Unstable Vibrations Induced by Rotationally Unsymmetric Inertia and Stiffness Properties

Abstract

In a rotating shaft system carrying an unsymmetrical rotor, or in a shaft with unequal stiffness, there occur two kinds of unstable vibrations. One is so called "statically unstable vibration" and the other is "dynamically unstable vibration" in the neighborhood of rotating speeds of shaft w_c and w_d, respectively. By solving numerically a frequency equation, we have been able to obtain exact values of the width of the unstable region and the negative damping coefficient. And also we could obtain the approximate values of them by applying the Taylor's expansion theorem to the frequency equation nearly about the rotating speeds w_c and w_d severally. In this paper, the authors deal with these unstable vibrations by considering an input energy from shaft end into the system. By this treatment we made clear the physical meaning and occurrence of these unstable vibrations. The approximate results derived from energy consideration coincide fairly well with exact results obtained by numerical calculation.