The contact of elastic regular wavy surfaces

A complete solution in closed form to the elastic contact of a one-dimensional sinusoidal surface with a flat surface was presented by Westergaard in 1939. This paper is concerned with the elastic contact of a two-dimensional sinusoidal surface with a flat. In this case the stress distribution within the elastic solids is three-dimensional. As the load is increased the contact areas change in shape from being circular to square and finally leave a circular region of no contact when the waves are almost squashed flat. The problem is solved in general using a numerical method due to Kalker, but asymptotic solutions in closed form have been found for light loads and also for heavy loads at which contact is almost complete. The variation of the mean separation with load, which determines the volume of the space trapped between the two surfaces, is also found.     

Mechanisms of elastic contact and friction between rough surfaces

The mechanisms of elastic contact and friction between two rough surfaces were analysed, assuming that the surface asperities were spherical, at least near their summits, and that they contacted elastically. It was found that the real contact area and the number of contact spots are approximately proportional to the load, whereas the mean area of contact spots and the mean pressure at the contact areas are almost independent of load. The frictional force F is almost equal to sA_r, where s is the shearing strength at the contact area and A_r is the real contact area. The experimental results using Pyrex glass specimens agreed within experimental limits with the theoretical results.     

The relation between the friction contact performance and the microgeometry of contacting surfaces

It is demonstrated how computer simulation can enable the assessment of the effect of microgeometrical parameters on some friction contact features. The findings of model experiments demonstrate how the distribution of the heights and radii of asperities affects the contact deformation and real contact area. The contact model reveals how the roughness parameters influence the friction coefficient and the contact conductivity. It is illustrated that computer simulation can be applied to the rating of the effect of temperature on the contact conductivity.     

Deformation component of friction force in a wavy elastic contact subjected to wear

The problem of frictional interaction between a wavy punch subjected to wear and an elastic strip is discussed. The contact of the punch and strip is assumed to cover the whole its lengths (complete contact). An analytic solution of the problem is presented, based on which the formula for the deformation component of the friction force is derived. Analysis of this formula enables us to represent visually certain features of the deformation component of the friction force, particularly in relation to its behavior in time.     

Hydrodynamical modelling of lubricant friction between rough surfaces

The steady Couette flow of a Newtonian fluid between two plates, one of them a plane, the other one provided with riblets aligned perpendicular to the flow direction, is taken as a model for lubricant friction with wall roughness. In cases where the amplitude of the riblets is small compared to the riblet spacing, Reynolds lubrication approximation leads to an explicit solution. In contrast to this, a treatment of the full hydrodynamic equations is required for higher amplitudes. Under creeping flow conditions, an analytical treatment of the Stokes equations based on complex function theory allows for a reduction of the problem to the solving of ordinary differential and integral equations for functions of one variable. After this problem reduction, the resulting equations are solved by Fourier analysis and computer algebra.The resulting streamline patterns of the flow reveal the formation of vortices under certain conditions. Since these vortices act like a kind of fluid roller bearings, their influence on the drag force and material transport of the lubricant is studied.     

Measurement of static friction coefficient between flat surfaces

An experimental device, called the centrifugal friction apparatus (CFA), was developed which is capable of measuring the static coefficient of friction, μ, between flat surfaces with very low normal forces. Experiments were performed with the CFA using the polished surface of n-type arsenic doped silicon wafers to investigate static frictional behavior under differing light load conditions. For loads less than 100 mgf, the average μ and the standard deviation were found to increase as the normal load decreased. For loads between 100 mgf and 1.1 gf μ was found to be a constant in the range of 0.30−0.40. Results suggest that despite extreme smoothness the real area of contact is still significantly smaller than the apparent area of contact and μ is still a function of load. Tests with solid particles between the silicon mating surfaces showed that under low load conditions ( <0.9 Pa), the change in μ was negligible for both abrasive particles and for solid lubricants. At the higher loads used ( ≈475–575 Pa) the expected changes in μ were starting to occur for both types of solid particles.     

