On the Spring Characteristics of a Ball Bearing : Extreme Characteristics with Many Balls

In this paper, a theoretical analysis of the radial spring characteristics of a ball bearing is presented, based on the studies by Perret/Meldau. We make clear 1) an improvement of the non-dimensional expression proposed in the former papers, 2) mean characteristics of fluctuation due to the change of configuration of balls, expressed as functions of a single variable: [radial clearance/(radial load/number of balls)2/3], and their approximate formulae (accuracy of about 0.2%), 3) exact solution when only two balls are loaded and 4) modification of the above results (2) by a function of number and revolution angle of balls, which is available for general cases. Also numerical examples of the motion of inner ring and the differential stiffness are shown.