Hi everyone.

I've been searching for hours and can't find an answer. So, first of all, I apologise if it's clearly out there and I couldn't find it.

I understand concept of ratio. I also understand the concept of pitch. I know that the same number of teeth gives the exact same ratio independent of the pitch you are using. The equation used to calculate the ratio doesn't account for the pitch.

Now, my issue understanding all this is when Xray, Robinsonracing and many others explain the the equivalent for pitch 48 and pitch 64.

Directly from other post and from Robinsonracing:
"Question: I am currently running 48 pitch gears and I know the tooth sizes that perform well in 48 pitch, but I want to change to 64 pitch. How do I convert the the number of teeth on gears from 48 pitch to 64 pitch?

Answer: Good question. The short answer is: take the number of teeth on the 48 pitch gear and divide that number by 1.5 and then muliply that answer by 2. Here's and example:

(81 tooth 48 pitch) 81 ÷ 1.5 = 54 x 2 = 108.

The answer of 108 will be the tooth size to use in 64 pitch. In that example we get a whole number after converting, 108. Not all of the numbers will work out this cleanly, lets take an 86 tooth gear for example:

86 ÷ 1.5 = 57.333 x 2 = 114.666.

We need to round this number off to the nearest whole number, 115 (a common 64 pitch spur gear size).
Just reverse the equation to convert 64 pitch to 48 pitch. 108 ÷ 2 x 1.5 = 81.
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Question: Will converting the number of teeth from 48 pitch to 64 pitch ( or vice a versa ) change my gear ratio?

Answer: Hmmm...another good question. The answer is no. Lets take a look with an example using a 21T pinion and an 81T spur. The gear ratio is found by dividing the spur by the pinion,

81 ÷ 21 = 3.857

a gear ratio of 3.857 to 1. ( for every 3.857 revolutions of the pinion the spur gear makes 1 revolution ). After converting the 21T and 81T 48 pitch gears to 64 pitch as shown above we come up with 28T pinion and 108T spur 64 pitch. So when we divide the spur by the pinion, 108 ÷ 28 we get 3.857 again. The same gear ratio."
Also Xray shows the different equivalent ratios for the 48 and 64 pitch gears.

For a 10.93 with pith 48 they state a 12 teeth pinion and a 69 teeth spur gear and for the closest ratio in pitch 64, that's 10.98, they state a 18 teeth and a 104 spur gear. I forget the internal ratio of 1.9, as it is the same for both, independent of the pitch it has. You can see that in this chart:

-See attached PDF from Xray.

Many articles show you how to calculate your ratio, but they don't have into account the pitch size. It clearly matters not just for smoothness. It is clear they search for the same diameter taking into account the pitch.

With different diameters, even if the number of teeth is the same, the length travelled isn't not the same, right? And a pitch 64 gear with the same number of teeth than a pitch 48 gear it's smaller. Is that what affects the conversion?

What's the right answer? What I'm not "seeing"? Why can't I find any gear ratio calculator that uses the pitch in the math or why not one states what pitch they use to give you the results?

Thanks!

Hi there,

I cannot find the original source, but sometime ago I read a post explaining with formulas why pitch does not affect to ratio.

In the end, what I understood was, more or less, that you have the pitch in both operators, so by dividing them you get rid of such "variable" (96t pich64 / 20t pitch64 = 96t pitch48 / 20t pitch48). Furthermore, final ratio is an scalar number so there are no units of measure.

All in all, you can just believe that, apart from sizing/smoothness/durability, final ratio is the same whether you use 48p or 64p.

So when deciding 48t vs 64t I'd say you should only take into account i) diameters (probably there is not enough room (excess or defect!) to use the desired pinion/spur to get a desired ratio) and ii) smoothness vs durability.

Hope it helps.
Regards

Pitch itself does not affect gear ratio - the number of teeth (or more precisely: their ratio) is all that matters. 100/25 is the same as 80/20 or 60/15, regardless of pitch.

The "conversion" is only needed if you want to keep the same size gears (in diameter, not teeth) in a different pitch. And there the formula /1,5*2 is just a shortened form of /48*64 - since gears with the same number of teeth, but in a different pitch, will be different in diameter.