Contact width and compliance between cylinders and rough plates

The contact mechanism between a cylinder and a rough plate is theoretically analysed for mixed, elastic and plastic contacts of asperities. The analysis leads to the result that the contact pressure, the contact width and the compliance between the cylinder and plate differ considerably from those calculated from the Hertz equation and the Lundberg equation when the surface roughness in contact is greater and the normal load is lower. It is also found that the difference between the calculated contact width and the compliance based on mixed asperity contacts and those based on elastic or plastic asperity contacts is small. To confirm the analysed results, the contact width between the cylinder and the rough steel or rough copper plate was measured by means of evaporated carbon and lamp black film coatings on the rough surfaces. The compliance between the surfaces was also measured using differential transformers. Little difference was found between the analysed results and the experimental results.     

Effects of Surface Roughness on Point Contact EHL

The effects of orientation of surface roughness, entrainment (rolling) velocity, and slide/roll ratio on micro-elastohydrodynamic lubrication (micro-EHL) are investigated under pointcontact conditions using the optical interferometry technique. Long bumps with constant height and wavelength produced artificially on the surface of a highly polished steel ball are used as a model roughness. It is shown that the asperities are elastically deformed and the magnitude depends on the film factor A, defined by the ratio of the central film thickness based on smooth surfaces to the composite surface roughness, as well as the surface kinematic conditions and the orientation of the asperities. It is also found that a thin or thick oil film formed at the inlet of the contact by a moving rough surface travels through the contact region at a speed very close to the average speed of the contacting surfaces. The possible mechanism is discussed.     

An Experimental Study of the Hertzian Contact of Surfaces Covered by Soft Metal Films

This paper describes an investigation of the static contact between a steel ball and a lead-plated steel flat. Both the normal approach of the surfaces and their area of contact have been measured as functions of normal load and the thickness of the lead film. It is shown that, at high loads where the radius of contact is greater than five times the film thickness, all the coated surfaces behaved elastically, and the elastic properties of the coated surfaces were identical to those of the uncoated steel. At lower loads and high film thicknesses, the films deform plastically. The transition from elastic to plastic deformation occurred when the radius of the contact area was approximately five times the film thickness.     

Contact between rough wavy surfaces allowing for the mutual effect of the asperities

The paper proposes a model of contact interaction between wavy rough surfaces allowing for the mutual effect of microasperities. The model is intended to calculate the contact parameters under heavy loadings and, correspondingly, at large contour areas. The model in question assumes that the contact waves deform elastically and the asperities deform plastically.     

Aspects Regarding the Use of Probabilistic Models for Isothermal Full Film Rough Line Contacts

This article presents a method to improve the classical probabilistic EHL models by incorporating deterministic EHL results. We first provide a review of the latest developments in the probabilistic approach for the solution of a mixed EHL problem, as well as a review of the latest deterministic EHL results that can impact the probabilistic formulations. Next, we present a probabilistic algorithm for the computations of the load supported by the fluid, the elastically deformed asperities, and the plastically deformed asperities in a mixed EHL contact. The Chang-Etsion-Bogy elastoplastic micro contact model is used together with a corresponding probabilistic fluid flow model. We also present an approach in which the elastic roughness deformation induced by the oil film can be incorporated into the probabilistic model via the use of the amplitude reduction technique.     

Temperature Analysis in Lubricated Simple Sliding Rough Contacts

A temperature analysis of dry sliding fully plastic contact is extended to calculate the asperity temperatures between a sliding lubricated rigid smooth plane and a stationary elastic rough surface. First, surface roughness is generated numerically to have a Gaussian height distribution and a bilinear autocorrelation function. Lai and Cheng's elastic rough contact computer program is then used to determine the asperity contact loads and geometries of real contact areas. Assuming different frictional coefficients for shearing the lubricant film at the noncontact areas, shearing the surface film at the asperity contacts and shearing the oxide film as the asperity temperature exceeds a critical temperature, asperity temperature distributions can be calculated. Eight cases in Durkee and Cheng's scuffing tests of lubricated simple sliding rough contacts are simulated by using 20 computer-generated rough surfaces. The results show that scuffing is correlated to high-temperature asperities which are above the material-softening temperature.     

