The effect of an asymmetric distribution of asperity heights is accounted for in a recently developed scale-dependent multi-asperity model of contact and friction. A Weibull distribution of asperity heights is used which allows the skew and kurtosis to be varied, but not independently of each other. The contact and friction model used includes the effects of adhesion and of scale-dependent friction. The results obtained demonstrate that positive/negative skew decreases/increases both the friction coefficient and its dependence on the magnitude of the normal load.

In practice, multi-asperity contact problems are often solved as two dimensional (2D) plane problems rather than true three dimensional (3D) problems. This is accomplished by assuming that each peak on a 2D scanned profile is the pinnacle of a half sphere. Hertz contact equations are then used to solve for the radius of contact and pressure profile. In reality, the local maximum in the plane may not be the maximum in the unmeasured depth direction, creating inherent errors in the contact model. This error is shown to be significant in contact problems when estimating the area of contact and total contact force over a single asperity. The pressure corrected Sternberg-Turteltaub model is introduced, in which a cylinder is used to model a sphere in a plane. This model is shown to improve the contact area and total force estimates for a range contact parameters.

One type of troublesome friction-induced noise, common in brakes, clutches and mechanical seals, is high frequency chirp or squeal. The frequencies at which these noises and underlying vibrations occur typically range from around 1 kHz to more than 10 kHz. We have found that the essential physical ingredients needed to model this problem are two finite elastic systems coupled by friction and a distributed interfacial contact stiffness, transverse to the direction of sliding. The contact stiffness is associated with the roughness of the sliding surfaces and, sometimes, with the presence of wear particles within the contact. Our approach is to perform an eigenvalue analysis, using finite elements, of pairs of coupled sliding elastic rings. Due to the presence of friction, the stiffness matrix is asymmetric and mode coupling or mode splitting can occur. Typically ten per cent of the first forty or so vibratory modes are potentially unstable. Generally one or two of these appear as instabilities in the actual physical system being modeled. No stick-slip action needs to be invoked and these instabilities can occur with a single constant coefficient of friction.

A new technique to measure the pressure in a real contact is proposed. One of contacting surfaces is covered, prior to contact establishment, by a special gel. The contact closing removes the excess gel and, during a certain time interval, the contact pressure transforms the entrapped substance in an amorphous solid. In each point, the refractive index of this solid depends on the pressure acting during transformation. After contact opening, the reflectivity of this coating depends on the former contact pressure and it is mapped by aid of a laser profilometer and becomes an indicator of contact pressure. Theoretical considerations show that the gel must possess certain optical parameters for the method to work. Several experimental reported results offer a clear image upon pressure distribution in Hertz point contacts, end effects in finite length line contacts, pressure distribution between rough surfaces and indicate the onset of plastic deformation.

This work describes application of fullerenes as additives for liquid lubricants such as motor oils. Experiments include dynamic tracking of friction coefficient and weight measurements of samples before and after experiments. Friction coefficient measurements have been done on computer-controlled wear-friction testing machine, which has been developed at Surface Engineering Laboratory in NJIT. For the proposed series of experiments, this machine employs conforming disc-on-ring arrangement of rubbing bodies at boundary lubrication; sample couple is steel AISI 4340 and bronze SAE 40; nominal contact pressure ranges from 1.9 MPa to 3.7 MPa with sliding speed of 0.61 m/s. Tested lubricants were prepared on the basis of super duty motor oil SAE 10 by adding one weight percent of additives: pure C 60 , mixture of C 60 and C 70 and graphite powder. Performance comparison of fullerene contained lubricants with pure oil and oil modified by graphite powder showed that although there is no any clear difference in friction coefficient value for tested lubricants, fullerene contained lubricants decrease wear rate of rubbing bodies.

A simulation is undertaken to consider the effects of the scale of surface roughness on elastic contact and friction. In the simulation, a cylindrical rigid indenter of a prescribed profile is brought into contact with an elastic half-space. Interaction between the indenter and the half-space occurs through an assumed surface potential derived from the 6-12 Lennard-Jones intermolecular potential. The hypothesis under investigation is that by assuming the frictional stress is proportional to the magnitude of the normal stress, irrespective of sign, one can account for the enhanced frictional stress at the nano-scale vs. the micro-scale that has been observed experimentally. Results of the simulations indicate qualitative agreement with recent experimental findings.

