How did that over pin calculation work out? My congratulations if you managed to work your way through it without tearing your hair out. Guess what? Those complicated formulas only work for “standard” dimension parts. If you do a “strength balance” on the gear pair or adjust diameters to avoid undercut you will want access to a computer program. And it better be a well vetted program.
Just as engineers had valid reasons for using “non-standard” tooth forms in their designs, they frequently found it necessary to use non-standard tooth depths. The “20 degree STUB” form is an excellent example. If you see a 20 degree stub part, the teeth just look stronger and the shallower depth allows the use of fewer teeth before undercutting occurs. Fewer, bigger teeth also look stronger. Modern stress analysis says otherwise, but to a trained mechanic appearance is more convincing than a bunch of numbers.
They could not just settle on a “standard” stub system though. We have AGMA stub and “Fellows” stub. One has a .80″/NDP addendum. The other is hybrid system with the pitch of one NDP and the depth of another. A Fellows 8/10, for example has the pitch of an 8 NDP and the depth of a 10 NDP — all to make calculations easier, they argued.
Even herringbones get complicated on depth. Some are .80″/TDP addendum; others are .90″/TDP. Conjugate action is at risk if you mix the cutting tools.
I am an advocate of high contact ratio gearing. This requires deeper than “standard” tooth depths to make certain at least two teeth are always sharing the load. How deep and what pressure angle? We have not found the “golden combination” yet and it may be years before consensus is reached.
Until then my advice remains the same: make sure you know the specifics of your tooth geometry!