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Objective

1.To the dynamics characteristics of catenary-pantograph interaction in high speed railway.

2.To develop a full kinematic and dynamics model of catenary, which is compatible with

high speed railway in indian context to minimize the contact loss between pantograph and

catenary by ensuring better current collection quality and also to decrease the occurrence

of arcing.

Introduction

Railways were the first form of rapid land transportation and had an effective monopoly on

passenger traffic until the development of motor car and airlines in the early mid twentieth century.However, subsequent development in aircraft technology had put it ahead of railways for several

decades. This played an important role in the birth of high speed railways (HSR). To sustain in the

competition, increasing speed was essentially needed. Research started with the improvement of

the existing systems to support high speeds. Research started with the improvement of the existing

systems to support high speeds. Later in 1964, Japan introduced dedicated HSR networks and a new

era in high speed train began. Current high speed trains are based on two discrete technologies -

1. Improvement of Conventional Systems which can support maximum speed of 200 - 250

km/h. But, principal drawback of this technology is that it is also used by regular services,

which limit the slot for HSR.

2. Exclusive and independent high speed networks. Dedicated and specially built tracks cansupport speed up to 350 km/h.

High speed is a relative concept and it has changed radically over time to time. Presently, the

speeds of 200 km/h and above are considered as high-speed. However, in 1830s, when railway was

an infant, the speed of 50 km/h was considered fast.

Japan was the first country to introduce an exclusive trunk line with standard-gauge infrastructure

for its Shinkansen from Tokyo to Osaka in 1964. In other countries initial emphasis was on the

optimisation of existing infrastructures. Thus, in Britain the first high speed rail services, running atup to 200 km/h, were provided by diesel-powered High Speed Trains, introduced in 1976. Over the

last decade, several other countries have also joined in this revolution. In Europe, Belgium and the

Netherlands are building lines which will enhance the PBKAL(ParisBrussels-Koln-Amsterdam-

London) network of Thalys services.

High Speed Railways in India

Unfortunately, India, having one of the largest rail network in the world, possesses no high speed

train. Current infrastructure is also not suitable for supporting speeds of 200 km/h or more. At

present, average speed for super-fast train is 80 km/h with a maximum operating speed of 130

km/h. Therefore, the Ministry of Railways, Government of India, for the development and

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implementation of high speed rail projects has taken some initiative. Their primary objective is to

increase the average speed of passenger trains on dedicated conventional tracks.

Challenges in Power Collection During High Speed Travel

Most of the todays high speed trains are electrically driven as they are considered as

environmentally friendly. They collect power either from overhead lines or catenary through a

steady contact of pantograph or from a third rail. However, use of third rail causes too much friction

during high speed travel which affects the performance of the train. Therefore, pantograph-catenary

system is always preferable. In ideal situation, carbon contact strips placed on the bow of the pan-

head of the pantograph should be in continuous contact with the current carrying wire by exerting a

specified and constant contact force. In real situation it is the biggest challenge. As high magnitude

in contact force causes wear and damage to the carbon contact strips as well as the contact wire, it

is mandatory to keep its value as low as possible. This leads to another problem of contact loss. Loss

of contact produces arcing between pan-head and overhead contact wire, which again results in

high damage to the whole system. Therefore, it is a trade-off between contact loss and excess

contact force.

Basic Current Collection System in Railways

The electric railway needs a power supply that the train can access at all times. It must be safe,

economical and easy to maintain. It can use either direct current (DC) or alternating current (AC). It

is easier to boost the voltage of AC than that of DC, so it is easier to send more power over long

distances through the transmission line in case of AC. DC, on the other hand, is preferred for shorter

lines. Moreover, AC systems are cheaper to install. However, 25 kV - 50 Hz AC system is used widely

around the world and has become, presently, an international standard for HSR.

Transmission of power is always performed along the track by means of an overhead wire system or

at ground level, using an extra third rail laid close to the running rails. AC systems always use

overhead wires known as catenary,DC can use either a catenary or a third rail, both are common.

However, the overhead system is always preferred since it is reliable and safe.It requires at least

one collector attached to the train so that it can always be in contact with the power cable. This is

accomplished by using apantograph. The return circuit is via the wheel and the running rails back to

the substation as shown in Fig. 1. The running rails are at earth potential and are connected to the

substations.

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The Catenary

A catenary is a periodic structure of overhead contact wires to provide electric power to the

locomotive which is equipped with a suitable current collecting apparatus, i.e.,pantograph. It makes

continuous contact with the catenary during travelling. To supply an uninterrupted and good quality

power, the overhead equipment must meet some basic requirements -

It must possess characteristics meeting train speed and current requirements.

It should maintain a uniform height (generally 5 m) above the rail track.

It should have uniform stiffness and bending rigidity along the span.

