2009 Paper VSD JPombo Et Al

7/28/2019 2009 Paper VSD JPombo Et Al

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Vehicle System Dynamics

Vol. 47, No. 11, November 2009, 13271347

Influence of the aerodynamic forces on the

pantographcatenary system for high-speed trains

J. Pomboa, J. Ambrsioa*, M. Pereiraa, F. Rauterb, A. Collinac and A. Facchinettic

aIDMEC/IST Technical University of Lisbon, Av. Rovisco Pais, Lisbon, Portugal; bSNCF Divisionof Innovation and Research, Paris, France; cDepartment of Mechanical Engineering, Politecnico di

Milano, Via Giuseppe La Masa Milan, Italy

(Received 8 September 2008; final version received 8 November 2008)

Most of the high-speed trains in operation today have the electrical power supply delivered through thepantographcatenary system. The understanding of the dynamics of this system is fundamental since itcontributes to decrease the number of incidents related to these components, to reduce the maintenanceand to improve interoperability. From the mechanical point of view, the most important feature of thepantographcatenary system consists in the quality of the contact between the contact wire of thecatenary and the contact strips of the pantograph. The catenary is represented by a finite elementmodel, whereas the pantograph is described by a detailed multibody model, analysed through twoindependent codes in a co-simulation environment. A computational procedure ensuring the efficientcommunication between the multibody and finite element codes, through shared computer memory,

and suitable contact force models were developed. The models presented here are contributions forthe identification of the dynamic behaviour of the pantograph and of the interaction phenomena inthe pantographcatenary system of high-speed trains due to the action of aerodynamics forces. Thewind forces are applied on the catenary by distributing them on the finite element mesh. Since themultibody formulation does not include explicitly the geometric information of the bodies, the windfield 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 experimentaltesting in a wind tunnel. The proposed methodologies are demonstrated by the application to realoperation scenarios for high-speed trains, with the purpose of defining service limitations based ontrain and wind speed combination.

Keywords: multibody dynamics; pantographcatenary interaction; contact forces; cross-wind

1. Introduction

The behaviour of the pantographcatenary system, which plays a key role in the railway

transportation reliability, is strongly influenced by deviations from the theoretical conditions

that are usually foreseen in simulations, in which disturbances are generally not considered.

For instance, extreme environmental conditions lead to limitations of train operation and/or

damage of components of the pantograph and catenary in the short or long run. In the worst

*Corresponding author. Email: [email protected]

ISSN 0042-3114 print/ISSN 1744-5159 online 2009 Taylor & FrancisDOI: 10.1080/00423110802613402http://www.informaworld.com


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1328 J. Pombo et al.

cases a complete service interruption may take place due to the need to repair equipment and

restore the normal operating conditions. Therefore, from the designers and operators points

of view, it is required that, after a pantographcatenary system is optimised, its sensitivity to

singularities and deteriorated conditions that occur in real operation scenarios is identified.

The evaluation of these effects, prior to a test run on a network, provides important indications

concerning the problems that are more likely to occur while contributing to the identification

of suitable solutions.

A class of problems that requires analysis relates to the climatic conditions of the

pantographcatenary systems operation, among them temperature and cross-wind are the

most influencing on service limitations and restrictions. Temperature has the effect of modify-

ing the static position and the tension of the catenary wires. This condition is more pronounced

in a curve and less important in a straight track. In case of very low temperature, the formation

of ice on the wires changes their mass modifying the static position of the overhead contact

line. The effect of the additional mass may also be relevant for the dynamics of the coupled

pantographcatenary system.For the cross-wind action the three relevant effects are the direct effect of the wind on the

overhead contact line; the direct effect on the pantograph components; and the indirect effect

due to the additional motion of the carbody imparted to the base of the pantograph. In the

work presented here, the wind forces are applied on the catenary by distributing them on the

finite element mesh and are applied to each body of the pantograph as timespace dependent

nonlinear external forces. The third effect is not considered here explicitly but can be applied

as a perturbation of the motion on the basis of the pantograph.

For the evaluation of the lateral wind effects on the current collection, it is thus necessary

to define in some way both the wind forces on the catenary and on the pantograph. Up to now

these topics have been generally treated separately, with different specific goals. In particular,considerable investigation has been developed for the definition of cross-wind effect on the

safety running of high-speed trains [1,2]. The effect of cross-wind on safety, in these studies,

is based on the combination of wind tunnel test, for the definition of aerodynamic coefficient

used for the calculation of aerodynamic forces acting on the carbody of the rail vehicle, and

on multibody simulation of rail vehicle dynamics running on a track.

Other topics of investigation concern the field of incoming flow around the carbody, which

represents the environment in which the pantograph is inserted, on the top of the carbody of

the locomotive [3,4]. Wind tunnel investigations have also been carried out with the purpose

of defining the aeroacoustic aspects of pantograph aerodynamics in terms of local effects at

relatively high frequency, in particular concerning the base insulators [5] and lateral horns

of the collector head [6]. Consideration of steady and low frequency effects have been made

defining the aerodynamic uplift on the articulated frame, and drag and lift forces on the

collectors, in order to take into account the effects of turbulence of the flow incident on the

pantograph in the dynamic simulation [7], as well as the unbalance of mean contact forces

created by the aerodynamic forces acting on the collectors.

