Simulation and Visualisation of the Dynamic Behaviour of an Overhead Power System with Contact Breaking

For high speed rail traffic it is necessary to design overhead power systems which minimize the contact loss between pantograph head and contact wire. To predict how different design solutions will behave it is favourable to model and simulate the dynamic behaviour. In this paper a model of an overhead power system is specified and used in simulation. The model is suitable for simulation with contact loss since it includes specifications of impact conditions between pantograph head and contact wire. Two sets of equations of motion are specified, one for the contact case and one for the non-contact case. The model also includes lateral movement of the wire due to the zigzag span and friction between the pantograph head and the contact wire. It is shown how to make animations of the system behaviour using a MCAE-system. The animations are made using a geometrical model of the system together with results from numerical simulations.

Through the examples provided, use of the mathematical model and the geometrical model is presented. The response is visualised as time histories and phase plane diagrams of different coordinates and as animations of the total system response. The different types of visualisations make an excellent combination when studying the system behaviour of different design solutions.

In one example, simulation using the linearised set of equations gives the same results as simulation using the set of fully nonlinear equations, due to periodic response and the simple alternation of contact conditions. It is shown that the situation when any of the parameters vary suddenly is possible to simulate using the fully nonlinear equations of motion.     

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.     

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.     

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.     

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.     

Innovative Solutions for Overhead Catenary-Pantograph System: Wire Actuated Control and Observed Contact Force

In this paper an innovative active pantograph for high-speed trains is proposed. The results presented are based on extensive simulation tests. The parameters used in the simulation are those of a real pantograph for high-speed trains: the pantograph model is modified by adding a wire actuation, in order to exert a constant contact force between the moving pantograph and the overhead contact wire. A wire-actuated control and contact force observers are proposed as effective solutions in the case of a possible implementation.     

Innovative Solutions for Overhead Catenary-Pantograph System: Wire Actuated Control and Observed Contact Force

In this paper an innovative active pantograph for high-speed trains is proposed. The results presented are based on extensive simulation tests. The parameters used in the simulation are those of a real pantograph for high-speed trains: the pantograph model is modified by adding a wire actuation, in order to exert a constant contact force between the moving pantograph and the overhead contact wire. A wire-actuated control and contact force observers are proposed as effective solutions in the case of a possible implementation.     

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.     

Coupled thermo-mechanical analysis and shape optimization for reducing uneven wear of brake pads

In vehicle braking systems, the non-uniform contact pressure distribution on the brake pad is a major cause of uneven wear. The experimental approach of the wear phenomenon is the time consuming and costly. For this reason, a threedimensional finite element (FE) model of a brake system is presented for numerical simulation in this paper. A coupled thermo-mechanical analysis is carried out to confirm the non-uniform contact pressure distribution. A correlation between the non-uniform contact pressure and uneven wear is confirmed by measuring the amount of wear in the brake pad. The shape optimization of the brake pad is performed to reduce the uneven wear. In addition, the simulation results, such as natural frequency and temperature, are compared to experimental results.     

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.     

Measurement and analysis of tyre and tread block dynamics due to contact phenomena

This paper deals with the dynamic behaviour of tyres and it is aimed at describing their dynamic features in the frequency band above 1 kHz, a range difficult to manage due to measurement noise and to the unreliability of numerical models, where the main influence is that of tread and blocks. Measurements have been made possible by fixing three three-axial micro-electro-mechanical system accelerometers on the liner and exciting the tyre under test by means of a dedicated test bench, suitably designed and constructed. Different kinds of tests have been considered in this research and described in the present paper. All of them show that a strong link exists between contact phenomena and tyre response in the frequency band over 1 kHz. This field is dominated by the tread and block dynamic responses. Furthermore, it is shown that vibrations of a sliding tyre give contributions in that frequency range for the above-mentioned reasons. It is thought that the study of the tyre behaviour over 1 kHz, though affected by significant uncertainties, can provide a proper knowledge to improve breaking effectiveness.     

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.     

