Hardware-in-the-loop (HIL) simulation is a promising technique to study the pantograph–catenary interaction problems by realising the interaction of a physical pantograph with a mathematical model of the overhead equipment (catenary). However, the computing power presently available on real-time CPUs only allows to run simplified models of the overhead equipment. Therefore, it is important to define catenary models that are suitable for real-time simulation and at the same time capable of accurately representing the dynamic behaviour of the catenary. In this paper, the use of a catenary model based on modal superposition is considered, and the effect of changing the number of modelled spans and the number of modal components allocated to the contact and messenger wires is investigated in view of finding the best model compatible with real-time simulation. Comparisons between HIL simulation results and line measurements are presented, to quantify the accuracy of the hybrid simulation method developed.

Real-time catenary models for the hardware-in-the-loop simulation of the pantograph–catenary interaction

Dynamic contact analysis of a tensioned beam with a moving mass–spring system

In this paper, a modeling method for a pantograph–catenary system is put forward to investigate the dynamic contact behavior in space, taking into consideration of the appearance characteristics of the contact surfaces of the pantograph and catenary. The dynamic performance of the pantograph–catenary system, including contact forces, accelerations, and the corresponding spectra, is analyzed. Furthermore, with the modeling method, the influences of contact wire irregularity and the vibration caused by the front pantograph on the rear pantograph for a pantograph–catenary system with double pantographs are investigated. The results show that the appearance characteristics of the contact surfaces play an important role in the dynamic contact behavior. The appearance characteristics should be considered to reasonably evaluate the dynamic performance of the pantograph–catenary system.

Dynamic performance of a pantograph-catenary system with the consideration of the appearance characteristics of contact surfaces

Treated herein is an elastic beam that is subjected to a constant load that travels continuously (back and forth) along its span. The dynamic deflection of the beam is investigated analytically so ...

Determination of Critical and Cancellation Speeds of Euler–Bernoulli Beam Subject to a Continuously Moving Load

The pantograph–catenary system is responsible for the electric transmission to the locomotive via the sliding contact between the pantograph head and the contact wire. The separation of the pantograph head from the contact wire is the main source of arcing, which challenges the normal operation of an electrified railway. To properly describe the contact loss procedure using simulation tools, a mathematical model of the reattachment momentum impact between the pantograph head and the contact wire is proposed in this paper. The Euler–Bernoulli beam is adopted to model the contact and messenger wires, which are connected by lumped mass-spring droppers. The Lagrange multiplier method is utilised to describe the contact between the pantograph head and the contact wire. The momentum impact generated during the reattachment process is derived based on the principle of momentum conservation. Through several numerical simulations, the contact wire uplift and the contact force are evaluated with the reattachment impact. The analysis result indicated that the velocities of the contact wire and the pantograph head experience a sudden jump at the time instant of reattachment, which leads to a sudden increase of the contact force. When the reattachment impact is included, the maximum value and the standard deviation of contact forces show a significant increase. The effect of reattachment impact is more significant with the increase of the pantograph mass and stiffness.

Study on Dynamic Interaction of Railway Pantograph–Catenary Including Reattachment Momentum Impact

This paper analyzes the dynamic contact between an overhead wire and a pantograph of a high-speed train. The analysis presents a numerical method used for solving equations that consider the motion of the wire and the pantograph subject to contact. Time integration applying the augmented Lagrange multiplier method is simultaneously introduced into the equations of wire motion and the pantograph. The velocity and acceleration contact conditions are especially considered—along with the displacement contact condition—regarding the movement of high-velocity contact point on the deformed wire. Results show that the Coriolis and centripetal accelerations of the rapidly moving contact point on the deformed wire play the crucial roles in the numerical solution's stability. The research also includes numerical simulations that are performed using a practical model consisting of suspension wire, contact wire, droppers, and pantograph.

Analysis of Dynamic Contact Between Overhead Wire and Pantograph of a High-Speed Electric Train

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Analysis of Dynamic Contact Between Overhead Wire and Pantograph of a High-Speed Electric Train