. B 0. (5) Now we can define, B A. (6) Where A is magnetic vector potential. Substituting equation (6) in to equation (2),

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1 Research Paper INVESTIGATING THE EFFECT OF CURRENT SHAPE ON RAIL GUN DESIGN AT TRANSIENT CONDITIONS Murugan.R 1, Saravana Kumar M.N 2 and Azhagar Raj.M 3 Address for Correspondence 1 Professor, Department of Electrical and Electronics Engineering, Easwari Engineering College, Chennai, Tamil Nadu, India 2 Research Scholar, Department of Electrical and Electronics Engineering, St Peters University, Chennai, Tamil Nadu, India 3 Department of Electrical and Electronics Engineering, Hibrise Technologies Pvt. Ltd, Chennai, Tamil Nadu, India ABSTRACT The performance parameters of the rail gun such as force and velocity acting on the armature, induced voltage, power loss and current density distribution and magnetic field distribution over rail and armature are greatly affected by the current distribution. These parameters depend on rail and armature dimension, shape, and the magnitude of current as well as the shape of the current supplied to rails. The rising, working and dropping characteristics of the current shape is greatly affecting current distribution on the rail and armature. So, understanding the profile of the current distribution on rail and armature due to various pulsed current shapes are essential to analyze the effect on the above performance characteristic parameters during transient conditions. In this paper the performance of rail gun is analyzed by exciting the rail with different current wave shapes using a 3-dimensional magnetic field simulator called ANSYS. The simulator uses finite element method to predict the magnetic field distribution. Pulsed mode current shape has been considered for this study. KEYWORDS - Current density, Current shape, Induced voltage, Power loss, Force. I. INTRODUCTION The rail gun is a type of electro mechanical projectile missile which accelerates the projectile to a higher velocity by converting the electrical energy into mechanical energy. Fig. 1. Structure of Rail gun [1]. Rail guns use very basic laws of the Lorentz force to accelerate the projectile. A specific amount of current is used to generate a magnetic field by which the projectile is accelerated. In its simplest appearance shown in Fig.1, a rail gun consists of two parallel conducting plates called rails between which the projectile closes the electrical circuit. The electrical current starts to flow through one rail, across the projectile and down the rail and forms a current loop [2]. The current distribution in the rails plays an significant role in rail gun design as it determine the force and velocity acting on the armature, induced voltage, power loss and current density distribution and magnetic field distribution over rail and armature. Examine the current distribution characteristics in the rails and armatures are critical to the design and development of rail guns. The current distribution in the rail and armature mainly depends on rail and armature dimension, shape of rail and armature and the magnitude of current as well as the shape of current supplied to rails [4]. Due to the rapid movement of the armature, it is very difficult to evaluate e the exact current distribution over the rail and armature. For the past several year numerical codes were developed to carry out the performance of rail gun systems [5-9]. In this work study is carried out to analyze the performance of rail gun by varying the current shape which is supplied to the rails using ANSYS. The force acting on the armature, induced voltage solid loss in the armature, magnetic field distribution and current density distribution over a rail and armature are calculated by varying the shape of current pulse. II. TRANSIENT ANALYSIS The following Maxwell s equation is relevant to transient application,[11] H J, (1) Where, E is Electric field intensity (V/m), H is magnetic field intensity (A/m), J is current density A/m 2 B E. (2) t J ( E B. (3) 1 B ( E) 0. (4) t. B 0. (5) Now we can define, B A. (6) Where A is magnetic vector potential. Substituting equation (6) in to equation (2), A E 0 t. (7) This equation has a solution of A E t, (8) Where φ is a random function that constitute the scalar potential contribution to the electric field. Substituting equation (3), (6) and (8) in to equation (1), A A A A t (9) The magnetic vector potential is calculated by solving the above equation then the electromagnetic field are calculated by using the A. The induced voltage can be derived from the following equation, d e B. ds dt. (V) (10) Force acting on the armature is given as, F J X Bdv. (N) (11) The instantaneous joule losses is given as, 2 p J dv. (W) (12)