It must have minimum vibration and motion to ensure a smooth passage for the pantograph.

It should be strong enough to withstand high tension and other environmental hazards with a

long operating life.

The most basic components of any catenary system (Fig. 2) are a messenger wire or catenary wire

(called so, because of its resemblance to the catenary curves) and a contact wire. The later is

attached to the former by means of equally spaced and varying length of droppers. The contact wire

is grooved to allow certain clips to be fixed on the top side. The clips are used to attach the

droppers. Droppers are stiff is tension but not so resistant to compression. They also ensure the

required hight of the overhead contact wire from the ground throughout the track. Both the

messenger and the contact wire are tensioned with high axial load by suspending weights to

minimise the sag. The whole system is periodically supported by masts. Every mast has a attached

mechanism which not only holds the catenary but also provides the whole overhead system with the

necessary allowance for movement along the track and and in upward direction. At the same time, it

does not allow any lateral movement of the catenary along the transverse direction of the track.

Fig. 2: A stitched catenary

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Choosing proper wires and other parameters for the catenary system are of great importance. It has

been observed that when the speed of the train approaches the propagating speed of travelling

wave in the wire (which is often termed as critical speed), the catenary experiences high amplitude

of excitation and loss of contact with the overhead line becomes inevitable for the pantograph.

Therefore, it is customary to select the wire in such a way that the wave propagation speed in it can

be made too fast to be exceeded by the maximum speed of the train. It is known that speed of

travelling wave in a string is directly proportional to the square root of the applied tension in the

string and inversely proportional to the square root of the linear density, i.e., mass per unit length of

the string. So, light wire and high tension will suffice the purpose. To sustain the high tension with

less mass per unit length indicates that high strength wire is required.

There are, in general, basic three types of catenary systems which are widely used :

1) Simple catenary 2) Compound catenary 3) Stitched catenary.

A simple catenary system has only one messenger and one contact wire as shown in Fig. 3( a ).

A compound catenary has a second support wire known as auxiliary wire (Fig. 3(b)). Droppers

support the auxiliary from the messenger wire and additional droppers support the contact wire

from the auxiliary wire.

On the other hand, a stitched catenary uses an additional wire at each pole structure as shown in

Fig. 3(c). However, the compound catenary has less stiffness variation over a span compared to that

of simple and stitched catenary (Wu and Brennan, 1998) and provides better pantograph passage

with larger current capacity. This is more desirable for the high speed trains. Unfortunately, high

price and a larger number of components are main disadvantages of this type of overhead system.

In Japan compound catenary is largely used, whether in Europe stitched catenary is mostly

preferred due to its better performance than simple catenary and low cost compared to compound

catenary.

(c) stitched catenary

(a) Simple catenary (b) Compound catenary

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The Pantograph

Apantograph is a mechanism mounted on the roof of a locomotive to collect power through contact

with the overhead catenary. Todays pantographs are asymmetric and Z-shaped unlike the

symmetric and delta shaped used in early days.They largely depend upon various matters like the

speed of the train, the catenary system used as overhead, the track on which the train will run,tunnels and bridges on the route, aerodynamic effects etc. However, here, more commonly used

asymmetric pantographs are discussed briefly. The GSE-100 Light Rail Pantograph of G&Z

Enterprises Ltd. is presented in Fig. 4(a) for illustration purpose. The lower part of the pantograph as

shown in kinematic diagram in Fig. 4(b) is basically a four-bar mechanism and responsible for raising

and lowering the system.

Fig. 4: Pantograph and its kinematics

The upper part controls thepan head. Thepantograph base is placed over insulators on the roof of

the train. The lower link and the lower arm are connected to the base by spherical and revolute

joint respectively. The extended top arm completes the lower four-bar linkage and is attached to the

lower link and lower arm. The pan head is linked to the top arm and to the top link by means of

stabilization arm. The contact strips which are in continuous contact with the overhead line are

mounted over isolators on the top of the pan head, so that the effect of base excitation does notaffect the current collection. Actuation is accomplished by pneumatic devices. Generally, piston of

the pneumatic device attached to the lower arm actuates it to raise the mechanism, and, on the

other hand, springs lower the pantograph.

(a) GSE-100 Light Rail Pantograph (url3) (b)Kinematic diagram(PomboandAmbrosio,2013)

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Interaction between Catenary and Pantograph

The carbon contact strips placed on the top of pan-head make contact with the contact wire of the

catenary system to collect required power for the locomotive. The contact point moves side wise on

the contact strips due to the stagger provided to the catenany to ensure an even wear of the strips.

