Logarithmic Profile of Rollers in Roller Bearing and Optimization of the Profile

Abstract

When a bearing roller is in contact with raceways, excessive pressure peaks occur at the ends of the contact rectangles. They are called edge loading. Roller and/or raceway profiles are usually crowned to prevent edge loads. Lundberg developed a logarithmic function as a crowned profile. The profile gives an axially uniform pressure distribution. Johns-Gohar improved the function for convenience of manufacturing. However, the Johns-Gohar profile yields edge loading when the roller is tilted. Also, 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. These have the following meanings : K1 : coefficient of load, K2 : ratio of crowning length to effective contact length, Zm : 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 adopted as the optimization algorithm. The 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.