The determination of coefficient of friction between a cylindrical indenter and a plastically deformed body by caustics

The contact between an elastic cylindrical indenter and a plastically deformed bar is examined. For this study it is assumed that the normal and tangential loads in the contact zone are related by a Coulomb-type relation. In order to determine the coefficient, which relates the normal and tangential loads, the method of reflected caustics was used. For the evaluation of this coefficient a single measurement of an appropriate length has to be made on the caustic, which was formed at the contact area of the two materials. This measurement allows the determination of the coefficient and in the case when the normal distribution of the contact load is known, the tangential load distribution can be readily obtained. The method was applied to the case of an uniformly distributed load, applied to an elastically deformed cylindrical indenter, which deforms the indented bar plastically.     

Elastic conformity in Hertzian contacts

The study of elastic conformity within rough surface contacts is presented in terms of a conformity parameter derived as a function of normal load, elastic-modulus and the geometry of asperities within the interface. The parameter can be used in conjunction with the profile structure function to determine the wavelength of features which will elastically conform, and those remaining, which will appear to the contact as roughness. Experimental confirmation of the parameter's ability to define the minimum wavelength of surface asperity conformity is shown through optical studies of the contact interface created when laser-milled steel balls are pressed against a chromium plated glass disc under various loads. Practical applications demonstrated include the parameter's ability to identify surface features responsible for generating vibration in rolling bearings by an elastic percussion mechanism, and to explain interactions between surface roughness structure and the apparent ehd film-thickness generated during rolling contact. The parameter is also shown to reduce to the well known plasticity index when conditions are allowed to approach the elastic limit.     

The contact pressure distribution during plastic compression of lead spheres

Pressure-sensitive film has been used to examine the form of the contact pressure distribution for lead spheres plastically compressed between hard steel platens. The mean contact pressure attained a maximum value of 0.6–0.7 times the Vickers hardness of the undeformed sphere when the sphere had been deformed to , where a is the contact radius and R is the radius of the undeformed sphere. The form of the pressure distribution changed markedly as the contact area increased in size, with an increasingly larger proportion of the load being supported towards the contact perimeter. The results are compared with theoretical pressure distributions proposed by Matthews [Acta Metall.28, 311–318 (1980)] for contact between spheres. Fair agreement is obtained if the sphere is assumed to deform by power-law creep, which is thought to reflect the observed time-dependent plastic deformation of the lead.     

Elastic–Plastic Spherical Contact Modeling Including Roughness Effects

The effect of material properties and surface roughness on the contribution of asperities and sphere bulk displacements to the total displacement of a rough spherical contact is investigated. A dimensionless transition load, above which the contribution of the bulk displacement exceeds the contribution of the asperities displacement, is found as a function of the plasticity index and dimensionless critical interference of the sphere bulk. A criterion is proposed for evaluating the importance of surface roughness in calculating the displacement of a rough spherical contact. Some experimental results with a spherical micro-contact are presented to verify the model.     

Mechanisms of elastic contact and friction between rough surfaces

The mechanisms of elastic contact and friction between two rough surfaces were analysed, assuming that the surface asperities were spherical, at least near their summits, and that they contacted elastically. It was found that the real contact area and the number of contact spots are approximately proportional to the load, whereas the mean area of contact spots and the mean pressure at the contact areas are almost independent of load. The frictional force F is almost equal to sA_r, where s is the shearing strength at the contact area and A_r is the real contact area. The experimental results using Pyrex glass specimens agreed within experimental limits with the theoretical results.     

