Asperity Contact Area Research Articles

A fractal model of rough surfaces based on ellipsoidal asperities

PurposeThis study aims to use fractal theory to investigate the contact mechanics of two bidirectional anisotropic surfaces, taking into account the friction coefficient of the contact interface. This study introduces a model that centers on normal contact load and contact stiffness, providing an extensive framework to elucidate the interactions between these surfaces.Design/methodology/approachThe research adopts the Weierstrass–Mandelbrot (W-M) function for simulating bidirectional surface profiles. Through the application of elastic-plastic contact theory, it evaluates the contact area and load of a singular asperity across elasticity, elastoplasticity and plasticity phases. The contact load and stiffness of the rough surface are determined using a refined asperity density distribution function, and these findings are juxtaposed with extant models to validate their precision and rationality.FindingsThe study delineates the influence of fractal dimension (D), surface roughness (G), ellipse eccentricity (e) and friction coefficient (µ) on the contact area, load and stiffness. It reveals that the contact area enlarges with the fractal dimension (D) yet diminishes with increased eccentricity (e), roughness (G) and friction coefficient (µ). These elements considerably affect the contact load and stiffness, underscoring their significance in comprehending surface interactions.Originality/valueThis study applies fractal theory to analyze the contact mechanics of bidirectional anisotropic surfaces, considering the geometry and mechanics of ellipsoidal asperities on rough surfaces to develop a contact mechanics model. This model clarifies the deformation of an asperity in normal contact, presenting a more rational alternative to current models.

Effect of squamous textured SiC on the dry-sliding tribological properties of graphite asperities

The graphite rough morphology influences the operating performance of the sealing surface. Texturing silicon carbide surfaces can considerably improve the tribological characteristics of sealing surface. Herein, a fractal model was established to study the contact and tribological characteristics of graphite asperities, and the pin-on-disk wear tests were conducted to investigate the influence of squamous texture on graphite asperities under dry-sliding condition. Results indicated that reducing the graphite surface roughness decreases the contact area to decrease the friction coefficient. The squamous texture increases the deformation and contact area of graphite asperities. But the wear debris collection of the squamous texture prevents the adhesive wear, and the microcutting effect promotes the formation of graphite transfer film on the silicon carbide surface. Therefore, the squamous texture has the low friction coefficient and excellent worn morphology. Especially, under the high load of 80 N, combining the textured silicon carbide with the optimal graphite surface roughness of 0.14 μm exhibits a synergistic anti-friction effect that the friction coefficient reduced by 19%.

Using electrical impedance spectroscopy to identify equivalent circuit models of lubricated contacts with complex geometry: In-situ application to mini traction machine

Electrical contact resistance or capacitance as measured between a lubricated contact has been used in tribometers, partially reflecting the lubrication condition. In contrast, the electrical impedance provides rich information of magnitude and phase, which can be interpreted using equivalent circuit models, enabling more comprehensive measurements, including the variation of lubricant film thickness and the asperity (metal-to-metal) contact area. An accurate circuit model of the lubricated contact is critical as needed for the electrical impedance analysis. However, existing circuit models are hand derived and suited to interfaces with simple geometry, such as parallel plates, concentric and eccentric cylinders. Circuit model identification of lubricated contacts with complex geometry is challenging. This work takes the ball-on-disc lubricated contact in a Mini Traction Machine (MTM) as an example, where screws on the ball, grooves on the disc, and contact close to the disc edge make the overall interface geometry complicated. The electrical impedance spectroscopy (EIS) is used to capture its frequency response, with a group of load, speed, and temperature varied and tested separately. The results enable an identification of equivalent circuit models by fitting parallel resistor-capacitor models, the dependence on the oil film thickness is further calibrated using a high-accuracy optical interferometry, which is operated under the same lubrication condition as in the MTM. Overall, the proposed method is applicable to general lubricated interfaces for the identification of equivalent circuit models, which in turn facilitates in-situ tribo-contacts with electric impedance measurement of oil film thickness – it does not need transparent materials as optical techniques do, or structural modifications for piezoelectric sensor mounting as ultrasound techniques do.

