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Research Papers: Hydrodynamic Lubrication

Dynamic Coefficients of a Tilting Pad With Active Lubrication: Comparison Between Theoretical and Experimental Results

[+] Author and Article Information
Alejandro Cerda Varela

Department of Mechanical Engineering,
Technical University of Denmark,
Lyngby 2800 Kgs, Denmark
e-mail: acer@mek.dtu.dk

Ilmar Ferreira Santos

Department of Mechanical Engineering,
Technical University of Denmark,
Lyngby 2800 Kgs, Denmark
e-mail: ifs@mek.dtu.dk

1Corresponding authors.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received November 24, 2014; final manuscript received February 25, 2015; published online April 17, 2015. Assoc. Editor: Mihai Arghir.

J. Tribol 137(3), 031704 (Jul 01, 2015) (10 pages) Paper No: TRIB-14-1288; doi: 10.1115/1.4029943 History: Received November 24, 2014; Revised February 25, 2015; Online April 17, 2015

This paper deals with the validation of the mathematical model for predicting the equivalent stiffness and damping of an active tilting-pad bearing. The active bearing design includes an injection nozzle in the pad and a hydraulic supply system featuring a servovalve, which enables to modify the pressurized oil flow into the bearing clearance. The servovalve is governed by a control signal, obtained in open- or closed-loop configuration. The mathematical model includes the dynamics related to journal, tilting pads, and associated hydraulic system. First, the model results are tested against experimental results from the literature for industrial grade passive tilting pad bearings. This initial validation is followed by a comparison with experimental identification results obtained from a test rig featuring the active bearing design. Good overall agreement is observed in both configurations. The results provide an overview about the feasibility of modifying the bearing impedance by means of the active lubrication system, both in open-loop (fixed control signal), or closed-loop, as a function of the journal position and proportional derivative (PD) controller gains.

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Figures

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Fig. 1

Conceptual picture of the test rig for the tilting-pad bearing with active lubrication: the arrangement consists of a rigid rotor supported vertically by two tilting pads (1). The rotor is attached to a tilting arm (2), pivoted in one end. A hydraulic system consisting of a servovalve and feed lines (3) controls the pressurized oil flow toward the injection nozzle on each pad.

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Fig. 2

Vertical view of the actual installation of the ALB test rig: the test rig (4) is driven by an electric motor (1) via a helical flexible coupling. The electromagnetic shaker (2) is suspended over the tilting arm free end. The servovalve (3) is connected to the bearing case via hydraulic hoses.

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Fig. 3

Tilting pads installed in the ALB test rig: the arrows show the position of the injection nozzles that render the bearing controllable

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Fig. 4

Schematics of the configuration used for performing the experimental study, and equivalent mechanical system for formulating the identification procedure

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Fig. 5

Impedance function H for a five-pad, load on pad TPJB with 60% offset: comparison between experimental results [28,40] and prediction considering rigid and flexible pivot

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Fig. 6

Impedance function H for a five-pad, load between pad TPJB with 50% offset: comparison between experimental results [29,41] and prediction considering rigid and flexible pivot

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Fig. 7

Finite element mesh used for discretizing the oil film fluid domain (left) and pad solid domain (right)

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Fig. 8

Pad modes used for the modal reduction scheme: tilting motion (left), bending deformation (center), and pivot deformation (right)

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Fig. 9

Bearing dynamic coefficients k and c: comparison between experimental and theoretical results for an applied load of 1400 N and constant values of servovalve control signal uV

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Fig. 10

Bearing dynamic coefficients k and c: comparison between experimental and theoretical results for an applied load of 2800 N and constant values of servovalve control signal uV

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Fig. 11

Bearing dynamic coefficients k and c: comparison between experimental and theoretical results for an applied load of 2800 N and derivative controllers (GD1=-20 sV/m and GD2=20 sV/m)

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Fig. 12

Bearing dynamic coefficients k and c: comparison between experimental and theoretical results for an applied load of 2800 N and proportional controllers (GP1=1×104 V/m and GP2=-1×104 V/m)

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Fig. 13

Bearing dynamic coefficients k and c: comparison between experimental and theoretical results for an applied load of 2800 N and proportional derivative controllers (GP1=1×104 V/m, GD1=-20 sV/m, and GD2=20 sV/m)

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Fig. 14

Comparison of the experimental FRF between applied force and resulting arm displacement for different configurations of the active lubrication system, for an applied load of 2800 N

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