On the Modeling of Elastic Contact between Rough Surfaces

The contact force and the real contact area between rough surfaces are important in the prediction of friction, wear, adhesion, and electrical and thermal contact resistance. Over the last four decades various mathematical models have been developed. Built on very different assumptions and underlying mathematical frameworks, model agreement or effectiveness has never been thoroughly investigated. This work uses several measured profiles of real surfaces having vastly different roughness characteristics to predict contact areas and forces from various elastic contact models and contrast them to a deterministic fast Fourier transform (FFT)-based contact model. The latter is considered “exact” because surfaces are analyzed as they are measured, accounting for all peaks and valleys without compromise. Though measurement uncertainties and resolution issues prevail, the same surfaces are kept constant (i.e., are identical) for all models considered. Nonetheless, the effect of the data resolution of measured surface profiles will be investigated as well. An exact closed-form solution is offered for the widely used Greenwood and Williamson (GW) model (Greenwood and Williamson, Proceedings of the Royal Society of London A, vol. 295, pp. 300–319), along with an alternative definition of the plasticity index that is based on a multiscale approach. The results reveal that several of the theoretical models show good quantitative and qualitative agreement among themselves, but though most models produce a nominally linear relationship between the real contact area and load, the deterministic model suggests otherwise in some cases. Regardless, all of the said models reduce the complicated surface profiles to only a few key parameters and it is therefore unrealistic to expect them to make precise predictions for all cases.     

Contact Analysis of Non-Gaussian Surfaces for Minimum Static and Kinetic Friction and Wear

Most statistical contact analyses assume that surface heights and peak (summit) height distributions follow a Gaussian distribution. However, engineering surfaces are frequently non-Gaussian with a degree of non-Gaussian character dependent upon materials and surface finishing processes used. For example, magnetic rigid disk surfaces used in magnetic storage industry are highly non Gaussian. The use of a Gaussian analysis in such cases can lead to erroneous results. This study for the first time presents a method to carry out a statistical analysis of non-Gaussian surfaces. Real area of contact, number of contacts, contact pressure and meniscus force (in wet interfaces) are calculated for probability density functions having different skewness and kurtosis. From these curves, the optimum value of skewness and kurtosis can be predicted for minimum static/kinetic friction. It is found that a range of positive skewness (between 0.3–0.7) and a high kurtosis (greater than five) significantly lower the real area of contact and meniscus contribution implying low friction and wear. Also, sensitivity of film thickness to static friction goes down for a surface with a positive skewness and a high kurtosis.     

The Subsurface Stress Field Created by Three-Dimensionally Rough Bodies in Contact with Traction

A numerical simulation technique for calculating the complete subsurface stress field for three-dimensionally rough bodies in sliding contact is described. The stresses are calculated using real digitized three-dimensional surface profiles. The effects of the surface roughness and the sliding friction are presented. Using an existing contact simulation code, the digitized surfaces are mathematically pressed together and the real areas of contact and the asperity pressures are calculated. The surfaces are assumed to remain elastic throughout the contact simulation process. The shear forces at the asperity contact interfaces are assumed to be proportional to their calculated normal pressures. The subsurface stresses are then determined with these known normal and tangential forces at the surface.     

A Wear Model of Plane Sliding Pairs Based on Fatigue Contact Analysis of Asperities

Wear modeling is essential to predict and improve wear resistance of machine parts. This article presents a fatigue wear model of plane sliding pairs under dry friction. The wear model is constructed through developing a dynamic contact model of surfaces and proposing a mean fatigue damage constant of asperities. It is simpler and more practical than existing fatigue wear models because it describes the quantitative relationship between the wear behaviors of the plane sliding pairs and the main factors including the load and sliding speed, material property, friction property, and surface topography of the pairs. Furthermore, the wear model can predict the wear of each component of the sliding pairs. Reasonability and applicability of the wear model are validated via pin-on-disc wear tests. The wear model is applicable to predict the wear of the plane sliding pairs, which is characterized by friction fatigue of contact surfaces. The wear model can also be used to guide the tribological design of sliding pairs in machinery.     

The Effect of Scale-Dependent Hardness on Elasto-Plastic Asperity Contact between Rough Surfaces

Statistical methods are used to model elasto-plastic contact between two rough surfaces using a recent finite element model of elasto-plastic hemispherical contact and also recent advances in strain gradient modeling. The elasto-plastic hemispherical contact model used to model individual asperities accounts for a varying hardness effect due to deformation of the contact geometry that has been documented by other works. The strain gradient model accounts for changes in hardness due to scaling effects. The contact between surfaces with hypothetical material and surface properties, such as the elastic modulus, yield strength, and roughness are modeled. A model is also constructed to consider a variable asperity contact radius to evaluate if the strain gradient model will affect it differently. The models produce predictions for contact area, contact force, and surface separation. The strain gradient effects decrease the real area of contact and increase the average contact load in comparison to the model without these effects. The strain gradient model seems to have a larger influence on the predictions of contact load and area than does considering a variable asperity contact radius for the cases considered in this work.     

