Friction Force During Lubricated Steady Sliding of a Rigid Cylinder on a Viscoelastic Substrate

Abstract

We study the friction force during lubricated sliding of a rigid cylindrical indenter against a viscoelastic substrate in the iso-viscous visco-elasto-hydrodynamic lubrication (VEHL) regime. The substrate is represented by a foundation model. The solution is controlled by three dimensionless parameters. The first of these, λ, measures the time for the indenter to move one contact zone relative to the viscoelastic relaxation time; the second is the ratio of the long time to short time compliance of the substrate, c ∞ ∕c 0 ; the third parameter, β, is the ratio of average fluid flow rate to the sliding velocity. Although our solution works well for the full range of parameters, we focus on the "Hertz" regime (β >>1) where practically all the fluid in the contact region is squeezed out. This regime is quite common in soft contact lubrication problems and presents significant numerical difficulties. Our analysis gives insight into why these numerical difficulties arise. The friction force can be decomposed into two parts, one due to viscoelastic dissipation and the other from hydrodynamics. Although these two are generally coupled, in the Hertz limit, an important result is that the viscoelastic portion of the friction force can be well approximated by the solution of the corresponding "dry" sliding problem, in which there is no lubricating fluid layer. This provides a simple way to decouple the hydrodynamic portion of the friction force from the viscoelasticity of the substrate. We study how hydrodynamic pressure and film thickness vary with the controlling dimensionless parameters. Scaling laws for these relationships are given in closed form.

Soft-lubrication interactions between a rigid sphere and an elastic wall

“…The previous EHD coupling is also widely encountered in soft condensed matter, but at very different pressure and velocity scales (Karan, Chakraborty & Chakraborty 2018). Examples encompass the remarkable frictional properties of eyelids (Jones et al 2008) and cartilaginous joints (Mow, Holmes & Lai 1984;Jahn, Seror & Klein 2016), as well as biomimetic gels (Gong 2006) and rubbers (Sekimoto & Leibler 1993;Moyle et al 2020;Wu et al 2020;Hui et al 2021). Of interest as well are the collisions and rebounds of spheres in viscous environments (Davis, Serayssol & Hinch 1986;Gondret, Lance & Petit 2002;Tan, Wang & Frechette 2019), the rheological properties of soft suspensions and pastes (Sekimoto & Leibler 1993;Meeker, Bonnecaze & Cloitre 2004), and the self-similar properties of the contact (Snoeijer, Eggers & Venner 2013).…”

Lubricated Sliding of a Rigid Cylinder on a Viscoelastic Half Space

“…However, previous work has not addressed the relationship between the mechanics of viscoelastic hydrodynamic lubrication and simpler cases of E and the pure dry sliding contact. Hui et al [33] recently showed that the full VEHL solution of a cylinder sliding on a thin viscoelastic foundation can be decomposed, to a good approximation, into a combination of the corresponding dry sliding and the EHL solutions. Whether this decomposition is obtained in the more general VEHL problem of lubricated sliding on a viscoelastic half space remains an open question, and this is the main focus of the work presented here.…”

“…A recent study by Hui et al [33] has shown that the friction force during viscoelasto-hydrodynamic lubrication can be well approximated as a combination of two simpler cases: the dry sliding case where the liquid is absent and the lubricated sliding case where the substrate is elastic. However, the substrate in that work was modeled as a viscoelastic spring foundation in which mechanical interactions are purely local, in the sense that the displacement of the substrate at a point is affected by the pressure only at that point.…”

Rotation–translation coupling of soft objects in lubricated contact

“…14,15 Theoretical treatments typically require numerical analysis, 16,17 although analytical solutions are available in asymptotic limits. In the limit of large normal loads, the geometry approaches that of classical Hertzian contact, 18,19 separated only by an extremely thin film of fluid supported by the relative motion of the surfaces. 20,21 In the opposite limit of small normal loads, the surfaces slide with a relatively thick fluid film and the surfaces are only slightly deformed.…”