A numerical model of friction between rough surfaces

This paper describes a computational method to calculate the friction force between two rough surfaces. In the model used, friction results from forces developed during elastic deformation and shear resistance of adhesive junctions at the contact areas. Contacts occur between asperities and have arbitrary orientations with respect to the surfaces. The size and slope of each contact area depend on external loads, mechanical properties and topographies of surfaces. Contact force distribution is computed by iterating the relationship between contact parameters, external loads, and surface topographies until the sum of normal components of contact forces equals the normal load. The corresponding sum of tangential components of contact forces constitutes the friction force. To calculate elastic deformation in three dimensions, we use the method of influence coefficients and its adaptation to shear forces to account for sliding friction. Analysis presented in Appendix A gives approximate limits within which influence coefficients developed for flat elastic half-space can apply to rough surfaces. Use of the method of residual correction and a successive grid refinement helped rectify the periodicity error introduced by the FFT technique that was used to solve for asperity pressures. The proposed method, when applied to the classical problem of a sphere on a half-space as a benchmark, showed good agreement with previous results. Calculations show how friction changes with surface roughness and also demonstrate the method's efficiency.     

Contact between rough wavy surfaces allowing for the mutual effect of the asperities

The paper proposes a model of contact interaction between wavy rough surfaces allowing for the mutual effect of microasperities. The model is intended to calculate the contact parameters under heavy loadings and, correspondingly, at large contour areas. The model in question assumes that the contact waves deform elastically and the asperities deform plastically.     

Methods for analysing partial contact between surfaces

This paper reviews methods available for the numerical solution of contact mechanics problems, in particular, those in which the extent of the contact(s) is not known at the start of the analysis. A new objective function is proposed which is generally smooth and which enables contact mechanics problems to be solved by unconstrained minimisation, in spite of the non-linear boundary condition at the interface. The application of the method to plane periodic elastic contacts, and the author's previously published M(x) formulation of such cases, is demonstrated in detail.     

The initial stage of friction contact between brittle bodies

It is proposed to estimate the surface fatigue of brittle crystalline bodies using experimental data on the initial stage of friction and wear. The mean fatigue stress is estimated from the relation between the force of friction and the size of the section of the surface layer characterized by the mean debris size; the number of fatigue fracture cycles is determined by the relation between the time of damage accumulation on the surface asperities before their total fracture and the mean profilogram step. The calculation includes the asperities that correspond to the initial portion of the reference curve, while the damage accumulation time is determined from the measurement of acoustic emission. There are no published data on the ultimate fatigue of brittle materials, though such data are essential for proper choice of materials for ceramic artificial joints and thrust bearings in some modern tools and for devices intended to withstand long-term operation in any harsh environment.     

The contact and friction between flat belts and pulleys

Rubber coated nylon flat belts running over pulleys in practice display friction coefficients between 0·3 and 0·8. This paper studies the causes of the friction variations. Adhesive friction theory considers the friction force to be the product of the real areas of contact between the sliding surfaces and the shear stress at the contacts: these two quantities have been separately measured by running belts over transparent perspex pulleys and directly observing the contacts. It has been found that variations in contact from one belt to another due to their method of manufacture are as significant in explaining differences in their friction behaviour as are variations in shear stress caused by their different rubber formulations. Real areas of contact were less than one third of the apparent area and varied with load, elastic modulus and roughness of the belt surface in a way broadly understandable in terms of elastic contact mechanics. Shear stress were about 0·5 Nmm⁻², perhaps determined by hydrocarbon films. Some belts showed real areas of contact not directly proportional to load. This led to their friction coefficients being load dependent.     

二维粗糙表面滑动摩擦的研究

能源接近一半消耗在摩擦上,摩擦引起的磨损为主要的机械零件失效方式,通过对摩擦和磨损机理的研究能有效地延长机械零部件的使用寿命。通过对建立的二维双粗糙弹塑性分形模型的实例分析,分析界面剪切强度和法向载荷对磨损率和平均摩擦系数的影响。界面剪切强度增加,磨损率增加较快。随着界面剪切强度的增加平均摩擦系数增加;当界面剪切强度较小时,随着法向载荷的增加平均摩擦系数增加,当界面剪切强度较大时,随着法向载荷的增大,平均摩擦系数先减小后又逐渐增大。     

The normal approach between curved surfaces in contact

The contact of rough curved sufaces has been studied by determining the Normal Approach between a sphere and a rough plane. Theoretical analysis is presented for estimating the Normal Approach from simplified surface maps with topographic features selected from actual surface measurements. It is demonstrated that with small contact zones, the local roughness defined by the asperity orientations over the surface becomes another important parameter to influence the behaviour of the contact of rough spheres. Results are also presented for experimentally determined values of the Normal Approach between a steel ball and a rough plane of various surface finishes. It is shown that the Hertzian values are not valid for rough surfaces, the discrepancy being greater for rougher surfaces.     

