Discrete-continuous computational model of the coupled dynamic system: pantograph – overhead contact line

Abstract

The paper presents the computational model of the pantograph – overhead contact line (OCL), which uses the theory of cable vibrations and Lagrange – Ritz approximation method to derive equations of motion of the overhead contact line subjected to moving pantographs. The pantograph is modelled as a dynamic system of two degrees of freedom describing the motion of two masses replacing a collector head and an articulating frame. The overhead contact line is defined as a catenary system with continuously distributed mass. It consists of a multi-span cable characterized by a curvilinear route (catenary wire) and a straight cable (contact wire) connected with a catenary wire by elastic droppers. The main objective of the paper is to present principal ideas of the computational model, with a particular emphasis on formulating the equation of motion of a pre-tensioned multi-span cable with non-negligible static sag. Much attention is paid to the description of dynamic interaction between the pantograph and overhead contact line. The model allows computer simulation of catenary vibrations induced by two pantographs passing over the contact line, as well as a simulation of dynamic increments of the contact force.