A reduced-order modeling technique for mistuned bladed disks

Abstract

The analysis of the response statistics of mistuned turbomachinery rotors requires an expensive Monte Carlo simulation approach. Simple lumped parameter models capture basic localization effects but do not represent well actual engineering structures without a difficult parameter identification. Current component mode analysis techniques generally require a minimum number of degrees of freedom which is too large for running Monte Carlo simulations at a reasonable cost. In the present work, a novel order reduction method is introduced which is capable of generating reasonably accurate, very low order models of bladed disks. This technique is based on component modes of vibration found from a finite element analysis of a single disk-blade sector.

Forced response of mistuned bladed disks using reduced-order modeling

“…In the ROM formulation for bladed disk free response, Ottarsson et al 3 introduce the idea that the motion of an individual blade consists of cantilever blade elastic motion and disk-induced static motion. (1) where U d is the blade portion of the disk-induced mode shapes, U b contains the mode shapes of the cantilevered blades, and a and b represent disk and blade modal coordinates, respectively.…”

“…The derivation of the ROM equations of free motion for tuned and mistuned bladed disks is detailed in Reference. 3 The final form of the equations is restated here for convenience:…”

“…Reduced-order modeling (ROM) is thus required in order to enable statistical analysis of bladed disk response. In 1994, Ottarsson et al 3 introduced a technique for developing ROM of bladed disks directly from finite element models. The procedure involves a component mode analysis of the bladed disk, with a truncated number of modal amplitudes describing the response of the assembly.…”

“…The procedure involves a component mode analysis of the bladed disk, with a truncated number of modal amplitudes describing the response of the assembly. The key idea introduced by Ottarsson et al 3 is that the motion of an individual blade consists of both cantilever blade elastic motion and diskinduced static motion. The principal advantage of the technique is the considerable computational savings associated with solving a full mistuned rotor with a reduced set of degrees of freedom.…”

Experimental Measurements of the Natural Frequencies and Mode Shapes of Rotating Disk-Blades-Disk Assemblies from the Stationary Frame

“…Bladed-disks (or blisk), which consist of a rotor disk and blades ( Figure 1b), are widely used in the field of stationary gas turbines and in aircraft engines. This kind of structure is said to have cyclic symmetry [20][21][22][23], which means that they are composed of identical sectors (each sector contains a part of the disk and the blade). A discussion of the natural frequencies and mode shapes of this kind of structures can be found in [20,21] for "tuned" bladed disks, which means that the condition of cyclic symmetry is accomplished.…”