PhD. Transactions of Machine Elements Division. Lund 1976

Abstract:

The whirling of a statically unbalanced rotor due to period disturbances of the driving torque is studied. External and internal viscous damping and internal hysteric and structural damping are considered. The methods of asymptotic expansion by Krylov and Bogolyubov is applied to derive solutions for the non-stationary and stationary state.

Numerical results showing transitions through secondary critical speeds and maximum amplitude diagrams are given. The existence of unstable solutions at the presence of internal damping is discussed. Some regularities between the whirl configuration and the frequency of the torque disturbance are shown.

To verify the calculations a test apparatus was built. The agreement between the theory and the test is quite satisfactory.

It is shown that the amplitude of a forward whirl is larger than that of a backward whirl at equal conditions and that a forward whirl becomes more dangerous the closer to the fundamental critical speed occurs. It also appears that the influence of internal damping is the largest at backward whirls.

Owing to the narrow frequency band of a secondary critical speed, the amplitude of a whirl becomes very muck reduced already at a moderate deviation from the stationary condition of the rotational speed.

This means that the non-stationary solution is of great interest.