The Long and Short of It

One of the problems with “tribal knowledge” is that the terminology can confuse those who are not fully immersed in that community. I have lost count of the number of times I have had to explain to people that long and short addendum gears have the same whole depth. Perhaps this is an appropriate point in our discussion of gear design to go over it once again.

If you want to use low tooth counts in your designs, you have to deal with the possibility of undercutting. Undercutting occurs when the cutting tool generates the tooth flank and destroys the profile in the root area. The “danger zone” varies with the number of teeth and the transverse pressure angle (TPA). Fewer teeth translate to greater danger; the lower the TPA, the greater the danger.

Before there were short lead hobs, some canny observer probably noticed that the damage did not occur until the tool reached a certain depth of cut. Knowing that the involute system is flexible on part outside diameters, they decided to increase the outside diameter on the low tooth count component and reduce it on the mating part so they could have an undamaged root fillet.

It worked great — increased tooth strength — and did not require special cutting tools.

Unfortunately, they decided to call the increased outside diameter component a “long addendum” design. This cast the reduced outside diameter part as “short addendum” and decades of confusion ensued. So, let us start with some nomenclature:

1. Both gears have the same nominal “whole depth.” There are slight differences in the measured depth of cut, but both members can be made with the same tool.
2. A gear does not really have a “pitch diameter” until it is in mesh. For calculation purposes it has several different “pitch diameters” that cause some unnecessary confusion.
3. The theoretical pitch diameter remains the number of teeth divided by the transverse diametrical pitch.
4. The operating pitch diameter involves tooth action with the mating part. It denotes the place where approach changes to recess. A part could have different operating pitch diameters if meshed with mates having different numbers of teeth, or if the center distance was varied from the “standard” amount.
5. Addendum is the radial distance between the outside diameter and the theoretical pitch diameter. A “long addendum” part had a larger value because the outside diameter is increased. Its mate has a “short addendum” because its outside diameter is reduced.
6. Dedendum is the whole depth minus the addendum, so a long addendum part has a short dedendum. A short addendum part has a long dedendum. They share the same nominal whole depth with the cutting tool.

We’ll continue our chat on diameter modification in the next blog posting.