non-Gaussian Height Distributions Research Articles

The Influence of Non-Gaussian Roughness and Spectral Properties on Mixed Lubrication for Heavily Loaded Counterformal Contacts

The impact of non-Gaussian height distribution and spectral properties on the lubrication performance of counterformal (point) contacts is quantitatively studied (film parameter, Λ, and asperity load ratio, La) by developing a mixed lubrication model. The Weibull height distribution function and power spectral density (PSD) are used to generate artificial surface topographies (non-Gaussian and Gaussian, isotropic), as these surface topographies are found in many tribological components. The set of variables needed to parametrize and their effect on mixed lubrication is discussed, including the shape parameter, the autocorrelation length, the wavelength ratio, and the Hurst coefficient. It is revealed that a rough surface with a lower shape parameter exhibits higher hydrodynamic lift. The spectral properties (the autocorrelation length and the wavelength ratio) of rough surfaces significantly affect the film parameter and the hydrodynamic and asperity pressures. The film parameter is slightly influenced by the Hurst coefficient.

High-Fidelity Computational Assessment of Aero-Thermal Performance and the Reynolds’ Analogy for Additively Manufactured Anisotropic Surface Roughness

Abstract Direct numerical simulations of incompressible turbulent forced convection over irregular, anisotropic surface roughness in a pressure-driven plane channel flow have been performed. Heat transfer was simulated by solving the passive scalar transport equation with Prandtl number Pr = 0.7. The roughness topographies under investigation here are based on an X-ray computed tomography scan of an additively manufactured internal cooling passage, which had an irregular, multiscale and mildly non-Gaussian height distribution. Three different roughness topographies and three different friction Reynolds numbers (Reτ = 395, 590, 720) were considered, along with reference smooth-wall simulations at matched Reτ. By systematically varying the roughness topography and flow conditions, a direct computational assessment of aero-thermal performance (pressure losses and heat transfer) and the Reynolds analogy factor, i.e., 2Ch/Cf, where Ch is the heat-transfer coefficient (Stanton number) and Cf is the skin-friction coefficient, was conducted. The results highlight the profound impact that the roughness orientation (relative to the flow direction) has upon the aero-thermal performance of additively manufactured internal passages, with transverse-aligned roughness augmenting heat transfer by as much as 33%, relative to its streamwise-aligned counterpart. An interrogation of velocity and temperature statistics in the near-wall region was also performed, which underlined the growing dissimilarity between heat transfer and drag as fully rough conditions are approached.

A closer look into slickensides: Deformation on and under fault surfaces

Accurate descriptions of natural fault surfaces and associated fault rocks are important for understanding fault zone processes and properties. Slickensides--grooved polished surfaces that record displacement and wear along faults-- develop measurable roughness and characteristic microstructures during fault slip. We quantify the roughness of natural slickensides from three different fault surfaces by calculating the surfaces power spectra and height distributions and analyze the microstructures formed below the slickensides. Slickenside surfaces exhibit anisotropic self-affine roughness with corresponding mean Hurst exponents in directions parallel-- 0.53 ± 0.07-- and perpendicular --0.6 ± 0.1-- to slip, consistent with reports from other fault surfaces. Additionally, surfaces exhibit non-Gaussian height distributions, with their skewness and kurtosis roughness parameters having noticeable dependence on the scale of observation. Below the surface, microstructural analyses reveal that S–C–C′ fabrics develop adjacent to a C-plane-parallel principal slip zone characterized by a sharp decrease in clast size and a thin (≤100 μm) nanoparticulate-rich principal slip surface (PSS). These microstructures are present in most analyzed samples suggesting they commonly form during slickenside development regardless of lithology or tectonic setting. Our results suggests that 1) PSS likely arise by progressive localization along weaker oriented fabrics 2) deformation along PSS's is energetic enough to comminute the rocks into nanometric grains, and 3) fault geometry can be further characterized by studying the height distributions of fault surfaces, which are likely to impact stress distributions and frictional responses along faults.