A Fractal Contact Model for Rough Surfaces considering the Variation of Critical Asperity Levels

A contact model for rough surfaces based on the fractal theory is proposed in the present work. Firstly, the deformation of the material is divided into four stages: elastic deformation, the first elastoplastic deformation, the second elastoplastic deformation, and full plastic deformation. And the variation of material hardness is considered when analyzing the contact characteristics of a single asperity within the first and second elastoplastic deformation stages. Secondly, the size distribution function of contact spots at different frequency levels is derived. And the expressions of asperity critical frequency levels are rederived. Lastly, the feasibility and credibility of the proposed model are verified by comparison with other contact models and experimental data. The results show that when the variation of the material hardness is considered, the contact area of a single asperity in the first elastoplastic deformation stage becomes larger, while the contact area of a single asperity in the second elastoplastic deformation stage becomes smaller. Moreover, the critical asperity frequency levels of the rough surface are not constant, but the variables are related to the total real contact area of the rough surface and decrease as the real contact area increases. The proposed model is a modification and improvement of the existing fractal contact models, which can lead to a more accurate relationship between the contact load and the total real contact area of the rough surface.

A micromechanics-based model for concrete-rock interface with similar triangular asperities

Direct shear tests on samples containing similar triangular asperities have been carried out under constant normal stiffness (CNS) conditions, and observations demonstrated that there exists local lift-off of shallower asperities across the interface, resulting in a redistribution of local stresses and further impacting the global shear behavior . This study further modifies the existing theoretical model based on multiple-asperity configurations, previously presented by the authors. The proposed method relates the normal and shear stresses on the individual asperity to interface strength and corresponding displacement in terms of the asperity inclination and contact areas. The emphasis is on quantifying the number of shallower asperities that would be lifted off when the closely contacted asperities are dislocated by an amount of interface dilation. In addition to the mechanism of local lift-off itself, the resultant redistribution of global shear stress on remaining asperities can be also taken into account. The proposed model is verified by predicting experimental observations published elsewhere, and the comparison appears to be satisfactory.

Influence of Cross-Grooved Texture Shape on Tribological Performance under Mixed Lubrication

Surface texture plays an important role in improving the tribological properties of materials. In this paper, the effect of different shapes (i.e., triangle, square, hexagon, round) on the tribological performance of cross-grooved texture was investigated. First, the mixed lubrication condition was used for the pin-on-disc rotating sliding tests. Then, the stress distribution of the four textures was analyzed to better explain the experimental results. Overall, the hexagon-textured specimens exhibited lower friction coefficients than the other shape-textured specimens under the examined conditions. Simulation results indicate that the contact stress can be reduced on the surface of hexagon-textured specimens, and this leads to a better oil film for lubrication. Furthermore, the hydrodynamic lubrication stood out with the increase of speeds to 250 rpm. However, as the test loads further increased, the film thickness decreased, resulting in the increase in the asperity contact areas, which dropped the above advantage of hexagon-textured specimens. This study would be beneficial for the texturing tribological and lubrication design.

Investigation of abrasive behavior between pad asperity and oxide thin film in chemical mechanical planarization

In this paper, tribological effects on the material removal rate (MRR) are investigated using two types of slurry abrasives (i.e., ceria and silica) and three types of pads. From a micro to macro viewpoint, the physico-chemical interaction between the pad-wafer interface and abrasive was studied based on multi-asperity contact. First, the relative contact pressure in high or low proportions among all asperities was calculated using a contact mechanics model. The results indicate that for the commercial slurry used in the semiconductor industry, relatively high contact pressure due to the asperities can be transferred to the ceria abrasives, and only a low contact pressure can be supported by these silica abrasives. Furthermore, it was confirmed that the two different slurry abrasives showed opposite behaviors according to the real contact area of the pad asperities. That is, as the pad texture changed from ‘Desired pad’ to ‘Smoothed pad’, the MRR of the ceria increased by 47%, while the MRR of the silica decreased 59%. Lastly, the Stribeck curve, which is suitable for the CMP process, was re-analyzed to clarify the abrasion mechanism under the pad asperity scale. The results showed that two-body abrasion may be maintained for the ceria CMP, and transition is possible from two-body to three-body abrasion at the silica CMP as the contact area increases. The present paper is expected to clarify the tribological mechanism of the oxide CMP and can provide further insight into optimizing and selecting consumables such as conditioner, pad, and slurry.

