Microcontact Model Research Articles

The Distribution of Microcontact Area, Load, Pressure, and Flash Temperature Under the Greenwood-Williamson Model

Microcontact models provide average values of the random interfacial load, area and pressure between rough contacting surfaces. They do not provide a measure of the variability about that average. Events of tribological importance, however, are likely to be dependent on extreme rather than average behavior conditions. In this paper Monte Carlo simulation is used to determine the 75th and 90th percentiles of three dimensionless random variables as a function of the dimensionless separation of two contacting rough surfaces. These values may be used to determine the corresponding percentiles under the Greenwood-Williamson microcontact model of the distributions of 1) real contact area fraction, 2) the radius of the microcontact area, 3) microcontact load, 4) the maximum microcontact pressure and 5) the asperity flash temperature under low speed sliding conditions. A numerical example illustrates the computations.

Relating Profile Instrument Measurements to the Functional Performance of Rough Surfaces

An easily programmed method is proposed for translating the rms height (Rq) and rms slope (Δq) determined using a profile measuring instrument, into more readily interpreted measures of functional severity such as the density of plastic contacts or the mean real contact pressure. The method involves estimation from the ratio Rq/Δq, of the exponent k of an assumed power function relation between the profile spectrum and the spatial frequency. Having estimated k, the mean square curvature is computed analytically and used together with Rq and Δq to determine the three input variables needed for the Greenwood-Williamson (GW) microcontact model. The GW model is then used to compute, as a function of the separation of two rough surfaces, the contact density, the plastic contact density, the mean load per unit area and the mean load per unit of real contact area. The mean square curvature estimated in this manner is compared to the directly measured mean square curvature for 12 distinct surface types. The values compared quite favorably (within 25 percent) for three of the specimens which included a bearing ball and the ground inner ring rolling path of a cylindrical roller bearing. The discrepancies exceeded a factor of 3 for three other specimens. The microcontact model output computed using both measured and estimated mean square curvature values showed that some output variables, e.g., plastic contact density, are more discrepant than the estimated and measured curvature values. Other output variables of the microcontact model, in particular, the mean real pressure, attenuate the discrepancies. The mean real pressures computed using the calculated and measured curvatures, were within 30 percent for all but three specimens. The maximum discrepancy observed was 55 percent. The results are sufficiently encouraging and the methodology so easy to apply, to commend the practice of routinely supplementing profile measurement data with microcontact model output.

Predicting Microfracture in Ceramics Via a Microcontact Model

The point of view is taken that for ceramics, cone cracking on the microscale assumes the same role as plastic asperity deformation in metal materials, namely, as the agent causing stress raising micropits which precipitate surface fatigue. Empirical fracture data are interpreted in the context of published fracture mechanics analyses of cone cracking in static and sliding contact and used within the Greenwood-Williamson stochastic microcontact model to predict the relative likelihood of cone cracking when a rough flat ceramic contacts a smooth ceramic flat of the same material. The Greenwood-Williamson model is reviewed and its predictions are shown, for the steel and ceramic surfaces considered, to compare favorably to the more general anisotropic microcontact model ASPERSIM. A microfracture index analogous to the Greenwood-Williamson plasticity index, is shown to be a determinant of the ability of a surface to resist cone cracking.

Comparison of models for the contact of rough surfaces

Numerical comparisons of the Greenwood-Williamson (GW) elastic microcontact model with two more general isotropic and anisotropic models suggest that the GW model gives good order-of-magnitude estimates of the number of contacts, real contact area fraction and nominal pressure that result at a given separation of a rough and a smooth flat plane. In effecting the comparisons, the three parameters of the GW model are related to the three spectral moments m 0, m 2 and m 4 of an isotropic or equivalently isotropic surface. It is shown that the real contact area at a given mean plane separation depends only on the bandwidth parameter α = m 0m 4 m 2 2 , while the elastically supported load depends on both α and m 2. On the basis of the comparisons it is suggested that the GW model be adopted by metrologists to relate measured microgeometry to physically more understandable quantities such as contact density, load, real area and plastic contact density. Accordingly, this paper includes an expository presentation of the GW model complete with tables and a detailed numerical example of their use.