Skip to main content

Friction-induced limit cycling in flexible rotor systems: An experimental drill-string set-up

Abstract

Friction-induced limit cycling deteriorates system performance in a wide variety of mechanical systems. In this paper, we study the way in which essential friction characteristics affect the occurrence and nature of friction-induced limit cycling in an experimental drill-string set-up. This study is performed on the level of a Lyapunov-based stability analysis and on the level of both numerical and experimental bifurcation analyses. The synthesis of these results confirms that friction-induced limit cycling is due to a subtle balance between negative damping at lower velocities and viscous friction at higher velocities. Moreover, it is shown how these essential friction characteristics depend on physical conditions such as temperature and normal forces in the frictional contact in the experimental set-up.

This is a preview of subscription content, access via your institution.

References

  1. Brett, J.F.: Genesis of torsional drillstring vibrations. SEP Drill. Eng. 7(3), 168–174 (1992)

    Google Scholar 

  2. Leine, R.I., van Campen, D.H., Keultjes, W.J.G.: Stick-slip whirl interaction in drillstring dynamics. ASME J. Vib. Acoust. 124, 209–220 (2002)

    Article  Google Scholar 

  3. Kreuzer, E., Kust, O.: Analyse selbsterregter drehschwin-gugnen in torsionsstäben. ZAMM — Journal of Applied Mathematics and Mechanics / Zeitschrift fuer Angewandte Mathematik und Mechanik 76(10), 547–557 (1996a)

    MATH  Google Scholar 

  4. Pfeiffer, F., Hajek, M.: Slip-stick motions of turbine blade damp. Philos. Transl. R. Soc. Lond. A 338(9), 503–517 (1992)

    Google Scholar 

  5. Hensen, R.H.A.: Controlled Mechanical Systems with Friction. Ph.D. thesis, Endhoven University of Technology, The Netherlands (2002)

  6. Cataldi, E., Glocker, Ch.: Curve squealing of railroad vehicles. In Proceedings of the 5th EUROMECH Nonlinear Oscillations Conference, Eindhoven, The Netherlands(2005)

  7. Cunningham, R.A.: Analysis of downhole measurements of drill string forces and motions. ASME J. Eng. Ind. 90, 208–216 (1968)

    Google Scholar 

  8. Jansen, J.D., van den Steen, L.: Active damping of self-excited torsional vibrations in oil well drillstrings. J. Sound Vib. 179(4), 647–668 (1995)

    Article  Google Scholar 

  9. Van den Steen, L.: Suppressing Stick-Slip-Induced Drill-string Oscillations: a Hyper Stability Approach. Ph.D. thesis, University of Twente (1997)

  10. Richard, T., Germay, C., Detournay, E.: Self-excited stick-slip oscillations of drill bits. C. R. Mec. 332, 619–626 (2004)

    Google Scholar 

  11. Brockley, C.A., Cameron, R., Potter, A.F.: Friction-induced vibrations. ASME J. Lubr. Technol. 89, 101–108 (1967)

    Google Scholar 

  12. Brockley, C.A., Ko, P.L.: Quasi-harmonic friction-induced vibrations. ASME J. Lubr. Technol. 92, 550–556 (1970)

    Google Scholar 

  13. Ibrahim, R.A.: Friction-induced vibration, chatter, squeal, and chaos: mechanics of contact and friction. Appl. Mech. Rev.: ASME 47(7), 209–226 (1994a)

    Google Scholar 

  14. Ibrahim, R.A.: Friction-induced vibration, chatter, squeal, and chaos: dynamics and modeling. Appl. Mech. Rev.: ASME 47(7), 227–253 (1994b)

    Article  Google Scholar 

  15. Popp, K., Stelter, P.: Stick-slip vibrations and chaos. Philos. Trans. R. Soc. Lond. 332, 89–105 (1990)

    MATH  Google Scholar 

  16. Popp, K., Rudolph, M., Kröger, M., Lindner, M.: Mechanisms to generate and to avoid friction induced vibrations. VDI-Berichte 1736, VDI-Verlag Düsseldorf 2002, 1–15 (2002)

