Rigid Rough Surface Research Articles

Impact of landscape attributes on the noise reduction effects of heritage landscapes

Heritage landscapes provide a cost-effective solution for mitigating noise and creating adaptable open spaces in urban ecological construction and planning. In this study, we examined 27 distinct landscapes in a city in northern China to assess their effectiveness in reducing traffic-related noise. The acoustic properties of the landscapes, considering various surfaces, slopes, elevations, structures, and topography, were systematically analysed and compared. The findings indicate that vertically rigid descending landscapes exhibit the highest acoustic performance, followed by vertically flexible dense landscapes without slopes. Additionally, the noise reduction effects of horizontal landscapes with rough rigid surfaces surpass those of landscapes covered by low-growing vegetation and landscapes with sparse high-growing vegetation. The insights derived from this study can enhance our understanding of heritage landscapes, provide valuable information for their protection and micro-updates, and support quantitative research in this field.

The Painlevé paradox in three dimensions: resolution with regularization

The classical Painlevé paradox consists of a slender rigid rod slipping on a rigid rough surface. If the coefficient of friction μ is high enough, the governing equations predict that the rod would be driven into the surface. The paradox is well studied in two dimensions, in which the paradox is resolved via regularization, where the rod tip meets the surface. In this paper, we consider the three-dimensional problem. There are two significant differences in three dimensions. Firstly, sticking now occurs on a co-dimension 2 surface. This results in a non-smooth problem, even when the three-dimensional problem is regularized. Secondly, unlike the highly singular two-dimensional problem, trajectories can now enter the inconsistent region from slipping, requiring a completely new analysis. We use blowup to investigate the problem and show that a key part of the dynamics of the regularized three-dimensional Painlevé problem is governed by a type I Painlevé equation.

Modeling sea state induced atmospheric sound transmission loss

This work presents a numerical study on atmospheric sound propagation over rough rigid surfaces. The intent is to simulate acoustic propagation over water. Methods to estimate sea state induced atmospheric sound transmission loss and relative uncertainties are evaluated. In previous studies, a flat surface with an equivalent impedance was used to account for the effect of surface roughness on sound transmission loss. Equivalent impedances were estimated based on time-domain numerical simulations of atmospheric sound propagation above pseudorandom sea surfaces coherent with a Pierson-Moskowitz spectra. Estimation of equivalent impedances using time- and frequency- domain approaches are compared for cases up to sea state 4. Acoustic excess attenuation due to propagation over a rough surface was predicted by the authors, in a previous work, by correcting the excess attenuation of a propagation over a flat, perfectly reflecting surface. The correction factor was frequency and sea state dependent and included an additional term to account for the uncertainties characteristic of different sea states. Excess attenuation predictions estimated using the equivalent impedance approach are compared with those obtained from the authors’ previous study. Implications of the use of these methods for source detectability determinations are discussed.

Combined effects of viscoelasticity and surface roughness on the adhesion behavior of a flat-end cylindrical microstructure

A theoretical modeling approach is developed to simulate the rate-dependent adhesion contact between a single flat-end cylindrical microstructure and a randomly rough rigid surface. This model combines the Greenwood-Williamson rough contact model and the rate-dependent JKR model for viscoelastic dynamic contact, which can comprehensively consider the roughness-induced adhesion hysteresis and the rate-dependent adhesion hysteresis. A numerical scheme is proposed to make the rate-dependent adhesion model compatible with the randomly rough contact equation. The proposed method is verified well by comparing with the Fuller & Tabor model at a very low approach/detachment speed. The effects of surface roughness and viscoelastic material constant on adhesion strength and energy dissipation are evaluated. Results indicate that there is an optimal surface roughness at which the surface adhesion strength is the strongest, and a worst roughness that minimizes the energy dissipation. The effect of viscoelastic material constant depends on the approach/detachment speed of the microstructure. A higher approach/detachment speed causes the adhesion strength and the energy dissipation to change significantly with viscoelastic material constant, while a low speed does not.

