Energy dissipation and hysteresis cycles in pre-sliding transients of kinetic friction

Michael Ruderman

Applications of Mathematics (2023)

  • Volume: 68, Issue: 6, page 845-860
  • ISSN: 0862-7940

Abstract

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The problem of transient hysteresis cycles induced by the pre-sliding kinetic friction is relevant for analyzing the system dynamics, e.g., of micro- and nano-positioning instruments and devices and their controlled operation. The associated energy dissipation and consequent convergence of the state trajectories occur due to the structural hysteresis damping of contact surface asperities during reversals, and it is neither exponential (i.e., viscous type) nor finite-time (i.e., Coulomb type). In this paper, we discuss the energy dissipation and convergence during the pre-sliding cycles and show how a piecewise smooth force-displacement hysteresis map enters into the energy balance of an unforced system of the second order. An existing friction modeling approach with a low number of the free parameters, the Dahl model, is then exemplified alongside the developed analysis.

How to cite

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Ruderman, Michael. "Energy dissipation and hysteresis cycles in pre-sliding transients of kinetic friction." Applications of Mathematics 68.6 (2023): 845-860. <http://eudml.org/doc/299430>.

@article{Ruderman2023,
abstract = {The problem of transient hysteresis cycles induced by the pre-sliding kinetic friction is relevant for analyzing the system dynamics, e.g., of micro- and nano-positioning instruments and devices and their controlled operation. The associated energy dissipation and consequent convergence of the state trajectories occur due to the structural hysteresis damping of contact surface asperities during reversals, and it is neither exponential (i.e., viscous type) nor finite-time (i.e., Coulomb type). In this paper, we discuss the energy dissipation and convergence during the pre-sliding cycles and show how a piecewise smooth force-displacement hysteresis map enters into the energy balance of an unforced system of the second order. An existing friction modeling approach with a low number of the free parameters, the Dahl model, is then exemplified alongside the developed analysis.},
author = {Ruderman, Michael},
journal = {Applications of Mathematics},
keywords = {hysteresis; friction; energy dissipation; nonlinear convergence; stick-slip cycles},
language = {eng},
number = {6},
pages = {845-860},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Energy dissipation and hysteresis cycles in pre-sliding transients of kinetic friction},
url = {http://eudml.org/doc/299430},
volume = {68},
year = {2023},
}

TY - JOUR
AU - Ruderman, Michael
TI - Energy dissipation and hysteresis cycles in pre-sliding transients of kinetic friction
JO - Applications of Mathematics
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 68
IS - 6
SP - 845
EP - 860
AB - The problem of transient hysteresis cycles induced by the pre-sliding kinetic friction is relevant for analyzing the system dynamics, e.g., of micro- and nano-positioning instruments and devices and their controlled operation. The associated energy dissipation and consequent convergence of the state trajectories occur due to the structural hysteresis damping of contact surface asperities during reversals, and it is neither exponential (i.e., viscous type) nor finite-time (i.e., Coulomb type). In this paper, we discuss the energy dissipation and convergence during the pre-sliding cycles and show how a piecewise smooth force-displacement hysteresis map enters into the energy balance of an unforced system of the second order. An existing friction modeling approach with a low number of the free parameters, the Dahl model, is then exemplified alongside the developed analysis.
LA - eng
KW - hysteresis; friction; energy dissipation; nonlinear convergence; stick-slip cycles
UR - http://eudml.org/doc/299430
ER -

References

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