It depends on the manufacturing method / "standard rack" used.
Usually it is (#teeth-2.25)*module, what creates 0.125*module clearance between the meshing gears' root and tip.
I agree with your formula for root diameter, but assuming the usual 2*module working depth, you would get a tip to root clearance of 0.25* module, not 0.125*module.
The formula above means, that the root DIAMETER is 2.25*m smaller than the pitch diameter.
Root RADIUS is half of that value, it means it is 1.125*m smaller than pitch radius. The meshing tooth' addendum = module, subtracting the addendum we'll get the clearance (0.125*m)
Of course, we are still talking about the standard ("N") teeth on both meshing gears; the pitch diameters (z*m) are tangent (they are operating diameters as well).
(the symbols in formulas above mean: z = # of teeth, m = module)
Diamondjim,
If dedendum is 1.25*m (depends on the rack) then
root diameter = pitch diameter - 2.50*module.
In such case I agree that the clearance is 0.25*module.
But in my example above the root dia = pitch dia - 2.25*m,
I calculated with the rack with 1.125*m addendum. For my example the clearance is 0.125*m.
The original question was "What is the rule of thumb for the root diameter", I answered it and calculated the clearance using that answer.
You did not mention that in your case the root dia is pitch diameter - 2.50*module
Gearguru,
Well I did read that too quickly.
Most module gearing was 1.166 times
the module until the last 8 years
where 1.25 times the module was adopted
for full depth gears. I have not seen
1.125 times the module on a rack so I
made the wrong assumption. Sorry!
