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TECHNICAL PAPERS

# Identification of Structural Stiffness and Damping Coefficients of a Shoed-Brush Seal

[+] Author and Article Information

Mechanical Engineering Department, Texas A&M University, College Station, Texas 77843-3123adelgam@tamu.edu

Luis San Andrés

Mechanical Engineering Department, Texas A&M University, College Station, Texas 77843-3123lsanandres@mengr.tamu.edu

The shaft stiffness calculated from $Kshaft=∫0LEI[∂2ψ(z)∕∂z2]2dz$ yields $54kN∕m$, a value within 2% of the experimental result.

Energy dissipated internally within the material itself due to cyclical stresses (11).

Static tests on the shoed-brush seal render two stiffness values, with and without including the stiffening effect of the dry friction interaction on the seal. As the test system is statically loaded, when tapping on the disk, the system is perturbed “to break” the friction interaction between the bristles (8).

The identified parameters do not include the effects of pressure differential (leakage) since the tests herein reported refer to a condition without pressurization. The stiffness of the seal (bristle pack) will certainly increase as the pressure differential across the seal increases.

J. Vib. Acoust 129(5), 648-655 (Jun 05, 2007) (8 pages) doi:10.1115/1.2775516 History: Received April 20, 2006; Revised June 05, 2007

## Abstract

The multiple-shoe brush seal, a variation of a standard brush seal, accommodates arcuate pads at the bristles’ free ends. This novel design allows reverse shaft rotation operation and reduces and even eliminates bristle wear, since the pads lift-off due to the generation of a hydrodynamic film during rotor spinning. This type of seal, able to work at both cold and high temperatures, not only restricts secondary leakage but also acts as an effective vibration damper. The dynamic operation of the shoed-brush seals, along with the validation of reliable predictive tools, relies on the appropriate estimation of the seal structural stiffness and energy dissipation features. Single-frequency external load tests conducted on a controlled motion test rig and without shaft rotation allow the identification (measurement) of the structural stiffness and equivalent damping of a 20-pad brush seal, $153mm$ in diameter. The seal energy dissipation mechanism, represented by a structural loss factor and a dry friction coefficient, characterizes the energy dissipated by the bristles and the dry friction interaction of the brush seal bristles rubbing against each other. The physical model used reproduces well the measured system motions, even for frequencies well above the identification range.

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## Figures

Figure 11

Work=Energy dissipated by test system versus frequency for one period of motion. External load (44N) on frequency range 30–300Hz.

Figure 12

Equivalent viscous damping coefficient of test system. External load (48N) on frequency range 25–95Hz. Test data and model results.

Figure 13

Displacement and acceleration versus external load (35N) for excitation frequency equal to (a) 43Hz, (b) 53Hz, and (c) 63Hz

Figure 1

Close-up view of a shoed-brush seal

Figure 2

Cut view of brush seal test rig

Figure 3

Schematic view of test system and representation of equivalent mechanical system

Figure 4

Measured amplitude of motion (∣X∣) synchronous with dynamic load excitation frequency. Test load magnitudes noted.

Figure 10

Work=Energy dissipated by test system versus frequency for one period of motion. External load (48N) on frequency range 25–95Hz.

Figure 14

Displacement and acceleration versus external load (44N) for excitation frequency equal to (a) 43Hz, (b) 53Hz, and (c) 63Hz

Figure 5

Waterfall plot of recorded displacement and acceleration responses due to a external harmonic load (35N). Frequency range (35–95Hz).

Figure 6

Waterfall plot of recorded displacement and acceleration responses due to a external harmonic load (48N). Frequency range (25–95Hz).

Figure 7

Amplitude of synchronous motion versus frequency. Load magnitude=48N. Correlation of model predictions to test results.

Figure 8

Test system identified dynamic stiffness versus frequency. Load magnitude=48N. Model predictions based on Keq−Meqω2. Curves derived from stiffnesses obtained from taping and nontapping static load tests also shown.

Figure 9

Phase angle lag between displacement response and excitation force versus frequency. Load amplitude (48N).

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