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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.

The paper presents the method of determining geometric contact pattern by using the direct computer-aided design (CAD) method for ideal globoid worm gear in which mounting deviations are considered. The tooth contact analysis was performed for all cycle of worm rotation. Based on the results of temporary contact pattern, graphical characteristics of the contact area size depending on worm position were made. A complete analysis of the correctness of gear meshing can be obtained based on presented method. If the worm or worm wheel is incorrectly designed in terms of the geometry, the meshing simulation of CAD models can indicate the collision. Geometric contact pattern analyses were made at two pressure angles of ideal gear. The analysis of the influence of mounting deviations was done against one selected pressure angle and one gear position.

In this article, a mathematical description of tooth flank surface of the globoidal worm and worm wheel generated by the hourglass worm hob with straight tooth axial profile is presented. The kinematic system of globoidal worm gear is shown. The equation of globoid helix and tooth axial profile of worm is derived to determine worm tooth surface. Based on the equation of meshing the contact lines are obtained. The mathematical description of globoidal worm wheel tooth flank is performed on the basis of contact lines and generating the tooth side by the extreme cutting edge of worm hob. The presented mathematical model of tooth flank of TA worm and worm wheel can be used e.g. to analyse the contact pattern of the gear.

Presented is the method of determining the contact pattern in globoidal worm gear using CAD environment. Contact pattern analysis was performed for the gear with straight tooth profile in the central plane. The influence of the pressure angle on the shape and size of the contact pattern was investigated.