CHAPTER 1

INTRODUCTION

1.1 Motivation and background

Transportation is the back bone of any nation. Among the available transportation

systems, railway is the cheaper, less polluted and eco friendly system. For faster

transportation and compete with roadways vehicle, there is very much need for increase

in speed. Indian Railway, introduced in 1853, is the world's fourth largest railway

network after those of the United States, Russia and China. It is world's second largest

commercial or utility employer. It is operated on three gauges- broad gauge (W-1676

mm), meter gauge (M-1000 mm) and narrow gauge (Y-762 and 610 mm). The presence

of the Indian Railways in the today’s world demands higher speed, better traffic safety,

better comfort and low running cost. Satisfying these demands is absolutely necessary to

maintain and increase the competitiveness of Indian Railway as public and goods

transport. Hence we can say Indian Railway is life line of our nation.

The motivation of this study originated due to increasing incidents of derailment

of the trains causing much harm to public property and lives, congestion in road traffic,

passenger’s time wastage at the bus terminals and fuel price hike all around the world.

Increasing rail car tonnages and speed are limited due to track conditions and

maintenance costs associated with degradation of track. Once the train speed reaches the

critical speed, the amplitude of the track vibration will increase significantly, and causes

safety problem of the railway system [1].

The interaction between vehicle and track dynamics plays an essential role. An

investigation of the dynamic interaction of rail track and wagon system has to be

exposed more in order to avoid train accidents and to increase passenger comfort while

travelling. The interactive forces developed between vehicle and track depends on the

dynamic properties of the vehicle speed and the irregularities along the track and vehicle

parameters. The dynamic behavior and, more specifically the interactive forces directly

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depend on the load and the mechanical systems (such as springs, dampers etc.) which

interact with the wheels, the train body and bogies etc.

In the present work an attempt has been made to investigate different aspects of

railway dynamics and interaction between vehicle and track by considering a coupled

vehicle track model. The effect of rail track structure on the vertical dynamics has been

studied by simulating the bond graph model of coupled wagon-track system.

1.2 Introduction

The rail track and wagon system is modeled as a discrete system of masses, springs and

viscous dampers, which is linear. The complete model of vehicle track system is

schematically represented in Fig. 1.1. The conventional railway track structures, consists

of the superstructure and the substructure. The superstructure contains the rails, the

fastening and the sleeper, while the sub-structure contains the ballast, sub-ballast and

sub-grade [1].

1.2.1 Rail vehicle and its components

Car body is assumed as a lumped mass and is connected to the bogie frame by secondary

Suspension System on which it is directly carried. This permits rotation and transverse

movement between the car-body and bogie. Complete railway system along with the car

body, bogie, wheel set, suspension system and track is shown in Fig. 1.1. The principal

functions of the primary suspension are guidance of wheelsets on straight track and in

curves, and isolation of the bogie frame from dynamic loads produced by track

irregularities. The primary suspension systems are typically made of coil springs that

minimize the impact and enhance the stability of wagon operation to cushion the ride,

consists of wheelset and wheel. The secondary suspension provides the reduction of

dynamic accelerations acting on the car body which determines passenger comfort. The

source of these accelerations is excitation from the track irregularity/roughness profile

and the natural oscillations of the bogie frame and car body on their suspension elements

A bogie is a structure underneath a train to which axle are attached through

bearings. Bogies serve several purposes

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To support the rail vehicle body.

To run stably on both straight and curved track.

Ensure ride comfort by absorbing vibration, and minimizing centrifugal forces

when the trains run on curves at high speed.

Minimize generation of track irregularities and rail abrasion.

Usually two bogies are fitted to each carriage, wagon or locomotive, one at each end.

Bogie frame consist of two side frames, which are connected together by to cross tubes.

Fig. 1.1: A dynamic schematic model of rail track and wagon system [2]

The wheelsets are coupled to the rail via non-linear Hertzian contact springs,

consists of two wheels fixed on a common axle, so that each wheel rotates with a

common angular velocity and a constant distance between the two wheels is maintained.

It provides the necessary distance between the vehicle and the track and transmitting

traction and braking forces to the rails to accelerate and decelerate the vehicle [3].

