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

Haojiong Zhang; Robert G. Landers; Brad A. Miller

doi:10.1115/1.2936383

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

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

Haojiong Zhang, Robert G. Landers and Brad A. Miller

[+] 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

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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Abstract

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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References

Miller, B., and Green, I., 2003, “Semi-Analytical Dynamic Analysis of Spiral-Grooved Mechanical Gas Face Seals,” ASME J. Tribol. [CrossRef], 125 (2), pp. 403–413.

Malanoski, S. B., and Pan, C. H. T., 1965, “The Static and Dynamic Characteristics of the Spiral-Grooved Thrust Bearing,” ASME J. Basic Eng., 87 , pp. 547–558.

Zirkelback, N., and San Andès, L., 1999, “Effect of Frequency Excitation on Force Coefficients of Spiral Groove Gas Seals,” ASME J. Tribol. [CrossRef], 121 (4), pp. 853–863.

Ruan, B., 2002, “A Semi-Analytical Solution to the Dynamic Tracking of Non-Contacting Gas Face Seals,” ASME J. Tribol. [CrossRef], 124 (1), pp. 196–202.

Elrod, H. G., McCabe, J. T., and Chu, T. Y., 1967, “Determination of Gas-Bearing Stability by Response to a Step-Jump,” ASME J. Lubr. Technol., 89 , pp. 493–498.

Zhang, H., Miller, B. A., and Landers, R. G., 2006, “Nonlinear Modeling of Mechanical Gas Face Seal Systems Using Proper Orthogonal Decomposition,” ASME J. Tribol. [CrossRef], 128 (4), pp. 817–827.

Friedland, B., 1986, "Control System Design: An Introduction to State Space Methods", McGraw-Hill, New York.

Green, I., and Etsion, I., 1985, “Stability Threshold and Steady-State Response of Noncontacting Coned-Face Seals,” ASLE Trans. [CrossRef], 28 (4), pp. 449–460.

Miller, B., and Green, I., 2002, “Numerical Techniques for Computing Rotordynamic Properties of Mechanical Gas Face Seals,” ASME J. Tribol. [CrossRef], 124 (4), pp. 755–761.

Kirby, M., 2001, "Geometric Data Analysis: An Empirical Approach to Dimensionality Reduction and the Study of Patterns", Wiley, New York.

Cohen, S. D., and Hindmarsh, A. C., 1994, “CVODE User Guide,” Lawrence Livermore National Laboratory, Technical Report No. UCRL-MA-118618.

Figures

Mechanical gas face seal schematic in a flexibly mounted stator configuration

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Figure 1

Mechanical gas face seal schematic in a flexibly mounted stator configuration

(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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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

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

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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

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

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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

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

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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

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

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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

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

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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

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

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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

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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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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Zhang H, Landers RG, Miller BA. Real-Time Force and Moment Estimation for Mechanical Gas Face Seal Systems Using Reduced-Order Kalman Filters. ASME. J. Dyn. Sys., Meas., Control. 2008;130(5):051001-051001-10. doi:10.1115/1.2936383.

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

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