On the dry elasto-plastic contact of nominally flat surfaces

A model to be used for numerical simulation of the contact of linear elastic perfectly plastic rough surfaces was developed. Energy dissipation due to plastic deformation is taken into account. Spectral theory and an FFT-techique are used to facilitate the numerical solution process.     

A thermal creep model for the contact of nominally flat surfaces: Jeffreys' linear visco-elastic model

This work considers the mechanics of contact of thermo-visco-elastic materials. In particular the creep behavior of a nominally flat rough surface in contact with a rigid half space is studied. The rough surface is modeled using fractal geometry. A synthesized profile, a Cantor structure, is utilized to model the surface. Such a profile has two scaling parameters and different heights for each generation of asperities. The effect of temperature will be included through the concept of activation energy using the Arrhenius equation.The objective of this model is to study the normal creep approach of the surface (punch) as a function of the applied creep load, time, and temperature. The material of the punch is assumed to behave according to Jeffreys' model. Such a model is an arrangement of springs and dashpots in parallel and/or in series.The creep approach of linearly visco-elastic materials is explored using elastic-visco-elastic correspondence analysis. An asymptotic power law is obtained, which relates the force and the bulk temperature acting on the punch to its approach. This model is valid only when the approach between the punch and the half space is in the range of the roughness size. The proposed model admits an analytical solution for the case when the deformation is linear thermo-visco-elastic. The obtained model shows a good agreement when compared with experimental results from literature.     

Evaluation of the real contact areas, pressure distributions and contact temperatures during sliding contact between real metal surfaces

A three-dimensional elastic contact algorithm has been developed to analyse the normal contact problems of bodies having rough surfaces. The algorithm can evaluate the real contact areas and contact pressure distributions using measured surface roughness data.

Following an approximate elastic-plastic contact solution the analysis produces more realistic elastic and plastic contact areas; in addition results of contact pressure distributions can be predicted according to a given maximum plastic limit pressure.

The technique can simulate (in an approximate way) the elastic-plastic sliding contact behaviour in the vicinity of asperities or concentrated contact areas by ignoring the effect of the tangential forces on the vertical displacement.

Assuming a certain sliding speed and a particular coefficient of friction the local temperature distribution due to the heat generation over the real contact areas can also be calculated for 'slow sliding' problems.

The results show the moving real contact areas and the contact temperature fields for an electric spark mechanical steel surface moving over a planed bronze surface. Changes of the rigid body displacement, as well as the average and maximum pressures are also presented during sliding.

The micro-contact or asperity contact behaviour for bodies having large nominal contact area and the macro-contact behaviour for bodies being in 'concentrated contact' are also compared. In the latter case an ideal smooth steel ball was slid over the previously mentioned bronze surface.     

Film-forming capability in rough surface EHL investigated using contact resistance

Highly loaded machine elements such as gears and cams have a non-smooth surface topography that is created during manufacturing. It is well known that the film-building properties of such surfaces may be different from those that are perfectly smooth. The capability to form a separating film may also be altered in time due to run-in phenomena. In this study, a smooth steel ball was loaded against rough steel discs and run under pure rolling as well as sliding conditions. Several different steel surfaces were tested under nominal EHL conditions, where the contact was monitored by means of its electrical resistance and capacitance. Each surface was first run in for 15 min, followed by a sweep-in speed determining the lift-off curve. Electrical contact measurements were continuously conducted during run in as well as lift-off. Fully formulated gear oil and its base fluid were used as test lubricants. Results show that run in of a surface seems to be a competition between conformation of surface topography and tribofilm formation. At the tested conditions, the formation of a tribofilm is dependent on the initial surface topography and is created rapidly causing less metal–metal contact. This film also seems to effectively prohibit changes in surface topography causing less structural run in than expected.     