Many authors attempted to establish a direct correlation between the equation of the surface of an equivalent rigid punch and the pressure distribution arising when this punch is pressed against a corresponding elastic half-space. The results are encouraging, but they have a limited applicability and the involved calculations are still complicated. This paper advances a simple correlation based on a new interpretation of integral condition of deformation of a contact and on the dependence of pressure or pressure gradient on singularities in surface gradient or curvature. Based on this correlation, a method to find the pressure distribution for contacts bound by surfaces described by up to second order polynomials is advanced. The new method is applied in several classical contact problems and a very good agreement is found with existing solutions.

An experimental investigation is presented to evaluate recently published models for the contact and sliding inception of a deformable sphere loaded against a smooth rigid flat. The effects of the normal load on the contact area, junction growth, and the static friction force in the elastic-plastic contact regime are presented. Very good correlation is found between the predicted and measured contact area. A dramatic decrease of the static friction coefficient with increasing normal loading is observed, similar to the trend predicted by the model. The quantitative agreement is, however, less satisfying. Some possible reasons for the poor agreement are pointed out.

In recent years, due to extensive development of depth-sensing indentation techniques, nanoindentation has been used to evaluate the mechanical properties of surface layers and thin films of different materials. However, current nanoindentation procedures are based on simplified assumptions about the material behavior during unloading and empirical relations of the contact area (e.g., Oliver and Pharr, 1992) with little input from analytical and numerical solutions. Therefore, it is unclear what properties can be measured using instrumented nanoindentation techniques and what is the validity of the present procedures for measuring reduced elastic modulus and material hardness. Thus, the main objective of the present study was to analyze the validity of the current approaches for determining material properties and to propose an alternative approach for measuring the reduced elastic modulus, yield strength, and material hardness.

A frictional force resists the relative motion of the two surfaces. An understanding of the difference between static and dynamic contact with friction can lead to methods, which reduce friction and wear. The main goal of the present work is to evaluate the various solutions for the dynamic contact problem with friction and to compare theirs with the solution of the static contact problem. Another goal of the present work is to clarify whether the perturbation of some problem parameters during sliding with time can lead to the difference between solutions of the static and dynamic contact problems with friction. The essential parameter determining friction is the number of asperities in contact. The number of asperities in contact changes as a consequence of the wear. As follows from the classical wear models the perturbation frequency of the number of asperities in contact depends on the sliding velocity. The model of dynamic contact with friction based on the perturbation of the number of asperities in contact, along with the alternative models, is discussed in the present work.

A multi-asperity model of the contact resistance in a MEMS microswitch has been developed. This model includes the effects of elastic and plastic deformation, adhesion, and scale-dependent constrictive resistance. The number of asperities in contact is small enough that a discrete, rather than a continuous, distribution of asperity heights is used. Due to the combined effects of plasticity and adhesion, the surface profile changes with repeated load and unload cycles. Furthermore, adhesion produces significant hysteresis in the contact resistance vs. contact force characteristics. Measurements of the contact resistance as a function of actuation voltage show good qualitative agreement with the model.

An experiment is conducted in which a free-standing bicycle wheel is given an initial angular speed and then allowed to slow down to rest. Measurements of the wheel speed, using a magnetic sensor, during the decay are compared to predictions from a model accounting for a combination of viscous and dry friction at the wheel bearing. The time history data indicate two dynamic regimes: (i) a higher speed phase corresponding to the first part of the motion for which a simple viscous friction model applies, and (ii) a slower speed phase corresponding to low speed to stop behavior for which a model involving both viscous and dry friction is proposed. A method is presented for finding the viscous and dry friction coefficients of the two phases.

To investigate the pressure distribution and the stress state in a real elasto-plastic circular contact, bearing balls of two different degrees of surface finishing were used. These were pressed against a polished flat surface made of softer steel. The surface microtopography data measured in each case by a laser profilometry was introduced in a numerical program developed to evaluate the pressure distribution, stress state and residual deformations for an elasto-plastic material with non-linear hardening. The dimension of calculated contact plastic deformations compare favorably with those found experimentally by aid of a laser profilometer.

The non-stationary character of roughness is a widely recognized property of surface morphology and suggests modelling several solid surfaces by fractal geometry. In the field of contact mechanics this demands for novel investigations attempting to clarify the role of multi-scale roughness during physical contact. Here we propose an experimental investigation of the mechanical response of SrTiO 3 substrates probed by a commercial nanoindentor. Load-displacement curves have been acquired respectively on well-defined crystalline surfaces and on mechanically lapped surfaces. We observe the first-loading cycles to be considerably affected by surface roughness whenever the penetration depth is kept below the interface width. The obtained results are analyzed within an elasto-plastic deformation model for fractal surfaces and a picture is developed to describe the deformation process with respect to surface roughness and structural parameters.

