Multi-asperity Contact Model Research Articles

Simplified Formulation for Bush, Gibson, and Thomas Model

Abstract The random process model, also known as the multi-asperity contact model or statistical model, is one of the dominant methodologies for analyzing the contact between nominally flat rough surfaces. In 1975, Bush, Gibson, and Thomas developed a complete random process model (known as the BGT model) assuming that solid–solid contacts occur on the summits of the asperities, which are semi-ellipsoids uniquely described by three random variables (the asperity height and two principal peak curvatures). The Hertzian elliptic contact theory states that the contact area and normal load are implicit functions of the random variables, which results in an original BGT model with a complex formulation. In this study, we used an adapted Hertzian elliptic contact theory to simplify the formulation of the BGT model. The relative contact area to normal load relation predicted by the simplified BGT model perfectly agrees with that of the original formulation. It is anticipated that rough surface contact models with complex asperity interactions can be effectively built under the framework of this simplified BGT model.

Selection of Silica Type and Amount for Flowability Enhancements via Dry Coating: Contact Mechanics Based Predictive Approach.

To investigate the effect of dry coating the amount and type of silica on powder flowability enhancement using a comprehensive set of 19 pharmaceutical powders having different sizes, surface roughness, morphology, and aspect ratios, as well as assess flow predictability via Bond number estimated using a mechanistic multi-asperity particle contact model. Particle size, shape, density, surface energy and area, SEM-based morphology, and FFC were assessed for all powders. Hydrophobic (R972P) or hydrophilic (A200) nano-silica were dry coated for each powder at 25%, 50%, and 100% surface area coverage (SAC). Flow predictability was assessed via particle size and Bond number. Nearly maximal flow enhancement, one or more flow category, was observed for all powders at 50% SAC of either type of silica, equivalent to 1wt% or less for both the hydrophobic R972P or hydrophilic A200, while R972P generally performed slightly better. Silica amount as SAC better helped understand the relative performance. The power-law relation between FFC and Bond number was observed. Significant flow enhancements were achieved at 50% SAC, validating previous models. Most uncoated very cohesive powders improved by two flow categories, attaining easy flow. Flowability could not be predicted for both the uncoated and dry coated powders via particle size alone. Prediction was significantly better using Bond number computed via the mechanistic multi-asperity particle contact model accounting for the particle size, surface energy, roughness, and the amount and type of silica. The widely accepted 200nm surface roughness was not valid for most pharmaceutical powders.

A novel fractal contact model based on size distribution law

This study develops a new fractal contact model to evaluate contact status on rough surfaces. Specifically, the three-dimensional Weierstrass-Mandelbrot function is used to characterize fractal surfaces, in which the asperity level range is determined by the power spectral density of surface. A novel size distribution law of truncation regions has been proposed based on rough surface truncation in our previous study to overcome the limitation of the law proposed by Mandelbrot. By using the size distribution law, a multi-asperity contact model is established to calculate the contact force and real contact area. The evolution of the asperity level range is considered during the compression process. Furthermore, the elastic or plastic deformation status of each asperity in the level range is determined. In the implementation of the proposed theoretical model, the numerical truncation of fractal surfaces is conducted to obtain the effective asperity level range. Finite element simulation of fractal surface contact and compression experiments of copper specimens are conducted to validate the fractal contact model. The theoretical results of the contact force and total contact area agree well with the simulation and experimental results. The effects of the fractal parameters on the contact behavior are further investigated. The results indicate that the proposed fractal contact model can provide an accurate prediction of rough contact behaviors.

A multi-asperity adhesive contact model for catheter and vascular artery contact in endovascular surgery.

Contact behaviors of medical devices, such as guidewires and catheters, are critical in endovascular surgeries. In this work, a new method to predict adhesive contact force between catheter and vascular artery is presented. Multi-asperity adhesion on the surface of vascular artery, deformation of asperity and deformation of vascular substrate are all considered. The single asperity behavior is described with Johnson-Kendall-Roberts (JKR) contact model. The multi-asperity behavior is based on Greenwood-Williamson (GW) asperity model. Vascular substrate is considered as elastic bulk substrate and its deformation is determined with Hertzian pressure from asperity on a circular region on the elastic half space. The model shows that the deformation of vascular substrate accounts for the majority of the total contact deformation and significantly affects the predicted contact force. The model is verified with published experimental data. The comparison shows that the model produces very accurate prediction of contact force between catheter and vascular artery when the contact force is compressive. Parametric analysis based on asperity topography is carried out. The analysis shows that the diameter of the circular region of the interface between asperity and vascular substrate has more significant effect on the estimation of contact force than the radius of asperity. Further validation of prediction accuracy of the model under experiment is needed.

