Skip to main content
Log in

The destabilization paradox applied to friction-induced vibrations in an aircraft braking system

  • Original
  • Published:
Archive of Applied Mechanics Aims and scope Submit manuscript

Abstract

Mechanisms of friction are known as an important source of vibrations in a large variety of engineering systems, where the emergence of oscillations is noisy and can cause severe damage to the system. The reduction or elimination of these vibrations is then an industrial issue that requires the attention of engineers and researchers together. Friction-induced vibrations have been the matter of several investigations, considering experimental, analytical, and numerical approaches. An aircraft braking system is a complex engineering system prone to friction-induced vibrations, and is the subject herein. By considering experimental observations and by evaluating the mechanisms of friction involved, a complete nonlinear model is built. The nonlinear contact between the rotors and the stators is considered. The stability analysis is performed by determining the eigenvalues of the linearized system at the equilibrium point. Parametric studies are conducted in order to evaluate the effects of various system parameters on stability. Special attention will be given to the understanding the role of damping and the associated destabilization paradox in mode-coupling instabilities.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Kinkaid N., O’Reilly O. and Papadopoulos P. (2003). Automotive disc brake squeal. J. Sound Vibr. 267: 105–166

    Article  Google Scholar 

  2. Ibrahim R. (1994). Friction-induced vibration, chatter, squeal and chaos. Part 1: mechanics of contact and friction. ASME Des. Eng. Techn. Conf. 7: 209–226

    Google Scholar 

  3. Ibrahim R. (1994). Friction-induced vibration, chatter, squeal and chaos. Part 2: dynamics and modeling. ASME Des. Eng. Techn. Conf. 7: 209–2269

    Google Scholar 

  4. Crolla D. and Lang A. (1991). Brake noise and vibration—state of art. Tribol.-Vehicle Tribol. 18: 165–174

    Article  Google Scholar 

  5. Spurr R. (1961). A theory of brake squeal. Proc. Auto. Div. Inst. Mech. Eng. 1: 33–40

    Google Scholar 

  6. Liu S., Özbek M. and Gordon J. (1996). A nonlinear model for aircraft brake squeal analysis. Part i: model description and solution methodology. ASME Des. Eng. Techn. Conf. 3: 406–416

    Google Scholar 

  7. Liu S., Özbek M. and Gordon J. (1996). A nonlinear model for aircraft brake squeal analysis. Part ii: stability analysis and parametric studies. ASME Des. Eng. Techn. Conf. 3: 417–425

    Google Scholar 

  8. Sinou J.-J., Dereure O., Mazet G.-B., Thouverez F. and Jézéquel L. (2006). Friction induced vibration for an aircraft brake system. Part 1: experimental approach and stability analysis. Int. J. Mech. Sci. 48: 536–554

    Article  Google Scholar 

  9. Sinou J.-J., Fritz G. and Jézéquel L. (2007). The role of damping and definition of the robust damping factor (rd-factor) for a self-exciting mechanism with constant friction. J. Vibr. Acoust. 129(3): 297–306

    Article  Google Scholar 

  10. Sinou J.-J. and Jézéquel L. (2007). Mode coupling instability in friction induced vibrations and its dependency on system parameters including damping. J. Eur. Mech. A Solids 26: 106–122

    Article  MATH  Google Scholar 

  11. Hoffmann N. and Gaul L. (2003). Effects of damping on mode-coupling instability in friction induced oscillations. ZAMM Z. Angew. Math. Mech. 83(8): 524–534

    Article  MATH  Google Scholar 

  12. Shin K., Brennan M., Oh J.-E. and Harris C. (2002). Analysis of disc brake noise using a two-degree-of-freedom model. J. Sound Vibr. 254: 837–848

    Article  Google Scholar 

  13. Gallina P. and Trevisani A. (2003). On the stabilizing and destabilizing effects of damping in wood cutting machines. Int. J. Mach. Tools Manuf. 43: 955–964

    Article  Google Scholar 

  14. Kirollov O. (2004). Destabilization paradox. Doklady Phys. 49(4): 239–245

    Article  Google Scholar 

  15. Kirollov O. and Seyranian A. (2005). The effetc of small internal and external damping on the stability of distributed non-conservative systems. J. Appl. Math. Mech. 69: 529–552

    Article  MathSciNet  Google Scholar 

  16. Bolotin V. (1963). Non-conservative Problems of the Theory of Elastic Stability. Pergamon, Oxford

    Google Scholar 

  17. Smith D.M. (1933). The motion of a rotor carried by a flexible shaft in flexible bearings. Proc. R. Soc. Lond. Ser. A Contain. Pap. Math. Phys. Character 142(846): 92–118

    Google Scholar 

  18. Crandall S. (1995). The effect of damping on the stability of gyroscopic pendulums. Zeitschrift für angewandte Mathematik und Physik 46: 761–780

    MathSciNet  Google Scholar 

  19. Kirillov O. (2007). Destabilization paradox due to breaking the hamiltonian and reversible symmetry. Int. J. Nonlin. Mech. 42(1): 71–87

    Article  MathSciNet  Google Scholar 

  20. Seyranian A., Kirillov O. and Mailybaev A. (2005). Coupling of eigenvalues of complex matrices at diabolic and exceptional points. J. Phys. A Math. Gen. 38(8): 1723–1740

    Article  MATH  MathSciNet  Google Scholar 

  21. Arnold V. (1983). Geometrical Methods in the Theory of Ordinary Differential Equations. Springer, New York

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to J. -J. Sinou.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chevillot, F., Sinou, J.J., Mazet, G.B. et al. The destabilization paradox applied to friction-induced vibrations in an aircraft braking system. Arch Appl Mech 78, 949–963 (2008). https://doi.org/10.1007/s00419-008-0208-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00419-008-0208-7

Keywords

Navigation