Mathematical model of the worm wheel tooth flank of a double-enveloping worm gear

Abstract

This paper presents a novel method for determining the worm wheel tooth flank surface. The worm wheel model is developed according to the theory of gearing and the gear generation mechanism. Two cases are considered simultaneously. In one case, the worm wheel is generated by the hourglass worm hob with a rectilinear tooth axial profile, while in the other case, it is generated with an arc (concave and convex) tooth axial profile. The contact lines between the hourglass worm hob and worm wheel surfaces are determined. Surface formation generated during processing by the tool external edge and formation so-called region II was presented. The manner of separating regions on the worm wheel tooth flank surface was developed. Because the difference between the parameters that describe the tool side surface, only the flowchart of the algorithm for determining the worm wheel tooth side surface of rectilinear profile is presented. For the arc profile, the algorithm flowchart is analogous. The proposed procedures and the developed computer-aided worm wheel generating program allow obtaining complete mathematical representation of worm wheel tooth flank surface.