The effects of the crack location on the whirl motion of a breathing cracked rotor with rotational damping. (15th May 2019) - Peng, Huichun; He, Qing
Highlights: The finite approach of the Eigen-problem. The effects of the crack position on the stability of the whirl motion. The effects of the crack position on the stiffness. Abstract: The stability analysis based on the root locus method is proposed to study the whirl motion of a breathing cracked rotor in different crack locations. By the multiple scales method, the eigen-value problem of the infinite order complex mode solutions of the breathing cracked rotor system is discussed. The Campbell diagrams, decay rate plots and roots locus plots of the finite approach from 1st order to 41th order complex mode solutions are compared to find that the 5th order finite approach of the complex mode solutions is the most efficient approximation order, which is verified by the ensuing numerical simulation of the transient response of the breathing cracked rotor system. The effects of the crack position on the stability of the whirl motion of the breathing cracked rotor are analyzed by the decay rate plot of the fifth order approach. The result shows that the crack position affects the super critical resonance region from the 2nd order to the 5th order complex mode, and has no effects on the 1st order complex mode of the whirl motion, and the vibration stability of the subcritical and critical resonance region are less affected. The super critical instability of the system in the crack position at 2 l / L = 0.75 is most affected by rotational damping. These results provide practical references for fault diagnosis, condition monitoring and dynamic balance control technology of heavy loading rotating machinery.