Modeling dynamic or kinetic friction for realistic engineering surfaces continues to be a challenge, partly due to the coupling between system dynamics and interfacial forces. In this paper, a dynamic friction coefficient model for realistic rough surfaces under external normal vibrations is developed. From the system dynamic model, the instantaneous time varying normal separation at the interface is obtained under normal harmonic excitation. Subsequently, the instantaneous dynamic contact and tangential (friction) forces are calculated as a function of the instantaneous normal separation. The dynamic friction coefficient defined as the ratio of the time varying friction to the interfacial normal forces that explicitly includes interfacial damping, is also calculated. The results show that a mean increase in the instantaneous normal separation may or may not lead to a decrease of the mean friction force and the mean friction coefficient, which is supported by published data. For unlubricated elastic sliding contact conditions considered in this paper, the effect of damping on the dynamic friction coefficient is found to be negligible, whereas loss of contact causes significant apparent dynamic friction force and dynamic friction coefficient reductions. Several different interpretations of the time varying dynamic friction coefficient are presented and the implications of using a simple constant value to represent the time varying dynamic friction coefficient are discussed.

1.
da Vinci, L., Notebooks and Manuscripts, presented in the late 1400s, as described in 2.
2.
Dowson, D., 1998, History of Tribology, 2nd ed., Professional Engineering Publishers, London.
3.
Amontons, G., 1699, “On the Resistance Originating in Machines,” Proceedings of the French Royal Academy of Sciences, pp. 206–222.
4.
Coulomb, C. A., 1785, “The´orie des machines simples, en ayant e´gard au frottement deleurs parties, et a la roideur dews cordages,” Me´m. Math Phys., pp. 161–342.
5.
Armstrong-He´louvry, B., 1991, Control of Machines with Friction, Kluwer Academic Publishers, Boston.
6.
Booser, E. R., 1997, Tribology Data Handbook, CRC Press, Boca Raton.
7.
Blau
,
P. J.
,
2001
, “
The Significance and Use of the Friction Coefficient
,”
Tribol. Int.
,
34
, pp.
585
591
.
8.
Blau, P. J., 2001, “Experimental Aspects of Friction Research on the Macroscale,” in Fundamentals of and Bringing the Gap Between Macro- and Micro-/Nanoscale Tribology, B. Bhushan, ed., Dordrecht, Kluwer, pp. 261–278.
9.
Godfrey
,
D.
,
1967
, “
Vibration Reduces Metal to Metal Contact and Causes an Apparent Reduction in Friction
,”
ASLE Trans.
,
10
, pp.
183
192
.
10.
Tolstoi
,
D. M.
,
1967
, “
Significance of the Normal Degree of Freedom and Natural Normal Vibrations in Contact Friction
,”
Wear
,
10
(
3
), pp.
199
213
.
11.
Soom
,
A.
, and
Kim
,
C.
,
1983
, “
Roughness-Induced Dynamic Loading at Dry and Boundary-Lubricated Sliding Contacts
,”
ASME J. Lubr. Technol.
,
105
, pp.
514
517
.
12.
Martins
,
J. A. C.
,
Oden
,
J. T.
, and
Simoes
,
F. M. F.
,
1990
, “
A Study of Static and Kinetic Friction
,”
Int. J. Eng. Sci.
,
28
, pp.
29
92
.
13.
Hess
,
D. P.
, and
Soom
,
A.
,
1991
, “
Normal Vibrations and Friction Under Harmonic Loads: Part I: Hertzian Contacts
,”
ASME J. Tribol.
,
113
, pp.
80
86
.
14.
Hess
,
D. P.
, and
Soom
,
A.
,
1991
, “
Normal Vibrations and Friction Under Harmonic Loads: Part II: Rough Planar Contacts
,”
ASME J. Tribol.
,
113
, pp.
87
92
.
15.
Hess, D. P., and Soom, A., 1992, “Unsteady Friction in the Presence of Vibrations,” in Fundamentals of Friction: Microscopic and Microscopic Processes, I. Singer, and H. Pollock, eds., Kluwer Academic Press, pp. 535–552.
16.
Budanov
,
B. V.
,
Kudinov
,
V. A.
, and
Tolstoi
,
D. M.
,
1980
, “
Interaction of Friction and Vibration
,”
Trenie Iznos
,
1
(
1
), pp.
79
89
.
17.
Soom, A., and Chopra, A., 2001, “In Search of Dynamic Effects in Dry Sliding Friction,” in Tribology Research: From Model Experiment to Industrial Problem, G. Dalmaz, A. A. Lubrecht, D. Dowson, and M. Priest, Eds., Elsevier, pp. 55–59.
18.
