Mesh theory of angle modified dual tori double-enveloping toroidal worm drive

In this paper, the meshing theory of the angle modified hourglass worm drive is enriched and developed. The ordinary condition of the angle modification is derived and the physical significance of the modification is interpreted. A normal section methodology is proposed for meshing analysis, which can be used to compute the normal distance near a singular meshing point of a conjugate surface couple. By means of the method and after analyzing the normal transversals, it is specified that the worm helicoid, the nominal former contact zone and the new contact zone intersect each other along the locus of singular points of the instantaneous contact lines of an angle-modified worm pair. As a result, it is explained clearly that those three osculate each other but the osculations are different in degree. Moreover, the mechanism of removing the twice-contacted zone from the worm gear tooth surface is clarified and the reason of shortening the worm working length is also elucidated. With the help of the theory described in the present paper and the thorough and systematic research on the relevant meshing characteristics, the angle modified dual tori double-enveloping toroidal worm drive has been shown to be an excellent new-fashioned hourglass worm set.