Effect of Angular Acceleration and Unbalance Force Orientation on the Backward Whirl in Cracked Rotors

Rotors have wide applications in several aerospace and industrial heavy-duty systems. In most of these applications, the rotating system reaches its steady state operational speed after the passage through at least one of its critical rotational speeds. In real-life applications, the probable appearance of a residual slight unbalance in the system could cause an elevation in vibration amplitudes at the critical rotational speeds. Accordingly, propagation of cracks in rotating shafts usually influences the level of these vibration amplitudes during start-up and cost-down operations. For such rotating systems, the critical whirl speeds are usually associated with forward and backward whirl responses where it has been always assumed that the backward whirl zone should precede the forward whirl zone. Here, two configurations of cracked rotor-disk systems are considered to study the effect of the angular acceleration and the unbalance force vector orientation with respect to the crack opening direction on the whirl response at the backward whirl zone of rotational speeds. The obtained numerical simulation results are verified through a robust experimental testing for system startup operations. The backward whirl zone is found here to appear immediately after the passage through the critical forward whirl rotational speed. The onset of the backward whirl is also found to be associated with a sharp drop in vibration whirl amplitudes. This backward whirl zone is found to be significantly affected by the unbalance force angle vector orientation and the shaft angular acceleration. More importantly, this zone of backward whirl orbits is not found to be preceding the critical forward whirl zone for the considered cracked shaft-disk configurations.