A Fractional Derivative Model for Rubber Spring of Primary Suspension in Railway Vehicle Dynamics

[+] Author and Article Information
Dawei Zhang

State Key Laboratory of Traction Power,
Train and Track Research Institute,
Southwest Jiaotong University,
Chengdu 610031, China
e-mail: dwzhang@my.swjtu.edu.cn

Shengyang Zhu

State Key Laboratory of Traction Power,
Train and Track Research Institute,
Southwest Jiaotong University,
Chengdu 610031, China
e-mail: syzhu@swjtu.edu.cn

1Corresponding author.

Manuscript received December 19, 2016; final manuscript received April 28, 2017; published online June 12, 2017. Assoc. Editor: Francesco Paolo Pinnola.

ASME J. Risk Uncertainty Part B 3(3), 030908 (Jun 12, 2017) (8 pages) Paper No: RISK-16-1146; doi: 10.1115/1.4036706 History: Received December 19, 2016; Revised April 28, 2017

This paper presents a nonlinear rubber spring model for the primary suspension of the railway vehicle, which can effectively describe the amplitude dependency and the frequency dependency of the rubber spring, by taking the elastic force, the fractional derivative viscous force, and nonlinear friction force into account. An improved two-dimensional vehicle–track coupled system is developed based on the nonlinear rubber spring model of the primary suspension. Nonlinear Hertz theory is used to couple the vehicle and track subsystems. The railway vehicle subsystem is regarded as a multibody system with ten degrees-of-freedom, and the track subsystem is treated as finite Euler–Bernoulli beams supported on a discrete–elastic foundation. Mechanical characteristic of the rubber spring due to harmonic excitations is analyzed to clarify the stiffness and damping dependencies on the excitation frequency and the displacement amplitude. Dynamic responses of the vehicle–track coupled dynamics system induced by the welded joint irregularity and random track irregularity have been performed to illustrate the difference between the Kelvin–Voigt model and the proposed model in the time and frequency domain.

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Fig. 1

Two models of the rubber spring: (a) Kelvin–Voigt model and (b) the proposed model

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Fig. 2

Vertical vehicle–track coupled dynamics model

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Fig. 3

Sketch of the local irregularity in welded joint: L donates the length of the long wave; λ is the length of the short wave; a1 and a2 are the amplitudes of the long wave and the short wave, respectively

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Fig. 4

Hysteresis loops of new rubber model with different amplitudes ranging from 0.2 mm to 1 mm while the frequency is held constant at 1 Hz

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Fig. 5

Variation of the equivalent stiffness and the damping ratio with the increasing of the harmonic excitation amplitude

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Fig. 6

Hysteresis loops of the new rubber model at different frequencies ranging from 1 Hz to 100 Hz while the amplitude is constant at 1 mm

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Fig. 7

Variation of the equivalent stiffness and the damping ratio with the increasing of the harmonic excitation frequency

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Fig. 8

Dynamic response of the vehicle computed by two different models for the primary suspension: (a) vertical wheel–rail force, (b) vertical displacement of the front bogie, (c) vertical acceleration of the front bogie, and (d) vertical acceleration of the carbody

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Fig. 9

Vertical wheel–rail force: (a) dynamic response in the time domain and (b) PSD in the frequency domain

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Fig. 10

Vertical acceleration of the front bogie: (a) dynamic response in the time domain and (b) PSD in the frequency domain

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Fig. 11

PSD of vertical carbody acceleration




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