Modeling the movement of a missile in the tubular guide of the starting installation

Abstract

The paper presents computational and mathematical model of the spatial motion of a rocket with centering bulges and a pin on the body in a thin-walled tubular guide mounted on two fixed supports and equipped with a screw groove. The models take into account the interaction of the projectile with the inner surface of the guide tube at the locations of the drive pin and the centering bulge. The strength of the normal reaction of the inner surface of the guide is found as a reaction to the elastic deformation of the pipe caused by normal to its inner surface displacements of the centering thickening at the point of contact with the guide. In this case, the tubular guide is considered as an elastic thin-walled shell. To calculate the values of the shell stiffness coefficient along its length, the finite element method implemented in the ANSYS Mechanical software package is used. The translational component of the projectile motion is investigated on the basis of the theorem on the motion of the center of mass. The rotational component is investigated on the basis of the Lagrange equations of the second kind. The generalized parameters of the rotational motion are the yaw Ψ and pitch θ angles, the angle of attack α, the angle of slip β, and the angle of rotation of the projectile around the longitudinal axis φ. The aerodynamic angle of heel γа is found from the transition formulas for the adopted coordinate systems. The yaw velocity angle Ψ, the pitch velocity angle θ, and the aerodynamic roll angle γа as well as the first time derivatives of these angles are converted into the yaw angles ψ and pitch υ of the projectile axis and their derivatives in the starting coordinate system.