Analysis of a Self-Tracking Rolling Element Bearing

A novel rolling bearing design, which is patented, is first described and second analyzed with a view to optimizing the bearing parameters. Usually the sides of grooves or ribs guide the rolling elements in ball and roller bearings. By using element-raceway profiles, which are essentially concave–convex, forces can be generated in the two contact regions which: (1) provide positive skew, (2) give stability to the roller motion in response to a disturbing force, and (3) balance lateral traction forces, thus alleviating the need for grooves or ribs. This allows for potential advantages of: (a) up to 50 percent savings in ring material, (b) no need for selective assembly, (c) insensitivity to misalignment, and (d) lighter rolling elements and less centripetal loading effects at high speed. The slip velocities and stress distributions as functions of roller skew are required in order to refine the bearing design parameters. To find the contact stress distributions in the inner and outer element-raceway contacts is not straightforward, as the profiles are non-Hertzian. In this paper an influence function approach is used where the two contact zones are meshed into appropriate grids and a piecewise-linear pressure is assumed to act over each grid element. By superposing the displacements produced by each grid element and equating this to the profiles of the roller and raceway the magnitudes of the pressure acting over each grid element may be found. The forces and moments developed in the contact zones may now be found and used to iteratively refine the initial bearing geometry for optimum performance. Finally, experimental tests are conducted on a prototype self-tracking bearing using a standard tapered bearing as a reference.