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TECHNICAL PAPERS

# Parametric Studies on Static and Dynamic Performance of Air Foil Bearings with Different Top Foil Geometries and Bump Stiffness Distributions

[+] Author and Article Information
Daejong Kim

Department of Mechanical Engineering, Texas A&M University, 3123 TAMU, College Station, TX 77843djkim@tamu.edu

J. Tribol 129(2), 354-364 (Nov 15, 2006) (11 pages) doi:10.1115/1.2540065 History: Received May 18, 2006; Revised November 15, 2006

## Abstract

Experimental and analytical studies on air foil bearings have been performed extensively over the past decades, and significant improvement in load capacity and rotor dynamics stability have been reported. Often, advanced air foil bearings are believed to have complicated bump foil structure to provide unique underlying support mechanism, which in turn make the bearing very stable and have high load capacity. However, all the analytical studies on air foil bearings so far assume a circular profile of top foil with uniform bump stiffness distribution because detailed information on bump stiffness distribution and overall bearing shape is not known to the public. This paper investigates load capacities and rotordynamic performances of two different types of air foil bearings, e.g., circular cylindrical bearings with single continuous top foil and noncircular preloaded bearings with three top foil pads. Within the two subcategories, stiffness variations along axial and circumferential directions were given to have a total of four types of air foil bearings with different overall bearing shapes and stiffness distributions. Overall static and dynamic performance of the four different types of air foil bearings are presented and compared via calculations of load capacities and dynamic force coefficients, modal stability analyses, and time domain orbit simulations. The major difference of load capacities comes from the overall bearing shape (circular continuous foil or preloaded three pad) rather than spatial variation of bump stiffness within the bump foils. Preloaded three-pad bearings have significantly reduced load capacity compared to the circular bearings because of small pad arc length. Rotordynamic performance is also much more sensitive to the overall bearing shape than spatial variation of bump stiffness and damping within the bump foils. The linear stability analyses predict modal natural frequencies very close to those from the orbit simulations. However, onset speeds of instability from these two approaches are quite different, manifesting the limitation of the linear stability analyses. The orbit simulations show the three-pad bearings have higher onset speeds of instability than circular bearing ($47,000rpm$ versus $24,000rpm$).

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Copyright © 2007 by American Society of Mechanical Engineers
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## Figures

Figure 1

Schematic description of Case 1 and Case 2 bearings

Figure 2

Schematic description of Case 3 and Case 4 bearings

Figure 3

Stiffness distribution for Case 4; stiffness of each bump is rescaled to computational grid points

Figure 4

Normalized pressure and bump deflection for Case 1 bearing under 248N at 40,000rpm

Figure 5

Load capacities of investigated bearings based on minimum air film thickness of 4μm: (a) stiffness coefficients; (b) damping coefficients

Figure 6

Synchronous stiffness and damping coefficients of Case 1 and 2 bearings; 30N, η=0.25: (a) stiffness coefficients; (b) damping coefficients

Figure 7

Frequency dependent stiffness and damping coefficients of Case 1; 40,000rpm, 30N, η=0.25: (a) stiffness coefficients; (b) damping coefficients

Figure 8

Frequency dependent stiffness and damping coefficients of Case 3; 40,000rpm, 30N, η=0.25: (a) direct stiffness; (b) cross-coupled stiffness; (c) direct damping; and (d) cross-coupled damping

Figure 9

Synchronous stiffness and damping coefficients of Case 1 and 3 bearings; 30N, η=0.25: (a) direct stiffness coefficients, kXX; and (b) direct damping coefficients, dXX

Figure 10

Direct stiffness and damping coefficients for Case 3 and Case 4 bearings; 30N, η=0.25: (a) 20,000rpm; (b) 30,000rpm; (c) 40,000rpm; and (d) 50,000rpm

Figure 11

Impedance contour of Case 1 bearings; η=0.25: (a) 20,000rpm; (b) 30,000rpm; (c) 40,000rpm; and (d) 50,000rpm

Figure 12

Impedance contour of Case 3 bearings; η=0.25: (a) 20,000rpm; (b) 23,000rpm; (c) 24,000rpm; and (d) 26,000rpm

Figure 13

Orbits of Case I bearings; imbalance 10gmm, rotor mass 3.061kg, η=0.25: (a) 40,000rpm; (b) 46,000rpm; (c) 47,000; and (d) 50,000rpm

Figure 14

Orbits of Case 3 bearings; imbalance 10gmm, rotor mass 3.061kg, η=0.25

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