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TECHNICAL PAPERS: Gas Turbines: Structures and Dynamics

# Dynamics of Multistage Bladed Disks Systems

[+] Author and Article Information
Denis Laxalde

École Centrale de Lyon, Laboratoire de Tribologie et Dynamique des Systèmes, 36 Avenue Guy de Collongue, 69134 Ecully Cedex, France; Snecma-Safran Group, 77550 Moissy-Cramayel, Francedenis.laxalde@ec.lyon.fr

Jean-Pierre Lombard

Snecma-Safran Group, 77550 Moissy-Cramayel, France

Fabrice Thouverez

École Centrale de Lyon, Laboratoire de Tribologie et Dynamique des Systèmes, 36 Avenue Guy de Collongue, 69134 Ecully Cedex, France

J. Eng. Gas Turbines Power 129(4), 1058-1064 (Apr 27, 2007) (7 pages) doi:10.1115/1.2747641 History: Received April 26, 2007; Revised April 27, 2007

## Abstract

This paper presents a new and original method for dynamical analysis of multistage cyclic structures such as turbomachinery compressors or turbines. Each stage is modeled cyclically by its elementary sector and the interstage coupling is achieved through a cyclic recombination of the interface degrees of freedom. This method is quite simple to set up; it allows us to handle the finite element models of each stage’s sector directly and, as in classical cyclic symmetry analysis, to study the nodal diameter problems separately. The method is first validated on a simple case study which shows good agreements with a complete 360 deg reference calculation. An industrial example involving two HP compressor stages is then presented. Then the forced response application is presented in which synchronous engine order type excitations are considered.

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## Figures

Figure 1

“Nodal diameter equivalence” rule; (a) N1=12 and N2=20, (b) N1=13 and N2=20

Figure 2

Finite element model of two cyclic structures—N1=24, N2=45

Figure 3

Eigenfrequency correlation (◻)/multistage cyclic symmetry (+)

Figure 4

One nodal diameter mode at 4824Hz

Figure 5

Five nodal diameter mode at 6147Hz

Figure 6

FRF correlation; (---) reference, (—) multistage cyclic symmetry; (a) Blade 1, (b) Blade 2

Figure 7

Finite element models of two HP compressor blisks; (a) 1st stage – 36 sectors, (b) 2nd stage – 60 sectors

Figure 8

Influence of interstage coupling, eigenfrequency/nodal diameter (ND) map (from 0 to 10 ND), stage 1 alone (×), stage 2 alone (+), coupled stages (◻)

Figure 9

Examples of modal deformed shapes; (a) 5th mode at 0 ND, 68 UF, (b) 7th mode at 9 ND, 124 UF, (c) 5th mode at 3 ND, 76 UF

Figure 10

Frequency responses with and without interstage coupling; (a) Blisk 1, (b) Blisk 2

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