Double grazing bifurcations of the non-smooth railway wheelset systems

Pengcheng Miao, Denghui Li, Shan Yin, Jianhua Xie, Celso Grebogi, Yuan Yue*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


There are numerous non-smooth factors in railway vehicle systems, such as flange impact, dry friction, creep force, and so on. Such non-smooth factors heavily affect the dynamical behavior of the railway systems. In this paper, we investigate and mathematically analyze the double grazing bifurcations of the rail-way wheelset systems with flange contact. Two types of models of flange impact are considered, one is a rigid impact model and the other is a soft impact model. First, we derive Poincare maps near the grazing trajectory by the Poincare-section discontinuity mapping (PDM) approach for the two impact models. Then, we analyze and compare the near grazing dynamics of the two models. It is shown that in the rigid impact model the stable periodic motion of the railway wheelset system translates into a chaotic motion after the grazing bifurcation, while in the soft impact model a pitchfork bifurcation occurs and the system tends to the chaotic state through a period doubling bifurcation. Our results also extend the applicability of the PDM of one constraint surface to that of two constraint surfaces for autonomous systems.

Original languageEnglish
Pages (from-to)2093-2110
Number of pages18
JournalNonlinear Dynamics
Early online date13 Oct 2022
Publication statusE-pub ahead of print - 13 Oct 2022

Bibliographical note

The funding was provided by the National Natural Science Foundation of China (12072291, 12202168 and 12172306).

Data Availability Statement

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.


  • Railway wheelset
  • Non-smooth
  • PDM
  • Double grazing bifurcations


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