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Research Papers

Tilting-Pad Journal Bearings With Active Lubrication Applied as Calibrated Shakers: Theory and Experiment

[+] Author and Article Information
Alejandro Cerda Varela

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

Ilmar Ferreira Santos

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

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received November 19, 2013; final manuscript received August 20, 2014; published online September 24, 2014. Assoc. Editor: Mary Kasarda.

J. Vib. Acoust 136(6), 061010 (Sep 24, 2014) (11 pages) Paper No: VIB-13-1407; doi: 10.1115/1.4028452 History: Received November 19, 2013; Revised August 20, 2014

In recent years, a continuous research effort has transformed the conventional tilting-pad journal bearing (TPJB) into a mechatronic machine element. The addition of electromechanical elements provides the possibility of generating controllable forces over the rotor as a function of a suitable control signal. Such forces can be applied in order to perform parameter identification procedures “in situ,” which enables evaluation of the mechanical condition of the machine in a noninvasive way. The usage of a controllable bearing as a calibrated shaker requires obtaining the bearing specific frequency dependent calibration function, i.e., the transfer function between control signal and force over the rotor. This work presents a theoretical model of the calibration function for a TPJB with active lubrication. The bearing generates controllable forces by injecting pressurized oil directly into the bearing clearance. The injected flow is controlled by means of a servovalve. The theoretical model includes the dynamics of the hydraulic system using a lumped parameter approach, which is coupled with the bearing oil film using a modified form of the Reynolds equation. The oil film model is formulated considering an elastothermohydrodynamic lubrication regime. New contributions to the mathematical modeling are presented, such as the inclusion of the dynamics of the hydraulic pipelines and the obtention of the bearing calibration function by means of harmonic analysis of a linearized form of the controllable bearing constitutive equations. The mathematical model is used to study the relevance and effects of different parameters on the calibration function, aiming at providing general guidelines for the active bearing design. Finally, experimental results regarding the calibration function and the usage of the studied bearing as a calibrated shaker provide insight into the possibilities of application of this technology.

Copyright © 2014 by ASME
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References

Figures

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Fig. 1

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 frame (2), pivoted in one end. An hydraulic system consisting of a servovalve and pipelines (3) controls the pressurized oil flow toward the injection nozzle on each pad.

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Fig. 2

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. 3

Schematics of the two configurations used for obtaining the experimental results presented in this study

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Fig. 4

Schematics depicting the nomenclature used for analyzing the ALB hydraulic system

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Fig. 5

Schematics depicting the nomenclature used for analyzing the ALB oil film pressure field

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Fig. 6

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

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Fig. 7

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

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Fig. 8

Validation of the linearized analysis for obtaining the ALB calibration function C(ω): comparison between results obtained by time integration of the nonlinear system, and by the harmonic analysis of the equivalent linearized system

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Fig. 9

The SV function, amplitude and phase lag of its response with respect to the input signal

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Fig. 10

Effect of pad dynamics over the ALB calibration function, in amplitude and phase lag: comparison of results when including tilting mode (T), bending mode (B), and pivot deformation for a pivot stiffness of 109 (N/m) (Piv1) and 108 (N/m) (Piv2). Results obtained for rotor eccentricity 0.6 and rotational speed 3000 rpm. The SV is given as reference.

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Fig. 11

Effect of pipeline dynamics over the ALB calibration function, in amplitude and phase lag: comparison of results for different fractions of air entrained within the oil flow. Results obtained for rotor eccentricity 0.6 and rotational speed 3000 rpm. The SV is given as reference.

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Fig. 12

Effect of bearing operational conditions over the ALB calibration function, in amplitude and phase lag: comparison of results for different rotor eccentricities and rotational speeds. The SV is given as reference.

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Fig. 13

Experimentally obtained ALB calibration function, in amplitude and phase lag. The SV is given as reference.

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Fig. 14

Experimentally obtained FRF, comparison between results obtained using an electromagnetic shaker and the ALB as the excitation source, with two different amplitudes of the input chirp signal. The supply pressure for the ALB hydraulic system is 2 MPa, rotor static loading is 400 N, and rotational speed is 3000 rpm.

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Fig. 15

Experimentally obtained FRF, comparison between results obtained using an electromagnetic shaker and the ALB as the excitation source, with two different amplitudes of the input chirp signal. The supply pressure for the ALB hydraulic system is 8 MPa, rotor static loading is 400 N, and rotational speed is 3000 rpm.

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