Anisotropic Rough Surfaces Research Articles

Anisotropic 3D rough surface reconstruction model based on fractal method and its application in contact characteristics

Anisotropic 3D rough surface reconstruction model based on fractal method and its application in contact characteristics

Anisotropic rough surfaces representation in geometrical deviations modeling for tolerance analysis

Accurate modeling of geometrical deviations is the premise and critical step for tolerance analysis. Traditional tolerance modeling methods usually simplify deviations to variations in degrees of freedom. Although this facilitates the uniform representation and accumulative calculation, it is not possible to consider the effects of real topography over mating interfaces on tolerance analysis in high-precision scenarios. In this regard, this paper proposed a tolerance modeling method for representing anisotropic rough surfaces information under the framework of Skin Model Shapes. Specifically, the spatial information on rough surfaces is represented by autocorrelation functions. A set of nonlinear equations are constructed according to given autocorrelation functions and then solved to obtain the desired surface topography. In case studies simulated rough surfaces with different input parameters are illustrated and the consistency of this method is verified. The proposed method provides an accurate and practical way to represent anisotropic rough surfaces for tolerance modeling and analysis.

Study on nonlinear dynamic characteristics of gear system with 3D anisotropic rough tooth surface based on fractal theory

Different from the mainstream research, this study fully considers the anisotropic micro-topography of the tooth surface when studying the dynamic characteristics of gears. An anisotropic 3D fractal rough tooth surface model is proposed based on fractal geometry theory. The major advantage of the novel model is that it contains more surface micro details, especially on the tooth width, which are ignored in general studies. The backlash and time-varying meshing stiffness (TVMS) are then revised on the basis of this model. Finally, a 6-degree-of-freedom nonlinear dynamic model considering surface topography is established and the influence of fractal parameters on gear dynamics is investigated. The results show that the fractal parameters change the backlash and TVMS and have an obvious impact on the dynamics and vibration responses of the transmission system. The rough gear system enters chaos earlier and has better stability at high speeds in comparison with the smooth system. As the fractal dimension increases, the dynamic transmission error amplitude gradually decreases and the system tends to stable periodic motion. The characteristic scale coefficient yields a more moderate but opposite effect on the dynamic response of the system compared with the fractal dimension. The finding of this study can provide theoretical guidance for tooth surface machining from the perspective of tooth surface morphology.

Gas Leakage Evaluation of Metallic Sealing Surfaces with Annular Morphology

The metallic seal has been widely used in many industries, and its seal performance is the guarantee of effective and safe applications. Therefore, it needs to clarify the efforts of sealing surface morphology and leak flow on seals. Aiming at the surface of annular morphology, this paper proposes a theoretical gas leakage evaluation of metallic sealing surfaces. The anisotropic rough surfaces were used to carry out the contact analysis. From the contact model, the leak channels were extracted and then applied to the gas slip nanofluidic simulation to quantitatively evaluate the leakage. The evaluation was finally validated by leakage experiments. This provides a valuable approach to explore the influence of the surface microscopic topology and the gas leak nanofluidic flow on the sealing performances.

Effect of Strain Hardening and Ellipticity on Elastic–Plastic Contact Behaviour between Ellipsoids and Rigid Planes

The contact behaviour between an ellipsoid and a rigid plane is significant in research on bearing and assembly joint surfaces. However, an empirical relationship between an elastic–plastic ellipsoid and a rigid plane has not been established. In this study, the elastic–plastic contact behaviour between a deformable ellipsoid and a rigid plane was investigated by establishing a new finite element model. The proposed elastic–plastic ellipsoid contact model was designed considering the effects of the ellipticity and strain-hardening rate of the ellipsoid. The strain-hardening rate and ellipticity of the ellipsoid affected the contact area, load and mean pressure. Furthermore, the effect gradually increased with an increase in interference. New dimensionless empirical formulas for determining the contact load and contact area were proposed based on the analysis. The proposed model was validated by comparing the obtained results with previous experimental results and those of theoretical models. This study can be used to predict the elastic–plastic contact parameters between a single ellipsoid and a rigid body, such as bearings, gears and cams. It can also be used to investigate the elastic–plastic contact behaviour between anisotropic rough surfaces composed of asperities with different radii of curvature.

