A mathematical model of a worm mechanism generated by a conical cutter

In this article, an imaginary conical cutter was used to determine the geometric models of the worm-gear mechanism including a worm and a gear. Mathematical models of the worm and the gear were derived using an imaginary conical cutter and gear theory. Based on the geometric relations between the worm and conical cutter surfaces and between the gear and conical cutter surfaces, the worm and the gear were regarded as an envelope to the family of conical cutter surfaces when they rotated for one cycle. Using the developed mathematical model, the stress analysis of the proposed mechanism was examined. The results show that the von Mises stress and volume of the proposed worm and gear were smaller than those of the conventional worm-gear mechanism. Lastly, a numerical example was used to illustrate the geometric model of a gear and a worm with a gear ratio of 30:1.