load is (i) enhanced initially for small values of Wi but decreases later at large Wi due to shear thinning), (ii) exhibits a non-linear dependence on the finite extensibility of the polymers, and finally (iii) is strenghtened (weakened) at low (high) eccentricity ratio.