On the Subharmonic Oscillations of Unsymmetrical Shafts

Abstract

When a rotating shaft is supported by single-row deep groove ball bearings, the restoring force of the shaft has nonlinear spring characteristics. In the case of an unsymmetrical shaft, the subharmonic oscillation of order 1/2 of the forward precession shows unique features owing to the influence of some of the nonlinear components which have no effects on such an oscillation of a symmetrical shaft. By changing the assembly of the experimental apparatus and the degree of unbalance, we could obtain three kinds of resonance curves concerning this subharmonic oscillation. They are the following: a stable resonance curve of the hard spring type, an unstable region where unstable vibration with frequency 1/2·ω(ω: angular velocity of the shaft) appears, and the case where no subharmonic oscillation appears. In the analysis of such an unsymmetrical shaft system with nonlinear characteristics, the method utilizing normal coordinates cannot be used. We can explain such phenomena theoretically by the method proposed in this paper.