Tariku
,
F. A.
, and
Rogers
,
R. J.
,
2001
, “
Improved Dynamic Friction Models for Simulation of One-Dimensional and Two-Dimensional Stick-Slip Motion
,”
ASME J. Tribol.
,
123
, pp.
661
669
.
19.
Polycarpou
,
A. A.
, and
Soom
,
A.
,
1996
, “
A Two-Component Mixed Friction Model for a Lubricated Line Contact
,”
ASME J. Tribol.
,
118
, pp.
183
189
.
20.
Greenwood
,
J. A.
, and
Williamson
,
J. B. P.
,
1966
, “
Contact of Nominally Flat Surfaces
,”
Proc. R. Soc. London, Ser. A
,
A295
, pp.
300
319
.
21.
Johnson, K. L., 2001, “Dynamic Friction,” in Tribology Research: From Model Experiment to Industrial Problem, G. Dalmaz, A. A. Lubrecht, D. Dowson, and M. Priest, eds., Elsevier, pp. 37–45.
22.
Sakamoto
,
T.
,
1987
, “
Normal Displacement and Dynamic Friction Characteristics in a Stick-Slip Process
,”
Tribol. Int.
,
20
, pp.
25
31
.
23.
Tabor
,
D.
,
1981
, “
Friction—The Present State of Our Understanding
,”
ASME J. Lubr. Technol.
,
103
, pp.
169
179
.
24.
Tabor
,
D.
,
1991
, “
Friction, Surface Science and Tribology—A Personal View
,”
Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
,
205
, pp.
365
378
.
25.
Tabor
,
D.
,
1995
, “
Tribology—The Last 25 Years: A Personal View
,”
Tribol. Int.
,
28
(
1
), pp.
7
10
.
26.
Chang
,
W. R.
,
Etsion
,
I.
, and
Bogy
,
D. B.
,
1987
, “
An Elastic-Plastic Model for the Contact of Rough Surfaces
,”
ASME J. Tribol.
,
109
, pp.
257
263
.
27.
Chang
,
W. R.
,
Etsion
,
I.
, and
Bogy
,
D. B.
,
1988
, “
Adhesion Model for Metallic Rough Surfaces
,”
ASME J. Tribol.
,
110
, pp.
50
56
.
28.
Chang
,
W. R.
,
Etsion
,
I.
, and
Bogy
,
D. B.
,
1988
, “
Static Friction Coefficient Model for Metallic Rough Surfaces
,”
ASME J. Tribol.
,
110
, pp.
57
63
.
29.
Derjaguin
,
B. V.
,
Muller
,
V. M.
, and
Toporov
,
Y. P.
,
1975
, “
Effect of Contact Deformations on the Adhesion of Particles
,”
J. Colloid Interface Sci.
,
53
, pp.
314
326
.
30.
Hamilton
,
G. M.
,
1983
, “
Explicit Equations for the Stresses Beneath a Sliding Contact
,”
Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
,
197
(
C
), pp.
53
59
.
31.
Pollock, H. M., 1992, “Surface Forces and Adhesion,” in Fundamentals of Friction: Microscopic and Microscopic Processes, I. Singer, and H. Pollock, eds., Kluwer Academic press, pp. 77–94.
32.
Huang
,
W.
,
Bogy
,
D. B.
, and
Honchi
,
M.
,
2000
, “
An Asperity Contact Model for the Slider Air Bearing
,”
ASME J. Tribol.
,
122
, pp.
436
443
.
33.
Yu
,
N.
, and
Polycarpou
,
A. A.
,
2002
, “
Contact of Rough Surfaces With Asymmetric Distribution of Asperity Heights
,”
ASME J. Tribol.
,
124
, pp.
367
376
.
34.
Polycarpou
,
A. A.
, and
Polycarpou
,
A. A.
,
1999
, “
Analytical Approximations in Modeling Contacting Rough Surfaces
,”
ASME J. Tribol.
,
121
, pp.
234
239
.
35.
Patel, J. J., 2001, “Investigation of the Scuffing Mechanism Under Starved Lubrication Conditions Using Macro, Meso, Micro and Nano Analytical Techniques,” M.S. thesis, University of Illinois at Urbana-Champaign.
36.
Soom
,
A.
, and
Chen
,
Jern-Wen
,
1986
, “
Simulation of Random Surface Roughness-Induced Contact Vibrations at Hertzian Contacts During Steady Sliding
,”
ASME J. Tribol.
,
108
, pp.
123
127
.
37.
Proakis, J. G., and Manolakis, D. G., 1996, Digital Signal Processing: Principles, Algorithms, and Applications, Englewood Cliffs, NJ, Prentice Hall.
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