Posted by BillS on July 19, 2007 at 17:30:28:
In Reply to: Re: change gears for a newark hobbing machine posted by brent on July 14, 2007 at 15:35:31:
It's simple, really. The important thing is that the ratio calculated from the numbers must always be the exact same as the original, which is:
12
----
168
Next, you need to form the numerator (12) into two factors. For example:
3 x 4
------
168
Since 3 can be divided into 3 and 168, do that:
1 x 4
------
56
Likewise 4 can be divided into 4 and 56:
1 x 1
-------
14
Next, factor the denominator:
1 x 1
--------
2 x 7
What is your largest gear size? let's assume you have a 100T. So, lets divide 2 into 100 = 50 and multiply 50 times 1 to get:
50 x 1
--------
100 x 7
Okay, we will need to use some of that 50 to make the other "1" larger, hopefully close to the "7" in size. But if we factor out "5" the 50 would become 10 which is too small a gear size. So let's factor 2 out of 50:
25 x 2
--------
100 x 7
let's divide 7 into 100 to see what is the largest integer value we can multiply the 7 by without going over 100. That turns out to be 14. So we can multiply the 2 and the 7 by 14 to get:
25 x 28
---------
100 x 98
I usually like to see the largest denominator size on the final shaft, so when we switch around, we get:
25 x 28
---------
98 x 100
See? we just played around with the factors to get sizes that are in the range of inventory gears available. After a while, this will seem natural :^)
'course, it can be impossible to get a gear set if the ratio is too small, or there is a big prime number that you don't have in your inventory.
Try this:
put the smallest number you have in the numerator twice, and the largest number you have in the denominator twice. This represents the smallest possible ratio that your inventory can provide (without going to 6 change gears). For example:
24 x 24
--------- = 0.0576
100 x 100
If you had to come up with a ratio smaller than 0.0576, it would not be possible to get a gearset.
And you'll find that just being close to such a small ratio will often prevent you from getting the gears.
It really helps to have a complete range of change gears, as you could see from not having an 84T gear. Try proving this setup:
24 x 25
----------
84 x 100
This is not the whole story, but maybe it will help those unfamiliar with the process of finding change gears.
Just remember, index gears for a hobbing machine must be exactly equal to the original ratio. (Okay, for spur gears and differential machines anyway.)
One last word - from the shameless commerce division. CPC-HOB does it's best to give you gearsets, and provides a special (dual) setup for those nasty prime numbers you run into from time to time. It let's you play with an index gearset on screen (like we did above), keeping the integrity of the ratio all the while. But even programs like CPC-HOB and CPC-RATIO can't make gold outa lead ;^).