Hopf bifurcation analysis of railway bogie
The railway bogie, the most important running component, has direct association with the dynamic performance of the whole vehicle system. The bifurcation type of the bogie that is affected by vehicle parameters will decide the behavior of the vehicle hunting stability. This paper mainly analyzes the effect of the yaw damper and wheel tread shape on the stability and bifurcation type of the railway bogie. The center manifold theorem is adopted to reduce the dimension of the bogie dynamical model, and the symbolic expression for determining the bifurcation type at the critical speed is obtained by the method of normal form. As a result, the influence of yaw damper on the bifurcation type of the bogie is given qualitatively in contrast to typical wheel profiles with high and low wheel tread effective conicities. Besides, the discriminant of bifurcation type for the wheel tread parameter variation is given which depicts the variation tendency of dynamics characteristics. Finally, numerical analysis is given to exhibit corresponding bifurcation diagrams.
KeywordsRailway bogie Hunting stability Hopf bifurcation Yaw damper Wheel tread
This work has been supported by the National Natural Science Foundation of China (Grant No. 51475388) and National Key R&D Program of China (2016YFB1200500).
- 3.Sedighi, H.M., Shirazi, K.H.: A survey of Hopf bifurcation analysis in nonlinear railway wheelset dynamics. J Vibroeng 14(1), 344–351 (2012)Google Scholar
- 6.Zhang, T.T., Dai, H.Y.: Bifurcation analysis of high-speed railway wheel-set. Nonlinear Dyn. 83(3), 1511–1528 (2016)Google Scholar
- 8.Younesian, D.: Effects of the bogie and body inertia on the nonlinear wheel-set hunting recognized by the hopf bifurcation theory. Int. J. Auto. Eng. 1(3), 186–196 (2011)Google Scholar
- 9.Wu, X., Chi, M.: Parameters study of Hopf bifurcation in railway vehicle system. J. Comput. Nonlinear Dyn. 10(3), 031012-1–031012-10 (2014)Google Scholar
- 11.Ding, W.C., Xie, J.H., Wang, J.T.: Nonlinear analysis of hunting vibration of truck due to wheel-rail impact. J. Lanzhou Univ. Technol. 30(1), 45–49 (2004)Google Scholar
- 15.Yang, S.P., Shen, Y.J.: Bifurcations and Singularities in Systems with Hysteretic Nonlinearity. Science Press, Beijing (2003)Google Scholar
- 18.Zhu, H., Wu, P., Zeng, J., Mai, G.: Dynamic performance influences on Hopf bifurcation characteristics for vehicles. Int. J. Smart Sens. Intell. Syst. 8(3), 1786–1805 (2015)Google Scholar
- 19.Zhang, J., Yang, Y., Zeng, J.: An algorithm criterion for Hopf bifurcation and its applications in vehicle dynamics. Acta Mech. Sin. 32(5), 596–605 (2000)Google Scholar