Closed-form analytical solutions for calculation of loads and contact pressures for roller and ball bearings

• Extend Persson's continuous contact solution to discrete contact of bearing rollers.
• Develop closed-form solutions for roller loads in cylindrical roller bearings.
• Develop closed-form solutions for roller loads in spherical roller bearings.
• Conduct 2-D and 3-D finite element analyses to validate closed-form solutions.
• Present a methodology for bearing fatigue analyses based on closed-form solutions.

Closed-form load distribution solutions for calculation of the loads exerted by the rolling elements on the outer raceway in cylindrical and spherical roller bearings under radial loading are proposed. The analytical solutions are derived from the non-conforming contact solution of Hertz and the conforming contact solution of Persson. The maximum pressures due to the maximum loads of the rolling elements calculated from the analytical solutions are within a few percents of the results from the corresponding two-dimensional and three-dimensional finite element analyses. A simple method to estimate the fatigue lives of bearings based on the analytical solutions is also presented for engineers to compare the fatigue performance of bearings with different designs.