Thermomechanical analysis of elastoplastic medium in sliding contact with fractal surface

The effects of mechanical and thermal surface loadings on deformation of elastic–plastic semi-infinite medium were analyzed simultaneously by using the finite element method. Rigid rough surface of a magnetic head and smooth surface of an elastic–plastic hard disk were chosen to perform a comprehensive thermo-elastic–plastic contact analysis at the head–disk interface (HDI). A two-dimensional finite element model of a rigid rough surface characterized by fractal geometry sliding over an elastic–plastic medium was then developed. The evolution of deformation in the semi-infinite medium due to thermomechanical surface loading is interpreted in terms of temperature, von Mises equivalent stress, and equivalent plastic strain. In addition to this, the effects of friction coefficient, sliding, and interference distance on deformation behavior were also analyzed. It is shown that frictional heating increases not only the contact area but also the contact pressure and stresses.     

Effect of asperity interactions on rough surface elastic contact behavior: Hard film on soft substrate

An improved elastic micro-contact model of rough surfaces accounting for asperity interactions is proposed. The contact behavior of a single asperity system is composed of a stiffer hemi-spherical asperity deformation and bellowing softer substrate deformation, which is then extended to rough surface contact including asperity interactions. Using the solution of substrate deformation, normal positions of individual asperities are adjusted during quasi-static contact, from which surface interactive forces are obtained. Analytical simulations are performed using the proposed rough surface contact model, whose results are compared to Greenwood-Williamson-based models and with experimental measurements.     

The influence of surface roughness and the contact pressure distribution on friction in rolling/sliding contacts

A numerical contact model is used to study the influence of surface roughness and the pressure distribution on the frictional behaviour in rolling/sliding contacts. Double-crowned roller surfaces are measured and used as input for the contact analysis. The contact pressure distribution is calculated for dry static contacts and the results are compared with friction measurements in a lubricated rolling/sliding contact made with a rough friction test rig. The mean pressure is suggested as a parameter that can be used to predict the influence of surface roughness on the friction coefficient in such contacts. The results show two important properties of the friction coefficient for the friction regime studied in this paper: (1) there is a linear decrease in friction coefficient as a function of the slide-to-roll ratio, and (2) the friction coefficient increases linearly with increasing mean contact pressure up to a maximum limit above which the friction coefficient is constant. The absolute deviation of experimental results from the derived theory is for most cases within 0.005.     

Evaluation of the wavelet transform method for machined surface topography 2: fractal characteristic analysis

In this paper, a new method based on wavelet transform is proposed as a means for studying the fractal characteristics of rough surfaces. Through estimation of normal mathematical curves with known fractal dimensions, generated by the Weierstrass-Mandelbrot function, Majumdar-Bhushan function, Fractal Brownian motion (including three methods: the Midpoint FBm, the Additions FBm, the Interpolated FBm) and Interposed method (Kiesswetter curve), it is validated that the wavelet transform method can accurately calculate the fractal dimension. These fractal functions have been used to simulate some surface profiles. The results indicate that the Wavelet transform method is the most precise in its calculation of the fractal dimensions of the curves. It obtains more accurate results than seven other methods, named the Box counting method, the Yardstick method, the Co-variation method, the Structure function method, the Variation method, the Power Spectrum method and the Rescaled range analysis method. Precisely calculating the fractal dimensions of the curves is the first step in characterising machined surface topography. In addition, this paper aims to further develop the evaluation procedure for the fractal characteristics of machined surface topography.     

A model for the liquid-mediated collapse of 2-D rough surfaces

Small-scale devices are particularly vulnerable to adverse effects of adhesion because of large surface area to volume ratios. Additionally, small gaps can be easily bridged at high humidity or when there are other contaminant liquids present. The bridging of a portion of an interface by a liquid droplet of given volume tends to pull surfaces in closer proximity due to the sub-ambient pressures that arise. In turn, the area spanned by the bridge will increase and lead to a greater adhesive force. A previous study considering a liquid bridge between two elastic half-spaces initially separated by a uniform gap demonstrated that, under certain conditions, an instability will arise whereby the surfaces come into full contact. Owing to the regularity of the geometry considered, the problem was amenable to a semi-analytical treatment and the stability condition was expressible analytically in terms of a single dimensionless group. In the present work, we develop a model to include the effects of surface roughness. The influence of asperities on the surface is treated by means of a recently developed multi-scale model that considers the full range of wavelengths comprising the surface profile. In the simulations, two nominally flat rough surfaces are brought together under a prescribed load and a liquid bridge of given volume is introduced in the contact, the initial areal coverage being determined by the initial mean surface separation. The interface configuration is then iterated until a configuration is found that satisfies the equations of elasticity and capillarity for the given liquid volume. As a result of the simulation, critical values are found for combinations of parameters that delineate stable and unstable conditions.     

