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Research Papers

# On the Singularity Theory Applied in Rail Vehicle Bifurcation Problem

[+] Author and Article Information
Hao Dong, Bin Zhao

Department of Mechanical Engineering,
Chengdu University,
Chengdu 610106, China

Jianhua Xie

School of Mechanics and Engineering,
Southwest Jiaotong University,
Chengdu 611756, China

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received March 30, 2017; final manuscript received December 13, 2017; published online February 23, 2018. Assoc. Editor: Katrin Ellermann.

J. Comput. Nonlinear Dynam 13(4), 041001 (Feb 23, 2018) (10 pages) Paper No: CND-17-1140; doi: 10.1115/1.4038991 History: Received March 30, 2017; Revised December 13, 2017

## Abstract

The application of Hopf bifurcation is essential to rail vehicle dynamics because it corresponds to the linear critical speed. In engineering, researchers always wonder which vehicle parameters are sensitive to it. With the nonlinear singularity theory's development, it has been widely applied in many other engineering areas. This paper mainly studies the singularity theory applied in nonlinear rail vehicle dynamics. First, the bifurcation norm forms of wheelset and bogie system are, respectively, deduced. Then the universal unfolding is obtained and the influences of perturbation on bifurcation are investigated. By the analysis of a simple bar-spring system, the relationship between the unfolding and original perturbation parameters can be found. But this may be difficult to calculate for the case in vehicle system because of higher degrees-of-freedom (DOFs) and indicate that can explain the influence of all possible parameters perturbations on vehicle bifurcation.

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## Figures

Fig. 2

Semicar body and bogie lateral mechanical model

Fig. 3

The curve for λ

Fig. 1

Bifurcation diagram for universal unfolding near V=Vlin−cr

Fig. 7

Bar-spring system with perturbation (Permission to use from Springer Nature copyright 1985)

Fig. 4

The curve for cx

Fig. 5

Bifurcation diagram for universal unfolding near V=Vcr

Fig. 6

Bar-spring system (Permission to use from Springer Nature copyright 1985)

Fig. 8

Bifurcation diagram for curve negotiation (wheelset model in Sec. 4.1)

Fig. 9

The asymmetric damper cy

Fig. 10

Bifurcation diagram

Fig. 11

The asymmetric creep force f22

Fig. 12

Bifurcation diagram

## Errata

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