Model of Rough Contacts using a Statistical Approach

The manufacture of any mechanical part generates a (micro)relief on its surface, called roughness or microgeometry, which is the signature of the manufacturing range used (combination between the manufacturing process used and the parameters that have been applied to this process). (Micro)relief is materialized by local variations in height at different scales, the description and characterization of which are particularly well detailed in various articles in Techniques de L'Ingénieur. These articles highlight two essential characteristics of microgeometry, namely the statistical variability of relief and its multi-scale nature:

• although machining processes use tools of controlled shape and reproducible cutting conditions, surface preparation processes involve tearing or cutting mechanisms which induce significant shape dispersions, all the more important as we tend towards the finest microgeometries. To take account of microgeometry, we need to translate this random statistical aspect into specific techniques that integrate these dimensional variabilities;

• surface microgeometries vary on different scales, as there are no less than three orders of magnitude of defects, or scales ranging from shape to roughness to waviness. The last scale is sub-micrometric, requiring a high degree of descriptive finesse for shape discretization, while the first scales impose domains exceeding millimetric scales.

The presence of this relief will be particularly important both visually, by affecting the surface of the part, and mechanically, by intervening when the parts are in contact. Indeed, variations in height, even if they occur on a fine scale, are sufficient to fragment the actual contact between the two parts, making it qualitatively very different from that which would exist between ideal surfaces. Thus, knowledge of the contact between rough surfaces will prove to be relatively relevant for the prediction of in-service behavior, as two elements will make it relatively decisive:

• the amplitude of microgeometry, which is likely to vary significantly through changes in part manufacturing conditions. Thus, for example, surface finishing processes such as turning can achieve roughness over three decades (R _a between 0.1 and 10 µm), which leaves considerable latitude for adjusting this parameter to the desired value ;

• microgeometry, which plays an important quantitative role in contact behavior.

Finally, given the small size of the microgeometric defects on the surface of the part and their spacing of a few tens of micrometers, a contact area larger...