This paper summarizes the submissions to a recently announced contact-mechanics modeling challenge. The task was to solve a typical, albeit mathematically fully defined problem on the adhesion between nominally flat surfaces. The surface topography of the rough, rigid substrate, the elastic properties of the indenter, as well as the short-range adhesion between indenter and substrate, were specified so that diverse quantities of interest, e.g., the distribution of interfacial stresses at a given load or the mean gap as a function of load, could be computed and compared to a reference solution. Many different solution strategies were pursued, ranging from traditional asperity-based models via Persson theory and brute-force computational approaches, to real-laboratory experiments and all-atom molecular dynamics simulations of a model, in which the original assignment was scaled down to the atomistic scale. While each submission contained satisfying answers for at least a subset of the posed questions, efficiency, versatility, and accuracy differed between methods, the more precise methods being, in general, computationally more complex. The aim of this paper is to provide both theorists and experimentalists with benchmarks to decide which method is the most appropriate for a particular application and to gauge the errors associated with each one

A model is developed for predicting the performance of spur gears with provision for surface roughness. For each point along the line of action, the contact of pinion and gear is replaced by that of two cylinders. The radii of cylinders, transmitted load, and contact stress are calculated, and lubricant film thickness is obtained using the load-sharing concept of Johnson et al. (1972, “A Simple Theory of Asperity Contact in Elastohydrodynamic Lubrication,” Wear, 19, pp. 91–108) To validate the analysis, the predicted film thickness and the friction coefficient are compared to published theoretical and experimental data. The model is capable of predicting the performance of gears with non-Newtonian lubricants—such as that of shear thinning lubricants—often used in gears. For this purpose, a correction factor for shear thinning film thickness introduced by Bair (2005, “Shear Thinning Correction for Rolling/Sliding Electrohydrodynamic Film Thickness,” Proc. Inst. Mech. Eng., Part J: J. Eng. Tribol., 219, pp. 1–6) has been employed. The results of a series of simulations presenting the effect of surface roughness on the friction coefficient are presented and discussed. The results help to establish the lubrication regime along the line of action of spur gears.

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A model is presented, which enables one to predict the running-in performance of the rolling/sliding surfaces subjected to mixed-lubrication line contact. The load-sharing concept was used, in which it is assumed that both the fluid film and the asperities contribute in carrying the imposed load. The plastic deformation of asperities during the running-in is taken into consideration. In the application of the load-sharing method, it is often assumed that asperity heights have a Gaussian distribution. This assumption has been relaxed in this model. Prediction results for the variation in the arithmetic average of asperity heights (Ra) during the running-in period for contact of two rollers are compared with published experimental data. Also presented are the results for the variation in wear volume, wear rate, and friction coefficient during the running-in period. The effect of surface pattern, speed, and load on the running-in behavior is studied. The steady-state wear rate for different surface patterns calculated from this model is compared with the wear rate predicted by the thermal desorption model, and the results are in agreement both in trend and magnitude. The effect of running-in on the Stribeck curve for different surface pattern is discussed.

The effect of surface pattern on frictional characteristics of lubricated contact is studied. An algorithm based on the load-sharing concept is developed which assumes that the total transmitted load is carried by the asperities as well as the fluid film. Surface roughness for specified values of surface pattern number is generated assuming a Gaussian height distribution and Stribeck-type curves are obtained for isotropic, transverse, and longitudinal surfaces. The predictions of the model are verified by comparing published results on non-conformal contact of rollers and also a heavily loaded, conformal pin-bushing assembly. The results reveal that surfaces with transverse pattern generate larger friction than those with longitudinal surfaces. Transverse surfaces perform a higher film-forming capacity compared to isotropic and longitudinal surfaces.

Thermoelastohydrodynamic lubrication (TEHL) analysis for spur gears with consideration of surface roughness is presented. The model is based on Johnson's load sharing concept where a portion of load is carried by fluid film and the rest by asperities. The solution algorithm consists of two parts. In the first part, the scaling factors and film thickness with consideration of thermal effect are determined. Then, simplified energy equation is solved to predict the surfaces and film temperature. Once the film temperature is known, the viscosity of the lubricant and therefore friction coefficient are calculated. The predicted results for the friction coefficient based on this algorithm are in agreement with published experimental data as well as those of EHL simulations for rough line contact. First point of contact is the point where the asperities carry a large portion of load and the lubricant has the highest temperature and the lowest thickness. Also, according to experimental investigations, the largest amount of wear in spur gears happens in the first point of contact. Effect of speed on film temperature and friction coefficient has been studied. As speed increases, more heat is generated and therefore film temperature will rise. Film temperature rise will result in reduction of lubricant viscosity and consequently decrease in friction coefficient. Surface roughness effect on friction coefficient is also studied. An increase in surface roughness will increase the asperities interaction and therefore friction coefficient will rise. Nomenclature bHalf-width of contact (m) BRoller's width (m) C pi Specific heat of roller i (J/kg/K) d wp Pitch radius of pinion (m) d wg Pitch radius of gear (m) E i Modulus of elasticity of roller i (N/m 2 ) E 0 2 1Àm 2 1 E 1

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In this study hybrid polytetrafluoroethylene (PTFE)/glass fibers were employed in hierarchical braided structure as a composite reinforcement. PTFE-covered glass fibers were braided to achieve the hierarchical structure, then the composites were prepared through vacuum assisted resin transfer molding (VARTM) process. Tribological experiments were performed on the composites. The results showed self-lubricating and lower dynamic friction coefficient due to the PTFE transfer film formation. SEM micrographs confirmed the transfer film formation. Friction coefficient of 0.112, 0.105 and 0.096 were obtained under loading of 20, 30 and 40 N forces, respectively. The experimental coefficient of friction results were confirmed by mixture theory. The self-lubricating feature of PTFE-glass braided epoxy composite along with its mechanical characteristics makes it a feasible alternative for traditional wet bearing parts.