Load–Displacement Relationship of a Ball Bearing With Axial, Radial, and Angular Displacements for Both the Inner and Outer Rings

This paper deals with the load–displacement relationship of a ball bearing with axial, radial, and angular displacements for both the inner and outer rings. First, the expressions for the load–displacement relationship of ball bearings with any number of balls under the combined axial, radial, and moment loads were presented by using a system in which both the inner and outer rings are allowed to move in the axial, radial, and angular directions. Second, the presented expressions were compared with Jones' expressions (which are typical conventional expressions for the load–displacement relationship), then the range of application of Jones's expressions were elucidated. Third, the relative axial displacement, the relative radial displacement, and the relative angular displacement of a miniature ball bearing type 692 under the combined axial, radial, and moment loads were calculated. Finally, it was shown that the relative angular displacement in the case with no inner ring angular displacement is R_i/R_o times the relative angular displacement in the case with no outer ring angular displacement, in which R_i and R_o are the radii of the inner and outer race curvature center loci.