The Archard and the Persson models for elastic contact of rough surfaces are critically assessed for a Weierstrass series profile, finding that they both do not take into account of redistribution of load and interaction effects fully, unless scales are separated enough.

We have long known that tangential contact forces and the friction coefficient at a sliding contact arises not due to some “law” but as a result of contact geometric and material properties in combination with physical processes that are not always accessible to direct experimental verification. While tribologists have occasionally sought alternatives to the coefficient of friction as the primary means to quantify tangential forces at sliding contacts, its convenience, simplicity, long history and lack of viable alternatives assure that it will be remain in use for some time to come. Sometimes the coefficient can remain constant with normal load over orders or magnitude. One can be led to believe that the coefficient is a property of the interface or there is a “law” at work. At other times, the coefficient, usually measured, is said to vary with time, sliding distance or some other variable with no explanation as to why the variation occurs. In the present paper we discuss aspects of friction behavior and modeling, focusing on mechanics and the nature of the friction coefficient. The point of departure is a case where the adhesion theory of friction can be used to understand the mechanics of friction. One can then consider a number of situations and concepts that arise as variations of this case including average versus instantaneous friction; cases when Amontons-Coulomb relations do or don’t apply; static versus dynamic friction; scale effects at rough surfaces; limits of applicability of the friction coefficient; friction measurements, thermal and velocity effects; and local versus global friction and constitutive relations.

Ultrasonically induced nanoscale fatigue and friction reduction phenomena are researched for nanometer order thick protective overcoats. The newly developed method described here is a synergy of the nanometer scale quantitative nanoindentation/scratch technique and ultrasonic excitation. A standing ultrasonic wave is generated at the sample holder during the quasi-static nanoindentation/scratch test at an excitation frequency of several hundreds of kilohertz. Due to the fact that high strain rates are being generated at the surface of the sample, nanofatigue phenomenon followed by delamination and overcoat chipping can be observed. Statistical investigation of fatigue inducing parameters, such as critical quasistatic load and amplitude of oscillations, leads to a means of comparative sample characterization.

Understanding subsurface stresses that occur during the mixed-EHL (elastohydrodynamic lubrication) contact of rough surfaces is fundamental to mechanical design and failure analysis. This is driven by the fact that most of the critical tribological components of heavy-duty machinery are subjected to asperity contact. Moreover, the trend towards increasingly compact design further necessitates incorporating surface roughness. The deviation of the subsurface stress field for rough surfaces from that of smooth surfaces can be used to identify the effect of roughness on stress distribution and variation. This study presents a transient contact stress analysis for rough surfaces in mixed-EHL problems. The solutions are illustrated using animation of the results, and the method of model-based simulation is summarized for a surface virtualization technology.

Because adhesion forces are especially important at the submicron scale, they play a dominant role in several fields of nanotechnology, such as biology, atomic force microscope (AFM) imaging, magnetic disk drives, and microelectromechanical systems (MEMS). The profound importance of adhesion forces in MEMS has been the principal theme of several studies. A common approach for measuring the surface energy is based on balancing the elastic energy stored in microcantilever beams partially adhered to substrates with the work of adhesion, assumed equal to the surface energy multiplied by the apparent area of the attached beam length. However, because the apparent contact area is significantly larger than the real contact area and the elastic energy stored in the deformed asperity microcontacts is neglected, this traditional method may greatly underestimate the interfacial adhesion energy. Consequently, the objective of this study was to develop a method for determining indirectly adhesion forces and adhesion energies form relatively simple in situ electrical contact resistance (ECR) measurements. The method presented herein is based on a theoretical treatment of the ECR encountered during contact of isotropic, conductive, rough surfaces, using multi-scale fractal description of the equivalent surface topography, constitutive contact relations for elastic-perfectly plastic asperity microcontacts, and size-dependent constriction resistance of microcontacts. Results are presented for the adhesion force and adhesion energy in terms of ECR for different surface topographies.

The purpose of this study is to investigate the dynamic response of axially translating continua undergoing both the effect of friction and axial acceleration. The axially moving continuum is initially modeled as a string, neglecting its flexural stiffness; the response, with particular interest given to transverse vibrations and dynamic stability, is studied through numerical methods. A finite element method is employed to discretize the space domain and an implicit α–method is employed to integrate the resulting matrix equation in the time domain. Results are given through time history diagrams and stability considerations.