CANDY statement of methods

This paper presents a detailed overview of CANDY, a catenary–pantograph dynamic interaction software. Authors describe the main key points of the formulation, focusing on its time-integration scheme, the pantograph and contact models as well as the solution of the initial equilibrium problem. Nonetheless one of the most important features of CANDY is its moving finite element mesh, which enables accurate results without excessive computational cost. The validation of the model against the European Standard EN 50318 and some conclusions and comments about the results of the benchmark are also included.     

Nonlinear modelling of high-speed catenary based on analytical expressions of cable and truss elements

Due to the intrinsic nonlinear characteristics and complex structure of the high-speed catenary system, a modelling method is proposed based on the analytical expressions of nonlinear cable and truss elements. The calculation procedure for solving the initial equilibrium state is proposed based on the Newton–Raphson iteration method. The deformed configuration of the catenary system as well as the initial length of each wire can be calculated. Its accuracy and validity of computing the initial equilibrium state are verified by comparison with the separate model method, absolute nodal coordinate formulation and other methods in the previous literatures. Then, the proposed model is combined with a lumped pantograph model and a dynamic simulation procedure is proposed. The accuracy is guaranteed by the multiple iterative calculations in each time step. The dynamic performance of the proposed model is validated by comparison with EN 50318, the results of the finite element method software and SIEMENS simulation report, respectively. At last, the influence of the catenary design parameters (such as the reserved sag and pre-tension) on the dynamic performance is preliminarily analysed by using the proposed model.     

Active control strategy on a catenary–pantograph validated model

Dynamic simulation methods have become essential in the design process and control of the catenary–pantograph system, overall since high-speed trains and interoperability criteria are getting very trendy. This paper presents an original hardware-in-the-loop (HIL) strategy aimed at integrating a multicriteria active control within the catenary–pantograph dynamic interaction. The relevance of HIL control systems applied in the frame of the pantograph is undoubtedly increasing due to the recent and more demanding requirements for high-speed railway systems. Since the loss of contact between the catenary and the pantograph leads to arcing and electrical wear, and too high contact forces cause mechanical wear of both the catenary wires and the strips of the pantograph, not only prescribed but also economic and performance criteria ratify such a relevance. Different configurations of the proportional-integral-derivative (PID) controller are proposed and applied to two different plant systems. Since this paper is mainly focused on the control strategy, both plant systems are simulation models though the methodology is suitable for a laboratory bench. The strategy of control involves a multicriteria optimisation of the contact force and the consumption of the energy supplied by the control force, a genetic algorithm has been applied for this purpose. Thus, the PID controller is fitted according to these conflicting objectives and tested within a nonlinear lumped model and a nonlinear finite element model, being the last one validated against the European Standard EN 50318. Finally, certain tests have been accomplished in order to analyse the robustness of the control strategy. Particularly, the relevance or the plant simulation, the running speed and the instrumentation time delay are studied in this paper.     

OSCAR statement of methods

OSCAR (Outil de Simulation du CAptage pour la Reconnaissance des défauts) is the pantograph–catenary dynamic software developed by Société Nationale des Chemins de fer Français (SNCF) since 2004. A three-dimensional finite element (FE) mesh allows the modelling of any catenary type: alternating current (AC) or direct current (DC) designs, and conventional or high-speed lines. It is a representative of the real overhead line geometry, with contact wire (CW) irregularities, staggered alignment of the CW, dropper spacing, wire tension, etc. Nonlinearities, such as slackening of droppers and unilateral contact between the pantograph and the CW, are taken into account. Several pantograph models can be used, with a complexity level growing from the three-lumped-mass model to the multibody model. In the second case, a cosimulation between the FE method catenary and the multibody pantograph models has been developed. Industrial features for pre- and post-treatments were developed to increase robustness of results and optimise computation time. Recent developments include volume meshing of the CW for stress computation or statistical analysis and lead to new fields of studies such as fatigue failure or design optimisation. OSCAR was fully validated against in-line measurements for its different AC and DC catenary models as well as its different pantograph models (with independent strips for instance) and has continuously been certified against EN50318 since 2008.     

