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Research Papers

Uncertainty Analysis of a Tilting-Pad Journal Bearing Using Fuzzy Logic Techniques

[+] Author and Article Information
A. A. Cavalini, Jr.

LMEst—Structural Mechanics Laboratory, Federal University of Uberlândia,
School of Mechanical Engineering,
Av. João Naves de Ávila, 2121,
Uberlândia, MG 38408-196, Brazil

A. G. S. Dourado, V. Steffen, Jr.

LMEst—Structural Mechanics Laboratory,
Federal University of Uberlândia,
School of Mechanical Engineering,
Av. João Naves de Ávila, 2121,
Uberlândia, MG 38408-196, Brazil

F. A. Lara-Molina

Federal University of Technology—Paraná,
Campus Cornélio Procópio,
Av. Alberto Carazzi, 1640,
Cornélio Procópio, PR 86300-000, Brazil

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received August 19, 2015; final manuscript received August 3, 2016; published online September 30, 2016. Assoc. Editor: John Yu.

J. Vib. Acoust 138(6), 061016 (Sep 30, 2016) (10 pages) Paper No: VIB-15-1330; doi: 10.1115/1.4034614 History: Received August 19, 2015; Revised August 03, 2016

This paper is dedicated to the analysis of uncertainties affecting the load capability of a 4-pad tilting-pad journal bearing in which the load is applied on a given pad load on pad configuration (LOP). A well-known stochastic method has been used extensively to model uncertain parameters by using the so-called Monte Carlo simulation. However, in the present contribution, the inherent uncertainties of the bearing parameters (i.e., the pad radius, the oil viscosity, and the radial clearance; bearing assembly clearance) are modeled by using a fuzzy dynamic analysis. This alternative methodology seems to be more appropriate when the stochastic process that characterizes the uncertainties is unknown. The analysis procedure is confined to the load capability of the bearing, being generated by the envelopes of the pressure fields developed on each pad. The hydrodynamic supporting forces are determined by considering a nonlinear model, which is obtained from the solution of the Reynolds equation. The most significant results are associated to the changes in the steady-state condition of the bearing due to the reaction forces that are modified according to the uncertainties introduced in the system. Finally, it is worth mentioning that the uncertainty analysis in this case provides relevant information both for design and maintenance of tilting-pad hydrodynamic bearings.

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Figures

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Fig. 1

Adopted coordinate frames. (a) Inertial system I, (b) auxiliary system B, (c) mobile system B′, and (d) curvilinear system B″.

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Fig. 2

Fuzzy set and α-levels representation. (a) Fuzzy set and (b) the α-levels.

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Fig. 3

The α-level optimization

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Fig. 4

Pressure fields generated on the pads considering the deterministic parameters of the bearing: (a) Pad j = 1, (b) pad j = 2, (c) pad j = 3, and (d) pad j = 4

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Fig. 5

Lower and upper limits of the forces for each pad considering the first uncertainty scenario. (a) Pad j = 1, (b) pad j = 2, (c) pad j = 3, and (d) pad j = 4. (*) nominal value, (x) lower limit, and (o) upper limit.

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Fig. 6

The angular position of the pads according to the considered α-levels and the first uncertainty scenario. (a) Pad j = 1, (b) pad j = 2, (c) pad j = 3, and (d) pad j = 4. (*) nominal value, (x) lower limit, and (o) upper limit.

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Fig. 7

Nominal value, lower limit, and upper limit of the pressure fields considering the first uncertainty scenario and α-level = 0. (*) Nominal value, (x) lower limit, and (o) upper limit.

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Fig. 8

Lower and upper limits of the forces for each pad considering the three uncertainty scenarios and α-level = 0. (a) Pad j = 1, (b) pad j = 2, (c) pad j = 3, and (d) pad j = 4. (*) Nominal value, (x) lower limit, and (o) upper limit.

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Fig. 9

Lower and upper limits of the forces for each pad considering the shaft at 3000 (Δ), 9000 (+), and 15,000 rpm (□). (a) Pad j = 1, (b) pad j = 2, (c) pad j = 3, and (d) pad j = 4.

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Fig. 10

Lower and upper limits of the forces for each pad considering the three uncertainty scenarios. (a) Pad j = 1, (b) pad j = 2, (c) pad j = 3, and (d) pad j = 4. (*) Nominal value, (x) lower limit, and (o) upper limit.

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Fig. 11

Membership functions of the three uncertain parameters. (a) Rs, (b) ho, and (c) Toil (…) membership function considered for modeling the uncertain parameter. (*) Nominal value, (x) lower limit, and (o) upper limit.

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