Subharmonic Rotor Instability Due to Elastic Asymmetry

Experimental studies were made of the instabilities of the lateral motion of a vertical rotor consisting of an asymmetric shaft having a central disk, a built-in upper bearing support, and an asymmetric set of springs for the lower bearing support. This system is statically indeterminant, and the motion of the disk is described by two coupled Hill equations. Major instabilities were observed when the rotational driving speed was near the maximum or minimum natural frequencies of lateral vibration. Very weak instabilities were observed at one-half of the above frequencies. These subharmonic instabilities are caused by inherent instabilities in the ideal system and also by bearing misalignment. Another very weak instability due to unbalance was observed at one-third of the natural frequencies. The subharmonic instabilities were observed by monitoring the motion of the central mass with two capacitance probes and displaying this motion on an oscilloscope. They were accurately predicted by first and second order perturbation-variation analyses using a method proposed by C. S. Hsu.