Elastohydrodynamic Lubrication of Soft, Highly Deformed Contacts

Abstract

Part 1 presents a theoretical solution to the problem of lubrication of soft, highly deformed surfaces. It is argued that with this type of contact the inlet and outlet regions can be separated and analysed independently. This approach leads to a single value of non-dimensional film thickness at the point of maximum contact pressure and to a non-dimensional minimum film thickness dependent on the relationship between the inlet and outlet parameters. In Part 2, these results are applied to the problems of a cylinder sliding on an elastomer lined surface, an elastomer lined journal bearing and a sliding O-ring seal.

Similarity theory of lubricated Hertzian contacts

“…27 The gap thickness h gap at the center of the sphere was found to scale with an exponent α 1 = 0.57 ± 0.05 (reported as α 1 = 0.6 in Ref. 28), in good agreement with 9,10 and the current analysis. This, however, is in significant disagreement with the scaling argument by Refs.…”

“…2,3,7 For the opposite case of strong deformations, the contact area becomes flat as in a classical Hertzian contact, 8 except for the effect of the thin lubrication layer. [9][10][11] Here we show that at the edge of the contact area, the film thickness is described by a similarity solution, whose shape is governed by an integro-differential equation, as opposed to the ordinary differential equations encountered in most singular fluid problems. 12 By solving the non-local similarity equation, we treat the selection problem for the film thickness, which turns out to be a non-local version of Bretherton's problem 13 for the motion of a bubble in a tube.…”

“…These scalings have been suggested before on the basis of numerical simulations, 21 scaling, 9 and asymptotic analysis. 10,11 Note that in the limit λ → 0 the profile is asymptotically flat: the characteristic scale for the gap height h ∼ λ 3/5 is much smaller than the scale for x ∼ λ 2/5 , ensuring that lubrication theory applies.…”

Analogies between elastic and capillary interfaces

“…2(c)]. The former is a paradigmatic example for capillary flows [8][9][10][11], while the latter is classical in the context of tribology [12][13][14][15][16]. Here we show that both flows exhibit the same mathematical structure and we will derive the resulting scaling laws using the very same method in both cases.…”

“…(Adapted from [23], reproduced with permission from Cambridge University Press.) (c) Sliding Hertzian contact [12,16]. (Reproduced from [16] with the permission of AIP Publishing.)…”