| The fundamental limits to the velocity of solid armatures in railguns are dependent upon the increase in temperature which melts the conducting medium or lowers the yield strength of the material. A two dimensional transient finite element electrothermal model is developed to determine the magnetic and temperature fields in the rails and armature of a railgun. The solution for the magnetic and temperature fields is based upon the fundamentals of Maxwell's equations and Fourier's law of heat conduction with no apriori assumptions about the current density distribution in the rails or the armature. The magnetic field and temperature field spatial variations are calculated using finite element techniques while the time variations are calculated using finite differencing methods. A thermal diffusion iteration is performed between each magnetic diffusion iteration. Joule heating information is provided by solving the magnetic diffusion problem and temperature data for calculating material properties such as the electrical resistivity, thermal conductivity, and specific heat is provided by solving the thermal diffusion problem. User inputs into the model include the geometry of the rails and armature, material properties versus temperature, current input profile versus time, mass of the armature, friction data versus speed at the rail-armature interface, and iteration step time.;Various types of rail and armature designs are simulated to include solid armatures consisting of different homogeneous materials, resistive rails, and a graded resistance armature. The analysis also includes different solid armature shapes such as the square, curved, and chevron designs. All solid armature designs tend to concentrate the current toward the trailing edge of the rail-armature interface since current diffusion in the rails is limited by a velocity skin effect. Copper rails and a molybdenum chevron armature are identified as good candidates for further solid armature testing. The results of the transient finite element electrothermal model are compared with laboratory test results. |