Evolution of the real contact area of self-affine non-Gaussian surfaces

The impact of non-Gaussian height distribution on the real contact area evolution of elastic, frictionless and non-adhesive contact is studied. The Weibull probability function is used to model the height distribution, as it can capture surfaces of practical relevance. The set of variables needed to parametrise the problem is discussed, including the shape parameter of the height distribution, the topography’s wavelength ratio and the Hurst exponent. As the topographies become more non-Gaussian, a significant deviation from the Gaussian case is observed. Moreover, the spectral properties show a distinct effect on different non-Gaussian surfaces and the dependency on Nayak’s parameter is not inherited. A power-law evolution of the real contact area is found to fit the numerical results obtained with the boundary element method precisely. Finally, two semi-analytical asperity-based models are compared with numerical results, using the statistics of artificially generated topographies. The qualitative behaviour predicted with the numerical simulations is captured.

Bistatic Radar Scattering from Non-Gaussian Height Distributed Rough Surfaces

In modeling a rough surface, it is common to assume a Gaussian height distribution. This hypothesis cannot describe an eventual asymmetry between crests and troughs of natural surfaces. We analyzed the bistatic scattering from a rough surface with non-Gaussian height distributions using the Kirchhoff scattering theory. Two extreme cases of Gamma-distributed surfaces were compared in particular: exponential and Gaussian distributions. The bistatic angular dependence was examined under various root mean square (RMS) heights and power spectrum densities. Contribution sources to the coherent and incoherent scattering components were singled out relating to the surface height distribution. For an exponential height surface, the coherent scattering strengthens even as the surface becomes rough. The non-Gaussian effect on the incoherent scattering is connected with surface power spectrum density. The height distribution impacts differ in the different regions of the bistatic scattering plane and thus complicate the differentiation of the scattering patterns due to height distribution.

The impact of non-Gaussian height distributions on the statistics of isotropic random rough surfaces

The impact of non-Gaussianity on the statistical geometry of isotropic random rough surfaces is analysed in this contribution. The non-Gaussian height distribution is modeled using the Weibull probability distribution. The summits height distribution, expected mean curvature and density of summits are obtained and compared with analytical solutions given by Nayak’s theory for the Gaussian case. A significant deviation from the Gaussian cases is observed. The mean curvature of negatively-skewed surfaces is found to decrease with the increase of height, contradicting the trend registered for the Gaussian case. Nayak’s parameter globally dominates the impact of the spectral properties. However, the wavelength ratio and the Hurst exponent are required to characterize the effect of the spectrum on the rough surfaces statistics.

Radar Imaging Statistics of Non-Gaussian Rough Surface: A Physics-Based Simulation Study

This paper investigates the radar image statistics of rough surfaces by simulating the scattered signal’s dependence on the surface roughness. Statistically, the roughness characteristics include the height probability density (HPD) and, to the second-order, the power spectral density (PSD). We simulated the radar backscattered signal by computing the far-field scattered field from the rough surface within the antenna beam volume in the context of synthetic aperture radar (SAR) imaging. To account for the non-Gaussian height distribution, we consider microscopic details of the roughness on comparable radar wavelength scales to include specularly, singly, and multiply scatterers. We introduce surface roughness index (RSI) to distinguish the statistical characteristics of rough surfaces with different height distributions. Results suggest that increasing the RMS height does not impact the Gaussian HPD surface but significantly affects the Weibull surface. The results confirm that as the radar frequency increases, or reaches a relatively larger roughness, the surface’s HPD causes significant changes in incoherent scattering due to more frequent multiple scattering contributions. As a result, the speckle move further away from the Rayleigh model. By examining individual RSI, we see that the Gaussian HPD surface is much less sensitive to RMS height than the Weibull HPD surface. We demonstrate that to retrieve the surface parameters (both dielectric and roughness) from the estimated RCS, less accuracy is expected for the non-Gaussian surface than the Gaussian surface under the same conditions. Therefore, results drawn from this study are helpful for system performance evaluations, parameters estimation, and target detection for SAR imaging of a rough surface.

