What is the correct formula for calculating the center distance between gears?

[wolterh]

Which is the correct formula to calculate the center distance between gears? I am designing a couple of spur gears in Autodesk Inventor and the application says that the center distance between them is 23.107 mm, but when I place them so far apart they seem to overlap.

The gears have the following dimensions:

Gear #1:
Pitch diameter = 6 mm
Number of teeth = 12

Gear #2:
Pitch diameter = 40 mm
Number of teeth = 80

The module consequently is 0.5 mm

Logic says that the center distance must be distance between the centers of the gears placed close enough so their pitch diameters are tangent - so the sum of the radii would be the center distance, but a distance of 23 mm seems way too small.

 

[pantaz]

... Logic says that the center distance must be distance between the centers of the gears placed close enough so their pitch diameters are tangent - so the sum of the radii would be the center distance, but a distance of 23 mm seems way too small.

Why "too small"? Without doing the actual math, I'd say the 23.107 mm you're getting from Inventor is very likely correct for the operational measurement. Much more than that will result in increased tooth loading, excessive backlash and damage to the gears.

I've seen several versions of the formula, based on varying levels of desired precision. Google "spur gear center distance".

 

[rsk2mc]

really it should be the diameter of one gear from the beginning of the tooth. Like the circle without any teeth on it. Then the other circle should be the outer diameter , like at the end of teeth. So the center distance should be between those if the gears mesh perfectly

 

[256bits]

Logic says that the center distance must be distance between the centers of the gears placed close enough so their pitch diameters are tangent - so the sum of the radii would be the center distance, but a distance of 23 mm seems way too small.

Isn't the sum of your pitch radii 23mm? The app states 23.107mm.

 

[wolterh]

Why "too small"? Without doing the actual math, I'd say the 23.107 mm you're getting from Inventor is very likely correct for the operational measurement. Much more than that will result in increased tooth loading, excessive backlash and damage to the gears.

I've seen several versions of the formula, based on varying levels of desired precision. Google "spur gear center distance".

Well needless to say I searched that in Google, even before registering to this forum. As you may find after looking into the results, there are different formulas and most of the websites listed read the formula I said logic dictated. I was looking for information that came from an experienced engineer or conoisseur in the topic, not for a lmgtfy kind of reply.

It is understandable for me how an operating center distance may be different from the one obtained by the very simple calculation I thought of, but my actual inquiry was to know about an adaptive formula that would take as parameters perhaps not only moduli and pitch diameters, but addendum and angle of attack too.

really it should be the diameter of one gear from the beginning of the tooth. Like the circle without any teeth on it. Then the other circle should be the outer diameter , like at the end of teeth. So the center distance should be between those if the gears mesh perfectly

Well the gears don't mesh perfectly and I think it would be rather uncommon to find gears which did. Before the top land of a gear touched the bottom land of the other, the teeth would have already collided.

Isn't the sum of your pitch radii 23mm? The app states 23.107mm.

Exactly, that's what I was stating: the sum of the radii is 23 mm but the application calculates a strange 23.107 mm distance.


Anyway, I noticed that if I zoomed into appreciate the interaction between teeth (which the 23.107 mm center distance), the teeth seem to overlap each other at some sections, which looks awfully incorrect.

 

[pantaz]

... I was looking for information that came from an experienced engineer or conoisseur in the topic, not for a lmgtfy kind of reply.

I apologize -- I wasn't trying to be flippant, but your use of the phrase, "seems way too small", implied a lack of research.

It is understandable for me how an operating center distance may be different from the one obtained by the very simple calculation I thought of, but my actual inquiry was to know about an adaptive formula that would take as parameters perhaps not only moduli and pitch diameters, but addendum and angle of attack too.
. . .
Exactly, that's what I was stating: the sum of the radii is 23 mm but the application calculates a strange 23.107 mm distance.

Some CAD software incorporates an estimated profile shift or addendum modification coefficent for calculating the operating center distance. A good explanation of the need for profile shift is http://www-mdp.eng.cam.ac.uk/web/library/enginfo/textbooks_dvd_only/DAN/gears/meshing/meshing.html" [/I]).

Anyway, I noticed that if I zoomed into appreciate the interaction between teeth (which the 23.107 mm center distance), the teeth seem to overlap each other at some sections, which looks awfully incorrect.

Assuming a standard pressure angle of 20 degrees, the http://www.qtcgears.com/Q410/QTC/Q410P344.htm" is 18 teeth, to prevent undercutting. (Profile shifting is also used for creating gears with fewer teeth.) Perhaps the software isn't properly interpreting the 12-tooth gear for graphical display.

 

[wolterh]

Thanks for your input, I find it very complete.

I read on later that I was using a lower number of teeth than the one recommended, and because of such, the application shifted some values in order to prevent mechanical failures. Unfortunately, I have to use these fewer teeth amounts because the project I am working on demands the copying of a mechanical device, so I cannot choose the number of teeth I want for my gears.

I also learned that if one used the minimum quantity of recommended teeth or more, the center distance could be calculated with the simple formula we have mentioned repeatedly.

This thread is now solved.