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Research Papers

Nonlinear Analysis and Characteristic Variation of Self-Excited Vibration in the Vertical Rotor System Due to the Flexible Support of the Journal Bearing

[+] Author and Article Information
Atsushi Nishimura

Department of Mechanical Systems Engineering,
Nagoya University,
Furo-cho, Chikusa-ku,
Nagoya 464-8603, Aichi, Japan

Tsuyoshi Inoue

Mem. ASME
Department of Mechanical Systems Engineering,
Nagoya University,
Furo-cho, Chikusa-ku,
Nagoya 464-8603, Aichi, Japan
e-mail: inoue.tsuyoshi@nagoya-u.jp

Yusuke Watanabe

Ebara Corporation,
4-2-1 Honfujisawa,
Fujisawa-shi 251-8502, Kanagawa, Japan
e-mail: watanabe.yusuke@ebara.com

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received January 30, 2017; final manuscript received July 27, 2017; published online September 29, 2017. Assoc. Editor: Miao Yu.

J. Vib. Acoust 140(1), 011016 (Sep 29, 2017) (13 pages) Paper No: VIB-17-1040; doi: 10.1115/1.4037520 History: Received January 30, 2017; Revised July 27, 2017

Various vibration problems occur in rotating machinery. Specifically, the large amplitude vibration may occur in the vertical pump using a journal bearing. In an actual vertical pump, the stator's structure supporting the pump shaft may be relatively flexible. In such a case, rotor's motion such as amplitude of the self-excited vibration is not able to be predicted accurately without considering the nonlinear fluid film force reacting in the relative motion between the shaft and the flexibly supported bearing stator. However, the vibration characteristics in such situations have not been explained theoretically so far. In this paper, the vibration characteristics of a vertical rotating shaft with journal bearing are investigated. The nonlinear steady-state vibration analysis of the self-excited vibration is demonstrated, and the influences of the parameters, such as fluid viscosity, radial clearance, and stiffness and damping coefficients of the flexible support of bearing stator, on the vibration characteristics of the system are explained. Moreover, these theoretical results of the self-excited vibration in the vertical rotating shaft with journal bearing are verified both numerically and experimentally.

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References

Figures

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Fig. 1

Theoretical model of a vertical rotor system with a flexibly supported journal bearing: (a) rotor system and (b) coordinate system and displacement of the shaft and bearing stator

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Fig. 2

Free-body diagrams for shaft and bearing stator

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Fig. 3

Comparison of numerical simulation of the cases with and without unbalance showing the influence of unbalance force on the self-excited vibration

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Fig. 4

Variation of eigenvalues for rotational speed: (a) real parts and (b) imaginary part

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Fig. 5

Comparison of frequency response between nonlinear steady-state analysis and numerical simulation: (a) shaft displacement, (b) displacement of flexibly supported bearing stator, (c) whirl frequency of the self-excited vibration, and (d) phase difference of the flexibly supported bearing stator's displacement from the shaft displacement

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Fig. 6

Real part of eigenvalues of the steady-state solution: (b) enlarged figure in ordinate of(a)

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Fig. 7

Time history of shaft motion rs in the self-excited vibration: (a) at 1495 rpm and (b) at 2143 rpm

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Fig. 8

Influence of flexible support's stiffness coefficient k̂b on the frequency response of the self-excited vibration

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Fig. 9

Influence of flexible support's damping coefficient ĉb on the frequency response of the self-excited vibration

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Fig. 10

Influence of radial clearance Ĉr of the journal bearing on the frequency response of the self-excited vibration

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Fig. 11

Influence of fluid viscosity μ̂ of the journal bearing on the frequency response of the self-excited vibration

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Fig. 12

Influence of shaft stiffness k̂s on the frequency response of the self-excited vibration

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Fig. 13

Experimental system: (a) photograph of system and (b) schematic of the system

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Fig. 14

Flexibly supported bearing stator of the journal bearing

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Fig. 15

Experimental result of frequency response in case 1: (a) frequency response of shaft amplitude and (b) waterfall diagram of the shaft displacement

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Fig. 16

Experiment on the influence of radial clearance (case 2): (a) frequency response of the shaft amplitude and (b) waterfall diagram of the shaft displacement

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Fig. 17

Experiment on the influence of water temperature (case 3): (a) frequency response of the shaft amplitude and (b) waterfall diagram of the shaft displacement

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Fig. 18

Experiment on the influence of the number of rubbers used in the flexible support of the bearing stator (case 4): (a) frequency response of the shaft amplitude and (b) waterfall diagram of the shaft displacement

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Fig. 19

Confirmation of influence of the change of rubbers number on the frequency response by simultaneous change of both the stiffness and damping coefficients of the flexible support

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