2 III. SIMULATION RESULTS Fig. 2. Geometric model of rail gun[12]. Fig.2 shows the geometric model of rail gun used in simulation. We assumed that the armature and rails are made up of copper and the dimensions of rails and armature used in simulation are given in Table 1. Table 1: Rail gun geometry parameter The rail gun parameters such as force and velocity acting on the armature, induced voltage, power loss and current density and magnetic flux over rail and armature are calculated by exciting the rail with different pulsed current shapes at transient conditions. The current pulse shown in Fig.3 given to the rail gun has three portions namely, a) Pulse rise time b) Pulse working time c) Pulse fall time The current supplied to the rail, Lorentz force developed in the armature, induced voltage over the armature and the power loss over armature obtained from the simulation for a various rise times are shown in Fig.4 to Fig 6. From the figure Fig.4 (a) Fig.4 (b) and Fig.4c it is observed that the shape of input current and force acting on the armature power loss over the armature are same. It validates that the force acting the projectile and power loss over the armature is directly proportional to the square of the current supplied to rails. It is also observed that as the rise time of current pulse increases force acting on the armature decrease. It is also observed that the induced voltage has positive value during the rise time and it maintain constant voltage during working time and it has negative value during fall time. It is validate that the induced voltage is directly proportional to the rate of change of current. It is also observed that as the rate of change of current is positive the induced voltage has positive value and for the rate of change of current is negative voltage will be negative. It is also observed that as the rise time of current pulse is increased the induced voltage in the armature decreased. B. Pulse working time variation The working time of the current pulse supplied to the rail gun varied for different duration s namely small working time, medium working time and large working time and characteristics of working time given Table 3. The induced current in the rail, Lorentz force developed in the armature, induced voltage over the armature, solid loss over armature obtained from the simulation for various rise shown in Fig7 to Fig 9.It is observed that as the working time increases the force acting on the armature increases. It is also observed that as the working time increases the induced voltage in the armature increases. Fig. 3. Current pulse given to the rail gun [2]. The current distribution changes significantly in rails and armature during the rising, working time and falls time of the exciting current source. Investigating the current distribution in rails and armature is useful to study the inductance gradient and to realize the current distribution in armature. Estimating the current distribution in armature is essential to analyze its stress, temperature rise, contact with rails, and motion characteristics. A. Pulse rise time variation The rise time of the current pulse supplied to the rail gun is varied for different duration s namely small rise time, medium rise time and large rise time, and the characteristic of rise time given in Table 2. Table 2: Characteristic of Rise time Fig. 4. Performance of Rail gun for small rise time.

3 Fig. 5. Performance of Rail gun for medium rise time. Fig. 7. Performance of Rail gun for small working time. Fig. 6. Performance of Rail gun for large rise time. Fig. 8. Performance of Rail gun for medium working time.

4 rise time. 1.54Tesla for medium rise time and 1.25 Tesla for large rise time of input current. It has been concluded that as the rise time of current pulse increases magnetic flux density over the rail and armature decreases. Fig. 10. (a). Small rise time. Fig. 10. (b). Medium rise time. Fig. 9. Performance of Rail gun for large working time. Table 3: Characteristics of working time Fig. 10. (c). Large rise time. Fig.10. Comparative plot of current density vector fields and magnitude fields. Fig. 11. (a). Small rise time. IV. ANALYSIS OF TRANSIENT RESULTS A. Rise time analysis The current density magnitude and vector plots obtained from the simulation for a different rise times are shown in Fig.10. All the results are compared at same time frame at 0.08ms. It is observed that the current density magnitude is high in corners where armature and rails cross. The peak average current density for small rise time is A/m 2, for the medium rise time it is A/m 2, and for the same condition in large rise time is 6.46X10 7 A/m 2.It has been concluded that as the rise time of current pulse increases the current density values over the rail and armature decreases Fig.11 shows the magnitude and vector plots of magnetic flux density over the rail and armature for a different rise time. It is observed that the magnetic flux density maintain a value of 1.55 Tesla for small Fig. 11. (b). Medium rise time. Fig. 11. (c). Large rise time. Fig.11 Comparative plot of Magnetic flux density vector fields and magnitude.

