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Research Papers: Gas Turbines: Structures and Dynamics

Reduction of Multistage Disk Models: Application to an Industrial Rotor

[+] Author and Article Information
Arnaud Sternchüss1

Laboratoire MSSMAT, École Centrale Paris, Grande Voie des Vignes, 92295 Châtenay-Malabry Cedex, Francearnaud.sternchuss@ecp.fr

Etienne Balmès

Laboratoire MSSMAT, École Centrale Paris, Grande Voie des Vignes, 92295 Châtenay-Malabry Cedex, France

Pierrick Jean, Jean-Pierre Lombard

 Snecma (Safran Group), Site de Villaroche, Rond-point René Ravaud, 77550 Moissy-Cramayel Cedex, France

1

Corresponding author.

J. Eng. Gas Turbines Power 131(1), 012502 (Oct 09, 2008) (14 pages) doi:10.1115/1.2967478 History: Received March 31, 2008; Revised April 11, 2008; Published October 09, 2008

The present study deals with the reduction of models of multistage bladed disk assemblies. The proposed method relies on the substructuring of the rotor into sectors. The bladed disks are coupled by intermediate rings, which remove the problem of incompatible meshes. The sectors are represented by superelements whose kinematic subspaces are spanned by a set of cyclic modeshapes and a set of normal modes when their left and right interfaces are fixed. The first step is to compute the cyclic modeshapes that are defined on the full rotor by enforcing the uncoupling of the spatial Fourier harmonics. This leads to a family of subproblems parametrized by the harmonic coefficient, similar to the classical approach used to deal with tuned bladed disks. The subsequent reduction process leads to compact reduced models whose accuracy has been extensively tested on simple but realistic academic models. The proposed methodology was then applied to an industrial rotor to conduct an analysis at a wider scale. This case was also the occasion to point out the fact that the assembly of individual disk models into a rotor model is really straightforward and provides an efficient tool to observe and predict coupled phenomena.

Copyright © 2009 by American Society of Mechanical Engineers
Topics: Rotors , Disks , Manufacturing
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Figures

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Figure 2

Spatial spectrum of the 74 first flexible modes of the sample rotor

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Figure 3

(a) Monoharmonic coupled mode at f=4.25 and (b) multiharmonic localized mode at f=2.99 and their harmonic content

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Figure 4

Near-pair of monoharmonic solutions with δ=2 at f=4.25

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Figure 5

Normalized frequency versus nodal diameter diagram for the monoharmonic eigensolutions of the rotor (○) and for the eigenmodes of disks D1(+) and D2(×) in free-free condition

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Figure 6

Sector model: sector superelement with an intersector slice and the trace of the mesh of the ring

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Figure 7

Reduced rotor model: sector superelements connected with intersector slices and the ring

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Figure 14

Coupled cyclic solution with δ=1 at f=15.53: (a) modeshape and (b) density of strain energy. Blade shapes are 2S1, 2F, and 1T.

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Figure 18

Generalized modes 7 to 300 (f∊[1,7.52]): (a) Spatial harmonic content; (b) participation factor in strain energy for disks D1 (down), D2 (middle), and D3 (up)

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Figure 19

Generalized odes 301–600 (f∊[7.52,13.74]): (a) Spatial harmonic content; (b) participation factor in strain energy for disks D1 (down), D2 (middle), and D3 (up)

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Figure 20

Generalized modes 601–900 (f∊[13.76,19.57]): (a) Spatial harmonic content; (b) participation factor in strain energy for disks D1 (down), D2 (middle), and D3 (up)

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Figure 21

Restored mode at f=10.23 localized to disk D2: (a) modeshape and (b) spatial harmonic content for disks D1 (up), D2 (middle), and D3 (down)

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Figure 22

Restored mode at f=15.89 with strong coupling: (a) modeshape and (b) spatial harmonic content for disks D1 (up), D2 (middle), and D3 (down)

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Figure 9

(a) Targeted frequency ranges, (b) frequency relative error, and (c) modeshape correlation between reference and generalized modes

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Figure 10

Industrial three stage high pressure (HP) compressor: (a) front and (b) rear

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Figure 11

Details of the rings (a) between D1 and D2 and (b) between D2 and D3

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Figure 12

Sector models and rings used in the computation of cyclic modeshapes: (a) front and (b) rear

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Figure 13

Normalized frequencies of the cyclic solutions for the rotor (○) and the modes of disk D1(+), disk D2(×), and disk D3(∗) in free-fix, fix-fix, and fix-free condition. Horizontal lines refer to blade frequencies of each stage.

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Figure 15

Cyclic solution localized to disk D1 with δ=4 at f=8.63. Blade shape is 2F.

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Figure 16

Cyclic solution localized to disk D2 with δ=2 at f=7.47. Blade shape is 1T.

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Figure 17

Cyclic solution localized to disk D3 with δ=0 at f=5.35. Blade shape is 1F.

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Figure 23

Partial postprocessing of the generalized mode at f=15.89 on disk D1: (a) normalized density of strain energy and (b) normalized distribution of Von Mises stress

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Figure 8

Reduced stiffness matrix [KM] (a) global shape: upper left blocks belong to disk D1, lower right blocks belong to disk D2, off-diagonal blocks belong to ring R, and (b) actual matrix

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