The literature on reduced-order modeling, simulation, and analysis of the vibration of bladed disks found in gas-turbine engines is reviewed. Applications to system identification and design are also considered. In selectively surveying the literature, an emphasis is placed on key developments in the last decade that have enabled better prediction and understanding of the forced response of mistuned bladed disks, especially with respect to assessing and mitigating the harmful impact of mistuning on blade vibration, stress increases, and attendant high cycle fatigue. Important developments and emerging directions in this research area are highlighted.

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Modeling and Analysis of Mistuned Bladed Disk Vibration: Status and Emerging Directions

The maximum blade forced response amplitudes for mistuned turbomachinery rotors are generally much greater than those of their tuned counterparts However, it is known that the ratio of mistuned to tuned maximum vibration amplitudes, the amplitude magnification, is often largest at a relatively small level of mistuning Increasing the level of mistuning beyond this critical value actually leads to a decrease in the amplitude magnification This suggests that it might be beneficial to introduce some level of mistuning into the nominal design of the system intentionally In this study, the effectiveness of this intentional mistuning strategy is investigated Intentional mistuning is introduced into the rotor design by varying the nominal blade stiffnesses in harmonic and square-wave patterns In addition, the unavoidable, random mistuning of the blades is included in the model as usual The statistics of the forced response are examined for lumped parameter models, as well as for a finite element based reduced-order model of an industrial rotor For the cases considered, it is found that intentional mistuning can greatly reduce a rotor's sensitivity to random mistuning

Using Intentional Mistuning in the Design of Turbomachinery Rotors

https://hal.archives-ouvertes.fr/hal-01537665/document

Component mode synthesis methods using partial interface modes: Application to tuned and mistuned structures with cyclic symmetry

A new reduction method for vibration analysis of intentionally mistuned bladed disks is presented. The method is built for solving the dynamic problem of cyclic structures with geometric modifications. It is based on the use of the cyclic modes of the different sectors, which can be obtained from a usual cyclic symmetry modal analysis. Hence the projection basis is constituted; as well as, on the whole bladed disk, each sector matrix is reduced by its own modes. The method is validated numerically on a real bladed disk model, by comparing free and forced responses of a full model finite element analysis to those of a reduced-order model using the new reduction method.

/pdf/a-reduced-order-model-of-detuned-cyclic-dynamical-systems-1nxiftq10h.pdf

A Reduced-Order Model of Detuned Cyclic Dynamical Systems With Geometric Modifications Using a Basis of Cyclic Modes

This paper focuses on the determination and study of the maximum amplification of the steady state forced response of bladed disks due to mistuning. First, an optimization strategy is proposed in which partially mistuned bladed disks are considered as physical approximations of the worst case disk and the mistuned properties are sought to maximize the response of a specific blade. This approach is exemplified on both a reduced order model of a blisk and a single-degree-of-freedom per blade disk model an extensive parametric study of which is conducted with respect to blade-to-blade coupling, damping, and engine order. A mode shape-based formulation of the amplification factor is then developed to clarify the findings of the parametric study in the strong coupling/small damping limit. In this process, the upper bound of Whitehead is recovered for all engine orders and number of blades and the conditions under which this limit is exactly achieved or closely approached are clarified. This process also uncovers a simple yet reliable approximation of the resonant mode shapes and natural frequencies of the worst disk.Copyright © 2002 by ASME

Maximum Amplification of Blade Response due to Mistuning: Localization and Mode Shape Aspects of the Worst Disks

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.

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

Optimization of intentional mistuning patterns for the reduction of the forced response effects of unintentional mistuning

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 describe 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.Copyright © 2001 by ASME

Components resistant to traveling wave vibration and methods for manufacturing the same are provided. The component comprises a component body and a plurality of features disposed thereabout according to an asymmetry pattern that separates a pair of repeated eigenvalues associated with a targeted mode that deflects in excess of a threshold deflection limit in response to traveling wave excitation. The method comprises identifying, in a model of a rotationally periodic component, one or more modes thereof that deflect in excess of a threshold deflection limit in response to a traveling wave excitation. Each of the modes has a pair of repeated eigenvalues associated therewith. An asymmetry pattern is determined that separates each pair of repeated eigenvalues by a desired frequency split. A plurality of features are formed and disposed according to the asymmetry pattern about the component body defining an asymmetrical component comprising the component resistant to traveling wave vibration.

Components resistant to traveling wave vibration and methods for manufacturing the same

A component for a gas turbine engine includes a rotor disk, a plurality of blade attachments, a plurality of retention flanges, and a plurality of retention tabs. The rotor disk has a plurality of slots formed in an outer surface thereof. Each blade attachment has an attachment region configured to be partially disposed within one of the slots. The plurality of retention flanges extend from the rotor disk outer surface, to thereby at least inhibit axial movement of the blade attachment, when the attachment region is fitted inside its corresponding slot. A retention tab extends from each attachment region and engages one of the retention flanges.

Jeff Lentz

Papers

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

Optimization of intentional mistuning patterns for the reduction of the forced response effects of unintentional mistuning

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

Components resistant to traveling wave vibration and methods for manufacturing the same

Blade attachment retention device