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Research Papers

Nonlinear Dynamic Analysis of a Cracked Rotor-Bearing System With Fractional Order Damping

[+] Author and Article Information
Junyi Cao

caojy@mail.xjtu.edu.cn

Jing Lin

State Key Laboratory for Manufacturing
Systems Engineering,
Research Institute of Diagnostics
and Cybernetics,
Xi'an Jiaotong University,
Xi'an 710049, China

Yangquan Chen

Center for Self-Organizing and
Intelligent Systems,
Department of Electrical and
Computer Engineering,
Utah State University,
4120 Old Main Hill,
Logan, UT 84322

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the Journal of Computational and Nonlinear Dynamics. Manuscript received September 10, 2012; final manuscript received November 2, 2012; published online December 19, 2012. Assoc. Editor: J. A. Tenreiro Machado.

J. Comput. Nonlinear Dynam 8(3), 031008 (Dec 19, 2012) (14 pages) Paper No: CND-12-1142; doi: 10.1115/1.4023010 History: Received September 10, 2012; Revised November 02, 2012

Fatigue cracking of the rotor shaft is an important fault observed in the rotating machinery of key industries, which can lead to catastrophic failure. Nonlinear dynamics of a cracked rotor system with fractional order damping is investigated by using a response-dependent breathing crack model. The fourth-order Runge–Kutta method and tenth-order continued fraction expansion-Euler (CFE-Euler) method are introduced to simulate the proposed system equation of fractional order cracked rotors. The effects of the derivative order of damping, rotating speed ratio, crack depth, orientation angle of imbalance relative to the crack direction, and mass eccentricity on the system dynamics are demonstrated by using a bifurcation diagram, Poincaré map, and rotor trajectory diagram. The simulation results show that the rotor system displays chaotic, quasi-periodic, and periodic motions as the fractional order increases. It is also observed that the imbalance eccentricity level, crack depth, rotational speed, fractional damping, and crack angle all have considerable influence on the nonlinear behavior of the cracked rotor system. Finally, the experimental results verify the effectiveness of the theoretical analysis.

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Figures

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Fig. 1

Jeffcott rotor system with three coordinate systems: (a) Jeffcott rotor model and (b) projection of the crack cross section along z direction

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Fig. 9

Bifurcation diagrams of X and Y versus s for r=0.5

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Fig. 10

Rotor orbit, Poincaré map, and power spectrum for s=0.3

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Fig. 11

Rotor orbit, Poincaré map, and power spectrum for s=0.51

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Fig. 2

Bifurcation diagrams of X versus r

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Fig. 3

Rotor orbit, Poincaré map, and power spectrum for r=0.28 and s=0.65

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Fig. 4

Rotor orbit, Poincaré map, and power spectrum for r=0.7 and s=0.65

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Fig. 5

Rotor orbit, Poincaré map, and power spectrum for r=1.1 and s=0.65

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Fig. 6

Rotor orbit, Poincaré map, and power spectrum for r=0.35 and s=2.0

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Fig. 7

Rotor orbit, Poincaré map, and power spectrum for r=0.7 and s=2.0

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Fig. 8

Rotor orbit, Poincaré map, and power spectrum for r=1.3 and s=2.0

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Fig. 12

Rotor orbit, Poincaré map, and power spectrum for s=0.65

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Fig. 13

Rotor orbit, Poincaré map, and power spectrum for s=0.8

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Fig. 14

Rotor orbit, Poincaré map, and power spectrum for s=1.1

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Fig. 15

Rotor orbit, Poincaré map, and power spectrum for s=2.0

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Fig. 16

Rotor orbit, Poincaré map, and power spectrum for s=3.0

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Fig. 17

Bifurcation diagrams of X and Y versus β

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Fig. 18

Rotor orbit, Poincaré map, and power spectrum for β=90 deg

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Fig. 19

Rotor orbit, Poincaré map, and power spectrum for β=150 deg

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Fig. 21

Bifurcation diagrams of X and Y versus s for e¯=1.0,β=0 deg,k¯=0.15

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Fig. 29

Rotor orbit and power spectrum at speed 1875 rpm (s = 0.78)

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Fig. 30

Waterfall of the cracked rotor in horizontal direction

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Fig. 31

Waterfall of the cracked rotor in vertical direction

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Fig. 20

Power spectrum at e¯=0.1,0.5,0.9

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Fig. 22

Bifurcation diagrams of X and Y versus k¯ for s=0.6,e¯=0.1,ζ=0.01

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Fig. 23

Rotor orbit, Poincaré map, and power spectrum for k¯=0.25

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Fig. 24

Rotor orbit, Poincaré map, and power spectrum for k¯=0.35

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Fig. 25

Rotor orbit, Poincaré map, and power spectrum for k¯=0.4

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Fig. 26

Rotor orbits for different crack depth k¯=0.15,0.2,0.3

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Fig. 27

Test rig of the rotating equipment

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Fig. 28

Rotor orbit and power spectrum in the neighborhood of the 1/2 first critical speed (1260 rpm)

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