1.2.2 Rail track

The purpose of a railway track is to guide the trains in a safe and economic manner. The

track and the switches should allow smooth passage of the trains. If the track is not

perfectly leveled and aligned, the irregularities will cause oscillations or vibrations of the

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train, and this may induce discomfort for passengers and damage for goods [4]. A

perfectly smooth track or rail never exists. There are always more or less irregularities

present on the track. The amplitude of these irregularities varies strongly with the

wavelength [5]. When a railway track is excited to generalize dynamic loading, the

railway track deforms and then vibrates for certain duration.

1.2.3 Track and its components

A railway track structure consists of rails, sleepers, rail pads, fastenings, ballast, sub-

ballast, and sub-grade as shown in Fig 1.2.

Fig. 1.2: Railway ballasted track components

The rail dampers reduce dynamic interaction forces and shift the force spectrum

to longer wavelengths [6] and their primary components are fastener and rail pad as

shown in Fig. 1.3. The fastening system connects the rail to the sleeper, and sometimes

acts as electrical insulation between the rail and the sleepers. Fasteners clamp the rail

gauge within acceptable tolerances and also absorb forces from the rails and transfer

them to the sleepers. Vibration and impact from various sources e.g. traffics, natural

hazards, etc. are also dampened and decelerated by fastenings.

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Fig. 1.3: Typical fastening system for concrete sleepers [7]

Rail pads are installed on rail seats to reduce the dynamic stress from axle loads

and wheel impact from both regular and irregular train movements and transfer the

dynamic forces from rails and fasteners to the sleepers. The rail pad (nominally ten mm

thick) is a rubber or a high-density polyethylene mat that is used as a bearing layer

between the rails and the concrete sleepers [8]. Its functions are to reduce the excessive

high-frequency forces, increase decay rate, decrease rail noise and provides a resiliency

between rail and sleeper [9]. The highest rail pad stiffness leads to the highest rail seat

loads, irrespectively of ballast stiffness [10]. Rail fastener connects the rail and the

sleeper together. The elasticity of the fastener is measured by the spring rate, which is

the amount of deflection proportional to the clamping force.

Railway concrete sleepers model using the beam on elastic foundation theory

[11], are more widely used because they are not affected very much by either climate or

weather. The important functions of sleepers are: To uniformly transfer and distribute

loads from the rail foot to the underlying ballast bed, To provide an anchorage for the

fastening system that holds the rails at their correct gauge and preserves inclination, and

to support the rail and restrain longitudinal, lateral and vertical movement by embedding

itself onto the substructures [12]. The gaps between the unsupported sleepers and ballast

masses have a great influence on the normal load of the wheel and the rail [13].

Ballast, a type of granular material is an insulating layer of crushed stone on

which the sleeper rest and supports the rails. It distributes the cyclic train loading from

sleeper to sub-grade [14] and anchors the track in place against lateral, vertical and

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longitudinal movement by the way of irregular shaped ballast particles that interlock

with each other. By giving resiliency and energy absorption to the sleeper it provides the

water drainage from the track structure, resilience to vibration and facilitates the

maintenance, reduce bearing stresses from the sleeper to acceptable stress levels for

underlying layers; retards the growth of vegetation and resists the effects of fouling from

deposited materials. The most important functions are to retain track position, reduce the

sleeper bearing pressure for the underlying materials, store fouling materials, provide

drainage for water falling onto the track, and rearrange during maintenance to restore

track geometry. Thus, ballast materials are required to be hard, durable, an angular, free

from dust and dirt, and have relatively large voids [15].

The rail sub-ballast is interposing a special semi-rigid layer in the area between

the ballast and the embankment and absorbs the train weight and distributes it from the

rails to the sub grade, thereby avoiding any deformation. The sub-ballast is normally laid

on a highly compacted embankment layer. The sub-ballast particles should be so graded

that do not penetrate into the sub grade and at the same time does not allow penetration

of ballast particles into the sub ballast zone. Sub-ballast functions are: To create a

working platform on which subsequent work operations, such as installation of electric

lines, ballast and rail laying; To assist in distributing the loads transmitted by passing

trains; To protect the embankment body from the seepage of rain-water and from

seasonal thermal extremes; To eliminate contamination of the ballast from fine material

migrating up from the foundation and To distribute the concentrated pressures and

eliminate any "rupture" of the embankment [16].

Sub-grade, or formation, is a surface of earth or rock levelled off to receive a

foundation for the track bed. Sometimes an extra layer, a formation layer, is put on the

earth so as to give the correct profile of the track bed. On this material the subballast and

ballast layers rest. The sub-grade is a very important component in the track structure

and has been the cause of track failure and development of poor track quality.

