On the Unstable Vibrations of a Shaft With Unsymmetrical Stiffness Carrying an Unsymmetrical Rotor

Abstract

In a rotating shaft system carrying an unsymmetrical rotor, or in a rotating shaft system with inequality in stiffness, there are unstable regions in the neighborhood of both the major critical speed ωc and the rotating speed ωd at which the sum of two natural frequencies of the system is equal to twice the rotating speed of the shaft. The unstable vibrations appearing in these unstable regions are treated for the system consisting of a rotor with unsymmetrical inertia and a shaft with unequal stiffness which rotates with the rotor. Simultaneous effects of the unsymmetrical rotor and the unsymmetrical shaft are appreciated and quantitative analytical results are obtained which relate the width of the unstable regions and the negative damping coefficients of the unstable vibrations to the asymmetry in inertia, the inequality in stiffness, and the relative orientation between the inequalities in inertia and stiffness. Furthermore, elimination of two kinds of unstable regions is realized theoretically and experimentally.