Response of a Rotating Shaft to Uniaxial Random Excitation

Abstract

Random vibrations are considered for a Jeffcott rotor subject to uniaxial broadband random excitation by a lateral force along one of its transverse axes. Exact analytical solution for mean square responses is obtained which provide quantitative description of two effects: the magnification of mean square whirl radius due to rotation; and the increasing mean square response along the nonexcited direction with increasing rotation speed, that is, the spread of vibration to all directions around the shaft. The latter effect clearly corresponds to the approaching forward whirl of the shaft approaching its instability threshold; it can be used for the on-line evaluation of the rotor’s stability margin from the simple processing of its measured response signals as demonstrated by direct numerical simulation.