0
Research Papers

A Reduced-Order Meshless Energy Model for the Vibrations of Mistuned Bladed Disks—Part I: Theoretical Basis

[+] Author and Article Information
O. G. McGee, III

Professor
Howard University,
Washington, D. C. 20059

C. Fang

Postdoctoral Research Associate
Howard University,
Washington, D. C. 20059

Y. El-Aini

Senior Fellow
Pratt and Whitney Rocketdyne,
West Palm Beach, FL 33401

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received December 16, 2005; final manuscript received January 1, 2011; published online September 13, 2013. Assoc. Editor: Matthew Montgomery.

J. Turbomach 135(6), 061001 (Sep 13, 2013) (20 pages) Paper No: TURBO-05-1153; doi: 10.1115/1.4004445 History: Received December 16, 2005; Revised January 01, 2011

In this paper, a reduced order model for the vibrations of bladed disk assemblies was achieved. The system studied was a 3D annulus of shroudless, “custom-tailored,” mistuned blades attached to a flexible disk. Specifically, the annulus was modeled as a spectral-based “meshless” continuum structure utilizing only nodal data to describe the arbitrary volume in which the system's dynamical energy was minimized. An extended Ritz variational procedure was used to minimize this energy, subjected to constraints imposed by an assumed 3D displacement field of mathematically complete, orthonormal “blade-disk” polynomials multiplied by generalized coefficients. The coefficients were determined by constraining the polynomial series to satisfy the extended Ritz stationary equations and essential boundary conditions of the bladed disk. From this, the governing equations of motion were generated into their usual dynamical forms to calculate upper-bounds on the actual free and forced responses of bladed disks. No conventional finite elements and element connectivity or component substructuring data were needed. This paper, Part I, outlines the theoretical foundation of the present model, and through extensive Monte Carlo simulations, establishes the analytical basis, predictive accuracy, and re-analysis efficiency of the present technology in the prediction of 3D maximum response amplitude of mistuned bladed disks having increasing numbers of nodal diameter excitations. Further applications validating the 3D approach against conventional finite element procedures of free and forced response prediction of a mistuned Integrally-Bladed Rotor used in practice is presented in a companion paper, Part II (Fang, McGee, and El-Aini, 2013, “A Reduced-Order Meshless Energy Model for the Vibrations of Mistuned Bladed Disks—Part II: Finite Element Benchmark Comparisons, ASME J. Turbomach., to be published.

FIGURES IN THIS ARTICLE
<>
Copyright © 2013 by ASME
Topics: Disks , Blades , Polynomials
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Fig. 1

Structural model of a mistuned bladed disk

Grahic Jump Location
Fig. 2

Gauss quadrature points for numerical volumetric integration

Grahic Jump Location
Fig. 3

Idealized 20-bladed disk

Grahic Jump Location
Fig. 4

Modern aeroengine featuring fan integrally bladed rotors (IBRs) (Pratt and Whitney, private communication of third author, Y. El-Aini)

Grahic Jump Location
Fig. 5

Integrally bladed rotor (IBR)

Grahic Jump Location
Fig. 6

Representative Campbell diagram [83] of a typical IBR in modern aeroengines showing definitions of flutter frequencies, integral order forced response (F.R.) resonant frequencies, separated flow vibration (SFV) frequencies, and nonsynchronous vibration (NSV) (or nonintegral order response) frequencies (see Refs. [4,5,8-5,8].)

Grahic Jump Location
Fig. 7

Campbell diagram [83] of a 3D ROME idealized 20-bladed disk (shown in Fig. 3), tuned resonant speeds (left), mistuned at σ = 5% resonant speeds (right) (Ω = 10,700 rpm)

Grahic Jump Location
Fig. 8

Campbell diagram [83] of a I-DEAS FEM idealized 20-bladed disk (shown in Fig. 3), tuned resonant speeds (left), mistuned at σ = 5% resonant speeds (right) (Ω = 10,700 rpm)

Grahic Jump Location
Fig. 9

Campbell diagram [83] of a 3D ROME model of an industry IBR (shown in Fig. 5), tuned resonant speeds (left), mistuned at σ = 5% resonant speeds (right) (Ω = 10,700 rpm)

Grahic Jump Location
Fig. 10

Statistical results and parameters

Grahic Jump Location
Fig. 11

Maximum response amplitude magnification with increasing IBR solidity (see Kenyon and Griffin [35]; Whitehead [37])

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In