Assessment of tangential and normal stiffness of contact between rough surfaces using ultrasonic method

The acoustic model of contact, previously proposed for longitudinal ultrasonic waves, was adopted for shear waves. It was found that the measurements of the phase shift of coefficient of reflection from the contact interface, taken both for shear and longitudinal ultrasonic waves of the same frequency, allows us to find the tangential to normal contact stiffness ratio for the contact tested.

However, an analysis based on the Greenwood-Williamson model and the Hertz-Mindlin theory revealed that for a contact between rough surfaces with spherical asperities, the ratio of the tangential to the normal contact stiffness is independent of surface height distribution and is, moreover, equal to that ratio for an elementary contact.

In order to verify the theoretical predictions, measurements of the phase shift of longitudinal and shear ultrasonic waves of frequency 10 MHz were carried out for the loaded contact (up to 300 MPa) between ground quartz samples. It appeared that the value of the tangential to normal contact stiffness ratio resulting from the ultrasonic measurements is fairly close to that predicted by the Hertz-Mindlin theory.     

A finite element-based model of normal contact between rough surfaces

Engineering surfaces can be characterized as more or less randomly rough. Contact between engineering surfaces is thus discontinuous and the real area of contact is a small fraction of the nominal contact area. The stiffness of a rough surface layer thus influences the contact state as well as the behavior of the surrounding system. A contact model that takes the properties of engineering surfaces into account has been developed and implemented using finite element software. The results obtained with the model have been verified by comparison with results from an independent numerical method. The results show that the height distribution of the topography has a significant influence on the contact stiffness but that the curvature of the roughness is of minor importance. The contact model that was developed for determining the apparent contact area and the distribution of the mean contact pressure could thus be based on a limited set of height parameters that describe the surface topography. By operating on the calculated apparent pressure distribution with a transformation function that is based on both height and curvature parameters, the real contact area can be estimated when the apparent contact state is known. The model presented is also valid for cases with local plastic flow in the bulk material.     

The dynamics of the dry friction oscillator taking into account pre-displacement and tangential contact stiffness

A one-dimensional model of the dry friction oscillator is considered taking into account the phenomena of pre-displacement and tangential contact stiffness. The dynamic parameters and characteristics of the basic mode of stabilized vibrations are determined for the cases of force and kinematic excitation. The obtained results are compared with the Coulomb model of the force of friction, which gives evidence that this model is inapplicable to calculating low-amplitude oscillations. The effect of the tribological contact parameters on the resonance characteristics of the oscillator and the damping properties of the friction contact are investigated.     

Development of a contact compliance method to detect the crack propagation under fretting

Partial slip fretting conditions are classically known to favor contact crack nucleation and crack propagation. Considered as a plague for modern industries, numerous theoretical researches have been conducted during the past two decades to predict such fretting damage. However, a review of last few years critically outlines the need of precise and in-situ experiments to qualify and quantify the given models. To palliate such aspect, an original approach which consists in following the contact stiffness evolution as an indicator of the fretting cracking phenomena, has been developed. Applied for an aluminium/steel contact, it demonstrates that the incipient crack propagation is related to a discontinuous decrease of the contact stiffness. Based on this online analysis, a fretting cracking endurance parameter has been extrapolated to develop fast and low cost fretting cracking endurance chart. A FEM analysis has been performed in an attempt to formalize the given experiments.     

Friction behavior of quenched and tempered steel in partial and gross slip conditions in fretting point contact

Tangential traction caused by friction in contacting surfaces is a major factor in fretting fatigue that increases stress levels and leads to a reduction in fatigue life. Friction in fretting contact was studied in partial, mixed and gross slip conditions on quenched and tempered steel. Measurements were made with sphere-on-plane contact geometry for polished and ground surfaces. Friction was evaluated from on-line energy ratio and, after the tests, from wear marks. A maximum friction coefficient of over 1.0 was measured at mixed slip zone with polished surfaces, whereas ground surfaces promote lower values in similar operating conditions. The friction coefficient dependence on load cycles and loading frequency is also presented and briefly discussed. The friction data and understanding thus gained is to be used for evaluation of crack initiation with the numerical fretting fatigue model.     

