Asymptotic Description of Maximum Mistuning Amplification of Bladed Disk Forced Response

Abstract

The problem of determining the maximum forced response vibration amplification that can be produced just by the addition of a small mistuning to a perfectly cyclical bladed disk still remains not completely clear. In this paper we apply a recently introduced perturbation methodology, the Asymptotic Mistuning Model (AMM), to determine which are the key ingredients of this amplification process, and to evaluate the maximum mistuning amplification factor that a given modal family with a particular distribution of tuned frequencies can exhibit. A more accurate upper bound for the maximum forced response amplification of a mistuned bladed disk is obtained from this description, and the results of the AMM are validated numerically using a simple mass-spring model. INTRODUCTIONThe term mistuning refers to the small differences among the (nominally designed to be identical) rotor blades in turbomachinery bladed disks. These small unavoidable imperfections typically result from the manufacturing process and wear, and break the cyclic symmetry of the structure, splitting the tuned eigenvalue pairs and preventing the existence of pure travellingwaves as natural vibration modes of the mistuned structure. This loss of cyclic symmetry has a dramatic effect in the forced response of the bladed disk: the resulting mistuned blade vibration patterns are no longer uniformly distributed circumferen-

Forced Response of Mistuned Bladed Disks: Quantitative Validation of the Asymptotic Description

“…The AMM has been already used by the authors for the study of the optimal intentional mistuning patterns for the stabilization of aerodynamically unstable rotors [18] and to obtain accurate upper bounds on the maximum mistimed response amplification that a forced bladed disk can experience [ 19]. In [ 19] the AMM results were also successfully compared with those of a lumped system with one DOF per sector.…”

“…In [ 19] the AMM results were also successfully compared with those of a lumped system with one DOF per sector.…”

“…(29), this simple case can be explicitly solved, and, as was obtained in [19], the response amplitude first grows as the mistuning is increased and then decays, with a maximum amplification factor The mistuned forced response amplification is plotted in Fig. 4.…”

“…(19)] exhibits off diagonal blocks, and, thus, the effect of mistiming is to couple TWs with a different number of nodal diameters, which are completely independent in the absence of mistiming.…”

“…In this section, we give abrief explanation of the derivation process of the AMM (see [19] for a more complete description).…”