Curvature Interference Characteristic of Plane Worm Gear in Offsetting Cylindrical Worm Drive

Abstract

In this paper, the theory of the curvature interference characteristic is well established for the plane worm gear in the offsetting cylindrical worm drive. The offsetting cylindrical worm drive investigated in this paper is composed of an Archimedes cylindrical worm having the asymmetric tooth profile and a plane worm gear. The equations of the tooth surfaces, the meshing function, the meshing limit function, and the curvature interference limit function are all obtained for the worm drive. In accordance with the geometric construction and the elimination method, the first type of limit point on the curvature interference limit line is determined by iteratively solving the established nonlinear equation set. The result of the numerical case demonstrates that the curvature interference limit line on the worm gear tooth surface and its conjugate line on the worm helicoid are all located out the meshing zone of the worm drive. The meshing zones of the worm drive are located on the non-undercutting side. The part most likely to be undercut for the plane worm gear is located at the tooth root of the toe of its concave surface.