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.     

PACDIN statement of methods

PAntograph–Catenary Dynamic Interaction (PACDIN) is a code developed by the vehicle technology research centre (CITV) of the Universitat Politècnica de València in collaboration with the railway company Talgo S.L. The model of the catenary is a finite element model using absolute nodal coordinates. It is based on a general formulation that can be applied for analysing a wide range of catenary configurations, including stitch wire, transitions or non-straight path tracks. The formulation is fully non-linear and includes large deformations, dropper slackening and contact interaction. The model is linearised when deformations are small, as in the case of the benchmark dynamic analysis. The results of the PACDIN code show a good agreement with the average results of other benchmark codes.     

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.     

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.     

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.     

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.     

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.     

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.     

Introduction of variability into pantograph–catenary dynamic simulations

Currently, pantograph–catenary dynamic simulations are mainly based on deterministic approaches. However, the contact force between catenary and pantograph depends on many key parameters that are not always quantified precisely and can vary in time and space. To get a better chance of addressing extreme or combined critical conditions, methodologies to consider variability are thus necessary. Aerodynamic forces and geometrical irregularities of catenaries are thought to be significant sources of variability in measurement and this paper proposes methods to take them into account. Results are compared with measurements to correlate the effect of the considered parameters with experimentally observed variability. Finally, a virtual certification example is shown, with a study of the influence of speed on the impact of variability.     

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.     

<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.     

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     

Program for catenary–pantograph analysis,PrOSA statement of methods and validation according EN 50318

DB Systemtechnik is a high-performing, customer-driven service provider that, as well as authoritatively serving the Deutsche Bahn Group by dint of its specialist knowledge is also increasingly active on the global railway market. Development and testing of pantograph models and catenary systems have been part of the company's essential activity fields from the beginning. Therefore, an efficient and high-performing simulation tool is indispensable. That is why DB Systemtechnik spent high efforts to develop the program PrOSA in cooperation with the Heinz–Nixdorf–Institut (HNI) of the university Paderborn to simulate the interaction of pantograph and catenary. This article gives an overview of the most relevant properties of PrOSA. Furthermore, it is described how the benchmark requirements were implemented and processed.     

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.     

Wear/comfort Pareto optimisation of bogie suspension

Pareto optimisation of bogie suspension components is considered for a 50 degrees of freedom railway vehicle model to reduce wheel/rail contact wear and improve passenger ride comfort. Several operational scenarios including tracks with different curve radii ranging from very small radii up to straight tracks are considered for the analysis. In each case, the maximum admissible speed is applied to the vehicle. Design parameters are categorised into two levels and the wear/comfort Pareto optimisation is accordingly accomplished in a multistep manner to improve the computational efficiency. The genetic algorithm (GA) is employed to perform the multi-objective optimisation. Two suspension system configurations are considered, a symmetric and an asymmetric in which the primary or secondary suspension elements on the right- and left-hand sides of the vehicle are not the same. It is shown that the vehicle performance on curves can be significantly improved using the asymmetric suspension configuration. The Pareto-optimised values of the design parameters achieved here guarantee wear reduction and comfort improvement for railway vehicles and can also be utilised in developing the reference vehicle models for design of bogie active suspension systems.     

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.     

Sensitivity of the wheel–rail contact interactions and Dang Van Fatigue Index in the rail with respect to irregularities of the track geometry

This paper investigates the effects of the track geometry irregularities on the wheel–rail dynamic interactions and the rail fatigue initiation through the application of the Dang Van criterion, that supposes an elastic shakedown of the structure. The irregularities are modelled, using experimental data, as a stochastic field which is representative of the considered railway network. The tracks thus generated are introduced as the input of a railway dynamics software to characterise the stochastic contact patch and the parameters on which it depends: contact forces and wheelset–rail relative position. A variance-based global sensitivity analysis is performed on quantities of interest representative of the dynamic behaviour of the system, with respect to the stochastic geometry irregularities and for different curve radius classes and operating conditions. The estimation of the internal stresses and the fatigue index being more time-consuming than the dynamical simulations, the sensitivity analysis is performed through a metamodel, whose input parameters are the wheel–rail relative position and velocity. The coefficient of variation of the number of fatigue cycles, when the simulations are performed with random geometry irregularities, varies between 0.13 and 0.28. In a large radius curve, the most influent irregularity is the horizontal curvature, while, in a tight curve, the gauge becomes more important.     

斜拉桥无应力索长实用迭代算法

通过选取合理的斜拉索参数,分析了基于抛物线理论、非弹性悬链线理论和弹性悬链线理论计算无应力索长的精确度;同时给出了基于牛顿迭代法求解弹性悬链线理论非线性方程组的详细步骤,得到了较高精度的无应力索长。该方法操作简单,计算精度高,能为设计人员计算精确拉索参数提供有效便捷的手段。     

Variation in predicting pantograph–catenary interaction contact forces,numerical simulations and field measurements

The contact force between the pantograph and the contact wire ensures energy transfer between the two. Too small of a force leads to arching and unstable energy transfer, while too large of a force leads to unnecessary wear on both parts. Thus, obtaining the correct contact force is important for both field measurements and estimates using numerical analysis. The field contact force time series is derived from measurements performed by a self-propelled diagnostic vehicle containing overhead line recording equipment. The measurements are not sampled at the actual contact surface of the interaction but by force transducers beneath the collector strips. Methods exist for obtaining more realistic measurements by adding inertia and aerodynamic effects to the measurements. The variation in predicting the pantograph–catenary interaction contact force is studied in this paper by evaluating the effect of the force sampling location and the effects of signal processing such as filtering. A numerical model validated by field measurements is used to study these effects. First, this paper shows that the numerical model can reproduce a train passage with high accuracy. Second, this study introduces three different options for contact force predictions from numerical simulations. Third, this paper demonstrates that the standard deviation and the maximum and minimum values of the contact force are sensitive to a low-pass filter. For a specific case, an 80?Hz cut-off frequency is compared to a 20?Hz cut-off frequency, as required by EN 50317:2012; the results show an 11% increase in standard deviation, a 36% increase in the maximum value and a 19% decrease in the minimum value.