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Research Papers

Optimal Vibration Reduction of Flexible Rotor Systems By the Virtual Bearing Method

[+] Author and Article Information
Shibing Liu

Mem. ASME
Hyperloop One,
2159 Bay Street,
Los Angeles, CA 90021
e-mail: shibing@hyperloop-one.com

Bingen Yang

Fellow ASME
Department of Aerospace and
Mechanical Engineering,
University of Southern California,
Los Angeles, CA 90089
e-mail: bingen@usc.edu

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received July 11, 2017; final manuscript received August 31, 2017; published online October 9, 2017. Assoc. Editor: Stefano Lenci.

J. Vib. Acoust 140(2), 021008 (Oct 09, 2017) (11 pages) Paper No: VIB-17-1315; doi: 10.1115/1.4037956 History: Received July 11, 2017; Revised August 31, 2017

This paper presents a new approach to optimal bearing placement that minimizes the vibration amplitude of a flexible rotor system with a minimum number of bearings. The thrust of the effort is the introduction of a virtual bearing method (VBM), by which a minimum number of bearings can be automatically determined in a rotor design without trial and error. This unique method is useful in dealing with the issue of undetermined number of bearings. In the development, the VBM and a distributed transfer function method (DTFM) for closed-form analytical solutions are integrated to formulate an optimization problem of mixed continuous-and-integer type, in which bearing locations and bearing index numbers (BINs) (specially defined integer variables representing the sizes and properties of all available bearings) are selected as design variables. Solution of the optimization problem by a real-coded genetic algorithm yields an optimal design that satisfies all the rotor design requirements with a minimum number of bearings. Filling a technical gap in the literature, the proposed optimal bearing placement approach is applicable to either redesign of an existing rotor system for improvement of system performance or preliminary design of a new rotor system with the number of bearings to be installed being unforeknown.

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Figures

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Fig. 1

Schematic of a flexible rotor system

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Fig. 2

A rotating shaft with a bearing: (a) physical bearing with finite length and (b) pointwise bearing model (pointwise springs and dampers)

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Fig. 3

A stepped flexible rotor system in design: (a) the bare system with mounted disks, (b) the bare system with nonbearing regions (shaded areas), (c) the bare system with virtual bearings, and (d) the virtual rotor system with pointwise bearings

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Fig. 4

Unbalanced mass response of a flexible rotor system versus its shaft rotation speed

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Fig. 5

Example I: (a) the bare system with virtual bearings and nonbearing regions and (b) the virtual rotor system with pointwise bearings

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Fig. 6

Example I: spatial distributions of vibration amplitude of the rotor system in the previous design and the proposed optimal design

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Fig. 7

A simply supported flexible rotor system in example II: (a) the bare system, (b) the bare system with virtual bearings, and (c) the virtual rotor system with pointwise bearings

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Fig. 8

Example II: the unbalanced mass response of the rotor system versus its rotation speed

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Fig. 9

The spatial distributions of vibration amplitude at operating speed (8000 rpm) in example II: dashed line—the optimally designed rotor system with three bearings, and the solid line—the virtual rotor system with nine bearings

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