Asperity-based modification on theory of contact mechanics and rubber friction for self-affine fractal surfaces

Modeling the real contact area plays a key role in every tribological process, such as friction, adhesion, and wear. Contact between two solids does not necessarily occur everywhere within the apparent contact area. Considering the multiscale nature of roughness, Persson proposed a theory of contact mechanics for a soft and smooth solid in contact with a rigid rough surface. In this theory, he assumed that the vertical displacement on the soft surface could be approximated by the height profile of the substrate surface. Although this assumption gives an accurate pressure distribution at the interface for complete contact, when no gap exists between two surfaces, it results in an overestimation of elastic energy stored in the material for partial contact, which typically occurs in many practical applications. This issue was later addressed by Persson by including a correction factor obtained from the comparison of the theoretical results with molecular dynamics simulation. This paper proposes a different approach to correct the overestimation of vertical displacement in Persson’s contact theory for rough surfaces with self-affine fractal properties. The results are compared with the correction factor proposed by Persson. The main advantage of the proposed method is that it uses physical parameters such as the surface roughness characteristics, material properties, sliding velocity, and normal load to correct the model. This method is also implemented in the theory of rubber friction. The results of the corrected friction model are compared with experiments. The results confirm that the modified model predicts the friction coefficient as a function of sliding velocity more accurately than the original model.

The influence of the mechanical properties of copper at elevated temperatures on the tightness of the sealing joint

The sealing joint is presented as the contact of a rigid rough surface with an elastoplastic half-space with the properties of C11000 copper at normal and elevated temperatures. To describe the elastoplastic hardened material, the Hollomon power law is used. The parameters of the true stress–strain curves at elevated temperatures are determined from the reference data of the conditional tensile diagram: yield strength, tensile strength, modulus of elasticity and residual deformation of 0.2% at the yield strength. A rigid rough surface is represented as a set of identical spherical segments, the distribution of which in height corresponds to the reference profile curve of the real surface. The relative contact area, the density of the gaps in the joint, and the permeability functional are determined depending on the dimensionless load for different temperatures according to methods previously developed by the authors. A method for calculating the amount of leakage through the sealing joint of the valves of the pipe fittings and pressure vessels depending on the contact characteristics, the probability of the medium flow and the properties of real gas is proposed. To accurately describe the real properties of technically important gases in a wide range of pressures and temperatures, the virial equation of state is used.

Elastic scattering from rough surfaces in three dimensions

Consider the elastic scattering of a plane or point incident wave by an unbounded and rigid rough surface. The angular spectrum representation (ASR) for the time-harmonic Navier equation is derived in three dimensions. The ASR is utilized as a radiation condition to the elastic rough surface scattering problem. The uniqueness is proved through a Rellich-type identity for surfaces given by uniformly Lipschitz functions. In the case of flat surfaces with local perturbations, an equivalent variational formulation is deduced in a truncated bounded domain and the existence of solutions are shown for general incoming waves. The main ingredient of the proof is the radiating behavior of the Green tensor to the first boundary value problem of the Navier equation in a half-space.

Statistics of the separation between sliding rigid rough surfaces: Simulations and extreme value theory approach.

When a rigid rough solid slides on a rigid rough surface, it experiences a random motion in the direction normal to the average contact plane. Here, through simulations of the separation at single-point contact between self-affine topographies, we characterize the statistical and spectral properties of this normal motion. In particular, its rms amplitude is much smaller than that of the equivalent roughness of the two topographies and depends on the ratio of the slider's lateral size over a characteristic wavelength of the topography. In addition, due to the nonlinearity of the sliding contact process, the normal motion's spectrum contains wavelengths smaller than the smallest wavelength present in the underlying topographies. We show that the statistical properties of the normal motion's amplitude are well captured by a simple analytic model based on the extreme value theory framework, extending its applicability to sliding-contact-related topics.

