Response of elastic/viscoelastic layers on an elastic half-space in rolling contacts: Towards a new modeling approach for elastohydrodynamic lubrication

Abstract

The 3D quasi-static contact problem of a rigid sphere rolling on an elastic half-space covered by a thin viscoelastic/elastic layer is studied as representative of soft layered contacts in engineering, physics, and biomedical applications, as well as for its potential merit to model Elasto-Hydrodynamically Lubricated (EHL) contacts in specific EHL film behavior suggested in earlier research. The viscoelastic layer behavior is modeled with a standard linear solid (SLS) model with a single relaxation time. Two approaches are used, the foundation (Winkler) reduced model assuming unidirectional stress–strain behavior normal to the surface only and the Papkovich–Neuber potential model which, based on the complete Navier–Cauchy equations, accounts for non-local support and bending effects. The models are validated against literature and compared. Whereas coated/layered contact problem studies mostly consider relatively thick coatings, and results focus on the pressure distribution and the contact area size, in this paper we consider layers with a thickness much smaller than the contact radius, i.e. of the order of a thickness of a conventional EHL film. The details of the layer deformation, pressure profiles and subsurface stresses are presented and interpreted in terms of the underlying physics, in particular the thin layer limit common also in thin fluid layers. It is shown that two dimensionless parameters, the ratio of the elastic modulus between the layer and the substrate and the ratio of the layer thickness to the corresponding Hertz contact width, dominate the systematic response for elastic layered contact problems. And four dimensionless parameters with two extras, the Deborah number based on the Hertz contact width and the ratio of the two elastic limits of the SLS viscoelastic material, are needed and analyzed for viscoelastic layered contacts. The results presented provide a good framework for the understanding and interpretation of the effects of viscoelastic layers on the deformation and pressure distribution of contact problems. Finally, the capability of actually modeling EHL film behavior via a viscoelastic layer suggested by van Emden et al. (2017) is discussed.