Rough Elastic Surfaces Research Articles

A comprehensive mathematical model for an accurate calculation of the oil film thickness of strip cold rolling

The surface quality of cold rolled strip is related to a greater extent on the rolling oil film thickness, and there are many factors that affect the oil film thickness. Considering the various factors comprehensively, an integrated mathematical model is established, such as roughness of rolls and strips, elastohydrodynamic lubrication, friction heat and plastic deformation heat in the rolling zone, viscosity varying with temperature and pressure, etc. A series of equations are developed, such as the Reynolds equation of partial membrane hydrodynamic lubrication based on average flow theory, equation of oil film thickness on rough elastic surface, the thermal interface equations between strip, oil film and roller surface, surface asperity contact pressure equation, lubricant viscosity and density equations, motion equation of the oil film, etc. This model is solved by finite difference method to get the film pressure, oil film thickness, and temperature distribution in the rolling zone. The average rolling pressure, the roll, and strip temperature calculated by the model are very close to the field test results. Comparing the minimum film thickness calculated by the model with the regression formula of other literature test, the error is less than 10%. The minimum oil film thickness is analyzed. It increases with the decrease of the rolling force and is approximately proportional to the rolling speed and lubricant viscosity.

Multibond Model of Single-Asperity Tribochemical Wear at the Nanoscale.

Single-asperity wear experiments and simulations have identified different regimes of wear including Eyring- and Archard-like behaviors. A multibond dynamics model has been developed based on the friction model of Filippov et al. [Phys. Rev. Lett. 92, 135503 (2004)]. This new model captures both qualitatively distinct regimes of single-asperity wear under a unified theoretical framework. In this model, the interfacial bond formation, wearless rupture, and transfer of atoms are governed by three competing thermally activated processes. The Eyring regime holds under the conditions of low load and low adhesive forces; few bonds form between the asperity and the surface, and wear is a rare and rate-dependent event. As the normal stress increases, the Eyring behavior of wear rate breaks down. A nearly rate-independent regime arises under high load or high adhesive forces, in which wear becomes very nearly, but not precisely, proportional to sliding distance. In this restricted regime, the dependence of wear rate per unit contact area is nearly independent of the normal stress at the point of contact. In true contact between rough elastic surfaces, where contact area is expected to grow linearly with normal load, this would lead to behavior very similar to that described by the Archard equation. Detailed comparisons to experimental and molecular dynamics simulation investigations illustrate both Eyring and Archard regimes, and an intermediate crossover regime between the two.

Characterization of interface stresses and lubrication of rough elastic surfaces under ball-on-disc rolling

This paper presents a statistical method for characterizing the interface stresses between an elastic rough ball and a smooth rigid disc under lubrication by considering the percolation effect of lubricant flow. The statistical analysis was carried out to integrate the random, microscopic asperity deformation with the asperity–lubricant interaction. An efficient solution process with the aid of the fast Fourier transform was developed for the multi-scale analysis. To avoid numerical instability, the Poiseuille term of the average Reynolds equation was turned off when the average lubricant film thickness was below the percolation threshold and the average hydrodynamic pressure was solved by using the Couette term. This successfully overcomes the limitation in the conventional statistical treatment of mixed lubrication. Moreover, it enables a smooth transition from mixed to boundary lubrication and allows a large range of dimensionless rolling speed, which cannot be achieved by conventional approaches. Also, an empirical formula was developed to evaluate the average central and minimum film thicknesses between lubricated rough surfaces in contact. It was found that the method developed can precisely predict the effect of surface roughness on contact stresses, can effectively estimate the contribution of the direct asperity–disc contacts, and can be used to describe the lubricant performance at a rolling–sliding contact interface.

Perfect Mechanical Sealing in Rough Elastic Contacts: Is It Possible?