On the size distribution of truncation areas for fractal surfaces

The size distribution of contact spot areas is critical for the evaluation of contact behavior of rough surfaces. A size distribution law proposed by Mandelbrot has been used widely in multi-asperity fractal contact models to predict the rough contact behavior. However, the Mandelbrot law has a limitation on the representation of the truncation area distribution for rough surfaces. Therefore, the present study develops a new size distribution law of the truncation areas for fractal surfaces. Specifically, the three-dimensional Weierstrass-Mandelbrot (WM) function is used to characterize rough surfaces. A novel method is proposed to determine the fractal parameters of the WM function. Numerical investigation of rough surface truncation is conducted to obtain size distribution information of the truncation regions for various rough surfaces. Based on the numerical results, the new size distribution law of the truncation areas is proposed and validated by fractal surface and realistic rough surface. It is found that the proposed law can accurately reproduce the size distribution of the truncation areas for rough surfaces with a wide range of fractal parameters.

Design and characterization of an instrumented slider aimed at measuring local micro-impact forces between dry rough solids

Sliding motion between two rough solids under light normal loading involves myriad micro-impacts between antagonist micro-asperities. Those micro-impacts are at the origin of many emerging macroscopic phenomena, including the friction force, the slider's vibrations and the noise radiated in the surroundings. However, the individual properties of the micro-impacts (e.g. maximum force, position along the interface, duration) are essentially elusive to measurement. Here, we introduce an instrumented slider aimed at measuring the position and the normal component of the micro-impact forces during sliding against a rough track. It is based on an array of piezoelectric sensors, each placed under a single model asperity. Its dynamical characteristics are established experimentally and compared to a finite elements model. We then validate its measurement capabilities by using it against a track bearing simple, well-defined topographical features. The measurements are interpreted thanks to a simple multi-asperity contact model. Our slider is expected to be useful in future studies to provide local insights into a variety of tribological questions involving dry rough sliding interfaces.

Assessing predictability of packing porosity and bulk density enhancements after dry coating of pharmaceutical powders

Ability to predict the porosity, and its reduction after nano-silica dry coating, based on the Bond number and cohesion force estimated via multi-asperity contact model was examined for twenty different pharmaceutical powders. A new model for first order estimates of bulk density improvements after dry coating was found to be reasonably predictive despite variations in size (10–225 μm), particle size distribution, aspect ratios (1–3.5), material density, and dispersive surface energy. For the porosity prediction model based on Bond numbers, Microcrystalline Cellulose (MCC) excipients were outliers, regardless of size (20–200 μm). Analysis of their shape, surface morphology and specific surface areas (SSA), indicated that compared to other powders, MCCs had the highest SSA compared to equivalent spheres and high macro-roughness, while having high aspect ratios. This unique characteristic made them effectively more cohesive leading to their poor packing independent of their size, which is in line with previous simulations.

Statistical contact model of rough surfaces: The role of surface tension

The sizes of most asperities on actual rough surfaces range from nanometers to microns. Recent investigations reveal that surface tension plays an important role in micro-/nano-sized contact. Therefore, in this paper, we address the influence of surface tension on the elastic contact of rough surfaces. Nayak's model is employed to describe rough surface with stochastic distribution of both heights and curvatures. As a fundament, we present the general relations of contact area and load as the function of indent depth for a single micro-/nano-sized asperity by accounting for surface tension. Based on the refined relations, we derive the general relations concerned in the contact of rough surfaces. Compared with the conventional multi-asperity contact models based on the Hertzian contact theory, the existence of surface tension decreases the real contact area and requires higher load to generate a given indent depth. It is found that the area of intimate contact is still approximately proportional to the external load, but the proportionality depends on the surface tension.

