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

This paper presents an in-depth study of blade vibration problems that seriously impact development of advanced gas turbine configurations. The motivation for this study arises from the author's conviction that structural integrity of power plants is the dominant factor that influences the quality, reliability, and marketability of the product. Implications of this study in the context of potential R&D challenges and opportunities of interest to industry, governments, and academia are discussed.

Flutter and Resonant Vibration Characteristics of Engine Blades

Component mode synthesis (CMS) techniques are widely used for dynamic analyses of complex structures. Significant computational savings can be achieved by using CMS since a modal analysis is performed on each component structure (substructure). Mistuned bladed disks are a class of structures for which CMS is well suited. In the context of blade mistuning, it is convenient to view the blades as individual components, while the entire disk may be treated as a single component. Individual blade mistuning may then be incorporated into the CMS model in a straightforward manner. In this paper, the Craig-Bampton (CB) method of CMS is formulated specifically for mistuned bladed disks, using a cyclic disk description. Then a novel secondary modal analysis reduction technique (SMART) is presented: a secondary modal analysis is performed on a CB model, yielding significant further reduction in model size. In addition, a straightforward non-CMS method is developed in which the blade mistuning is projected onto the tuned system modes. Though similar approaches have been reported previously, here it is generalized to a form that is more useful in practical applications. The theoretical models are discussed and compared from both computational and practical perspectives. It is concluded that using SMART, based on a CB model, has tremendous potential for highly efficient, accurate modeling of the vibration of mistuned bladed disks.

Component-Mode-Based Reduced Order Modeling Techniques for Mistuned Bladed Disks—Part I: Theoretical Models

New techniques are presented for generating reduced-order models of the vibration of mistuned bladed disks from parent finite element models. A novel component-based modeling framework is developed by partitioning the system into a tuned bladed disk component and virtual blade mistuning components. The mistuning components are defined by the differences between the mistuned and tuned blade mass and stiffness matrices. The mistuned-system model is assembled with a component mode synthesis technique, using a basis of tuned-system normal modes and attachment modes. The formulation developed is general and can be applied to any mistuned bladed disk, including those with large geometric mistuning (e.g., severe blade damage). In the case of small (i.e., blade frequency) mistuning, a compact reduced-order model is derived by neglecting the attachment modes. For this component mode mistuning model, the blade mistuning is projected first onto the component modes of a tuned, cantilevered blade, and then projected again onto the tuned-system normal modes via modal participation factors. In this manner, several natural frequencies of each mistuned blade can be used to capture systematically the effects of the complex physical sources of mistuning. A numerical validation of the developed methods is performed for both large and small mistuning cases using a finite element model of an industrial rotor.

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Compact, Generalized Component Mode Mistuning Representation for Modeling Bladed Disk Vibration

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, an order reduction method is introduced which is capable of generating reasonably accurate, very low order models of tuned or mistuned bladed disks This technique is based on component modes of vibration found from a finite element analysis of a single disk-blade sector It is shown that the phenomenon of mode localization is well captured by the reduced order modeling technique

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A reduced-order modeling technique for mistuned bladed disks

This analysis is aimed at determining the influence of blade mistiming on the vibratory stress levels of turbine and compressor blades A frequency response analysis for a given rotor configuration shows that a large number of resonances may occur over a frequency band, the width of which is nearly 20% of the mean blade frequency The resonant amplitudes are a function of blade frequency and location on the rotor, and the amount of damping present in the system A parametric study is carried out to evaluate the response levels due to engine order excitation, aerodynamic and mechanical damping, and blade frequency deviation The resulting mode shapes and frequencies are in good agreement with the experimental findings reported earlier in the literature

Influence of Mistuning on Rotor-Blade Vibrations

The aeroelastic stability of a long, thin cylindrical shell with the outer surface exposed to an inviscid, helical flow of ah* is investigated. The cylinder behavior is described by classical shell equations, whereas the aerodynamic forces are described by the linearized potential theory. The approach that is used herein examines the nature of stability of the system when the system is "slightly" perturbed from its initial equilibrium state. In this paper, numerical results are presented only for the special case of swirl flow around a nonrotating shell, i.e., the axial flow velocity is set to zero. These results indicate that traveling wave type of flutter can be caused by coalescence of backward and forward traveling waves. Two approximate theories are presented and the results are compared.

A. V. Srinivasan

Papers

Influence of Mistuning on Rotor-Blade Vibrations

Flutter analysis of rotating cylindrical shells immersed in a circular helical flowfield of air