I have engineering manuals that state absolutely that coarse or fine
splines are the strongest, depending on which manual you happen to be
reading. All complete with formulas.
Here's my take on it based on observation and a smidge of experience.
First and foremost, heavy industrial equipment will use coarse splines.
You will not find fine splines on bulldozer sprockets, ship propellers,
tractor PTO's, jack hammer shanks or other heavy devices.
Fine splines are inherently short. As such, it takes far less wear on
them to result in loss of engagement.
Don't focus on the root of the splines. For each root is interfaced
with a tip. Focus instead midway along the splines. This is where the
forces are maximized and where failures will result.
In any spline fitting, due to machining tolerances, only a few splines
are actually taking the load. If those splines are weak, they will
deform and even fracture.
Fine splines will result in a more precise mounting then coarse
splines.
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