Fast simulation of the pantograph–catenary dynamic interaction

Abstract

Simulation of the pantograph-catenary dynamic interaction has now become a useful tool for designing and optimizing the system. In order to perform accurate simulations, including system non-linearities, the Finite Element Method is commonly employed combined with a time integration scheme, even though the computational time required may be longer than with the use of other simpler approaches. In this paper we propose a two-stage methodology (Offline/Online) which notably reduces the computational cost without any loss in accuracy and makes it possible to successfully carry out very efficient optimizations or even Hardware in the Loop simulations with real-time requirements.

An approach to geometric optimisation of railway catenaries

“…MatrixK is obtained by applying the Newmark time discretization to Eq. (6), (see [25]). F kn is the vector of known forces, which depends on information of the previous time step, F dr is the force vector necessary to compensate the slackened droppers and F inter accounts for the interaction force terms.…”

“…is suitable for modelling the whole behaviour of the system [25]. The stiffness matrix K is obtained from linearisation of dynamic equation at the static equilibrium position resulting from solving Eq (5).…”

“…The initial configuration problem of the catenary is treated in Section 3, while Section 4 is devoted to explaining the dynamic interaction problem, which is solved efficiently. These three sections are included for the sake of completeness since they provide a summary of the models presented in [9], the shape-finding problem solved in [24] and the time integration procedure proposed in [25], respectively. The optimisation problem is set in Section 5, together with the Genetic Algorithm used to solve it.…”

A Numerical Method Based on the Parametric Variational Principle for Simulating the Dynamic Behavior of the Pantograph‐Catenary System

“…A moving mesh method was presented by JimenezOctavio et al [24] to analyze the dynamic interaction of the pantograph-catenary system. Gregori et al [25] presented a highly computational-cost-saving approach (Offline/Online approach) to simulate the pantograph-catenary dynamic interaction. Bruni et al [26] described the results of a voluntary benchmark initiative concerning the simulation of pantograph-catenary interaction, which can be used to demonstrate the accuracy of numerical methodologies and simulation models.…”

Effect of the nonlinear displacement-dependent characteristics of a hydraulic damper on high-speed rail pantograph dynamics

“…In the pantograph model, the hydraulic damper was considered a single-parameter linear model with the damping coefficient as the only parameter. In many similar studies, in both lumped-mass [10][11][12][13][14][15] and multibody [16][17][18] pantograph models, the hydraulic damper was treated as a single-parameter model. Zhou and Zhang [19] optimized the pantograph parameters using the sensitivity analysis and experience, and the optimal results were experimentally validated.…”