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.     

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.     

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     

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.     

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.     

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.     

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.     

销接节点考虑接触特性的设计讨论

销接连接形式具有接触受力的特性。若不考虑这种特性,按现行设计思路将会夸大销轴受力的不利情况。参考Winkler弹性基础模型的假定,建立了一种新的简化计算模型。在此基础上推导出销轴跨中弯矩的设计计算公式。分析表明跨中弯矩在按规范JTJ025-86计算结果的基础上应乘以系数β进行折减,以考虑荷载沿销轴轴向的分布。销接节点实例分析证实按该模型计算的结果与接触仿真模拟的结果吻合程度较好。     

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.     

‘Gasen-do FE’ statement of methods

Gasen-do FE is a simulation software for pantograph/catenary dynamic interaction analysis. Gasen-do FE is based on the non-linear finite element method, and its code is implemented in Matlab. This program corresponds to 2D and 3D models of simple and compound catenaries. Steady arms and catenary suspension equipments such as droppers and hangers are modelled as bar elements taking into consideration the tangential stiffness due to their geometrical non-linearity. It is possible to simulate the effect of slackening of droppers and hangers. This paper will introduce the computational algorithm of this program and the validation result by comparing with experimental data.     

体外预应力结构计算的接触分析方法

提出采用接触分析方法进行体外预应力结构的计算模拟。同时,为验证此方法的可行性,依据相关试验参考文献资料数据,建立对应的有限元结构分析模型,采用有限元分析接触单元法和原普遍采用的共用结点法,分别对梁体进行数值模拟计算,结果表明,接触单元法具有更好的计算精度和准确性。而后,采用接触单元法针对不同体外预应力筋线形布置情况进行接触模拟计算,找到加固效果最好的体外预应力筋布设位置。     

Normal and shear forces in the contact patch of a braked racing tyre. Part 1: results from a finite-element model

In this first part of a two-part article, a previously described and validated finite-element model of a racing-car tyre is developed further to yield detailed information on carcass deflections and contact pressure and shear stress distributions for a steady rolling, slipping, and cambered tyre. Variations in running conditions simulated include loads of 1500, 3000 and 4500 N, camber angles of 0° and ?3°, and longitudinal slips from 0% to?20%. Special attention is paid to heavy braking, in which context the aligning moment is of great interest. Results generated are in broad agreement with limited experimental results from the literature and they provide considerable insight into how the tyre deforms and how the contact stresses are distributed as functions of the running conditions. Generally, each rib of the tyre behaves differently from the others, especially when the wheel is cambered. The results form a basis for the development of a simpler physical tyre model, the purpose of which is to retain accuracy over the full operating range while demanding much less computational resource. The physical tyre model is the topic of the second part of the article.     

连续配筋混凝土路面温度应力分析

基于钢筋混凝土间粘结滑移的线性和非线性本构关系,建立了连续配筋混凝土路面(CRCP)在温度荷载作用下的力学模型以及按接触理论推导的有限元刚度矩阵。得出了考虑粘结滑移线性和非线性本构关系的有限单元数值解,据此分析了降温荷载作用下路面应力、位移的分布规律。同时讨论了裂缝间距和配筋率、配筋方式对裂缝宽度的影响。结果表明,在相同的降温荷载作用下,随着裂缝间距的增大,钢筋和混凝土的应力呈现非线性增加;采用不同配筋方式对裂缝宽度的影响较大,建议设计时尽量采用小直径多根数的配筋方式。按接触有限元法进行温度应力的非线性分析,为今后的科研和设计提供了很好的理论依据。     

Tyre rolling kinematics and prediction of tyre forces and moments: part II – simulation and experiment

There are two aims for the second part of this paper: verifying the theory presented in the first part through parameter variation and comparison between simulation and experiment, and to study the effect of the belt structure on the cornering properties of radial tyres. Research has been carried out with a passenger car radial tyre and two different kinds of truck or bus radial tyres using both simulation and experiment. This second part of the paper shows that belt structure plays an important role in the generation of tyre forces and moments in addition to the effects of the tread stiffness and friction coefficients. The theory and method presented in this paper opens a new robust way to predict the tyre forces and moments from the tyre design and provides a reliable model for a generation mechanism.     

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.     

沥青路面结构有限元建模计算误差研究

建立轮胎接地形状分别为圆形和矩形两种沥青路面结构有限元模型,并对建模计算结果误差进行对比分析,并与HPDS设计程序计算结果进行比较。结果表明,沥青路面轮载接地形状对路表的影响大于面层层底和基层层底,对剪应力的影响比较大,但这些结果对HPDS设计的结果影响不大,基本接近,矩形形式的荷载结果更接近HPDS程序设计结果。说明轮胎接地形式在有限元分析中采用矩形形式是可行的。     

基于拱梁分载法变形假定的拱坝有限元分析探讨

该文提出了一种基于拱梁分载法变形假定的拱坝有限元分析方法。利用大型通用软件ANSYS,在坝体径向纤维各结点处引入位移约束方程,进行基于径向纤维直线假定的典型拱坝三维有限元分析。研究表明,该方法的分析成果与拱梁分载法的成果十分吻合,有效地解决了有限元计算的应力集中难题;同时该方法对坝体网格划分的敏感性较小,具有一定的参考价值。     

电控高压泵凸轮机构从动部异常磨损分析及试验研究

针对高压、高转速工况下高压泵滚轮工作表面出现异常磨损的现象,利用ANSYS软件对不同偏心轮转角下的偏心轮与滚轮进行了三维弹塑性摩擦接触有限元分析,在此基础上提出了解决方案。试验结果表明方案可行。这对提高高压泵的工作可靠性具有重要的意义。为同类问题的解决提供了一条有效途径。     

弹性接触下车辆—变截面梁桥竖向振动分析

基于Hertz弹性接触理论,分别推导了变截面梁单元和车辆动力方程,然后根据分析目的提出了系统方程组装和求解思路,解决了传统分析中“车轮密贴”假设和结构简单的不足.新方法系统质量和阻尼矩阵不再时变,采用Newmark-β方法直接求解,不需迭代,并采用自动半步长法准确确定接触状态发生改变时刻.数值算例表明,新方法能更为精细分析系统动力响应,并能准确模拟脱离现象.应用新方法分析了两种不同车辆模型对耦合系统动力响应的影响,结果表明:整车模型能直接准确获得车辆动力响应;若采用集总车辆模型,可采用将其前后两簧上质量加速度平均的方法近似评估车体加速度.