Catenaries are large cable structures which transmit electric current to trains through sliding contact with a pantograph. The finite element method is widely used to model this dynamic interaction problem and obtain the contact force between the pantograph and the catenary. As an alternative, analytical models can also be used to study catenary dynamics, although they require certain simplifications of the features considered in numerical models. In this paper, an analytical model composed of an infinite string and a visco-elastic support is introduced and enhanced by considering a Kelvin-Voigt damping model and the initial height of the contact wire. Considering the finite element (FE) model as a reference, the analytical model parameters are properly adjusted through static and wave propagation analyses to achieve similar behaviour in both the analytical and the FE models. To check the performance of the proposed model, the steady-state response of the pantograph–catenary coupled system is calculated and compared with the results of the FE model. Finally, the analytical model is used to analyse the interference phenomenon produced during two-pantograph operation.

Catenary–pantograph contact force is generally used for assessment of the current collection quality. A good current collection quality not only increases catenary lifetime but also keeps a stable electric supply and helps to avoid accidents. Low contact forces lead to electric arcs that degrade the catenary, and high contact forces generate excessive wear on the sliding surfaces. Railway track operators require track tests to ensure that catenary–pantograph force remains between safe values. However, a direct measure of the contact force requires an instrumented pantograph which is generally costly and complicated. This paper presents a test bench that allows testing virtual catenaries over real pantographs. Therefore, the contact point force behavior can be tested before the track test to guarantee that the test is passed. Moreover, due to its flexibility, the system can be used for model identification and validation, catenary testing, or contact loss simulation. The test bench also explores using computer vision as an additional sensor for each application. Results show that the system has high precision and flexibility in the available tests.

Accurate pantograph models are crucial to obtain reliable simulations of the pantograph-catenary dynamic interaction. Non-linearities can make it a challenge to find a model design that fits the dynamic behaviour of the real pantograph. In this work, we propose a novel pantograph model including a particular non-linear mechanism, whose dynamic behaviour significantly affects the pantograph response. This mechanism is composed of two rigid bars and an oblique pre-stressed spring with dry friction and exhibits a complex non-linear behaviour. The objective is to design a model capable of reproducing the behaviour of the real pantograph, which is represented by the dataset of dynamic measurements in the pantograph tests. From a proper parametric representation of the model, the optimisation of the parameters by a genetic algorithm has achieved a good agreement with the experimental data. The resulting optimised model behaves similarly to the real pantograph for a wide range of excitations that vary in type, amplitude and position. Since the higher number of simulations performed in the optimisation makes it necessary to use an efficient simulation tool, we propose an efficient strategy to integrate systems with Coulomb’s friction.

Pantograph hardware-in-the-loop (HIL) testing is an experimental method in which a physical pantograph is excited by an actuator which reproduces the movement of a virtual catenary. This paper proposes a new method that uses analytical catenary models for HIL tests. The approach is based on an iterative scheme until achieving a steady-state regime. Some of the method's advantages include its ability to consider the delay in the control and communication system and its applicability to a wide range of analytical catenary models. The proposed algorithm was validated both numerically and experimentally. The experimental results obtained in the HIL pantograph tests were compared with those obtained from pure numerical simulations using a linear pantograph model and showed good accuracy with pantograph running at different speeds.

The pantograph-catenary dynamic interaction problem is addressed by Hardware-in-the-Loop (HIL) tests to simulate the dynamic interaction between a numerical model (the catenary) and a physical device (the pantograph). The real-time simulation requires a computationally efficient numerical model and an on time and accurate transference of the response to the pantograph, for which a Periodic Finite Element Model (PFEM) of the catenary is considered. Firstly because of the acceptable computation time required to solve it, makes it suitable for real-time simulations and, secondly, its ability to allow for the delay caused by the transfer of the numerical model response. The catenary PFEM we used considers the non-linear behaviour of the dropper slackening, leading to highly accurate HIL test results, which were validated up to a frequency of 25 Hz.