Sliding friction characteristics of styrene butadiene rubbers with varied surface roughness under water lubrication

We investigated the effect of the surface topography of rubbers on their wet sliding friction characteristics. For six types of rubber samples with different viscoelastic properties, rubber specimens with five levels of surface roughness were prepared and slid against a rough rigid surface under water lubrication. The friction coefficient increased with increasing surface roughness for each of the rubber samples, and the rank of the friction coefficient of different samples varied depending on the surface roughness. These results indicate that the effect of hysteresis friction becomes more significant as the surface roughness of the rubber increases, and the effect of the inhibition of adhesion friction caused by lubrication becomes more significant as the surface roughness decreases. Our findings demonstrate the importance of rubber surface topography in determining the friction coefficient under water lubrication. The results of this study may lead to new design criteria for high-wet-grip rubber tires.

A non-iterative approach to inverse elastic scattering by unbounded rigid rough surfaces

This paper is concerned with the inverse time-harmonic elastic scattering problem of recovering unbounded rough surfaces in two dimensions. We assume that elastic plane waves with different directions are incident onto a rigid rough surface in a half plane. The elastic scattered field is measured within a finite distance above the rough surface. A sampling-type imaging algorithm is proposed to recover the unbounded rough surface from the scattered near-field data, which involves only inner products between the data. Numerical experiments are presented to show that the inversion scheme is not only efficient but also accurate and robust with respect to noise.

Near-Field Imaging of an Unbounded Elastic Rough Surface with a Direct Imaging Method

This paper is concerned with the inverse scattering problem of time-harmonic elastic waves by an unbounded rigid rough surface. A direct imaging method is developed to reconstruct the unbounded rou...

Nonlinear reflection of weak shock waves from a rough surface in air

Irregular reflection of weak acoustic shock waves occurs under the framework of the von Neumann paradox. In this study, the influence of the surface roughness on the reflection pattern was studied experimentally using spark-generated spherically divergent N-waves of 1.4 cm length reflecting from rigid rough surfaces in air. Dimensions of the roughness were varied from 20 up to 500 μm for different surfaces. A Mach-Zehnder interferometry method was used to reconstruct the pressure waveforms near the surface. The reconstruction was performed by applying the inverse Abel transform to the phase of the signal measured by the interferometer. It was shown that the height of the Mach stem became shorter for surfaces with larger dimensions of the roughness and disappeared when the surface roughness was large enough. Such tendency was also observed in simulations based on the Euler equations where the acoustic source was introduced as a Gaussian-envelope energy injection and the roughness was either sinusoidal or random and described by a Gaussian correlation function. [Work supported by RSF-17-72-10277 and by the Labex CeLyA of Universite de Lyon, operated by the French National Research Agency (ANR-10-LABX-0060/ ANR-11-IDEX-0007).]Irregular reflection of weak acoustic shock waves occurs under the framework of the von Neumann paradox. In this study, the influence of the surface roughness on the reflection pattern was studied experimentally using spark-generated spherically divergent N-waves of 1.4 cm length reflecting from rigid rough surfaces in air. Dimensions of the roughness were varied from 20 up to 500 μm for different surfaces. A Mach-Zehnder interferometry method was used to reconstruct the pressure waveforms near the surface. The reconstruction was performed by applying the inverse Abel transform to the phase of the signal measured by the interferometer. It was shown that the height of the Mach stem became shorter for surfaces with larger dimensions of the roughness and disappeared when the surface roughness was large enough. Such tendency was also observed in simulations based on the Euler equations where the acoustic source was introduced as a Gaussian-envelope energy injection and the roughness was either sinusoidal or r...