3D micromorphology-contact resistance-conductivity insights of quasi 2D Cd1-xPbxS thin films: Investigation based on stereometric and fractal analysis

In this work, stereometric and fractal analysis of Lead (Pb) doped Cadmium sulfide (CdS) thin films synthesized by pulsed laser deposition is reported. The atomic force microscopy (AFM) data were studied to understand the influence of doping on micromorphology, contact resistance and conductivity of CdS films. Stereometric analysis exhibits a non-linear behavior, from Pb doping, in surface roughness with non-Gaussian height distribution in addition to influence on microtexture surface porosity and elastic deformation. A sinusoidal behavior of local surface smoothness with lesser surface complexities for higher Pb concentrations is confirmed from the Hurst coefficient and fractal dimension values of the film surfaces. Surface entropy reveals a uniform deposition of the thin films while a non-linear variation in surface percolation is justified from fractal succolarity values. The tuning of contact resistance between window and buffer layer and thus, enhancement in efficiency of Cadmium indium gallium selenide (CIGS) solar cells is possible with Pb doping in CdS thin films, in the framework of fractal dimension. Additionally, the enhancement in conductivity of Cd1-xPbxS thin films is attributed to surface smoothening process mediated by the large values of Hurst coefficient and autocorrelation length with a consequent decline in RMS roughness.

On the stiffness of surfaces with non-Gaussian height distribution

In this work, the stiffness, i.e., the derivative of the load-separation curve, is studied for self-affine fractal surfaces with non-Gaussian height distribution. In particular, the heights of the surfaces are assumed to follow a Weibull distribution. We find that a linear relation between stiffness and load, well established for Gaussian surfaces, is not obtained in this case. Instead, a power law, which can be motivated by dimensionality analysis, is a better descriptor. Also unlike Gaussian surfaces, we find that the stiffness curve is no longer independent of the Hurst exponent in this case. We carefully asses the possible convergence errors to ensure that our conclusions are not affected by them.

Topographic evolution of balls used in microabrasion tests

This work aims to contribute to the understanding of the topographic modification of the surface of the counter-body during micro-abrasion and its complex relationship with specimen wear. The topographic evolution of the surface of five different balls (Ø25.4 mm) was monitored: one ceramic (Si3N4), one metal (AISI 52100 steel), and three thermoplastic polymers (polypropylene, polyacetal and polyamide 6.6). AISI 304 austenitic stainless steel specimens were tested in a fixed-ball micro-abrasion test rig using a silica slurry (10%wt. in water), rotation speed of 150 rpm, and total test time of 90 min (in 15 min intervals). The topographic evolution of the ball topography was monitored by laser interferometry of the abrasive tracks at each measurement interval, always in the same region. The parameters Sq, Sz, Ssk, Sku, λq, Sdq and Str were computed. Significant wear and changes of the surface topography of the balls were observed along the tests. Harder balls underwent evident grooving, while the softer polymeric balls showed fibrillation characteristics, alignment of polymeric chains and transfer film. For the initial 15 min of test, before reaching a steady-state wear regime, the softer balls (polypropylene, polyamide 6.6 and polyacetal) showed, in general, an increase in Sq, λq and Sdq, possibly by the generation of a transfer film on the surface, which was not observed for the harder balls. After the steady-state regime was achieved, all balls reduced their values of Sq, λq and Sdq. Plots of Sku x Ssk identified non-Gaussian height distribution curves (mostly with high kurtosis and negative asymmetry) for all balls. Sq and Sdq presented a linear relationship with the wear coefficients of the specimens (k) dependent on the material of the ball, whereas an overall linear relationship between λq and k was observed independently of the ball material. Str was a good indicator of aligned grooving abrasion, but showed a linear relationship with k only for the steel ball.

Influence of the probe sizes on the parameters of the surface morphology of hemispherical-grain polysilicon films: Estimation via atomic-force microscopy

The influence of probe sizes on the basic surface-morphology parameters of hemispherical-grain polysilicon films which possess substantial surface roughness and non-Gaussian height distribution functions with appreciable negative skewness is studied. The dependences between the basic surface morphology parameters Sdr, Sq, Sal, Sz, Sv, Sp, and Ssk defined by the ISO 25178-2:2012 standard and the probe width-to-tip height (W/L) ratio are determined. It is ascertained that the relative increase Sdr in the surface area is most sensitive to the “degree of sharpness” (W/L ratio) and, on the contrary, the autocorrelation length Sal is least sensitive. Hemispherical-grain silicon films with considerable parameter Sdr can be employed as test samples in estimating the degree of sharpness of a probe.

