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.
Nonlinear Dynamic Analysis of a Cracked Rotor-Bearing System With Fractional Order Damping
Research Institute of Diagnostics
Xi'an Jiaotong University,
Department of Electrical and
Utah State University,
Logan, UT 84322
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.
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Cao, J., Xue, S., Lin, J., and Chen, Y. (December 19, 2012). "Nonlinear Dynamic Analysis of a Cracked Rotor-Bearing System With Fractional Order Damping." ASME. J. Comput. Nonlinear Dynam. July 2013; 8(3): 031008. https://doi.org/10.1115/1.4023010
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