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Research Papers

Parameters Study of Hopf Bifurcation in Railway Vehicle System

[+] Author and Article Information
Xingwen Wu

State Key Laboratory of Traction Power,
Southwest Jiaotong University,
Chengdu, China
e-mail: xingwen_wu@163.com

Maoru Chi

State Key Laboratory of Traction Power,
Southwest Jiaotong University,
Chengdu, China
e-mail: cmr2000@163.com

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received July 7, 2013; final manuscript received May 12, 2014; published online February 11, 2015. Assoc. Editor: Dr. Corina Sandu.

J. Comput. Nonlinear Dynam 10(3), 031012 (May 01, 2015) (10 pages) Paper No: CND-13-1171; doi: 10.1115/1.4027683 History: Received July 07, 2013; Revised May 12, 2014; Online February 11, 2015

Roller rig tests were adopted to illustrate two typical types of Hopf bifurcations existing in the railway vehicles. In order to investigate the influence of the vehicles' parameters on the features of Hopf bifurcation, a suspended single wheel set model was formulated. In this model, the lateral and yaw motions of the wheel set were taken into account; Restoring forces between the flange and rail were considered as a smooth function through polynomial fitting; Wheel tread profile was assumed to be conical; Suspension elements and creep forces were considered to be linear properties. The continuation method was utilized to study the features of Hopf bifurcation of the wheel set model. Based on the suspended single wheel set model the effect of the primary suspension, the equivalent conicity of the wheel tread, the mass and spin moment of inertia of the wheel set, and the axle loads on the characteristics of Hopf bifurcation were investigated. Furthermore, the combined effect of parameters was analyzed, and the coupling regions between the parameters were found. In the coupling region, the characteristics of Hopf bifurcation are very sensitive to the variation of the parameters. Therefore, in order to avoid the abrupt change of features of Hopf bifurcation, the coupling region of parameters should be taken into account in the design stage of railway vehicles.

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Figures

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Fig. 1

Typical types of Hopf bifurcations of a railway vehicle system

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Fig. 2

Roller rig tests for high-speed railway vehicles

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Fig. 3

Hopf bifurcation diagrams for two high-speed trains measured in the roller rig tests, (a) Type One Vehicle and (b) Type Two Vehicle

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Fig. 4

Lateral displacements of the wheel set for two types of railway vehicles: (a) type 1 vehicle and (b) type 2 vehicle

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Fig. 5

Model of wheel set

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Fig. 6

Continuation with a predictor/corrector scheme

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Fig. 7

Effect of the lateral stiffness Kpy (MN/m) of the primary suspension on Hopf bifurcation with Kpx = 5 MN/m: (a) wheel lateral displacement versus vehicle speed and (b) Hopf bifurcation point and uncertain degree versus lateral stiffness of the primary suspension

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Fig. 8

(a) Effect of the lateral stiffness Kpy (MN/m) of the primary suspension on Hopf bifurcation with Kpx = 10 MN/m: (a) wheel lateral displacement versus vehicle speed and (b) Hopf bifurcation point and uncertain degree versus lateral stiffness of the primary suspension

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Fig. 9

Effect of the longitudinal stiffness Kpx (MN/m) of the primary suspension on Hopf bifurcation: (a) wheel lateral displacement versus vehicle speed and (b) Hopf bifurcation point and uncertain degree versus longtudinal stiffness of the primary suspension

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Fig. 10

Equivalent conicity measured in high-speed railway vehicle

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Fig. 11

Effect of the conicity λ of the wheel tread on Hopf bifurcation: (a) wheel lateral displacement versus vehicle speed and (b) Hopf bifurcation point and uncertain degree versus equivalent conicity of wheel

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Fig. 12

Effect of the spin moment of inertia of the wheel set on Hopf bifurcation: (a) wheel lateral displacement versus vehicle speed and (b) Hopf bifurcation point and uncertain degree versus equivalent conicity of the wheel tread

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Fig. 13

Effect of the mass of the wheel set on Hopf bifurcation: (a) wheel lateral displacement versus vehicle speed and (b) Hopf bifurcation point and uncertain degree versus mass of the wheel set

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Fig. 14

Effect of the axle load on the Hopf bifurcation: (a) Kpx = 9 MN/m, (b) Kpx = 2 MN/m

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