Torsional Vibration of a Rotating Shaft in Passing through the Critical Speed of Whirling Vibration.

When a flexible shaft carrying a rotor passes through the critical speed of shaft whirling, the flexible shaft experiences not only bending but also torsional vibration. The torsional vibration may resonate at a certain rotational speed. Analyses for the precise torsional vibration require equations of motion with an accuracy to the second-order of shaft deformations, shaft deflection, angle of deflection, and torsion. The shaft is assumed to be driven with a constant angular acceleration. The present numerical solutions demonstrate that a torsional vibration occurs immediately after the rotating shaft passes through the critical speed of shaft whirling. The rotational speed where the torsional vibration grows is nearly equal to the sum or difference of the natural angular frequency for whirling and that for torsion.