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Research Papers: Gas Turbines: Combustion, Fuels, and Emissions

Numerical Analysis of the Impact of Manufacturing Errors on the Structural Stiffness of Foil Bearings

[+] Author and Article Information
Aurelian Fatu

PPRIME Institute,
UPR CNRS 3346,
Université de Poitiers,
ENSMA ISAE,
Chasseneuil Futuroscope 86962, France
e-mail: aurelian.fatu@ univ-poitiers.fr

Mihai Arghir

PPRIME Institute,
UPR CNRS 3346,
Université de Poitiers,
ENSMA ISAE,
Chasseneuil Futuroscope 86962, France
e-mail: mihai.arghir@univ-poitiers.fr

Contributed by the Combustion and Fuels Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received July 20, 2017; final manuscript received July 31, 2017; published online October 31, 2017. Editor: David Wisler.

J. Eng. Gas Turbines Power 140(4), 041506 (Oct 31, 2017) (9 pages) Paper No: GTP-17-1380; doi: 10.1115/1.4038042 History: Received July 20, 2017; Revised July 31, 2017

The dynamic characteristics of foil bearings operating at high rotation speeds depend very much on the mechanical characteristics of the foil structure. For this reason, the stiffness and damping of the structure of foil bearings are problems that are the focus of many analyses. The mechanical characteristics of the foil structure (top and bump foil) are analyzed either by using a simple approach obtained for an isolated bump modeled as a beam or with more elaborate ones taking into account the three-dimensional nature of the bumps and their mutual interactions. These two kinds of models give different foil structure stiffness, with lower values for the simplified model. However, the published experimental results of the foil bearing structure tend to validate the simplified model. The present paper explains the differences between the simplified and the elaborate models by taking into account the manufacturing errors of the foil structure. A three-dimensional model based on the nonlinear theory of elasticity is developed. The model offers a unique insight into the way the bearing structure deforms when the rotor is incrementally pushed into the foil structure. Three realistic manufacturing errors, bump height, bump length, and radius of the bump foil, are analyzed. Bump height and length vary following a normal distribution with a given standard deviation while the radius of the bump foil is given a waviness form with an imposed peak-to-peak amplitude. Three to five cases were calculated for each kind of error. Results show that only the manufacturing errors of the bump height affect the stiffness of the foil structure by diminishing its values. Height errors of 20 μm standard deviation (4% of the average bump height and 60% of the radial clearance) may induce a 40–50% reduction of the stiffness of the foil structure, i.e., in the range of the predictions of the simplified model.

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Figures

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Fig. 1

Cut view of a generation 1 foil bearing

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Fig. 2

Geometric characteristics of the bump: (a) schematic representation and (b) scaled representation

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Fig. 3

The free–free ends simplified bump model

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Fig. 4

The simplified bump model with zero-rotation b.c. at foil segments ends

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Fig. 5

Static load versus rotor displacement

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Fig. 6

Radial displacement of the bump foil

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Fig. 7

Angular displacement of the bump foil

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Fig. 8

Details of the displacements of the bump foil for rotor pushing opposite to the welding

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Fig. 9

Static load versus rotor displacements opposite to the welding (reference case)

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Fig. 10

Structural stiffness versus rotor displacement for the reference case

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Fig. 11

Description of bump height errors

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Fig. 12

Static load (a) and structural stiffness (b) versus rotor displacement for 10 μm standard deviation of bump height

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Fig. 13

Static load (a) and structural stiffness (b) versus rotor displacement for 20 μm standard deviation of bump height

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Fig. 14

Description of bump length errors

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Fig. 15

Static load (a) and structural stiffness (b) versus rotor displacement for 40 μm standard deviation of bump length

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Fig. 16

Description of bump foil outer radius geometry errors

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Fig. 17

Static load (a) and structural stiffness (b) versus rotor displacement for a maximum error of 25.4 μm of bump foil radius

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Fig. 18

Influence of combined bump height and bump foil outer radius errors: static load (a) and structural stiffness (b) versus rotor displacement

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