Analysis of nonlinear viscoelastic lubrication using Giesekus constitutive equation

Abstract

Recent research has shown that adding polymeric materials to mineral oils and consequently changing the behavior of Newtonian lubricants into viscoelastic materials will enhance the lubrication performance. Therefore, in order to examine theoretically the actual behavior of such lubricants, a suitable viscoelastic model must be considered. Hence, in this paper, the solution of fluid film lubrication is presented analytically using the Giesekus viscoelastic model. This constitutive model is based on the concept of configuration-dependent molecular mobility and is suitable for predicting the nonlinear viscoelastic properties. Indeed, it can describe the power-law regions for viscosity, the normal-stress coefficients, the elongational viscosity, and also the complex viscosity. In order to linearize the momentum and constitutive equations and obtain the generalized Reynolds equation, the perturbation method is used and the mobility factor is considered as the perturbation parameter. Here, the effects of mobility factor, outlet-to-inlet height ratio, and Weissenberg number on fluid film pressure distribution, velocity profiles, load capacity, friction coefficient, and first normal stress difference are investigated in detail. Due to the normal stress difference in viscoelastic fluids, using a viscoelastic fluid in contrast a Newtonian fluid can significantly increase the load-carrying capacity of bearing. Another result is with increasing the value of mobility factor, the fluid viscosity decreases and consequently the pressure distribution decreases simultaneously while the lateral normal stress in the y-direction increases. The term pressure distribution is more negligible than the term lateral normal stress and as a result by increasing the mobility factor the load-carrying capacity increases too. It is also observed that, when the Weissenberg numbers tend to infinity regardless of the mobility factor, the friction coefficient tends towards a constant value and rubber-like elasticity is responses.

Keywords

Lubrication Giesekus model Reynolds equation viscoelastic fluid

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