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Research Papers: Hydrodynamic Lubrication

Analytical Model of Bump-Type Foil Bearings Using a Link-Spring Structure and a Finite-Element Shell Model

[+] Author and Article Information
Kai Feng

Department of Mechanical Engineering, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japankfeng@fiv.t.u-tokyo.ac.jp

Shigehiko Kaneko

Department of Mechanical Engineering, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan

J. Tribol 132(2), 021706 (Apr 26, 2010) (11 pages) doi:10.1115/1.4001169 History: Received March 17, 2009; Revised January 05, 2010; Published April 26, 2010; Online April 26, 2010

A complete analytical model of bump-type foil bearings taking into consideration the effects of four factors, i.e., the elasticity of bump foil, the interaction forces between bumps, the friction forces at the contact surfaces, and the local deflection of top foil, is presented in this investigation. Each bump is simplified to two rigid links and a horizontally spaced spring, the stiffness of which is determined from Castigliano’s theorem. The interaction forces and the friction forces are coupled with the flexibility of bumps through the horizontal elementary spring. The local deflection of the top foil is described using a finite-element shell model and added to the film thickness to predict the air pressure with Reynolds’ equation. The bump deflections of a strip with ten bumps calculated using the presented model under different load distributions are consistent with the published results. Moreover, the predicted bearing load and film thickness obtained from a foil bearing with a bump circumferential extend of 360 deg also agree very well with the experimental data, especially for predictions with a proper selection of radial clearance (preload of foil structure) and friction coefficients. In addition, the radial clearance and friction force variations in the foil bearing are noted to significantly change the performance of the foil bearing. The predictions demonstrate that the radial clearance of the foil bearing has an optimum value for the maximum load capacity.

Copyright © 2010 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Schematic view of bump-type foil bearings

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Figure 3

Simplified equivalent model of bump-type foil bearings

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Figure 4

Relationship between vertical and horizontal deflections in link-spring structure

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Figure 5

Force distribution analysis at the ith segment

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Figure 6

Force analysis at the free end

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Figure 7

Link-spring model for pinned-end bumps

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Figure 8

Equivalent vertical stiffness of bumps as a function of bump deflection

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Figure 9

Assembly of global stiffness matrix with bump stiffness

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Figure 10

Comparison of bump deflections under different load distributions with Ref. 11

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Figure 12

Flowchart of calculation program

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Figure 15

Minimum film thickness with respect to bearing load; 45 krpm, μ=0.1, and η=0.1

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Figure 17

Minimum film thickness versus bearing load with different radial clearances (preloads of foil structure). Rotational speed: 45 krpm, μ=0.1, and η=0.1.

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Figure 18

Minimum film thickness versus bearing load with different friction coefficients. Rotational speed: 45 krpm and C=Cm.

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Figure 19

Minimum film thickness versus static load. Predictions with C=0.63Cm and μ=0.15, η=0.1 and experimental data (21); 45 krpm

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Figure 20

Bearing-load capacity versus radial clearance, μ=0.1, and η=0.1

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Figure 21

Equivalent stiffness of horizontal spring

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Figure 2

Link-spring model of bump-type foil bearings

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Figure 11

Shaft displacement versus static load of foil structure

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Figure 13

Predicted results with static load of 188.5 N and rotational speed of 45 krpm, μ=0.1, and η=0.1. (a) Dimensionless pressure distribution and (b) top foil deflection.

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Figure 14

Comparison of film thickness at bearing midplane from calculation and experiment (22); 134.1 N, 30 krpm, μ=0.1, and η=0.1

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Figure 16

Radial clearance (preload of foil structure) in foil bearings

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Figure 22

Equivalent stiffness of bevel spring

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