Full Spectrum Analysis for Studying the Backward Whirl in Accelerated Rotor Systems

The backward whirl (BW) phenomena in intact and cracked rotor systems that exhibit recurrent acceleration and deceleration during startup and coast down operations has not been well-studied in the literature. However, for startup and coast down operations during which a frequent passage through critical forward whirl (FW) speeds takes place, the BW orbits are found to be immediately captured after the passage through these critical FW rotational speeds. The zones of BW orbits are observed to be significantly affected by the appearance of crack damages that are accompanied with isotropic or anisotropic bearings at the shaft supports. The 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 numerical simulation. The obtained LTV mathematical model represents a nonlinear dynamical model of the system. Consequently, the full spectrum analysis (FSA) is successfully employed here to the numerical simulation and the experimental whirl responses of the considered system to confirm the existence of the BW zones of shaft rotational speeds that exist after the passage through the critical and subcritical FW whirl rotational speeds. The obtained results for the intact and cracked rotor systems with anisotropic bearings verify the robustness of the FSA as a powerful tool of capturing the BW zones in cracked rotor systems, especially in the experimental whirl response.