Forward and Backward Whirling of a Rotor with Gyroscopic Effect

Abstract

The determination of whirling frequencies of high speed turbines is always challenging in rotor dynamics. The natural frequencies of a Jeffcott rotor are split in the presence of gyroscopic effect. It is quite well known that the lower branch corresponds to the backward whirl and the upper branch corresponds to forward whirl. The forward whirl mode of the rotor has been observed experimentally, however, the backward whirl has not been observed. In this study it is shown that the backward whirl can be observed when the rotor is coasting down to rest from above the critical speed corresponding to the backward whirl. In order to illustrate the forward and the backward critical speeds of a simple Jeffcott rotor, the natural frequencies are obtained analytically for the second natural frequency of the system because of the large gyroscopic effect present in that mode. An experimental set up was used to verify the presence of backward whirl while the rotor is coasting down to rest. The rotor is also simulated using finite element method by ANSYS, and Campbell diagram is plotted. The analytical, experimental and ANSYS simulations confirm the existence of the backward whirl when the rotor is coasting down.