Surface Roughness Power Spectrum Research Articles

Ice breakloose friction.

We discuss the origin of the breakloose (or static) friction force when an ice block is slid on a hard randomly rough substrate surface. If the substrate has roughness with small enough amplitude (of order a 1nm or less), the breakloose force may be due to interfacial slip and is determined by the elastic energy per unit area, Uel/A0, stored at the interface after the block has been displaced a short distance from its original position. The theory assumes complete contact between the solids at the interface and that there is no elastic deformation energy at the interface in the original state before the application of the tangential force. The breakloose force depends on the surface roughness power spectrum of the substrate and is found to be in good agreement with experimental observations. We show that as the temperature decreases, there is a transition from interfacial sliding (mode II crack propagation, where the crack propagation energy GII = Uel/A0) to opening crack propagation (mode I crack propagation with GI the energy per unit area to break the ice-substrate bonds in the normal direction).

On the Use of Surface Roughness Parameters

In most practical applications, surface roughness is characterized by just one or two parameters (numbers). I show that the standard maximum surface height parameters fluctuate strongly between different surface realizations (or measurements), and should not be used in the design of engineering components. I show how some roughness parameters depend on the size of the roll-off region in the surface roughness power spectra, and introduce a new height parameter which is very reproducible. The numerical results presented agree well with experimental observations.Graphical

Influence of Surface Roughness on Press Fits

A press fit, also known as interference fit or friction fit, is a form of fastening between two tight fitting mating parts (usually two bodies with cylinder or conical surfaces) that produces a joint which is held together by friction after the parts are pushed together. I discuss the influence of surface roughness on the design of press fits. This topic has been addressed in the engineering community but only on an empirical level without a scientific backup. Here, I will apply the Persson contact mechanics theory to show how to include the surface roughness in the design criteria. I argue that one should use what I denote as the cylinder “stylus width” rather than the “caliper width” when determining the influence of the surface roughness of the compression (also denoted as the interference). In the classical approach using the caliper width, the compression is assumed to be independent of the elastic properties of the solids, but in the more accurate approach presented here using the stylus width the compression depends on the elastic properties and on the surface roughness power spectra of the involved solids. A detailed discussion of the relation between the root-mean-square roughness amplitude h_{mathrm{rms}} and the maximum asperity height h_{mathrm{max}}, of interest in its own right, is also presented as it is needed for determining the relation between the stylus and caliper derived compression’s.Graphical

Leakage of Metallic Ball Seat Valves with Anisotropic Surfaces

AbstractMetallic ball seat valves are an essential component of many hydraulic systems. They are used for many different purposes such as pressure relief valves or check valves. Despite their universal usage, their sealing mechanism is not yet fully understood. In previous works, a successful method for the simulation of the fluid leakage of metallic ball seat valves has been developed and confirmed experimentally. The method is based on Persson's contact mechanics theory, which is based on surface roughness power spectrum C(q). This theory takes a wide range of roughness values at different length scales into account. The previous method has been restricted to isotropic surfaces, but most surfaces of practical interest are highly anisotropic. A method for the calculation of pressure flow factors using Persson's method is presented. Based on these, a model for the leakage calculation can be developed. The simulation results are validated using an experiment.

An investigation of gecko attachment on wet and rough substrates leads to the application of surface roughness power spectral density analysis

The roughness and wettability of surfaces exploited by free-ranging geckos can be highly variable and attachment to these substrates is context dependent (e.g., presence or absence of surface water). Although previous studies focus on the effect of these variables on attachment independently, geckos encounter a variety of conditions in their natural environment simultaneously. Here, we measured maximum shear load of geckos in air and when their toes were submerged underwater on substrates that varied in both surface roughness and wettability. Gecko attachment was greater in water than in air on smooth and rough hydrophobic substrates, and attachment to rough hydrophilic substrates did not differ when tested in air or water. Attachment varied considerably with surface roughness and characterization revealed that routine measurements of root mean square height can misrepresent the complexity of roughness, especially when measured with single instruments. We used surface roughness power spectra to characterize substrate surface roughness and examined the relationship between gecko attachment performance across the power spectra. This comparison suggests that roughness wavelengths less than 70 nm predominantly dictate gecko attachment. This study highlights the complexity of attachment in natural conditions and the need for comprehensive surface characterization when studying biological adhesive system performance.

