Simon Medina

Meeting the Contact-Mechanics Challenge

This paper summarizes the submissions to a recently announced contact-mechanics modeling challenge. The task was to solve a typical, albeit mathematically fully defined problem on the adhesion between nominally flat surfaces. The surface topography of the rough, rigid substrate, the elastic properties of the indenter, as well as the short-range adhesion between indenter and substrate, were specified so that diverse quantities of interest, e.g., the distribution of interfacial stresses at a given load or the mean gap as a function of load, could be computed and compared to a reference solution. Many different solution strategies were pursued, ranging from traditional asperity-based models via Persson theory and brute-force computational approaches, to real-laboratory experiments and all-atom molecular dynamics simulations of a model, in which the original assignment was scaled down to the atomistic scale. While each submission contained satisfying answers for at least a subset of the posed questions, efficiency, versatility, and accuracy differed between methods, the more precise methods being, in general, computationally more complex. The aim of this paper is to provide both theorists and experimentalists with benchmarks to decide which method is the most appropriate for a particular application and to gauge the errors associated with each one.

Analytical and Numerical Models for Tangential Stiffness of Rough Elastic Contacts

The paper considers elastic contact of rough surfaces and develops a simple analytical expression for the stiffness of the contact under tangential loading, which predicts that the contact stiffness is proportional to normal load and independent of Young’s Modulus. The predictions of this model are compared to a full numerical analysis of a rough elastic contact of finite size. The two approaches are found to be in good agreement at low loads, when the asperity spacing is large, but the numerical approach predicts much lower stiffnesses at medium and high loads. It is shown that the overall stiffness cannot exceed that of the equivalent smooth contact, and a simple means of modifying the analytical approach is proposed and validated.

Direct observations of a micropit in an elastohydrodynamic contact

Abstract A hard steel roller from a disc tester which had an isolated micropit and associated cracks on its surface was pressed against a glass plate and subjected to a range of lubricated, rolling–sliding conditions, with the objective of observing the effect on the distribution of film thickness in an EHL contact. The results show a remarkable interaction between the micropit, the direction of sliding and the thickness of the elastohydrodynamic film. Fluid expulsion into the cavitated region can be observed as the micropit emerges from the contact.

Transient effects in lubricated textured bearings

The aim of this paper is to study the transient phenomena in hydrodynamic textured bearings. Both convergent and convergent–divergent reciprocating textured bearings are considered. A mass-conserving formulation of the Reynolds equation recently proposed by some of the authors and used to capture cavitation in steady-state lubricated contacts has been implemented to study transient effects in lubricated textured bearings. It is shown that the proposed solver is capable of capturing the frictional response of bearings characterised by various geometries and loading conditions in both steady-state and transient configurations. Depending on the boundary conditions governing the problems under investigation, changes in load support or film thickness variations are correctly predicted, demonstrating that the methodology developed in this paper is suitable to provide an efficient tool for the design and optimisation of textured bearings. A qualitative comparison with preliminary experimental data obtained using an apparatus developed to study reciprocating textured surfaces is performed, showing that the characteristic transient behaviour of such surfaces in different loading regimes can be correctly captured using the proposed numerical implementation.

The Influence of Surface Topography on Energy Dissipation and Compliance in Tangentially Loaded Elastic Contacts

The influence of non-Gaussian surface roughness on elastic contacts loaded in both normal and tangential directions has been investigated. A numerical solution method based on the multilevel scheme and incorporating the theorem of Ciavarella/Jaeger has been implemented, which allows fast calculation of partial slip loading conditions, including the energy dissipation for a fully reversed tangential loading cycle. The effect of varying roughness rms, skewness, kurtosis, and correlation lengths on contact areas, stiffness values, and energy dissipation is presented, and the significance of these parameters and of the loading method are discussed. It was found that the energy dissipation can be greatly increased by greater surface roughness. Maps showing how the energy dissipation is distributed within the contact are presented, which provide some explanation for this observation and the scatter that may occur for surfaces of nominally similar roughness. The suitability of these parameters for predicting the contact behavior of rough surfaces is also considered.

Adhesive Contact Between Atomistic Surfaces Using a Continuum Analysis

We have previously shown that, for non-adhesive conditions, an atomic scale contact can be adequately represented by a continuum analysis despite the physical shortcomings at this scale. Here we have extended the approach to include effects of the adhesive forces that become significant at this level of contact. Adhesive forces are obtained directly from the surface separation across the contact rather than through a total surface energy approach; this allows a complete representation of local surface features. The pull-off characteristics and pressure profiles have been obtained for several different atomistic AFM tip profiles and compared to those obtained from molecular dynamics simulations presented in the literature [1].Copyright

A Fast Deterministic Model to Study Adhesion in Rough Contacts

As two bodies come into contact, attractive forces occur wherever a gap exists between the two surfaces. The forces are significant at distances of atomic order but become negligible at much larger separations. Their effect is insignificant in most situations for which engineers wish to understand the state of the contact since the adhesive forces are usually much smaller than the net load applied and/or surface roughness results in non-contacting areas being far enough apart that the attractive force is negligible. There are, however, certain cases in which adhesion forces do contribute to the contact mechanics and must be accounted for in any valid analysis. Materials with low elastic modulus, such as rubber, may deform sufficiently around surface asperities such that the surface separation is small and adhesion is apparent.A model for arbitrary geometry (with surface roughness) that includes adhesive forces is reported here. It is based upon the multi-level method of contact analysis developed by Venner and Lubrecht [1]. Adhesion has been implemented using the Lennard-Jones potential as applied to two parallel surfaces, adding the requirement of specific negative pressures for the separated surface nodes [2]. The model is then compared to theoretical and numerical analysis of smooth spherical contacts and to rough contacts of different scales and material properties.© 2012 ASME

Development of rolling contact damage in two bronze alloys

When metallic materials are subjected to rolling contact at sufficiently high loads, the possible outcomes include initial plastic deformation, shakedown, residual stresses, ratchetting, strain localisation, crack initiation and the formation of fatigue pits. The resultant damage is often a life or performance limiting factor in machine elements but the details of the processes responsible are poorly understood because direct observation of the small regions affected is difficult. In the present paper we have studied the early development of damage in two model bronze alloys, selected because they show contrasting strain hardening behaviour and are suitable for detailed metallographic analysis. One alloy, a nickel-bronze used as a bearing cage material showed evidence of cyclic softening and of ratchetting. The second alloy, a phosphor-bronze used for worm wheels, showed steady cyclic hardening. The development of damage for each bronze during the first 1–3000 cycles of rolling contact has been studied using optical and scanning electron microscopy. This enables, the progressive microstructural changes leading to fatigue in local subsurface regions to be observed and quantified. The nickel bronze showed strong evidence of cyclic slip and strain localisation leading to cracking, despite a higher initial yield stress.

Tribology of spline couplings

Toothed spline couplings are ubiquitous in mechanical transmission systems and have been studied experimentally for many years. Recently it has become possible to construct useful three-dimensional numerical models of complete couplings and this has led to a number of surprising findings which cast new light on the mechanics and durability of the contacting spline teeth. The analysis presented includes misalignment, elasticity and friction. Among the new findings are the existence of discontinuous tooth loadings, of unsymmetrical pressure-slip behaviour and of a “toppled” regime in which the two halves of the coupling are suddenly displaced through their mutual clearance. The results of the study are used to reassess wear testing and to propose a new, more logical approach to coupling design.