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Research Papers

Lateral Bifurcation Behavior of a Four-Axle Railway Passenger Car

[+] Author and Article Information
Xuejun Gao

School of Mechanics and Engineering, and State Key Laboratory of Traction Power, Southwest Jiaotong University, Chengdu 610031, P.R.C.

Yinghui Li1

School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, P.R.C.yinghui.li@home.swjtu.edu.cn

Qing Gao

School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, P.R.C.

1

Corresponding author.

J. Appl. Mech 77(6), 061001 (Aug 16, 2010) (8 pages) doi:10.1115/1.4001544 History: Received January 04, 2009; Revised March 23, 2010; Posted April 02, 2010; Published August 16, 2010; Online August 16, 2010

We investigate the kinematics and dynamics of a high-speed four-axle railway passenger car, which has 17 degrees of freedom, considering the lateral motion, roll and yaw angles of the car body and the bogie frame, and the lateral motion and yaw angle of the four wheelsets. The creep forces and the flange forces between the oscillating wheels and the rails are main nonlinearities and can be estimated by the Vermeulen–Johnson creep force laws and a piecewise linear function, respectively. The dynamical equations for the motion of the vehicle running with constant speed along an ideal, rigid, straight, and perfect track are formulated, and the lateral bifurcation behavior of the vehicle system is investigated numerically. The results indicate that both stable and unstable orbits are obtained, and the linear and nonlinear critical speeds are determined as well. Several kinds of dynamical behaviors, such as stationary equilibrium point, symmetric or asymmetric periodic oscillations, and symmetric or asymmetric chaotic motions, are found and described in great detail within the investigated speed range.

Copyright © 2010 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

A typical bifurcation diagram of the vehicle system

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Figure 2

Model of four-axle railway passenger car system

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Figure 3

Bifurcation diagram of the leading wheelset of the front bogie showing the maximum lateral amplitude of the periodic solution from the stationary solution versus the speed

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Figure 4

Bifurcation diagram of the car body showing the maximum lateral deviation versus the speed, in the speed range 110.5 m/s<V<140.0 m/s

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Figure 6

Phase trajectories and power spectra of the car body for periodic motion at V=111.0 m/s

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Figure 7

A projection of Poincare sections at V=112.0 m/s and V=116.0 m/s

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Figure 8

Enlarged part of Fig. 4 in the speed range 126.0 m/s<V<135.0 m/s

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Figure 9

The projected Poincare maps at V=127.0 m/s and V=131.0 m/s

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Figure 10

Convergence of the four largest Lyapunov exponents at V=127.0 m/s

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Figure 12

A projection of the Poincare sections at some key velocities showing the period doublings to chaos

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Figure 13

Bifurcation diagram of the car body in the speed range 68.0 m/s<V<138.0 m/s (decreasing speed, jump around V=135.0 m/s)

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Figure 14

Enlarged part of Fig. 1 in the speed range 69.0 m/s<V<78.0 m/s

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Figure 15

Bifurcation diagram of the car body in the speed interval 68.0 m/s<V<128.0 m/s (decreasing speed, jump around V=126.0 m/s)

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Figure 16

Enlarged part of Fig. 1 in the speed range 112.0 m/s<V<126.0 m/s

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Figure 17

The projected Poincare maps at V=125.2 m/s and V=125.5 m/s

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Figure 5

Enlarged portion of Fig. 4 in the speed interval 110.5 m/s<V<126.0 m/s

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Figure 11

Enlarged part of Fig. 4 in the speed range 136.0 m/s<V<138.5 m/s

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