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Rolling Friction: Comparison of Analytical Theory with Exact Numerical Results

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Abstract

We study the contact mechanics of a smooth hard cylinder rolling on a flat surface of a linear viscoelastic solid. Using the measured viscoelastic modulus of unfilled and filled (with carbon black) nitrile rubber, we compare numerically exact results for the rolling friction with the prediction of a simple analytical theory. For the unfilled rubber, the two theories agree perfectly while some small difference exists for the filled rubber. The rolling friction coefficient depends nonlinearly on the normal load and the rolling velocity.

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Notes

  1. It can be easily shown that the discrete formulation of the viscoelastic line contact kernel presents an analytical formulation as it occurs for the elastic case. This largely simplifies the viscoelastic integration.

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Acknowledgments

We thank K.W. Stöckelhuber and G. Heinrich (Leibniz-Institut für Polymerforschung, Dresden) for supplying the nitrile rubber and B. Lorenz (FZJ) for measuring the viscoelastic modulus. MS acknowledges FZJ for the support and the kind hospitality received during his visit to the PGI-1, where this work has been performed. MS also acknowledges COST Action TD0906 for grants STSM-TD0906-020613-031727 and STSM-TD0906-230413-030252.

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Authors and Affiliations

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

    Michele Scaraggi & Bo N. J. Persson

  2. DII, Universitá del Salento, 73100, Monteroni-Lecce, Italy

    Michele Scaraggi

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  1. Michele Scaraggi
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  2. Bo N. J. Persson
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Correspondence to Michele Scaraggi.

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Scaraggi, M., Persson, B.N.J. Rolling Friction: Comparison of Analytical Theory with Exact Numerical Results. Tribol Lett 55, 15–21 (2014). https://doi.org/10.1007/s11249-014-0327-y

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  • DOI: https://doi.org/10.1007/s11249-014-0327-y

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