This paper presents a method for estimating Coulomb and viscous friction coefficients from responses of a harmonically excited dual-damped oscillator with linear stiffness. The identification method is based on existing analytical solutions of non-sticking responses excited near resonance. The method is applicable if the damping ratio of viscous component can be considered small. The Coulomb and viscous friction parameters can be extracted from two or more input-output amplitude pairs at resonance. The method is tested numerically and experimentally. Experimental results are cross checked with estimations from free-vibration decrements and also from friction measurements.
Issue Section:
Technical Papers
1.
Den Hartog
, J. P.
, 1931
, “Forced Vibration with Combined Coulomb and Viscous Damping
,” Trans. ASME
, 53
, pp. 107
–115
.2.
Hundal
, M. S.
, 1979
, “Response of a Base Excited System with Coulomb and Viscous Friction
,” J. Sound Vib.
, 64
, pp. 371
–378
.3.
Jacobsen, L. S., and Ayre, R. S., 1958, Engineering Vibrations, McGraw-Hill, New York.
4.
Helmholtz, H. L. F., 1877, On the Sensations of Tone as Physiological Basis for the Theory of Music, translation by A. J. Ellis of Die Lehre von den Tonempfindungen, fourth edition; first edition published in 1863, Dover, New York, pp. 406.
5.
Rayleigh, Lord, 1877, The Theory of Sound, Vol. 1, reprinted by Dover, New York, 1945, pp. 46–51.
6.
Lorenz, H., 1924, Lehrbuch der Technischen Physik Erster Band: Technische Mechanik Starrer Gebilde, Verlag von Julius Springer, Berlin.
7.
Watari, A., 1969, Kikai-rikigaku, Kyouritsu (publisher).
8.
Feeny
, B. F.
, and Liang
, J.-W.
, 1996
, “A Decrement Method for the Simultaneous Estimation of Coulomb and Viscous Friction
,” J. Sound Vib.
, 195
(1
), pp. 149
–154
.9.
Liang
, J.-W.
, and Feeny
, B. F.
, 1998
, “Identifying Coulomb and Viscous Friction from Free-Vibration Decrements
,” Nonlinear Dyn.
, 16
, pp. 337
–347
.10.
Tomlinson
, G. R.
, and Hibbert
, J. H.
, 1979
, “Identification of the Dynamic Characteristics of a Structure with Coulomb Friction
,” J. Sound Vib.
, 64
(2
), pp. 233
–242
.11.
Tomlinson
, G. R.
, 1980
, “An Analysis of the Distortion Effects of Coulomb Damping on the Vector Plots of Lightly Damped System
,” J. Sound Vib.
, 71
(3
), pp. 443
–451
.12.
Chen
, Q.
, and Tomlinson
, G. R.
, 1996
, “Parametric Identification of Systems with Dry Friction and Nonlinear Stiffness Using a Time Series Model
,” ASME J. Vibr. Acoust.
, 118
, pp. 252
–263
.13.
Iourtchenko
, D. V.
, and Dimentberg
, M. F.
, 2002
, “In-service Identification of Nonlinear Damping from Measured Random Vibration
,” J. Sound Vib.
, 255
(3
), pp. 549
–554
.14.
Dimentberg, M. F., 1968, “Determination of Nonlinear Damping Function From Forced Vibration Test of a SDOF System,” Mechanica Tverdogo Tela, N.2, pp. 32–34 (in Russian).
15.
Iourtchenko, D. V., Duval, L., and Dimentberg, M. F., 2002, “The Damping Identification for Certain SDOF Systems,” Proceedings of the SECTAM-XX, Developments in Theoretical and Applied Mechanics, April 16–18, Callaway Gardens, Pine Mountain, GA, pp. 535–538.
16.
Stanway
, R.
, Sproston
, J. L.
, and Stevens
, N. G.
, 1985
, “A Note on Parameter Estimation in Nonlinear Vibrating Systems
,” Proc. Inst. Mech. Eng., Part C: Mech. Eng. Sci.
, 199
(C1
), pp. 79
–84
.17.
Yao
, G. Z.
, Meng
, G.
, and Fang
, T.
, 1997
, “Parameter Estimation and Damping Performance of Electro-Rheological Dampers
,” J. Sound Vib.
, 204
(4
), pp. 575
–584
.18.
Shaw
, S. W.
, 1986
, “On the Dynamic Response of a System with Dry Friction
,” J. Sound Vib.
, 108
(2
), pp. 305
–325
.19.
Marui
, E.
, and Kato
, S.
, 1984
, “Forced Vibration of a Base-Excited Single-Degree-of-Freedom System with Coulomb Friction
,” ASME J. Dyn. Syst., Meas., Control
, 106
, pp. 280
–285
.20.
THK, 1996, “Linear Motion System,” THK Co., Ltd., Catalog No. 200-1AE, Tokyo, Japan.
21.
Yeaple
, F.
, 1986
, “Precision Linear Bearings Speed Up Chip Handler
,” Des. News
, 42
(18
), pp. 86
–87
, USA.22.
Culley
, S. J.
, and van Raalte
, N. J.
, 1991
, “The Modeling of Linear Motion Systems at the Design Concept Stage
,” J. Eng. Design
2
(4
), pp. 303
–319
, UK.23.
Anon
, 1994
, “Linear Motion Systems
,” Industrial Lubrication and Tribology
, 46
(6
), pp. 12
–21
.24.
Liang
, J.-W.
, and Feeny
, B. F.
