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Research Papers

A Reduced-Order Meshless Energy Model for the Vibrations of Mistuned Bladed Disks—Part II: Finite Element Benchmark Comparisons

[+] Author and Article Information
C. Fang

Postdoctoral Research Associate

O. G. McGee, III

Professor
Howard University,
Washington, DC 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), 061002 (Sep 13, 2013) (26 pages) Paper No: TURBO-05-1154; doi: 10.1115/1.4007256 History: Received December 16, 2005; Revised January 01, 2011

This paper draws upon the theoretical basis and applicability of the three-dimensional (3-D) reduced-order spectral-based “meshless” energy technology presented in a companion paper (McGee et al., 2013, “A Reduced-Order Meshless Energy Model for the Vibrations of Mistuned Bladed Disks—Part I: Theoretical Basis,” ASME J. Turbomach., to be published) to predict free and forced responses of bladed disks comprised of randomly mistuned blades integrally attached to a flexible disk. The 3-D reduced-order spectral-based model employed is an alternative choice in the computational modeling landscape of bladed disks, such as conventionally-used finite element methods and component mode synthesis techniques, and even emerging element-free Hamiltonian–Galerkin, Petrov–Galerkin, boundary integral, and kernel-particle methods. This is because continuum-based modeling of a full disk annulus of mistuned blades is, at present, a steep task using these latter approaches for modal-type mistuning and/or rogue blade failure analysis. Hence, a considerably simplified and idealized bladed disk of 20 randomly mistuned blades mounted to a flexible disk was created and modeled not only to analyze its free and forced 3-D responses, but also to compare the predictive capability of the present reduced-order spectral-based “meshless” technology to general-purpose finite element procedures widely-used in industry practice. To benchmark future development of reduced-order technologies of turbomachinery mechanics analysts may use the present 3-D findings of the idealized 20-bladed disk as a new standard test model. Application of the 3-D reduced-order spectral-based “meshless” technology to an industry integrally-bladed rotor, having all of its blades modally mistuned, is also offered, where reasonably sufficient upper-bounds on the exact free and forced 3-D responses are predicted. These predictions expound new solutions of 3-D vibration effects of modal mistuning strength and pattern, interblade mechanical coupling, and localized modes on the free and forced response amplitudes.

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Figures

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Fig. 1

Idealized 20-bladed disk

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Fig. 4

3-D ROME and I-DEAS/ANSYS FEM cyclic frequencies of an isolated blade

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Fig. 5

3-D ROME and I-DEAS/ANSYS FEM cyclic frequencies of an isolated disk

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Fig. 6

3-D ROME and I-DEAS/ANSYS FEM predictions of the cyclic frequencies (Hz) versus disk nodal diameters of the tuned rotating idealized 20-bladed disk (Ω = 10,700 rpm)

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Fig. 7

3-D ROME and I-DEAS/ANSYS FEM predictions of the cyclic frequencies (Hz) of the modally mistuned rotating idealized 20-bladed disk (Ω = 10,700 rpm)

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Fig. 8

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

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Fig. 9

Integrally-bladed rotor (IBR)

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Fig. 10

Isolated IBR blade (cyclic symmetry tuned IBR model)

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Fig. 11

Comparison of the 3-D ROME and I-DEAS/ANSYS FEM cyclic frequencies of a stationary isolated IBR blade (cyclic symmetry IBR analysis)

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Fig. 12

Comparison of the 3-D ROME and I-DEAS/ANSYS FEM cyclic frequencies of a rotating isolated IBR blade (Ω = 10,700 rpm) (cyclic symmetry IBR analysis)

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Fig. 13

The 3-D ROME cyclic frequencies versus disk nodal diameters of a tuned IBR (Ω = 10,700 rpm)

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Fig. 14

The 3-D ROME cyclic frequencies of a modally mistuned IBR (Ω = 10,700 rpm)

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Fig. 15

Maximum response of the tuned and modally mistuned rotating industry IBR (Ω = 10,700 rpm) with increasing interblade mechanical coupling 5% ≤R≤ 30% (at the 0th engine order (i.e., physically corresponding to a constant unit force excitation at the blade tips) and moderate mistuning strength σ = 5%)

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Fig. 16

Maximum response of the rotating industry IBR (Ω = 10,700 rpm) with increasing modal mistuning strength 0 ≤σ≤ 10% (at the 0th engine order (i.e., physically corresponding to a constant unit force excitation at the blade tips) and weak mechanical coupling R = 17%)

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