Mechanical interaction of a projectile body with a bore walls of an electromagnetic accelerator. Numerical solution

The vibration of the accelerator rails under the action of electromagnetic forces, the right boundary of which is moving along with the armature along the barrel bore, is considered. The rail accelerator is simply considered as a Bernoulli-Euler beam of finite length, lying on a viscoelastic foundation, with cantilever support from the side of the accelerator breech. The rail vibration is described by a differential equation in partial derivatives of the fourth order in coordinate and the second order in time. The equation is solved numerically by combined method: finite differences in time and finite elements in coordinate. A comparison of the results of numerical calculations with an analytical solution showed that the developed code evaluates the behavior of the rail well under the influence of an EM load moving along its length along the entire trajectory of the accelerated body.
Using the developed code, the influence of the current profile in the accelerator circuit and the foundation parameters on the dynamics of bending waves arising and propagating in the rail, the position and magnitude of the maximum rail deflection was studied. It is shown that it is possible to select a current profile that minimizes the rail accelerator deflection during acceleration. It is also found that the choice of the optimal current profile has no less effect on the maximum rail deflection than improving the parameters of the accelerator foundation. The calculation results may be useful in the design of an electromagnetic rail accelerator.