Parametric instability of a rotor-bearing system with two breathing transverse cracks

When the rotor rotates at a constant speed, the transverse crack opens and closes alternatively, due to gravity, and thus a “breathing effect” occurs. This variance in shaft stiffness is time-periodic, and hence a parametrically excited system is expected. The parametric excitation from the time-varying stiffness causes instability and severe vibration under certain operating conditions. Current research mostly focused on the rotor with single transverse crack. There are few studies on the multi-cracked rotor system. In fact, the interaction between the multiple parametric excitations with various phasing and amplitude, which are induced by the multiple breathing transverse cracks, would make the instability behavior of the system differ distinctly from that of the single cracked rotor system. Moreover, how the instability regions change with various crack breathing mechanisms should also be investigated. Thus, the parametric instability of a rotor-bearing system with two breathing transverse cracks is studied in the paper. First, the finite element equations of motion are established for the cracked rotor system. Two types of crack breathing mechanisms, of which one is more accurate (new) and the other is empirical (old), are adopted in the finite element formulation. Then, a generalized Bolotin's method is introduced for determining the boundaries of the primary and secondary instability regions. Based upon these, instability analysis for a practical used rotor-bearing system with single and two cracks are conducted, respectively. The instability regions induced by the single transverse crack with new and old breathing mechanisms are compared with each other. For the two-cracked rotor system, the variations of the unstable boundaries with crack depths, orientation angles and positions are observed and discussed in detail. It is shown from the results that the dynamic instability of the two-cracked rotor-bearing system indeed have some unique features that differ from that of the single cracked rotor system.

► Parametric instability of a rotor system with two breathing cracks is studied.
► Variations of instability boundaries with crack parameters are observed.
► Estimated unstable speeds are relatively high if new breathing crack is adopted.
► Crack orientation angle and relative position significantly affect the instability.
► The results are useful for condition monitoring of cracked rotor system.