This paper presents the stability analysis of a system sliding at low velocities (<100 μm⋅s−1) under a periodically modulated normal load, preserving interfacial contact. Experiments clearly evidence that normal vibrations generally stabilize the system against stick-slip oscillations, at least for a modulation frequency much larger than the stick-slip one. The mechanical model of L. Bureau, T. Baumberger, and C. Caroli validated on the steady-state response of the system, is used to map its stability diagram. The model takes explicitly into account the finite shear stiffness of the load-bearing asperities, in addition to a classical state and rate-dependent friction force. The numerical results are in excellent quantitative agreement with the experimental data obtained from a multicontact frictional system between glassy polymer materials. Simulations at larger amplitude of modulation (typically 20 percent of the mean normal load) suggest that the nonlinear coupling between normal and sliding motion could have a destabilizing effect in restricted regions of the parameter space.

1.
Dieterich
,
J. H.
,
1979
, “
Modeling of Rock Friction 1. Experimental Results and Constitutive Equations
,”
J. Geophys. Res.
,
84
, pp.
2161
2168
.
2.
Rice
,
J. R.
, and
Ruina
,
A. L.
,
1983
, “
Stability of Steady Frictional Slipping
,”
ASME J. Appl. Mech.
,
105
, pp.
343
349
.
3.
Rabinowicz, E., 1965, Friction and Wear of Materials, John Wiley and Sons, New York.
4.
Heslot
,
F.
,
Baumberger
,
T.
,
Perrin
,
B.
,
Caroli
,
B.
, and
Caroli
,
C.
,
1994
, “
Creep, Stick-Slip, and Dry Friction Dynamics: Experiments and a Heuristic Model
,”
Phys. Rev. E
,
49
, pp.
4973
4988
.
5.
Baumberger
,
T.
,
Berthoud
,
P.
, and
Caroli
,
C.
,
1999
, “
Physical Analysis of the State- and Rate-Dependent Friction Law: II. Dynamic Friction
,”
Phys. Rev. B
,
60
, pp.
3928
3939
.
6.
Ronsin
,
O.
, and
Labastie-Coueyrehourcq
,
K.
,
2001
, “
State, Rate and Temperature-Dependent Sliding Friction of Elastomers
,”
Proc. R. Soc. London, Ser. A
,
457
, pp.
1277
1294
.
7.
Berthoud
,
P.
,
Baumberger
,
T.
,
G’Sell
,
C.
, and
Hiver
,
J.-M.
,
1999
, “
Physical Analysis of the State- and Rate-Dependent Friction Law: Static Friction
,”
Phys. Rev. B
,
59
, pp.
313
14
.
8.
Dieterich
,
J. H.
, and
Kilgore
,
D.
,
1994
, “
Direct Observation of Frictional Contacts: New Insights for State-Dependent Properties
,”
Pure Appl. Geophys.
,
43
, pp.
283
302
.
9.
Greenwood
,
J. A.
, and
Williamson
,
J. B. P.
,
1966
, “
Contact of Nominally Flat Surfaces
,”
Proc. R. Soc. London, Ser. A
,
295
, pp.
300
319
.
10.
Baumberger
,
T.
,
Caroli
,
C.
,
Perrin
,
B.
, and
Ronsin
,
O.
,
1995
, “
Nonlinear Analysis of the Stick-Slip Bifurcation in the Creep-Controlled Regime of Dry Friction
,”
Phys. Rev. E
,
51
, pp.
4005
4010
.
11.
Bowden, F. P., and Tabor, D., 1950, Friction and Lubrication of Solids, Clarendon, Oxford, UK.
12.
Dupont
,
P. E.
, and
Bapna
,
D.
,
1994
, “
Stability of Sliding Frictional Surfaces With Varying Normal Force
,”
ASME J. Vibr. Acoust.
,
116
, pp.
237
242
.
13.
Linker
,
M.
, and
Dieterich
,
J. H.
,
1992
, “
Effects of Variable Normal Stress on Rock Friction: Observations and Constitutive Equations
,”
J. Geophys. Res.
,
124
, pp.
445
485
.
14.
Perfettini
,
H.
,
Schmittbuhl
,
J.
,
Rice
,
J. R.
, and
Cocco
,
M.
,
2001
, “
Frictional Response Induced by Time-Dependent Fluctuations of the Normal Loading
,”
J. Geophys. Res.
,
106
(
B7
), pp.
455
13
.
15.
Richardson
,
E.
, and
Marone
,
C.
,
1999
, “
Effects of Normal Stress Vibrations on Frictional Heating
,”
J. Geophys. Res.
,
104
, pp.
859
28
.
16.
Akay
,
A.
,
2002
, “
Acoustics of Friction
,”
J. Acoust. Soc. Am.
,
111
, pp.
1525
1548
, and references therein.
17.
Polycarpou
,
A. A.
, and
Soom
,
A.
,
1995
, “
Boundary and Mixed Friction in the Presence of Dynamic Normal Loads: Part II—Friction Transients
,”
ASME J. Tribol.
,
117
, pp.
261
266
.
18.
Bureau
,
L.
,
Baumberger
,
T.
, and
Caroli
,
C.
,
2000
, “
Shear Response of a Frictional Interface to a Normal Load Modulation
,”
Phys. Rev. E
,
62
, pp.
6810
6820
.
19.
Baumberger
,
T.
,
Bureau
,
L.
,
Busson
,
M.
,
Falcon
,
E.
, and
Perrin
,
B.
,
1998
, “
An Inertial Tribometer for Measuring Microslip Dissipation at a Solid-Solid Multicontact Interface
,”
Rev. Sci. Instrum.
,
69
, pp.
2416
2420
.
20.
Berthoud
,
P.
, and
Baumberger
,
T.
,
1998
, “
Shear Stiffness of a Solid-Solid Multicontact Interface
,”
Proc. R. Soc. London, Ser. A
,
454
, pp.
1615
1634
.
21.
Feudel
,
U.
, and
Jansen
,
W.
,
1992
, “
CANDYS/QA—A Software System for the Qualitative Analysis of Nonlinear Dynamical Systems
,”
Int. J. Bifurcation Chaos Appl. Sci. Eng.
,
2
, pp.
773
794
. See also http://www.agnld.uni-potsdam.de/wolfgang/wolfgang.html
22.
Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P., 1992, Numerical Recipes, Cambridge University Press, Cambridge, UK.
23.
Baumberger
,
T.
, and
Gauthier
,
L.
,
1996
, “
Relaxation at the Interface Between Rough Solids Under Shear
,”
J. Phys. I
,
6
, pp.
1021
1025
.
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