A Study on the Critical Speed of Railway Vehicles

철도차량의 임계속도에 관한 연구

  • Published : 2000.08.01


This research has been performed to reveal the hysteresis phenomena of the hunting motion in a railway passenger car having a bolster. Since linear analysis can not explain them, bifurcation analysis is used to predict its outbreak velocities in this paper. However bifurcation analysis is attended with huge computing time, thus this research proposes more effective numerical algorithm to reduce it than previous researches. Stability of periodic solution is obtained by adapting of Floquet theory while stability of equilibrium solutions is obtained by eigen-value analysis. As a result, linear and nonlinear critical speed are acquired. Full scale roller rig test is carried out for the validation of the numerical result. Finally, it is certified that there are many similarities between numerical and test results.


Bifurcation;Critical Speed;Rolling Testing Rig;Creep Theory;Periodic Solution;Hunting Phenomena


  1. Ali H. Nayfeh and Balakumar Balachandran, 1994, 'Applied Nonlinear Dynamics,' John Wiley & Sons
  2. Steven H. Strogatz, 1994, 'Nonlinear Dynamics and Chaos,' Addison-Wesley
  3. 김현영, 신응수, 1999, '매개 변수 가진을 받는 유연관절 로봇의 비선형 진동해석,' 대한기계학회논문집, 제23권, 제2호, pp. 199-208
  4. 정우진, 김성원, 1999, '비선형 임계속도 검증을 위한 실험적 연구,' 추계학술대회논문집, 한국철도학회, pp. 574-581
  5. Mehdi Ahmadian and Shaopu Yang, 1998, 'Effect of Suspension Nonlinearities on Rail Vehicle Bifurcation and Stability,' Rail Transportation, ASME, pp. 97-106
  6. Pascal and Sauvage, 1991, 'New Method for Reducing the Multi Contact Wheel/rail Problem to One Equivalent Contact Patch,' Proc. 12. IAVSD Symposium
  7. Vijay K. Garg and Rao V. Dukkipati, 1984, 'Dynamics of Railway Vehicle Systems,' Academic Press, pp. 103-176
  8. Carsten Kundsen, Rasmus Feldberg and Alfred Jaschinski, 1991, 'Non-linear Dynamic Phenomena in the Behavior of a Railway Wheelset Model,' J. Nonlinear Dynamics, pp. 389-404
  9. Kalker, J. J., 1991, 'Wheel-rail Rolling Contact Theory,' Wear 144, pp. 243-261
  10. Gasch R, Moelle D and Knothe K, 1984, 'The Effect of Nonlinearities on the Limit Cycles of Railway Vehicles,' in Proc. 8th IAVSD Symosium on Vehicle Systems Dynamics in The Dynamics of Vehicles on Roads and Tracks, Swets & Zeitlinger, Amsterdam/Lisse, pp. 207-224
  11. Hans True, 1993, 'Dynamics of a Rolling wheelset,' Appl. Mech. Rev., Vol. 46, ASME, pp. 438-444
  12. Carter, F. W., 1928, 'On the Stability of Running of Locomotives,' Proceedings of the Royal Society of London, Series A, Vol. 121, pp. 585-611
  13. Huilgol, RR, 1978, 'Hof-Friedrichs Bifurcation and the Hunting of a Railway Axle,' Quart J. Appl. Mech. Vol. 36, pp. 85-94
  14. Moelle D and Gasch R, 1982, 'Nonlinear Bogie Hunting,' in Proc. 7th IAVSD Symp. Cambridge, Swets & Zeitlinger, Lisse, pp. 455-467
  15. Cooperrider, N. K., 1972, 'The Hunting Behaviour of Conventional Railway Trucks,' ASME J. Eng. Industry 94, pp. 752-762