Acceleration of unbalanced flexible rotors through the critical speeds

The bending vibrational behaviour of a flexible rotor with a continuous mass distribution passing its critical speeds under a driving torque is considered. It is shown that the (non-linear) equations of motion for an actual shaft can be formally traced back to those of a Laval rotor. In this way, the results for a Laval rotor, which, in an earlier publication by the authors 1], have been presented generally for constant load torque can be applied to actual rotors. The system parameters of the Laval rotor merely have to be replaced by the generalized parameters of the respective bending modes. A special study shows that the effect of the torsional flexibility of the shaft on the bending vibrational behaviour is negligible.