Optimization of Intentional Mistuning Patterns for the Reduction of the Forced Response Effects of Unintentional Mistuning: Formulation and Assessment

Abstract

The focus of the present investigation is on the use of intentional mistuning of bladed disks to reduce their sensitivity to unintentional random mistuning. The class of intentionally mistuned disks considered here is limited, for cost reasons, to arrangements of two types of blades (A and B, say). A two-step procedure is then described to optimize the arrangement of these blades around the disk to reduce the effects of unintentional mistuning. First, a pure optimization effort is undertaken to obtain the pattern(s) of the A and B blades that yields small/the smallest value of the largest amplitude of response to a given excitation in the absence of unintentional mistuning. Then, in the second step, a pattern screening technique based on a recently introduced measure of localization is used to determine which of the patterns does have a large/small sensitivity to random unintentional mistuning. In this manner, expensive Monte Carlo simulations can be eliminated. Examples of application involving both simple bladed disk models and a 17-blade industrial rotor clearly demonstrate the significant benefits of using this class of intentionally mistuned disks.

Robust Analysis of Design in Vibration of Turbomachines

“…This analysis shows that although the detuning pattern is not optimized, the geometrical modifications of blades can reduce blade sensitivity to mistuning. Then, by combining blade geometric modifications with a detuning pattern optimization, as the one proposed in [5,28], an optimal robust design model minimizing the forced responses, while keeping stability, can be obtained. This is the purpose of works in progress.…”

“…However, it is possible (e.g. see [4][5][6][7][8]) to intentionally detune the mistuned system in order to reduce the forced response amplification. The main technologic solutions to introduce detuning are based on modifying blade material properties, the interface between blade and disk, or the blade shape by introducing several types of blades with different geometries corresponding to geometrical modifications of the nominal blades.…”

A numerical and experimental investigation on passive piezoelectric shunt damping of mistuned blisks

“…The bladed drum tested in this project is a laboratory prototype which exhibits a substantial mistuning, with frequency deviations well in excess of the 1%–2% usually met in industrial bladed structures (Choi et al, 2003). Figure 12(c) shows the distribution of the frequency deviation of individual blades (measured from impulse responses) of the test structure; one notices that most of the blades have a frequency deviation of the order of 2% or less, but a few of them, in the vicinity of blade # 65 have abnormally large deviations.…”

Derivative-free mixed binary necklace optimization for cyclic-symmetry optimal design problems

“…This optimization problem involves a vector, x ∈ R m , of m continuous variables, each of which describes one blade shape parameter, such as the thickness or the length of the blades. There are also integer variables that locate pre-defined possible blade geometries around the disk, as in [13]. In this study, we focus on the case involving only two different blade geometries; if we consider n blades, their relative positions are indicated with a binary vector y ∈ {0, 1} n , where y i indicates whether the ith blade is of a given type (a) or of the other type, (b), for i = 1, 2, .…”