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Research Papers: Hydrodynamic Lubrication

A Contribution to the Thermal Modeling of Bump Type Air Foil Bearings: Analysis of the Thermal Resistance of Bump Foils

[+] Author and Article Information
Andreas Lehn

Department of Mechanical Engineering,
Institute of Applied Dynamics,
Technical University Darmstadt,
Otto-Berndt-Strasse 2,
Darmstadt 64287, Germany
e-mail: lehn@ad.tu-darmstadt.de

Marcel Mahner, Bernhard Schweizer

Department of Mechanical Engineering,
Institute of Applied Dynamics,
Technical University Darmstadt,
Otto-Berndt-Strasse 2,
Darmstadt 64287, Germany

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received August 19, 2016; final manuscript received April 11, 2017; published online July 10, 2017. Assoc. Editor: Daejong Kim.

J. Tribol 139(6), 061702 (Jul 10, 2017) (10 pages) Paper No: TRIB-16-1272; doi: 10.1115/1.4036631 History: Received August 19, 2016; Revised April 11, 2017

A detailed analysis of the effective thermal resistance for the bump foil of air foil bearings (AFBs) is performed. The presented model puts emphasis on the thermal contact resistances between the bump foil and the top foil as well as between the bump foil and the base plate. It is demonstrated that most of the dissipated heat in the lubricating air film of an air foil bearing is not conducted by microcontacts in the contact regions. Instead, the air gaps close to the contact area are found to be thin enough in order to effectively conduct the heat from the top foil into the bump foil. On the basis of these findings, an analytical formula is developed for the effective thermal resistance of a half bump arc. The formula accounts for the geometry of the bump foil as well as for the surface roughness of the top foil, the bump foil, and the base plate. The predictions of the presented model are shown to be in good agreement with measurements from the literature. In particular, the model predicts the effective thermal resistance to be almost independent of the applied pressure. This is a major characteristic property that has been found by measurements but could not be reproduced by previously published models. The presented formula contributes to an accurate thermohydrodynamic (THD) modeling of AFBs.

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Figures

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Fig. 1

Heat flow in the foil sandwich of an AFB

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Fig. 2

Illustration of a general thermal contact and the schematic temperature distribution within two contacting bodies

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Fig. 3

Loading condition for the foil sandwich of an AFB

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Fig. 4

Calculation results for the contact between top and bump foils based on the configuration shown in Fig. 3 (for a load of p = 105 Pa). Illustration of the used finite element mesh, the calculated contact width 2b, and the calculated contact pressure pcont between top and bump foils.

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Fig. 5

Half contact width b between top and bump foils as a function of the pressure p (gage pressure) on the top foil

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Fig. 6

Model for the effective thermal resistance of the half bump arc

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Fig. 7

(a) Illustration of the air gap within the mechanical contact region between top and bump foils and the air gaps close to the mechanical contact region (an exploded view of top and bump foils is shown). (b) Size of the effective air gap lTB(x) in the interface between top and bump foils.

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Fig. 8

(a) Thermal resistance of the air gap in the interface between the top foil and the half bump arc as a function of the width of the interface air gap xTB. (b) Relative difference between the thermal resistance RTB,air(xTB) and the thermal resistance RTB,air(lB0).

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Fig. 9

Relative difference between the undeformed gap size lTB(x) and the deformed gap size lTB,def(x) for the configuration analyzed in the contact analysis of Sec. 2.2 (for a load of p = 105 Pa)

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Fig. 10

(a) Illustration of the contact situation between the bump foil and the base plate. (b) Domain and boundary conditions for the calculation of the temperature distribution T(x, z) within a half of the bridge. (c) Thermal resistance RBb,air between the bump foil and the base plate for two different surface roughnesses Ra = Ra,bump = Ra,base of the bump foil and the base plate.

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Fig. 11

Minimal and maximal effective thermal resistance of a half bump arc as a function of the surface roughness of top foil, bump foil, and base plate

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Fig. 12

Comparison of different models for the effective thermal resistance of a half bump arc to the measurement by Lee and Kim [19]

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