- Before we start modeling a gear
it's important that you have a basic understanding
of how gear equations differ
between the metric and English system.
We'll quickly go through the English
for gear equations here.
The diametrical pitch is the English equivalent
to the metric module.
As you can see
it's actually the inverse of the module equation
with the number of teeth
divided by the pitch circle diameter.
The number of teeth using that same equation
can be derived as equal to the diametrical pitch
times the pitch circle diameter.
And of course you can also get the pitch circle diameter
by taking the number of teeth
and dividing it by the diametrical pitch.
Just manipulating that same equation
based on your knowns and unknowns.
The center point distance equation is the same
between English and metric.
So, it still the sum of
the mating gears pitched diameters divided by two.
The English outer diameter
is equal to the number of teeth plus two
divided by the diametrical pitch.
The circular pitch is equal to pi
divided by the diametrical pitch.
And the circular tooth thickness
is the same between metric and English.
So, it's still the circular pitch divided by two
minus the circumferential backlash.
The whole tooth depth equation
varies based on the diametrical pitch
as it varied based on the module and metric gear equations.
If the diametrical pitch is less than or equal to 20
the whole tooth depth is equal to 2.2
divided by the diametrical pitch plus 0.002.
If the diametrical pitch is greater than 20
then the whole tooth dept is equal to 2.157
divided by the diametrical pitch.
And lastly, the addendum is simply the inverse
of the diametrical pitch
and the dedendum is the tooth depth minus the addendum.