5 Fig. 12. (a). Small working time. Fig. 12. (b). Medium working time. Fig. 12. (c). Large working time. Fig.12 Comparative plot of Current density Vector fields and magnitude fields. Fig. 13. (a). Small working time. Fig. 13. (b). Medium working time. Fig. 13. (c). Large working time Fig.13. Comparative plot of Magnetic flux density vector fields and magnitude fields B. Working time analysis The working time variation is varied from small working time to large steady time. The analysis is studied in same time frame of 0.36ms. Fig.12 shows the current density distribution over rail and armature for different working time. From the figures it is observed that maximum current density over the armature for small working time is 3.44X10 7 A/m 2, for the medium working time it is 5.16X107 A/m 2 and for the same condition in larger working time it is 7.45X10 7 A/m 2. It has been concluded that as the working time of current pulse increases the current density over a rail and armature increases. Fig.13 shows the magnetic flux density distribution over rail and armature for different working time. From the figures it is observed that maximum magnetic flux density over the armature for small working time is 0.67 Tesla, Tesla and 1.45 Tesla for the medium and large working time respectively. It has been concluded that as the working time of current pulse increases the magnetic flux density over armature increases. V. CONCLUSIONS The performance characteristics parameters of the rail gun such as force and velocity acting on the armature, induced voltage, power loss and B field plots over rail and armature are greatly affected by its current distribution. In this paper the performance of rail gun is analyzed by exciting the rail with different current wave shape using 3-dimensional magnetic field simulator. Pulsed mode current shape has been considered for this study. The rise and working time of current pulse is varied and performance of rail gun is analyzed. It is also observed that as the rise time of current pulse increases force acting on the armature decreases. It is also observed that as the rise time of current pulse is increased the induced voltage in the armature decreased. For varying working time of current pulse, it is observed that as the working time of current pulse increases the force acting on the armature increases. It is also observed that as the working time increases the induced voltage in the armature increases. It is also observed that varying the time period of current pulse does not give any effects on solid loss over armature. The current density and magnetic flux density over a rail and armature are obtained for different rise and working time of current pulse. It is observed that current density and magnetic flux density decreases as the rise time of current pulse increases and increases as the working time of current pulse increases. It also been observed that current density distribution are greatly affected by working time comparing to rising time of current pulse. Thus the results hereby prove that the working time of input pulse is essential as it decides design parameters of the rail gun system. REFERENCES [1] Asghar Keshtkar, Sadjad Bayati and Ahmad Keshtkar, Derivation of a formula for inductance gradient using intelligent estimation method, IEEE Trans. Magnetics, Vol. 45, No. 1, pp , [2] Nikolaos Pratikakis Mathematical Modeling Of Rail Gun M.S. Thesis,Naval Postgraduate School, Monterey, California pp [3] C. G. Hodge and J. O. Flower, A Comparison of Co Energy and Lorenz Force Based Simulations Of Rail Guns BMT Defence Services Ltd., pp. 1-6, April [4] Peng Zuo, Jun Li, Xiangqian Song, and Jiansheng Yuan Characteristics of Current Distribution in Rails and Armature With Different Section Shape Rails IEEE Trans. Plasma Sci., vol. 41, no. 5,Jan [5] S. Hundertmark and M. Roch Transient 3-d Simulation of an experimental rail gun using

6 Finite Element Methods 16 th Electromagnetic launcher symposium pp.1-5 May [6] Tao Huang, Jiangjun Ruan, Yujiao Zhang, Yadong Zhang, JunpengLiao, and Yuanchao Hu Effect of Geometry Change on the Deformation in C- Shaped Armatures Through 3-D Magnetic-Structural Coupling FE Analysis IEEE Trans. Plasma Sci., vol. 41, no. 4, pp.71-74, Jan [7] Asghar Keshtkar, Shahab Mozaffari, and Ahmad Keshtkar Effect of Rail Tapering on the Inductance Gradient Versus Armature Position by 3D- FEM IEEE Trans. Plasma Sci., vol. 39, no. 1, pp.71-74, Jan [8] Gallant, Parametric study of augmented railguns, IEEE Trans. Magn., vol. 39, no. 1, pp , Jan [9] A. Musolino, M. Raugi, R. Rizzo, and A. Tellini, Analysis of the performance of a multistage railgun, IEEE Trans. Magn., vol. 39, no. 1, pp , Jan [10] Peng Zuo, Jun Li, Member, IEEE, Xiangqian Song, and Jiansheng Yuan Characteristics of Current Distribution in Rails and Armature With Different Section Shape Rails IEEE Trans. Plasma Sci., vol. 41, no. 5,Jan [11] John D, Powell and Alexander E. Zielinski Two dimensional Current Diffusion in the Rails of a Railgun Army research laboratory October 2008 [12] Inaki caldicoury and Pierre L Eplattenier Simulation of a rail gun: A contribution to the validation of the electromagnetism module in LS-DYNA v th International conference.