Nonlinear Dynamics

, Volume 15, Issue 1, pp 15–30 | Cite as

Hopf Bifurcation and Hunting Behavior in a Rail Wheelset with Flange Contact

  • Mehdi Ahmadian
  • Shaopu Yang


An analytical investigation of Hopf bifurcation and hunting behavior of a rail wheelset with nonlinear primary yaw dampers and wheel-rail contact forces is presented. This study is intended to complement earlier studies by True et al., where they investigated the nonlinearities stemming from creep-creep force saturation and nonlinear contacts between a realistic wheel and rail profile. The results indicate that the nonlinearities in the primary suspension and flange contact contribute significantly to the hunting behavior. Both the critical speed and the nature of bifurcation are affected by the nonlinear elements. Further, the results show that in some cases, the critical hunting speed from the nonlinear analysis is less than the critical speed from a linear analysis. This indicates that a linear analysis could predict operational speeds that in actuality include hunting.

Rail vehicle hunting nonlinear Hopf bifurcation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Law, E. H. and Cooperrider, N. K., ‘A survey of railway vehicle dynamics research’, ASME Journal of Dynamic Systems, Measurement, and Control 96, 1974, 132–146.Google Scholar
  2. 2.
    Law, E. H. and Brand, R. S., ‘Analysis of the nonlinear dynamics of a railway vehicle wheelset’, ASME Journal of Dynamic Systems, Measurement, and Control, Series G 95, 1973, 28–35.Google Scholar
  3. 3.
    Abel, S. G. and Cooperrider, N. K., ‘An equivalent linearization algorithm for nonlinear system limit cycle analysis’, ASME Journal of Dynamic Systems, Measurement, and Control 107, 1985, 117–122.Google Scholar
  4. 4.
    Hedrick, J. K. and Arslan, A. V., ‘Nonlinear analysis of rail vehicle forced lateral response and stability’, ASME Journal of Dynamic Systems, Measurement, and Control 101, 1979, 230–237.Google Scholar
  5. 5.
    Huilgol, R. R., ‘Hopf–Friedrichs bifurcation and the hunting of a railway axle’, Quarterly Journal of Applied Mathematics 36, 1978, 85–94.Google Scholar
  6. 6.
    True, H. and Kaas-Petersen, C., ‘A bifurcation analysis of nonlinear oscillations in railway vehicles’, in The Dynamics of Vehicles on Road and on Tracks, 8th IAVSD Symposium, 1984, pp. 438-444.Google Scholar
  7. 7.
    Kaas-Petersen, C. and True, H., ‘Periodic, biperiodic and chaotic dynamical behavior of railway vehicles’, in Proceedings 9th IAVSD Symposium, 1986, pp. 208–221.Google Scholar
  8. 8.
    True, H., ‘A method to investigate the nonlinear oscillations of a railway vehicle’, Applied Mechanics Rail Transportation Symposium–1988, presented at the Winter Annual Meeting of ASME.Google Scholar
  9. 9.
    True, H., ‘Dynamics of a rolling wheelset’, Applied Mechanics Review 46(7), 1993, 438–444.Google Scholar
  10. 10.
    Cooperrider, N. R., ‘The hunting behavior of conventional railway trucks’, ASME Journal of Engineering in Industry 94, 1972, 752–762.Google Scholar
  11. 11.
    True, H., ‘Some recent developments in nonlinear railway vehicle dynamics’, in 1st European Nonlinear Oscillation Conference, Proceedings of the International Conference, Hamburg, 1993, pp. 129–148.Google Scholar
  12. 12.
    True, H., ‘Does a critical speed for railroad vehicle exist?’, in Proceedings of the IEEE/ASME Joint Railroad Conference, 1994, pp. 125–131.Google Scholar
  13. 13.
    Yang, S. and Chen, E., ‘The Hopf bifurcation in a railway bogie with hysteretic nonlinearity’, Journal of the China Railway Society 15(4), 1993.Google Scholar
  14. 14.
    Scheffel, D. H., ‘The influence of the suspension on the hunting stability of railway vehicles’, Rail International 10(8), 1979, 662–696.Google Scholar
  15. 15.
    Yang, S. and Ahmadian, M., ‘The Hopf bifurcation of a rail wheelset with nonlinear damping’, in Proceedings of Rail Transportation Division, 1996 ASME International Mechanical Engineering Congress and Exposition, Atlanta GA, November 17–22, 1996, pp. 113–120.Google Scholar
  16. 16.
    True, H. and Jensen, J. C., ‘Parameter study of hunting and chaos in railway vehicle dynamics’, in Vehicle System Dynamics, Proceedings of 13th IAVSD Symposium, Chengdu, Sichuan, China, August 23–27, 1994, pp. 508–520.Google Scholar
  17. 17.
    Bogoliubov, N. N. and Mitropolsky, Y. A., Asymptotic Method in the Theory of Nonlinear Oscillations, Hindustan Publishing, Delhi, India, 1961.Google Scholar
  18. 18.
    Szulczyk, A., Chudzikiewicz, A., Drozdziel, J., and Kisilowski, J., ‘Analysis of nonlinear mathematical models of track-vehicle system’, in Proceedings of the 8th IAVSDIUTAM Symposium on the Dynamics of Vehicles on Roads and Tracks, Cambridge, MA, August 14–19, 1983.Google Scholar
  19. 19.
    Garg, V. K. and Dukkipati, R. V., Dynamics of Railway Vehicle Systems, Academic Press, Canada, 1984.Google Scholar

Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • Mehdi Ahmadian
    • 1
  • Shaopu Yang
    • 2
  1. 1.Advanced Vehicle Dynamics Laboratory, Department of Mechanical EngineeringVirginia Polytechnic Institute and State UniversityBlacksburgU.S.A.
  2. 2.Division of Vibration and Noise ControlShijiazhuang Railway InstituteShijiazhuangP.R. China

Personalised recommendations