Contact compliance, which may arise from elastic deformation near the contact point or in the surrounding structure, affects the dynamical friction behaviors in mechanical oscillators. An idealized model consisting of a mass sliding harmonically on a mass-less compliant contact produces hysteresis in friction-velocity plots. Dynamical friction features, depending on the contact stiffness, friction level, and the frequency and amplitude of oscillation, are predicted and quantified. Contact compliance can also lead to oscillations at the transition from slip to stick. Experiments and simulations verify the model and tie together phenomena of both continuous sliding and stick-slip.

Issue Section:
Technical Papers
Topics:
Friction, Oscillations, Deformation, Simulation, Stick-slip, Stiffness
1.
Canudas de Wit
C.
,
Olsson
H.
,
Astrom
K. J.
, and
Lischinsky
,
1995
, “
A New Model for Control of System with Friction
,”
IEEE Transactions on Automatic Control
, Vol.
40
, No.
3
, pp.
419
–
425
.
2.
Cattaneo
C.
,
1938
, “
Sul Contatto di due Corpi Elastici
,”
Accademia dei Lincei, Rendiconti
, Series 6, Vol.
27
, pp.
342
–
348
.
3.
Cetinkunt, S., and Donmez, A., 1993, “CMAC Learning Controller for Servo Control of High Precision Machine Tools,” Proceedings of the American Control Conference, IEEE, San Francisco, pp. 1976–1980.
4.
Chung, Y.-W., 1993, “Characterization of Topography of Engineering Surfaces,” Surface Diagnostics in Tribology, K. Miyoshi and Y.-W. Chung, eds., World Scientific, Singapore, pp. 33–46.
5.
Courtney-Pratt
J.
, and
Eisner
E.
,
1957
, “
The Effect of a Tangential Force on the Contact of Metallic Bodies
,”
Proceedings of the Royal Society of London
, Vol.
A238
, pp.
529
–
550
.
6.
Dahl, P., 1968, “A Solid Friction Model,” Tech. Rep. Tor-0158(3197–18)–1, Aerospace Corp., El Segundo, CA.
7.
Dugas, R., 1955, A History of Mechanics, E´ditions du Griffon, Neuchaˆtel.
8.
Feeny
B. F.
,
1992
, “
A Nonsmooth Coulomb Friction Oscillator
,”
Physica D
, Vol.
59
, pp.
25
–
38
.
9.
Feeny
B. F.
, and
Moon
F. C.
,
1994
, “
Chaos in a Forced Dry-Friction Oscillator: Experiments and Numerical Modelling
,”
Journal of Sound and Vibration
, Vol.
170
, No.
3
, pp.
303
–
323
.
10.
Ferri
A. A.
,
1995
, “
Friction Damping and Isolation Systems
,”
Journal of Mechanical Design
, Vol.
117(B)
, pp.
196
–
206
.
11.
Ferri, A. A., and Heck, B. S., 1997, “Vibration Analysis of Dry Damped Turbine Blades Using Singular Perturbation Theory,” Journal of Vibration and Acoustics, to appear.
12.
Guillen
J.
, and
Pierre
C.
,
1996
, “
Analysis of the Forced Response of Dry-Friction Damped Structural Systems Using an Efficient Hybrid Frequency-Time Method
,”
Nonlinear Dynamics and Controls
, DE-Vol.
91
, pp.
41
–
50
.
13.
Griffin
J. H.
,
1980
, “
Friction Damping of Resonant Stresses in Gas Turbine Engine Airfoils
,”
Journal of Engineering for Power
, Vol.
102
, pp.
329
–
333
.
14.
Harnoy
A.
,
Friedland
B.
, and
Rachoor
H.
,
1994
, “
Modeling and Simulation of Elastic and Friction Forces in Lubricated Bearing for Precise Motion Control
,”
Wear
, Vol.
172
, pp.
155
–
165
.
15.
Hinrichs, N., Oestreich, M., and Popp., K., 1997, “Friction-Induced Vibrations: Experiments, Modeling and Analysis,” ASME Design Engineering Technical Conferences, Sacramento, in press.
16.
Ibrahim
R. A.
,
1994
, “
Friction-Induced Vibration, Chatter, Squeal and Chaos
,”
ASME Applied Mechanics Reviews
, Vol.
47
, No.
7
, pp.
209
–
253
.
17.
Kappagantu, R., 1997, An “Optimal” Modal Reduction of Systems with Frictional Excitation, Ph.D. thesis, Michigan State University, East Lansing, MI.
