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REVIEW ARTICLES

Friction modeling for dynamic system simulation

[+] Author and Article Information
EJ Berger

CAE Laboratory, Department of Mechanical, Industrial, and Nuclear Engineering, University of Cincinnati, PO Box 210072, Cincinnati, OH 45221-0072ed.berger@uc.edu

Appl. Mech. Rev 55(6), 535-577 (Oct 16, 2002) (43 pages) doi:10.1115/1.1501080 History: Online October 16, 2002
Copyright © 2002 by ASME
Topics: Friction , Force
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Figures

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Notation for parameter-dependent friction: a) velocity dependence, b) dwell time dependence, c) time lag, d) pre-slip displacement
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Contact system showing angular deflection for Vo≠0 (due to friction asymmetry)
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Schematic of Mindlin (partial slip) result for nominal Hertzian contact: contact half-width a and stick zone half-width c<a
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Variation of fatigue life in fretting contacts as a function of a) interface slip displacement ux and b) applied normal load Fn (after Vingsbo and Söderberg 110, Figs. 10 and 11 respectively)
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Lumped-parameter models for friction contact: a) macroslip (bilinear hysteresis) element, b) Iwan parallel-series model, c) Iwan series-parallel model
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Single-dof stick-slip oscillations, two possible cases: a) single-dof forced system, b) short stick response, c) long stick response
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SFA experiment schematic showing glass substrate, epoxy, and atomically-smooth mica sheets
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AFM experiment schematic: a) AFM cantilever and tip, with incident light for displacement measurement, b) AFM cantilever deformed shape
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Atomic-scale stick-slip response
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Single-dof structural model for study of self-excited problems
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Velocity-dependent friction curve showing dependence upon three independent parameters (μo1,α)
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Stability map for velocity-dependent friction and single-dof structural model
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Stability map for velocity-dependent friction and single-dof structural model, with time-dependent normal force: a) ε=0.001,b) ε=0.01
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Step-plus-evolutionary response of state-variable friction laws to step changes in sliding velocity
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Stability map in the (S⁁,V⁁,f⁁) parameter space: a family of stability boundaries (solid lines) above which the steady-sliding response is unstable; response is unconditionally unstable above dashed line
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Lumped-parameter (viscoelastic) model for rate- and state-dependent friction
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Stick-slip response: a) time history, b) phase plane
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Time response of friction coefficient in stick-slip oscillations
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Sample calculations from Shaw 135 showing frequency response of stick-slip oscillations with continuous amplitude curve through the stick-slip boundary
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Smoothing of friction discontinuity using an arctan-type approximation: mutli-valued friction at zero relative velocity (and therefore inclusion of true sticking) is neglected
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Three continuous systems with different boundary friction conditions: a) coulomb friction support, b) in-plane displacement-dependent normal force, c) out-of-plane displacement-dependent normal force (schematic from Ferri and Bindemann 144)
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Schematic of result from Ferri and Bindemann 144 showing hardening behavior with increasing contact angle (case II from Fig. 21b)
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Calibration of lumped-parameter partial slip models using monotonic loading and a collocation procedure at discrete points xcr,i (monotonic loading)
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Cyclic loading behavior of lumped-parameter partial slip models showing hysteresis (single-element model of Fig. 5a, multi-element model of Fig. 5b); pre-slip displacement for single-element model is shown
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Single-dof structural model with bilinear hysteresis friction damper
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Steady-state response x⁁(τ) under single-frequency excitation; damper sticks more than one-half of the time per forcing cycle yet x⁁(τ) is substantially harmonic
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Steady-state response amplitude X⁁ss and time-averaged percent sticking per forcing cycle variations with coupling parameter γ
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Damper mass effects on steady-state forced response. An example result from Ferri and Heck 137 showing a qualitative difference in predictions for massless (bilinear hysteresis) and non-zero-mass models.
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The Menq-Griffin two elastic bar partial slip model
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Menq-Griffin partial slip model characteristics (F1<F2<F3<F4)
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Comparison of Menq-Griffin partial slip model and bilinear hystersis model under monotonic loading
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Break-away behavior of elastic block on rigid support under monotonically-increasing tangential load; inset: schematic of system geometry and loading
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Comparison of friction modeling approaches against key performance criteria: ability to capture relevant problem physics, computational efficiency, and model fidelity

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