Summed-and-Differential Harmonic Oscillations of an Unsymmetrical Shaft

Abstract

We have already reported about subharmonic oscillations of an unsymmetrical shaft with nonlinear spring characteristics, and made clear that unique vibration phenomena which were not observed in a shaft with circular cross section appeared. Similar phenomena appear in summed-and differential harmonic oscillations of the same system. We show analytically in this report that the following types of resonance curves are obtained depending on the degrees of nonlinearity and unbalance. They are a stable resonance curve of hard spring type, a stable resonance curve of soft spring type, an unstable region where unstable vibration appears, and the case where no summed-and-differential harmonic oscillation occurs. We made experiments with an unsymmetrical shaft supported by single-row deep groove ball bearings. The above-mentioned resonance curves were obtained in experiments.