Hello Kirk,
I wonder how much fuss you guys are making about gear cutting.

Small machine (table mill):
Last year I bought a small, but high precision table mill with most of the
gears missing, so I had to make them myself. They are module 0.8. I
bought a set of 8 cutters in ebay from an ukrainian dealer for less
than 15 Euros, set up my small division head, equipped with a stepper
and off we went! I made a set of some 60 gears up to 200 teeth within a week,
only after work. One tooth takes about 45 seconds. (Note: I never before made gear wheels!)

1.) Determine the number of teeth desired, add 2 and multiply by the
module. That gives you the blank diameter in mm.
2.) Get a suiting blank (I got mine from the guy at the band saw
cutting hydraulic piston rods, fine molybdenum steel for a tip).
3.) Turn blank to size, finish faces and bore.
4.) Mount blank on the mill's dividing head, center axes, adjust cutter to just scratch surface (touch off, is that right?)
5.) Move slide out of the way and adjust cutting depth (from the excel
sheet)
6.) Lubricate, start mill and PC and watch.

Large machine:
I made a lot of other gears for my lathe, module 2, with the larger
knee mill, but same setup except for mechanical feed in X. All the gears turned out to be of perfect
shape, except for a few mischiefs I caused by my own fault. Those I
turned down to make the next smaller blank. After about 2 or 3 gear wheels
grind the cutter slightly. When making different size gears be sure to
change the cutter according to the table.

There is no need for much math, you need not even to use pi, even EMC
isn't really necessary. The only figuring is to divide the number of
teeth into the number of steps for one rotation of the dividing head.
In my case:
40 (number of crank turns per rev.)
60 / 11 = 5.454545...: ratio of the gear belt drive on the dividing head
400: number of steps per rev. of the stepper motor
40 * 60 / 11 * 400 = 87272.727272... steps per one rev. of the divider

For a 44 teeth gear:
87272.72727 / 44 = 1983.5 steps per tooth

I give the stepper those 1983 pulses with a very simple demo software
from the manufacturer of my stepper board (http://www.emisgmbh.de/fsoftware.htm";), to avoid errors alternatingly
1984, make the mill go through a cut once, crank back, start the
stepper again etc. Module 2 gears I cut in two turns, smaller ones in
one. After the last cut I add another just to listen if there has been
any division error (you would hear one or two steps lost on the way
because the cutter bites a few hundredths quite audibly). You'll know
immediately if you had produced garbage or not. Keep in mind that you
are cutting spaces, not teeth.

I made a whole drawer full of these module 2 gears for the lathe.
Hardening is not necessary for use in a lathe or mill, since there is
little power transmitted, comparing the size, and short term use only.
If a gear wears out, just make another one, or make two from the
beginning. Telling from your picture, I would guess that the large red
gear in front had module 3, the smaller in the background maybe 2, the
small ones in the gear transmission on the left 1.75. Hard to tell
without a measure in the picture (hint!).

Determine your module from the formula in the excel sheet: Count the
teeth, add two and divide this into the outer diameter. The figure two
accounts for the fact that you can't very well measure the theoretical
diameter where the gears really mesh.

I managed to buy module 0.5 to 2 sets of 8 cutters each, in beautiful
wooden boxes, almost unused, from a machine factory which had to move
out of the town, for 50 Euros. Just keep looking! Large factories don't
use this method of gear making because it takes longer than hobbing.
Take to the guys at their coffee break. Look into ebay, not only in
ebay.com for the US, but for instance at ebay.de or ebay.at. Don't be
afraid of eastern European dealers, they need to make money just as we
all and are as honest as we all are. :-)) There seems to be a lot of
material the communist era has left which is now being socialized by
private hands.

Best regards
Peter Blodow

PS: Don't get me wrong: I studied physics and have been working in a
research company for 34 years, so I know when to use complicated
theory, but from my own private work I know when not... 

Attachment: gear teeth.xls
Description: Binary data

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