Using the Multiasperity Models to Investigate the Effect of Cylindrical Micro/Nanoparticle Roughness on the Critical Manipulation Forces

In this paper, the process of moving rough cylindrical bacteria micro/nanoparticles on a smooth substrate by means of an atomic force microscope's (AFM) probe has been investigated. For this purpose, three common adhesion models of Rumpf, Rabinovich, and Cooper have been further developed in the form of multiasperity contact models and with regards to the cylindrical geometry of bacteria nanoparticles. The number of asperities in contact and also the areas of contact between nanoparticle/substrate and nanoparticle/AFM probe tip have been calculated. Then, a dynamic model for simulating rough cylindrical nanoparticles displacement on a smooth substrate has been presented and adhesive forces obtained from the aforementioned three models have been employed in this model to determine the critical force and time values for onset of rolling and sliding of particles on the substrate. Then, the effect of geometrical and roughness parameters on critical forces has been investigated. The simulation results have shown that critical forces required for pushing a rough particle are less than a smooth one. Also, the simulation results indicated that with increasing particle radius, the critical sliding force increases while the critical rolling force diminishes. For the results to be more realistic, simulations have been performed based on the roughness and geometrical parameters extracted from topographical images of bacteria micro/nanoparticles. For this purpose, two different bacteria samples were obtained and after preparing them, the topographic images of these samples were acquired by means of the AFM. Then, the roughness and geometrical parameters of these particles were extracted from the topographic images and using these parameters the manipulation process was simulated for these particles. The simulation results indicate that the maximum difference between Rumpf and Rabinovich models is 8%, so these model results are in a good agreement. Finally, the models developed in this research were validated by comparing the results with the findings of a research on gold nanoparticles.

Investigating the effect of surface roughness on the critical sliding and rolling forces of cylindrical nanoparticles based on the multi-asperity contact models

This paper has investigated the dynamic behavior of a cylindrically shaped DNA nanoparticle during its displacement on a rough substrate by an atomic force microscope. Due to the cylindrical geometry of the DNA nanoparticle, two multi-asperity models have been considered for the adhesion between nanoparticle and rough substrate. The two selected models for the contact between smooth and rough surfaces have been further developed for cylindrical geometries. One of these models is analytical and based on uniform asperities and the other one is based on random asperities. Also, in each of these models, the real area of contact between particle and rough substrate has been calculated based on the number of asperities in contact. Then, a 3D dynamic model for the manipulation of cylindrical nanoparticle on rough substrate has been developed and simulated. The maximum difference between the results obtained from the two multi-asperity models is <5 %, indicating a good agreement between the two models. The comparison of critical forces indicates that the critical force necessary for moving a particle is smaller for rough substrates than for smooth substrates and larger compared to the critical force obtained from the Rabinovich model, which is single-asperity model. Finally, the surface roughness parameters were estimated from the topographic images, and the manipulation process was simulated for these substrates by developing the relevant equations. The obtained results indicated that the critical force for a substrate with a higher root-mean-square roughness is smaller and particles can be moved easier on such a substrate.

EFFECT OF INITIAL CONTACT LOCATION ON MULTIASPERITY NANOCONTACT: QUASICONTINUUM SIMULATION

Two nanocontact models with different initial contact locations are built to simulate the process of the multiasperity nanocontact for investigating the effect of initial contact location on the nanocontact process by using the quasicontinuum method. The indenter is initially located on the top of the middle wave crest (MWC) of the substrate and the top of the wave trough on the left side (LWT) of the substrate, respectively. The microscopic deformation mechanism, the load–displacement curve and the nanohardness–displacement curve are examined. It is found that the deformation mechanisms in the two multiasperity contact models are different. During the initial contact stage, in the MWC model, the twinning deformation dominates the whole contact process, while in the LMT model many Lomer-Cottrell locks are generated in the copper substrate, which inhibits the occurrence of twinning deformation.

Adhesive contact of an elastic semi-infinite solid with a rigid rough surface: Strength of adhesion and contact instabilities

The effect of adhesion on the contact behavior of elastic rough surfaces is examined within the framework of the multi-asperity contact model of Greenwood and Williamson (1966), known as the GW model. Adhesive surface interaction is modeled by nonlinear springs with a force–displacement relation governed by the Lennard–Jones (LJ) potential. Constitutive models are presented for contact systems characterized by low and high Tabor parameters, exhibiting continuous (stable) and discontinuous (unstable) surface approach, respectively. Constitutive contact relations are obtained by integrating the force–distance relation derived from the LJ potential with a finite element analysis of single-asperity adhesive contact. These constitutive relations are then incorporated into the GW model, and the interfacial force and contact area of rough surfaces are numerically determined. The development of attractive and repulsive forces at the contact interface and the occurrence of instantaneous surface contact (jump-in instability) yield a three-stage evolution of the contact area. It is shown that the adhesion parameter introduced by Fuller and Tabor (1975) governs the strength of adhesion of contact systems with a high Tabor parameter, whereas the strength of adhesion of contact systems with a low Tabor parameter is characterized by a new adhesion parameter, defined as the ratio of the surface roughness to the equilibrium interatomic distance. Applicable ranges of aforementioned adhesion parameters are interpreted in terms of the effective surface separation, obtained as the sum of the effective distance range of the adhesion force and the elastic deformation induced by adhesion. Adhesive strength of rough surfaces in the entire range of the Tabor parameter is discussed in terms of a generalized adhesion parameter, defined as the ratio of the surface roughness to the effective surface separation.

