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Journal of Dynamic Systems, Measurement, and Control | Volume 130 | Issue 5 | Research Paper
Research Papers

Real-Time Force and Moment Estimation for Mechanical Gas Face Seal Systems Using Reduced-Order Kalman Filters

[+] Author and Article Information
Haojiong Zhang

 Quickset International, Inc., 3650 Woodhead Drive, Northbrook, IL 60062hzhang@quickset.com

Robert G. Landers1

 Missouri University of Science and Technology, 500 West 16th Street, Rolla, MO 65409-0050landersr@mst.edu

Brad A. Miller

 Harding University, 915 East Market Avenue, Searcy, AR 72149-2290bmiller7@harding.edu

1

Corresponding author.

J. Dyn. Sys., Meas., Control 130(5), 051001 (Jul 29, 2008) (10 pages) doi:10.1115/1.2936383 History: Received June 08, 2006; Revised March 10, 2008; Published July 29, 2008
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A method using reduced-order Kalman filters is developed to estimate the thin gas film axial force and moments in real time for mechanical gas face seal systems in a flexibly mounted stator configuration. First-order Gauss–Markov stochastic models, combined with the stator motion equations, form the basis for the reduced-order Kalman filter estimators. Two schemes are presented to estimate axial force and moments based on stator motion measurements. In one scheme, the force and moments are directly estimated and, in another scheme, a set of proper orthogonal decomposition weighting functions is estimated, from which the gas film force and moments are computed. Both estimators are shown to approximate the gas film axial force and moments successfully for different forcing functions over a wide range of compressibility numbers.
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Copyright © 2008 by American Society of Mechanical Engineers
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Grahic Jump Location
+Mechanical gas face seal schematic in a flexibly mounted stator configuration
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Mechanical gas face seal schematic in a flexibly mounted stator configuration
Figure 1

Mechanical gas face seal schematic in a flexibly mounted stator configuration

Grahic Jump Location
+(a) Mechanical gas face seal kinematic model in a flexibly mounted stator configuration; (b) mechanical seal with the seal faces aligned showing the coning angle β
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(a) Mechanical gas face seal kinematic model in a flexibly mounted stator configuration; (b) mechanical seal with the seal faces aligned showing the coning angle β
Figure 2

(a) Mechanical gas face seal kinematic model in a flexibly mounted stator configuration; (b) mechanical seal with the seal faces aligned showing the coning angle β

Grahic Jump Location
+Estimation of gas film force, moments, and POD weighting functions with zero initial conditions, Λ=311.04, uZ=5N, uX=1Nm, and uY=1Nm: (a) axial force, (b) moment about X axis, (c) estimation errors from direct estimation, and (d) estimation errors from indirect estimation based on POD model
View Large  |  Save Figure  |  Download Slide (.ppt)
Estimation of gas film force, moments, and POD weighting functions with zero initial conditions, Λ=311.04, uZ=5N, uX=1Nm, and uY=1Nm: (a) axial force, (b) moment about X axis, (c) estimation errors from direct estimation, and (d) estimation errors from indirect estimation based on POD model
Figure 3

Estimation of gas film force, moments, and POD weighting functions with zero initial conditions, Λ=311.04, uZ=5N, uX=1Nm, and uY=1Nm: (a) axial force, (b) moment about X axis, (c) estimation errors from direct estimation, and (d) estimation errors from indirect estimation based on POD model

Grahic Jump Location
+Estimation of gas film force, moments, and POD weighting functions with zero initial conditions, Λ=311.04, uZ=5sin(628.32t)N, uX=sin(628.32t)N∕m, and uY=sin(628.32t)N∕m: (a) axial force, (b) moment about X axis, (c) estimation errors from direct estimation, and (d) estimation errors from indirect estimation based on POD model
View Large  |  Save Figure  |  Download Slide (.ppt)
Estimation of gas film force, moments, and POD weighting functions with zero initial conditions, Λ=311.04, uZ=5sin(628.32t)N, uX=sin(628.32t)N∕m, and uY=sin(628.32t)N∕m: (a) axial force, (b) moment about X axis, (c) estimation errors from direct estimation, and (d) estimation errors from indirect estimation based on POD model
Figure 4

Estimation of gas film force, moments, and POD weighting functions with zero initial conditions, Λ=311.04, uZ=5sin(628.32t)N, uX=sin(628.32t)N∕m, and uY=sin(628.32t)N∕m: (a) axial force, (b) moment about X axis, (c) estimation errors from direct estimation, and (d) estimation errors from indirect estimation based on POD model

