Maybe I have my terms wrong. I tried machining it with a flat face and the teeth were equal depth but the width of the teeth changed as they got closer to the center.
I was thinking of a pitch cone angle of 90*, which would be flat, should not have said "flat face" because the face would be concave
/me bad.
Pitch cone angle on a bevel gear is similar to pitch diameter on a spur or helical. So if the pitch cone is 90*, it's flat but the addendum will be above that and the dedendum below. That would make what looks like two shallow concave toothed cones that mate with each other.
Straight bevel gear teeth are tapered in both directions - height and thickness. So if you think of a regular bevel gear then push the ouside edge of the teeth forward until a plane through the middle of the teeth is flat across, that's what I am talking about. Make another one just like that for a mate.
Pretty bad description, hunh ?
That's basically what a hirth coupling is like. Easy to make bevel gears on a bevel gear machine but you can also do it by hand. That's what you are trying, I think.
Jones & Ryffel has the cleanest description and formulas for doing that. If you have nc you can generate the tooth shape with a dinky little ball end mill, that's how DMG does some great big spiral bevels now. It's not a very good method but for a one-off, it's a lot better than buying a slew of special machines.
Gleason actually built a "#5 Curvic coupling generator" if you want to go into production
@ EPAIII, the coolest thing about both curvics and hirth couplings is, the more you index them the more accurate they get. Wear will even them out. That's the opposite of usual machine tool behaviour
This is pretty bad, sorry, but I hope it gets the idea across - very much like a bevel gear, use a pitch cone angle of 90* (got that wrong too, dang) and then use bevel gear calcs out of the book to get the proportions. If you run a plane thru the red lines, that's your flat face, with the big ends of the teeth going deeper into the spaces at the outer ends than in the center. Teeth tapered in both directions.
View attachment 276434
(You could probably use any dimensions you want, just do the math for inscribed arcs and so on, but I would use the proportions of a bevel gear because it's all been worked out over the past century to be practical sizes.)
Don't forget to leave clearance at the roots, but again, if you use addendum and dedendum from gear practice, that will be all worked out for you.