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Research Papers

Nonlinear Analysis of Bifurcation Phenomenon for a Simple Flexible Rotor System Supported by a Full-Circular Journal Bearing

[+] Author and Article Information
Tatsuya Miura

Mitsubishi Hitachi Power Systems, Ltd.,
Minatomirai 3-chome, Nishi-ku,
Yokohama 220-8401, Japan

Tsuyoshi Inoue

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

Hiroshi Kano

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

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received December 28, 2015; final manuscript received January 10, 2017; published online April 28, 2017. Editor: I. Y. (Steve) Shen.

J. Vib. Acoust 139(3), 031012 (Apr 28, 2017) (12 pages) Paper No: VIB-15-1544; doi: 10.1115/1.4036098 History: Received December 28, 2015; Revised January 10, 2017

This paper demonstrates nonlinear theoretical analysis of a flexible rotor system supported by a full-circular journal bearing focusing on the bifurcation phenomenon in the vicinity of the stability limit (bifurcation point). A third-order polynomial approximation model is used for the representation of the oil film force of the journal bearing. The reduced-order model, with modes concerning the bifurcation, is deduced using the center manifold theory. The dynamical equation in the normal form relating the bifurcation which leads to the oil whirl is obtained using the normal form theory. The influences of various parameters are investigated based on the analysis of a deduced dynamical equation in the normal form. Furthermore, the validity of the derived analytical observation is confirmed by comparing it with the numerically obtained frequency response result.

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References

Figures

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Fig. 1

Flexible rotor—journal bearing system

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Fig. 2

Coordinate systems at the journal bearing

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Fig. 3

Rectangular coordinates based on an equilibrium point

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Fig. 4

Eigenvalue analysis (real part)

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Fig. 5

Example of dimensionless nonlinear coefficients of FJBx: (a) second-order coefficients and (b) third-order coefficients

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Fig. 6

Bifurcation analysis (influence of rotor mass m̂1): (a) bifurcation point and (b) amplitude of limit cycle

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Fig. 7

Bifurcation analysis (influence of radial clearance Ĉr): (a) bifurcation point and (b) amplitude of limit cycle

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Fig. 8

Bifurcation analysis (influence of kinematic viscosity ν̂): (a) bifurcation point and (b) amplitude of limit cycle

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Fig. 9

Bifurcation analysis (influence of bearing length L̂): (a) bifurcation point and (b) amplitude of limit cycle

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Fig. 10

Bifurcation analysis (influence of bearing diameter D̂): (a) bifurcation point and (b) amplitude of limit cycle

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Fig. 11

Bifurcation analysis (influence of shaft stiffness k̂1): (a) bifurcation point and (b) amplitude of limit cycle

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Fig. 12

Frequency response (m1=1): (a) amplitude at rotor and (b) amplitude at journal

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Fig. 13

Frequency response (m1=3.5): (a) amplitude at rotor and (b) amplitude at journal

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Fig. 14

Frequency response (L = 0.65): (a) amplitude at rotor and (b) amplitude at journal

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