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Research Papers: Elastohydrodynamic Lubrication

A Neural Network Identification Technique for a Foil-Air Bearing Under Variable Speed Conditions and Its Application to Unbalance Response Analysis

[+] Author and Article Information
Mohd Firdaus Bin Hassan

School of Mechanical, Aerospace and
Civil Engineering,
University of Manchester,
Pariser Building, Sackville Street,
Manchester M13 9PL, UK

Philip Bonello

School of Mechanical, Aerospace and
Civil Engineering,
University of Manchester,
Pariser Building, Sackville Street,
Manchester M13 9PL, UK
e-mail: philip.bonello@manchester.ac.uk

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received September 2, 2015; final manuscript received April 12, 2016; published online August 11, 2016. Assoc. Editor: Daejong Kim.

J. Tribol 139(2), 021501 (Aug 11, 2016) (13 pages) Paper No: TRIB-15-1328; doi: 10.1115/1.4033455 History: Received September 02, 2015; Revised April 12, 2016

This paper proposes and studies the nonparametric system identification of a foil-air bearing (FAB). This research is motivated by two advantages: (a) it removes computational limitations by replacing the air film and foil structure equations by a displacement/force relationship and (b) it can capture complications that cannot be easily modeled, if the identification is based on empirical data. A recurrent neural network (RNN) is trained to identify the full numerical model of a FAB over a wide range of speeds. The variable-speed RNN-FAB model is then successfully validated against benchmark results in two ways: (i) by subjecting it to different input data sets and (ii) by using it in the harmonic balance (HB) solution process for the unbalance response of a rotor-bearing system. In either case, the results from the identified variable-speed RNN maintain very good correlation with the benchmark over a wide range of speeds, in contrast to an earlier identified constant-speed RNN, demonstrating the great potential of this method in the absence of self-excitation effects.

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References

Figures

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Fig. 1

Cross section of FAB

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Fig. 2

RNN model of the bearing force Fu and its identification procedure, where χ(τk)=γ′(τk)−Ω̃(τk) (TDL: tapped delay line; N: network normalization; N−1: denormalization)

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Fig. 3

The rotor system used for both training data generation and validation

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Fig. 5

Complete algorithm for solving the unbalance response of a rotordynamic system with nonlinear FABs using RNN andHB

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Fig. 6

Comparison of RNN-FAB radial force with true (benchmark) force the same journal displacement inputs corresponding to the true displacement response at 10 g mm unbalance (—— benchmark force; force prediction from identified RNN-FAB (variable-speed RNN, defined before Sec. 5.1); force prediction from identified RNN-FAB (constant-speed RNN, defined before Sec. 5.1))

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Fig. 7

Comparison of the mean and the first three harmonic components of the RNN-FAB radial force with those of the true (benchmark) force for the same journal displacement inputs corresponding to the true displacement response at 10 g mm unbalance ( benchmark force; force prediction from identified RNN-FAB (variable-speed RNN, defined before Sec. 5.1); force prediction from identified RNN-FAB (constant-speed RNN, defined before Sec. 5.1)): (a) mean, (b) first harmonic, (c) second harmonic, and (d) third harmonic

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Fig. 8

Comparison of RNN-FAB tangential force with true (benchmark) force the same journal displacement inputs corresponding to the true displacement response at 10 g mm unbalance (—— benchmark force; force prediction from identified RNN-FAB (variable-speed RNN, defined before Sec. 5.1); force prediction from identified RNN-FAB (constant-speed RNN, defined before Sec. 5.1))

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Fig. 9

Comparison of the mean and the first three harmonic components of the RNN-FAB tangential force with those of the true (benchmark) force for the same journal displacement inputs corresponding to the true displacement response at 10 g mm unbalance ( benchmark force; force prediction from identified RNN-FAB (variable-speed RNN, defined before Sec. 5.1); force prediction from identified RNN-FAB (constant-speed RNN, defined before Sec. 5.1)): (a) mean, (b) first harmonic, (c) second harmonic, and (d) third harmonic

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Fig. 10

Comparison of RNN-FAB tangential force with true (benchmark) force the same journal displacement inputs corresponding to the true displacement response at 20 g mm unbalance (—— benchmark force; force prediction from identified RNN-FAB (variable-speed RNN, defined before Sec. 5.1); force prediction from identified RNN-FAB (constant-speed RNN, defined before Sec. 5.1))

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Fig. 11

Validation of identified RNN-FAB by application of RNN-FAB to HB analysis at different speeds with unbalance mass of 10 g mm (—— benchmark time domain solution; prediction from HB using identified RNN-FAB (variable-speed RNNs, defined before Sec. 5.1); prediction from HB using identified RNN-FAB (constant-speed RNNs, defined before Sec. 5.1))

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