Logarithmic Profiles of Rollers in Roller Bearings and Optimization of the Profiles

When a bearing roller is in contact with raceways, excessive pressure peaks occur at the ends of the contact rectangles. This is called edge loading. Roller and/or raceway profiles are usually crowned to prevent edge loads. Lundberg developed a logarithmic function for a crowned profile. The profile gives an axially uniform pressure distribution. Johns-Gohar improved the function for the convenience of manufacturing. However, the Johns-Gohar profile yields edge loading when the roller is tilted. In addition, the profile allows no straight portion on the roller surface although it is desirable to have a flat region from the viewpoint of machining. In this study, we modified the Johns-Gohar logarithmic function to exclude edge loading even when the roller is tilted, allowing a flat region. Three parameters, K1, K2 and zm, are introduced into the Johns-Gohar function. K1 is coefficient of load, K2 is ratio of crowning length to effective contact length, and zm is crown drop at edge of effective contact length zone. In addition, a mathematical optimization method is used to efficiently determine a set of the parameters. An optimization problem is considered to minimize the maximum contact pressure Pmax , or to maximize the rolling fatigue life L10. A Rosenbrock method is also adopted as the optimization algorithm. This method requires no evaluation of gradients of the objective function. Pressure distribution is calculated by making use of a multilevel method. Some examples are demonstrated to verify the proposed method for both Pmax and L10.