As far as the catenary is concerned, apart from the consideration of a mean wind speed for

the design of catenary and its supporting structure, according to wind maps [8], investigations

have been carried out for the consideration of galloping instability of catenary wires motion,

due to wind action in particularly exposed areas. Mitigations of such phenomena based on

wind shield or increase damping of catenary have been considered [9,10].

Clearly, the motion of the catenary induced by wind has an effect on the current collection,whereas on the other side the aerodynamic forces acting on the pantograph induce supplemen-

tary motion, which in turns modifies again contact force. The aim of the article is to combine

both effects on the catenary and on the pantograph in order to define realistic scenarios for

lateral wind. The wind field is considered dependent on space and time and characterised


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Vehicle System Dynamics 1329

through its main statistical characteristics, such as its mean value, turbulence, integral scale

and lateral cross-correlation. The direct action on the pantograph is calculated considering the

instantaneous relative flow speed, resulting from the combination of train speed with lateral

wind. In order to calculate the aerodynamic forces acting on the elements of the pantograph, the

aerodynamic coefficients of the different pantograph components are necessary. This is done

through the elaboration of wind tunnel tests, or by means of a computational fluid dynamics

simulation. Although wind tunnel identified forces are used in this work, the methodology

presented here to characterise the pantographcatenary dynamics is general and independent

from the source of the wind force data.

The catenary and pantograph subsystems are modelled and analysed in this work using

linear finite element and multibody codes, respectively. The forward dynamics solution of

the problem is obtained through the co-simulation of these codes according to the strategies

described in [1113]. Other approaches to solve the dynamics of the catenarypantograph

interaction recently reported in the literature include modelling the catenary as a nonlinear

flexible body, using a finite element procedure, and the pantograph as a multibody system inthe same software being the contact between these two elements represented by a sliding joint

[14]. In one hand, the sliding joint representation of the catenarypantograph interaction does

not allow for the separation between the contact wire and contact strips [14,15], and on the

other hand, the use of nonlinear finite elements to represent the catenary adds unnecessary

complexity to the methodology while it does not allow for the use of realistic catenary models.

Consequently, in this work the contact interaction uses continuous contact force models, such

as those described in [1619], which are based on penalty formulations and allow for the

separation of the components in contact. The multibody description of the pantograph, in

itself, also requires that contact between its mechanical components is accounted for and that

the stick-slip phenomena are also represented [20,21].In the work presented here the effect of the wind field forces is investigated by means of suit-

able models developed in this work which include the effects of the aerodynamic forces on the

behaviour of the pantographcatenary interaction. The methodologies proposed are demon-

strated by their application to real operation scenarios of a high-speed train on a straight track.

The results are discussed against those obtained for standard running conditions, i.e. without

aerodynamic forces.

2. Aerodynamic forces on pantographcatenary system

Cross-winds have a direct effect on the pantographcatenary dynamics for two main reasons:

(i) on the catenary, it causes a mean lateral displacement of the wires and a lateral/vertical

dynamic motion induced by turbulence; (ii) on the pantograph, it causes a variation of the

uplift force according to the relative wind angle of incidence, and additional vibration due to

the turbulence of the incoming wind.

The catenary is represented here by a finite element model of the complete system, whereas

the pantograph is described by a detailed multibody model. The wind forces are applied on

the catenary by distributing them on the finite element mesh. Since the multibody formulation

[2224] 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.The finite element and the multibody models are evaluated by separate codes that use

different time integration algorithms. Therefore, an extra difficulty that arises in the study of

the complete pantographcatenary interaction concerns the need for the co-simulation of the

two independent codes. In order to be computationally efficient, the communication between


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the multibody and finite element codes, which ensures the co-simulationprocedure, is achieved

by using shared computer memory. The gluing mechanical element between the two codes

is the contact model. It is through the representation of the contact and of the integration

schemes applied to the referred models that the co-simulation is carried on. An integrated

methodology to represent the contact between the finite element and multibody models, based

on a continuous contact force model that takes into account the co-simulation requirements

of the integration algorithms used for each subsystem model is proposed in [11,12,25], and

therefore, it is not discussed here any further.

2.1. Wind field forces acting on the catenary

Cross-winds influence the dynamic behaviour of the overheadcontact line because the catenary

exhibits vertical and lateral motion due to the turbulent wind forces acting on the wires. The

lateral displacement of the catenary is generally prevailing, modifying the location of the

contact point between contact wires and pantograph collectors. Unless there is a direct action

along the longitudinal axis of the line, motion of the contact wire along this direction can be

neglected.

A brief description of the procedure used to calculate the forces acting on the catenary, and

the corresponding vector of generalised forces referred to its degrees of freedom (d.o.f.), is

presented. The wind is considered as an ergodic phenomenon, which enables it to be described

by means of significant statistical characteristics, i.e.:

Mean speed (1015 period mean) u in the y direction, w in the vertical direction.

Index of turbulence IU, defined as IU,W = U,W/U , being U,W the standard deviation of

the wind speed and U the mean value of the horizontal component.

Integral scale LU, LW, which are related to the dimension of the wind vortex.

