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ABSTRACT

The rail gun is an electromagnetic apparatus that drives an armature

along rails to achieve velocities going up to several thousand of metres per

second by means of magnetic repulsion without using an explosive propellant.

This is achieved by converting electric energy into kinetic energy. The ratio

of kinetic energy to electrical energy is called efficiency of rail gun. The

overall efficiency of the rail gun depends on the rail gun design and its pulsed

power supply (PPS) system. The rail gun design depends on the rail gun key

parameters such as current density distribution over a rail cross section,

magnetic flux density between the rails, temperature distribution in the rails

and armature surface, and repulsive force acting on the rails. One of the

biggest problems in the analysis of the rail gun is the determination of the

current density distribution in a massive moving conducting part. The

knowledge of the distribution of current density in the rails against the time is

very important as it determines the joule energy dissipated in the rails. As a

very high value of current and short duration pulse is applied to the rail gun,

the current does not penetrate the rails and armature completely and the

current density is not uniform over the rail cross section it is called skin

effect. Moreover, the current density will be higher at the rails inner edges.

This phenomenon produces a hot spot that fuses the rail edges. In order to

prevent rail gun damage due to ohmic heating and internal forces, it is

essential to understand the current density distribution within the conducting

medium. The magnetic flux density between the rails and inductance gradient

of the rails plays an important role in the performance of rail gun which

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directly determines the force that accelerates the projectile. The parallel

conductor couples that carries current experiences two forces namely

repulsive force or attractive force. As in the case of rail gun, the flow of

current in the rails is in opposite direction which results in repulsive force. In

order to mechanically brace the rails against the high forces which results

from the large current the repulsive force acting on the rail should be

calculated. The separation force is not exactly calculated, as short acceleration

pulse current produces non linear effect and uneven current distribution. The

temperature in the rails, increases due to two factors, first is when the rail gun

is supplied with large current at short duration thermal energy is generated in

rails and armature. Due to this thermal energy the electrical, thermal and

mechanical properties of the rail and armature structure get changed. The

maximum temperature occurs at the trailing edge of the armature as it

proceeds along the different position of the rail. The second is the friction

between the rails and the armature.

In the operation of rail gun highly coupled phenomena are present.

The motion of the armature is governed by thermal and electromagnetic

components that are coupled together. In this work, because of computational

limitations, the coupled phenomena are decoupled into previously mentioned

individual components and each effect is studied in detail. Since, the time is

short and the current density is not uniform over the rail cross section, the

calculation of rail gun key parameters is extremely complex. Hence, in order

to gain a quantitative understanding of these parameters, it is desirable to

calculate them well in advance before real time system. For the past several

years, various numerical methods and analytical methods were developed to

compute the rail gun key parameters and researchers also focused on

computation of these parameters. These parameters can be calculated either

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by transient analysis or by A.C method in the high frequency limit. The aim

of this work is to analyze the performance of rail gun using computer

simulation techniques which can be used as a design tool to acquire

conditions for the best performance. In this work, finite element analysis

software package named Maxwell Electro Magnetic Field Solver is employed

to calculate the rail gun key parameters such as magnetic field generated by

the rail current, current density in the rails, inductance gradient of the rails,

repulsive force acting on the rails, and temperature distribution inside the

rails using A.C eddy current analysis.

For the past several years, the values of inductance gradient of the

rails were calculated using numerical methods and analytical methods. The

analytical method is suitable for solving simple problems and the numerical

problem needs code and programs as it is a time consuming process. Hence, a

simple method is needed to calculate inductance gradient of the rails. As the

inductance gradient (L’) depends on rail dimensions, the researchers are now

focused on obtaining a simple formula through which the L’ values can be

computed. In this work, an attempt is made to extract an empirical formula,

which can be used to compute the L’ of the rails, using curve fitting software

called Oakdale Data Fit Engineering. This software uses regression analysis

technique to obtain the empirical formula for the given set of data.

The key part of the electromagnetic rail gun system is the pulsed

power supply system. Generally, the PPS is made up of modules called Pulse

Forming Network (PFN’s). The PFN is connected to choice of energy

sources. The energy is required to be stored properly and is to be delivered at

an appropriate time to the load. Today, the energy storage systems which

feed the rail launcher are large. Extensive work and research is being

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conducted all over the world for the minimization of the volume occupied by

the power supply and its weight. These constraints have always been

deadlocks in the design of high caliber electromagnetic launcher even though

researches have begun well before 1980. Due to constraints on compact

power source feasibility study is being carried out by the Government of India

and Anna University Chennai to design pulsed power supply capable of

storing the energy of 500-kJ, which can be used to accelerate the projectile at

a velocity of 1000 m/s to 1500 m/s. To carry out this study in this work,

different types of pulsed power supplies which produce pulsed output are

studied. Based on the resources and the proposed application, it is decided

that the 500-kJ pulsed power supply will be designed as a capacitor based

system. Then the basic electric requirements of electromagnetic guns to be

fulfilled by the appropriate PPS systems are discussed. From these

requirements, design criteria for high energy discharge modules and their

auxiliary systems are derived. Finally, an attempt is made to design a 500-kJ

pulsed power supply for rail gun system using PSPICE software and

MATLAB software. In PSPICE simulation a study was made to find out the

optimum number of capacitor stages to get desired pulse shape and rail

parameters. MATLAB is used to obtain optimum solution of rail parameters

such as muzzle velocity, peak current, and effective barrel length of the rails.

By applying a systematic approach to optimizing the 500-kJ pulsed power

supply this study has shown that the 75 grams of projectile can be able to

accelerate with a velocity of 1.25 km/s by distributing the capacitance over

five equal sized banks. Design is achieved by trial and error method by

changing rail parameters and pulsed power supply parameters. Finally, work

is carried out to give some basic considerations on volume and weight

requirements of capacitive PPS systems to be applied for rapid fire of

electromagnetic rail guns due to the current status of the investigations by the

Government of India.