On the Critical Speed Regions of an Asymmetric Rotating Shaft Supported by Asymmetrically Elastic : 1st Report, On the Unstable Regions

Abstract

To make clear the dynamic characteristics of a rotating shaft exactly, we should take into consideration both the asymmetry of a shaft and the elasticity, especially the asymmetric elasticity of supports. The authors considered an idealized model, in which a disk was mounted at the center of a flat shaft with different bending rigidities in two mutually vertical directions corresponding to the principal axes of inertia of the section. The supporting parts of both ends were supported by springs in two vertical directions, as a concentrated masses system, in which masses were concentrated at the central disk part and supporting parts of both ends, and the equations of motion with periodic coefficients were derived in terms of springs. As a first step, analyses were made by the asymptotic method to know what effects would be caused to the unstable regions of this system by the asymmetry of the shaft, the rigidities of the supporting parts and their asymmetry, the internal and external dampings, and others, and in what relation these acted with each other. Some of the results of analyses have been experimentally confirmed.