Pressure Angles

" Pressure angle affects the force that tends to separate mating gears. High pressure angle decreases the contact ratio but provides a tooth of higher capacity and allows gears to have fewer teeth without undercutting."

By what factor are 20PA gears stronger than 14.5?

Also, what is the formula to calculate the max force on a gear?

I’m far from a gear expert, so I’m hoping Dr. Joe shows up in this thread at some point, but to get you started, 20deg PA gears are something like 14 to 18 percent stronger, going by these formulae I’m about to give you. The easiest ones to use are at Martin Gears:

This is not a simple question to answer.

Yes, in general, 14.5 degree PA teeth are weaker than 20 deg PA teeth, but unless the number of teeth are small (under 14 if you are looking for a rule of thumb) the difference is not huge.

Higher pressure angles are a generally good thing but not always. In the area of sound some folks claim they can get better sounding gears with lower pressure angles.

The major benefit of using higher pressure angles is that it reduces undercut for small gears.

To first order, you can get a good estimate of the strength of the tooth by approximating the tooth as beam and estimating what force the bending stress at the thinnest section of the tooth would exceed your material stress.

There are other places on these fora where these calculations are discussed. I don’t have time right now to search for them, but I hope someone will and link to them.

Joe J.

I could only find one formula, on this thread:

However the formulas from Martin are great!

And i just learned about for all sorts of great material info

The best resource that I have ever found for a really good introduction to gear design is the technical section in the Handbook of Gears by Stock Drive Products. You can download the whole thing as PDF files from the SDP web site. As good as the stuff on the Martin site is, they really don’t get into the background knowledge you really need to understand what is going on and why the formulae work. The Handbook Of Gears is a bit surprising because it is tucked away inside the SDP catalog. But it is a great reference for understanding both introductory gear theory and application considerations.

There is a whole section (see Section 13) on gear tooth strength and design. Most of their calculations are based on the Lewis formula, or a modified (Barth) Lewis formula. As has been discussed several times on these forums, the Lewis formula calculations are based on industrial duty cycles, and the assumption that the gears will undergo millions of rotations. For almost every FIRST application this will result in a very conservative solution. While these calculations will provide a workable solution, it will be a bit of “overkill” for most FIRST robots (and therefore, lead to a potentially heavier gear system than is really needed, as the recommended gears are larger - and heavier - than need be). Joe Johnson’s suggestion of using a beam stress calculation to determine tooth size will provide a very workable answer that will be closer to the optimal solutions for FIRST applications.


This is very true. For one reason and another, my formal education skipped Gear Design. When I was transfered to a group that eats & sleeps gears, I needed a gear primer ASAP. I read the Stock Drive Products handbook cover to cover. Not only did it allow me to pass as a gear guy, I was quickly regarded by many as the group’s go to guy with regard to gear design.

Surely there is a lot to learn beyond the pages of the SDP catalog, but it is a great start. One bit of advice. Learn the ideas, look up the formulas. The other way round will drive you mad in gear design.

Finally, the Lewis formulas are a wonderful tool that is just plain too conservative for intermittent use applications. FYI, I found this old thread and this old thread where I give some details as to making the calculation. In case my recommendation is not convincing enough, even Ol’ Man Beatty told me uses the method I described to size gear teeth.

Joe J.

Thanks for the great link to more helpful gear stuff! Im really getting into it. Theres so much to learn, so many diferent aspects and such. But my theory is: if you want to know it, youll learn it.

And thanks for the good advice! Im def. remembering that one.

Maybe one day ill have my own office and i can cover the walls with posters of various useful formulas lol.

Hmm…but now im starting to think…what about chain and sprockets?