Tyre/road noise: Influence of multi-asperity road surface properties on tyre-road contact stresses

This paper deals with the relation between properties of road surfaces and measured tyre/road noise. A number of artificial road surfaces composed of academic asperities of simple shapes (spherical, conical or cylindrical) are generated. The dynamical contact forces are calculated over several loops for a slick tyre rolling at different speeds. A multi-asperity contact model developed by the authors is used. The spectra for a periodic road surface clearly show that the excitation frequency of the tyre within the contact area is directly due to the speed and the distance between asperity tips in the rolling direction. For randomly distributed artificial surfaces, broad band spectra are obtained with a cut off frequency linked to distance between successive contacts in the rolling direction while the mean relative height has few influence. The results are discussed and compared with spectra of contact stresses for real road surfaces within the framework of tyre/road noise.

Statistical estimation of low frequency tyre/road noise from numerical contact forces

This paper deals with the relation between tyre/road numerical contact data and close-proximity (CPX) rolling noise measurements. The noise was measured on several road surfaces together with the road texture in three dimensions on two-metre-long sections. A multi-asperity contact model was used to calculate successively the contact forces distribution and the contact pressure distribution between a tyre (slick or patterned) and the road during rolling. The correlation between third-octave contact force levels and noise levels was studied on a set of road surfaces with various textures. A high positive correlation was found at low frequency, which allows the estimation of noise levels by means of statistical relations for each third-octave band between 315Hz and 1000Hz for the slick tyre and between 315Hz and 800Hz for the patterned tyre. The results of the model are discussed in relation to the standard deviation of CPX measurements.

Comparative Contact Analysis Study of Finite Element Method Based Deterministic, Simplified Multi-Asperity and Modified Statistical Contact Models

The study of the contact stresses generated when two surfaces are in contact plays a significant role in understanding the tribology of contact pairs. Most of the present contact models are based on the statistical treatment of the single asperity contact model. For a clear understanding about the elastic-plastic behavior of two rough surfaces in contact, comparative study involving the deterministic contact model, simplified multi-asperity contact model, and modified statistical model are undertaken. In deterministic contact model analysis, a three dimensional deformable rough surface pressed against a rigid flat surface is carried out using the finite element method in steps. A simplified multi-asperity contact model is developed using actual summit radii deduced from the rough surface, applying single asperity contact model results. The resultant contact parameters like contact load, contact area, and contact pressure are compared. The asperity interaction noticed in the deterministic contact model analysis leads to wide disparity in the results. Observing the elastic-plastic transition of the summits and the sharing of contact load and contact area among the summits, modifications are employed in single asperity statistical contact model approaches in the form of a correction factor arising from asperity interaction to reduce the variations. Consequently, the modified statistical contact model and simplified multi-asperity contact model based on actual summit radius results show improved agreement with the deterministic contact model results.

Interacting and coalescing Hertzian asperities: A new multiasperity contact model

Starting from the multiasperity contact theory, firstly addressed by Greenwood and Williamson [1] and Bush et al. [2], in the present paper we suggest a new methodology to take into account the lateral interaction between the asperities and their coalescing, neglected in the first formulation of the theory. When two opposing rough surfaces approach, the number and the size of the contacts grow, and some contacts spots may merge to form larger contact areas.This phenomenon is modeled, in this paper, in a simple way replacing the overlapping contact spots with a single ‘appropriate’ equivalent asperity.The method has been then utilized to analyse the contact between an elastic half-space and a numerically generated self-affine fractal rigid surface. The fractal surface has been generated by employing spectral methods. Results predict linearity between contact area and load and are in good agreement with numerical and experimental investigations.