Unfortunately, in existing tracks the subgrade is not involved in the maintenance

operations, and once the track has been laid, little can be done to alter its characteristics.

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1.3 Modeling and simulation

Modeling and simulation has an increasing importance in the development of complex

or large mechanical systems. In areas such as rail vehicles, high speed mechanisms,

industrial robots and road vehicles etc., modeling is an inexpensive way to experiment

with different system design concepts and to aid the design and development of an

appropriate system. In classical mechanics several methods exist by which differential

equations can be derived from a system of rigid bodies. In the case of large systems,

these procedures are labour-intensive and consequently error-prone, unless they are

computerised. A disadvantage of these methods is that they offer a systematic procedure

for the mechanical part only. Most modern mechanical systems, however, form a part of

multi-disciplinary system and are closely coupled with the hydraulic, magnetic,

electrical or other energy domains. A unified approach to the modeling of

multidisciplinary physical system was introduced by Paynter [17] and perfected by other

researchers. Using this approach every kind of lumped physical system can be modelled

by ideal elements, having the properties of storage, dissipation or transformation of

energy. The elements are interconnected in an energy conserving way by bonds and

junctions. The resulting network structure is represented by a diagram, called a Bond

Graph.

In modeling dynamic systems the bond graph technique appears to be a powerful

tool. In order to analyze the behavior of a dynamical system, the physical and the

mathematical substitute models must be drawn up according to functional principles in

view of the demands. The model has to represent the kinematic, static and dynamical

behavior of the system. The entire process of simulation is shown in Fig 1.4.

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Fig. 1.4: Process of simulation

1.3.1 Kinematic model

The kinematic behavior of the system is determined by the degrees of freedom and the

geometry of the suspension/tilt module. Ten degrees of freedom rigid body model has

been used to study the vertical dynamic behavior of passenger car system.

1.3.2 Dynamic model

The dynamic model describes the dynamical behaviour under the effect of force. Thus a

mathematical statement on the system behaviour, using the principles of physics, can be

made.

1.3.3 Statical model

The statical model describes the Statical behaviour of the rail road vehicle when it is at

rest.

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Fig. 1.5: Computer modeling and simulation process [18]

Three basic elements can be defined in the computer modeling and simulation

process: reality, conceptual model and computerized model as shown in Fig. 1.5. The

process which relate the elements to each other are described by the inner arrows. The

outer arrows refer to the procedures where by the credibility of these processes are

evaluated. Reality is an entity, situation, or system which has been selected for analysis.

For example, it could be a railway train, vehicle, bogie or wheelset operating under

specified conditions.

The domain of intended application of a conceptual model is a set of prescribed

conditions for which the conceptual model is intended to match reality. The conceptual

model may be a verbal description, equations, governing relationships or a natural law

that describes reality. Newton’s laws of motion are natural laws used in deriving the

differential equations of railway components or systems.

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The computerized model (sometimes called computer model) is an operational

computer program which implements a conceptual model. It is the result of an activity

called programming. The domain of applicability of a computerized model consists of

the prescribed conditions for which it has been tested, compared against reality to the

extent possible, and judge suitability for uses [18].

1.4 Bond graph modeling

The laws of thermodynamics are relevant to systems in all science and engineering

domains. The first law of thermodynamics states that energy can neither be created nor

be destroyed but simply changes from one form to another. By modeling the flow of

energy from one form to another, a methodology that describes systems in multiple

energy domains is obtained. One such methodology is bond graph modeling.

Bond graph modeling is a graphical modeling technique that preserves the

computational structure and the topological structure of the system being modeled and a

methodology that maps power flow and signal flow throughout thus allowing the user to

define the cause and effect relationships between all describing variables of the system.

The ability to map power flow across energy domain boundaries, and map signal flow

information across the same boundaries, is an indispensable aid in the user’s quest to

form cause and effect relationships within interdisciplinary systems. Bond graphs are

able to connect model sub-systems of different domains together to form a larger,

mixed-domain model, in a concise and meaningful way.

Bond graphs are pictorial representations of essential dynamics of physical

systems through exchange of power amongst the basic elements the system is composed

of, and its environment. Powers being the common currency of exchange, interaction of

several energy domains are represented in a unified manner. The entire process of

modeling is algorithmic, making it suitable for implementation on computer.

