Modelling of the transient diffusion of current and heat in railguns via an equivalent network

The coupled problem of the three-dimensional diffusion of current and heat in railguns with a solid armature is formulated by means of a circuital approach. Rails and projectile are divided in a high number of small-size parallelepipeds, so that temperature and current density may be imagined uniform in every parallelepiped. By integrating Ohm´s law over each parallelepiped an equivalent R-L electrical network is obtained, whose resistive and inductive parameters are evaluated by means of explicit analytical expressions, possible in the case of discretization in parallelepipeds. The voltage fall in the boundary layers between rail and moving armature are taken into account by means of suitable driven generators. The position of the projectile is deduced by the application of the virtual displacement principle, where the discretization in parallelepipeds allows one to express the Lorentz´s force again by means of explicit analytical relations. The nonlinear differential equations system so obtained fully simulates the behaviour of a solid armature railgun, and is solved in time, updating at each time-step the coefficients variable with current density, temperature, and projectile displacement.<>