On Fri, 18 Mar 2005 22:17:32 GMT, "Karl Townsend"
remove .NOT to reply wrote:

I need to know the exact gearing ratio for my mill in backgear. This is for
a gear hobbing project I hope to finish within the next X years (X has been
less than one for a couple years now)

Anyway, I have an encoder on my drive spindle that does 4000 counts per
turn. I ran the machine in backgear exactly 100 revolutions and got
2,451,765 pulses. I didn't use an indicator for the begin or end stop point
(mark at end of 4" fly cutter lined up) so the true total could be +/- 250
pulses

This gives a gear ratio of 6.1294. I need a really good guess on the number
of teeth in the drive and driven gear. For example, if the drive gear has 10
teeth and the driven gear has 60 teeth, the ratio would be exactly 6.00.
There's a zillion possibles, I'm looking for one that give a number within a
couple tenths(.0002) of this ratio.

If I have too, I'll tear the machine down. But, I'm hoping there's a math
genious out there. If needed, I could put a counter on the spindle and do
1000 turns.

Someone said it was probably two sets of gears. I wrote a simple
program having 4 gears, with net ratio of a/b * c/d. I ran this for
all combinations of teeth with the following ranges:

a 8 to 100
b 8 to 50
c 8 to 50
d 8 to 100

as a more-or-less arbitrary set of values. I had it save all sets
with total ratio within 0.0001 of 6.1294. There were 24 successes.
The one with the smallest max number of teeth on any gear was:

65, 8, 43 and 57 teeth, ratio of 6.12939.

These are all prime numbers in the sense that they are divisible by no
number less than 8. (I figure 8 is about the minimum number of teeth
on a real gear)

There were two other sets with same ratio:
65, 12,43, 38
65, 24 43, 19

When I did it with a single pair of gears I got no hits even with
tolerance loosened to .001.