, 1998
, “A Comparison between Direct and Indirect Friction Measurements in a Forced Oscillator
,” ASME J. Appl. Mech.
, 65
(3
), pp. 783
–786
.25.
Antoniou
, S. S.
, Cameron
, A.
, and Gentle
, C. R.
, 1976
, “The Friction-Speed Relation from Stick-Slip Data
,” Wear
, 36
, pp. 235
–254
.26.
Liang, J.-W., 1996, “Characterizing the Low-Order Friction Dynamics in a Forced Oscillator,” Ph.D. Thesis, Michigan State University, East Lansing, MI.
27.
Liang
, J.-W.
, and Feeny
, B. F.
, 1998
, “Dynamical Friction Behavior in a Forced Oscillator with a Compliant Contact
,” ASME J. Appl. Mech.
, 65
(1
), pp. 250
–257
.28.
Hinrichs
, N.
, Osetreich
, M.
, and Popp
, K.
, 1998
, “On the Modeling of Friction Oscillator
,” J. Sound Vib.
, 216
(3
), pp. 435
–459
.29.
Harnoy
, A.
, Friedland
, B.
, and Rachor
, H.
, 1994
, “Modeling and Simulation of Elastic and Friction Force in Lubricated Bearing for Precise Motion Control
,” Wear
, 172
, pp. 155
–165
.30.
McMillan
, A. J.
, 1997
, “A Non-Linear Friction Model for Self-Excited Vibration
,” J. Sound Vib.
, 205
(3
), pp. 323
–335
.31.
Kappagantu
, R. V.
, and Feeny
, B. F.
, 2000
, “Part 1: Dynamical Characterization of a Frictionally Excited Beam
,” Nonlinear Dyn.
, 22
(4
), pp. 317
–333
.32.
Ibrahim
, R. A.
, 1994
, “Friction-Induced Vibration, Chatter, Squeal and Chaos
,” Appl. Mech. Rev.
, 47
(7
), pp. 209
–253
.33.
Kappagantu
, R. V.
, and Feeny
, B. F.
, 2000
, “Part 2: Proper Orthogonal Modal Modeling of a Frictionally Excited Beam
,” Nonlinear Dyn.
, 23
(1
), pp. 1
–11
.34.
Griffin
, J. H.
, 1980
, “Friction Damping of Resonant Stresses in Gas Turbine Engine Airfoils
,” ASME J. Eng. Power
, 102
, pp. 329
–333
.35.
Wang, J.-H., 1996, “Design of a Friction Damper to Control Vibration of Turbine Blades,” Dynamics with Friction: Modeling, Analysis, and Experiments, A. Guran, F. Pfeiffer, and K. Popp, eds., World Scientific, Singapore, pp. 169–195.
36.
Wang
, Y.
, 1996
, “An Analytical Solution for Periodic Response of Elastic-Friction Damped Systems
,” J. Sound Vib.
, 189
(3
), pp. 299
–313
.37.
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, ASME DE-Vol. 91, pp. 41–50.
38.
Sanliturk
, K. Y.
, and Ewins
, D. J.
, 1996
, “Modeling Two-Dimensional Friction Contact and its Application Using Harmonic Balance Method
,” J. Sound Vib.
, 193
(2
), pp. 511
–524
.39.
Ferri
, A. A.
, and Heck
, B. S.
, 1998
, “Vibration Analysis of Dry Friction Damped Turbine Blades Using Singular Perturbation Theory
,” ASME J. Vibr. Acoust.
, 120
(2
), pp. 588
–595
.40.
Hess
, D. P.
, and Soom
, A.
, 1990
, “Friction at a Lubricated Line Contact Operating at Oscillating Sliding Velocities
,” ASME J. Tribol.
, 112
, pp. 147
–152
.41.
Rice
, J. R.
, and Ruina
, A. L.
, 1983
, “Stability of Steady Friction Slipping
,” ASME J. Appl. Mech.
, 50
, pp. 343
–349
.42.
Dieterich, J. H., 1991, “Micro-mechanics of Slip Instabilities with Rate- and State-Dependent Friction,” Volume Fall Meeting Abstract, Vol. 324, Eos, Trans., Am. Geophys. Union.
43.
Ruina, A., 1980, “Friction Laws and Instabilities: A Quasistatic Analysis of Some Dry Frictional Behavior,” PhD Thesis, Division of Engineering, Brown University.
44.
Canudas de Wit
, C.
, Olsson
, H.
, Astrom
, K. J.
, Lischinsky
, P.
, 1995
, “A New Model for Control of Systems with Friction
,” IEEE Trans. Autom. Control
, 40
(3
), pp. 419
–425
.45.
Haessig
, D. A.
, and Friedland
, B.
, 1991
, “On the Modeling and Simulation of Friction
,” ASME J. Dyn. Syst., Meas., Control
, 113
, pp. 354
–362
.46.
Oden
, J. T.
, and Martins
, J. A. C.
, 1985
, “Models and Computational Methods for Dynamic Friction Phenomena
,” Comput. Methods Appl. Mech. Eng.
, 52
(1–3
), pp. 527
–634
.47.
Tolstoi
, D. M.
, 1967
, “Significance of the Normal Degree of Freedom and Natural Normal Vibrations in Contact Friction
,” Wear
, 10
, pp. 199
–213
.48.
Dankowicz
, H.
, 1999
, “On the Modeling of Dynamic Friction Phenomena
,” Zeitschrift fuer angewandte Mathematik und Mechanik
, 79
(6
), pp. 399
–409
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