Numerical method for simulating tire rolling noise by the concept of periodically exciting contact force

For the numerical simulation of tire rolling noise, an important subject is the extraction of normal velocity data of the tire surface that are essential for the acoustic analysis. In the current study, a concept of periodically exciting contact force is introduced to effectively extract the tire normal velocity data. The ground contact pressure within contact patch that is obtained by the static tire contact analysis is periodically applied to the whole tread surface of stationary tire. The periodically exciting contact forces are sequentially applied with a time delay corresponding to the tire rolling speed. The tire vibration is analyzed by the mode superposition in the frequency domain, and the acoustic analysis is performed by commercial BEM code. The proposed method is illustrated through the numerical experiment of 3-D smooth tire model and verified from the comparison with experiment, and furthermore the acoustical responses are investigated to the tire rolling speed.     

An efficient approach to the analysis of rail surface irregularities accounting for dynamic train–track interaction and inelastic deformations

A two-dimensional computational model for assessment of rolling contact fatigue induced by discrete rail surface irregularities, especially in the context of so-called squats, is presented. Dynamic excitation in a wide frequency range is considered in computationally efficient time-domain simulations of high-frequency dynamic vehicle–track interaction accounting for transient non-Hertzian wheel–rail contact. Results from dynamic simulations are mapped onto a finite element model to resolve the cyclic, elastoplastic stress response in the rail. Ratcheting under multiple wheel passages is quantified. In addition, low cycle fatigue impact is quantified using the Jiang–Sehitoglu fatigue parameter. The functionality of the model is demonstrated by numerical examples.     

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.     

An Investigation into Stick-Slip Vibrations on Vehicle/Track Systems

A model for the numerical simulation of vehicle/track interaction and stick-slip vibration is presented. A finite element model is developed to calculate vertical contact forces. These forces are then coupled through the contact patch into a non-linear time-domain model by which the stick-slip vibration behaviour of a wheel-rail system is analysed. The investigation suggests that stick-slip vibration may occur if a vehicle which has a maligned or an initial 'wind-up' wheeiset meets a vertical irregularity or contaminants on the track.     

Basic Analytical Study of Pantograph-catenary System Dynamics

For a high speed electrical rail system, good dynamic performance of the pantograph-catenary system is vital for smooth and continuous current collection. It has been known for many years that to achieve this the head of the pantograph should be made as light as possible and the average stiffness of the catenary should be high. These conclusions, however, have been reached by numerical modelling and operational experience. In this paper the pantograph-catenary system is modelled as a time-varying, single degree-of-freedom system to facilitate an analytical investigation of the system dynamics. Although the model is very simple, it allows physical insight into the dynamic behaviour of the system, and because the excitation is parametric it also allows the stability of the system to be investigated. The finite element method is used to determine the catenary characteristics and Floquet theory is used to analyse the behaviour of the coupled system.     

特大断面隧道原位扩建的施工力学特性分析

以金鸡山特大断面隧道原位扩建工程为背景，介绍了核心五步法的原位扩挖方案，并通过数值模拟与现场监测手段，分析了特大断面隧道原位扩建的施工力学特性。结果表明:目标断面附近掌子面右上、左上部围岩开挖，以及临时竖撑拆除、仰拱回填，使得拱顶沉降显著增大。同时临时竖撑的支承作用，使得作用在衬砌拱顶与拱底处的围岩压力较集中，而先右后左的扩挖方案使得衬砌右侧围岩压力明显大于左侧。金鸡山隧道原位扩建施工过程中，对目标断面的拱顶沉降和水平收敛进行了长期跟踪监测，其结果与数值模拟较为吻合。     

Method for obtaining the wheel–rail contact location and its application to the normal problem calculation through ‘CONTACT’

This work presents a robust methodology for calculating inter-penetration areas between railway wheel and rail surfaces, the profiles of which are defined by a series of points. The method allows general three-dimensional displacements of the wheelset to be considered, and its characteristics make it especially suitable for dynamic simulations where the wheel–rail contact is assumed to be flexible. The technique is based on the discretisation of the geometries of the surfaces in contact, considering the wheel as a set of truncated cones and the rail as points. By means of this approach, it is possible to reduce the problem to the calculation of the intersections between cones and lines, the solution for which has a closed-form expression. The method has been used in conjunction with the CONTACT algorithm in order to solve the static normal contact problem when the lateral displacement of the wheelset, its yaw angle and the vertical force applied in the wheelset centroid are prescribed. The results consist of smooth functions when the dependent coordinates are represented as a function of the independent ones, lacking the jump discontinuities that are present when a rigid contact model is adopted. Example results are shown and assessed for the normal contact problem for different lateral and yaw positions of the wheelset on the track.