A high performance tool for the simulation of the dynamic pantograph–catenary interaction

doi:10.1016/j.matcom.2008.04.016

Mathematics and Computers in Simulation

Volume 79, Issue 3, 1 December 2008, Pages 652-667

https://doi.org/10.1016/j.matcom.2008.04.016 Get rights and content

Abstract

In this paper a computer tool for the simulation of the dynamic pantograph–catenary interaction is presented. We model this interaction and study its behavior in the energy transmission process. The calculation of the dynamic equation of the pantograph–catenary interaction is considered from a simulation point of view by means of a high performance computing algorithm, where the amount of data and the time requirements have been dramatically reduced. Finally, the present algorithm has been used to implement an user-friendly, interactive and graphically oriented toolbox whose design is presented in this work. This tool is used for the static and dynamic analysis of a catenaries system, which is shown by means of a real case of study.

Introduction

In order to achieve adequate benefits in the circulation of railway units, the pantograph–catenary contact force has to be maintained as uniform as possible, avoiding contact losses. Developing a mathematical model, which allows us to simulate the mechanical behavior of the system, can be helpful in specifying optimal assembly conditions in the catenary or aerial contact lines.

As it is indicated by Simeon and Arnold (see [16]), this part is the most critical in the transmission of the electrical energy in the modern high-speed trains, and therefore, many studies have been developed in this field; about the design of new models of pantographs and catenaries, or about the simulation of this interaction, obtaining results used in the new installations with the objective of obtaining a permanent contact between the pantograph and the contact wire.

During the last years, passengers transportation by railway has experienced a considerable increase in some European countries (Germany, France, Spain, …). For that reason, reaching of higher velocities in railways has become a very important target. In that scenario, the pantograph/catenary system, with its dynamic behavior, becomes a crucial component (see [12], [13], [16]), because at high speed it is very difficult to guarantee the permanent contact of the pantograph head and the contact wire, more over without the increase of noise and wear.

To do this simulation, the numeric integration of the differential equation of the pantograph–catenary system presents a great difficulty due to fact that it is a system of nonlinear equations with constraints and there are also a high number of variables that appears on the mathematical formulation, which has the consequent requirements of memory and computation time. The aerial contact line is built considering a range of spans, normally 15 or 20, which are 60 m long, constituting each series an independent system, being necessary to consider a lot of short cable elements, when carrying out discretization by the Finite Elements Method (FEM) [4], [6].

Besides, the resulting differential equations are not linear, when varying the stiffness matrix of the system each time, being also a sparse matrix type. The complete study of this mathematical model may has been presented in [1].

Related work with our tool present in the literature are the following:

•
The PANDA tool for pantograph design and testing, presented in [3]. In this tool, four classes of pantograph structures can be chosen to do the simulation, but the model of the contact line and the catenary is simpler than ours.
•
Drugge et al. [9] present some ideas to simulate the interaction pantograph–catenary. In this work is well defined the state of the art, and there are described the main concepts that should be present in a tool useful for engineers, design experts and simulation experts. Up to our knowledge these ideas have not been implemented by the authors.
•
Arnold and Simeon [15], [16] have made a considerable effort in the solution of the pantograph–catenary dynamics. Some of this work has been taken into account in our work, but the solution proposed is limited to the mathematical model, and no considerations about the amount of time and space are taken into account to solve the problem in the proposed way. Moreover, there is no algorithm to be implemented in a tool suitable for engineers.

Thus, the objective of this work is the implementation, by means of a high performance algorithm, described in the previously indicated paper [1], for the calculation of the dynamical equation of the pantograph–catenary interaction, and obtaining a software tool. This tool will be very interesting to obtain simulation results, in particular, the height of contact wire and the pantograph force are plotted.

This work has been structured as follows: In Section 2 some computational aspects are presented together with the algorithm. After that, in Section 3 some of the features of the software tool implementing this algorithm is outlined. The experimental results are outlined in Section 4. Finally, the conclusions and future work are commented in Section 5.

Section snippets

High performance computing approach

As Balestrino et al. [3], the modeling of the pantograph–catenary system is extremely complex, and it is necessary to consider some restrictions in order to obtain a system adequate to evaluate the behavior. Thus, in order to solve a mathematical problem in an efficient way on a computer, the following steps are involved [7]:

(1)
Making a mathematical model of the problem, translating the problem into a mathematical language, e.g. ordinary differential equations.
(2)
Finding or developing constructive

The software tool

The algorithm presented in the previous section has been implemented as part of a software tool, called CALPE 6.0. The software package has been developed on an object-oriented database system with a visual interface under Windows. This framework is supported in the Visual FoxPro ( $©$ Microsoft) environment, and it is currently used by Adif (former part of Renfe), the Spanish company of railway infrastructures, in the development of its electrical catenary systems. This tool, whose current user

Experimental results

In this section, the experimental results obtained with the new HPC implementation of the algorithm for solving the dynamic problem is presented, considering a stitched catenary. According to that, some of the input data, that the user introduces to realize the calculation, are the following:

•
Type of catenary systems: simple with one contact wire, simple with two contact wires, stitched with one contact wire and stitched with two contact wires.
•
Number of droppers and spans.
•
Length of the section.
•

Conclusions and future work

In this work, a high performance tool which covers different issues related to the pantograph/catenary system of high-speed railways has been presented. This new approach is based on the implementation philosophy of High Quality Software. This new tool consists on two parts: a user-friendly environment for graphic data input by the user, and a set of high performance computing algorithms.

As we have commented, this tool is not only an academic study, but it is currently used in the real

Acknowledgements

This work has been partially supported by the PCI05-019 JCCM project (CEDIPAC). Also, we are very grateful to Jesus Montesinos for his kind collaboration in the development of this research.

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Damping is an important property in predicting the response of any civil or mechanical engineering structure, including railway catenary systems. Numerical models describing the pantograph–catenary interaction are dependent on a proper description of the structural damping for both systems to obtain accurate results. A proper description of the damping in different pantographs can easily be found in the literature. However, few studies have considered the damping properties in railway catenary systems even though such systems are considered to be lightly damped. The aim of this study was to identify the system damping of catenary sections by thoroughly analyse several recorded acceleration time series. These time series were sampled in several points on three different existing railway catenary systems, rendering a good description of the system damping in the frequency range of 0–20 Hz. The covariance-driven stochastic subspace identification (Cov-SSI) method was used to analyse the time series, and Rayleigh coefficients were successfully identified for all three catenary sections.
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In this work, the model adopted for the catenary has been based on the Finite Element Method, while for the pantograph a model based on the complete dynamics equations as an articulate multibody system was adopted. Thus, the work here presented is an extension of the method presented in Alberto et al. (2008), but considering now a three-dimensional model. This new version allows us more realistic simulations, and includes some details not found in traditional models, as the lateral displacement of the contact wire, or a lateral wind load actuating on the catenary.
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A high performance tool for the simulation of the dynamic pantograph–catenary interaction

Abstract

Introduction

Section snippets

High performance computing approach

The software tool

Experimental results

Conclusions and future work

Acknowledgements

Solution of the dynamical problem of pantograph–catenary interaction: a high performance computing approach

Panda: a friendly cad tool for pantograph design and testing

Finite Element Procedures in Engineering Analysis

A tool to calculate catenaries in railways

Concepts and Applications of Finite Element Analysis

Numerical Linear Algebra and Applications