Model and Stability Analysis of a Flexible Bladed Rotor

This paper presents a fully bladed flexible rotor and outlines theassociated stability analysis. From an energetic approach based onthe complete energies and potentials for Euler-Bernoulli beams, asystem of equations is derived, in the rotational frame, for therotor. This later one is made of a hollow shaft modelled by anEuler-Bernoulli beam supported by a set of bearings. It isconnected to a rigid disk having a rotational inertia. A full setof flexible blades is also modelled by Euler-Bernoulli beamsclamped in the disk. The flexural vibrations of the blades as wellas those of the shaft are considered. The evolution of theeigenvalues of this rotor, in the corotational frame,is studied. A stability detection method, bringing coalescence andloci separation phenomena to the fore, in case of an asymmetricrotor, is undertaken in order to determine a parametric domainwhere turbomachinery cannot encounter damage. Finally, extensiveparametric studies including the length and the stagger angle ofthe blades as well as their flexibility are presented in order toobtain robust criteria for stable and unstable areas prediction