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TECHNICAL PAPERS: Gas Turbines: Structures and Dynamics

# Structural Stiffness, Dry Friction Coefficient, and Equivalent Viscous Damping in a Bump-Type Foil Gas Bearing

[+] Author and Article Information
Dario Rubio

Bechtel Corporation, 3000 Post Oak Boulevard, Houston, TX 77056drubio@bechtel.com

Luis San Andres

Mechanical Engineering Department, Texas A&M University, College Station, TX 77843-3123

The authors recognize that the temperature ranges tested are well below those expected in actual applications for gas turbines.

In a linear mechanical system, an increase in the excitation force, $nF$, leads to a proportional increase in the system response, $nX$, where $n$ is a constant. The system is characterized by material parameters not determined by the motion or system state.

J. Eng. Gas Turbines Power 129(2), 494-502 (Feb 01, 2006) (9 pages) doi:10.1115/1.2360602 History: Received October 01, 2005; Revised February 01, 2006

## Abstract

High performance oil-free turbomachinery implements gas foil bearings (FBs) to improve mechanical efficiency in compact units. FB design, however, is still largely empirical due to its mechanical complexity. The paper provides test results for the structural parameters in a bump-type foil bearing. The stiffness and damping (Coulomb or viscous type) coefficients characterize the bearing compliant structure. The test bearing, $38.1mm$ in diameter and length, consists of a thin top foil supported on bump-foil strips. A prior investigation identified the stiffness due to static loads. Presently, the test FB is mounted on a non-rotating stiff shaft and a shaker exerts single frequency loads on the bearing. The dynamic tests are conducted at shaft surface temperatures from $25to75°C$. Time and frequency domain methods are implemented to determine the FB parameters from the recorded periodic load and bearing motions. Both methods deliver identical parameters. The dry friction coefficient ranges from 0.05 to 0.20, increasing as the amplitude of load increases. The recorded motions evidence a resonance at the system natural frequency, i.e., null damping. The test derived equivalent viscous damping is inversely proportional to the motion amplitude and excitation frequency. The characteristic stick-slip of dry friction is dominant at small amplitude dynamic loads leading to a hardening effect (stiffening) of the FB structure. The operating temperature produces shaft growth generating a bearing preload. However, the temperature does not significantly affect the identified FB parameters, albeit the experimental range was too small considering the bearings intended use in industry.

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## Figures

Figure 6

Estimated dry-friction force versus frequency for three load levels. Tests at room temperature=25°C.

Figure 7

Dynamic load level 3 (nominal 12N at 400Hz) and estimated dry-friction force versus frequency for test at T=25°C

Figure 8

Estimated fry friction coefficient versus frequency for three load levels. Tests at room temperature ∼25°C. (a) Over entire frequency range, (b) for constant phase angle (θ), i.e., f<150Hz.

Figure 9

Real part of test system impedance versus frequency for three load levels and T=25°C

Figure 10

(a) Identified structural stiffness versus amplitude of dynamic load at 20Hz. Three test temperatures: (b) Predictions of FB static load stiffness for various friction coefficients (μ=0.05–0.35) and preload of 6.4μm.

Figure 11

Identified structural damping loss factor versus frequency for three load levels and at T=25°C

Figure 12

Limped parameter thermal model for shaft and foil bearing system

Figure 13

Percent precision uncertainty for identified bearing parameters versus frequency. Load level 4, room temperature tests.

Figure 1

Schematic representation of a bump-type foil bearing. (a) Contact in relative motion between top foil and bump foil; (b) contact in relative motion between bumps and bearing sleeve.

Figure 2

Test setup for dynamic load experiments

Figure 3

Foil bearing single-frequency force excitation and dynamic responses from identified Fourier coefficients and from fast Fourier transfer of dynamic time signals. (a) Dynamic load amplitude, (b) foil bearing displacement, and (c) foil bearing acceleration. Load level 1 (nominal 4N and 400Hz), and T=25°C.

Figure 4

Identified FB equivalent viscous damping coefficient versus frequency for three load levels. Test at room temperature=25°C. (a) Ceq, (b) Ceq.

Figure 5

Equivalent viscous damping coefficient versus frequency for three test temperatures. Load level 4 (nominal 12N at 400Hz).

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