Blade Manufacturing Tolerances Definition for a Mistuned Industrial Bladed Disk

Abstract

This paper deals with the characterization of the blade manufacturing geometric tolerances in order to get a given level of amplification in the forced response of a mistuned bladed-disk. The theory is based on the use of a nonparametric probabilistic model of blade random uncertainties. The dispersion parameters controlling the nonparametric model are estimated as a function of the geometric tolerances. The industrial application is devoted to the mistuning analysis of a 22 blades wide chord fan stage. Centrifugal stiffening due to rotational effects is also included. The results obtained validate the efficiency and the reliability of the method on three dimensional bladed disks.

A state-of-the-art review on uncertainty analysis of rotor systems

“…A few works also studied the uncertain dynamics of dual-rotor-bearing systems [96,161,211]. Capiez-Lernout et al [212] defined the blade manufacturing tolerances for the mistuned industrial bladed disks and Capiez-Lernout et al [213] further analyzed the mistuning effects and relevant uncertain dynamics based on the nonlinear ROMs using the nonparametric probabilistic approach. Picou et al [214] presented a robust analysis of the influences of the geometric nonlinearities in rotating bladed disks with the intentional and unintentional mistuning.…”

Uncertainty Quantification

“…− the robust analysis of the mistuning that is induced by the manufacturing tolerances in a bladed disk [28,29]. − the robust design that is based on a detuning technique by modifying some blade shapes in presence of mistuning with rotation and unsteady flow [132].…”

Nonparametric Probabilistic Approach of Model Uncertainties Introduced by a Projection-Based Nonlinear Reduced-Order Model

“…The second step consists in constructing a SROM by substituting the deterministic matrices of the ROM (such as the mass, the damping, and the stiffness reduced matrices) with random matrices for which the probability distributions are constructed using the Maximum Entropy (MaxEnt) principle [40,41,42] under the constraints defined by available information assocaited with algebraic properties (such as lower bounds, positiveness, integrability of the inverse, etc) and statistical information (such as the mean value equals to the nominal values, etc), and for which advanced algorithms have been developed for the high dimensions [39,43,44]. This approach has been extended to different ensembles of random matrices (see [38,45]), static boundary value problems [46], and has been experimentally validated and applied in many areas, including: dynamics of composite structures [47] and viscoelastic structures [48,49], dynamic substructuring techniques [50,51,52,53,54], vibroacoustic systems [48,55,56,57], soil-structure interactions and earthquake engineering [58,59,60], robust design and optimization [61,62], to name only a few. More recently, this nonparametric probabilistic approach has been extended in structural dynamics to nonlinear geometrical effects [63,64].…”