Load-Bearing Capacity Investigation of Friction Pairs in Hydro-Viscous Drive Based on Fractal Contact Theory

Abstract Hydro-viscous drive has gained extensive application in fans, pumps, belt conveyors, and scraper conveyors for step-less speed regulating, soft starting, and overload protection. In the mixed friction stage, the state of contact and load-bearing capacity are always changing with the pressure of control oil. In order to predict the load-bearing capacity of friction pairs, a description of the frictional and hydrodynamic lubrication states was first made. Oil film’s pressure distribution and load-bearing capacity were analyzed with the average flow model. The fractal contact model of the asperity surface was proposed for simulating mutual contact state and contact load between the asperities. The influences of fractal parameters on the contact performance of friction pairs were conducted. Eventually, test rig of load-bearing capacity was established. As indicated by the experiment, asperity contact area and load-bearing capacity of the asperity contact increase slowly at first and then rapidly with reduced film thickness ratio. Correspondingly, oil film load-bearing capacity progressively reduces. Due to the reduction of film thickness ratio, friction pairs’ load-bearing capacity increases gradually. The load-bearing capacity of friction pairs is affected by the fractal dimension and scale factor. Results of the experiment well conform to the theoretical values, which illustrates that friction pairs’ load-bearing capacity can be accurately predicted and computed using the average flow model and M-B fractal contact model. The calculation offers a theoretical reference to the survey about friction and torque properties of the hydro-viscous drive.

A multi-scale model of real contact area for linear guideway based on the fractal theory

High precision, efficiency and reliability are the unremitting pursuits of machinery manufacturing industry. As one of the pivotal function parts of high-end NC machine tool, precise linear guideway determines the machining precision and operation performance. Accurate evaluation and prediction of surface topography are the crucial effects on the matching performance of linear guideway. In this paper, the real contact area is regarded as a key parameter, a multi-scale method with the fractal theory is proposed. First, the contact area of a single asperity was obtained with Hertz contact theory. Afterwards, the contact area between rough surfaces was deduced by the fractal theory. Finally, using the proposed multi-scale contact mechanics model, the real contact area between rough plane and cylinder was obtained by integral solution. Compared with the former fractal model and GW model, the proposed model on the real contact area calculation of linear guideway is more accurate and comprehensive. The effect factors of load, fractal parameter and friction were discussed, the increasing rate of real contact area of smoother surface is greater as load increases. The proposed model may provide practical guidance for assembly accuracy and surface quality requirements at design stage.

New analytical model of elastic-plastic contact for three-dimensional rough surfaces considering interaction of asperities

The contact calculation of three-dimensional real rough surfaces is the frontier field of tribology and surface science. In this study, we consider the interaction and elastic-plastic deformation characteristics of asperities and further, propose an analytical contact calculation method for rough surfaces considering the interaction of asperities. Based on the watershed algorithm, the rough surface is segmented and the asperities are reconstructed into ellipsoids. According to the height relationship between the asperities, the definition of the deformation reference height of the matrix between each couple of asperities is provided. Subsequently, the calculation formula of the substrate deformation is provided according to the local contact pressure considering the elastic-plastic deformation of the asperity, and the contact state under a specific load is determined using the iterative correction method. The results correspond with those of finite element numerical calculation and the study reveals the following: (1) compared with the results obtained without considering the asperity interaction, contact area, distance, and stiffness will be reduced by 6.6%, 19.6%, and 49.5%, respectively, when the influence of asperity interaction is considered; (2) the interaction of the asperities has the greatest influence on the surface contact distance and stiffness. Under the same load, the existence of asperity interaction will reduce the contact distance, area, and stiffness; (3) considering the interaction of the asperities, the higher asperity will bear more load, but it will simultaneously reduce the contact of the surrounding area and increase that of the distant area. The calculation method proposed in this study has the advantages of high calculation efficiency and accuracy, thus, providing the calculation basis and method for subsequent studies on service performance of rough surfaces, such as the calculation of contact stiffness and fatigue performance analysis of rough surfaces.