Generally, it is assumed that under any applied force there will always be some gap between the surfaces in a contact of rough elastic surfaces, resulting in a discontinuous (i.e., multiply connected) contact. The presence of gaps along the line contact relates to the ability to form an adequate mechanical seal across an interface. This paper will demonstrate that for a twice continuously differentiable rough surface with sufficiently small asperity amplitude and/or sufficiently large applied load and/or sufficiently low material elastic modulus, singly connected contacts exist. The solution of a contact problem for a rough elastic half-plane and a perfectly smooth rigid indenter with sharp edges is considered. First, a problem with artificially created surface irregularity is considered and it is shown that, for such a surface, the contact region is always multiply connected. An exact solution of the problem for an indenter with sharp edges resulting in a singly connected contact region is considered and it is conveniently expressed in the form of a series in Chebyshev polynomials. A sufficient (not necessary) condition for a contact of an indenter with sharp edges and a rough elastic surface to be singly connected is derived. The singly connected contact condition depends on the surface microtopography, material effective elastic modulus, and applied load. It is determined that, in most cases, a normal contact of a twice continuously differentiable rough surface with sufficiently small asperity amplitude, sufficiently low material elastic modulus, and/or sufficiently large applied load is singly connected.

Simulation of friction phenomena between randomly rough elastic surfaces

AbstractFriction induced vibrations are a widely studied field in which the friction coefficient is one of the most important parameters. Measurements show that the friction coefficient underlies stochastic fluctuations. To gain more knowledge about the friction coefficient a finite element study is carried out in order to simulate the friction forces. The Bowden‐Tabor model is implemented which calculates the friction force as the force which is needed to shear apart contact areas hold together by welding or adhesion. The dependency of the friction value on sliding velocity and normal pressure can be determined with this model. Different realization are studied and the stochastic properties of the friction value such as mean value, standard deviation, amplitude spectrum and correlation coefficient can be calculated depending on the roughness of the surface. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Contact Fatigue of Rough Elastic Surfaces in Two-Dimensional Formulation

Solution of a contact problem for a rough elastic half-plane is considered. Surface roughness is assumed to be small and stochastic. A perturbation solution of the problem for relatively small roughness with singly connected contact region is proposed and is conveniently expressed in terms of Chebyshev polynomials. Mean distribution of pressure and mean size of the contact are obtained analytically. A pitting model for rough surfaces is considered based on a generalization of an earlier proposed contact model with some stochastic parameters. An analytical formula relating subsurface originated fatigue is considered and fatigue life of rough and smooth surfaces is obtained which shows that fatigue life of rough solids is slightly shorter than of the smooth ones. In the general case of a contact region of rough surfaces with multiple connectivity subsurface originated fatigue possesses properties similar to the case of singly connected contact region. Surface roughness may have a significant effect only on surface and near surface originated fatigue such as wear, micropitting, and shallow flaking.

Linear elastic contact of the Weierstrass profile

A contact problem is considered in which an elastic half–plane is pressed against a rigid fractally rough surface, whose profile is defined by a Weierstrass series. It is shown that no applied mean pressure is sufficiently large to ensure full contact and indeed there are not even any contact areas of finite dimension — the contact area consists of a set of fractal character for all values of the geometric and loading parameters. A solution for the partial contact of a sinusoidal surface is used to develop a relation between the contact pressure distribution at scale n − 1 and that at scale n . Recursive numerical integration of this relation yields the contact area as a function of scale. An analytical solution to the same problem appropriate at large n is constructed following a technique due to Archard. This is found to give a very good approximation to the numerical results even at small n , except for cases where the dimensionless applied load is large. The contact area is found to decrease continuously with n , tending to a power–law behaviour at large n which corresponds to a limiting fractal dimension of (2 − D ), where D is the fractal dimension of the surface profile. However, it is not a ‘simple’ fractal, in the sense that it deviates from the power–law form at low n , at which there is also a dependence on the applied load. Contact segment lengths become smaller at small scales, but an appropriately normalized size distribution tends to a limiting function at large n . † The authors dedicate this paper to the memory of Dr J. F. Archard, 1918–1989.

