Vibration of Rotor Based on Ball Bearing : 2nd Report, Static Stiffness of Ball Bearing Containing a Small Number of Balls

Abstract

An analysis of static stiffness of a ball bearing which contains three and/or four balls is made as an extension of the former report. Though the bearing is far from being useful, it provides us with one of the most important models in examining the spring property inherent in this mechanism. All the effects due to the irregularity usually arising in the course of manufacturing and assembling are taken up for consideration, while the exciting forms of oscillation, as suggested in the former report, are actually represented by this ball bearing which is the most simple practical one. The excitation in the direction of rotor axis is motivated variously : (a) by simple force due to inner ring rotation, (b) by displacement due to rotation of inner ring and balls, (c) by parametric as a Mathieu system due to ball rotation and (d) by variable clearance due to inner ring rotation. Correspondence of exciting form to its cause was disclosed clearly by means of an approximated analytical expression. For instance, it is possible that a mounting error, e.g. an obliqueness of rings, constitutes an important origin of oscillation, especially in the direction of rotor axis, i.e. the so-called abnormal vibration.