Dynamics of a Vertical Unbalanced Gas Centrifuge Supported by Magnetic Bearings
Abstract
The gas centrifuge is modeled as a rigid rotor supported by two magnetic bearings with eight-pole structures. To describe the system dynamics, the coupled nonlinear ordinary differential equations (ODE) of the second order are derived, to solve which the Fourier method (FM) is used, i.e. the solution to the system of differential equations of motion is obtained in the form of a trigonometric series. The use of FM provides the possibility of representing a harmonic semi-analytical solution. The dynamics of forced vibrations and self-excited vibrations under the action of harmonic forces is studied, and free oscillations are analyzed. Various parameters influencing the vibration behavior of the rotor are studied. The dependence of the amplitudes and phases of vibrations on the excitation frequency is analysed. Ultraharmonic and subharmonic vibrations, as well as self-exсited vibrations of the gas centrifuge on magnetic bearings (GCMB or a rotor) are studied.