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Contact Mechanics for Randomly Rough Surfaces: On the Validity of the Method of Reduction of Dimensionality

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Abstract

Recently, a 1D mapping procedure has been applied to many contact mechanics problems between randomly rough surfaces. I present a simple “back-of-the-envelope” argument to show that this theory fails qualitatively, in particular when surface roughness occurs on many length scales.

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Notes

  1. In the contact mechanics theory of Popov et al., the roughness of the 1D substrate has a power spectrum related to that of the original 2D surface via the equation: \(C_\mathrm{1D} (q) = \pi q C_\mathrm{2D}(q)\). This definition of \(C_\mathrm{1D}\) result in a 1D line profile having the same mean-square (ms) roughness as the original 2D surface (with the power spectrum \(C_\mathrm{2D}\)). Using standard methods, a randomly rough line profile was generated using \(C_\mathrm{1D} (q)\). This line profile will have nearly the same statistical properties as a line scan from the original 2D surface with the power spectrum \(C_\mathrm{2D}\).

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Acknowledgments

The research work was performed within a Reinhart-Koselleck project funded by the Deutsche Forschungsgemeinschaft (DFG). The authors would like to thank DFG for the project support under the reference German Research Foundation DFG-Grant: MU 1225/36-1. This work is supported in part by COST Action MP1303.

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  1. Peter Grünberg Institut-1, FZ-Jülich, 52425, Jülich, Germany

    Bo N. J. Persson

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Correspondence to Bo N. J. Persson.

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Persson, B.N.J. Contact Mechanics for Randomly Rough Surfaces: On the Validity of the Method of Reduction of Dimensionality. Tribol Lett 58, 11 (2015). https://doi.org/10.1007/s11249-015-0498-1

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