On the beneficial effect of rotor suspension anisotropy on viscous-dry hysteretic instability

Abstract

The destabilizing influence of the internal friction on the supercritical rotor whirl can be efficiently counterbalanced by other external dissipative sources and/or anisotropic suspension systems. The theoretical approach may take the internal dissipation into consideration either by dry or viscous models. Nevertheless, several numerical results and a new perturbation technique of the averaging type prove that similar rotor motions and stability limits are achievable by both models, whence the linear viscous assumption appears preferable. Thus, the internal hysteretic force may be expressed by the product of an equivalent viscous coefficient and the rotor centre velocity relative to a reference frame rotating with the shaft end sections. After calculating the natural frequencies and the response to dynamic imbalances, the stability of the steady motion is checked by the Routh-Hurwitz criterion, focusing the analysis on the individual influence of several characteristic properties, like the gyro structure, the stiffness anisotropy of the supports and their asymmetry, and searching for the external damping level needed for stability. A fairly interesting result is that the benefit of the suspension anisotropy is most effective for a symmetric rotor mounted at the shaft mid-span and decreases significantly on increasing the configuration asymmetry, even moderately. It is also observed how the stability may somehow be associated with the coupling between progressive and retrograde precession motions.