Effects of Friction on the Contact and Deformation Behavior in Sliding Asperity Contacts

Finite-element analyses are carried out to study the effects of friction on the contact and deformation behavior of sliding asperity contacts. In the analysis, on elastic-perfectly-plastic asperity is brought in contact with a rigid flat at a given normal approach. Two critical values of the normal approach are used to describe the asperity deformation. One is the approach corresponding to the point of initial plastic yielding, and the other at the point of full plastic flow. Additional variables used to characterize the deformation behavior include the shape and size of the plastic zone and the asperity contact size, pressure, and load capacity. Results from the finite-element analysis show that the two values of critical normal approach decrease significantly as the friction in the contact increases, particularly the approach that causes plastic flow of the asperity. The size of the plastically deformed zone is reduced by the friction when the contact becomes fully plastic. The reduction is very considerable with a high friction coefficient, and the plastic deformation is largely confined to a small thin surface layer. For a low friction coefficient, the contact size, pressure and load capacity of the asperity are not very sensitive to the friction coefficient. For a moderate friction coefficient, the contact pressure is reduced and the junction size increased; the load capacity of the asperity is not significantly affected due to the compensating effects of the pressure reduction and the junction growth. For a high friction coefficient, the pressure-junction compensation is not longer sufficient and the asperity load capacity is reduced. The degree of the friction effects on these contact variables depends on the applied force or the normal approach. Although the analyses are conducted using a line-contact model, the authors believe that the effects of friction in sliding asperity contacts of three-dimensional geometry are essentially the same and the same conclusions would have been reached. These results may provide some guidance to the modeling of rough surfaces in boundary lubrication, in which the asperity friction coefficient can be high and vary significantly both in time and from one micro-contact to another.     

Topographic Investigation of the Wear Resistance of PTFE Seals in Sliding Contact with Ceramic Materials

This paper is concerned with the wear of PTFE seals used in connection with reciprocating ceramic-coated rods. An analysis of the relationship between the surface topography of ceramics and wear of PTFE seals was undertaken, formulating three hypotheses which have been investigated experimentally using a seal test rig and a system for three-dimensional surface roughness analysis. It was observed that no running-in of the rod surface lakes place and, consequently, the tribological situation never stabilizes. It was shown that seal wear rate is dependent on the number of asperities penetrating the lubricant film thickness, the wear rate being correlated to a functional parameter (S_{pk_0}) which was especially developed to describe the peak height above the mean plane. Furthermore, it was illustrated how the structure of ceramics allows the lubricant to flow unhindered between isolated asperities in contrast to the traditionally polished structure of steel which restricts the lubricant flow.     

The Contact of a Compliant Curved and a Nominally Flat Rough Surfaces

The contact problem of a compliant curved beam loaded by a rigid flat surface is analyzed. This problem is typical of compliant metallic configured seals and electrical connectors. Both the elastic deformation of the curved beam and elastic-plastic deformation of the asperities are considered. A model for calculating the contact parameters like minimum separation, contact length and real area of contact is developed. The effect of the applied load as well as the plasticity index and other geometrical variables on the various contact parameters is investigated. It is shown that, contrary to common intuition, smaller radius of curvature is beneficial for both the sealing and electrical connector applications.     

A New Roughness Parameter Including Hardness and Contact Frequency Effects on Lubricated Rolling/Sliding Wear

Surface roughness, roughness arrangement, film thickness, material hardness, and run-in process have significant effects on the lubricated rolling/sliding wear of mechanical components such as gears and bearings. In conventional analysis, a film thickness parameter is calculated by a geometric approach to study the wear resistance of a contact system without considering the effects of material hardness and run-in process. Although the conventional parameter is simple, it does not correlate with some experimental observations. In this work, a new roughness parameter is developed for the prediction of lubricated rolling/sliding wear. Surface roughness will be adjusted by its hardness and contact frequency. The calculation results are consistent with four groups of experimental data. It is proved that the conventional models can be derived as a special case of the new model when two contact surfaces have the same properties. The new model can be used in the optimal design and manufacturing of mechanical interfaces to reduce lubricated rolling/sliding wear.     