A statistical model of elasto-plastic asperity contact between rough surfaces

This work models statistically elasto-plastic contact between two rough surfaces using the results of a previous finite element analysis of an elasto-plastic sphere in contact with a rigid flat. The individual asperity contact model used accounts for a varying geometrical hardness effect that has recently been documented in previous works (where geometrical hardness is defined as the uniform pressure found during fully plastic contact). The contact between real surfaces with known material and surface properties, such as the elastic modulus, yield strength, and roughness are modeled. The asperity is modeled as an elastic-perfectly plastic material. The model produces predictions for contact area, contact force, and surface separation. The results of this model are compared to other existing models of asperity contact. Agreement exists in some cases and in other cases it corrects flaws, especially at large deformations. The model developed by Chang, Etsion and Bogy is also shown to have serious flaws when compared to the others. This work also identifies significant limitations of the statistical models (including that of Greenwood and Williamson).     

Study of seizure of coated and treated titanium alloy under fretting conditions

Titanium alloys are well known to present poor sliding behaviour and high wear values. Various coatings (soft thick coatings and thin hard coatings) and treatments have been tested to prevent such an occurrence under fretting conditions at high frequency of displacement (100 Hz). An original test apparatus, using an open-loop system, has been performed to directly display the phenomenon of seizure. No seizure was recorded at low load (6 N), while, at higher load (10 N), all samples undergo a more or less early seizure. The total sliding distance D₀ proved to be a pertinent parameter to study the seizure resistance. Furthermore, the results highlight that D₀ is linked to the total energy dissipated in the contact, E_dt, and reveal two distinct behaviours at low load, which suggest two distinct dissipating mechanisms of energy. The first trend can be connected with the plastic deformation and the trapping process of debris within the contact zone occurring on soft coatings. The second trend can be related to the higher debris ejection observed on hard samples. So, soft thick coating satisfies most of the chosen criteria except those of wear. In contrast, thin and hard coatings are not sufficient to totally protect the substrate but they are already able to efficiently reduce wear.     

Cutter mark cross method for improvement of contact stiffness by controlling distribution of real contact area

Contact surfaces do not make contact perfectly because such surfaces have a lot of asperities. The real contact area is much smaller than the nominal contact area, and the real contact areas has a non-uniform distribution because of the waviness in the contact surface. The contact stiffness is influenced not only by the deformation of the asperities, but also by the distribution of the real contact areas. In general, a contact surface with a uniform distribution of the real contact areas has greater contact stiffness. However, this requires a grinding finish and costs more than the cutting finish. In this study, a method for uniformly distributing the real contact areas easily, is proposed to improve the contact stiffness of a contact surface finished by cutting. The method is called the cutter mark cross (CMC) method. The allowable waviness in the CMC method is shown. In addition, the effect of the CMC method is investigated by experimentation. The results show that the real contact areas can be distributed uniformly using the CMC method. The horizontal and vertical contact stiffness can also be improved.     

Effect of start-up schemes and amplitude of tangential motion on friction behavior in fretting point contact

The friction coefficient is an important factor in fretting fatigue. The frictional behavior of quenched and tempered steel 34CrNiMo6 was studied in smooth fretting point contact with measurements at partial and gross slip conditions. The effect of the start-up scheme is studied by altering the way the displacement amplitude is developed to the target value. This only has a minor effect on the maximum friction coefficient but it does alter the frictional behavior. The friction coefficient increases as tangential displacement amplitude is increased and it has a maximum value of 1.5-1.6 at the transition to gross sliding.     

