Procedure to Approximately Estimate the Uncertainty of Material Ratio Parameters due to Inhomogeneity of Surface Roughness

Roughness parameters that characterize contacting surfaces with regard to friction and wear are commonly stated without uncertainties, or with an uncertainty only taking into account a very limited amount of aspects such as repeatability of reproducibility (homogeneity) of the specimen. This makes it difficult to discriminate between different values of single roughness parameters. Therefore uncertainty assessment methods are required that take all relevant aspects into account. In the literature this is scarcely performed and examples specific for parameters used in friction and wear are not yet given. We propose a procedure to derive the uncertainty from a single profile employing a statistical method that is based on the statistical moments of the amplitude distribution and the autocorrelation length of the profile. To show the possibilities and the limitations of this method we compare the uncertainty derived from a single profile with that derived from a high statistics experiment.Comment: submitted to Meas. Sci. Technol., 12 figure

Multi-scale roughness transfer in cold metal rolling

We report on a comparative Atomic Force Microscope (AFM) multi-scale roughness analysis of cold rolled Al alloy and steel roll, in order to characterize the roughness transfer from the steel roll to the workpiece in cold strip rolling processes. More than three orders of length-scale magnitudes were investigated from 100 microns to 50 nanometers on both types of surfaces. The analysis reveals that both types of surfaces are anisotropic self-affine surfaces. Transverse and longitudinal height profiles exhibit a different roughness exponent (Hurst exponent) z֊=0.93±0.03 and zʈ=0.5±0.05 Different length-scale cut-offs are obtained in each direction lsup=50mm, lsupՆ100mm. Height and slope distributions are also computed to complement this study. The above mentionned self-affine characteresitics are found to be very similar for the roll and the strip surfaces, which suggest that roughness transfer takes place from the macroscopic (100 µm) to the very small scale (50 nm)

Two-Scale Kirchhoff Theory: Comparison of Experimental Observations With Theoretical Prediction

We introduce a non-perturbative two scale Kirchhoff theory, in the context of light scattering by a rough surface. This is a two scale theory which considers the roughness both in the wavelength scale (small scale) and in the scales much larger than the wavelength of the incident light (large scale). The theory can precisely explain the small peaks which appear at certain scattering angles. These peaks can not be explained by one scale theories. The theory was assessed by calculating the light scattering profiles using the Atomic Force Microscope (AFM) images, as well as surface profilometer scans of a rough surface, and comparing the results with experiments. The theory is in good agreement with the experimental results.Comment: 6 pages, 8 figure

Roughness Signature of Tribological Contact Calculated by a New Method of Peaks Curvature Radius Estimation on Fractal Surfaces

This paper proposes a new method of roughness peaks curvature radii calculation and its application to tribological contact analysis as characteristic signature of tribological contact. This method is introduced via the classical approach of the calculation of radius of asperity. In fact, the proposed approach provides a generalization to fractal profiles of the Nowicki's method [Nowicki B. Wear Vol.102, p.161-176, 1985] by introducing a fractal concept of curvature radii of surfaces, depending on the observation scale and also numerically depending on horizontal lines intercepted by the studied profile. It is then established the increasing of the dispersion of the measures of that lines with that of the corresponding radii and the dependence of calculated radii on the fractal dimension of the studied curve. Consequently, the notion of peak is mathematically reformulated. The efficiency of the proposed method was tested via simulations of fractal curves such as those described by Brownian motions. A new fractal function allowing the modelling of a large number of physical phenomena was also introduced, and one of the great applications developed in this paper consists in detecting the scale on which the measurement system introduces a smoothing artifact on the data measurement. New methodology is applied to analysis of tribological contact in metal forming process

Numerical study of geometrical dispersion in self-affine rough fractures

We report a numerical study of passive tracer dispersion in fractures with rough walls modeled as the space between two complementary self-affine surfaces rigidly translated with respect to each other. Geometrical dispersion due to the disorder of the velocity distribution is computed using the lubrication approximation. Using a spectral perturbative scheme to solve the flow problem and a mapping coordinate method to compute dispersion, we perform extensive ensemble averaged simulations to test theoretical predictions on the dispersion dependence on simple geometrical parameters. We observe the expected quadratic dispersion coefficient dependence on both the mean aperture and the relative shift of the crack as of well as the anomalous dispersion dependence on tracer traveling distance. We also characterize the anisotropy of the dispersion front, which progressively wrinkles into a self-affine curve whose exponent is equal to that of the fracture surface

