Instability due to internal damping of symmetrical rotor-bearing systems

Forrai, László (2000) Instability due to internal damping of symmetrical rotor-bearing systems. JOURNAL OF COMPUTATIONAL AND APPLIED MECHANICS, 1 (2). pp. 137-147. ISSN 1586-2070

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Abstract

This paper deals with the stability analysis of self-excited bending vibrations of linear symmetrical rotor-bearing systems with internal damping using the finite element method. The rotor system consists of uniform circular Rayleigh shafts with both internal viscous and hysteretic damping, symmetric rigid disks, and discrete isotropic damped bearings. The effect of rotatory inertia and gyroscopic moment are also included in the mathematical model. By combining the sensitivity analysis and the eigenvalue problem of the rotor dynamics equations presented in complex form, it is proved theoretically that the whirling motion of the rotor system becomes unstable at all speeds beyond the threshold speed of instability. Furthermore, it is found that the rotor stability is improved by increasing the damping provided by the bearings, whereas increasing internal hysteretic damping will result in a reduction in the threshold speed of instability. It is also shown that the corresponding whirling speed of the rotor is always higher than the first forward bending critical speed. Numerical examples are given to confirm the validity of the theoretical results.

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