Unified Terrain Mapping Model With Markov Random Fields

A terrain mapping model is proposed using a generalized Markov random field (MRF) representation. Unlike previous work, the proposed MRF can fully represent uncertainties due to sensor pose and measurement errors, as well as data association errors in a single model. Additionally, neither homoscedasticity nor a predefined shape of the likelihood distribution is assumed. The flexibility of an MRF model allows spatial height correlations to be incorporated. The ability to include spatial correlations not only improves the accuracy through the benefits of Bayesian prior modeling, but also serves as a basis for terrain property characterization. Maximum likelihood solutions of terrain roughness are derived. Benefits of the proposed model are demonstrated experimentally on indoor and outdoor datasets. Results show that the MRF model leads to lower height estimation errors. In addition, the capability of estimating non-Gaussian height distributions allows the information about individual terrain features to be preserved. Finally, the model is able to accurately estimate the roughness of the terrain, which is beneficial for edge detection of obstacles and nontraversible terrain regions.

Measurement of the roughness of nano-scale surfaces, both unannealed and with limited anneal, by atomic force microscopy

The roughness and bias measured for surfaces scanned by a parabolic atomic-force microscope tip are analyzed computationally for surfaces exhibiting a random, Gaussian population of heights, uncorrelated from pixel to pixel. The fraction of the surface with which the probe is in contact is then analyzed in detail to show the area fraction of the surface that is, in practice, contacted within a defined tolerance. This shows that it is very difficult to measure much of these surfaces for any significant roughness even though the roughness value may sometimes be approximately correct. The surface is then allowed a limited anneal, and the improvement in the validity of the measurement is determined. Annealing removes the very short-range structure and permits more meaningful roughnesses to be determined with a greater fraction of the surface contacted by the probe. This limited anneal may simulate the behaviour of hot atoms that are incident or impacted by energetic ions and that rapidly cool at the surface. Asymmetric, non-Gaussian height distributions are also analyzed, and these generate a significantly different measurement bias that can be more sensitive to the tip radius. The height distribution shapes alter with the tip radius, so accurate estimation of the originating height distribution is not possible. Simple equations are provided to describe the effects.

Quantification of AES depth profiling data of polycrystalline Al films with Gaussian and non-Gaussian surface height distributions

Sputtering-induced roughness is the main distortional factor on the depth resolution of measured depth profiles, in particular, for sputtering of polycrystalline metals. Frequently, the surface height distribution of the sputtering-induced roughness exhibits an asymmetrical feature. In such a case, a non-Gaussian height distribution function (HDF) has to be applied for the quantification of a measured depth profile. By replacing the usually applied Gaussian HDF with that of an asymmetrical triangle in the Mixing-Roughness-Information depth model, measured Auger electron spectroscopy depth profiling data of the interface of polycrystalline Al films on Si are perfectly fitted. The asymmetric triangle height distributions obtained from the best fit are a reasonable approximation of the height distributions measured by atomic force microscopy. Copyright © 2013 John Wiley & Sons, Ltd.

Analysis and Modeling of the Topography of Mechanical Seal Faces

The aim of this article is to provide some relevant statistical parameters for mechanical seal faces and to present some methods of modelling them in order to study mixed lubrication. Three mechanical seals with faces of three different material combinations were analyzed at three operating times (unused, run-in, and worn). Surface roughness and waviness were analyzed. Generally speaking, the amplitude of the waves tends to increase with time, whereas roughness height shows the opposite trend, except in the case of the hard faces combination. The seal surfaces are extremely skewed, this phenomenon being enhanced by wear. The surfaces are nearly isotropic with a slightly higher correlation length in the sliding direction. Two models with two different autocorrelation functions (ACFs) were used to simulate surfaces. These models, based on the Patir approach (Patir (1)), used the Johnson translation curves to impose non-Gaussian height distribution. Even if the models are able to reproduce experimental tendencies, there are some difficulties with the modeling of large structures, leading to the overestimation of summit density and underestimation of the radius of the asperities’ curvature. Generally speaking the exponential ACF gives better results than the bilinear ACF.

Comparative study of surface roughness and tribological behavior during running-in period of hard coatings deposited by lateral rotating cathode arc

This study focuses on the influence of surface geometry of hard coatings on tribological behavior. TiN, TiAlN, AlTiN and nanocomposite (nc-Ti 1− x Al x N)/(a-Si 3N 4) (nACo) coatings were deposited by means of the lateral rotating cathode arc method on high speed steel (HSS) substrates. Surface topology (area of 50 μm × 50 μm, 10 μm × 10 μm and 5 μm × 5 μm) investigations by the atomic force microscopy (AFM) revealed that for all types of coatings the non-Gaussian height distribution function (HDF) is mainly due to the macroparticles. Factors and mechanisms affecting the value of the coefficient of friction (COF) during the running-in period were discussed.

