Keywords: pantograph-catenary interaction, three-dimensional model, central differences method.

In order to ensure an adequate performance during the railway unit circulation, the pantograph-catenary contact force must be kept as uniform as possible, avoiding contact losses. The development of a mathematical model to evaluate the mechanical behaviour of the system can be very helpful in order to specify optimal assembly conditions on the overhead contact line, also known as the catenary.

The simulation of the pantograph catenary system presents a special difficulty due to the great number of variables that appears in the equations and the consequent computing time required for its solution. Another important drawback is the complexity of the mathematical model. For this reason, in recent years, different kinds of approaches have been developed in order to solve this problem.

Most of the papers presented thus far are based on two-dimensional models, however, such a model is not entirely accurate because the catenary is a three-dimensional structural system consisting of cables, with vertical and lateral displacements, appearing vertical loads due to the weight of the components and the pantograph-catenary contact forces, and also lateral loads caused by wind and by the lateral components of the contact forces. In the study of this problem, there are also some critical issues that have not been explained with sufficient detail in the scientific literature, including: the pantograph-catenary contact, the model and slackening of the droppers, the losses of contact, and the interaction with several contact wires and several pantographs.

A method to analyze and solve this problem with these critical issues, using an efficient approach based on a three-dimensional model, is presented in this work, which is an extension of the method presented in [1] considering only two dimensions. The models for the catenary, pantograph and pantograph-catenary contact are explained initially. A non-linear system of differential equations is obtained, and a numerical algorithm is presented using the explicit central difference method, that solves the problem as a system of ordinary differential equations. This procedure was applied to develop high performance software using the visual C language, which allows us to simulate the mechanical behaviour of the system considering several kinds of effects, not considered in a conventional two-dimensional model. The method presented can be extended to perform simulations with several pantographs interacting with one or two contact wires and overlapped spans. To illustrate the advantages of the method, six tests have been developed, obtaining very precise information about the system.

1

A. Alberto, J. Benet, E. Arias, C. Cebrian, T. Rojo, F. Cuartero, "A High Performance Tool for the Simulation of the Dynamic Pantograph-Catenary Interaction", Mathematics and Computers in Simulation, 3(79), 652-667, 2008. doi:10.1016/j.matcom.2008.04.016

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £145 +P&P)