A Mixed Soft Elastohydrodynamic Lubrication Model With Interasperity Cavitation and Surface Shear Deformation

A deterministic mixed lubrication model, governing the interface between a moving smooth rigid surface and a stationary rough elastic surface, has been developed. Both the normal and shear deformations of the elastic surface are considered, as well as interasperity cavitation. Utilizing an analogy between the hydrodynamic lubrication (with cavitation) problem and the asperity contact problem, a generalized computational formulation is derived and a unique solution scheme constructed to solve these seemingly different problems. The model has been applied to the rotary lip seal, and used to predict the performance characteristics over a range of shaft speeds. [S0742-4787(00)04101-1]

Experimental evidence of self organized criticality in the stick-slip dynamics of two rough elastic surfaces

An expenment on the stick slip dynamics of two elastic rough surfaces is de- scnbed. This dynamics produces a self organized cntical state on a wide range of control parameters, namely loading speed and pressure. The dependence on the system size has also been studied. A comparison with the stick-slip dynamics produced by a one d1nlensional system and by two rigid surfaces is made.

Velocity weakening in a dynamical model of friction

We introduce a discrete model for friction between rough elastic surfaces which is based on the microscopic description of contacts between asperities. Rough surfaces are modeled as spring-mass arrays with superposed asperities. The linear elastodynamics of the underlying surfaces is treated in the model separately from the nonlinear contact behavior of asperities. Unlike usual spring-block models, noa priori friction law is imposed in the model, which allows the frictional behavior corresponding to a chosen microscopic physics of contacts and topography of the rough surfaces to be simulated. We use the model to study the elastodynamical mechanism of friction related to the inertial response of the elastic medium to suddenly imposed tractions, and perturbations of contact properties due to the elastic waves propagating along the interface. The contribution of this mechanism to friction becomes important at high slip rates (above 1% of the wave speed in our simulations), where it results in the velocity weakening behavior. The mechanism of velocity weakening is first studied analytically on an isolated model element. The predicted behavior is then reproduced in numerical simulations with large surfaces. Simulations with stepping of the driving velocity demonstrate a difference between the frictional force measured directly on contacts, and at the loading point. The latter corresponds to laboratory measurements and includes the inertial response of both the loading mechanism and the elastic body to the variations of driving velocity. We speculate that a similar inertial response is present in certain experimental data.

An experimental study of the coherent under-ice reflectivity of sound in the Greenland Sea Marginal Ice Zone (MIZ)

The coherent component of acoustic under-ice reflectivity was investigated as a function of frequency and grazing angle in the MIZ. Measured reflectivity was compared with scattering theory predictions to test the hypothesis of ridge scattering dominance in the MIZ. Explosive source acoustic signals were received on a vertical array, during the Marginal Ice Zone Experiment (MIZEX 84), and deconvolved to separate the direct and ice-reflected arrivals. Ice-reflected signals received on individual hydrophones at different ranges and depths, and on different days, were aligned in time and coherently ensemble averaged within a moving 10-deg grazing angle window. The resulting reflectivity was found to decrease with increasing frequency from 64–256 Hz and with increasing grazing angle from 12–35 deg. Comparison was made with predictions from smooth elastic plate theory, perturbation theory for a rough pressure release surface, perturbation theory for a rough elastic surface, Twersky theory for hemispherical bosses on a plane, and Twersky theory for infinite, semielliptical cylinders on a plane. The Twersky theory for semielliptical cylinders gave a significantly better fit to the data than the other theories. This suggests that, although the under-ice topography may be a good deal more complicated, scattering may, nevertheless, be dominated by remnants of elongated pressure ridge keels. Remote sensing data, taken during the experiment, showed that the ice cover was primarily composed of small floes (< 200 m in diameter). Laser ice-surface height measurements were analyzed to obtain the pressure-ridge sail-height distribution. The Twersky theory modeling gave predictions within 1 dB of the measured mean reflectivity when a ridge keel-to-sail ratio of 6.5 was assumed.