Post-resonance backward whirl in accelerating cracked rotor systems

Rotating machinery are known to exhibit backward whirls (BW), which means that the rotating system precesses in the direction opposite to that of its rotation. Since backward whirl is an important characteristic of the dynamic response that almost always points to significant problems and degradations within the system, it is of high interest to study, characterize and predict this phenomenon. To this end, the Campbell diagram is used to predict BW rotational speeds at steady-state operations of rotor systems to precede the critical forward whirl (FW) rotational speeds (i.e., pre-resonance BW). Still, the BW phenomenon in rotor systems that exhibit recurrent passage through critical rotational speeds during startup and coast down operations has not been fully studied and described in the literature. Notably, a recent study of startup and coast down operations found backward whirl orbits appearing immediately after the passage through the critical FW rotational speed (i.e., post-resonance BW). The difference between the well-known pre-resonance BW and this new kind of post-resonance BW phenomenon is further investigated in this paper for rotor systems with an open crack and anisotropic bearings. In addition, Full Spectrum Analysis (FSA) is employed to capture the BW zones in both numerical and experimental data. A finite element model of the cracked rotor-bearing-disk system is employed here to obtain the linear-time-variant (LTV) equations of motion for the considered system. The whirl response is obtained by the numerical integration of the LTV equations of motion. From results obtained from three different rotor configurations it is observed that the post-resonance BW has a different dynamical behavior compared with the pre-resonance BW. Furthermore, the application of the FSA has confirmed the existence of post-resonance BW zones in both numerical and experimental whirl responses. Successful application of the FSA for capturing the post-resonance BW zones of rotational speeds in the experimental response suggests that it has the potential to be a used as a powerful tool for BW-based crack detection.