Measurements of Temperature Distributions around Longitudinally Grooved Rough Surfaces in Sliding Elastohydrodynamic Point Contacts

This paper describes the temperature measurements in the EHL conjunction area comprising a longitudinally grooved steel ball and a sapphire disk under high slip conditions. The authors measured the temperatures of the oil film as well as both the disk and ball surfaces; furthermore, they estimated the temperature profile across the oil film by means of experimental values. The experimental results show that the temperature of the grooved ball surface increased considerably compared with that of a non-grooved ball. The temperatures of the faster surface for the grooved ball became sensitive to the slip ratio, whereas that for the non-grooved surface was almost constant. The temperature distribution had a higher value at the land zones and a lower one at the grooved zones. The temperature rise in the grooved zones varied qualitatively depending on the thermal conditions of both the sliding surfaces.     

Mechanics of Fretting Fatigue Tests of Contacting Dissimilar Elastic Bodies

A popular fretting fatigue test applies a bulk compression that oscillates in phase with the fretting force. To understand the effect of the bulk compression on fretting, the effect of the bulk compression alone on the fretting stress state and microslip for contacting dissimilar elastic bodies is analyzed. This is accomplished by modeling the fretting configuration with a rigid indenter contacting a plane-strain elastic half-space with the effective elastic properties of the contacting pair. The indenter is loaded by a constant normal load while the half-space is subjected to remote compression parallel to its surface. The bulk compression has a pronounced effect on the stick-slip geometry underneath the contact of dissimilar materials. It is shown that the contacting pads serve as stress concentrators and a mechanism for the initiation of fretting fatigue cracks is discussed. This stress concentration effect is not present when the indenter and the half-space have the same elastic constants.     

Crack Propagation of Rolling Contact Fatigue in Ball Bearing Steel Due to Tensile Strain

Crack propagations or failure modes in rolling element bearings, which had been difficult to explain via conventional crack propagation mechanisms such as the orthogonal shear stress mechanism, were discussed from the viewpoint of a tensile strain mechanism. Contact stresses are compressive in three axes, whose values differ from each other; then strain can be tensile in one of these directions, acting at a right angle to the direction of maximum compressive stress. A crack is considered to propagate by this tensile strain. When contact stress is small, a crack produced by some cause can propagate by this elastic tensile strain. When contact stress is large, residual tensile strain is produced by plastic deformation, which can also influence the crack propagation. Several failure modes of rolling element bearings, which had been difficult to explain, were explained by tensile strain.     

A New Contact Model for Multilayered Solids with Rough Surfaces

A new numerical model is proposed to investigate the normal contact of multilayered solids with rough surfaces. The Hankel transform and the transfer matrix technique are used to solve the problem of the deformation of a multilayered solid. Then, the normal contact of an asperity is solved with Abel transform. Using this solution, an asperity-based contact model of rough surfaces is developed considering interactions between asperities. Numerical results are presented and compared to finite element calculations. The present model provides good results. The effects of interactions and the solid layers properties are discussed.     

钢铜摩擦副摩擦磨损特性的试验研究

本文试验分析了ＺＱＡ１９－４和ＺＱＺｎ６－６－３两种铜合金材料在不同的表面粗糙度下对摩擦系数和出口区油温的影响，以及改变载荷和相对滑动速度时，摩擦系数的变化状况。结果表明；铜合金成分不同时具有不同的硬度。     

A Study of the Effect of Wear Particles and Adhesive Wear at High Contact Pressures

The wear rate and friction characteristics were determined for certain combinations of cobalt base alloys and stainless steels when rubbed together at unit pressures up to 300,000 psi in an environment of demineralized water at room temperature. Wear rate and friction data were collected both in the presence and absence of wear particles. A study was also made on the effect of sliding-surface geometry in trapping wear particles.

The results suggest that an exponential relationship exists between wear rate and stress for the materials of test and this relationship is influenced by material combinations and sliding velocity. Entrapped wear particles also affect the wear rate.

Because the wear rate appears to increase sharply at some nominal contact stress when the data is plotted on Cartesian coordinates, the authors define an “Apparent Critical Stress”, using this term and a wear factor term to aid in the evaluation and discussion of results.     

