The solution to an elastic-plastic rough surface contact problem can be applied to phenomena such as friction and contact resistance. Many different types of models have therefore been developed to solve rough surface contact. A deterministic approach may accurately describe the entire surface, but the computing time is too long for practical use. Thus, mathematically abbreviated models have been developed to describe rough surface contact. Many popular models employ a statistical methodology to solve the contact problem, and they borrow the solution for spherical or parabolic contact to represent individual asperities. However, it is believed that a sinusoidal geometry may be a more realistic asperity representation. This has been applied to a newer version of the stacked multiscale model and statistical models. While no single model can accurately describe every contact problem better than any other, this work aims to help establish guidelines that determine the best model to solve a rough surface contact problem by applying mathematical and deterministic models to two reference surfaces in contact with a rigid flat. The discrepancies and similarities form the basis of those guidelines.

This work presents a finite-element model-based study of elastic cylindrical contact. The aim is to evaluate the transition between the plane stress and plane strain-based Hertz solutions when each assumption is most applicable. To accomplish this, a range of curvatures, widths, Poisson’s ratios, and friction coefficients are considered. The finite-element model results for the elastic cylindrical contact cases are compared with the Hertz contact model when assuming plane stress or plane strain. Perhaps, surprisingly, the finite-element model predictions show little dependence on Poisson’s ratio and friction coefficient. The finite-element model predictions of force as a function of deflection agree relatively well with the plane stress Hertz prediction for all cases considered. The finite-element model predictions of contact width as a function of force actually fall below all the analytical Hertz predictions. Therefore, an adapted version of the Hertz equations is provided, which shows better agreement with the cases considered in this work.

This work develops a numerical methodology for predicting the performance of an automotive piston ring system by considering contact and lubrication mechanics. The rough surface contact mechanics and lubrication occurs on a scale much smaller than the size of the piston rings and therefore the key aspect of the model is an algorithm that simultaneously solves the multiple mechanisms at different scales. The finite element method will be used to model the mechanical deformations of the piston ring surfaces at large scales. The quasi-steady state model includes heat generation due to solid and viscous friction. This heat generation will then be used to predict the temperature rise and thermal effects in the lubricant and component. A statistical rough surface method that renders asperities as elastic–plastic wavy surfaces predicts the solid contact area. The modified Reynolds equation will be solved to consider the effects of mixed hydrodynamic lubrication while using flow factors formulated for actual piston and ring surfaces. The lubricant viscosity depends both on temperature and shear rate. This will allow for the regimes of boundary, mixed, and full-film lubrication to be considered. The model predicts friction for various loads and speeds that are then compared to experimental measurements. Although the contacts operate mostly in the mixed lubrication regime, the model and experiments show changes in friction with load, speed, and temperature.

The potential lubrication mechanisms for articular cartilage remain as complex as the material itself. Many studies have examined systematically the effects of sliding velocity on the frictional response of cartilage but a systematic analysis of contact area remains largely uncharted. Here we explore this potential effect three ways: a constant force experiment, a constant pressure experiment, and a non-constant pressure and force experiment. Hard, impermeable spheres are used as probes and with sizes varied between 1.6 mm and 25.4 mm allowing a sweep of physiologically relevant pressures. The aim is to effectively isolate the influence of the probe curvature on the friction measurements. Articular cartilage samples were collected from horses at necropsy from the left and right distal, medial aspect of the radius. Each test was run for five minutes at a reciprocated sliding speed of 1 mm/s. Two lubrication regimes are observed during testing, an area-dependent regime at lower areas and an area-independent regime at higher areas. Therefore measurements made using different probe sizes will most likely result in different measurements of the friction behavior and great care should be given when comparing these results.