| Summary: | A logarithmic profile is essentially optimal crowning geometry for rolling machine elements such as bearing rollers and raceways. Although some design methods of the profile have been proposed, they do not refer to the tolerance of the geometry required in engineering applications and in production. This paper shows how to define the tolerance range associated with the optimum roller profile, previously suggested by one of the authors. The overall tolerance is reasonably defined by giving the reduced amount of roller radius at three points so that the von Mises equivalent stress will not exceed a specified limit, where the point locations are not measured from the roller end but from the intersection of the crowning and the chamfer. For the purpose of design usefulness, the tolerance expression is offered in dimensionless form.
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