DEVELOPMENT AND ANALYSIS OF THE ACCURACY OF ENGINEERING METHODS FOR DETERMINATION OF INTERACTION VOLUME FOR CALCULATION OF THE TIGHTNESS OF NON-LUBRICATING CYLINDER-PISTON SEALS

Based on the theory of stochastic processes, methods of engineering calculation of the contact volume for the calculation of the tightness of non-lubricating cylinder-piston seals of compressors have been developed. The result is the creation of methods for calculating the tightness (duration of gas flow) in non-lubricating cylinder-piston metal-polymer seals, as well as assessing the accuracy of the created methods for piston seals. The article considers the elastic contact of a strongly anisotropic rough surface (polymer surface) with a smooth (metal) surface. The dependence of the intercontact gas volume on the complex of contact conditions based on the theory of stochastic fields is investigated. An estimate of the error that occurs when replacing the exact formula for calculating the contact volume with an approximate formula is performed. The values ​​calculated according to the exact and calculated formula of the consolidated inflow differ by no more than 0.17 percent. Accurate methods for calculating the tightness of non-lubricating cylinder-piston seals for molecular and viscous modes of gas flow, which is the basis for practical calculations of the tightness of the seals of non-lubricating pneumatic compressors, are theoretically substantiated and developed. The dependence of the contact volume, the effective level of deformation and the average height of the gap on the set of contact conditions has been studied. It is established that at low loads the deformation level, the effective deformation level, the reduced contact volume and the reduced average gap height are numerically equal. The values ​​calculated by the exact and calculated formula of the contact volume differ by no more than 0.17 percent at K 1 and no more than 0.00029 percent at K> 1.

Tungsten Based Spectrally Selective Absorbers with Anisotropic Rough Surface Texture.

Spectrally selective absorbers have received considerable interest due to their applications in thermophotovoltaic devices and as solar absorbers. Due to extreme operating conditions in these applications, such as high temperatures, thermo-mechanically stable and broadband spectrally selective absorbers are of interest. This paper demonstrates anisotropic random rough surfaces that provide broadband spectrally selective absorption for the thermo-mechanically stable Tungsten surfaces. Anisotropic random rough surface has different correlation lengths in the x- and y-directions, which means their topography parameters have directional dependence. In particular, we demonstrate that spectral absorptance of Tungsten random rough surfaces at visible (VIS) and near-infrared (NIR) spectral regions are sensitive to correlation length and RMS height variations. Our results indicate that by optimizing random rough surface parameters, absorption values exceeding 95% can be obtained. Moreover, our results indicate that anisotropic random rough surfaces broaden the bandwidth of the high absorption region. It is shown that in VIS and NIR regions, the absorption enhancements of up to 47% and 52% are achieved for the isotropic and anisotropic rough surfaces, respectively.

Modelling of three-dimensional particle rebound from an anisotropic rough wall

In gas-solid confined flows, particle rebound on a rough wall may have a great influence on the macroscopic properties of both phases. Existing simulation methods use simplified approaches where surface roughness is modelled as two-dimensional or isotropic. To improve the accuracy of such simulations, an anisotropic virtual rough wall statistical approach and the corresponding Lagrangian stochastic particle-wall collision model are proposed. From deterministic simulations of the impact of particles on the anisotropic virtual wall given as correlated bi-Gaussian surface, wall-normal vector angle statistics are used for model development. Rebound angle statistics computed from deterministic simulations and using the proposed stochastic model are in very good agreement. Incident particles in vertical planes not collinear with one of the principal directions of the anisotropic rough surface are bouncing with a mean transverse angle towards the principal direction of lower roughness.

Analysis of the Carreau fluid model presenting physical properties along different molecular axes near an anisotropic rough surface

We present the theoretical and mathematical studies of the flow over a heated rough rotating surface for non-Newtonian fluid. Utilizing Carreau fluid model which is used for pseudoplastic and dilantant fluids, we determine, for the first time, base flow profile under the partial slip near a rough surface. The thermo-physical properties are considered for heat and mass phenomena. This study has received a great interest in applied engineering due to its improved mathematical and theoretical advantages. We examined the solutions for fluid and thermo-physical properties of the Carreau fluid model. The similarity transformation was initially introduced by von-Kàrmàn, it is useful for the Carreau fluid by converting the boundary layer equations into ordinary differential equations. Shooting technique is employed to solve the dimensionless differential equations. It is well known that the Carreau fluid model is significant for infinite high shear rates, that's why we examined the Carreau fluid over a heated rough rotating disk. Numerical results are used to illustrate the figures and tables.