SPOPS statement of methods

The Simulation Programme for Overhead contact lines – Pantograph System (SPOPS) is based on a two-dimensional finite element model of an overhead contact line and a lumped mass model for a pantograph. The SPOPS allows for a lateral change of contact points between the pantograph and the contact wire and for the rolling motions of contact strips in the pantograph model. Thus, the programme can consider the stagger of a contact wire in a dynamic simulation. Either a penalty method or a Lagrange multiplier method can be chosen to model the contact phenomenon between a pantograph and a contact wire. According to pantograph–catenary benchmark results, the simulation results obtained from the SPOPS are very close to the average values of the simulation results obtained from programmes implemented in the benchmark work in all cases, including a three-dimensional (3-D) case. These benchmark results demonstrate that the SPOPS is as accurate as other fully 3-D simulation programmes while utilising minimal computational efforts.     

The results of the pantograph–catenary interaction benchmark

This paper describes the results of a voluntary benchmark initiative concerning the simulation of pantograph–catenary interaction, which was proposed and coordinated by Politecnico di Milano and participated by 10 research institutions established in 9 different countries across Europe and Asia. The aims of the benchmark are to assess the dispersion of results on the same simulation study cases, to demonstrate the accuracy of numerical methodologies and simulation models and to identify the best suited modelling approaches to study pantograph–catenary interaction. One static and three dynamic simulation cases were defined for a non-existing but realistic high-speed pantograph–catenary couple. These cases were run using 10 of the major simulation codes presently in use for the study of pantograph–catenary interaction, and the results are presented and critically discussed here. All input data required to run the study cases are also provided, allowing the use of this benchmark as a term of comparison for other simulation codes.     

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

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.     

Analysis of dynamic interaction between catenary and pantograph with experimental verification and performance evaluation in new high-speed line

Understanding the dynamic interaction between the catenary and pantograph of a high-speed train is the one of the most important technical issues in the railway industry. This is because the catenary–pantograph system plays a crucial role in providing electric power to the railway vehicle for stable operation. The aim of the present paper is to estimate the current-collection performance of this system by using numerical analysis, in particular, the flexible multibody dynamic analysis technique. To implement large deformable catenary wires, an absolute nodal coordinate formulation is used for the cable element. Additionally, an efficient contact element and an interactive model for the catenary–pantograph system are introduced. Each developed model is then used for analytical and experimental verification. Actual on-line test results of existing high-speed railway vehicles are presented and used to verify the analysis model. Finally, the performance characteristics of a new 400 km/h-class high-speed line are estimated and evaluated on the basis of international standards.     

On the implementation of an auxiliary pantograph for speed increase on existing lines

The contact between pantograph and catenary at high speeds suffers from high dynamic contact force variation due to stiffness variations and wave propagation. To increase operational speed on an existing catenary system, especially for soft catenary systems, technical upgrading is usually necessary. Therefore, it is desirable to explore a more practical and cost-saving method to increase the operational speed. Based on a 3D pantograph–catenary finite element model, a parametric study on two-pantograph operation with short spacing distances at high speeds shows that, although the performance of the leading pantograph gets deteriorated, the trailing pantograph feels an improvement if pantographs are spaced at a proper distance. Then, two main positive effects, which can cause the improvement, are addressed. Based on a discussion on wear mechanisms, this paper suggests to use the leading pantograph as an auxiliary pantograph, which does not conduct any electric current, to minimise additional wear caused by the leading pantograph. To help implementation and achieve further improvement under this working condition, this paper investigates cases with optimised uplift force on the leading pantograph and with system parameter deviations. The results show that the two positive effects still remain even with some system parameter deviations. About 30% of speed increase should be possibly achieved still sustaining a good dynamic performance with help of the optimised uplift force.     

Stochastic Monte Carlo simulations of the pantograph–catenary dynamic interaction to allow for uncertainties introduced during catenary installation

The simulation of the pantograph–catenary dynamic interaction is at present mainly based on deterministic approaches. However, any errors made during the catenary stringing process are sources of variability that can affect the dynamic performance of the system. In this paper, we analyse the influence of dropper length, dropper spacing and support height errors on the current collection quality by applying a classic Monte Carlo method to obtain the probability density functions of several output quantities. The effects of installation errors are also studied for a range of train speeds. Finally, the pre-sag that, on average, produces the best behaviour of the system is identified, allowing for the uncertainty in the catenary installation. The results obtained show the convenience to consider variability in pantograph–catenary dynamic simulations.     

