Abstract
Based on the finite element method (FEM), the parametric variational principle (PVP) is combined with a numerical time-domain integral method to simulate the dynamic behavior of the pantograph-catenary system. Based on PVP, formulations for the nonlinear droppers in the catenary and for the contact between the pantograph and the contact wire are proposed. The formulations can accurately determine the tension state or compression state of the nonlinear droppers and the contact state between the pantograph and the contact wire. Based on the periodicity of the catenary and the precise integration method (PIM), a numerical time-integration method is developed for the dynamic responses of the catenary. For this method, the matrix exponential of only one unit cell of the catenary is computed, which greatly improves the computational efficiency. Moreover, the validation shows that the formulations can compute the contact force accurately and represent the nonlinearity of the droppers, which demonstrates the accuracy and reliability of the proposed method. Finally, the dynamic behaviors of the pantograph-catenary system with different types of catenaries are simulated.
Highlights
High-speed railway is an inexpensive, secure, comfortable, and efficient mode of transportation, even more time-saving and cheaper than airlines for relatively short journeys
Where subscript d denotes the dropper, yd,k denotes vertical displacement of the kth dropper from the equilibrium profile, EAd,k denotes the axial stiffness of the kth dropper, lk denotes the length of the kth dropper, fm,k denotes an external force caused by the messenger wire, fc,k denotes an external force caused by the contact wire, and yd,k,0(y) denotes the initial displacement of the kth dropper
The formulations for the nonlinear droppers and for the contact between the pantograph and the contact wire will be proposed based on parametric variational principle (PVP), and a numerical time-integration algorithm for computing the response of the catenary will be developed based on precise integration method (PIM)
Summary
High-speed railway is an inexpensive, secure, comfortable, and efficient mode of transportation, even more time-saving and cheaper than airlines for relatively short journeys. Bruni et al [26] described the results of a voluntary benchmark initiative concerning the simulation of pantograph-catenary interaction, which can be used to demonstrate the accuracy of numerical methodologies and simulation models These studies suggest that wave reflection and the variation of the stiffness are the main causes of contact force variation when a pantograph moves at a constant speed. The slackening of a dropper reflects a strong nonlinear characteristic Another important problem associated with the dynamic simulation of the pantograph-catenary system is determining the tension state or compression state of every dropper at every time step. The significant wave effect of the contact wire subjected to a moving pantograph at high speed makes precise simulation more difficult, when contact problems and nonlinear droppers are involved.
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