Bistatic Scattering From Anisotropic Rough Surfaces via a Closed-Form Two-Scale Model

Bistatic radars have been a topic of increasing interest in recent years, thanks to the introduction of new bistatic (and multistatic) configurations, including those based on the opportunistic exploitation of global navigation satellite systems (GNSSs). The research on bistatic electromagnetic scattering models plays an important role in the analysis of these systems, in their simulation, and in the prediction of their performance. The two-scale model (TSM) is a widely used approach for the computation of scattering from rough surfaces, since it is able to account for depolarization effects due to surface tilting. However, in its original formulation, it requires a computationally intensive numerical integration, in order to perform appropriate average over surface random slopes. To overcome this limitation, a closed-form polarimetric TSM (PTSM) was developed, which has been also recently extended to the case of anisotropic rough surfaces (A-PTSM), with a focus on the sea surface. The A-PTSM can be efficiently used to compute the backscattering from anisotropic rough surfaces and can support the development and analysis of monostatic radar missions. In order to extend its scope to the general case of bistatic and multistatic configurations, in this article, we extend the A-PTSM to the case of bistatic electromagnetic scattering, presenting the evaluation of all the elements of the bistatic polarimetric covariance matrix. Due to the relevance of circularly polarized signals in opportunistic GNSS reflectometry applications, both the linear and the circular polarization bases are considered. The behavior of the obtained elements is discussed, and simplified expressions of the elements of the covariance matrix are provided for the case of scattering within the incidence plane. Relevant numerical examples are provided and compared to those obtained by the more refined, but more computationally intensive, second-order small-slope approximation (SSA2) method. In the examples, we consider both a wind-driven sea surface and a tilled soil, and both L-band and X-band frequencies. However, the presented method can be used at all frequencies of interest for microwave remote sensing and for all observation geometries, except for near grazing incidence and/or scattering.

Development of Si-chips with anisotropic rough surface

The areal roughness of a surface can be described by a number of parameters including the texture aspect ratio S tr as the degree of isotropy or anisotropy. For the comparison of roughness with optical instruments silicon reference samples with the anisotropical roughness of S a ≈ 280 nm and 4 different values of the texture aspect ratio S tr (0.9; 0.75; 0.65; 0.50) have been developed. The anisotropy is produced by scratching of grooves on the lapped surface using a suitable stylus. Different distances of grooves in different regions of the chip result in different values of S tr representing distinct anisotropies. Special marks etched in the silicon chip allow the positioning of the measurement fields with micrometer precision. Measurements performed with a confocal microscope have shown that the grooves do not noticeably influence the parameters of height and the hybrid parameters of roughness. The process of manufacturing by lapping followed by scratching guaranties a good reproducibility of the surface attested by comparison of two chips. Consequently the described reference sample can play the role of a material measure.

Polarized Backscattering From Spatially Anisotropic Rough Surface

This paper examines the polarized backscattering of spatially anisotropic rough surfaces. To better explore the physical mechanisms that control the azimuthal dependence of the backscattering from anisotropic surfaces, the effects of surface roughness [correlation length and root-mean-square (rms) height], dielectric constant, and radar parameters from anisotropic surfaces are studied. The advanced integral equation model (AIEM) is used to simulate both co- and cross-polarized backscattering coefficients, including the single and multiple scattering. Numerical results suggest that the multiple scattering exhibits a stronger azimuthal dependence for HH than VV polarization, especially more so at a larger incident angle. For weakly anisotropic surface, the azimuthal variation of backscattering tends to be a sinusoidal-like pattern. However, with the enhancement of anisotropy, such a scattering pattern is distorted, and the sharp dip appears at up/down direction. As the rms height and dielectric constant increase, the scattering is enhanced on the whole. The HH/VV ratio at lower dielectric constant is greater than that at higher one. In comparison, scattering shows stronger dependence on anisotropy at lower dielectric constant, especially at a larger incident angle. As an application example, we compare the model predictions with reported measurements from two different sites. Preliminary results are quite encouraging, and thus, the analysis presented in this paper is potentially useful to predict and interpret backscattering from crop field surface, where strong anisotropic surfaces commonly present due to plowing or raking practice.