Effect of surface roughness on contact between solid surfaces

The analysis of the mechanism of contact between two solids was carried out considering the distribution of the radii of curvature of asperity peaks. The analytical results show that the mean radius of curvature of asperity peaks has a considerable effect on the nature of the deformation of contact asperities, i.e. whether the contact is plastic or elastic, and more effect on the real area of contact than the variation of the distribution of the radii of curvature.The radii of curvature at the asperity peaks and the real area of contact between two smooth surfaces were measured for comparison with the theoretical results. The results for isotropic surfaces produced by buffing and sandpaper agree with the theory; the real area of contact increases with decreasing surface roughness.     

考虑齿间滑动摩擦的齿轮接触疲劳强度计算

齿轮啮合中轮齿间除了滚动接触外还存在相应的滑动接触,使轮齿间具有较大的摩擦力,针对传统赫兹理论形成的齿面接触疲劳强度计算没有考虑齿间摩擦,将摩擦系数引入计算公式,并给出相应摩擦系数的计算.     

The mechanism of interaction between natural laminar hydrosilicates and friction surfaces

Analytical results are presented regarding how powder-like laminar hydrosilicates of the serpentinite type interact with the surfaces of components in tribointerfaces. The greatest amount of attention is paid to the processes of the formation of protective cermet layers on friction surfaces due to the atomic and molecular structure of laminar hydrosilicates.     

The normal approach between rough flat surfaces in contact

The relationship between the normal approach and load for a variety of rough flat surfaces has been considered experimentally and theoretically. The experimental values of normal approach measured by a capacitance technique correlate well with the theoretical values based on the measured surface parameters. For smooth surfaces the texture deformation is essentially elastic whilst the rough surfaces behave plastically. Linearity between the normal approach and the surface roughness at any given load is established and is thereby in agreement with theoretical expectation.     

基于ANSYS的轮轨摩擦滑动接触应力分析

以Hertz接触理论为依据,利用ANSYS建立2D有限元计算模型,模拟原地打滑、完全制动等轮轨滑动摩擦接触行为。分析了轮轨静接触和滑动接触时接触应力分布情况,研究了接触状态、轴重、滑动速度、载荷类型和钢轨轨顶圆半径对接触应力的影响。结合Hertz接触理论计算结果、剥离损伤理论和自激振动理论进行了轮轨损伤分析。     

The variation of real contact area between surfaces with contact pressure and material hardness

The real area of contact between solids under high contact pressure is examined, and values obtained experimentally are compared with theoretical predictions. The theory considers the compression of an array of uniform prismatic wedges, and predicts a rise in the strength of the asperities when adjacent plastic deformation fields interact. It is assumed that the material on which the wedge-shaped asperities are supported is in a state of hydrostatic stress; this is replicated in the experiment by constraining the bulk material of the specimens. One specimen was single point machined to produce a uniform array of wedges and the other specimen abraded to produce a more random surface texture. Good agreement was found between the compression of the machined surface and the theory. The behaviour of the abraded surface was found to be in good agreement with predictions based on an equivalent uniform array; however, the rigorous theory gave too much strength to the smaller asperities, as their substrate material was found to deform both elastically and plastically.It is demonstrated that material hardness is an important variable; knowledge of initial hardness is not adequate since final contact area depends on final hardness.     

Plane contact problems involving frictional heating for wavy half-space

Contact problems of a rigid punch sliding over the wavy thermoelastic half-space are studied. The punch geometry is considered to be parabolic or flat-ended. It is assumed that the contact between bodies occurs within a finite number of separated contour areas. The frictional heating in these regions is involved. The problem is reduced to the non-linear system of algebraic equations, which is solved iteratively. The effects of the boundary waviness on the heat generation are studied and presented in diagrams.