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Research Papers

Vibrations of an Asymmetrical Shaft With Gravity and Nonlinear Spring Characteristics (Isolated Resonances and Internal Resonances)

[+] Author and Article Information
Yukio Ishida

Department of Mechanical Science and Engineering, School of Engineering, Nagoya University, Nagoya, Aichi 464-8603, Japanishida@nuem.nagoya-u.ac.jp

Jun Liu

Department of Mechanical Science and Engineering, School of Engineering, Nagoya University, Nagoya, Aichi 464-8603, Japanliu@nuem.nagoya-u.ac.jp

Tsuyoshi Inoue

Department of Mechanical Science and Engineering, School of Engineering, Nagoya University, Nagoya, Aichi 464-8603, Japaninoue@nuem.nagoya-u.ac.jp

Akihiro Suzuki

Department of Mechanical Science and Engineering, School of Engineering, Nagoya University, Nagoya, Aichi 464-8603, Japansuzuki@nuem.nagoya-u.ac.jp

J. Vib. Acoust 130(4), 041004 (Jul 01, 2008) (8 pages) doi:10.1115/1.2889475 History: Received May 12, 2006; Revised August 12, 2006; Published July 01, 2008

An asymmetrical shaft supported by single-row deep groove ball bearings with clearance has nonlinear spring characteristics, rotating stiffness difference in shaft, and static stiffness difference in support at the shaft ends. When an asymmetrical rotor is supported horizontally, a harmonic excitation due to the unbalance and a double frequency excitation due to the coexistence of gravity and shaft asymmetry work simultaneously. As a result, this system becomes a nonlinear parametrically excited system with multiple periodic excitation forces. In this paper, nonlinear forced vibrations and parametrically excited vibrations are investigated theoretically and experimentally. Vibration characteristics of both isolated resonances and internal resonances are studied.

Copyright © 2008 by American Society of Mechanical Engineers
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References

Figures

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Figure 12

Bifurcation curves and phase plane of backward component (−2ω⋅ip=0.5)

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Figure 13

Experimental setup

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Figure 14

Response with internal resonance at the major critical speed (experiment)

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Figure 15

Response with internal resonance at the secondary critical speed (experiment)

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Figure 1

4DOF rotor model

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Figure 2

Natural frequency diagrams of 2DOF analytical model

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Figure 3

2DOF theoretical model (inclination)

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Figure 4

Resonance curves and spectra

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Figure 5

Derivation of vibration components

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Figure 6

Natural frequency diagram

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Figure 7

Resonance curves (harmonic-type vibration)

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Figure 8

Supercombination type (τ≠0)

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Figure 9

Harmonic type (+ω) with internal resonance

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Figure 10

Superharmonic type with internal resonance

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Figure 11

Poincaré maps at ω=0.47 and ω=0.58 in Fig. 1

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