Hi BlackBird, so yeah check out the PDF that Brian links to above for especially where it shows the worm gear contact area (section titled "Worm Gear Contact") - I think for the red area you would want to have an extrusion for that area rather than actually bending any kind of sweep or helix like shape at all.

The spur gear profile plug-in that is mentioned above is available here (actually I think Petr wrote it, not me):
http://kyticka.webzdarma.cz/3d/moi/#SpurGear

See the attached file for an example - there I created a spur gear profile, scaled it and cut it into half and then used the half piece with boolean difference on your red part to make the bottom part of the shape to have an extruded gear form. The boolean will cut up the red part into multiple pieces and then just delete the pieces you don't want.

This attached example does not have the proper number of teeth but I hope it shows you the general kind of structure that I think you would want to make, with just an extrusion of a gear on your red piece rather trying to have another helical shape around there.

I think you only need one piece with a sweep done on it for making the wormthread, and then basically flat gears (meaning extruded from 2D shapes) for the other part, not another wormthread for the second part.

- Michael