Simulation model of erosion and deposition on a barchan dune

Erosion and deposition over a barchan dune near the Salton Sea, California, are modeled by bookkeeping the quantity of sand in saltation following streamlines of transport. Field observations of near surface wind velocity and direction plus supplemental measurements of the velocity distribution over a scale model of the dune are combined as input to Bagnold type sand transport formulas corrected for slope effects. A unidirectional wind is assumed. The resulting patterns of erosion and deposition compare closely with those observed in the field and those predicted by the assumption of equilibrium (downwind translation of the dune without change in size or geometry). Discrepancies between the simulated results and the observed or predicted erosional patterns appear to be largely due to natural fluctuations in the wind direction. The shape of barchan dunes is a function of grain size, velocity, degree of saturation of the oncoming flow, and the variability in the direction of the oncoming wind. The size of the barchans may be controlled by natural atmospheric scales, by the age of the dunes, or by the upwind roughness. The upwind roughness can be controlled by fixed elements or by sand in the saltation. In the latter case, dune scale is determined by grain size and wind velocity

Surface correlations of hydrodynamic drag for transitionally rough engineering surfaces

Rough surfaces are usually characterised by a single equivalent sand-grain roughness height scale that typically needs to be determined from laboratory experiments. Recently, this method has been complemented by a direct numerical simulation approach, whereby representative surfaces can be scanned and the roughness effects computed over a range of Reynolds number. This development raises the prospect over the coming years of having enough data for different types of rough surfaces to be able to relate surface characteristics to roughness effects, such as the roughness function that quantifies the downward displacement of the logarithmic law of the wall. In the present contribution, we use simulation data for 17 irregular surfaces at the same friction Reynolds number, for which they are in the transitionally rough regime. All surfaces are scaled to the same physical roughness height. Mean streamwise velocity profiles show a wide range of roughness function values, while the velocity defect profiles show a good collapse. Profile peaks of the turbulent kinetic energy also vary depending on the surface. We then consider which surface properties are important and how new properties can be incorporated into an empirical model, the accuracy of which can then be tested. Optimised models with several roughness parameters are systematically developed for the roughness function and profile peak turbulent kinetic energy. In determining the roughness function, besides the known parameters of solidity (or frontal area ratio) and skewness, it is shown that the streamwise correlation length and the root-mean-square roughness height are also significant. The peak turbulent kinetic energy is determined by the skewness and root-mean-square roughness height, along with the mean forward-facing surface angle and spanwise effective slope. The results suggest feasibility of relating rough-wall flow properties (throughout the range from hydrodynamically smooth to fully rough) to surface parameters

The structure of gravel-bed flow with intermediate submergence: a laboratory study

The paper reports an experimental study of the flow structure over an immobile gravel bed in open channel at intermediate submergence, with particular focus on the near-bed region. The experiments consisted of velocity measurements using three-component (stereoscopic) Particle Image Velocimetry (PIV) in near-bed horizontal plane and two-component PIV in three vertical planes that covered three distinctly different hydraulic scenarios where the ratio of flow depth to roughness height (i.e., relative submergence) changes from 7.5 to 10.8. Detailed velocity measurements were supplemented with fine-scale bed elevation data obtained with a laser scanner. The data revealed longitudinal low-momentum and high-momentum "strips'' in the time-averaged velocity field, likely induced by secondary currents. This depth-scale pattern was superimposed with particle-scale patches of flow heterogeneity induced by gravel particle protrusions. A similar picture emerged when considering second-order velocity moments. The interaction between the flow field and gravel-bed protrusions is assessed using cross correlations of velocity components and bed elevations in a horizontal plane just above gravel particle crests. The cross correlations suggest that upward and downward fluid motions are mainly associated with upstream-facing and lee sides of particles, respectively. Results also show that the relative submergence affects the turbulence intensity profiles for vertical velocity over the whole flow depth, while only a weak effect, limited to the near-bed region, is noticed for streamwise velocity component. The approximation of mean velocity profiles with a logarithmic formula reveals that log-profile parameters depend on relative submergence, highlighting inapplicability of a conventional "universal'' logarithmic law for gravel-bed flows with intermediate submergence

Low surface brightness galaxies mass profiles as a consequence of galactic evolution

This paper presents a principal components analysis of rotation curves from a sample of low surface brightness galaxies. The physical meaning of the principal components is investigated, and related to the intrinsic properties of the galaxies. The rotation curves are re-scaled using the optical disk scale, the resulting principal component decomposition demonstrates that the whole sample is properly approximated using two components. The ratio of the second to the first component is related to the halo steepness in the central region, is correlated to the gas fraction in the galaxy, and is un-correlated to other parameters. As a consequence the gas fraction appear as a fundamental variable with respect to the galaxies rotation curves, and its correlation with the halo steepness is especially important. Since the gas fraction is related to the degree of galaxy evolution, it is very likely that the steepness of the halo at the center is a consequence of galaxy evolution. More evolved galaxies have shallower central profile and statistically less gas, most likely as a consequence of more star formation and supernovae. The differences in evolution, gas fractions and halo central steepness of the galaxies could be due to the influence of different environments.Comment: 8 pages, 4 figure