Elastic contact between rough surfaces: Effect of roughness at large and small wavelengths

The area and pressure distribution in elastic contacts between frictionless, nonadhesive surfaces is studied as a function of load and surface geometry using finite element calculations. Surfaces that follow self-affine scaling on all resolved scales are compared to surfaces with cutoffs at small and large length scales, and experimental surfaces that are not self-affine. In all cases the true area of contact is proportional to load and inversely proportional to elastic modulus and the mean slope of the surface. The constant of proportionality κ is nearly constant and lies between analytic predictions. Large wavelength cutoffs lead to a small increase in κ, a homogeneous distribution of contacts at large scales, and limit the size of the largest connected regions. Small wavelength cutoffs lead to local redistributions in pressure that decrease the probability of low and high local pressures.     

Evaluation of the real contact areas, pressure distributions and contact temperatures during sliding contact between real metal surfaces

A three-dimensional elastic contact algorithm has been developed to analyse the normal contact problems of bodies having rough surfaces. The algorithm can evaluate the real contact areas and contact pressure distributions using measured surface roughness data.

Following an approximate elastic-plastic contact solution the analysis produces more realistic elastic and plastic contact areas; in addition results of contact pressure distributions can be predicted according to a given maximum plastic limit pressure.

The technique can simulate (in an approximate way) the elastic-plastic sliding contact behaviour in the vicinity of asperities or concentrated contact areas by ignoring the effect of the tangential forces on the vertical displacement.

Assuming a certain sliding speed and a particular coefficient of friction the local temperature distribution due to the heat generation over the real contact areas can also be calculated for 'slow sliding' problems.

The results show the moving real contact areas and the contact temperature fields for an electric spark mechanical steel surface moving over a planed bronze surface. Changes of the rigid body displacement, as well as the average and maximum pressures are also presented during sliding.

The micro-contact or asperity contact behaviour for bodies having large nominal contact area and the macro-contact behaviour for bodies being in 'concentrated contact' are also compared. In the latter case an ideal smooth steel ball was slid over the previously mentioned bronze surface.     

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.     

Contact analysis of three-dimensional rough surfaces under frictionless and frictional contact

A methodology for surface and sub-surface stress calculation of nominally flat on flat rough surface contact has been developed. This methodology is applicable for both large area contact (Hertzian contact) and small area of asperity contact (point load contact) with and without surface friction. A total of nine rough surfaces are generated by the computer with specified standard deviation of surface heights, σ, of 0.3, 1.0 and 3.0 nm, and correlation length, β^*, of 0.1, 0.5 and 0.9 μm. Under the typical applied load at the magnetic head slider-disk interface, small numbers of contact points are obtained and the deformation is purely elastic. Since these contact points are scattered and isolated, asperity contact behaves like point load contact. As β^* becomes larger, more adjacent points will be in contact at a certain contact spot and this is especially true at small σ. All the cases of flat on flat rough surface contact yield maximum von Mises stress on and near the surface at both frictionless and frictional contacts; no local maximum occurs in the sub-surface. In general, the friction effect in the vicinity of contact point is to increase the stress magnitude, while outside this region it also alters the stress distribution. For a surface of small β^* and large σ at high load of 1000 times of the nominal pressure at the head-disk interface, the contact pressure reaches the hardness at a few contact points and plastic deformation takes place in the near surface.     

Effect of age on the friction and wear behaviors of human teeth

Friction and wear behavior of human teeth at different ages against titanium alloy have been investigated using a reciprocating apparatus containing an artificial saliva solution. Human teeth at different ages of 8, 18, 35 and 55 years old were selected for tests. Both hardness and distribution of enamel rods on the occlusal surface, two of factors most important to tribological behavior of human teeth, are close to the age of teeth. It is found that not only the evolution of friction coefficient but also the wear behavior changes between teeth of different ages. Delamination and ploughing mechanisms are dominant for wear of human teeth, and more severe wear is observed for the primary and the permanent teeth at the old age accompanied by remarkable fluctuation in the friction coefficient. Compared with the primary teeth and the permanent teeth at the old age, the permanent teeth at the young and middle ages have better wear-resistance.     

