Critical velocity for rails in hypervelocity launchers

This paper is related to the dynamic and strength analysis and optimized design of hypervelocity electromagnetic launchers. Projectile motion along the rails at critical velocity is associated with damaging resonant regimes. These regimes reveal increased displacements and stress that can lead to failure of a launcher. To calculate critical velocity and to visualize dynamic deformations of the launcher we have developed two alternative approaches utilizing analytical and finite element models. The first approach employs a closed form analytical solution for critical velocity that is based on the Bernoulli–Euler model of a beam resting on an elastic foundation and subjected to a moving load. The critical velocity is expressed as a function of geometric and material parameters of the rail and equivalent stiffness of the supporting structure. The stiffness of the supporting structure is found from a 2D finite element model. In the second approach, we employed beam finite element and 3D solid finite element models to visualize and measure the “natural” and “forced” bending waves traveling along the rails. These approaches helped to better understand the transient resonant dynamic processes and offered insight on how to alter the launching device materials and geometry to reduce the critical-velocity effects.