Abstract
In addition to the strict geometrically defined cases that were mapped in Chap. 3 with the method of dimensionality reduction, we would now like to devote ourselves to the question of whether rough surfaces can also be handled with the reduction method. The importance of surface roughness for tribological processes was already emphasized by Bowden and Tabor in the 1940s and since that time has become generally accepted. The most important fundamental work dealing with the contact mechanics of rough surfaces was conducted in the 1950s by Archard and in the 1960s by Greenwood and Williamson. However, the contact mechanics of rough surfaces remains even today a current and to some extent, controversial topic. In this chapter, we will show that there exist theoretical as well as the empirical reasons for why the method of dimensionality reduction is also able to be applied to randomly rough surfaces. In this way, the method presents itself as a practical tool for the fast calculation of contact problems.
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Notes
- 1.
As can be seen in the further considerations, this relationship between the Hurst exponent and the form of the power spectrum is valid over an even larger interval: \( 0 < H < 2 \).
- 2.
We will later see that the interactions between the asperities play no role in the method of dimensionality reduction: The only property that is required is the self-affinity of the surface, regardless of whether the profile is regular or randomly rough.
- 3.
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Pohrt, R., Popov, V.L., Heß, M. (2015). Normal Contact of Rough Surfaces. In: Method of Dimensionality Reduction in Contact Mechanics and Friction. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-53876-6_10
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DOI: https://doi.org/10.1007/978-3-642-53876-6_10
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