A Hybrid Multiscale Approach for Rubber Contact

Contact mechanics models based on linearity assumptions, often using the viscoelastic half space theory and numerically implemented with the boundary element method, are known to provide accurate results for small mean square slope of the surface roughness. For large mean square slope, models accounting for finite deformations, often implemented with the non-linear finite element method, are more accurate but lead to a prohibitive computational cost. We propose a new hybrid multiscale approach able to account for the finite deformations arising due to large mean square slope, while keeping a computational cost similar to that associated to linear approaches. The basic strategy is a decomposition of the surface roughness power spectrum into a discrete number of waves, whose spectral range is partitioned into a high mean square slope range and a low mean square slope range. The contact mechanics in the former is accurately solved with the kinematically non-linear model and the results averaged out at the larger wavelength scale in terms of an effective interface interaction law. This law is then applied in the linear simulation involving the scales within the low mean square slope range. The proposed approach is a more accurate alternative to fully linear and a computationally faster alternative to fully non-linear contact mechanics approaches.

Finger Pad Topography beyond Fingerprints: Understanding the Heterogeneity Effect of Finger Topography for Human-Machine Interface Modeling.

With the rapid development of haptic devices, there is an increasing demand to understand finger pad topography under different conditions, especially for investigation of the human-machine interface in surface haptic devices. An accurate description of finger pad topography across scales is essential for the study of the interfaces and could be used to predict the real area of contact and friction force, both of which correlate closely with human tactile perception. However, there has been limited work reporting the heterogeneous topography of finger pads across scales. In this work, we propose a detailed heterogeneous finger topography model based on the surface roughness power spectrum. The analysis showed a significant difference between the topography on ridges and valleys of the fingerprint and that the real contact area estimation could be different by a factor of 3. In addition, a spatial-spectral analysis method is developed to effectively compare topography response to different condition changes. This paper provides insights into finger topography for advanced human-machine interaction interfaces.

Multiscale Assessments on the Frictional Sliding Surface and Wear Volume of Tire Rubber by Use of the Surface Roughness Power Spectrum

本研究では，3次元表面形状のパワースペクトル密度(PSD)を計測するときに生じる様々なノイズやバイアスを自然に除去できる補正手法を提案する．そして，その補正手法を用いて自己アフィンフラクタル表面の指標となるハースト指数の高精度な推定方法を開発する．上記の手法を砥石と摺動前後のタイヤゴムに適用してその有用性を実証する．特にタイヤゴム表面は全波数域で自己アフィン性が成立しないことを明らかにし，K相関モデルを用いた表面粗さPSDのパラメータ同定に応用する．最後に摩耗体積量と二乗平均平方根粗さとの関連付けを行い，本手法の妥当性を確認する．

Contact Mechanics for Solids with Randomly Rough Surfaces and Plasticity

We present experimental results for the elastic and plastic deformation of sandblasted polymer balls resulting from contacts with flat smooth steel and silica glass surfaces. Nearly symmetric, Gaussian-like height probability distributions were observed experimentally before and remarkably, also after the polymer balls were deformed plastically. For all the polymers studied we find that the surface roughness power spectra for large wavenumbers (short length scales) are nearly unchanged after squeezing the polymer balls against flat surfaces. We attribute this to non-uniform plastic flow processes at the micrometer length scale. The experimental data are analyzed using the Persson contact mechanics theory with plasticity and with finite-element method (FEM) calculations.