Contact mechanics of rough surfaces: a comparison between theories

In this paper the authors briefly review the most important theories of contact mechanics between randomly rough surfaces. The multiasperity contact theories are here shown under a unifying point of view and compared with the more recent approach developed by Persson. In particular we focus on the relation between the applied load and separation, which is fundamental in many engineering applications as seals, lubrication and wear. We found that the difference between the multiasperity contact models and Persson’s theory is not only quantitative, as in case of area-load linearity, but also qualitative. A brief comparison with existing experiments and numerical calculations shows that Persson’s predictions should be more accurate.

Effects of Contacting Surfaces on MEMS Device Reliability

A multi-asperity contact model with adhesion is presented to analyze the real contact of microdevices, including contact force, contact area, and pull-off force. Since the macroscopic contact of two contacting surfaces is the statistical average of many individual micro/nano contacts, the key point is to include an accurate analysis of the discrete contacts. A finite element model which is applicable to a wide range of material properties was developed to study adhesion and plasticity of a single contact during both loading and unloading cycles in a previous investigation. The best fits of the results by comparing with the existing models are introduced in this work for both the loading and unloading (pull-off force) analyses. Pearson Type distributions which can independently adjust the skewness and kurtosis of surface heights are used to study the multi-asperity contact. The significance of this work is not only to predict adhesion of the existing devices, but to provide an optimal design of surface characteristics and material properties to improve device reliability. An overview of the status of surface roughening indicates that various techniques exist to tailor surface morphological properties, but that these techniques mainly target the mean and root-mean-square (rms) values of the roughness. This approach insufficiently utilizes all available techniques to minimize adhesion force between surfaces. New approaches that include surface roughness process development should include a range of skewness and kurtosis values of the resulting surface as a design consideration in addition to the mean and rms values of the roughness.

Numerical Investigation of Bouncing Vibrations of an Air Bearing Slider in Near or Partial Contact

Near or partial contact sliders are designed for the areal recording density of 1 Tbit/in.2 or even higher in hard disk drives. The bouncing vibration of an air bearing-slider in near or partial contact with the disk is numerically analyzed using three different nonlinear slider dynamics models. In these three models, the air bearing with contact is modeled either by using the generalized Reynolds equation modified with the Fukui–Kaneko slip correction and a recent second order slip correction for the contact situation, or using nonlinear springs to represent the air bearing. The contact and adhesion between the slider and the disk are considered either through an elastic contact model and an improved intermolecular adhesion model, respectively, or using an Ono–Yamane multi-asperity contact and adhesion model (2007, “Improved Analysis of Unstable Bouncing Vibration and Stabilizing Design of Flying Head Slider in Near-Contact Region,” ASME J. Tribol., 129, pp. 65–74.). The contact friction is calculated by using Coulomb’s law and the contact force. The simulation results from all of these models show that the slider’s bouncing vibration occurs as a forced vibration caused by the moving microwaviness and roughness on the disk surface. The disk surface microwaviness and roughness, which move into the head disk interface as the disk rotates, excite the bouncing vibration of the partial contact slider. The contact, adhesion, and friction between the slider and the disk do not directly cause a bouncing vibration in the absence of disk microwaviness or roughness.

Asperity contact theories: Do they predict linearity between contact area and load?

During the last few years, the scientific community has been debating about which theory of contact between rough surfaces can be considered as the most accurate. The authors have been attracted by such a discussion and in this paper try to give their personal thought and contribution to this debate. We present a critical analysis of the principal contact theories of rough surfaces. We focus on the multiasperity contact models (which are all based on the original idea of Greenwood and Williamson (GW) [1966. Proc. R. Soc. London A 295, 300]), and also briefly discuss a relatively recent contact theory developed by Persson [2001. J. Chem. Phys. 115, 3840]. For small loads both asperity contact models and Persson's theory predict a linear relation between the area of true contact and the applied external load, but the two theories differ for the constant of proportionality. However, this is not the only difference between the two approaches. Indeed, we show that the fully calculated predictions of asperity contact models very rapidly deviates from the predicted linear relation already for very small and in many cases unrealistic vanishing applied loads and contact areas. Moreover, this deviation becomes more and more important as the PSD breadth parameter α (as defined by Nayak) increases. Therefore, the asymptotic linear relation of multiasperity contact theories turns out to be only an academic result. On the contrary, Persson's theory is not affected by α and shows a linear behavior between contact area and load up to 10–15% of the nominal contact area, i.e. for physical reasonable loads. The authors also prove that, at high separation, all multiasperity contact models, which take into account the influence of summit curvature variation as a function of summit height, necessarily converge to a (slightly) improved version of the GW model, which, therefore, remains one of the most important milestones in the field of contact mechanics of rough surfaces.