Spatial correlationcoefficient CUx, CWx related to the correlation of the UandWcomponents

along the x-direction.

Power spectral density (PSD) of the wind, which establishes the distribution of the power

along the frequencies.

Various formulations can be used to interpret the real wind PSD. The Von Karman formulation

is adopted, which has the following formulation, for the horizontal and vertical components:

PSDU =42/f(fLU/U)

[1 + 70.8(f Lux/U)2

]5/6

PSDW =(1 + 188.8(fLW/U)

2)2/f

[1 + 70.8(f Lwx/U)2

]5/6

(1)

In both expressions f is the frequency, expressed in Hz. Wind is generated according to its

timespace distribution along the line, related to the horizontal and vertical dynamics variation

of wind speed occurs. A time-varying wind field is then artificially generated, and the forces

acting on the wires are calculated with the quasi-static theory (q.s.t.).

The overall procedure for the side wind simulation on the catenary follows several steps.

First, a subdivision of the line along x intervals spaced according to dropper distance is made,

then the time history of wind in the first section, based on integral scale, index of turbulence,

mean wind speed for the horizontal Uand(eventually) for the vertical component is carried out:

u1(t) = Um +

Narm

1

un cos(not+ 1n) (2)

where the amplitude un of the generic harmonic is in accordance with the PSD, and the

phase is randomly generated. The PSD in the subsequent sections is defined according to


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Figure 1. Drag and lift wind force components according to relative wind speed.

Davenports [26] expression:

= e(Cfnx/Um) (3)

considering a coherent part and a non-coherent part following the procedure already used for

other structures with longitudinal prevalent dimension, such as suspended bridges, and for

investigation of cross-wind on trains [2729]. The generation of the time histories for each

wind section is carried out by means of the wave superposition method. Once the wind time

histories are defined in all sections, the aerodynamic force per unit length on the catenary are

calculated considering the drag FD and lift FL force components, represented in Figure 1, as

function of the relative wind speed vrel, and according to

fD =1

2CDv

2rel fL =

1

2CLv

2rel (4)

where is the air density and CD and CL represent the drag and lift coefficients of each wire

(contact wire and messenger wire).

Using the principle of virtual work, the distributed aerodynamic forces are then converted

into generalised forces associated with the finite element d.o.f. of the wires. These forces are

function of time t, of their longitudinal location along the catenary and of the catenary nodal

velocities x , being described as

fwind = fwind(u(,t),w(,t), x) (5)

where u and w are, respectively, the lateral and vertical components of the wind velocity. The

wind force vector fwind is assembled in the finite elements formulation together with the force

vector resultant from the contact with the pantograph.

2.2. Wind forces acting on the pantograph

With the cross-winds the pantograph uplift is modified since the relative flow speed incident on

the pantograph is composed of longitudinal and lateral components, being the vertical compo-

nent induced due to the geometry and orientations of the pantograph mechanical components.Generally, the main direct effect of the cross-winds on the pantograph is the increase of the

uplift forces, which lead not only to a higher, and sometimes unacceptable, vertical motion of

the contact wire but also to a wider range of its variation. This problem can be aggravated due

to the wind-induced perturbation of the suspension of the catenary.


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Figure 2. General view of the CX pantograph installation in the wind tunnel.

The pantograph used in this work for the study of the wind effects on the dynamics of

the electric power collectors is the Faiveley CX pantograph, shown in Figure 2. In order to

study the effect of the wind field forces on the pantograph, time-dependent nonlinear external

forces are applied on the bodies that compose the pantograph model. These forces represent

the aerodynamic forces expressed by means of drag, lift and couple coefficients. The effect of

turbulence is also included by considering the time-varying features of the wind velocity and

the fact that the pantograph is moving into the wind field, where it experiences a wind time

history that depends on the instantaneous wind speed and on its position along the line.

The evaluation of the aerodynamic forces acting on the elements of the pantograph requires

the calculation of the aerodynamic coefficients of the different pantograph components,retaining only the forcing effects:

FDi =1

2(CDA)iV

2P,rel FLi =

1

2(CLA)iV

2P,rel CMi =

1

2(CMAh)iV

2P,rel (6)

with VP,rel representing the relative flow speed incident on the pantograph, (CDA)i, (CLA)iand (CMAh)i being the pressure coefficients, respectively, for drag, lift and couple for the ith

element into which the pantograph has been divided. This is done here by using wind tunnel

experimental tests, carried out in the wind tunnel located at Politecnico di Milano, which has

a section with 44 m duct. Figure 2 shows a general view of the CX pantograph installed

in the wind tunnel, in the open chamber configuration, recommended for use in this kind oftests. Drag, lift and couple coefficients have been estimated for the following elements:

fixed frame;

lower arm of the articulated frame;

upper arm of the articulated frame;

knee.

