Stability and Stability Degree of a Cracked Flexible Rotor Supported on Journal Bearings

Abstract

This paper investigatesthe stability and the stability degree of a flexible cracked rotor supported on different kinds of journal bearings. It is found that no matter what kind of bearings is used, the unstable zones caused by rotor crack locate always within the speed ratio 1 -< fl < _ when gravity parameter Ate 2nWz> !.0; and locate always within the speed ratioAge is the crack stiffness ratio, N= i, 2, 3, 41 5 .-. and fl == ( 1 + 2a_ 1/2 lion, where no unstable zones caused by rotor crack exist. ' t _/ • When 0.1 < W z < 1.0, there is a reOutside the crack ridge zones, the rotor crack has almost no influence on system/s stability and stability degree; while within the crack ridge zones, the stability and stability degree depend both on the crack and sys.temrs parameters. In s6me cases, the system may still be stable even the crack is very large. For small gravity parameter (We< 0.1), the mass ratio = has large influence on the position of unstable reg/on, but its influence on the stability degree is small. The influence of fixed Sommeffeld number S O on the crack stability degree is small although $o has large influence on the stability degree of untracked rotor.

Damping by parametric excitation in a set of reduced-order cracked rotor systems

“…Earlier, Floquet's method was used by Huang et al [12], Gasch [13], Meng and Gasch [14], Fu and Zheng [15], and Dai and Chen [2] to calculate stability maps of cracked rotors.…”

Bifurcation and chaotic response of a cracked rotor system with viscoelastic supports

“…The dynamic stability of cracked rotors also attracted the attention from the researchers in this field. Floquet theory was widely used in the stability analysis [20][21][22][23][24]. Research results show that a cracked rotor system may lead to instability when the rotation speed of the shaft reaches the certain values of the system's critical speeds.…”

Effects of a crack on the stability of a non-linear rotor system

“…Consequently, the detection of variations in the shaft's orbital movements at one-half and one-third of the first critical speed can be used as a diagnostic tool. Similarly, the influence of a single transverse crack on the stability of the periodic response of a rotor has been studied by various researchers [4,[16][17][18][19][20][21][22][23]. As an example, Gasch [4] studied the influence of imbalance on the stability of a simple rotor with a transverse crack, and indicated that increased damping reduces the extent of the unstable region, whereas increased crack depth has the opposite effect.…”

“…They also indicated that a cracked rotor with high damping is normally stable, even when the crack depth increases. In order to determine the instability boundaries of a nonlinear cracked rotor system, the Floquet theory is generally used [20,22,23]. This approach requires the numerical calculation of the state transition matrix over a period of motion [20,22].…”

“…In order to determine the instability boundaries of a nonlinear cracked rotor system, the Floquet theory is generally used [20,22,23]. This approach requires the numerical calculation of the state transition matrix over a period of motion [20,22]. However, most existing studies that takes into account the stability of a cracked rotor system, only considers the first threshold speed limits and/or the first instability region beyond the first critical speed [23].…”