The Flow Factors Considering the Elastic Deformation for the Rough Surface with a Non-Gaussian Height Distribution

In the mixed lubrication regime, the roughness effects are very important due to the presence of interacting asperities. Patir and Cheng derived a method that rewrites the Reynolds equation in terms of the averaged flow factors. The flow factor method has been used in many applications to demonstrate the effects of surface roughness on the mixed lubrication. In this study, the flow factors considering the elastic deformation of the rough surface due to a direct contact of asperities are calculated. The pressure flow factor and the shear flow factor are evaluated for the rough surfaces with both Gaussian and non-Gaussian height distributions. The results show that there is a large difference of flow factors between the rough surface considering the elastic deformation and that assuming the rigid body due to an increase of the film thickness and a decrease of the slope of asperities after the elastic deformation of asperities.

Contact Behavior of Surfaces Containing Elliptical Asperities With Gaussian and Non-Gaussian Height Distributions

This study investigates the effects of asperity interactions on the mean surface separation and real contact area of rough surfaces containing elliptical asperities with Gaussian and non-Gaussian height distributions. The elastic-plastic contact behavior of surfaces with elliptical asperities with both single-mode and bimodal height distributions are studied. The results indicate that the effects of asperity interactions become more pronounced as the effective radius ratio of the asperities increases. The findings also reveal that the real contact load, the real contact area, and the surface contact mode observed for elliptical asperities are significantly different from those noted for spherical asperities. Furthermore, it is found that the form of the non-Gaussian height distribution has a significant effect on the contact mode of rough surfaces. Specifically, the contact mode of surfaces with a negatively skewed height distribution is found to be more elastic than that of surfaces with a Gaussian height distribution.

Asymmetric surface roughness measurements and meniscus modeling of polysilicon surface micromachined flaps

Polycrystalline silicon (polysilicon) films are primary structural materials for microelectromechanical systems (MEMS). Due to relatively high compliance, large surface-to-volume ratio, and small separation distances, micromachined polysilicon structures are susceptible to surface forces which can result in adhesive failures. Since these forces depend on surface properties especially surface roughness, three types of microhinged flaps were fabricated to characterize their roughness and adhesive meniscus properties. The flaps enabled access to both the top and bottom surfaces of the structural polysilicon layers. Roughness measurements using an atomic force microscope revealed that MEMS surfaces primarily exhibit non-Gaussian surface height distributions, and for the release procedures studied, the bottom surface of the structural layers was significantly smoother and prone to higher adhesion compared to the top surface. A non-symmetric surface roughness model using the Pearson system of frequency curves was coupled with a capillary meniscus adhesion model to analyze the effects of surface roughness parameters (root-mean-square, skewness, and kurtosis), relative humidity, and surface contact angle on the interfacial adhesion energy. Using the measured roughness properties of the flaps, four different surface pairs were simulated and compared to investigate their effects on capillary adhesion. It was found that since the base polysilicon layer (poly0) was rougher than the base silicon nitride and the structural layer on poly0 was also rougher than that on silicon nitride, depositing MEMS devices on poly0 layer rather than directly on silicon nitride will reduce the adhesion energy.

Elastic-Plastic Contact Behavior Considering Asperity Interactions for Surfaces With Various Height Distributions

Abstract This study investigates the effects of asperity interactions on the mean surface separation and the real contact area for rough surfaces with non-Gaussian height distributions. The effects of the asperity interactions on the local deformation behavior of a given microcontact are modeled using the Saint Venant principle and Love’s formula. The non-Gaussian rough surfaces are described by the Johnson translatory system. The results indicate that asperity interactions can significantly affect the mean separation of surfaces with non-Gaussian height distributions. The findings also reveal that the contact load and the real contact area of surfaces with non-Gaussian height distributions are significantly different from those of surfaces with Gaussian height distributions. This study uncovers that skewed surfaces tend to deform more elastically, which provides underlying physics for the long-time conventional wisdom and recent experimental data [Y. R. Jeng, 1996, Tribol. Trans., 39, 354–361;Y. R. Jeng, Z. W. Lin, and S. H. Shyo, 2004, ASME J. Tribol., 126, 620–625] that running-in surfaces have better wear resistance.