van Dokkum J S, Khajeh Salehani M, Irani N, Nicola L
1Department of Materials Science and Engineering, Delft University of Technology, 2628 CD Delft, The Netherlands.
2Department of Industrial Engineering, University of Padova, 35131 Padua, Italy.
Tribol Lett. 2018;66(3):115. doi: 10.1007/s11249-018-1061-7. Epub 2018 Aug 2.
The relative contact area of rough surface contacts is known to increase linearly with reduced pressure, with proportionality factor . In its common definition, the reduced pressure contains the root-mean-square gradient (RMSG) of the surface. Although easy to measure, the RMSG of the entire surface does not coincide, at small loads, with the RMSG over the actual contact area , which gives a better description of the contact between rough surfaces. It was recently shown that, for Hertzian contacts, linearity between area and load is indeed obtained only if the RMSG is determined over the actual contact area. Similar to surface contacts, in line contacts, numerical data are often studied using theories that predict linearity by design. In this work, we revisit line contact problems and examine whether or not the assumption of linearity for line contacts holds true. We demonstrate, using Green's function molecular dynamics simulations, that for line contacts is not a constant: It depends on both the reduced pressure and the Hurst exponent. However, linearity holds when the RMSG is measured over the actual contact area. In that case, we could compare for line and surface contacts and found that their ratio is approximately 0.9. Finally, by analytically deriving the proportionality factor using in the original model of Greenwood and Williamson, a value is obtained that is surprisingly in good agreement with our numerical results for rough surface contacts.
已知粗糙表面接触的相对接触面积会随着减压而线性增加，比例系数为 。在其通常定义中，减压包含表面的均方根梯度（RMSG）。尽管整个表面的RMSG易于测量，但在小载荷下，它与实际接触面积上的RMSG并不一致，而实际接触面积上的RMSG能更好地描述粗糙表面之间的接触。最近有研究表明，对于赫兹接触，只有在实际接触面积上确定RMSG时，面积与载荷之间才会呈现线性关系。与表面接触类似，在线接触中，数值数据通常使用通过设计预测线性关系的理论进行研究。在这项工作中，我们重新审视线接触问题，并研究线接触的线性假设是否成立。我们使用格林函数分子动力学模拟证明，对于线接触， 不是一个常数：它取决于减压和赫斯特指数。然而，当在实际接触面积上测量RMSG时，线性关系成立。在这种情况下，我们可以比较线接触和表面接触的 ，发现它们的比值约为0.9。最后，通过在格林伍德和威廉姆森的原始模型中使用 解析推导比例系数，得到了一个与我们粗糙表面接触的数值结果惊人一致的值。
