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TECHNICAL PAPERS

Detection of a Rotor Crack Using a Harmonic Excitation and Nonlinear Vibration Analysis

[+] 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

Tsuyoshi Inoue

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

J. Vib. Acoust 128(6), 741-749 (Jun 09, 2006) (9 pages) doi:10.1115/1.2346693 History: Received December 02, 2005; Revised June 09, 2006

Detection of a rotor crack based on the nonlinear vibration diagnosis using harmonic excitation force is investigated. The open-close mechanism of crack is firstly modeled by a piecewise linear function. In addition, another approximation crack model using a power series function that is convenient for the theoretical analysis is used. When the power series function crack model is used, the equations of motion of a cracked rotor have linear and nonlinear parametric terms. In this paper, a harmonic excitation force is applied to the cracked rotor and its excitation frequency is swept, and the nonlinear resonances due to crack are investigated. The occurrence of various types of nonlinear resonances due to crack are clarified, and types of these resonances, their resonance points, and dominant frequency component of these resonances are clarified numerically and experimentally. Furthermore, nonlinear theoretical analyses are performed for these nonlinear resonances, and it is clarified that the amplitudes of these nonlinear resonances depend on the nonlinear parametric characteristics of rotor crack. These results enable us to detect a rotor crack without stopping the system during on-line operation.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

Theoretical model of a cracked rotor. (a) DOF inclination motion model. (b) Restoring characteristics.

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Figure 2

Second power approximation of My′ (dashed line: PWL model, solid line: Second order PS model)

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Figure 3

The relationship between dimensionless parameters Δ1, Δ2 of PWL model and dimensionless parameters Δ, ε2 of PS model

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Figure 4

Frequencies variations of resonances (● shows the resonance that occurs due to the second-order nonlinear parametric characteristic of a crack, 엯 shows the resonance that do not occur in the second order PS model, ◻ shows the resonance that occurs due to the linear parametric characteristic)

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Figure 5

Resonance curves (ω=3.0)

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Figure 6

The variation of frequencies of vibration components in resonance ω−Ω=pf

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Figure 7

Resonance curve of resonance ω−Ω=pf,pb (solid lines represent analytical solutions, and symbols 엯 and ● show the numerical results by Eq. 4 of the PWL model and Eq. 7 of the PS model)

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Figure 8

Resonance curve of resonance ω+Ω=pf,pb (solid lines represent analytical solutions, and symbols 엯 and ● show the numerical results by Eq. 4 of the PWL model and Eq. 7 of the PS model)

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Figure 9

Resonance curve of −ω+Ω=pf,pb (solid lines represent analytical solutions, and symbols 엯 and ● show the numerical results by Eq. 4 of the PWL model and Eq. 7 of the PS model)

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Figure 10

Resonance curve of resonance 2ω−Ω=pf,pb (solid lines represent analytical solutions, and symbols 엯 and ● show the numerical results by Eq. 4 of the PWL model and Eq. 7 of the PS model)

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Figure 11

Resonance curve of resonance 3ω−Ω=pf,pb (solid lines represent analytical solutions, and symbols 엯 and ● show the numerical results by Eq. 4 of the PWL model and Eq. 7 of the PS model)

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Figure 12

Experimental system (shaft length l=730mm and its diameter d=12mm. Disk-rotor position ld=200mm, disk diameter 220mm, and thickness 15.3mm. Crack position lc=460mm, width wc=20mm depth dc=4mm. Sensor position ls=45mm from the disk. Rotating shaft is excited in the horizontal direction at position le=290mm)

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Figure 13

External excitation force (1DOF periodic force can be regarded as the sum of the forward harmonic force +Ω and backward harmonic force −Ω with same amplitudes)

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Figure 14

Resonance curve and resonance frequencies. Experiment, rotational speed ω=400rpm and magnitude of external force is about 8N. 엯 ● ⊗ show maximum amplitudes of experimental results. ● shows the occurrence of resonance due to crack. Solid lines and dashed lines correspond to the lines in the positive part and negative part of Fig. 4, respectively. Notations A, B, C, D, E, and F show resonance points of resonances 2ω−Ω=pf, −ω+2Ω=pb, ω+Ω=pf,−pb, 3ω−Ω=pf, −ω+2Ω=pf and −ω+Ω=pf,−pb, respectively. ⊗ shows the resonances 2Ω=pf,−pb and 3Ω=pf,−pb that occur due to the neglected nonlinear effect of magnetic force. When Ω approaches to ω=400rpm(≈6.67Hz), the vibration becomes large or small because the external force Ω acts as a kind of unbalanced force and increases or decreases the actual unbalanced force.

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