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Research Papers: Hydrodynamic Lubrication

# Characterization of a Foil Bearing Structure at Increasing Temperatures: Static Load and Dynamic Force Performance

[+] Author and Article Information
Tae Ho Kim

Energy Mechanics Research Center, Korea Institute of Science and Technology, 39-1 Hawolgok-dong, Songbuk-gu, Seoul 136-791, Koreathk@kist.re.kr

Anthony W. Breedlove

Schlumberger Drilling and Measurements, Av Prefeito Aristeu Ferreira da Silva, 702B Barrio Novo Cavaleiros, Macae 27930-310, Brazil

Luis San Andrés

Turbomachinery Laboratory, Texas A&M University, College Station, TX 77843-3123lsanandres@tamu.edu

Iordanoff (13) provides stiffness formulas for a single bump, with either free ends or one end free and the other fixed. The model accounts for dry-friction effects between the bump and the bearing surface. See later Eq. 1 and Fig. 5.

See Ref. 21 for details on sensor calibration at increasing shaft temperatures.

Breedlove (21) reported the coefficients of thermal expansions for the hollow shaft $(CTES=12.2 μm/m °C)$ and the floating bearing cartridge $(CTEB=17.3 μm/m °C)$. As temperature increases, the shaft outer diameter grows and the floating bearing cartridge being unconstrained also grows outwards. Since $CTEB>CTES$, the differences in the thermal growth give a net increase in GFB radial clearance as the temperature raises.

The shaker mount natural frequency in the direction of loading is approximately 1 Hz.

Once the shaft surface attains the target temperature, the system stands for 30 min before testing begins. The shaft temperatures are controlled at $±1°C$ via a cartridge heater and control circuit.

The energy dissipation mechanism in a GFB is of dry-friction type. However, conventional predictive models assume a viscous damping coefficient. Thus, the need to characterize both dissipative type actions becomes evident.

J. Tribol 131(4), 041703 (Sep 22, 2009) (9 pages) doi:10.1115/1.3195042 History: Received January 15, 2009; Revised June 18, 2009; Published September 22, 2009

## Abstract

Oil-free turbomachinery relies on gas bearing supports for reduced power losses and enhanced rotordynamic stability. Gas foil bearings (GFBs) with bump-strip compliant layers can sustain large loads, both static and dynamic, and provide damping to reduce shaft vibrations. The ultimate load capacity of GFBs depends on the material properties and configuration of the underlying bump-strip structures. In high temperature applications, thermal effects, which change the operating clearances and material properties, can considerably affect the performance of the GFB structure. This paper presents experiments conducted to estimate the structural stiffness of a test GFB for increasing shaft temperatures. A 38.17 mm inner diameter GFB is mounted on a nonrotating hollow shaft affixed to a rigid structure. A cartridge heater inserted into the shaft provides a controllable heat source and thermocouples record the temperatures on the shaft and GFB housing. For increasing shaft temperatures (up to $188°C$), increasing static loads (0–133 N) are applied to the bearing and its deflection recorded. In the test configuration, thermal expansion of the GFB housing, larger than that of the shaft, nets a significant increase in radial clearance, which produces a significant reduction in the bearing’s structural stiffness. A simple physical model, which assembles the individual bump stiffnesses, predicts well the measured GFB structural stiffness. Single frequency periodic loads (40–200 Hz) are exerted on the test bearing to identify its dynamic structural stiffness and equivalent viscous damping or a dry-friction coefficient. The GFB dynamic stiffness increases by as much as 50% with dynamic load amplitudes increasing from 13 N to 31 N. The stiffness nearly doubles from low to high frequencies, and most importantly, it decreases by a third as the shaft temperature rises to $188°C$. In general, the GFB dynamic stiffness is lower than its static magnitude at low excitation frequencies, while it becomes larger with increasing excitation frequency due apparently to a bump slip-stick phenomenon. The GFB viscous damping is inversely proportional to the amplitude of the dynamic load, excitation frequency, and shaft temperature. The GFB dry-friction coefficient decreases with increasing amplitude of the applied load and shaft temperature, and increases with increasing excitation frequency.

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## Figures

Figure 1

Schematic representation of a second generation bump-type foil gas bearing

Figure 2

Dimensions of a rigid test shaft and cartridge heater

Figure 3

Test setup for static load—GFB deflection tests at room temperature (side view)

Figure 4

45 deg and 225 deg bearing orientations for applied static loads. Note locations of spot weld every 72 deg.

Figure 5

Dimensional parameters for estimation of the stiffness of a single bump

Figure 6

Measured and predicted static loads versus GFB deflection at 22°C(E=213 GPa,C= 15μm), 89°C(E=208 GPa,CT=19 μm), and 188°C(E=201 GPa,CT=23 μm); assumed dry-friction coefficient μf=0.1

Figure 7

Experimental and predicted GFB structural stiffness versus deflection at 22°C(E=213 GPa,C=15 μm), 89°C(E=208 GPa,CT=19 μm), and 188°C(E=201 GPa,CT=23 μm)

Figure 8

Test setup for dynamic load tests and increasing shaft temperatures (top view)

Figure 9

Schematic view of the setup for dynamic load excitation of the foil bearing

Figure 10

Surface plot of GFB structural stiffness (K) for increasing excitation frequencies and shaft temperatures at a dynamic load of 22 N

Figure 11

Surface plot of GFB structural stiffness (K) for increasing excitation frequencies and dynamic loads at a shaft temperature of 77°C

Figure 12

Time domain GFB displacement versus dynamic load for three excitation frequencies at a shaft temperature of 22°C

Figure 13

Surface plot of the GFB stiffness for increasing dynamic loads and shaft temperatures at excitation frequency of 40 Hz. Test data for a static load of 9 N are also included.

Figure 14

Surface plot of GFB viscous damping coefficient (Ceq) for increasing excitation frequencies and shaft temperatures at a dynamic load of 22 N

Figure 15

Surface plot of GFB viscous damping coefficient (Ceq) for increasing excitation frequencies and dynamic loads at a shaft temperature of 22°C

Figure 16

Surface plot of dry-friction coefficient (μf) for increasing excitation frequencies and shaft temperatures at a dynamic load of 22 N

Figure 17

Surface plot of dry-friction coefficient (μf) for increasing excitation frequencies and dynamic loads at a shaft temperature of 22°C

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