The ideal interaction between the contact wire and the pantograph should be the steady andcontrolled contact to get maximum efficiency in current collection. . However, in actual condition,

this is not possible and the rate of loss of contact increases with the increase in train speed. The loss

of contact is determined by contact force at the interface. . If the contact force is too low, increased

separation will result in excessive arc which causes erosion in contact strips as well as damage to the

contact wire due to excessive heat generation. On the other hand, if the contact force is too high,

the pantograph will always maintain the contact with the contact wire, but at a cost of increased

wear in the carbon strips .Therefore, the contact force needs to be maintain within a specified range

and this leads to the necessity of dynamic analysis of both the systems as well as the contact

interface.

Literature Review

Since, speed is a relative concept it is very hard to distinguish researches which are exclusively for

high speed trains. It has been going hand in hand with the development of railways. However,

research on pantograph-catenary system is quite recent and started only after the electrification of

railways. First dynamic model of catenary came in 1971 and wave based solution of catenary

subjected to a moving point load was proposed in 1975. In the following decade dynamics of

droppers was also taken into account in the wave equations. . Study of pantograph-catenary coupled

system became relatively easier with the fast development of computation devices in 90s. It also

made possible to analyse the system with more complex models. As a result, modelling of

pantographs as a multibody system started after 2000. Development of multibody dynamics and

finite element analysis softwares helped to model the coupled system in more realistic manner.

The literatures available in this domain are vast and largely interconnected with each other. They

can be categorised loosely as - literatures on 1) catenary

2)pantograph

3) coupled dynamics and interaction of both the

systems

Literatures on Catenary

Probably the first mathematical study of overhead wire was performed by Fox (1976). On some basic

assumptions the author derived a wave based solution of simple catenary subjected to a time

dependent travelling concentrated load. The same procedure was followed for a rigid mass travelling

with a point contact with the contact wire. It was observed that the wave solution diverged whenthe mass approaches a dropper with a velocity which is beyond a critical value.

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An analytical method was proposed by Kumaniecka and Snamina(2008) to find out the steady state

response of a two level catenary, i.e, having messenger and contact wire. The droppers were

modelled as mass-spring-damper elements, placed uniformly along the span and connecting both

the wires. The upper string was assumed to be fixed at periodically spaced points. The model was

capable of describing coupled dynamics of the wires subjected to a moving point load.

Displacements of the wires for varying frequency were computed.

Literatures on Pantograph

Galeotti and Toni (1993) first developed a non-linear model of pantograph used in Italian Railway

considering the effects of friction torques which were present in the joint bearing, bounded dampers

which showed non-linear behaviour by providing damping effect when the pantograph head leaved

contact with the catenary and no resistance when it restored contact and stop used for limiting therelative displacements between the main-frame and the pan-head. It was found that the effect of

non-linearity did not play a severe role in the dynamic behaviour of the system, therefore, the linear

model is well enough to serve the purpose.

Kim et al. (2007) conducted a sensitivity analysis of pantograph. The catenary was modelled with

beam elements using finite element method and a 3-dof model for pantograph was used. Direct

differential method was applied for sensitivity analysis. Span length, static uplift force along with

system parameters of pantograph were also considered as design variables. The dominantparameters which mostly affected the displacement of the pan-head were found to be span length

and plunger stiffness.

Literatures on Pantograph-Catenary Interaction

Wu and Brennan (1998)performed a very good basic analytical study of pantograph catenary

coupled dynamics. The stiffness variation of catenary was found using FE method and finally it was

modelled as time varying stiffness for the sake of simplicity. Pantograph contact was well defined by

kinematic constraints at the point of contact. The pantograph was represented by 1-dof and 2-dof

lumped parameter models and their results were compared. The authors concluded that the simplemodel of catenary and pantograph was able to retain the essential dynamic features of the system.

Seo et al. (2005)studied the non-linear behaviour of pantograph-catenary coupled system

considering the effect of large deformation of the flexible catenary which was modelled with 3-dof

finite element with absolute nodal coordinate formulation. Contact was defined in a unique way by

modelling it as a sliding joint. The effect of rail road which was modelled with multibody approach

was also considered in the dynamic interaction of pantograph-catenary.

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Modelling of Catenary

1.Wave propagation based model

As speed of the train increases, wave reflection plays the major role and the simplified modelbecomes insufficient to predict the variation in contact force. Therefore, a suitable homogeneous

string model or beam model like Euler-Bernoulli-Timoshenko beam model becomes more efficient.

The Euler-Bernoulli beam model takes the bending stiffness of the wire into account and, in addition,

the Timoshenko beam model considers the effects of shear deformation and rotary inertia.

However, Kumaniecka and Snamina(2008) modelled the two level catenary which consists of two

infinitely long homogeneous strings.