The total secondary electron yield of a conductive random rough surface

One problem with current 3D printed microwave components is that they usually have more surface roughness than components manufactured with traditional machining processes. To estimate the multipactor threshold of 3D printed microwave components, it is important to evaluate the total secondary electron yield (TSEY) of the random rough surface. In this work, taking copper as an example, we conduct TSEY simulations for random rough surfaces. First, we generate both isotropic and anisotropic Gaussian type random rough surfaces; then, the dependence of the TSEY on both the roughness and correlation length is studied using Monte-Carlo simulations. Results show that when the root-mean-square roughness increases from 0 to 30 μm, the maximum TSEY increases slowly at first and then decreases rapidly. In other words, roughness can also enhance and not just suppress the TSEY. The results can be interpreted as follows: for a relatively smooth/rough surface, the TSEY enhancement/suppression induced by oblique incidence/a shadowing effect plays a dominant role. Simulation results also show that correlation length has a notable effect on the TSEY. Furthermore, for anisotropic surfaces, the azimuthal angle also influences the TSEY. Compared with currently published work, we provide an optional evaluation method for the TSEY of random rough surfaces. The predictions in this work not only confirm existing observations (the TSEY suppression effect) but also present new predictions (the TSEY enhancement effect and the azimuthal angle effect).

The Effect of Anisotropy on the Percolation Threshold of Sealing Surfaces

The percolation threshold strongly affects sealing performance. This paper investigates the relationship between the percolation threshold and the rough surface anisotropy, which is represented by the Peklenik number, γ. A series of anisotropic rough surfaces were generated and the conjugate gradient-fast Fourier transform (CG-FFT) method was used to determine the percolation threshold. The percolation threshold was found to be A/A0≈0.484±0.009 (averaged over 45 surfaces) was established for an isotropic rough surface (γ=1). Furthermore, it was also found that the percolation threshold decreased from A/A0≈0.528±0.011 to A/A0≈0.431±0.008 as 1/γ increased from 0.6 to 2. Our results differ from the theoretical result of Persson et al., where A/A0=γ/(1+γ). Comparing our calculated results with the theoretical results established the presence of an intersection value of 1/γ that was related to the effect of elastic deformation on the percolation threshold. When 1/γ was smaller than the intersection value, our calculated results were lower than the theoretical ones; and when 1/γ was greater than the intersection value, our calculated results were higher than the theoretical ones.

The study of anisotropic rough surfaces contact considering lateral contact and interaction between asperities

Abstract Interfacial performances are dissimilar due to the different surface topographies and materials. The aim of this paper is to study the effect of the surface topography on the contact force, contact area and contact stiffness. The distributions of the contact azimuthal angles and the contact angles were introduced in the model to build an anisotropic interface model, which includes the asperity lateral contact and the interaction. The simulation results indicate that the normal contact force, real contact area and contact stiffness decrease with the increasing separation. The standard deviations of asperity heights and asperity contact angles have significant influences on the contact of rough surfaces, while the interfacial anisotropy does not influence the contact performances in the normal direction.

Topography Analysis of Random Anisotropic Gaussian Rough Surfaces

Engineered surfaces (ground and similarly structured rough surfaces) show anisotropic characteristics and their topography parameters are direction dependent. Statistical characterization of these surfaces is still complex because of directional nature of surfaces. In this technical brief, an attempt is made to simulate anisotropic surfaces through use of topography parameters (three-dimensional (3D) surface parameters). First, 3D anisotropic random Gaussian rough surface is generated numerically with fast Fourier transform (FFT). Numerically generated anisotropic random Gaussian rough surface shows statistical properties (texture direction, texture ratio) similar to ground and similarly directional anisotropic rough surfaces. For numerically generated anisotropic Gaussian rough surface, important 3D roughness parameters are determined. Sayles and Thomas' (1976, “Thermal Conductance of Rough Elastic Contact,” Appl. Energy, 2(4), pp. 249–267.) theoretical model for directional anisotropic rough surface is adopted here for calculating the summit parameters, i.e., equivalent bandwidth parameter, mean summit curvature, skewness of summit height, standard deviation of summit height, and equivalent spectral moments. This work demonstrates the variation of spectral moments in both across and parallel to the lay directions with pattern ratio (γ=βx/βy). Correlation length (βx) is fixed 10μm and correlation length (βy) is varied from 100 to 10 μm. Variation of summit parameters with pattern ratio is also discussed in detail. Results shows that mean summit curvature and skewness of summit heights increase with increase in pattern ratio, whereas standard deviation of summit heights and equivalent bandwidth parameter (αe) decreases with pattern ratio. A significant difference is found in “Abbott-Firestone” parameters when calculated in both perpendicular and parallel to lay directions. Effect of these parameters on wear process is discussed in brief.

