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Research Papers

Application of the Proper Orthogonal Decomposition Method for Cracked Rotors

[+] Author and Article Information
Mohammad A. Al-Shudeifat

Aerospace Engineering Khalifa,
University of Science and Technology,
Abu Dhabi 127788, United Arab Emirates
e-mail: mohd.shudeifat@ku.ac.ae

Ayesha Al Mehairi

Aerospace Engineering Khalifa,
University of Science and Technology,
Abu Dhabi 127788, United Arab Emirates
e-mail: ayesha.almehairi@etic.ac.ae

Adnan S. Saeed

Aerospace Engineering,
Khalifa University of Science and Technology,
Abu Dhabi 127788, United Arab Emirates
e-mail: adnan.saeed@kustar.ac.ae

Shadi Balawi

Mechanical Engineering,
Texas A&M,
College Station, TX 77843
e-mail: Sbalawi@tamu.edu

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received January 19, 2018; final manuscript received August 11, 2018; published online September 12, 2018. Assoc. Editor: Anindya Chatterjee.

J. Comput. Nonlinear Dynam 13(11), 111006 (Sep 12, 2018) (9 pages) Paper No: CND-18-1020; doi: 10.1115/1.4041234 History: Received January 19, 2018; Revised August 11, 2018

The application of the proper orthogonal decomposition (POD) method to the vibration response of a cracked rotor system is investigated. The covariance matrices of the horizontal and vertical whirl amplitudes are formulated based on the numerical and experimental whirl response data for the considered cracked rotor system. Accordingly, the POD is directly applied to the obtained covariance matrices where the proper orthogonal values (POVs), and the proper orthogonal modes (POMs) are obtained for various crack depths, unbalance force vector angles, and rotational speeds. It is observed that both POVs and their corresponding POMs are highly sensitive to the appearance of the crack and the unbalance force angle direction in the neighborhoods of the critical rotational speeds. The sensitivity zones of the POVs and POMs to the crack propagation are found to be coinciding with the unstable zones found by the Floquet's theory of the considered cracked system.

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References

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Figures

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Fig. 1

Schematic diagrams of the crack in the shaft cross section: (a) before the shaft rotation and (b) after the shaft rotation

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Fig. 2

Jeffcott rotor model

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Fig. 3

The cracked Jeffcott rotor with an open crack model

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Fig. 4

The critical rotational speeds versus μ in (a) and the variation of maximum Floquet's multiplier with respect to rotational speed and μ in (b)

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Fig. 5

Unbalance force angle effect on λ1 for varying shaft rotational speed in (a) at μ=0, in (b) at μ=0.05, in (c) at μ=0.1, and in (d) at μ=0.2

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Fig. 6

The variation in the first POM eigenvalue λ1 with respect to rotational speed and the normalized crack depth μ for β=0 in (a) and for β=π/4 in (b)

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Fig. 7

The variation in the second POM eigenvalue λ2 with respect to rotational speed and the normalized crack depth μ for β=0 in (a) and for β=π/4 in (b)

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Fig. 8

The variation in λ2 with respect to λ1+λ2 versus the rotational speed and the normalized crack depth μ for β=0 in (a) and for β=π/4 in (b)

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Fig. 9

The variations in the first POM slope with respect to the shaft rotational speed and the unbalance force vector angle of the cracked system at μ=0.2

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Fig. 10

The MFS-RDS Spectra-Quest rotordynamic simulator used for experimental analysis

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Fig. 11

Experimental results of the unbalance force angle effect on the peak values of λ1 in the neighborhood of the critical rotational speed in (a) for μ=0.22 and in (b) for μ=0.44

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Fig. 12

Experimental results of the unbalance force angle effect on the peak values of λ2 in the neighborhood of the critical rotational speed in (a) for μ=0.22 and in (b) for μ=0.44

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Fig. 13

Experimental results of the unbalance force angle effect on the peak values of the ratio of λ2 to λ1+λ2 in the neighborhood of the critical rotational speed in (a) for μ=0.22 and in (b) for μ=0.44

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Fig. 14

Comparison of experimental results of the effect of Ω on λ1 in the neighborhood of the critical rotational speed for the intact and the cracked shaft of μ=0.22 at β=π/6

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Fig. 15

Comparison of experimental results of the effect of Ω on λ2 in the neighborhood of the critical rotational speed for the intact and the cracked shaft of μ=0.22 at β=π/6

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Fig. 16

Comparison of experimental results of the effect of Ω on the ratio of λ2 to λ1+λ2 in the neighborhood of the critical rotational speed for the intact and the cracked shaft of μ=0.22 at β=π/6

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Fig. 17

Comparison of experimental results of the effect of Ω on POM1 slope at neighborhood of the critical rotational speed for the intact and the cracked shaft of μ=0.22 at β=π/6

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Fig. 18

Comparison of experimental results of the effect of Ω on POM2 slope in the neighborhood of the critical rotational speed for the intact and the cracked shaft of μ=0.22 at β=π/6

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