TRIBOS: A Performance Evaluation Tool for Traction-Transmitting Partial EHD Contacts

The details are given of a computer model for performing a state-of-the-art tribological assessment of the performance of a lubricated concentrated rolling/sliding/spinning/contact comprising general anisotropic rough surfaces. The name chosen for this program is TRIBOS.

It computes: 1. The contact ellipse dimensions and area

2. The elastohydrodynamic (EHD) film thickness both at the plateau and at the constriction that forms at the rear of a lubricated concentrated contact under fully flooded (un-starved) and isothermal lubricant inlet conditions

3. The apportionment of the applied load between the asperities and the lubricant film

4. The magnitude and direction of the tractive force transmitted between the contacting bodies by the combined effects of (a) shearing of the fluid film and (b) coulomb friction between contacting asperities

5. The mean number of asperity contacts and the real contact area, i.e. the total contact area of the elastically deformed asperities

6. A film thickness correction factor accounting for lubricant starvation in the contact inlet

7. A film thickness correction factor accounting for a viscosity decrease of the inlet oil due to fluid heating

8. An index of surface fatigue behavior

The program is a synthesis of computational tools from the current literature for the computation of fluid film thickness and traction, and a general asperity simulation model for the elastic contact of anisotropic rough surfaces. In the example given, it is used to perform a comparative evaluation of the performance of 18 combinations of 9 surface roughnesses and 2 lubricants in a traction drive contact.     

Deformation due to contact between a rough surface and a smooth ball

Theoretical and experimental results are presented to evaluate the deformation behavior of the contact between a real rough flat surface and a smooth ball. There are three deformation responses: plastic deformation of the asperities only, plastic deformation of the bulk only and combined plastic deformation of both the asperities and the bulk. The effects of the surface roughness and the Hertzian contact parameters on the effective contact pressure are presented. The experimental results confirmed the theoretical prediction very well. For a given Hertzian contact situation the surface roughness plays an important role in controlling the deformation behavior of the contacting surfaces. A criterion is presented to predict the deformation behavior of contacting engineering surfaces.     

Theoretical and Finite Element Analysis of Static Friction Between Multi-Scale Rough Surfaces

The current work considers the multi-scale nature of roughness in a new model that predicts the static friction coefficient. This work is based upon a previous rough surface contact model, which used stacked elastic–plastic 3-D sinusoids to model the asperities at multiple scales of roughness. A deterministic model of a three-dimensional deformable rough surface pressed against a rigid flat surface is also carried out using the finite element method (FEM). The accuracy of the deterministic FEM model is also considered. At the beginning of contact, which is surface-point contact, the asperities or peaks are isolated, sharp, and the contact areas consist of an inadequate number of elements and sources of error. In this range of contact, the results are not presented as real or accurate. As the normal load increases, the number of the contact elements become larger, and thus, the results become more accurate. That is, the deterministic FEM results are most accurate at high loads. Spectral interpolation is used to smooth the geometry in between the original measured nodes. The effects of normal load and plasticity index on static friction are then analyzed. The results predicted by the theoretical model are also compared to other existing rough surface friction contact models and the FEM results. They are in a good qualitative agreement, especially for higher loads and higher plasticity indices. The FEM model also has significant error, but it is more accurate at higher loads where the proposed multi-scale static friction model and FEM model are in better agreement.     

Correlation between the frictional behaviour and the physical properties of metals

The surface topography of mating surfaces is characterized by plastically deformed asperities which form real areas of contact. As sliding leads to the shearing of junctions, it is feasible that physical properties will affect adhesion and shear strength and influence frictional behaviour.The sliding friction of similar metals and of metals sliding against a steel specimen was investigated for most commonly used metals in terms of their fundamental physical properties including atomic volume, surface energy and thermal properties.     