The coefficients for the secondary lever of the articulated frame, for which only the drag and

lift components have been evaluated, are deduced from a CFD analysis on the pantograph,

and graphically shown in Figure 3. For all the elements into which the pantograph has been

divided into, drag, lift and couple coefficients have been considered for a total of 12 unknowns.Four relationships hold at each speed, considering the global drag, lift and moment aerody-

namic actions on the entire pantograph, calculated from the contributions of the different

sub-elements, and the aerodynamic uplift S, evaluated also, respectively, for the drag, lift and

aerodynamic couple, through the Jacobian Xi, Yi and i of each component expressed


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Figure 3. Drag and lift wind equivalent forces and moments on the pantograph components.

with respect to the rotation angle of the lower arm of the articulated frame:

FD =

N

i=1

FDi; FL =

N

i=1

FLi

CM =

N

i=1

FDi (hb + Yi)+

N

i=1

FLi (Xi XCB)+

N

i=1

CMi

S=1

YC

N1

i=1

FDiXi + FLiY i + CMi i

(7)

where Yi and Xi describe the location of the application point of the aerodynamic force for

each pantograph element, and hb andXCB are the reduction point of the dynamometric balance

used in the tests. The pressure coefficients are presented in Figure 4 as function of the yaw

angle.

Since four speeds have been considered for each configuration, 16 measured values are avail-

able, so that a minimisation process can be undertaken considering the 12 coefficients (CDA)i,

Figure 4. Pressure coefficients of drag longitudinal components of the sub-elements of the pantograph, identifiedfrom the wind tunnel tests.


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Figure 5. Forces on the collector bow for a train speed = 300 km/h, wind speed= 20 m/s, turbulence= 15%.

(CLA)i, (CAA)i, which through the definition in Equation (6) are implied in Equation (7).

Once the pressure coefficients are determined, the aerodynamic forces can be extrapolated toa different flow speed, from the range of the wind tunnel test (1550 m/s) to the considered

value around 83 m/s (300 km/h), provided that the pressure coefficients do not depend on the

Reynolds number. This hypothesis can be confirmed considering that the aerodynamic uplift

force acting on the pantograph, determined from trial tests on the train according to EN50317

procedure available from SNCF, indicates a dependence on the square of the train speed, which

implies that formulation of Equation (6) is valid. Figure 5 illustrates the forces obtained in the

bow for a train speed of 300 km/h, wind speed of 20 m/s and turbulence of 15%.

The drag forces on the upper and lower arms act in the same way for the global drag on the

pantograph and act on the opposite way on the uplift. The same occurs for the couples, whereas

the inverse occurs for the lift forces. This different effect of the singular forces on the globaldrag, lift, uplift and couple on the pantograph allows to bind the values of the coefficients to

be identified and improves the numerical stability when using the least square minimisation.

2.3. Wind input data for the pantograph

The pantograph is loaded with the wind field forces with the characteristics measured exper-

imentally. A possible cross-wind loading situation is represented in Figure 6 for the CX

pantograph.

The pantograph model is based on a multibody methodology in which each component is

treated as a rigid body [2224]. The wind load fi(t) over component i of the pantograph isrepresented by a force and applied at its centre of mass. Because the location of the component

centre of mass is not necessarily coincident with the point of application of the resultant of the

wind forces, which is generally the aerodynamic centre of the component, a transport moment

ni(t) needs to be applied on the component. The loading of each of the pantograph mechanical


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Figure 6. Wind-loaded CX pantograph.

Figure 7. Equivalentwindloads on thepantographmechanicalelements: (a)lower arm loading; (b)top armloading;(c) registration strip loading.

components is schematically presented in Figure 7. Notice that the body-fixed coordinate

system (, , ) associated to each rigid body is attached to the body centre of mass.

Note that the equivalent loading procedure that is referred to here only applies for pantograph

models made of rigid bodies. For flexible multibody models the force (or pressure) distribution

and the respective area of application must be known and, consequently, the data must have a

different format from the one considered here.

The wind load on the pantograph and catenary, obtained experimentally, are supplied in

data files for application on the finite element and multibody modules. According to this

methodology, for each loading case there are two consistent files generated: one that contains

the description of the wind forces on the catenary and another that contains the values of the

wind equivalent forces in each mechanical component of the pantograph.

The structure of the data file that contains the description of the equivalent wind loading on

the pantograph is described in Figure 8. For each mechanical component of the pantograph

the values for the force and for the transport moment are defined for prescribed instants in

time. Note that forces and moments are vectorial quantities, and therefore, each has three

components. The inertial frame (x, y, z) is used to express the force and moment vectors.

At this point it must be emphasised that the importance of the clear definition of the inertial

frame (x, y, z), which is not to be confused with the body-fixed coordinate frames (, , )

that generally have orientations that vary in time and that are not coincident with that of the

inertial frame. The components of the wind forces and moments are inserted in the data file

for a discrete number of time instants. Such time instants may be uniformly or non-uniformlyspaced. Furthermore no time-stepping strategy is suggested for this table.

Any nonlinear load applied in any body of the system must be continuous in time, i.e. it

must be readily available at any time step of the dynamic integration procedure. Because the

force data contained in the data files, represented in Figure 9a, is not only discrete but also


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Figure 8. Structure of the data files with the wind forces on the different elements of the pantograph, as if appliedin the centre of mass with the transport moments.

Figure 9. Conversion of the nonlinear force database: (a) data file with irregular time stepping; (b) data file withsmall constant time step.

follows a non-constant time stepping with no particular time step size limit, an interpolation

procedure must be used to generate intermediary data. Instead, another data file with a very

small and constant time step is produced from the original nonlinear force/moment data file,

with the structure described in Figure 9b.

