Could I get two gears cut by a forum member? - Page 2

Thread: Could I get two gears cut by a forum member?

1. Cast Iron
Join Date
Sep 2014
Country
UNITED STATES
State/Province
Georgia
Posts
349
Post Thanks / Like
Likes (Given)
259
128
Originally Posted by Dan from Oakland
In my experience, as long as the feed constant is exactly the same for both the index and feed gear calculations, it should work. As long as the feed constant will allow an exact index ratio to be selected, life will be good. Most times there is error in the feed gear ratio at the 5th, 6 or 7th decimal anyway, but the lead error introduced is so small, we never see it.
Just to show that the C constant is exactly the same for the Index and the Feed. Here goes:

The C constant is 10.7011494252873563218390804597 with the pattern 7011494252873563218390804597 repeating forever. To make that into a perfectly accurate fraction place the pattern over 9's:

7011494252873563218390804597/9999999999999999999999999999 which when reduced equals 61/87

10 61/87 (the C constant in fraction form) made into an improper fraction is equal to 931/87.

So the formula looks like 30 * 931 / (33 * 931) - 87 after cancelling the 87's. 87 now takes the place of the constant 1 to give a one unit reduction between the numerator and denominator.

30 * 931 = 27930

33 * 931 = 30723 - 87 = 30636

27930 / 49 = 570

570 / 95 = 6

30636 / 74 = 414

414 / 69 = 6

=

49 * 95 * 6
-------------- =
74 * 69 * 6

cancelling the 6's leaves:

49 * 95
---------- for the index gearing.
74 * 69

For the feed gearing:

Circular pitch of 20 = 0.15707963267948966192313216916398

Sine of 30 = .5

Feed constant = 0.075

Feed gearing =

0.15707963267948966192313216916398 / .5 * 0.075 * 931 / 87 =

0.15707963267948966192313216916398 / 0.40129310344827586206896551724138 =

0.39143367112396994163444321424321

28 * 47
--------- = 0.39143367043426531826293872694825
82 * 41

0.39143367112396994163444321424321
- ----------------------------------------------------
0.39143367043426531826293872694825

=

-0.000000000689704623371504487295 feed error (9 zeros and an error at the tenth decimal place)

If the extra accuracy isn't needed, what about if the program can produce good results from a very small selection of change gears. In the following case 35 to 65 tooth range of the change gears:

The above C constant is 11 2/57 by the way.