Pardon me for labouring this but I want to
be right (And if I'm also proved to be right, so much the
better, but that's completely unimportant, as always!).

1. The hob is set over at its own helix angle so that it
traverses in a direction parallel to the cut of the teeth. We
agree on this - this is the essence of being able to cut
normal spur gears with manual feed.

2. The blank must rotate one tooth's distance according
to the way the hob's teeth are cutting. We agree on this.
From (1) above, the direction of rotation of this one tooth's
distance is at right angles to the direction of traverse.

3. BUT BUT BUT the axis of the blank is set over at its
own helix angle and therefore to achieve the rotational
speed of (2), the blank's rotational speed must be increased
by 1/cos. We DON'T agree on this, but it seems to me
from a vector analysis of speeds that it must be so.

4. For spur gears, the blank must be geared down by 1/N
from the hob. We agree on this.

5. From (3) and (4), therefore, the blank must be geared
down by 1/(N * cos(Blank's Helix Angle)), and because all
cosines are less than 1, this will mean a slight increase in
rotational speed of the blank. I don't think that we agree
on this (Yet?!).

So, resolving vectorially the movement of the teeth at
right angles to the direction of traverse we'll end up
with (1/(N * cos)) * cos = 1/N

6. However, if we could put ourselves in the position of the
teeth (gaps between the teeth?) being cut, our appreciation
of what is happening to us is the same irespective of whether
a spur gear or a helicla is being cut and that therefore manual
feed is possible, (With, of course, the proviso that manual
irregular feed will result in a difference of quality across the
face of the teeth)


Boo wrote:
In the case of helicals, AIUI the setup is the same with the only
difference that you additionally must angle the blank by the gear's
helix angle wrt the table travel direction. The same relationship in
respect of the rotation speeds applies : AFAIK there is no sin or cos
term in the rotational gearing it's still just 1 / (number of teeth) as
for spur gears.