Advertisement

Bifurcation-Based Shimmy Analysis of Landing Gears Using Flexible Multibody Models

  • C. J. J. Beckers
  • A. E. Öngüt
  • G. Verbeek
  • R. H. B. FeyEmail author
  • Y. Lemmens
  • N. van de Wouw
Chapter
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 69)

Abstract

Shimmy oscillations are undesired vibrations in aircraft landing gears. In this chapter, the onset of shimmy vibrations, marked by Hopf bifurcations, is investigated in the parameter space of high-fidelity, flexible multibody landing gear models. Such a bifurcation analysis is performed by combining the Virtual.Lab Motion multibody solver with the numerical continuation software AUTO. The resulting quasi-2-parameter bifurcation diagrams, involving aircraft velocity and normal load, are verified using conventional time-simulation methods and are shown to be computationally more efficient. A sensitivity study reveals the influence of design parameters, such as the shimmy damping coefficient, mechanical trail, and steering actuator stiffness, on the occurrence of shimmy.

Keywords

Bifurcation analysis Flexible multibody dynamics Shimmy Landing gear dynamics 

Notes

Acknowledgements

The work in this chapter was supported by Siemens PLM Software and Fokker Landing Gear. Their cooperation is gratefully acknowledged.

References

  1. 1.
    Bampton, M.C.C., Craig Jr., R.R.: Coupling of substructures for dynamic analyses. AIAA J. 6(7), 1313–1319 (1968).  https://doi.org/10.2514/3.4741CrossRefzbMATHGoogle Scholar
  2. 2.
    Beckers, C.J.J., Ongüt, A.E., Verbeek, B., Fey, R.H.B., Lemmens, Y., van de Wouw, N.: Bifurcation analysis of landing gear shimmy using flexible multibody models. In: Ambrósio, J. (ed.) 5th Joint International Conference on Multibody Systems and Dynamics (IMSD), 46. Portugal, June, 24–28 Lisboa (2018). http://imsd2018.tecnico.ulisboa.pt/Web_Abstracts_IMSD2018/pdf/WEB_PAPERS/IMSD2018_Full_Paper_46.pdf
  3. 3.
    Coetzee, E., Thota, P., Rankin, J.: Dynamical Systems Toolbox. https://nl.mathworks.com/matlabcentral/fileexchange/32210-dynamical-systems-toolbox (2011). Accessed 14 June 2018
  4. 4.
    Doedel, E., Keller, H.B., Kernevez, J.P.: Numerical analysis and control of bifurcation problems (I): bifurcation in finite dimensions. Int. J. Bifurc. Chaos 01(03), 493–520 (1991).  https://doi.org/10.1142/S0218127491000397MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Doedel, E.J., Oldeman, B.E.: AUTO-07P: Continuation and bifurcation software for ordinary differential equations. Technical Report, Concordia University, Montreal. http://indy.cs.concordia.ca/auto (2012). Accessed 14 June 2018
  6. 6.
    Haug, E.J.: Computer Aided Kinematics and Dynamics of Mechanical Systems, 1st edn. Allyn and Bacon, 160 Gould Street, Needham Heights, Massachusetts 02194 (1989)Google Scholar
  7. 7.
    Howcroft, C., Lowenberg, M.H., Neild, S., Krauskopf, B., Coetzee, E.: Shimmy of an aircraft main landing gear with geometric coupling and mechanical freeplay. J. Comput. Nonlinear Dyn. 10(5), 051,011 (2015)Google Scholar
  8. 8.
    Shabana, A.A.: Dynamics of Multibody Systems, 4th edn. Cambridge University Press, Cambridge (2013)Google Scholar
  9. 9.
    Siemens Product Lifecycle Management Software Inc.: Case study—GKN Aerospace Fokker Landing Gear. https://www.plm.automation.siemens.com/pub/case-studies/64181?resourceId=64181 (2017). Accessed 6 Apr 2018
  10. 10.
    Siemens Product Lifecycle Management Software Inc.: LMS Virtual.Lab Motion Online Help (documentation) (2017)Google Scholar
  11. 11.
    Tartaruga, I., Lowenberg, M.H., Cooper, J.E., Sartor, P., Lemmens, Y.: Bifurcation analysis of a nose landing gear system. In: 15th Dynamics Spectral Conference, American Institute of Aeronautics and Astronautics, San Diego, California, USA, AIAA SciTech Forum (2016).  https://doi.org/10.2514/6.2016-1572
  12. 12.
    Thomsen, J.J.: Vibrations and Stability, 2nd edn. Springer, Berlin, Heidelberg,  https://doi.org/10.1007/978-3-662-10793-5 (2003)
  13. 13.
    Thota, P., Krauskopf, B., Lowenberg, M.H.: Interaction of torsion and lateral bending in aircraft nose landing gear shimmy. Nonlinear Dyn. 57(3), 455–467 (2009).  https://doi.org/10.1007/s11071-008-9455-yCrossRefzbMATHGoogle Scholar
  14. 14.
    Yoo, W.S., Haug, E.J.: Dynamics of articulated structures. Part I. Theory. J. Struct. Mech. 14(1), 105–126 (1986).  https://doi.org/10.1080/03601218608907512
  15. 15.
    Yoo, W.S., Haug, E.J.: Dynamics of flexible mechanical systems using vibration and static correction modes. J. Mech. Trans. Autom. 108(3), 315–322 (1986b).  https://doi.org/10.1115/1.3258733CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • C. J. J. Beckers
    • 1
  • A. E. Öngüt
    • 4
  • G. Verbeek
    • 5
  • R. H. B. Fey
    • 1
    Email author
  • Y. Lemmens
    • 4
  • N. van de Wouw
    • 1
    • 2
    • 3
  1. 1.Dynamics and Control Group, Department of Mechanical EngineeringEindhoven University of TechnologyEindhovenThe Netherlands
  2. 2.Department of Civil, Environmental and Geo-EngineeringUniversity of MinnesotaMinneapolisUSA
  3. 3.Delft Center for Systems and ControlDelft University of TechnologyDelftThe Netherlands
  4. 4.Siemens PLM SoftwareLeuvenBelgium
  5. 5.Fokker Landing GearHelmondThe Netherlands

Personalised recommendations