The methodology used in the software program to create the new nonlinear force/moment

database starts by reading the data file withthe original information of the wind forces, depicted

in Figure 9a. Despite the number of control points provided to define the nonlinear curves,

represented in Figure 10a, a pre-processing procedure is implemented in order to interpolate

the data points with shape preserving splines [30,31]. This procedure allows continuous time-

dependent forces and moments to be obtained, as represented in Figure 10b. The advantage of

using shape preserving splines is that this interpolation scheme is consistent with the concavity

of the data, which is rather useful when it is important to preserve the convex and concave

regions implied by the control points. This interpolation scheme also ensures C2 continuity

between spline segments, i.e. it guarantees that the parameterised curves have continuouscurvatures.

With the continuous description of the wind loads, the new database with a small constant

time step can be created. In this way, during the dynamic analysis the multibody program

interpolates linearly the refined database in order to obtain all required characteristics to


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Figure 10. Interpolation of the nonlinear forces from a datafile with irregular time stepping: (a)data points provided;(b) spline interpolation; (c) data points in the refined database.

define the nonlinear forces and moments, with a marginal increase of computer cost. As

shown in Figure 10c, if the refinement of the new data file is suitable, i.e. it has the magnitude

of the normal integration time step, then only a few number of interpolations, if any, will be

performed in between two successive lines of the table. It should be noted that the interpolation

and creation of the new data files are done automatically by the software in a pre-processing

phase without any user intervention.

3. Multibody model of the CX pantograph

The construction details of the multibody model of the CX pantograph are presented here.

In this application example, the CX pantograph is constrained to follow a prescribed trajectory

and subjected to aerodynamic forces.

3.1. General description

Consider a general multibody model composed of one CX pantograph constrained to followa reference path, which represents the trajectory of the pantograph base. Also assume that the

pantograph is acted upon by wind field forcesw(x,y,z, t), as represented in Figure 3. Since the

multibody formulation does not include explicitly the geometric information of the bodies, the

aerodynamic forces are applied to the bodies of the pantograph as nonlinear external forces,

as previously described. A schematic representation of the CX pantograph in such conditions

is depicted in Figure 11. Notice that the reference frame (x, y, z) represents the global inertial

frame of the general multibody system and (x, y, z) represents the reference frame associated

to the pantograph subsystem.

3.2. Rigid bodies data

The construction of the multibody model of the CX pantograph, represented in Figure 12,

involves the definitions of the data for the rigid bodies, kinematic joints, linear force elements,

nonlinear external applied forces, prescribed motion constraints and registration strips for


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Figure 11. Representation of the CX pantograph subjected to aerodynamic forces.

Figure 12. Multibody model of the CX pantograph.

Table 1. Rigid bodies data for the CX pantograph multibody model.

Inertia properties (kg m2) Initial position (m) Initial orientation

ID Rigid body Mass (kg) I/I/I x0/y0/z0 e1/e2/e3

1 Pantograph base 32.65 2.76/4.87/2.31 0.00/0.00/0.00 0.00/0.00/0.00

2 Lower arm 32.18 0.31/10.43/10.65 0.57/0.00/0.41 0.00/0.17/0.003 Top arm 15.60 0.15/7.76/7.86 0.39/0.00/1.06 0.00/ 0.18/0.004 Lower link 3.10 0.05/0.46/0.46 0.89/0.00/0.28 0.00/0.21/0.005 Top link 1.15 0.05/0.48/0.48 0.36/0.00/1.00 0.00/ 0.16/0.006 Stabilisation arm 1.51 0.07/0.05/0.07 0.55/0.00/1.42 0.00/0.00/0.00

7 Registration strip 9.50 1.59/0.21/1.78 0.55/0.00/1.51 0.00/0.00/0.00

pantographcatenary contact. Seven rigid bodies are used to represent the CX pantograph

defined according to the data presented in Table 1. The information presented in Table 1

includes the mass, the inertia properties with respect to their principal axes (, , ) and the

initial position and orientation of each body. In the first column of the table the reference

numbers that identify the bodies in the model shown in Figure 12 are presented.

A local reference frame (, , ) is rigidly attached to the centre of mass of each bodyin such a way that the axes are aligned with the principal inertia directions of the bodies, as

depicted in Figure 7. In this way, the inertia tensor of the bodies is completely defined by the

inertia moments I, I and I . Also notice that the initial position and orientation of each

body in the subsystem are given, respectively, by the location of its centre of mass and by the


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orientation of its local reference frame (, , ) with respect to the subsystem reference frame

(x, y, z).

When defining the input data for the rigid bodies that compose the CX pantograph, it

is also necessary to provide information about the external constant forces and moments

that are associated to each one of the bodies and that remain constant during the dynamic

analysis. The only value that is not null is the vertical force (FStatic) on the stabilisation arm,

as represented in Figure 12. This force represents the static force that is applied to ensure the

pantographcatenary contact.

3.3. Kinematic joints data

After the description of the data for the rigid bodies, it is necessary to define the information

about the kinematic joints that compose the multibody model of the CX pantograph. In a

multibody system, the kinematic joints are used to connect the bodies in order to restrain

some of their relative motions. Such joints are expressed as algebraic constraint equations thatintroduce kinematic relations between the coordinates that describe the system [2224,32].