Finite element model of the contact between a vibrating conductor and a suspension clamp

Aeolian vibrations may lead to failure of the overhead conductors of electrical transmission lines. Damages are caused by fretting fatigue at the attachment position of pieces of hardware. This phenomenon depends much on contact mechanics. The contact between a wire and a suspension clamp, a critical location, was modelled using the finite element method. Results from strain measurements on vibrating conductors served as input. The numerical results gave estimates of stresses and slip amplitudes. We can use these results to compute crack initiation criteria. The Ruiz and Chen criterion was chosen here and results compared well with experimental data.     

Potential of functional image processing technique for the measurements of contact area and contact pressure of a radial ply tire in a soil bin testing facility

The exploration principally deals with a promising applicability of image processing method for contact area determination. A digital camera mounted on a single-wheel tester was utilized to take images of contact area at four levels of tire inflation pressure (i.e. 70, 100, 140, and 175 kPa) and six levels of wheel load (i.e. 0.75, 1.75, 2.75, 3.75, 4.75, and 5.75 kN). Contact pressure measurements, subsequently, were performed utilizing seven embedded load cells incorporated in an instrumented housing in longitudinal and perpendicular direction of traversing. It was observed that contact area is a polynomial (with order of two) function of wheel load while there was a reverse linear relation between contact area and inflation pressure. Furthermore, contact pressure has linear relation with vertical load and inflation pressure. Models for contact area and contact pressure were developed by multiple regression analysis while a classical predicting model was assessed using contact area results of image processing technique. The models indicated acceptable coefficient of determinations amounts of 0.974 and 0.953 for contact area and contact pressure models, respectively. However, applied image processing method denoted R²-value of 0.988 for contact pressure equation.     

Measurement of surface roughness on rough machined surfaces using spectral speckle correlation and image analysis

A speckle pattern is formed when a rough surface is illuminated with coherent light. The properties of this pattern can be used in the calculation of roughness parameters. Spectral speckle correlation (SSC) is a technique applicable to the measurement of roughness on rough machined surfaces. This paper presents the SSC obtained from measurements on specimens with a surface roughness in range R_a = 0.5–5 μm. The measurement results correspond to reference measurements made using a stylus instrument, Form Talysurf.     

Friction mechanisms and abrasion of the human finger pad in contact with rough surfaces

The friction and abrasion behaviour of the finger pad on abrasive papers was investigated in friction experiments, combined with microscopic analyses and a protein assay to quantify skin particles abraded in friction contacts. Friction measurements at varied normal forces resulted in relatively high and load-independent friction coefficients, pointing to ploughing and abrasion as important friction mechanisms. The microscopic analyses revealed that large numbers of skin particles are abraded in form of single corneocytes, corneocyte fragments and agglomerates of corneocytes. In addition, micro-scratches were observed on the epidermal ridges of the finger pad after friction contacts. In friction measurements at the same conditions, the amount of abraded skin particles varied for abrasive papers with different roughness, while friction coefficients were comparable.     

Influence of testing method on the contact pressure distribution and its effect on coefficient of friction in polymeric bearings

Influence of contact pressure distribution on the coefficient of friction was investigated for some polymeric bearings in dry and lubricated conditions. Reciprocal pin on plate sliding test and Soda pendulum type sliding tests were carried out. It was found that the contact pressure distribution had a significant effect on the coefficient of friction in lubricated condition. The coefficient of friction became smaller when the pin was sliding with the lower contact pressure side ahead. The coefficient of friction in dry condition does not depend on sliding direction regardless of contact pressure distribution. Furthermore a parametric equation was derived to calculate contact pressure in polymeric journal bearings. The accuracy of the equation was confirmed by Finite Element Method (FEM).