Post on 23-Feb-2018
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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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