Grahic Jump Location
+Estimation of gas film force, moments, and POD weighting functions with zero initial conditions, Λ=311.04, uZ=5sin(3141.5t)N, uX=sin(3141.5t)Nm, and uY=sin(3141.5t)Nm: (a) axial force, (b) moment about X axis, (c) estimation errors from direct estimation, and (d) estimation errors from indirect estimation based on POD model
View Large  |  Save Figure  |  Download Slide (.ppt)
Estimation of gas film force, moments, and POD weighting functions with zero initial conditions, Λ=311.04, uZ=5sin(3141.5t)N, uX=sin(3141.5t)Nm, and uY=sin(3141.5t)Nm: (a) axial force, (b) moment about X axis, (c) estimation errors from direct estimation, and (d) estimation errors from indirect estimation based on POD model
Figure 5

Estimation of gas film force, moments, and POD weighting functions with zero initial conditions, Λ=311.04, uZ=5sin(3141.5t)N, uX=sin(3141.5t)Nm, and uY=sin(3141.5t)Nm: (a) axial force, (b) moment about X axis, (c) estimation errors from direct estimation, and (d) estimation errors from indirect estimation based on POD model

Grahic Jump Location
+Estimation of gas film force, moments, and POD weighting functions with zero initial conditions, Λ=31,104, uZ=10N, uX=5Nm, and uY=5Nm: (a) axial force, (b) moment about X axis, (c) estimation errors from direct estimation, and (d) estimation errors from indirect estimation based on POD model
View Large  |  Save Figure  |  Download Slide (.ppt)
Estimation of gas film force, moments, and POD weighting functions with zero initial conditions, Λ=31,104, uZ=10N, uX=5Nm, and uY=5Nm: (a) axial force, (b) moment about X axis, (c) estimation errors from direct estimation, and (d) estimation errors from indirect estimation based on POD model
Figure 6

Estimation of gas film force, moments, and POD weighting functions with zero initial conditions, Λ=31,104, uZ=10N, uX=5Nm, and uY=5Nm: (a) axial force, (b) moment about X axis, (c) estimation errors from direct estimation, and (d) estimation errors from indirect estimation based on POD model

Grahic Jump Location
+Estimation of gas film force, moments, and POD weighting functions for a sinusoidal response with zero initial conditions, Λ=31,104, uZ=10sin(628.32t)N, uX=5sin(628.32t)Nm, and uY=5sin(628.32t)Nm: (a) axial force, (b) moment about X axis, (c) estimation errors from direct estimation, and (d) estimation errors from indirect estimation based on POD model
View Large  |  Save Figure  |  Download Slide (.ppt)
Estimation of gas film force, moments, and POD weighting functions for a sinusoidal response with zero initial conditions, Λ=31,104, uZ=10sin(628.32t)N, uX=5sin(628.32t)Nm, and uY=5sin(628.32t)Nm: (a) axial force, (b) moment about X axis, (c) estimation errors from direct estimation, and (d) estimation errors from indirect estimation based on POD model
Figure 7

Estimation of gas film force, moments, and POD weighting functions for a sinusoidal response with zero initial conditions, Λ=31,104, uZ=10sin(628.32t)N, uX=5sin(628.32t)Nm, and uY=5sin(628.32t)Nm: (a) axial force, (b) moment about X axis, (c) estimation errors from direct estimation, and (d) estimation errors from indirect estimation based on POD model

Grahic Jump Location
+Estimation of gas film force, moments, and POD weighting functions with zero initial conditions, Λ=31,104, uZ=10sin(3141.5t)N, uX=5sin(3141.5t)Nm, uY=5sin(3141.5t)Nm: (a) axial force, (b) moment about X axis, (c) estimation errors from direct estimation, (d) estimation errors from indirect estimation based on POD model
View Large  |  Save Figure  |  Download Slide (.ppt)
Estimation of gas film force, moments, and POD weighting functions with zero initial conditions, Λ=31,104, uZ=10sin(3141.5t)N, uX=5sin(3141.5t)Nm, uY=5sin(3141.5t)Nm: (a) axial force, (b) moment about X axis, (c) estimation errors from direct estimation, (d) estimation errors from indirect estimation based on POD model
Figure 8

Estimation of gas film force, moments, and POD weighting functions with zero initial conditions, Λ=31,104, uZ=10sin(3141.5t)N, uX=5sin(3141.5t)Nm, uY=5sin(3141.5t)Nm: (a) axial force, (b) moment about X axis, (c) estimation errors from direct estimation, (d) estimation errors from indirect estimation based on POD model

Grahic Jump Location
+Gas film force and moment estimation average errors of the direct estimator using different forcing frequencies and with different measurement corruptions, Λ=31,104: (a) axial force and (b) moment about X axis
View Large  |  Save Figure  |  Download Slide (.ppt)
Gas film force and moment estimation average errors of the direct estimator using different forcing frequencies and with different measurement corruptions, Λ=31,104: (a) axial force and (b) moment about X axis
Figure 9

Gas film force and moment estimation average errors of the direct estimator using different forcing frequencies and with different measurement corruptions, Λ=31,104: (a) axial force and (b) moment about X axis

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