Investigations on machined metal surfaces through the stylus type and optical 3D instruments and their mathematical modeling with the help of statistical techniques

The measurement of roughness on machined metal surfaces is of considerable importance to manufacturing industries as the roughness of a surface has a significant influence on its quality and function of products. In this paper, an experimental approach for surface roughness measurement has been based on the comparison of roughness values taken from the stylus and optical type instruments on the machined metal surfaces (turning, grinding and milling) is presented.Following this experimental study, all measured surface roughness parameters have been analyzed by using Statistical Package for Social Science (SPSS 15.0) statistically and mathematical models for the two most important and commonly used roughness parameters R_a and R_z have been developed so that R_a = R_a (F, P, C) and R_z = R_z (F, P, C, M), whereas F expresses feed, P periodicity, C contrast and M the type of material. The statistical results from numerous tests showed that there has been a correlation between the surface roughness and the properties of the surface topography and there have been slight differences among three measurement instruments on machined metal surfaces in this experimental study.     

The factors affecting surface roughness measurements of the machined flat and spherical surface structures – The geometry and the precision of the surface

The quantitative determination of surface roughness is of vital importance in the field of precision engineering. This paper presents an experimental study of the roughness analyses for the flat and spherical surfaces of machined metal in order to compare the roughness data taken from the cloud data produced by the stylus type profilometer and two optical-based measurement instruments, namely the infinite focus microscope and the confocal laser scanning microscope.In this experimental study, the roughness measurements for fifteen flat and six spherical surfaces were repeated six times using three different measurement instruments. Great care was paid to measure the same location for each measurement. For the comparison of the measurement techniques, the same measurement process was applied to the flat and spherical surfaces individually, and the configurations of the measurement instruments (filter type, cut-off, resolution etc.) were synchronized. R_a, two-dimensional (2D) roughness parameter and S_a, three-dimensional (3D) roughness parameter were also compared. The measurement results for the samples having spherical surfaces indicated a considerably high difference in values taken from the stylus profilometer and two optical-based measurement instruments in contrast to those for flat surfaces.     

Contact and thermal analysis of transfer film covered real composite-steel surfaces in sliding contact

For composite-steel surfaces in sliding contact an anisotropic numerical contact algorithm has been developed to study the ‘layer type’ problems. An FE contact analysis was applied to evaluate the contact parameters (real contact area, contact pressure distribution and normal approach). The contact temperature rise was determined by using both a numerical thermal algorithm for stationary and a FE transient thermal technique for ‘fast sliding’ problems.The effect of a continuous transfer film layer (TFL), that had built up during wear of the PEEK matrix material on the steel counterpart, was considered. Its thickness was assumed to be t=1 μm, and its material properties were that of PEEK at room temperature or, in the case of frictional heating, at a temperature of 150°C (i.e. above the glass transition temperature of the polymer matrix).Results are presented for a spherical steel asperity, with/without TFL, sliding over composite surfaces of different fibre orientation, and in addition, for real composite-steel surfaces (based on measured surface roughness data) in sliding contact. The TFL has an effect on the contact parameters especially at higher operating temperatures (i.e. 150°C); it results in the production of a larger contact area and a lower contact pressure distribution. The contact temperature rise is clearly higher if a TFL is present. Due to the low thermal conductivity of PEEK, the TFL is close to the melting state or it even gets molten within a small vicinity of the contact area.     