Wetting theory for small droplets on textured solid surfaces.

Conventional wetting theories on rough surfaces with Wenzel, Cassie-Baxter, and Penetrate modes suggest the possibility of tuning the contact angle by adjusting the surface texture. Despite decades of intensive study, there are still many experimental results that are not well understood because conventional wetting theory, which assumes an infinite droplet size, has been used to explain measurements of finite-sized droplets. Here, we suggest a wetting theory applicable to a wide range of droplet size for the three wetting modes by analyzing the free energy landscape with many local minima originated from the finite size. We find that the conventional theory predicts the contact angle at the global minimum if the droplet size is about 40 times or larger than the characteristic scale of the surface roughness, regardless of wetting modes. Furthermore, we obtain the energy barrier of pinning which can induce the contact angle hysteresis as a function of geometric factors. We validate our theory against experimental results on an anisotropic rough surface. In addition, we discuss the wetting on non-uniformly rough surfaces. Our findings clarify the extent to which the conventional wetting theory is valid and expand the physical understanding of wetting phenomena of small liquid drops on rough surfaces.

Modeling and simulating the bidirectional reflectance distribution function (BRDF) of seawater covered by oil slicks

A high-efficiency anisotropic model for bidirectional reflectance distribution function (BRDF) of seawater covered by oil slicks (SWCOS) was proposed. This model was set by combining a BRDF model for anisotropic rough sea surface whose slopes follow Gaussian distribution and the two-beam inference theory of a thin film. We have simulated the BRDFs of oil slicks by using the above model and the measured complex refractive index data of Romashkino crude oil. In addition, the relationships between the BRDF of oil slicks and the wind speed of sea surface, thickness of oil slick, complex refractive index of crude oil and the incident zenith angle were analyzed. Also, the differences between optical characteristics of clean water and of polluted water were discussed in the context of the optical contrast of SWCOS. With high simulation speed and reliable simulation precision, this model provides a theoretical basis for rapid detection of oil spill.

Statistical theory of wetting of liquid drops on superhydrophobic randomly rough surfaces.

It is well known that hydrophobic surfaces may become superhydrophobic when their surface is properly roughened. However, the role of roughness is not yet very clear, notwithstanding several theoretical and experimental investigations. In the present paper, we propose a relatively simple theory aiming at calculating the apparent contact angle (ACA) and the contact area occurring in the case of drops gently deposited on two-dimensional randomly rough surfaces. Our theory applies both to isotropic and anisotropic rough surfaces, although in the latter case the predicted ACA has to be interpreted as the average contact angle at the triple line. We assume large separation of scales, i.e., that the spectral content of the surface lies in a range of wavelengths much smaller than the size of the apparent liquid-solid contact area. Results show that anisotropy negligibly affects the ACA, and a very reasonable agreement is obtained between theoretical ACA values and experimental data.

A Numerical Model for Wet-adhesive Line Contact

Typical rough surface contact models are meant for dry conditions. They often assume hemispherical shaped asperities when predicting load carrying capacity between the opposing surfaces (e.g. isotropic surfaces). However, modern engineering surfaces are often modified to reduce friction. Surface modifications (e.g. plateau honing in engine cylinder liners) produce anisotropic surfaces, dominated by directional features, resembling ridges. They act as micro-reservoirs, trapping fluids to enhance the lubrication process, leading to lower friction. However, the ridges resemble cylinder-on-a-flat contact, when for example a ring of parabolic face-width profile passes over a cross-hatch honed liner surface. These render the typical rough surface contact models inappropriate when applied to understand the contact behavior of such surfaces. Therefore, as a first approximation to understand anisotropic rough surfaces dominated by directional features, the current study proposes a wet-adhesion line contact model. The model includes the influence of boundary lubrication and asperity adhesion upon the contact load carrying capacity and its deformation. The model considers contribution to boundary lubrication at the assumed smooth summits of asperities due to solvation in diminishing gaps. Solvation has an oscillatory characteristic of fluid molecules. This phenomenon not only generates load carrying capacity, but also prevents direct surface-to-surface interaction. It is also shown that as a result of boundary adsorbed film formation, fluid with long chain molecules and boundary active ends (e.g. 16-mer or hexadecane) has a more significant effect in reducing the chance of adhesion in diminishing gaps, when compared with fluids of simple spherical molecules.