A Formula for Determining Limit Noninterference Curvature in Pure Rolling Conjugation Gears by Using Geometro-Kinematical Concepts

Abstract

Pure rolling conjugation gears are very useful in the cases where lubrication is difficult to implement, such as in cryogenic and/or vacuum environments, and at slow operating speeds. The main problem confronted in the design of the pure rolling conjugation gears is to determine the limit noninterference curvature of one gear when the curvature of the conjugate gear is prescribed. The way of solving this problem becomes very complicated when using the conventional concepts from the classical differential geometry. However, when using the geometro-kinematical concepts from the theory of conjugate surfaces, this problem can be solved explicitly and simply. In this paper, these concepts are introduced, and a closed-form formula for determining the limit noninterference curvature is derived. A numerical example is cited.