CaPaSIM statement of methods

In the present paper, the method for calculation of the dynamic pantograph–catenary interaction developed by the Royal Institute of Technology and the Swedish National Rail/Road administration (Trafikverket) is described and the results of the benchmark exercise are discussed. The method is based on the commercial Finite Element software ANSYS. The geometry of the catenary and pantograph is defined in a pre-processor, BARTRAD, developed by Trafikverket, and is automatically translated into an ANSYS model. Basically all types of catenary systems could be handled as well as different types of non-linearity. There are both 2D and 3D versions of the code existing. The results achieved in this first stage of the benchmark are well in line with the results from the other partners in the benchmark study     

PantoCat statement of method

The pantograph–catenary dynamic interaction analysis program (PantoCat) addresses the need for a dynamic analysis code able to analyse models of the complete overhead energy collecting systems that include all mechanical details of the pantographs and the complete topology and structural details of the catenary. PantoCat is a code based on the finite element method, for the catenary, and multibody dynamics methods, for the pantograph, integrated via a co-simulation procedure. A contact model based on a penalty formulation is selected to represent the pantograph–catenary interaction. PantoCat enables models of catenaries with multiple sections, including their overlap, the operation of multiple pantographs and the use of any complex loading of the catenary or pantograph mechanical elements including aerodynamic effects. The models of the pantograph and catenary are fully spatial being simulated in tangential or curved tracks, with or without irregularities and perturbations. User-friendly interfaces facilitate the construction of the models while the post-processing facilities provide all quantities of interest of the system response according to the norms and industrial requirements.     

Hybrid Simulation of Dynamics for the Pantograph-Catenary System

Summary In order to examine the static and dynamic behavior of the pantograph-catenary system, a special teat facility is established and described in this paper. Since the catenary is difficult to be modeled by a hardware teat facility indoor, a mixed theoretical-experimental technique is introduced, in which the pantograph is an actual one but the catenary is just an input of a mathematical model. Bayed on setting up the hybrid simulation teat device of the pantograph-catenary system, the dynamic behavior of the system under overhead equipment with variant parameters is analyzed for different speed. The effect of the presag and the surface irregularities of contact wire on current-collection has been studied.     

Nonlinear analysis of wind-induced vibration of high-speed railway catenary and its influence on pantograph–catenary interaction

The wind-induced vibration of the high-speed catenary and the dynamic behaviour of the pantograph–catenary under stochastic wind field are firstly analysed. The catenary model is established based on nonlinear cable and truss elements, which can fully describe the nonlinearity of each wire and the initial configuration. The model of the aerodynamic forces acting on the messenger/contact wire is deduced by considering the effect of the vertical and horizontal fluctuating winds. The vertical and horizontal fluctuating winds are simulated by employing the Davenport and Panofsky spectrums, respectively. The aerodynamic coefficients of the contact/messenger wire are calculated through computational fluid dynamics. The wind-induced vibration response of catenary is analysed with different wind speeds and angles. Its frequency-domain characteristics are discussed using Auto Regression model. Finally, a pantograph model is introduced and the contact force of the pantograph–catenary under stochastic wind is studied. The results show that both the wind speed and the attack angle exert a significant effect on the wind-induced vibration. The existence of the groove on the contact wire cross-section leads to a significant change of the aerodynamic coefficient, which affects largely the aerodynamic forces applied on the catenary wires, as well as the vibration response. The vibration frequency with high spectral power mainly concentrates on the predominant frequency of the fluctuating wind and the natural frequency of catenary. The increase in the wind speed results in a significant deterioration of the current collection. The numerical example shows that a relatively stable current collection can be ensured when the wind flows at the relatively horizontal direction.     

Hybrid Simulation of Dynamics for the Pantograph-Catenary System

Summary In order to examine the static and dynamic behavior of the pantograph-catenary system, a special teat facility is established and described in this paper. Since the catenary is difficult to be modeled by a hardware teat facility indoor, a mixed theoretical-experimental technique is introduced, in which the pantograph is an actual one but the catenary is just an input of a mathematical model. Bayed on setting up the hybrid simulation teat device of the pantograph-catenary system, the dynamic behavior of the system under overhead equipment with variant parameters is analyzed for different speed. The effect of the presag and the surface irregularities of contact wire on current-collection has been studied.     

