A formulation of the linear discrete Coulomb friction problem via convex optimization
This paper presents a new formulation of the dynamical Coulomb friction problem in finite dimension with discretized time. The novelty of our approach is to capture and treat directly the friction model as a parametric quadratic optimization problem with second‐order cone constraints coupled with a...
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Veröffentlicht in: | Zeitschrift für angewandte Mathematik und Mechanik 2011-02, Vol.91 (2), p.155-175 |
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Sprache: | eng |
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Zusammenfassung: | This paper presents a new formulation of the dynamical Coulomb friction problem in finite dimension with discretized time. The novelty of our approach is to capture and treat directly the friction model as a parametric quadratic optimization problem with second‐order cone constraints coupled with a fixed point equation. This intrinsic formulation allows a simple existence proof under reasonable assumptions, as well as a variety of solution algorithms. We study mechanical interpretations of these assumptions, showing in particular that they are actually necessary and sufficient for a basic example similar to the so‐called “paradox of Painlevé”. Finally, we present some implementations and experiments to illustrate the practical aspect of our work.
This paper presents a new formulation of the dynamical Coulomb friction problem in finite dimension with discretized time. The novelty of this approach is to capture and treat directly the friction model as a parametric quadratic optimization problem with second‐order cone constraints coupled with a fixed point equation. This intrinsic formulation allows a simple existence proof under reasonable assumptions, as well as a variety of solution algorithms. The authors study mechanical interpretations of these assumptions, showing in particular that they are actually necessary and sufficient for a basic example similar to the so‐called “paradox of Painlevé”. Finally, the authors present some implementations and experiments to illustrate the practical aspect of their work. |
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ISSN: | 0044-2267 1521-4001 |
DOI: | 10.1002/zamm.201000073 |