In the case studied here three revolute joints (RJ) and four spherical joints (SJ) are used,

as represented in Figure 13. The revolute joints [2224,32] restrain the motion between two

bodies i and j, allowing only a relative rotation about the joint axis, as depicted in Figure 13a,

representing mechanical components such as roller bearings. As input data, the revolute joint

requires the positions of points P and Q in bodies i and j. These points must be defined in such

a way that they are aligned with the rotation axis of the revolute joint, where points Pi and Pjmust be coincident and points Qi and Qj are defined anywhere along the joint revolution axis.

Notice that the pair of points Pi and Qi is defined in the body i coordinate frame, whereas the

pair Pj and Qj is defined in the body j coordinate frame.The spherical joint [2224,32] is a ball and socket type of joint that constrains the relative

translations between two bodies i and j, only allowing three relative rotations, as represented

in Figure 13b. As input data, the spherical joint requires the position of point P in bodies i and

j coordinate frames. Notice that point Pi must be coincident with point Pj and defined as the

centre point of the spherical joint.

In Table 2, the data required to define the kinematic joints for the multibody model of the

CX pantograph is presented. The quantities in the first column of the table are references that

identify the kinematic joints in Figure 12.

3.4. Linear force elements data

The next step for the construction of the multibody model is the definition of the linear force

elements that compose the CX pantograph. These elements represent the internal forces that

Figure 13. Kinematic joints: (a) revolute joint; (b) spherical joint.


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Table 2. Kinematic joints data for the CX pantograph multibody model.

Attachment points local coordinates (m)

Connected bodies Body i Body j

ID Kinematic joint i j i/i/i j/j/j

RJ-1 Revolute joint 1 2 (0.02/0.00/0.13)P (0.82/0.00/0.00) P(0.02/1.00/0.13) Q (0.82/1.00/0.00) Q

RJ-2 Revolute joint 2 3 (0.82/0.00/0.00)P (1.01/0.00/0.00)P(0.82/1.00/0.00)Q (1.01/1.00/0.00)Q

RJ-3 Revolute joint 3 6 (1.01/0.00/0.00)P (0.00/0.00/0.00) P(1.01/1.00/0.00) Q (0.00/1.00/0.00) Q

SJ-1 Spherical joint 1 4 (0.26/0.00/0.00)P (0.69/0.00/0.00) PSJ-2 Spherical joint 3 4 (1.19/0.00/0.13)P (0.62/0.00/0.03)PSJ-3 Spherical joint 2 5 (0.78/0.00/0.00)P (1.00/0.00/0.00)PSJ-4 Spherical joint 5 6 (0.96/0.00/0.00)P (0.00/0.00/0.10)P

Table 3. Linear force elements data for the CX pantograph multibody model.

Attachment points local coordinates (m)

Spring element Bodies Body i Body j

k (N/m) L0 (m) c (N s/m) i j i/i/i j/j/j

1000 1.51 3000 1 2 0.57/0.00/0.00 0.00/0.00/0.003600 0.12 13 6 7 0.00/0.34/0.00 0.00/0.34/0.00

3600 0.12 13 6 7 0.00/ 0.34/0.00 0.00/ 0.34/0.0010000 0.10 300 6 7 0.10/0.00/0.09 0.00/0.00/0.00

develop between the bodies that are connected by linear springs and dampers, and depend

on the relative motion between the bodies. In Table 3 the data required to define the four

linear force elements that exist in the CX pantograph model is presented, where kis the spring

stiffness, L0 is the undeformed length and c is the damping coefficient.

The undeformed length of each spring is calculated in such a way that the bodies are in static

equilibrium when the dynamic analysis starts. This means that the spring increment, resultant

from the difference between the undeformed length and the assembled length of each spring,

produces an elastic force that balances the gravity forces of the bodies that are supported by

the spring.

3.5. Nonlinear external forces representing the wind forces

In the studies performed here, the CX pantograph is acted upon by aerodynamic forces. In the

multibody formulation these loads are represented by nonlinear forces and moments acting

on the bodies of the model as a consequence of the interaction of the wind field forces with

the pantograph. The data required to define the five nonlinear external forces applied on the

pantograph model are presented in Table 4.

In Table 4, the identifier nonlinear force data file indicates the filename where all data

necessary to define the nonlinear characteristic curves associated to each external load isstored, such as those shown in Figure 5. All the nonlinear external forces defined here to

represent the aerodynamic forces are time dependent and defined with respect to the global

reference frame. For reasons of conciseness, the contents of these data files is not presented

in this work.


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Table 4. Nonlinear external forces on the CX pantograph multibody model.