Mathematical modelling of superhydrophobic surfaces for determining the correlation between water contact angle and geometrical parameters

Water-repellent surfaces have recently become an active area of research due to the desire to achieve self-cleaning, anti-sticking, and non-wetting properties on surfaces. These surfaces are required for different engineering applications. A superhydrophobic (SHP) surface achieves a water contact angle (CA) of 150° or greater. The physical understanding of the process by which surfaces attain superhydrophobicity is still limited, making it difficult to fabricate such surfaces by machining due to the hierarchical scale of the features involved. This work, therefore, aims to shed light on the physical understanding of the behaviour of a water droplet as it rests on a micro textured surface. In the first part of the work, a mathematical model is developed that follows a basic and novel approach of force balance considering a water drop sitting on a surface under static conditions. The various forces responsible for equilibrium are individually evaluated. The model used to describe a surface's interaction with water establishes the relationships between various parameters in the force balance system. From these relationships, the water contact angle (CA) required for superhydrophobicity was found through a simulation. In the second part of this work, arrays of projected micro-features were fabricated on different materials using deep X-Ray lithography (DXRL), micro wire EDM, and the wire wound method. The measured values of the CA on the fabricated surfaces were similar to the values obtained from the model. The proposed model, therefore, helps in designing SHP surfaces (SHSs) on large-scale arrayed micro-features based on several geometrical parameters.     

Stress history in rolling–sliding contact of rough surfaces

An investigation into the non-Hertzian, elastic stress history, due to the contact of two rough surfaces is presented. A complex evolution of stress is produced whose magnitude and rate depend strongly upon the roughnesses and speeds of the contacting bodies. The key features of the stress fields are illustrated by plots of stress versus time and horizontal distance, for a range of depths and for various contact conditions. The stresses near the surface are many times higher than in an equivalent smooth contact and the roughness on thecounterface generates a moving stress field which, when sliding is present, greatly increases the number of cycles of stress during each passage of the contact. This may account, in part, for the observation that the rolling fatigue life of hard steels declines more rapidly with sliding speed for rough, than for smooth surfaces and suggests that counterface roughness is especially important in determining the fatigue life.     

Surface morphology in engineering applications: Influence of roughness on sliding and wear in dry fretting

Influence of initial surface roughness on friction and wear processes under fretting conditions was investigated experimentally. Rough surfaces (Ra=0.15-2.52 μm) were prepared on two materials: carbon alloy (AISI 1034) and titanium alloy (Ti-6Al-4V). Strong influence of initial surface roughness on friction and wear processes is reported for both tested materials. Lower coefficient of friction and increase in wear rate was observed for rough surfaces. Wear activation energy is increasing for smoother surfaces. Lower initial roughness of surface subjected to gross slip fretting can delay activation of wear process and reduce wear rate; however, it can slightly increase the coefficient of friction.     

On the elastic contact of rough surfaces: Numerical experiments and comparisons with recent theories

Some numerical experiments are conducted for studying the decrease of the elastic contact area in the elastic contact of fractal random surfaces when adding components of roughness of progressively smaller wavelengths. In particular, Fourier and Weierstrass random series are used, and a recent accurate and efficient method developed by the authors is used, involving superpositions of overlapping triangles. Some comparisons are made using two recent theories, that of Ciavarella et al. published in 2000 on the deterministic Weierstrass fractal profile, and that of Persson published in 2001 on random generic contact. We show that both theories tend to underpredict the contact area by a significant (and similar) factor in these representative cases in the region of light loads (partial contact), where the non-linearities of the contact mechanics are not included in neither of the formulations. In Persson's theory case, the discrepancy is particularly large at high fractal dimensions of the profile, where in theory the numerical experiments should be more closely reproducing a true Gaussian process. The Ciavarella et al. “Archard-like” theory, is only accurate when the parameter γ (the ratio of successive wavelengths) is unrealistically large. However, we only tested the Ciavarella et al. theory in the simplified “Hertzian approximation” form assuming partial contact at the peaks of contact, although we don’t expect the full version to improve dramatically the results.     

