Tooth flank modification theory of dual-torus double-enveloping hourglass worm drives

In this paper, the theory of tooth flank modification is enriched and developed for a double-enveloping toroidal worm drive. The goal and significance of the modification are expounded from the point of view of changing the tooth flank configuration for the worm gear pair. It is pointed out that the constant center distance modification, the constant transmission ratio modification, and the combination of the previous two are the convenient and reasonable modification strategies. All the corrected hourglass worm pairs, attained by employing the preceding modification methodology, can be divided into two fundamental types: the type I worm pair and the type II worm pair, from the perspective of the meshing behavior. The division criterion of the worm drive type is moreover provided on the basis of the value range of the modification parameters in this study. The meshing characteristics of the two types of the modified globoidal worm drive are summarized in detail. The results indicate that the type II worm gearing with slight modification should be the preferred style for the double-enveloping toroidal worm drive.

► Proofs of the division criteria for the transmission type of a double-enveloping toroidal worm pair.
► A configuration theory of the tooth flank of a worm gear based on the theory of trigonometric equations.
► Explanation for a type II worm wheel to avoid the curvature interference.
► A modified dual-torus double-enveloping hourglass worm drive, which is produced under the direction of the proposed theory.