Indentation and flattening of rough surfaces spherical asperities

The paper indicates that the application of roughness models and the theories of contacting rough surfaces developed by Greenwood-Williamson and N.B. Demkin for solving the problems of hermetology leads to significant errors. This is explained by much greater contact pressures than for the tribology problems, by describing only the initial part of the reference surface curve, the lack of allowance for the plastic extrusion of the material. A brief review of methods for describing the introduction of a sphere into an elastoplastic reinforced half-space is given. The properties of the elastoplastic reinforced material are described by the power law of Hollomon. To describe the indentation and flattening of single spherical asperity, the results of finite element modeling are used. The cases of contacting a rigid rough surface with an elastoplastic half-space and a rigid smooth surface with a rough surface are considered. To determine the relative contact area, the discrete roughness model is used in the form of a set of spherical segments distributed along the height in accordance with the curve of the reference surface.

Indentation of rigid rough surface into polymer coating layer

An analysis of engineering approaches to determining the value of the introduction of spherical asperity and a rough surface into the polymer layer is given. It is shown that engineering methods of solving contact problems on the basis of simplifying hypotheses are more practical, for example, the representation of a layered body as a construction with special mechanical properties that depend on the mechanical properties of base and coating materials and the thickness of the coating. Analysis of the use of the proposed engineering solutions in calculating the value of the indentation of the sphere showed the advantages of the method based on the rigid model of a layered body. In this case, the effective modulus of elasticity and the Poisson's ratio are determined for any values of the coating thickness for an axisymmetric loading of a layered half-space. To determine the value of the indentation of a rough surface into the polymer layer, a discrete model of a rough surface is used. When contacting a rough surface through a polymer layer, it was taken into account that each asperity corresponds to a certain modulus of elasticity, which is determined by the level of the peak and the value of approach.

Static and sliding contact of rough surfaces: Effect of asperity-scale properties and long-range elastic interactions

Friction in static and sliding contact of rough surfaces is important in numerous physical phenomena. We seek to understand macroscopically observed static and sliding contact behavior as the collective response of a large number of microscopic asperities. To that end, we build on Hulikal et al. (2015) and develop an efficient numerical framework that can be used to investigate how the macroscopic response of multiple frictional contacts depends on long-range elastic interactions, different constitutive assumptions about the deforming contacts and their local shear resistance, and surface roughness. We approximate the contact between two rough surfaces as that between a regular array of discrete deformable elements attached to a elastic block and a rigid rough surface. The deformable elements are viscoelastic or elasto/viscoplastic with a range of relaxation times, and the elastic interaction between contacts is long-range. We find that the model reproduces the main macroscopic features of evolution of contact and friction for a range of constitutive models of the elements, suggesting that macroscopic frictional response is robust with respect to the microscopic behavior. Viscoelasticity/viscoplasticity contributes to the increase of friction with contact time and leads to a subtle history dependence. Interestingly, long-range elastic interactions only change the results quantitatively compared to the meanfield response. The developed numerical framework can be used to study how specific observed macroscopic behavior depends on the microscale assumptions. For example, we find that sustained increase in the static friction coefficient during long hold times suggests viscoelastic response of the underlying material with multiple relaxation time scales. We also find that the experimentally observed proportionality of the direct effect in velocity jump experiments to the logarithm of the velocity jump points to a complex material-dependent shear resistance at the microscale.

FFT-Based Methods for Solving a Rough Adhesive Contact: Description and Convergence Study

The contact problem of a semi-infinite elastic body with a rigid rough surface with adhesive forces is modeled using a boundary element method (BEM). An original theoretical framework for this problem is presented. Four original BEM algorithms are studied, for both prescribed normal pressure and prescribed penetration, in primal and dual forms. They are all based on a conjugate gradient iterative solver. For each case, the solver is finely tuned to tackle the current problem. Using fast Fourier transforms (FFT) speeds up the computation of the matrix–vector multiplications. A new way of computing the coefficients of the conjugate gradient solver which reduces the number of FFTs at each step is presented. The stability and efficiency of the different methods are compared, showing a great sensitivity to the Tabor coefficient and to the contact area ratio. The most stable algorithm proved to be reliable for very large-scale computations through a participation to M. Mueser’s Contact Mechanics Challenge.