Influence of the aerodynamic forces on the pantograph–catenary system for high-speed trains

Most of the high-speed trains in operation today have the electrical power supply delivered through the pantograph–catenary system. The understanding of the dynamics of this system is fundamental since it contributes to decrease the number of incidents related to these components, to reduce the maintenance and to improve interoperability. From the mechanical point of view, the most important feature of the pantograph–catenary system consists in the quality of the contact between the contact wire of the catenary and the contact strips of the pantograph. The catenary is represented by a finite element model, whereas the pantograph is described by a detailed multibody model, analysed through two independent codes in a co-simulation environment. A computational procedure ensuring the efficient communication between the multibody and finite element codes, through shared computer memory, and suitable contact force models were developed. The models presented here are contributions for the identification of the dynamic behaviour of the pantograph and of the interaction phenomena in the pantograph–catenary system of high-speed trains due to the action of aerodynamics forces. The wind forces are applied on the catenary by distributing them on the finite element mesh. Since the multibody formulation does not include explicitly the geometric information of the bodies, the wind field forces are applied to each body of the pantograph as time-dependent nonlinear external forces. These wind forces can be characterised either by using computational fluid dynamics or experimental testing in a wind tunnel. The proposed methodologies are demonstrated by the application to real operation scenarios for high-speed trains, with the purpose of defining service limitations based on train and wind speed combination.     

Analysis of the evolvement of contact wire wear irregularity in railway catenary based on historical data

This paper studies the evolvement of the wear irregularity of contact wire using wire thickness data measured yearly from a section of railway catenary. The power spectral density and time–frequency representation based on the wavelet transform are employed for data analysis, with an emphasis on local wear irregularities that are crucial for contact wire condition assessment. To investigate the cause of wear irregularity evolvement and the mutual influence with the pantograph–catenary dynamic interaction, simulations considering the influence of wear irregularity are carried out based on the finite element method. Analyses of the actual wear irregularities and the dynamic contact force under singular and complex wear irregularities are performed. Although the wear irregularity has limited impact on the pantograph–catenary interaction, it can induce the vibration of pantograph and contact wire that will lead to a notable increase of contact force standard deviation. The evolvement of wear irregularity is closely associated with the span length and dropper distribution of catenary structure and the running direction of pantograph. In addition, it is found feasible to detect the wear irregularity based on contact force, on condition that the sampling frequency is high enough to reflect the indicative frequencies.     

Evaluation of the coupled dynamical response of a pantograph—catenary system: contact force and stresses

In this article, the static stresses in a catenary and its vibration modes are calculated by establishing the FEM model of the catenary with Euler-Bernoulli beam elements. The mode shapes of the catenary obtained are considered as the generalized variables which are used in the establishment of the motion equations of the catenary system. The physical model of the pantograph is simplified as a multi-body system with mass, stiffness, damping, and friction. On the basis of having derived the coupled motion equations of the pantograph-catenary system, its dynamic behavior is analyzed in detail and the contact force is calculated. Using the contact force as the external moving load of the FEM model of the catenary, the dynamic stress in the catenary is simulated. Through the detailed analysis and calculation, we not only obtain the dynamic stress response at any element of the catenary, but also its frequency responses. As the dynamic stress in the assistant wire is quite large, the influence of its structure on dynamic stress is analyzed and the way to reduce the dynamic stress is suggested. At last, the calculation method of dynamic stress is validated by a test.     

PCaDA statement of methods

This paper describes the methods for the numerical simulation of pantograph–catenary interaction developed at Politecnico di Milano and implemented in the simulation software PCaDA (Pantograph–Catenary Dynamic Analysis). The paper also describes how these methods were applied in the pantograph–catenary interaction benchmark treated in this special issue and provides some evaluation of the results obtained using PCaDA in this benchmark.     

Dynamic analysis of a pantograph-catenary system using absolute nodal coordinates

The dynamic interaction between the catenary and the pantographs of high-speed trains is a very important factor that affects the stable electric power supply. In order to design a reliable current collection system, a multibody simulation model can provide an efficient and economical method to analyze the dynamic behavior of the catenary and pantograph. In this article, a dynamic analysis method for a pantograph-catenary system for a high-speed train is presented, employing absolute nodal coordinates and rigid body reference coordinates. The highly flexible catenary is modeled using a nonlinear continuous beam element, which is based on an absolute nodal coordinate formulation. The pantograph is modeled as a rigid multibody system. The analysis results are compared with experimental data obtained from a running high-speed train. In addition, using a derived system equation of motion, the calculation method for the dynamic stress in the catenary conductor is presented. This study may have significance in providing an example that a structural and multibody dynamics model can be unified into one numerical system.