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Transitions and singularities during slip motion of rigid bodies

Published online by Cambridge University Press:  23 February 2018

P. L. VÁRKONYI
P. L. VÁRKONYI*
Affiliation:
Department of Mechanics, Materials and Structures, Budapest University of Technology and Economics, Budapest, Hungary email: vpeter@mit.bme.hu
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Abstract

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The dynamics of moving solids with unilateral contacts are often modelled by assuming rigidity, point contacts, and Coulomb friction. The canonical example of a rigid rod with one endpoint slipping in two dimensions along a fixed surface (sometimes referred to as Painlevé rod) has been investigated thoroughly by many authors. The generic transitions of that system include three classical transitions (slip-stick, slip reversal, and liftoff) as well as a singularity called dynamic jamming, i.e., convergence to a codimension 2 manifold in state space, where rigid body theory breaks down. The goal of this paper is to identify similar singularities arising in systems with multiple point contacts, and in a broader setting to make initial steps towards a comprehensive list of generic transitions from slip motion to other types of dynamics. We show that – in addition to the classical transitions – dynamic jamming remains a generic phenomenon. We also find new forms of singularity and solution indeterminacy, as well as generic routes from sliding to self-excited microscopic or macroscopic oscillations.

Keywords

Contact dynamicsfrictionrigid body dynamicssingularitypiecewise smooth systems37J5570F4070E1870K7070F35
Type
Papers
Information
European Journal of Applied Mathematics , Volume 29 , Special Issue 5: Theory and applications of nonsmooth dynamical systems , October 2018 , pp. 778 - 804
Copyright
Copyright © Cambridge University Press 2018 

Footnotes

†This work was supported by Grant 124002 of the National Research, Development, and Innovation Office of Hungary.

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