Limits of applicability of elastic contact models of rough surfaces

Recent stochastic models for analyzing the contact of rough surfaces assume that the asperities are microhertzian, i.e. that they can be approximated as second-order surfaces in the vicinity of contact points, and that the asperities deform elastically. Using a plane strain solution from the literature for a sinusoidally corrugated half-space, the range of validity of these assumptions is shown to be related to the mean square surface slope and the macrocontact pressure. By extension to random surfaces characterized by a one-dimensional spectral density function an interval on the surface spatial frequency is found over which the asperities deform elastically but without completely flattening. A numerical example is given.     

Experimental Study of Lubricant Film Thickness Behavior in the Vicinity of Real Asperities Passing through Lubricated Contact

This article presents an experimental study of the influence of real surface micro-geometry on the film thickness in a circular elastohydrodynamic (EHD) contact formed between a real, random, rough surface of steel ball and smooth glass disk. Phase shifting interferometry was used to measure in situ initial undeformed rough surface profiles, whereas thin film colorimetric interferometry provided accurate information about micro-EHD film thickness behavior over a wide range of rolling speeds. Two real roughness features were studied in detail—a 56-nm-high ridge and a 90-nm-deep groove, both transversely oriented to the direction of surface motion. It was shown that the ridge is heavily deformed in a loaded contact and its height increases with increasing rolling speed. The asperity tip film thickness behavior is quite similar to the contact average film thickness when the film thickness is higher than the undeformed ridge height. However, below this limit the film is thicker than what the EHD theory predicts. For the groove, a local reduction in film thickness at the leading edge was observed. When the groove is passing through the EHD conjunction, it maintains its undeformed shape. The behavior of both roughness features studied shows good agreement with previous experimental observations conducted using an artificially produced ridge and groove.     

Research on the Friction Behaviors of Two Rough Surfaces Covered with Boundary Film

Boundary film plays an important role in improving the lubricating characteristics of mixed lubrication. But due to the complication of surface profile and the microscale of boundary film, progress made on the boundary lubrication is relatively less than that of fluid film lubrication. A friction model of two rough surfaces covered with the boundary film is studied in the paper. The rough surface is modeled by a collection of spherical asperities with the same curvature radius and the Gaussian height distribution, the shearing force of asperities over the boundary film is expressed by the linear equation, and the plowing force of asperities over the solid flat is modeled by considering the possibility of asperities being sheared off. Then, the friction behaviors are researched by analyzing the effects of boundary film and surface topography in different values. The results demonstrate that the effects of boundary film on the friction coefficient are enhanced with the increase in the thickness of boundary film and are weakened with the increase in the contact load. And surface profile parameters also affect the friction behaviors of boundary lubrication, the smoother the surface is, the more significant the boundary lubricating effect is.     

An unsteady mixed soft EHL model, with application to a rotary lip seal

A rotary lip seal usually operates with full-film lubrication. However at low speeds, such as those encountered during startup and shutdown, mixed lubrication occurs and asperities on the lip contact the shaft. To simulate this condition, a mixed soft EHL model has been constructed. The fluid mechanics of the lubricating film is described by a Reynolds equation that can handle interasperity cavitation. The bulk deformation of the lip is computed using influence coefficients, while the junctions between the asperities and the shaft are modeled as Hertzian contacts. Since the shaft is rough, the flow is unsteady and an unsteady analysis is required. The model shows how the shaft roughness affects such seal characteristics as load support, contact load ratio, contact area ratio, cavitation area ratio, reverse pumping rate and average film thickness.     

Experimental study of the behaviour of real asperities within lubricated contacts

Thin film colorimetric interferometry was used in combination with phase shifting interferometry for the detailed experimental investigation of changes in real surface microgeometry within the elastohydrodynamic conjunction formed between a real, random, rough surface, a steel ball and a smooth glass disc. Three real roughness features were studied in detail — the transverse ridge, transverse groove and longitudinal groove. The ridge was found to be heavily deformed within lubricated contact and its height increased with increasing rolling speed. For the transverse groove, a local reduction in film thickness at the leading edge was observed, while the longitudinal groove maintained its undeformed shape. Copyright © 2006 John Wiley & Sons, Ltd.