Investigation of Tangential Contact Damping of Rough Surfaces From the Perspective of Viscous Damping Mechanism

AbstractThe contact damping between rough surfaces has an important influence on the wear, vibration, contact fatigue, and energy dissipation between interfaces. In this paper, based on contact theory, a tangential damping mathematical model of rough surfaces is established from the point of view of viscous contact damping energy dissipation mechanism of asperities and considering the fractal characteristics of three-dimensional topography of rough surfaces. Through the combination of micro-contact modeling and macro dynamic testing of composite beams, the analysis results show that there are important evolution rules between tangential damping and surface fractal parameters and material parameters. The nonlinear relations between them are as follows: tangential contact damping is positively correlated with normal load, load ratio, and maximum contact area of asperity, and negatively correlated with fractal roughness; tangential contact damping increases first and then decreases with the increase of three-dimensional fractal dimension. The results of computational and experimental modal analysis show that the established mathematical model is feasible for predicting tangential damping. The study of tangential contact damping between surfaces can lay a foundation for improving the performance of assembly interfaces.

Sliding on ice: Real contact area, melted film thickness, and friction force

It is easy to slide on ice because of water films arising as a consequence of frictional melting. Although the friction force of ice and a slider critically depends on the area and thickness of the liquid film as well as the sliding speed, direct experimental visualization and quantification of temporal evolutions of the contact area, film thickness, and the resulting friction force have been scarce to date. Here we develop an experimental technique to visualize the contact area of ice asperities and a high-speed sliding surface in situ based on the optical principle of total internal reflection. We construct a hydrodynamic model to predict the contact area, liquid film thickness and friction force of a model system of hemispherical ice on a flat solid surface. Upon showing good agreement between theory and experiment, we briefly discuss how the fundamental understanding of the friction behavior of a single ice bump can be extended to understand the friction behavior of flat ice surfaces.

Impact of normal stress-induced closure on laboratory-scale solute transport in a natural rock fracture

The impact of normal stress-induced closure on fluid flow and solute transport in a single rock fracture is demonstrated in this study. The fracture is created from a measured surface of a granite rock sample. The Bandis model is used to calculate the fracture closure due to normal stress, and the fluid flow is simulated by solving the Reynold equation. The Lagrangian particle tracking method is applied to modeling the advective transport in the fracture. The results show that the normal stress significantly affects fluid flow and solute transport in rock fractures. It causes fracture closure and creates asperity contact areas, which significantly reduces the effective hydraulic aperture and enhances flow channeling. Consequently, the reduced aperture and enhanced channeling affect travel time distributions. In particular, the enhanced channeling results in enhanced first arriving and tailing behaviors for solute transport. The fracture normal stiffness correlates linearly with the 5th and 95th percentiles of the normalized travel time. The finding from this study may help to better understand the stress-dependent solute transport processes in natural rock fractures.

