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RESEARCH PAPERS

Nonlinear Modeling of Mechanical Gas Face Seal Systems Using Proper Orthogonal Decomposition

[+] Author and Article Information
Haojiong Zhang

Department of Mechanical and Aerospace Engineering, University of Missouri-Rolla, 1870 Miner Circle, Rolla, MO 65409-0050hztfc@umr.edu

Brad A. Miller1

Department of Mechanical and Aerospace Engineering, University of Missouri-Rolla, 1870 Miner Circle, Rolla, MO 65409-0050millerba@umr.edu

Robert G. Landers

Department of Mechanical and Aerospace Engineering, University of Missouri-Rolla, 1870 Miner Circle, Rolla, MO 65409-0050landersr@umr.edu

1

Corresponding author.

J. Tribol 128(4), 817-827 (Jul 05, 2006) (11 pages) doi:10.1115/1.2345405 History: Received August 26, 2005; Revised July 05, 2006

An approach based on proper orthogonal decomposition and Galerkin projection is presented for developing low-order nonlinear models of the gas film pressure within mechanical gas face seals. A technique is developed for determining an optimal set of global basis functions for the pressure field using data measured experimentally or obtained numerically from simulations of the seal motion. The reduced-order gas film models are shown to be computationally efficient compared to full-order models developed using the conventional semidiscretization methods. An example of a coned mechanical gas face seal in a flexibly mounted stator configuration is presented. Axial and tilt modes of stator motion are modeled, and simulation studies are conducted using different initial conditions and force inputs. The reduced-order models are shown to be applicable to seals operating within a wide range of compressibility numbers, and results are provided that demonstrate the global reduced-order model is capable of predicting the nonlinear gas film forces even with large deviations from the equilibrium clearance.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic of a mechanical gas face seal in a flexibly mounted stator configuration

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Figure 2

Kinematic model of the mechanical gas face seal in the flexibly mounted stator configuration

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Figure 3

Basis functions for pressure profile along seal radius

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Figure 4

Seal clearance response to an initial condition of Ż(0)=0.1m∕s. (a) Λ=7776, (b) Λ=486.

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Figure 5

Seal clearance response to a step in axial force. (a) FC=35N, Λ=7776. (b) FC=10N, Λ=486.

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Figure 6

Seal clearance steady state response to a sinusoidal axial force with a frequency of 200Hz. (a) ∣FC∣=100N, Λ=7776. (b) ∣FC∣=60N, Λ=486.

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Figure 7

Seal clearance steady state response to a square wave axial force with a frequency of 100Hz. (a) Fmax=60N, Fmin=−10N, Λ=7776, (b) Fmax=25N, Fmin=−10N, Λ=486.

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Figure 8

Magnitude of frequency responses for seal axial mode. (a) Λ=7776. (b) Λ=486.

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Figure 9

Seal clearance response for operating conditions (Λ=65,144) above the range where basis functions were constructed. (a) Step response with FC=10N. (b) Sinusoidal force response with ∣FC∣=50N and f=100Hz.

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Figure 10

Seal clearance response for operating conditions (Λ=163) below the range where basis functions were constructed. (a) Step response with FC=4N. (b) Sinusoidal force response with ∣FC∣=25N and f=100Hz.

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Figure 11

Stator dynamic response for an initial condition response with Ż(0)=0.05m∕s, γ̇X(0)=0.1rad∕s, and γ̇Y(0)=0.1rad∕s. (a) axial translation, Λ=7776. (b) axial translation, Λ=486. (c) Stator tilt, Λ=7776. (d) Stator tilt, Λ=486.

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Figure 12

Stator dynamic response to a step in back pressure force with Ż(0)=0m∕s, γ̇X(0)=0.1rad∕s and γ̇Y(0)=0.1rad∕s. (a) Axial translation, FC=35N, Λ=7776. (b) Axial translation, FC=35N, Λ=486. (c) Stator tilt, FC=35N, Λ=7776. (d) Stator tilt, FC=35N, Λ=486.

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Figure 13

Stator dynamic response to a 200Hz sinusoidal back pressure force with Ż(0)=0m∕s, γ̇X(0)=0.1rad∕s and γ̇Y(0)=0.1rad∕s. (a) Axial translation, ∣FC∣=100N, Λ=7776. (b) Axial translation, ∣FC∣=60N, Λ=486. (c) Stator tilt, ∣FC∣=100N, Λ=7776. (d) Stator tilt, ∣FC∣=60N, Λ=486.

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Figure 14

Stator dynamic response to a 100Hz square back pressure force with frequency with Ż(0)=0m∕s, γ̇X(0)=0.1rad∕s and γ̇Y(0)=0.1rad∕s. (a) axial translation, Fmax=25N, Fmin=−10N, Λ=7776. (b) Axial translation, Fmax=60N, Fmin=−10N, Λ=486. (c) Stator tilt, Fmax=25N, Fmin=−10N, Λ=7776. (d) Stator tilt, Fmax=60N, Fmin=−10N, Λ=486.

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