Re-estimation of thermal contact resistance considering near-field thermal radiation effect

Thermal contact has always been a hot issue in many engineering fields and thermal contact resistance (TCR) is one of the important indicators weighing the heat transfer efficiency among the interfaces. In this paper, the contact heat transfer of conforming rough surfaces is theoretically re-estimated considering both the heat transfer from contact and non-contact regions. The fluctuational electrodynamics (an ab initio calculation) is adopted to calculate the thermal radiation. The contribution of the contact regions is estimated by the CMY TCR model and further studied by modelling specific surfaces with the corresponding surface roughness power spectrum. Several tests are presented where aluminum and amorphous alumina are mainly used in the simulations. Studies showed that there exists a significant synergy between the thermal conduction and near-field thermal radiation at the interface within a certain range of the effective roughness. When the effective roughness is near to the scales of submicron, the near-field thermal radiation effect should not be neglected even at room temperature.

Investigation of tribological behavior of Styrene-Butadiene Rubber compound on asphalt-like surfaces

Abstract Tribological behavior of Styrene-Butadiene Rubber (SBR) compound reinforced by silica and carbon-black fillers on two different asphalt-like surfaces is studied using theoretical and experimental approaches. Linear sliding friction and wear tests were performed on two different roofing asphalt papers. The surface roughness power spectra of asphalts and the master curves of the large-strain viscoelastic modulus of SBR compound were used to model the contact area and friction coefficient theoretically. The theoretical results are in good agreement with experiment providing the tribochemical degradation is not the dominant wear mechanism. When the formation of a tribo-modified layer prevails the mechanical abrasion, the wear rate, in terms of mass loss, does not necessarily increase with the increase of frictional work as expected theoretically.

Ice friction: Glacier sliding on hard randomly rough bed surface.

I present a theory for ice friction for ice sliding on a hard randomly rough surface which includes ice melting-freezing (regelation), viscoelastic energy dissipation, and cavitation. The theory is an extension of earlier work by Weertman, Lliboutry, Nye, and Kamb. I present numerical results for surfaces with realistic surface roughness power spectra. I consider both airfilled and (pressurized) waterfilled cavities. The calculated frictional shear stresses are consistent with experimental observations for temperate glaciers.

On the Use of Silicon Rubber Replica for Surface Topography Studies

Silicone rubber is often used to obtain replica of surfaces which are hard to study directly. Here we discuss under what conditions engineering stylus measurements can be used to obtain the correct surface roughness from the replica. We also show how thin vertical slices of the silicone rubber can be used to obtain the surface roughness power spectra for the long-wavelength roughness on even very rough surfaces, such as road surfaces, which may be hard to probe directly with standard optical or stylus instruments.

Relationship between the surface roughness power spectra of abrasive specimens and the friction and abrasion of tire rubber

Relationship between the surface roughness power spectra of abrasive specimens and the friction and abrasion of tire rubber

Simple contact mechanics model of the vertebrate cartilage.

We study a simple contact mechanics model of the vertebrate cartilage, which includes (bulk) osmotic effects. The surface roughness power spectrum of a pig cartilage is obtained from the measured surface topography. Using the Reynolds equations with fluid flow factors, calculated using the Persson contact mechanics theory and the Bruggeman effective medium theory, we show how the area of contact and the average interfacial separation change with time. We found that in most cases the contact area percolates, resulting in islands of confined fluid which carry most of the external load. Most importantly, we find that the pressure in the area of real contact is nearly independent of the external load, and well below 1 MPa. This allows the surfaces in the area of "real contact", to be separated (at nanometer range separation distance) by osmotic repulsion, resulting in a very small (breakloose) friction force observed even after a long time of stationary contact.

Top topography surface roughness power spectrum for pavement friction evaluation

This article deals with the most suitable calculation procedure for top topography surface roughness power spectrum (PSD). The information top PSD provides about the roughness characteristics and its practical application in tyre-road friction studies are covered. The influence of portions of top topography used for calculations on the realization these PSDs give about surface height distributions is investigated. Results of roughness PSDs generally proved to be dependent on portions of top topography used for calculations. A high correlation with an average around 0.8 was found with friction and top 20% of PSDs, but only at a short-scale surface roughness λ≤1mm. Low correlation coefficients between friction and longer λ were discussed through the depth of the penetration of the rubber into each pavement.

