Mathematical model of a stepped triple circular-arc gear

An imaginary rack cutter with stepped triple circular-arc tooth profile is presented. The concept of stepped triple circular-arc tooth comes from the standard Chinese double circular-arc tooth profile and involute tooth profile. Based on the proposed tooth, a mathematical model of the meshing principles of a gear meshed with a pinion is developed for an imaginary triple circular-arc teeth rack cutter. The developed geometric models of the pinion and the gear are used to investigate the contact stress of stepped triple circular-arc tooth via finite element analysis. A structural load is assumed to act on a pinion of the proposed tooth. The goal of the current study is to investigate the von-Mises stress for one tooth contact pairs. Using the mathematical models developed, variation of the angular velocity is investigated according to the obtained geometric modeling of the designed gear meshing when assembly errors are present. The influence of misalignment on variation of the angular velocity is also been investigated. As an example, a spur gear with a gear ratio of 3:4 is presented.