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Research Papers: Gas Turbines: Structures and Dynamics

Nonlinear Numerical Prediction of Gas Foil Bearing Stability and Unbalanced Response

[+] Author and Article Information
Sébastien Le Lez, Mihaï Arghir, Jean Frêne

Laboratoire de Mécanique des Solides,  Université de Poitiers, Téléport 2-SP2MI, Boulevard Marie et Pierre Curie, BP 30179, 86962 Futuroscope Chasseneuil Cedex, France

J. Eng. Gas Turbines Power 131(1), 012503 (Oct 09, 2008) (12 pages) doi:10.1115/1.2967481 History: Received March 31, 2008; Revised April 02, 2008; Published October 09, 2008

One of the main interests of gas foil bearings lies in their superior rotordynamic characteristics compared with conventional bearings. A numerical investigation on the stability limit and on the unbalanced response of foil bearings is presented in this paper. The main difficulty in modeling the dynamic behavior of such bearings comes from the dry friction that occurs within the foil structure. Indeed, dry friction is highly nonlinear and is strongly influenced by the dynamic amplitude of the pressure field. To deal with these nonlinearities, a structural dynamic model has been developed in a previous work. This model considers the entire corrugated foil and the interactions between the bumps by describing the foil bearing structure as a multiple degrees of freedom system. It allows the determination of the dynamic friction forces at the top and at the bottom of the bumps by simple integration of ordinary differential equations. The dynamic displacements of the entire corrugated sheet are then easily obtained at each time step. The coupling between this structural model and a gas bearing prediction code is presented in this paper and allows performing full nonlinear analyses of a complete foil bearing. The bearing stability is the first investigated problem. The results show that the structural deflection enhances the stability of compliant surface bearings compared with rigid ones. Moreover, when friction is introduced, a new level of stability is reached, revealing the importance of this dissipation mechanism. The second investigated problem is the unbalanced response of foil bearings. The shaft trajectories depict a nonlinear jump in the response of both rigid and foil bearings when the value of the unbalance increases. Again, it is evidenced that the foil bearing can support higher mass unbalance before this undesirable step occurs.

Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 4

Boundary conditions for calculating the elementary stiffnesses

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Figure 5

Stiffness matrices

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Figure 6

Minimum film thickness at 30,000 rpm

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Figure 7

Minimum film thickness at 45,000 rpm

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Figure 8

Static equilibrium locus curve—influence of the structural model

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Figure 9

Foil bearing stability, single strip without friction, μf=0

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Figure 10

Foil bearing stability, single strip with friction, μf=0.1

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Figure 11

Influence of the friction coefficient on the foil bearing stability

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Figure 12

Influence of the spot weld location on the foil bearing stability, single strip

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Figure 13

Influence of the friction coefficient on the critical mass, 30,000 rpm, static load W0=Mg

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Figure 14

Influence of the friction coefficient on the threshold speed of instability, M=5 kg, W0=Mg

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Figure 15

Foil bearing nonlinear unbalanced response (single strip)

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Figure 16

Foil bearing nonlinear unbalanced response (single strip), nonlinear jump phenomenon

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Figure 17

Foil bearing nonlinear unbalanced response (five strips)

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Figure 18

Poincaré maps obtained for unbalanced values of (a) eb=0.3C0 and (b) eb=0.35C0

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Figure 19

Foil bearing nonlinear unbalanced response (five strips), FFT analysis

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Figure 20

Unbalanced response for both foil bearings and for the rigid bearing

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Figure 21

Foil bearing nonlinear unbalanced response (five strips, Ω=18,000 rpm)

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Figure 22

Shaft trajectory for an unbalanced eccentricity eb=0.125C0

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Figure 23

FFT analysis of the shaft motion, eb=0.125C0

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Figure 24

Unbalanced response for the five strip foil bearing and for the rigid bearing (Ω=18,000 rpm)

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Figure 1

Coordinate system of the foil bearing

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