18.
Ko, P. L., and Brockley, C. A., 1970, “The Measurement of Friction and Friction-Induced Vibration,” Journal of Lubrication Technology, Oct., pp. 543–549.
19.
Liang
J.-W.
, and
Feeny
B. F.
,
1996
, “
The Effects of Tangential Contact Stiffness on a Harmonically Forced Oscillator
,”
Elasto-Impact and Friction in Dynamic Systems, A. A. Ferri, G. T. Flowers, and S. C. Sinha, eds., ASME
DE-Vol.
90
, pp.
85
–
96
.
20.
Marui
E.
, and
Kato
S.
,
1984
, “
Forced Vibration of a Base-Excited Single-Degree-of-Freedom System With Coulomb Friction
,”
ASME Journal of Dynamical Systems, Measurement, and Control
, Vol.
106
, pp.
280
–
285
.
21.
Mindlin
R. D.
,
1949
, “
Compliance of Elastic Bodies in Contact
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
16
, pp.
259
–
268
.
22.
Mindlin
R. D.
, and
Deresiewiez
H.
,
1953
, “
Elastic Spheres in Contact Under Varying Oblique Forces
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
20
; pp.
327
–
344
.
23.
Oancea, V. G., and Laursen, T. A., 1996, “Experimental and Numerical Study of Low Frequency Stick-Slip Motion,” Sixth Conference on Nonlinear Vibrations, Stability, and Dynamics of Structures, Blacksburg, VA, June 9–13.
24.
Oden
J. T.
, and
Martins
J. A. C.
,
1985
, “
Models and Computational Methods for Dynamic Friction Phenomena
,”
Computer Methods in Applied Mechanics and Engineering
, Vol.
52
, Nos.
1–3
, pp.
527
–
634
.
25.
Polycarpou
A.
, and
Soom
A.
,
1992
, “
Transitions Between Sticking and Slipping
,”
Friction-Induced Vibration, Chatter, Squeal, and Chaos, ASME
DE-Vol.
49
, pp.
139
–
148
.
26.
Rorrer
R. A. L.
,
1995
, “
Friction-Induced Vibration of Multi-Degree of Freedom Sliding Subsystems
,”
ASME Design Engineering Technical Conference 3-A, Boston, Sept.
, DE-Vol.
84–l
, pp.
1179
–
1186
.
27.
Ruina, A. L., 1985, “Constitutive Relations for Frictional Slip,” Mechanics of Geomaterials, Z. Bazant, ed., John Wiley and Sons, pp. 169–188.
28.
Sanliturk
K. Y.
, and
Ewins
D. J.
,
1996
, “
Modeling Two-Dimensional Friction Contact and its Application Using Harmonic Balance Method
,”
Journal of Sound and Vibration
, Vol.
193
, No.
2
, pp.
511
–
524
.
29.
Shaw
S. W.
,
1986
, “
On the Dynamic Response of a System with Dry Friction
,”
Journal of Sound and Vibration
, Vol.
108
, No.
2
, pp.
305
–
325
.
30.
Threlfall
D. C.
,
1978
, “
The Inclusion of Coulomb Friction in Mechanisms Programs with Particular Reference to DRAM
,”
Mechanisms and Machine Theory
, Vol.
13
, pp.
475
–
483
.
31.
Vielsack
P.
,
1996
, “
Regularisierung des Halftzustandes bei Coulombscher Reibung
,”
Zeitschrift fu¨r angewandte Mathematik und Mechanik
, Vol.
76
, No.
8
, pp.
439
–
446
.
32.
Wang, J.-H., 1996, “Design of a Friction Damper to Control Vibration of Turbine Blades,” Dynamics with Friction: Modeling, Analysis, and Experiment, A. Guran, F. Pfeiffer, and K. Popp, eds., World Scientific, Singapore, pp. 169–195.
33.
Wang
J.-H.
, and
Chen
W. K.
,
1993
, “
Investigation of the Vibration of a Blade with Friction Damper by HBM
,”
Journal of Engineering for Gas Turbines and Power
, Vol.
115
, pp.
294
–
299
.
34.
Wang
Y.
,
1996
, “
An Analytical Solution for Periodic Response of Elastic-Friction Damped Systems
,”
Journal of Sound and Vibration
, Vol.
189
, No.
3
, pp.
299
–
313
.
This content is only available via PDF.
Copyright © 1998
 by The American Society of Mechanical Engineers
You do not currently have access to this content.