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Research Papers

Finite Element Analysis and Experimental Validation of Transfer Function of Rotating Shaft System With Both an Open Crack and Anisotropic Support Stiffness

[+] Author and Article Information
Qiang Yao

Department of Mechanical Systems Engineering,
Nagoya University,
Furo-cho, Chikusa-ku,
Nagoya 464-8603, Japan
e-mail: yq3010201207@gmail.com

Tsuyoshi Inoue

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

Shota Yabui

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

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received April 15, 2018; final manuscript received July 25, 2018; published online October 16, 2018. Assoc. Editor: Izhak Bucher.

J. Vib. Acoust 141(2), 021002 (Oct 16, 2018) (15 pages) Paper No: VIB-18-1164; doi: 10.1115/1.4041078 History: Received April 15, 2018; Revised July 25, 2018

In this paper, transfer function of rotating shaft system for detecting transverse open crack is developed. Rotating shaft system is modeled using one-dimensional finite element method (1D-FEM), and quantitative analysis is performed. Open crack is modeled as weak asymmetry rotating with shaft's rotation. It is known that, when both open crack and support stiffness anisotropy coexist, various frequency components of shaft's vibration are generated through their successive interaction. This paper evaluates the order of these components, and concludes that first five main components are enough to investigate interaction of open crack and support stiffness anisotropy. Then, five sets of transfer functions for these components are derived. The validity of this set of transfer functions is confirmed by numerical simulation. Moreover, excitation experiment utilizing active magnetic bearing (AMB) is performed, and the validity of derived transfer function was verified experimentally.

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References

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Figures

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Fig. 1

One-dimensional finite element model of rotating shaft system: (a) flexible shaft with an open crack and (b) bearing model with anisotropic support stiffness

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Fig. 2

Cross section view of cracked shaft: (a) coordinate systems and (b) neutral axes

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Fig. 3

Variation of the second area moment of inertia of crack cross section with relative crack depth

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Fig. 4

Variation of the second area moment of inertia of around open crack

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Fig. 5

Derivation of natural angular frequency of rotating shaft system with an open crack and anisotropic support stiffness

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Fig. 6

Natural angular frequency analysis considering both anisotropic support stiffness and open crack: (a) natural angular frequency diagram and (b) comparison between natural angular frequency diagram and resonance curve (rotating speed is set to be ω=1000 rpm)

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Fig. 7

Components in the whirling motion generated by the effects of crack and support anisotropy

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Fig. 8

Transfer function H11(disk) between excitation with angular frequency Ω applied for disk and whirling motion of disk in case of normal rotating shaft system with isotropic support stiffness (ω=1000 rpm)

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Fig. 9

Transfer functions in case of normal rotating shaft system with anisotropic support stiffness (ω=1000 rpm): (a) transfer function H11(disk) between excitation with angular frequency Ω applied for disk and whirling motion of disk and (b) transfer function H12(disk) between excitation with angular frequency −Ω applied for disk and whirling motion of disk

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Fig. 10

Transfer functions in case of cracked rotating shaft system with isotropic support stiffness (ω=1000 rpm): (a) transfer function H11(disk) between excitation with angular frequency Ω applied for disk and whirling motion of disk and (b) transfer function H13(disk) between excitation with angular frequency 2ω−Ω applied for disk and whirling motion of disk

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Fig. 11

Transfer functions in case of cracked rotating shaft system with anisotropic support stiffness (ω=1000 rpm): (a) transfer function H11(disk) between excitation with angular frequency Ω applied for disk and whirling motion of disk, (b) transfer function H12(disk) between excitation with angular frequency −Ω applied for disk and whirling motion of disk, (c) transfer function H13(disk) between excitation with angular frequency 2ω−Ω applied for disk and whirling motion of disk, (d) transfer function H14(disk) between excitation with angular frequency −2ω+Ω applied for disk and whirling motion of disk, and (e) transfer function H15(disk) between excitation with angular frequency 2ω+Ω applied for disk and whirling motion of disk

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Fig. 12

Variation of transfer function H13(disk) with depth of crack

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Fig. 13

Verification of resonance peaks Ω=−pf, pb of transfer function H13(disk) by sweep excitation simulation

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Fig. 14

Experimental system: (a) photograph of experimental setup, (b) configuration of experimental setup, (c) open crack, and (d) AMB

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Fig. 15

Block diagram of the AMB controller for experimental system

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Fig. 16

Comparison between experimental and theoretical results: (a) transfer function H12(disk) in the case with normal rotating shaft with anisotropic bearing support and (b) transfer function H13(disk) in the case with cracked rotating shaft with anisotropic bearing support

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