A logarithmic profile is an essentially optimal geometry for rolling machine elements such as bearing rollers and raceways. Under most conditions of loading, it yields less stresses to give longer endurance. Lundberg first suggested the basic profile, and some researchers followed him by modifying it to satisfy engineering requirements. In this paper, the authors propose a mathematical optimization method for various profiles including a logarithmic one in roller bearing applications. Moreover, rolling contact fatigue life tests are carried out to make a comparison among logarithmically-crowned, standard partially-crowned and modified partially-crowned rollers. Results show that the logarithmic and modified partially crowned rollers are comparable in fatigue life, although the logarithmic rollers require less working effort to process the crowning.

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