Investigation on the polishing of aspheric surfaces with a doughnut-shaped magnetic compound fluid (MCF) tool using an industrial robot

Aspheric elements have become essential optical surfaces for modifying optical systems due to their abilities to enhance the imaging quality. In this work, a novel method employing a doughnut-shaped magnetic compound fluid (MCF) polishing tool, and an industrial robot was proposed for polishing aspheric surfaces. Firstly, investigations on the MCF tool, including the formation process and geometry, were conducted to form an appropriate polishing tool. The distribution of abrasive particles was observed using SEM and EDX mapping. Thereafter, a conic workpiece constructed from 6061-aluminum alloy was selected as the workpiece, which was used to discover the effects of the parameters on the polishing ability of aspheric surfaces. Finally, a polishing experiment was conducted with an aspheric element under the optimized conditions. The obtained results are shown as follows. (1) A relatively regular MCF tool was obtained when the eccentricity (r), amount of MCF slurry supplied (V), revolution speed of the MCF carrier and magnet (n_c and n_m, respectively) were given at appropriate values. (2) Abrasive particles entrapped in or attached to the clusters were observed abundantly on the MCF tool sample. (3) The surface profile of the conic workpiece after 60 min of polishing indicated that material was removed evenly, and an annular polishing area was attained. Meanwhile, a higher material removal rate and better surface roughness were achieved with a smaller working gap (h) and larger volume of the MCF slurry supplied (V). (4) The roughness (Ra) of the aspheric surface decreased from 49.81 to 10.77 nm after 60 min of polishing. The shape retention obtained a Pearson correlation coefficient (Pcc) of 0.9981, which demonstrated that this novel method is appropriate for polishing aspheric elements.     

Contact mechanics of rough surfaces in tribology: multiple asperity contact

Contact modeling of two rough surfaces under normal approach and with relative motion is carried out to predict real area of contact and surface and subsurface stresses affecting friction and wear of an interface. When two macroscopically flat bodies with microroughness come in contact, the contact occurs at multiple asperities of arbitrary shapes, and varying sizes and heights. Deformation at the asperity contacts can be either elastic and/or elastic-plastic. If a thin liquid film is present at the interface, attractive meniscus forces may affect friction and wear. Historically, statistical models have been used to predict contact parameters, and these generally require many assumptions about asperity geometry and height distributions. With the advent of computer technology, numerical contact models of 3-D rough surfaces have been developed, particularly in the past decade, which can simulate digitized rough surfaces with no assumptions concerning the roughness distribution. In this article, a comprehensive review of modeling of multiple-asperity contacts in dry and wet conditions is presented. Contact models for homogeneous and layered, elastic and elastic-plastic solids with and without tangential loading are presented. The models reviewed in this paper fall into two groups: (a) analytical solutions for surfaces with well-defined height distributions and asperity geometry and (b) numerical solutions for real surfaces with asperities of arbitrary shape and varying size and height distributions. Implications of these models in friction and wear studies are discussed. This revised version was published online in June 2006 with corrections to the Cover Date.     

The optimization of the surface roughness in the process of tangential turn-milling using genetic algorithm

Turn-milling is a relatively new process in manufacturing technology, where both the workpiece and the tool are given a rotary movement simultaneously. This paper presents an approach for optimization of cutting parameters at cylindrical workpieces leading to minimum surface roughness by using genetic algorithm in the tangential turn-milling process. During testing, the effects of the cutting parameters on the surface roughness were investigated. Additionally, by using genetic algorithms for each of the cutting parameters (depth of cut, workpiece speed, tool speed and feed rate) minimum surface roughness for the process of tangential turn-milling was determined according to the cutting parameters.     

Mathematical modeling of the periodic wear process in elastic contact between two bodies

A mathematical model is constructed of periodic phenomena that evolve in the process of wearing of two contacting bodies in dry friction. The derivation of the solution assumes that the Kragelskii criterion is a variable value. In particular, the model describes combined fluctuations of wear rates of subsurface layers and values characterizing variations in the roughness of each contacting surface. The main results of the work are theoretical in nature and they can be treated as the basis of experimentation with two contacting bodies exposed to periodic wear.