In 1959, Henry Paynter [17] introduced at first depicting systems in terms of

power bonds, connecting the elements of the physical system to the so called junction

structures which were manifestations of the constraints. Bond Graph theory has been

developed and consolidated further by many researchers Karnopp, Margolis, and

Rosenberg [19], Thoma [20], Cellier [21], Breedveld and Dauphin-Tanguy [22],

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Gawthrop and Smith [23], Mukherjee and Karmakar [24], Brown [25], who have worked

on extending this modeling technique to power hydraulics, mechanics, mechatronics,

general thermodynamic systems and recently to electronics and non-energetic systems

like economics and queuing theory.

The language of bond graphs aspires to express general class of physical systems

through power interactions. The factors of power, i.e., Effort and Flow, have different

interpretations in different physical domains. Yet, power can always be used as a

generalized co-ordinate to model coupled systems residing in several energy domains. In

bond graphs, one needs to recognize only four groups of basic symbols, i.e., three basic

one port passive elements inertance (I), capacitance (C), and resistance (R); two basic

active elements source of effort (SE), and source of flow (SF); two basic two port

elements gyrator (GY), and transformer (TF); and two basic junctions i.e., constant

effort junction (0), and constant flow junction (1). The basic variables are effort (e), flow

(f), time integral of effort (P) and the time integral of flow (Q).

In the context of mathematical models of dynamical system, the equations for the

system can be easily formulated in a systematic way from the bond graph representation.

The bond graph representation of a system may be constructed in total abstraction from

the mathematical model of the system. The bond graph causality concept, presented by

Karnopp and Rosenberg [26], orientates the calculus schemes in the system model. This

constitutes the physical level of the description contained in the bond graph

representation.

By this approach, a physical system can be represented by symbols and lines,

identifying the power flow paths. The lumped parameter elements of resistance,

capacitance and inertance are interconnected in an energy conserving way by bonds and

junctions resulting in a network structure. From the pictorial representation of the bond

graph, the derivation of system equations is so systematic that it can be algorithmized.

The whole procedure of modeling and simulation of the system may be performed by

some of the existing software e.g., ENPORT, Camp-G, SYMBOLS, COSMO, SIM-20,

etc.

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Main advantages of bond graph techniques may be summarized as

Bond graphs provide a useful notation for the purpose of modeling physical

systems.

Systems with diverse energy domains are treated in a unified manner.

Graphical representations document complex models clearly and unambiguously.

Easiest way to communicate the description of energy flows in dynamic systems.

Since a bond graph is an unambiguous representation of an energy system, it is

possible for a computer program to automatically generate the equations for

dynamic analysis of the system.

By using bond graphs power conservation properties one may need to constraints

velocities only and the forces will automatically balance.

The present dissertation work explores the ability of the bond graphs to obtain

dynamic behavior of railway vehicle by using bond graph based on the physical

paradigm of the system. Bond graph technique generally offers flexibility in modeling

and formulation of system equations. A very large system may also be modeled in a

modular form by creating sub -system models and then joining them together at their

interaction port to create an integrated system model. Models may be easily modified

making it a powerful tool for system synthesis and consolidation of innovative ideas.

Bond graph equations normally use generalized displacement and generalized momenta

as state variables. The bond graph modeling and simulation is performed using Symbol

Shakti® software [27].

1.5 Objective of the research work

The following objective are set for the research work

To create a coupled model of the rail track and wagon system by using bond

graph technique.

Simulation of the bond graph model to obtain vertical dynamic behavior of

railway vehicle on straight track at different operating speeds.

Analysis of the result obtained through simulation of coupled bond graph model

of rail track- wagon system.

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To validate the model by comparing the results obtained through simulation with

available literatures.

1.6 Organization of thesis

The chapters of the thesis are organized in the following manner. The second chapter is

focused on the latest work that has been reported by many researchers and scientists in

the field of rail vehicle dynamics. Third chapter presents the mathematical modeling of

the rail track and wagon system. Fourth chapter deals with the rail track and wagon

system modeling through the bond graph. Fifth chapter consists of simulation of rail

track and wagon system through Symbol Shakti® software for analyzing the behaviour of

the vehicle at different operating speeds. In the sixth chapter, results and discussions

have been presented. The final (seventh) chapter concludes the thesis and also suggests

some future scope.

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