Rubber Friction on Ice: Experiments and Modeling

Rubber friction on ice is studied both experimentally and theoretically. The friction tests involve three different rubber tread compounds and four ice surfaces exhibiting different roughness characteristics. Tests are carried out at four different ambient air temperatures ranging from $$-5$$ to $$-13\,^{\circ }\hbox {C}$$ , under three different nominal pressures ranging from 0.15 to $$0.45\,\hbox {MPa}$$ , and at the sliding speed 0.65 m/s. The viscoelastic properties of all the rubber compounds are characterized using dynamic mechanical analysis. The surface topography of all ice surfaces is measured optically. This provides access to standard roughness quantities and to the surface roughness power spectra. As for modeling, we consider two important contributions to rubber friction on ice: (1) a contribution from the viscoelasticity of the rubber activated by ice asperities scratching the rubber surface and (2) an adhesive contribution from shearing the area of real contact between rubber and ice. At first, a macroscopic empirical formula for the friction coefficient is fitted to our test results, yielding a satisfactory correlation. In order to get insight into microscopic features of rubber friction on ice, we also apply the Persson rubber friction and contact mechanics theory. We discuss the role of temperature-dependent plastic smoothing of the ice surfaces and of frictional heating-induced formation of a meltwater film between rubber and ice. The elaborate model exhibits very satisfactory predictive capabilities. The study shows the importance of combining advanced testing and state-of-the-art modeling regarding rubber friction on ice.

Rubber friction on road surfaces: Experiment and theory for low sliding speeds.

We study rubber friction for tire tread compounds on asphalt road surfaces. The road surface topographies are measured using a stylus instrument and atomic force microscopy, and the surface roughness power spectra are calculated. The rubber viscoelastic modulus mastercurves are obtained from dynamic mechanical analysis measurements and the large-strain effective modulus is obtained from strain sweep data. The rubber friction is measured at different temperatures and sliding velocities, and is compared to the calculated data obtained using the Persson contact mechanics theory. We conclude that in addition to the viscoelastic deformations of the rubber surface by the road asperities, there is an important contribution to the rubber friction from shear processes in the area of contact. The analysis shows that the latter contribution may arise from rubber molecules (or patches of rubber) undergoing bonding-stretching-debonding cycles as discussed in a classic paper by Schallamach.

Surface topography and contact mechanics of dry and wet human skin.

The surface topography of the human wrist skin is studied by using optical and atomic force microscopy (AFM) methods. By using these techniques the surface roughness power spectrum is obtained. The Persson contact mechanics theory is used to calculate the contact area for different magnifications, for the dry and wet skin. The measured friction coefficient between a glass ball and dry and wet skin can be explained assuming that a frictional shear stress σf ≈ 13 MPa and σf ≈ 5 MPa, respectively, act in the area of real contact during sliding. These frictional shear stresses are typical for sliding on surfaces of elastic bodies. The big increase in friction, which has been observed for glass sliding on wet skin as the skin dries up, can be explained as result of the increase in the contact area arising from the attraction of capillary bridges. Finally, we demonstrated that the real contact area can be properly defined only when a combination of both AFM and optical methods is used for power spectrum calculation.

Measuring nanoparticle size using phase-stepping interferometry: quantifying measurement sensitivity to surface roughness.

A method for sizing nanoparticles using phase-stepping interferometry has been developed recently by Little et al. [Appl. Phys. Lett. 103, 161107 (2013)]. We present an analytical procedure to quantify how sensitive measurement precision is to surface roughness. This procedure computes the standard deviation in the measured phase as a function of the surface roughness power spectrum. It is applied to nanospheres and nanowires on a flat plane and also a flat plane in isolation. Calculated sensitivity levels demonstrate that surface roughness is unlikely to be the limiting factor on measurement precision when measuring nanoparticle size using this phase-shifting-interferometry-based technique. The need to use an underlying surface that is very smooth when measuring nanoparticles is highlighted by the analysis.