Acoustic imaging in application to reconstruction of rough rigid surface with airborne ultrasound waves.

Accurate reconstruction of the surface roughness is of high importance to various areas of science and engineering. One important application of this technology is for remote monitoring of open channel flows through observing its dynamic surface roughness. In this paper a novel airborne acoustic method of roughness reconstruction is proposed and tested with a static rigid rough surface. This method is based on the acoustic holography principle and Kirchhoff approximation which make use of acoustic pressure data collected at multiple receiver points spread along an arch. The Tikhonov regularisation and generalised cross validation technique are used to solve the underdetermined system of equations for the acoustic pressures. The experimental data are collected above a roughness created with a 3D printer. For the given surface, it is shown that the proposed method works well with the various number of receiver positions. In this paper, the tested ratios between the number of surface points at which the surface elevation can be reconstructed and number of receiver positions are 2.5, 5, and 7.5. It is shown that, in a region comparable with the projected size of the main directivity lobe, the method is able to reconstruct the spatial spectrum density of the actual surface elevation with the accuracy of 20%.

УПРУГИЙ КОНТАКТ ЖЕСТКОЙ ШЕРОХОВАТОЙ ПОВЕРХНОСТИ С НИЗКОМОДУЛЬНЫМ ПОЛУПРОСТРАНСТВОМ

УПРУГИЙ КОНТАКТ ЖЕСТКОЙ ШЕРОХОВАТОЙ ПОВЕРХНОСТИ С НИЗКОМОДУЛЬНЫМ ПОЛУПРОСТРАНСТВОМ

Mechanics of unloading of a rough surfaces pre-loaded joint

In this paper we study the problem of the contact characteristics changing on a decrease of the load applied to the preloaded joint of roughness surfaces. The penetration of a rigid sphere (indenter) into the elastic hardenable half-space is considered originally. The elastic crater restoring by unloading is also considered. In elastic-plastic material´s describing, Hollomon´s pawer law is used. To describe a contact of a rigid rough surface with an elastic plastic half-space, the discrete model of a rough surface is used. Microasperities are represented as a set of identical spherical segments, the height distribution of which corresponds to the bearing profile curve of the surface. To describe the bearing profile curve, incomplete beta function ratio is used. The relations of relative contact areas ƞ and ƞ e and gap densities at the joint Λ e and Λ ce on dimensionless loading F q and F qe at loading and unloading for different values of ɛ y and n are given. The obtained results are of practical importance for the sealing ability prediction of fixed sealing joints at the design stage, in particular for tightness supply of flange couplings and high pressure vessels seals.

Influence of Materials Hardenability Parameters on the Machine Parts Characteristics after Unloading

This paper studies the problem of the relative area changing on a decrease of the load applied to the joint of roughness surfaces. The penetration of a rigid rough sphere (indenter) into the elastic hardenable half-space is initially considered, then the elastic crater restoring by unloading is considered. To defining elastic-plastic material, Hollomon’s power law is used. To describe a contact of a rigid rough surface with an elastic plastic half-space, the discrete model of a rough surface is used. Microasperities are represented as a set of identical spherical segments, the height distribution of which corresponds to the bearing profile curve of the real surface. The dependence the dimensionless force elastic-geometric parameter Fq on a relative amount of indentation ε at loading and the dependence of analogous parameter Fqe on amount of ε-Dε at unloading are obtained. The relations of relative contact areas h and he on dimensionless loading Fq and Fqe at loading and unloading for different values of a hardening exponent n and parameter are given. The obtained results are of practical importance for the performance prediction of fixed machine elements’ joints at the design stage, in particular for tightness supply of flange couplings and high pressure vessels seals.