Improved mixed elastohydrodynamic lubrication of hypoid gears by the optimization of manufacture parameters

Extensive wear appears in the case of dry contacts, or when the lubrication of the contacting surfaces is not appropriate. The aim of this research is to improve the mixed elastohydrodynamic lubrication in hypoid gears by the optimization of manufacture parameters for tooth surface processing.A full numerical analysis of the thermal mixed EHL in hypoid gears is applied. The equation system and the numerical procedure are unified for a full coverage of all the lubrication regions including the full film, mixed, and boundary lubrication. In the hydrodynamically lubricated areas the calculation method employed is based on the simultaneous solution of the Reynolds, elasticity, energy, and Laplace's equations. In the asperity contact areas the Reynolds equation is reduced to an expression equivalent to the mathematical description of dry contact problem. The real geometry and kinematics of the gear pair based on the manufacturing procedure is applied, thus the exact geometrical separation of the mating tooth surfaces is included in the oil film shape, and the real velocities of these surfaces are used in the Reynolds and energy equations. The transient nature of gear tooth mesh is included. The oil viscosity variation with respect to pressure and temperature and the density variation with respect to pressure are included. The non-Newtonian behaviour of the lubricant is considered. Using this model, the pressures, film thickness, temperatures, and power losses in the mixed lubrication regime are predicted. By using the developed method, the influence of the manufacturing parameters on the conditions of mixed elastohydrodynamic lubrication is investigated. On the basis of the obtained results recommendations are formulated to improve the mixed EHL and the efficiency of face-milled hypoid gears.

Improvements in the mixed elastohydrodynamic lubrication and in the efficiency of hypoid gears

In this paper, the influence of the manufacturing parameters on the conditions of mixed elastohydrodynamic lubrication is investigated. On the basis of the obtained results, recommendations are formulated to improve the mixed EHL and the efficiency of face-milled hypoid gears. A full numerical analysis of the mixed EHL in hypoid gears is applied. The equation system and the numerical procedure are unified for a full coverage of all the lubrication regions, including the full film, mixed, and boundary lubrication. In the hydrodynamically lubricated areas, the calculation method employed is based on the simultaneous solution of the Reynolds, elasticity, energy, and Laplace's equations. In the asperity contact areas, the Reynolds equation is reduced to an expression equivalent to the mathematical description of dry contact problem. The real geometry and kinematics of the gear pair based on the manufacturing procedure are applied; thus, the exact geometrical separation of the mating tooth surfaces is included in the oil film shape, and the real velocities of these surfaces are used in the Reynolds and energy equations. The transient nature of gear tooth mesh is included. The oil viscosity variation with respect to pressure and temperature and the density variation with respect to pressure are included. The non-Newtonian behaviour of the lubricant is considered. Using this model, the pressures, film thickness, temperatures, and power losses in the mixed lubrication regime are predicted. The effectiveness of the presented method is demonstrated by using hypoid gear examples.

Numerical simulation of transient mixed elastohydrodynamic lubrication for spiral bevel gears

Abstract In spiral bevel gears, the entraining velocity, contact load and radii of curvature along tooth surface are always changed dramatically, which results in remarkable transient squeezing effect on lubricating performance, especially it operates in high-speed and heavy-load conditions. Available elastohydrodynamic lubrication (EHL) and mixed EHL studies for spiral bevel gears are mainly performed under quasi-static (steady-state) assumptions which ignores these transient influences. Therefore, in this paper, a transient mixed EHL model for spiral bevel gears is presented, in which takes into account most variable parameters along meshing surface including contact load, contact radii of curvature, entraining and sliding velocity vectors. Note that all these transient parameters of spiral bevel gears are employed from the results of loaded tooth contact analysis (LTCA). In order to improve the computational efficiency and convergent accuracy with a relatively dense grids, the progressive mesh densification (PMD) method for this transient mixed EHL model is also introduced. A comparison between the present transient mixed EHL model and those data from literature is executed to verify the correctness of the newly developed model. After that, systematically investigations of transient squeezing impact are carried out for spiral bevel gears and compared with the corresponding steady-state EHL results with and without real machined surface roughness. The obtained results reveal that the transient squeezing action can significantly affect the film thickness distribution in each contact zone and along the meshing track line in spiral bevel gears, and lead to dramatic growth in asperity contact area as well. Besides, the steady-state EHL appears to be greatly overestimated the lubricating characteristics for spiral bevel gears.

