The whirling frequency of high speed shaft with torsional effect

Abstract

The study on whirling frequency of high speed shaft is necessary as the current trend of rotor system is to operate at high speed. Fur-thermore most studies on whirling frequency of shaft have developed formulations that are based on the Timoshenko beam theory that neglects the torsional effect of shaft. In this research, the effect of boundary condition and slenderness ratio on the whirling frequency behavior of high speed shaft is studied. A finite element formulation for the whirling frequency problem of shaft has been developed based on the 5 degree of freedom per node element that includes the torsional degree of freedom. The derived Mathieu-Hill equation is solved using the Bolotin’s method. It was found that the effect of torsional degree of freedom on the whirling frequency behaviour is significant especially for shaft at high speed where at the spin speed of 20000 RPM, the difference between the whirling frequencies corresponds to FEM model that considers torsional degree of freedom and model that does not consider can be as high as 45.3%.