On the Critical Speeds with Peculiar Modes of Vibration

Abstract

When single-row radial ball bearings are used the stiffness of a shaft has non-symmetrical, non-linear spring charactristics. In experiments using such a shaft mounting one disc, several critical speeds of peculiar modes of vibration occurred with a critical speed of sub-harmonic oscillation of order 1/2. These critical speeds consist of two vibrations having the same frequencies pi and pj as the natural frequencies of this system. It is remarkable that the absolute value of sum of or difference in two frequencies pi and pj is equal to the rotating speed of the shaft. In numerous experiments with several kinds of shafts, this relation between pi and pj always held at these critical speeds. For a system having linear spring characteristics or a system with one degree of freedom, this type of critical speed does not appear ; it occurs only in the system with multiple degrees of freedom and non-linearity.