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Bevel gear equations

Bevel gear equations

Bevel gear equations

(OP)
Hello.

I have a couple of questions concerning the Machinery Handbook's equations for bevel gears, and was hoping someone could shed some light on them. In that text, a set of equations are given for bevel gears with flat-sided teeth and a pressure angle of 20 deg. But most production bevel gears as I understand it, are manufactured with involute curves for the teeth sides. In looking at the equations, it looks like involutes can simply replace the flat-sides (so long as the tooth circular distance at the pitch circle is maintained), and the pressure angle can be dispensed with (as far as solid-modeling is concerned) because the only place where pressure angle enters into the equations is for machine settings when cutting the teeth.

Is this correct?

Also, when I ran some tests, I found that there was clearance between the two gears except when I tested for a "radical" gerar where the pitch angle of the gear was very shallow, and the pinion's pitch angle was correspondingly high. What I ended up with was 18 teeth on the gear and 6 on the pinion. Well enough, I suppose, except that the two gears had serious overlap issues, and the pinion involutes on each tooth intersected each other before the outside diameter was reached. In other words, the teeth came to points below the outside diameter. So my second question is, are the equations in the Machinery's handbook only good for gears with large numbers of teeth for both gear and pinion? I feel my math is correct, so my conclusion is that the equations are good, but care needs to be taken when the pitch angles divert too far from 45 deg.

Thanks in advance! :)

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