Stability Analysis of a Flexible Bladed-Rotor

Abstract

In any high-performance turbo-machinery, instability prediction and damage are commonly occurring problems. The aim of this paper is to present stability analysis of a fully-bladed flexible rotor. The flexural vibrations of the blades as well as those of the shaft are considered; the energetic approach used includes the effect of the rotational inertia. Then stability detection, bringing loci veering phenomena and coalescence, in case of asymmetric rotor, to the fore, is made in order to determine a parametric domain where turbomachinery cannot encounter damages. Moreover, extensive parametric studies including for instance the length and the stagger angle of the blades are presented in order to obtain robust criterion for stable and unstable areas prediction. Finally, the rotor/stator contact is introduced and the effect of the radial load acting on the blades when rubbing against a carter is considered. IntroductionThe basic objective of turbo-machinery designers is to increase the efficiency of their machine. The efficiencies of both turbo-generators and jet engines depend strongly on the clearance between the rotating and the stationary parts [1,2]: the wider the clearance, the less efficient the machine. Hence it is desirable to reduce the clearance by as much as possible. It cannot be reduced below a certain minimum level due to uncertainties in the dynamics, fluid dynamics [3,4], thermal loads [5], the machining tolerances and material properties [6,7]. The more accurate these parameters are known, the smaller the clearance can be made. However, reduced clearances increase the possibility of violent contacts between rotor and stator and under certain operating conditions, including the dynamic properties of the rotor and the stator and the speed of rotation, the contacts may continue and drive the rotor-stator system unstable [8,9,10]. A common interest of the rotating-machinery industry is to better understand the dynamic behaviour of rotating structures and in particular that of flexible bladed-rotor whose dynamic behaviour differs from those usually studied in rotor-dynamics. Thus, the instability of

Contact analysis of a flexible bladed-rotor

“…3(b) representing the evolution of the eigenvalues' imaginary parts but as a function of the associated eigenvalues' real parts. In this case, it can be seen that the system is perfectly stable because there is no eigenvalues having a real part positive.Such stability analysis can be performed for several rotating systems and stability maps can also be obtained (Lesaffre et al, 2004). …”