Abstract
Abstract This paper presents a gear pair mechanism, a pinion, and a gear with conical teeth. The gear, or generating surface, has conical teeth distributed on a cylindrical surface. The purpose here was to present a mathematical model and equation for meshing of the proposed gear with conical teeth. A simple method using gear theory was used to determine a generated surface that meshes with the generating surface. The mathematical model of the generated surface can be obtained by the envelope of the family of the generating surfaces. As an example, the proposed gear pair for a gear ratio of 4:3 was demonstrated through the aid of the proposed mathematical model. Based on the geometrical models presented, the author varied the conical angle of the proposed gear between 0 and 20° and examined their contact stresses and deformation. Results showed that the minimum von-Mises stress was at the conical angle of 15° and the minimum deformation was at the conical angle of 17°. If the given parameters are over the dimensional limit of the generating surface, the equation of meshing of generated surface cannot exist. The condition of the dimensional limit was determined in this paper. Results from these mathematical models should have applications in the design of gear mechanism.
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