Aspects of modeling and numerical simulation of dry point contacts between viscoelastic solids

Abstract

The virtual absence of pressure driven flow inside an elastohydrodynamic lubrication (EHL) contact leads to remarkable similarity between lubricated film thickness and separation by a viscoelastic layer as is suggested by experimental and theoretical results, see [1]. This offers interesting opportunities for mixed lubrication modeling without needing the flow continuity-based Reynolds equation. In this paper numerical simulation of viscoelastic concentrated contact modeling is revisited, first considering the problem of a viscoelastic half-space and a rigid sphere, both in static (squeeze) as well as (frictionless) rolling/sliding conditions. In particular modeling aspects are discussed so that the efficiency of computation of the viscoelastic deformation remains close to the efficiency of computation of an elastic deformation. This is achieved by rewriting Hunter’s [2] deformation equation from an integral form into a differential form by applying the Leibnitz integral theorem, even for complex materials with multiple relaxation times to represent complex viscoelastic properties of materials. The approach can be straightforwardly implemented in any (EHL) contact solver regardless of the numerical method. Detailed results are presented, such as the effect of the Deborah number, the relation between the extreme cases of the rolling problem and the static problem, and discussed in detail. In addition to the rigid sphere against a viscoelastic half-space, also the case of two viscoelastic bodies is considered.