The problem rotor’s movement in a stationary circular cylindrical chamber having finite length and filled with viscous gas is solved by the method of direct numerical integration of the set of equations describing pressure distribution in a thin layer of viscous gas and the motion of a rotating statically disbalansed cylinder. The rotor moving in the gravitational field is influenced by the impressed forces which vary periodically in time. Unsteady pressure equation is approximated by the symmetric stable finite-difference scheme of the second order accuracy. Stability criteria of a rotating rigid unstable cylinder (a rotor) motion subject to problem parameters are studied. The inner cylinder is influenced by outer forces which vary periodically in time. Trajectories of the rotor stationary motion for various velocities of rotation, disbalance values, amplitudes and frequencies of outer forces are calculated. Conditions of contact free motion of the cylinder, rotating in the chamber, are determined.
Author: Dementev O.
MATHEMATICAL MODELLING OF TECHNOLOGICAL PROCESSES AND SYSTEMS
Influece of form errors of a chamber filled with a liquid on the movement and stability of a ball, rotating in the chamber, is studied. Two cases of the influence of a chamber form errors on the forces, acting on the ball, are defined. The first case describes the situation when limitations on the rotor shift are not imposed and disturbances of the chamber form are set by spherical harmonics not above the first order. Then the chamber of a disturbed form, form the point of view of the reaction forces of the liquid and their moments, does not differ from a similar spherical chamber. In the second case disturbance of a chamber form are arbitrary and the rotor shift is supposed small. Then the force, acting on the rotor, depends on its displacement only, and the momentum does not depend on shift. A chamber of any form is equivalent to an ellipsoid. A rising here diflective moment tends to direct the angular speed vector along the small semiaxis of the ellipsoid, i.e., a stable position of the rotor appears.