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Research Papers

An Efficient Approach for the Frequency Analysis of Nonaxisymmetric Rotating Structures: Application to a Coupled Bladed Birotor System

[+] Author and Article Information
Cécile Dumartineix

École Centrale de Lyon,
Laboratoire de Tribologie et Dynamique des
Systèmes,
UMR-CNRS 5513,
Écully cedex 69134, France;
Safran Aircraft Engines,
Rond Point René Ravaud—Réau,
Moissy-Cramayel 77550, France
e-mail: cecile.dumartineix@doctorant.ec-lyon.fr

Benjamin Chouvion, Fabrice Thouverez

École Centrale de Lyon,
Laboratoire de Tribologie et Dynamique des
Systèmes,
UMR-CNRS 5513,
Écully cedex 69134, France

Marie-Océane Parent

Safran Aircraft Engines,
Rond Point René Ravaud—Réau,
Moissy-Cramayel 77550, France

1Corresponding author.

Manuscript received June 26, 2018; final manuscript received July 4, 2018; published online December 10, 2018. Editor: Jerzy T. Sawicki.

J. Eng. Gas Turbines Power 141(4), 041033 (Dec 10, 2018) (8 pages) Paper No: GTP-18-1371; doi: 10.1115/1.4040865 History: Received June 26, 2018; Revised July 04, 2018

The improvement of efficiency in the design of turbomachines requires a reliable prediction of the vibrating behavior of the whole structure. The simulation of blades vibrations is decisive and this is usually based on elaborated finite element model restricted to the bladed-disk. However, the blades dynamic behavior can be strongly affected by interactions with other parts of the engine. Global dynamic studies that consider these other parts are required but usually come with a high numerical cost. In the case of a birotor architecture, two coaxial rotors with different rotating speeds can be coupled with a bearing system. The mechanical coupling between the shafts generates energy exchange that alters the dynamic behavior of the blades. The equations of motion of the whole structure that take into account the coupling contain periodic time-dependent coefficients due to the difference of rotational speed between both rotors. Equations of this kind, with variable coefficients, are typically difficult to solve. This study presents a preprocessing method to guarantee the elimination of time-dependent coefficients in the birotor equations of motion. This method is tested with a simplified finite element model of two bladed-disks coupled with linear stiffnesses. We obtain accurate results when comparing frequency analysis of preprocessed equations with time-integration resolution of the initial set of equations. The developed methodology also offers a substantial time saving.

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Figures

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Fig. 1

Sectional view of a two-spool turbofan. Low pressure rotor () and high pressure rotor (), stator ().

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Fig. 2

Studied birotor system: (a) simplified model of the bladed birotor system and (b) bearing model

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Fig. 3

Fixing area of the bearing (circular line) on one bladed-disk for our studied case

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Fig. 4

Finite element model of one sector of each bladed-disk of the studied birotor system

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Fig. 5

Modal deformation of the first 2-diameter mode of the rotor R1

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Fig. 6

Time radial displacements of a node of each rotor in the bearing area. Time integration of the initial equation of motion (), frequency resolution of the preprocessed equation (): (a) radial displacements of rotor R1 over time. Zoom on the stationary state () and (b) radial displacements of rotor R2 over time.

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Fig. 7

Maximum radial displacements of a node of each rotor in the bearing area computed for a range of rotation speeds with a corotative configuration: (a) radial displacements of rotor R1 (left) and rotor R2 (right) at the bearing and (b) zoom on the crossing of resonance frequencies of both rotors

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