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.     

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.     

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.     

Pantograph/Catenary Dynamics and Control

The pantograph-catenary system with its dynamic behaviour turned out to be a crucial component for new train systems required to run at higher speeds. With the present systems, operational limitations have to be accepted when running with several pantographs in the train set, when tilting trains are employed, when running on low quality catenary sections or when stricter noise reduction regulations are forcing lower noise emissions also for the pantographs. This paper gives an overview of the methods to describe the catenary and the pantograph system dynamics. Furthermore, aspects concerning the interaction between current collectors and overhead equipment, the acquisition of the model data and the verification are presented. Finally various constructions of passive pantographs and proposals for active control concepts are discussed.     

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.     

Numerical Simulation of Pantograph-Overhead Equipment Interaction

Summary The main features of a mathematical model for the simulation of pantograph-catenary dynamic interaction are presented and, in particular, some aspects related to the catenary and pantograph schematisation are outlined. The model enables to investigate the behaviour of the system in a relatively large frequency range (up to 100 Hz), due to the inclusion of the bending modes of the collector head. In order to simulate the contact between wire and collector, a procedure based on the penalty method is adopted, and it is shown by means of a numerical test case that the method reproduces the constraint acting at the pantograph-catenary interface over a wide frequency range with high accuracy, provided that suitable values are given to the contact parameters. The problem of minimising the numerical disturbances due to the discretisation of the contact wire is also discussed, showing that the entity of these disturbances can be reduced to acceptable values by adopting a proper discretisation of the contact wire, so that no post-filtering of simulation results is required. Applications to some specific aspects of current collection are presented, and comparisons with available experimental data from line tests are shown.     

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.     

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.     

Simulation model for the study of overhead rail current collector systems dynamics, focused on the design of a new conductor rail

Overhead rigid conductor arrangements for current collection for railway traction have some advantages compared to other, more conventional, energy supply systems. They are simple, robust and easily maintained, not to mention their flexibility as to the required height for installation, which makes them particularly suitable for use in subway infrastructures. Nevertheless, due to the increasing speeds of new vehicles running on modern subway lines, a more efficient design is required for this kind of system.

In this paper, the authors present a dynamic analysis of overhead conductor rail systems focused on the design of a new conductor profile with a dynamic behaviour superior to that of the system currently in use. This means that either an increase in running speed can be attained, which at present does not exceed 110 km/h, or an increase in the distance between the rigid catenary supports with the ensuing saving in installation costs.

This study has been carried out using simulation techniques. The ANSYS programme has been used for the finite element modelling and the SIMPACK programme for the elastic multibody systems analysis.     

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.     

Dynamic assessment of existing soft catenary systems using modal analysis to explore higher train velocities: a case study of a Norwegian contact line system

Significant advances made on the rolling stock have considerably increased the possibility of higher speeds in existing railways. Thus, it is important to explore higher speeds and potential limiting factors of existing soft catenary systems. The present paper investigates procedures to assess the dynamic behaviour of these systems using response sampling and modal analysis. The assessment evaluates and quantifies dynamic response along the section. To verify the approach, a case study is conducted and the following assessment methods are used: lengthwise track correlation estimating dynamic predictability, power spectral density estimations before and after passage and short-time Fourier transforms and spectrograms. The combination provides detailed information on the dynamic behaviour. The first part introduces necessary considerations for suggested modal analysis. The second part describes an existing Norwegian section. The case study is conducted using a finite element model including a straight and a given section between Oslo-Trondheim, providing detailed evaluations and system limitation detections.     

Yaw damper modelling and its influence on railway dynamic stability

This paper deals with the modelling of yaw dampers and determining the influence of the modelling of this component on the results obtained when predicting the dynamic stability of a vehicle. The first part of the work analyses the influence of the yaw damper characteristics on railway dynamic stability. Following this, a physical model of the damper is developed which allows its performance to be reproduced accurately in the whole range of operating conditions the damper is envisaged to operate in. Once obtained, it was found that the computational cost of the model was relatively high. Therefore, a simplified model has been developed. The simplified model allows obtaining accurate results without excessively increasing the time required to perform the simulations. Analysing the results obtained with this model, it has been concluded that with respect to previous model based on conventional approaches, it improves the accuracy of dynamic calculation for the stability assessment. Also, it has been found that the accurate modelling of the yaw damper is critical when dealing with the vehicle's dynamic performance. In the last part of the paper, a special type of yaw damper was studied as well as its effect on the dynamic behaviour of the vehicle.     

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.     

<TPL-PCRUN> Statement of methods

TPL-PCRUN is a software program for the dynamic interaction simulation of pantograph–catenary systems. In the benchmark, based on the finite element method, the catenary model was built and the pantograph was considered as a three-level spring–damper–mass system. Then, through the contact definition between pantograph and catenary, the coupled model of the pantograph and catenary system was established. The respective dynamic equations of motions were solved by the time integration method. Thus, the simulation results were obtained and submitted for the comparison with the other software. On the other hand, a standard model from EN50318 was established and analysed by TPL-PCRUN. The simulation results by TPL-PCRUN were remarkably consistent with the reference values given by EN50318. It was proved that the results by TPL-PCRUN can be reliable. Recently, the software has been updated and improved. Some new models and algorithms are proposed, including the rigid–flexible hybrid pantograph model, contact definition considering appearance characteristics of the contact surfaces, a fluid–solid coupling algorithm of the pantograph and catenary system, etc.     

An Active Pantograph with Shaped Frequency Response Employing Linear Output Feedback Control

In pantographs used for current collection on high speed electric trains it is desirable to minimise the fluctuations in the contact force between the collector head and the catenary. A simple two-mass linear model is employed for the pantograph and the design of the proposed control system is based on the input admittance at low frequencies. Frequency shaping is incorporated in the performance index, and a simple dynamic controller is employed to achieve optimality in an equivalent transformed system, while minimising the number of feedback quantities to be measured. A significant reduction in the average contact force appears possible.     

An Active Pantograph with Shaped Frequency Response Employing Linear Output Feedback Control

SUMMARY

In pantographs used for current collection on high speed electric trains it is desirable to minimise the fluctuations in the contact force between the collector head and the catenary. A simple two-mass linear model is employed for the pantograph and the design of the proposed control system is based on the input admittance at low frequencies. Frequency shaping is incorporated in the performance index, and a simple dynamic controller is employed to achieve optimality in an equivalent transformed system, while minimising the number of feedback quantities to be measured. A significant reduction in the average contact force appears possible.     

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.     

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.     

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.