Contact Area and Shear Stress in Repeated Single-Asperity Sliding of Steel on Polymer

A model for the contact area of a single asperity sliding in a groove after repeated cycles is presented. Based only on the asperity geometry and on data from friction experiments, the model predicts the area of the asymmetric elliptical contact of the asperity sliding in its own groove. It thus allows to determine the shear stress of the steel–polymer couple in the relevant geometry without need for further microscopy of indenter or groove. The model was validated by experiments with an indenter manufactured from slide bearing steel and polyether-ether ketone (PEEK) as substrate. In experiments of 1000 repeated cycles, the contact area was found to vary with varying load and sliding velocity, while the shear stress was 20.5 MPa at a normal pressure of 50–70 MPa, independent of velocity when friction heating is still negligible. Model and experimental confirmation advance single-asperity friction experiments into an efficient method to extract shear stress and contact area for an understanding of sliding friction in metal-polymer contacts.

An Effort to Reconcile Time‐ and Slip‐Dependent Friction Evolution

AbstractIn rate and state friction (RSF) theory, time‐dependent evolution (represented by the Aging law) and slip‐dependent evolution (represented by the Slip law) both succeed in explaining some features of the friction curves while failing in explaining others. Nevertheless, experimental results provided strong evidence for the two ideas and suggested that they are both critical components in friction evolution. Making a first attempt toward reconciling these two ideas, we developed a new friction model for RSF evolution assuming combined physical mechanisms that highlight asperities' plastic behavior: the time‐dependent growth of asperity contact area and the slip‐dependent enhancement (slip strengthening) of asperity intrinsic strength. Our model adopts a two‐scale mathematical structure developed by Li and Rubin (2017; https://doi.org/10.1002/2017JB013970), where the specification of the surface distribution of asperity ensembles and their geometry facilitates the numerical construction of the state variable in the RSF equation. Results show that this new model's fit to the slide‐hold‐slide experiments is similar to the best fits of the Slip law, while it provides an improved physical picture; however, for velocity steps it fails to match the symmetry of step ups and downs, although the general fit is acceptable. By introducing two new parameters to specify the slip‐hardening mechanism, we allow the model to incorporate as a subset the pure time‐dependent model discussed in Li and Rubin (2017). Although failing to completely reconcile time‐ and slip‐dependent friction evolution, this study produced useful insights for future research; for example, a granular numerical description of the frictional surface might be convenient for modeling the physics of friction.

Prediction of the Shear Failure of Opened Rock Fractures and Implications for Rock Slope Stability Evaluation

Rock slope commonly fails due to the shear failure of rock fractures. Shear strength of rock fractures are reduced substantially once the fracture surfaces are mismatched or opened. We propose a new criterion to predict the shear strength of rock fractures in different opening states. The degree of interlocking representing the true asperity contact area is incorporated into the modified model of Saeb and Amadei. The effect of fracture opening on asperity dilation and degradation is separately considered. The transitional stress that is a critical parameter involved in the model is analytically determined based on energy consideration. The new model is validated with experimental results from direct shear tests on synthetic fractures with regular‐shaped asperities. Good agreement between the analytical solution and the experimental data confirms the capacity of the proposed model. Therefore, the model has great potential for assessing the stability of rock slopes where fractures are often opened due to stress relief and engineering disturbances.

Multiscale boundary frictional performance of diamond like carbon coatings

This paper investigates the frictional performance of a PECVD hydrogenated undoped DLC coating and the alternative super-finished gear steel surface pairs. A tribometer replicates the conditions found in the conjunction of a performance racing transmission spur gear pair. In mixed and boundary regimes of lubrication the DLC contact is shown to have lower friction despite having comparable surface topography when measured using optical interferometry. To determine the mechanisms responsible for improved friction of DLC coated tribo-pairs AFM is used. It is shown that the nanoscale surface topography of the investigated DLC coated pairs reduces the real asperity contact area formed at the same load carrying capacity. This highlights a contributing mechanism for improved friction with the DLC coating.