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.     

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.     

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.     

<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.     

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.     

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.     

连续梁拱桥空间计算分析

就一个连续梁拱桥方案论证过程,运用ansys有限元软件建立空间模型,对该桥的静力、动力及稳定性等控制因素进行了计算分析.结果表明,该连续梁拱桥各项特性均满足规范要求.     

Development of simulation technology for dynamic behavior of crankshaft systems in motorcycle engines

In order to improve durability and marketability of an engine and reduce the development period, a crankshaft system simulation technology was developed.A crankshaft and a crankcase are modeled using the finite element method (FEM). The models and a calculation model of the hydrodynamic reaction force of bearings are linked and the crankshaft behavior is calculated using numerical integration within the time domain. Therefore, this simulation technology enabled accurate prediction of the motion behavior of a crankshaft up to the high operating speeds that are unique to motorcycle engines.     

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.     

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.     

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.     

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.     

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.     

配气机构凸轮—挺柱接触应力的数值模拟

针对常规理论解法和有限元方法求解凸轮—挺柱之间接触应力简化过多的问题,并考虑凸轮动力学设计要求,应用TYCON软件对某型号发动机建立配气机构多质量动力学模型,对凸轮—挺柱接触应力进行了计算,分析接触应力最大值分布情况以及各因素对其影响,其结果可为凸轮挺柱机构的动力学设计提供依据。     

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.     

滑板式侧滑仪受力特性及测量误差机理分析

为了解决滑板式侧滑仪测滑量检测结果离散性大、重复性差的问题,以滑板为研究对象,通过滑板与轮胎胎面之间侧向力的相互作用,从理论上分析滑板在检测过程中的受力特性,建立滑板横向运动的力学模型和相应的运动微分方程,并对其进行求解,得出滑板位移的理论计算公式和前转向轮在滑板上的运动胎迹;最后分析和讨论了侧滑值受到回位弹簧的刚度、滑板的质量、被检车辆的质量和被检车辆速度的影响规律以及侧滑仪测量误差的形成机理。计算和分析结果表明:滑板的位移是滚动轮胎在滑板上的位置函数,其按一定的角频率波动变化;滑板位移的最大值与滑板所受的侧向力成正比,与弹簧刚度成反比。     

Establishment and verification of three-dimensional dynamic model for heavy-haul train–track coupled system

For the long heavy-haul train, the basic principles of the inter-vehicle interaction and train–track dynamic interaction are analysed firstly. Based on the theories of train longitudinal dynamics and vehicle–track coupled dynamics, a three-dimensional (3-D) dynamic model of the heavy-haul train–track coupled system is established through a modularised method. Specifically, this model includes the subsystems such as the train control, the vehicle, the wheel–rail relation and the line geometries. And for the calculation of the wheel–rail interaction force under the driving or braking conditions, the large creep phenomenon that may occur within the wheel–rail contact patch is considered. For the coupler and draft gear system, the coupler forces in three directions and the coupler lateral tilt angles in curves are calculated. Then, according to the characteristics of the long heavy-haul train, an efficient solving method is developed to improve the computational efficiency for such a large system. Some basic principles which should be followed in order to meet the requirement of calculation accuracy are determined. Finally, the 3-D train–track coupled model is verified by comparing the calculated results with the running test results. It is indicated that the proposed dynamic model could simulate the dynamic performance of the heavy-haul train well.     

桥梁平转施工中球铰界面的摩擦力精确计算方法及验证

转体施工是桥梁施工中的重要方法,中国已成功将该技术应用于数百座大跨桥梁的施工。大吨位转体施工中,摩擦力的计算至关重要,但现有工程实践中给出的近似计算方法与工程试验值有较大差距。因此,精确的摩擦力和摩阻力矩计算理论,是转体施工中亟待解决的问题。首先采用称重原理获得竖向摩阻力矩,然后利用接触理论求得接触面的应力分布规律,并推导出竖向摩阻力矩理论公式,进而求得摩擦因数。之后,利用获得的摩擦因数,根据接触面的应力分布规律,获得了平转过程中的水平摩阻力矩和牵引力。最后,进一步将前述方法推广到带滑块的转体装置中,获得统一的摩擦因数、摩阻力矩计算方法。将该方法和有限单元法的计算结果进行对比,两者高度吻合;和实际工程数据对比,显示所提方法的结果更加合理、准确。主要结论如下：①根据称配重方法计算摩擦因数时,现有近似计算方法获得的摩擦因数,随着球铰参数α的增加误差逐渐增大。②球铰表面接触应力呈现出中间向两边逐渐增大的分布特征,现有计算方法假设均匀的法向接触应力分布与实际应力分布差距较大。无滑块转体装置中,有限元模型计算所得水平转动摩阻力矩比现有近似方法计算的大14.3%;而该方法计算值与有限元结果误差仅为3.0%。③在带滑块转体装置中,与工程实测值相比,现有近似方法和该改进方法获得的水平转动摩阻力矩误差分别为31.4%和23.7%。由此可见,该方法进一步提高了计算准确度。