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.     

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.     

Dynamic Behaviour of a Mobile Robot Vehicle with a Two Caster and Two Driving Wheel Configuration

The actual trajectory covered by a mobile robot in motion differs from the trajectory planned on the basis of the kinematic characteristics of its directional control system. This difference is essentially related to the behaviour of wheel-road contact, the influence of dynamic loads and the presence of caster wheels.

This paper presents a mathematical model (“ DDPP) which simulates the motion of a generic mobile robot vehicle with a propulsion and directional control system based on two independent driving wheels and two caster wheels.

The differential equations of motion have been obtained by applying modified equations of Lagrange.

The role played by the dynamic loads, the wheel-road contact features and the caster wheels is discussed hereof.     

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.     

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.     

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.     

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.     

Very-High-Speed Tests on the French Railway Track

The very-high-speed tests carried out by SNCF between the end of 1989 and May 1990, are an extension of the investigations which have been made for many years in order to acquire the control of high speeds. The high-speed run which ended the tests is well known [1], [2],[3].

In order to place the final test campaign in its context, we can recall progression made during the last decade.

In February 1981, the maximal speed of 380 km/h was reached with a TGV-PSE¹ train set, having the same configuration as the series, but only seven trailers instead of eight.

During the following years, until 1986, the pneumatic suspension and the new Y 231 carrying bogies designed for TGV-ATL train sets were developed, with numerous test runnings in the speed range from 300 to 350 km/h, in order to obtain certitudes as regards the stability of the bogies and the appropriate choice of anti-hunting devices for commercial speeds of 270 km/h (LGV-PSE) or 300 km/h (LGV-ATL).

These tests allowed the definition of the TGV equipment design principles, which are applied today as regards the critical speed of the bogies.

Between 1985 and 1988, the development of the prototype train set equiped with self-controlled synchronous motors (March 1988) led once more to numerous runnings at high speed, in December 1988 with the so-called “operation TGV 88”. During this operation, the speed range from 350 to 400 km/h was investigated (maximal speed 408,4 km/h on December 12th 1988).

Apart from the capability of the synchronous traction equipment to develop the required power and the performance consisting in the realization of such tests on a line kept in operation (LGV-PSE), the teachings gathered together during this test campaign were decisive for the pursuit of the operation.

On this occasion, we discovered that:

-with the single-phase GPU pantograph mounted on this train set, we could get the current collection under control without difficulties inside the studied speed range,

-the bogies presented a stability margin distinctly higher than that which had been estimated, according to the results of former experiences.

Consequently, the test campaign of the TGV 117 could be engaged with a great confidence in the capabilities of the TGV equipment to achieve markedly higher speeds with full safety. The preparation of this test campaign had begun in 1986 and was conducted in a parallel direction to the above mentioned experimentation.

The campaign was preceded by a preliminary test campaign with the train set TGV-ATL n° 308, with a reduced train composition, including eight trailers. The goal was the validation, until 390 km/ h, of the test field consisting in the TGV-ATL Aquitaine branch, as well for the track as for the overhead contact line, the achievement of which was just ended.

The operation TGV 117 was then carried out in two phases:

-in December 1989 the train set TGV-ATL 325 with a reduced train composition consisting in four trailers between two motor cars reached the maximal speed of 482,4 km/h on December 5th,

-in May 1990 the same train set, but with only three trailers, improved the performance unto the final record: the speed of 515,3 km/h was reached on May 18th.     

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.     

On Inverse Equations for Vehicle Dynamics

Instead of writing equations which when solved yield the response of a vehicle to an input such as the front wheel steer angle, one can often invert the equations so that a response quantity is specified as an input and a new set of equations is solved yielding the steer angle required as an output. Using these equations one can discover the input steer angle a driver would need to impose in order to accomplish a specific maneuver for various vehicles.

It is shown that there are many possible inverse equation sets and that the eigenvalues of the inverse equations are hard to interpret since they may have little to do with the vehicle parameters. The linear single-input single-output case is studied first to fix ideas using a simple example. For the bicycle model vehicle, it is shown that any vehicle may have unstable inverse equations depending upon the response quantity used. Extensions to nonlinear and multiple-input multiple output systems are discussed.     

Longitudinal Oscillations of Vehicle/Trailer Combinations Induced by Overrun Braking

A mathematical model for the representation of longitudinal oscillations which can occur in car/trailer systems in braking, when the trailer brakes are applied through compression of the towing hitch, is described. The model is used to show how the trailer braking system parameters affect the steady deceleration performance of the vehicle combination, and the stability, in the linear system sense, of the steady motions. The sensitivity of the stability to other system design parameters is also examined.

Digital simulation of the motions occurring in response to a step input of car braking torque is reported, with the results confirming the predictions of the linear stability analysis, and also showing the influence of backlash in the trailer brake actuating mechanism.

The system is shown to be capable of self-excitation in a “shunting” mode, in which the car and trailer motions are in antiphase, with the stability/damping property critically dependent on drawbar damping, and only weakly dependent on other system parameters. The characteristic frequency of the “shunting” mode oscillations is shown to be controllable via the stiffness of the trailer brake linkage, but this frequency is closely related to the steady drawbar deflection which occurs in uniform deceleration.

The model behaviour described provides a basis for the design of relevant systems whose longitudinal dynamic characteristics will be satisfactory.     

Dynasim 3: A Computer Program for Simulation Of Vehicle Riding Motions

The purpose of this paper is to present analytical techniques for evaluating the dynamic riding behaviour of a vehicle. These techniques have been applied to a fairly sophisticated model of a bus, where a three-dimensional structure, elastic frame and non-linear shock-absorbers have been considered.

A computer simulation program (DYNASIM 3) has been set up, which is actually used at FIAT corporation for evaluating vehicle riding qualities and improving the design process.     

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.     

Critical Speed and Limit Speed in Phenomena of Lateral Instability on Railway Vehicles

A comparison between theoretical calculations on dynamic lateral behaviour of railway vehicles and experimental results shows quite a sizeable difference between the calculated critical speed and the actual speed at which side impact phenomena will repeatedly occur between wheel flange and rail (running speed limit), such impact speed being remarkably lower than calculated.

Another typical experimental aspect is that the running speed limit will considerably vary for the same vehicle depending on the test track conditions. Such difference is usually attributed to alterations of the wheel-rail contact surfaces, only.

This paper will discuss some concurrent causes which may prove far from negligible, such as the effects of track defects, an amplification of the dynamic lateral displacement between wheel and rail on approaching the critical speed, the track mechanical properties, and in particular the track lateral rigidity.

The influence of some geometrical factors typical of the wheel-rail contact, such as side clearance and linearized conicity, will also be discussed. The approach is based on the application of statistical methods to dynamic linear systems.     

<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.     

Lateral Dynamic Behaviour of Truck-Trailer Combinations due to the Influence of the Load*

Calculations using a 3-D simulation model which was verified by means of measurements from systematic field tests are used to investigate the influence of the load on the lateral dynamic behaviour of two different truck-trailer combinations by changing the mass and the yaw moment of inertia.

Critical oscillation frequencies, the lateral dynamic damping behaviour of the truck-trailer combinations and their instabilities under extreme driving conditions are discussed.