Application point

Nonlinear external Nonlinear force local coordinates (m)

force applied data file Body //

Wind force lower arm Wind_Lower_Arm.DAT 2 0.0/0.0/0.0

Wind force top arm Wind_Top_Arm.DAT 3 0.0/0.0/0.0Wind force pan head Wind_Pan_Head.DAT 6 0.0/0.0/0.0

Wind force low lever Wind_Low_Lever.DAT 1 0.2/0.0/0.132

Wind force knee joint Wind_Knee_Joint.DAT 2 0.820/0.0/0.0

3.6. Prescribed motion constraint

During the dynamic analysis the CX pantograph must be guided along a trajectory that repre-

sents the reference path of the pantograph base. In the multibody formulation this is achieved

by using a prescribed motion constraint [3336]. The prescribed motion constraint enforces acertain point, of a given body, to follow a reference path. Consider a point P, located on a rigid

body i, that has to follow a specified path, as represented in Figure 14. The path is defined

by a parametric curve g(L), which is controlled by a global parameter L that represents the

length travelled by the point along the curve from the origin to the current location of point

P. Furthermore, the prescribed motion constraint also ensures that the spatial orientation of

body i, defined by its local reference frame (, , ), remains unchanged with respect to the

moving Frenet frame (t , n, b) associated to the reference path [37], as depicted in Figure 14.

The only requirement to use the prescribed motion constraint is to define the three-

dimensional parametric curve g(L) that represents the path to be followed by one or more

bodies of the multibody model. For this purpose, a pre-processing tool [3336] is used inorder to define the reference path g by a set of control points that are representative of the

trajectory and parameterise it as a function of the curve length parameter L. Also the roll

angle of the trajectory is parameterised as function of the curve length and the principal unit

vectors (t, n, b), which define the moving Frenet frame [37] associated to the reference path,

are calculated. Then, a database is created and all quantities necessary to define the geomet-

ric characteristics of the reference trajectory are stored in it. These geometric quantities are

organised in columns as a function of the curve length parameter L, measured from curve

origin up to the actual point. Each reference path database has a length parameter step L as

small as desired by the user.

At this point, a remark should be made on the necessity of building reference path databasesfor the prescribed motion constraints. In fact, the direct use of the geometric equations that

define a reference trajectory is neither practical nor efficient from the computational point of

Figure 14. Prescribed motion constraint.


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Table 5. Prescribed motion constraint for the CX pantograph multibody model.

Attachment point local

Curve parameter L coordinates (m)Filename of the

reference path database Initial value (m) Initial velocity (m/s) Body //

DB_Panto_Base.PMC 5.0 83.3333 1 0.00/0.00/ 1.709069

view. As the prescribed motion constraint is to be used in the framework of a dynamic analysis

program, where the multibody models may have a large number of bodies constrained to move

in spatial curves, the solution of the resulting nonlinear equations at every time step would be

an heavy burden on the code. An alternative implementation to the direct use of these equations

is the construction of lookup tables where all quantities required for the construction of the

prescribed motion constraints are tabulated as function of the curve length parameters.

During dynamic analysis, the multibody program interpolates linearly each reference path

database in order to obtain all required geometric characteristics of the trajectories to set up

the constraints. If the size of the length parameter step L is set to be similar to the product of

the vehicle velocity by the average integration time step used during dynamic analysis, then

only a few number of interpolations, if any, will be performed in between two successive lines

of the table.

In the application case studied here, the prescribed motion constraint is defined in order to

enforce the CX pantograph to travel on a straight track with a null roll angle.The data required to

define the prescribed motion constraint applied on the pantograph base are presented in Table 5.

It should be emphasised that the features of the prescribed motion constraint allow studying

railway dynamic problems with straight or curved tracks, or to perform pantographcatenarystudies with full three-dimensional trajectories imposed on the pantograph base.

Notice that the file DB_Panto_Base.PMC contains the pre-computed database of the

reference trajectory where all quantities [3336] required for the construction of the prescribed

motion constraint are tabulated as function of the curve length parameter L. This parameter

represents the length travelled by the pantograph along the reference path, from the origin to

its current location. The initial value of L is 5 m which corresponds to the initial position of

the pantograph base on the prescribed trajectory. The initial velocity of the curve parameter

L corresponds to the initial velocity of the CX pantograph, which is 300 km/h (83.3 m/s) for

this particular case.

3.7. Registration strips data

The last step for the construction of the multibody model of the CX pantograph is the definition

of the registration strips, i.e. the bodies that touch the catenary and to which the contact forces,

resultant from the pantographcatenary interaction, are applied. In Table 6 the data required

to define the registration strip that exists on the CX pantograph are presented, where points P

and Q represent the start and end points of the registration strip.

Table 6. Registration strip data for the CX pantograph multibody model.

Body Point P local coordinates (m) Point Q local coordinates (m)

P/P/P Q/Q/Q

7 0.000/0.335/0.000 0.000/ 0.335/0.000


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Figure 15. Wind-loaded pantographcatenary system on a straight track.

4. Study of wind-loaded pantographcatenary system

With the objective of evaluating the effect of the aerodynamic forces on the behaviour of the

pantographcatenary interaction and, consequently, on the operating conditions, the method-

ologies proposed here are demonstrated by their application to real operation scenarios for

high-speed trains on a straight track. For this purpose, the complete overhead electric power

system is modelled for the SNCF catenary 25 kV LN5 and for the Faiveley CX pantograph.

The simulations are performed for a train velocity of 300 km/h, wind speed of 20 m/s and air

turbulence of 15%. The simulation conditions are pictured in Figure 15.