Effect of Load and Composition on Friction and Dry Sliding Wear Behavior of Tungsten Carbide Particle-Reinforced Iron Composites

Investigations on the dry sliding wear behavior of tungsten carbide (WC)-reinforced iron matrix composites were carried out at room temperature. Three sets of samples (unreinforced iron, 4 wt% micrometer-size (～5–15 μm) WC-reinforced iron and 4 wt% nanosize (～30 nm) WC-reinforced iron were prepared using a powder metallurgy route to assess their friction and wear behaviors under two different loads. The relative dry sliding wear performances of the micrometer-size and nanosize WC-reinforced composites were compared with unreinforced matrix. An increase in microhardness of the order of 2.5 times was observed in the case of 4 wt% nanosize WC-reinforced iron matrix compared to the unreinforced iron matrix. The wear rate was 1.35 to 1.45 times lower in the case of nanocomposites compared to the unreinforced iron matrix (under different experimental conditions). The values of the coefficient of friction (COF) of composites were found to decrease with increase in load. Nanocomposites showed lower COF, surface roughness, and fractal dimension (D) values than micrometer-size WC-reinforced composites and the unreinforced iron matrix.     

Acoustic Emission and Its Relationship with Friction and Wear for Sliding Contact

Further investigation of the relationships between friction and wear properties and the characteristics of acoustic emission was conducted in the case of dry and grease-lubricated sliding contact using a ball-on-cylinder testing apparatus. The effect of contamination simulated by the inclusion of glass bead particles was also explored. Experiments were performed at sliding speeds ranging from 0.09 m/s to 1.47 m/s, while maintaining a fixed load and duration. As a first observation and contrary to what could be expected, the higher speed did not contribute to the decrease in friction interpreted by a worsening of the starved regime that had a consequence of increasing wear. However, the results revealed a good correlation between the friction coefficient and acoustic emission (AE) rms voltage for dry sliding. Such a relationship may allow the prediction of a reasonable friction coefficient μ from an AE signal. It was also determined that the friction work correlated well with the corresponding integrated AE voltage over time, intRMS. The detection of the sliding speed threshold beyond which accelerated wear would occur was possible from the intRMS variation. Proportionality between the theoretically determined grease film thickness and the intRMS was observed.     

粗糙表面弹性微动接触数值研究

由于实际工程表面多为粗糙表面,这里研究了粗糙表面对微动接触中压力和切向应力的影响.研究接触过程中法向载荷保持不变,切向载荷为周期性的交变载荷.首先,建立接触算法和模型,其算法核心是利用共轭梯度法(CGM)计算微动接触中的表面压力及切向应力并使用快速傅里叶变换(FFT)加快计算速度.然后,在验证算法正确的基础上,分析正弦...     

Tribological Sensitivity of PTFE/Alumina Nanocomposites to a Range of Traditional Surface Finishes

Wear tests were performed with polytetrafluoroethylene (PTFE) + Al ₂ O ₃ nanocomposites on various manufactured surfaces to determine whether or not the wear resistance of these nanocomposites is a strong function of surface preparation. Four different surface finishes of grade 304 stainless steel counterfaces were used: electropolished (R _q = 88 nm), lapped (R _q = 161 nm), wet-sanded (R _q = 390 nm), and dry-sanded (R _q = 578 nm). PTFE + Al ₂ O ₃ nanocomposites made from powders of roughly 2-20 μm PTFE (matrix) and ～44 nm Al ₂ O ₃ (filler) were prepared at filler weight percentages of 0, 1, 5, and 10% and tested on each surface finish. Additionally, 5 wt% 44-nm nanocomposites were compared to identically prepared 5 wt% 80- and 500-nm Al ₂ O ₃ filled PTFE composites on each surface. Friction coefficients were between 0.12 and 0.19 and wear rates decreased from K = 810 × 10^{? 6} mm ³ /(Nm) for the 5 wt% 500-nm alumina-filled PTFE on the dry-sanded surface to K = 0.8 × 10^{? 6} mm ³ /(Nm) for the 5 wt% 80-nm filled composite on the lapped surface. It was found that the minimum wear rate occurred on the lapped counterface for every composite, and the wear rate is a strong function of the transfer film thickness and morphology.     

About Joint Deformations of Asperities and the Destruction of Rough Surfaces During Friction

The mechanics of the deformations and the destruction of the asperities of rough surfaces has been considered, taking into account the mutual influence of the elastic constants of the materials participating in the friction couple.

The case when the destruction is taking place inside of the contact layer is assumed to have the highest probability. The tight bear of the peaks of one body against the valleys of the other and the adhesion phenomena are leading to a mutual deformation of the prevailing number of asperities of both surfaces. This allows one to consider the contact layer as a composite body consisting of two solid phases and voids.

It has been shown that such an approach does not exclude the possibility of shearing off only the soft material of the couple.

For the asperities subject to bending deformations, the mutual influence of the elastic constants is conditioned by the mutual angle of rotation of the cross sections.

In this case consideration of the tangential stresses in the destruction of the short bars (asperities) is essential.