Fig.6 : A model of simple catenary (Kumaniecka and Snamina, 2008)

The upper string or the messenger wire is supported periodically from rigid supports with a span of L

as shown in Fig. 6. The lower string or the contact wire is supported by equidistantly placed mass-

spring-damper elements (which represent the droppers) from upper string with a periodic distance

of Ld. The rigid support points arex =pL and the dropper connection points are x = qLd, where,p,q =

0,1,2,.... It is also assumed that support span length is a multiple of dropper span length, i.e., L =

rLd, where, r N. The dynamics of the catenary was studied subjected to a harmonic concentrated

load moving with a constant velocity, V0and is exerted to the lower string. The governing equations

of the model are given by

= 0

)

where,x denotes the horizontal coordinate, t is time, indicates density of the string,A is the cross

sectional area of the string, T is tension in the string and w denotes the vertical displacement of the

string. The subscripts m,c stand for messenger and contact wire, respectively. F(t) is the moving

load and () denotes Dirac delta function.

The boundary condition at dropper supports, i.e., atx = qLd can be expressed as

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wm|x=qLd+ wm|x=qLd= 0 (4)

wc|x=qLd+ wc|x=qLd= 0 (5)

where, m,c and k are equivalent mass, damping and stiffness coefficients of the droppers,

respectively. On the other hand, boundary conditions at the rigid supports, i.e., at x = pL are given

by

The model shown in Fig. 6 is spatially periodic and under a harmonic moving load of F(t) = F0

exp(it) that moves at a constant speed the following periodicity condition of displacements for

both the strings can be written as

where, is the frequency of applied force. Steady-state solution can be found out by transforming

the whole problem into frequency domain. Therefore, Fourier transform of string displacement is

denoted by

w j(x,) = wj(x,t)eit

dt, j = m,c

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Work Plan

To develop an compatible catenary system for high speed railway proposed research methodology

being considered are as follows:-

1.Effective one level model

To analyse the steady-state dynamics response of simple one level model catenary where only

dynamics of contact wire is being taken into consideration while neglecting the dynamics of

messenger wire.

2.Non-linear dropper

To the behaviour of catenary system by introducing non-linear dropper between messenger and

contact wire.

Effective one level model

In this section, an effective one-level model of the catenary is presented, in which the carrying cable

is considered as infinitely stiff.The model is depicted in Fig.7.

It is composed of an infinitely long string (contact cable), which is suspended by means of lumpedmass-spring-dashpot elements, which are placed periodically at x =nd, n = 0,1,2,....along the string.

The upper ends of these elements are assumed immovable.

Fig. 7. Effective one-level model of the catenary

The governing equations for the model at hand read

Steady-state solution can be found out by transforming the whole problem into frequency domain.

Therefore, Fourier transform of string displacement is denoted by

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Applying to Eqs. the Fourier transform defined above, the following system of equations is

obtained in the frequency domain:

The general solution of Eq. (38) in the interval x< [0,d] can be written as

Employing the periodicity condition, which, for the problem at hand, has the following form:

the solution in the interval x belong to [d, 2d] can be expressed as

Substitution of expression of w1into the boundary conditions following respective interval gives a

system of two linear algebraic equations with respect to C1 and C2. This system can be readily

solved analytically.Substituting obtained expressions for C1 and C2 into above equation, the steady-state response of the contact cable in the frequency domain can be derived in the interval x belong

to [0,d].

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Conclusions

A very basic knowledge about the power collection in high speed railway has been reported in this

study. Different parts and the functionalities of the principal components in power collection, i.e.,

the pantograph and the catenary have also been described. Different types of pantographs andcatenary systems used in different countries are also reported. After a broad literature review it is

found that an effective dynamic model of catenary is required in Indian context prior to the

installation of high speed railway. Therefore, a tentative objectives of this research are also

proposed. Subsequent sections of this report have presented a few mathematical models of

catenary which are proposed model for efficient system performance.

References

1.Alberto, J. Benet, E. Arias, D. Cebrian, T. Rojo, and F. Cuartero. A high performance tool for thesimulation of the dynamic pantograph-catenary interaction. Mathematics and Computers in

Simulation, 79(3):652667, 2008.

2. Galeotti and P Toni. Nonlinear modelling of a railway pantograph for high speed running.

Transaction of Modeling and Simulation, 5, 1993.

3. J.S. Kim. An experimental study of the dynamic characteristics of the catenary pantograph

interface in high speed trains.Journal of Mechanical Science and Technology, 21(12):21082116,

2007.

4. Kumaniecka and J. Snamina. Dynamics of the catenary modelled by a periodical structure. Journal

of Theoretical and Applied Mechanics, 46(4):869878, 2008.

5. Pombo and J. Ambrosio. Environmental and track perturbations on multiple pantograph

interaction with catenaries in high-speed trains. Computers and Structures, 124: 88101, 2013.

6. Petri and J. Wallaschek. Analytical models for the dynamics of catenary-pantograph systems.

ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik, 76( SUPPL. 5):381382, 1996.

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