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.

Vibration Characteristics of Slotted Shafts

“…The dynamics of asymmetric rotors has been the subject of interest for several decades and many papers were published on this, to name a few by Brosens and Crandall [1], Yamamoto and Ota [2,3], and Arday"o and Frohrib [4]. Yuan Kang et al [5] utilizing "nite element formulation generalized the previous works to accommodate the asymmetry e!ects.…”

Dynamic instability of a rotor-bearing system with two asymmetric disks

“…Later, a series of in-depth theoretical and experimental studies on the unstable vibrations of a rotating shaft carrying an unsymmetrical rotor were carried out by Yamamoto et.al. [3] [4]. Ardayfio and Frohrib [5] extended the four degree-of-freedom rotor system of Yamamoto and Ota [3] to include flexibility in the bearing supports.…”

Stability of asymmetric rotors with asymmetric flexible disks

“…Yamamoto and Ota (1964) showed that a rotating shaft system carrying unsymmetrical rotor experiences instability in the neighborhood of rotating speeds when the sum of the two natural frequencies of the system is equal to twice the rotating speed. Later, Yamamoto et al (1968) examined the unstable vibration of a system consisting of a rotor with unsymmetrical inertia, supported by rotating flexible shaft with unequal stiffness. Ardayfio and Frohrib (1976) examined instabilities of an asymmetric rotor with asymmetric shaft mounted on symmetric elastic supports.…”