Maximum mistuning amplification of the forced response vibration of turbomachinery rotors in the presence of aerodynamic damping

Abstract

Mistuning can dangerously increase the vibration amplitude of the forced response of a turbomachinery rotor. In the case of damping coming from aerodynamic effects the situation is more complicated because the magnitude of the damping changes for the different travelling wave modes of the system. This damping variability modifies the effect of mistuning, and it can even result in a reduction of the mistuned forced response amplitude below that of the tuned case (this is not possible in the usual case of constant material damping). In this paper the Asymptotic Mistuning Model (AMM) methodology is used to analyze this situation. The AMM is a reduced order model that is systematically derived from the mistuned bladed disk full model using a perturbative procedure based on the small size of the mistuning and the damping. The AMM allows to derive a very simple expression for an upper bound of the maximum amplification factor of the vibration amplitude that the system can experience (an extension of the well known Whitehead 1966 result to include the effect of non-uniform aerodamping). This new upper bound gives information on the mechanisms involved in the amplification/reduction of the mistuned response: (i) the number of modes participating in the response, and (ii) the ratio between the aerodamping of the directly forced mode and that of the of the rest of the modes. A FEM of a mistuned bladed disk is also used to verify the AMM predictions for several different forcing configurations, and both results show a very good quantitative agreement.

Vibration Characteristics of Rotating Mistuned Bladed Disks considering the Coriolis Force, Spin Softening, and Stress Stiffening Effects

“…is phenomenon has been found in previous investigations [18,20,22]. With respect to the specific influences of rotordynamic effects, the influences of rotordynamic effects on relative AMF are consistent with those shown in Figure 15.…”

“…In the early stage of studies, most investigations focused either on the structural vibrations of mistuned bladed disks [5][6][7][8][9] or on the beneficial effects of mistuning to flutter [10][11][12][13]. In recent years, a number of investigations have been published to address the effects of aerodynamic damping [14][15][16][17][18][19] and to develop effective reduced-order models for quantitative vibration analysis. In obtaining reduced-order models of mistuned bladed disks, the substructure techniques and component-mode synthesis methods [20][21][22] are commonly employed in the early stage.…”