Analyzing the electromagnetic launcher with combination both FEM-3D and IEM methods in time domain

The inductance gradient, current density, Force, Pressure, and Electrical Resistance are essential quantities in Railgun. The Inductance Gradient in the railgun is a function of bore dimension, Rails thickness and ohmic losses. On the other hand, moving Projectile inside the rails or in other words Time-Changing has directly effects on the inductance gradient. In this paper, first the IEM technique in time domain with introduced calculation algorithm is proposed then using the IEM-TD, a model for Railgun in time domain is presented. Using this model and its analytical solution, a basic formula for Inductance Gradient is derived with unknown coefficients versus Railgun parameters in time domain. For completing this closed formula and calculating its unknown coefficients, the samples from Railgun based on the FEM, were analyzed. From outcomes and using the smallest Square of error method, unknown coefficients are calculated. Using achievement L´ formula the applied force of Projectile is calculated and compared with other results that achievement from numerical methods in the some papers. One algorithm for calculating the output velocity of Projectile is proposed and using this algorithm, velocity of Projectile is calculated for different sizes of Rails. Effects of Rails dimension on the Inductance Gradient and current distribution at this formula are calculated and are shown in the different Figures.