Dry Friction with Various Frictions Laws: From Wave Modulated Orbit to Stick-Slip Modulated


Choices of excitation signals are important in engineering sciences and in physical simulations; a sufficient excitation can be critical in modelling a complicated nonlinear dynamic system. The discontinuous dynamic of a non-linear, friction-induced with two idealized periodical forced oscillators is studied. The dry friction in the system follows the classical Coulomb law, and various friction characteristics of dry friction laws in engineering sciences. To capture the presence of the two driving forces, the system must be studied as a function of their frequency-modulated and its equivalent amplitude modulated waveforms. Our numerical investigation shows a rich dynamical behaviour including periodic, quasi-periodic motions, thus a variable dynamics phenomenon among others; such as modulated waves, modulated stick-slip, periodic oscillation, and periodic stick-slip. It seems that such excitation forces can be used to conveniently identify the existence of nonlinearity, dry friction effects, and strength degradation in the system. The results achieved via the Coulomb’s law are compared with those obtained via two others particular friction laws: the complete model with Stribeck effect and Coulomb viscosity.

Share and Cite:

Kluge, P. , Germaine, D. and Crépin, K. (2015) Dry Friction with Various Frictions Laws: From Wave Modulated Orbit to Stick-Slip Modulated. Modern Mechanical Engineering, 5, 28-40. doi: 10.4236/mme.2015.52004.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Ewins, D.J. (2001) Modal Testing: Theory, Practice and Application, Mechanical Engineering Research, Studies Engineering Design Series. Research Studies Pre, 2nd Edition.
[2] Piyawat, K. and Pei, J.S. (2005) Idealized Excitation Forces for Nonlinear SDOF Systems with Memory and Degradation. School of Civil Engineering and Environmental Science, The University of Oklahoma, Norman.
[3] Den Hartog, J.P. (1931) Forced Vibrations with Combined Coulomb and Viscous Friction. Trans ASME, 53, 107-115.
[4] Wojewoda, J., Kapitaniak, T., Barron, R. and Brindley, J. (1993) Complex Behaviour of a Quasiperiodically Forced System with Dry Friction. Chaos, Solitons & Fractals, 3, 35-46.
[5] Shaw, S.W. (1986) On the Dynamic Response of a System with Dry Friction. Journal of Sound and Vibration, 108, 305-325.
[6] Ibrahim, R. (1994) Friction Induced Vibration, Chatter, Squeal and Chaos—Part I: Mechanics of Contact and Friction. Applied Mechanics Review, 47, 209-226.
[7] Andreaus, U. and Casini, P. (2001) Dynamics of Friction Oscillators Excited by a Moving Base and/or Driving Force. Journal of Sound and Vibration, 245, 685-699.
[8] Stefannski, A., Wojewoda, J., Wiercigroch, M. and Kapitaniak, T. (2003) Chaos Caused by Non-Reversible Dry Friction. Chaos, Solitons and Fractals, 16, 661-664.
[9] Wiercigroch, M., Vwt, S. and Zfk, L. (1999) Non-Reversible dry Friction Oscillator: Design and Measurements. Proceedings of the Institution of Mechanical Engineers, 213, 527-534.
[10] Fenny, B. and Moon, F.C. (1994) Chaos in a Forced Dry Friction Oscillator: Experiment and Numerical Modelling. Journal of Sound and Vibration, 170, 303-323.
[11] Kardan, I., Kabganian, M., Abiri, R. and Bagheri, M. (2013) Stick-Slipconditions in the General Motion of a Planar Rigid Body. Journal of Mechanical Science and Technology, 27, 2577-2583.
[12] Cao, Y. and Chen, X.B. (2015) An ARX-Based PID-Sliding Mode Control on Velocity Tracking Control of a Stick- Slip Piezoelectric-Driven Actuator. Modern Mechanical Engineering, 5, 10-19.
[13] Thomsen, J.J. (1999) Using Fast Vibrations to Quench Friction-Induced Oscillations. Journal of Sound and Vibration, 228, 1079-1102.
[14] Cheng, G. and Zu, J.W. (2004) Dynamics of a Dry Friction Oscillator under Two-Frequency Excitations. Journal of Sound and Vibration, 275, 591-603.
[15] Awrejcewics, J. and Dzyubak, L. (2003) Stick-Slip Chaotic Oscillations in Aquasi-Autonomous Mechanical System. International Journal of Nonlinear Sciences and Numerical Simulation, 4, 155-160.
[16] Awrejcewicz, J. and Pyryev, Yu. (2002) Thermo Elastic Contact of a Rotating Shaft with a Rigid Bush in Conditions of Bush Wear and Stick-Slip Movements. International Journal of Engineering Science, 40, 1113-1130.
[17] Voldrich, J. (2009) Modelling of Three-Dimensional Friction Contact of Vibrating Elastic Bodies with Rough Surfaces. Applied and Computational Mechanics, 3, 241-252.
[18] Reinhorn, A.M. and Sivaselvan, M.V. (2000) Hysteretic Models for Deteriorating Inelastic Structures. ASCE Journal of Engineering Mechanics, 126, 633-640.
[19] Sergienko, O.V., Macayeal, D.R. and Bindschadler, R.A. (2009) Stick-Slip Behavior of Ice Streams: Modelling Investigations. Annals of Glaciology, 50, 87-94.

Copyright © 2023 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.