    Google Scholar 

  17. Krauter, A.I.: Generation of squeal/chatter in water-lubricated elastomeric bearings. ASME J. Lubr. Technol. 103, 406–413 (1981)

    Google Scholar 

  18. Hensen, R.H.A., van de Molengraft, M.J.G., Steinbuch, M.: Friction induced hunting limit cycles: an event mapping approach, in Proceeding of the 2002 American Control Conference, Anchorage, AK (2002)

  19. Putra, D., Nijmeijer, H.: Limit cycling in an observer-based controlled system with friction: numerical analysis and experimental validation. Int. J. Bifurcation Chaos 14(9), 3083–3093 (2004)

    MATH  MathSciNet  Article  Google Scholar 

  20. Olsson, H., Áström, K.J.: Friction generated limit cycles. In Proceeding of the 1996 IEEE Conference on Control Applications, Dearborn, MI, (1996)

  21. Olsson, H., Áström, K.J.: Friction generated limit cycles. IEEE Conf. Control Syst. Technol. 9(4), 629–636 (2001)

    Article  Google Scholar 

  22. Van de Wouw, N., Mallon, N.J., Nijmeijer, H.: Friction compensation in a controlled one-link robot using a reduced-order observer, in Proceedings of 6th IFAC Symposium on Nonlinear Control Systems (NOLCOS), (2004)

  23. Mihajlović, N., Van Veggel, A.A., Van de Wouw, N., Nijmeijer, H.: Analysis of friction-induced limit cycling in an experimental drill-string set-up. ASME J. Dyn. Syst. Meas. Control 126(4), 709–720 (2004)

    Article  Google Scholar 

  24. Mihajlovic, N.: Torsional and Lateral Vibrations in Flexible Rotor Systems with Friction. Ph.D. thesis, Eindhoven University of Technology, The Netherlands,(2005)

  25. Mihajlović, N., Van Veggel, A.A., Van de Wouw, N., Nijmeijer, H.: Friction-induced torsional vibrations in an experimental drill-string system, in Proceedings of the 23rd IASTED International conference on Modelling, Identification, and Control, Grindelwald, Switzerland(2004)

  26. Ascher, U.M., Mattheij, R.M.M., Russell, D.R.: Numerical Solution of Boundary Value Problems for Ordinary Differential Equations. SIAM, Philadelphia, (1995)

    MATH  Google Scholar 

  27. Parker, T.S., Chua, L.O.: Practical Numerical Algorithms for Chaotic Systems Springer-Verlag, (1989)

  28. Leine, R.I., Nijmeijer, H.: Dynamics and Bifurcations of Non-smooth Mechanical Systems, Springer, Berlin, (2004)

    MATH  Google Scholar 

  29. Leine, R., Van Campen, D., van de Vrande, B.: Bifurcations in nonlinear discontinuous systems. Nonlinear Dyn. 23, 105–164 (2000)

    MATH  Article  Google Scholar 

  30. Galvanetto, U., Bishop, S.: Dynamics of a simple damped oscillator undergoing stick-slip vibrations. Meccanica 34(5), 337–347 (1999)

    MATH  MathSciNet  Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to N. van de Wouw.

Additional information

This work was performed while affiliated to the Eindhoven University of Technology.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Mihajlovic, N., van de Wouw, N., Hendriks, M.P.M. et al. Friction-induced limit cycling in flexible rotor systems: An experimental drill-string set-up. Nonlinear Dyn 46, 273–291 (2006). https://doi.org/10.1007/s11071-006-9042-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-006-9042-z

Keywords

  • Discontinuous bifurcations
  • Experimental non-smooth dynamics
  • Flexible rotor systems
  • Friction-induced vibrations