In order to evaluate the deviation on the contact forces, from the nominal operation condi-tions, and study the influence of the wind loading on the different components of the overhead

electric power system, four dynamic analyses are performed. First, a nominal case with a train

velocity of 300 km/h and no wind is simulated. Then the same case is simulated with the wind

loads, with a wind speed of 20 m/s and a turbulence of 15%, applied on the catenary only. The

third simulation corresponds to the same wind conditions but the wind loading is applied on

the pantograph only. Finally, a fourth simulation is performed with the wind loads applied in

the complete overhead system.

The contact force results obtained on the simulation of the pantographcatenary interaction

for the nominal conditions (train speed of 300 km/h and no wind) are displayed in Figure 16

for a train run of about 1000 m.

In Figure 17, the contact force is reported for the case in which only the catenary is subjected

to cross-wind loading with a speed of 20 m/s and a turbulence of 15%. The simulation of

this particular case intends to understand the contributions of the different overhead system

components for the total contact force. It is noticeable that only small deviations on the

contact forces with respect to the nominal conditions are observed. Therefore, the influence

of the catenary wind perturbations on the quality of the contact seems to be negligible.

The contact force results obtained on the simulation where the wind loads are applied only

on the pantograph are shown in Figure 18. It is clear that a large perturbation on the contact

forces is observed for the wind-loaded pantograph. Due to the pantograph head uplift, the

mean contact force increases by about 50 N.

In Figure 19, the contact force is reported for the case in which the wind load is applied inthe complete overhead system; that is, in the catenary and pantograph. The results are obtained

for a train moving with a velocity of 300 km/h, a wind speed of 20 m/s and a turbulence of 15%.

In all simulations described here the contact forces exhibit a rather periodic characteristic

for the length travelled after 300 m. During the first 300 m of the train displacement, the


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Figure 16. Contact force for the nominal case: train velocity = 300 km/h and no wind.

Figure 17. Contact force for the nominal case with wind forces only on catenary: train velocity = 300 km/h; windspeed = 20 m/s; turbulence= 15%.

Figure 18. Contact force for the nominal case with wind forces only on pantograph: train velocity= 300 km/h;wind speed = 20 m/s; turbulence= 15%.


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Figure 19. Contact force for the nominal case and wind forces on the catenary and pantograph: trainvelocity = 300 km/h; wind speed= 20 m/s; turbulence= 15%.

Figure 20. Details of the contact force with wind forces on the catenary and pantograph and without wind.

pantograph is raised and the contact force reflects such transient behaviour. Therefore, all the

contact forces for the first 300 m of the run should not be considered in any kind of analysis

since they do not correspond to realistic system conditions. In order to have an appraisal

for the contribution of the different components of the overhead electrical collector system

to the catenarypantograph contact forces, details of the contact force while the pantograph

registration strip travels between four catenary registration arms are presented in Figure 20

for all simulations considered before.

The observation of Figure 20 clearly shows that the wind loads have the tendency to raise

the pantograph and increase the contact forces. Not only the average contact force increases

but also the peak forces observed when the pantograph passes under the droppers increases

significantly. However, the lowest contact forces do not seem to change due to the loading,except for some of these peaks on the case when only the catenary is loaded with wind forces.

Generally, it is observed that all components of the overhead system have an incremental

contribution to the increase of the contact force due to wind loads. However, it is the wind on

the pantograph that has the most noteworthy influence on the force, as expected.


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5. Conclusions

Generally the effect of cross-winds on the catenary is considered as a static load, not consid-

ering turbulence effects or its action on the pantograph itself. This work presents one of the

first numerical studies on the effect of the cross-winds on the dynamics of the pantograph

catenary contact quality. Simulating extreme condition scenarios in railway operation allows

the impact of the most important variables/events on operating conditions to be assessed.

Alarm values for the environmental variables (such as wind speed) can be defined, induc-

ing operating limitations, for instance limitations on the train speed. Additionally, computer

simulations promote the development of the diagnostic activity, i.e. the early detection of prob-

lems, allowing proper counter-measures to be taken before a dramatic event takes place. In this

work, the pantographcatenary dynamic interaction has been studied considering, as external

inputs for the pantograph and catenary models, the wind forces acting on both subsystems.

The aim was to model and study the effects of the aerodynamic forces on the behaviour of the

pantographcatenary interaction and, consequently, on the operating conditions. The resultsobtained show that the wind loads have the tendency to raise the pantograph and increase the

contact forces. It is also observed that all components of the overhead power system have an

incremental contribution to the increase of the contact force due to wind loads, the pantograph

having the most noteworthy influence. It is also observed that the range of variation of the

contact forces, in windy conditions, is much wider than if no wind forces are considered.

This suggests that a detailed evaluation on the wind forces over the pantograph and catenary

is required to allow improving the predictive capabilities of models to detect loss of contact

conditions or exaggerated contact forces.

Acknowledgements

The work presented here has been developed in the framework of the European funded project EUROPAC(European Optimised Pantograph Catenary Interface, contract no STP4-CT-2005-012440). The support of Fundaopara a Cincia e Tecnologia (FCT) through the grants with the references BPD/19066/2004 and BD/18848/2004made this work possible and it is also gratefully acknowledged.

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