Before we move on from helix angle restrictions, I want to say a few things about face contact ratio. Soon after the appearance of the first helical gear, designers and engineers found an entirely new topic to argue about, i.e. — how many teeth were sharing the load across the face of the gear mesh.
With a spur gear, the face contact ratio is clearly zero. If you lay a straight edge on top of a spur gear, you quickly see that the load shifts from one tooth to another rather abruptly. In actuality, there are portions of the cycle where two teeth are in contact, but most of the time a conventional spur gear puts the entire load on one tooth and this “single tooth loading” is the basis of our strength rating formulas. [I have blogged before about my role in destroying the giant strain gauged tooth that was used in the late 1930s to validate AGMA’s understanding of bending stresses. It is one of the biggest regrets of my professional life.]
If you repeat that exercise with a helical gear, you can count the number of tooth tips that intersect the straight line and get a good approximation of the face contact ratio. Some gears will not even get to “two” — reflecting a face contact ratio of less than one. Rating standards penalize the designer for this “error” because “true helical action” never occurs; at some point there is a dramatic change in the number of teeth sharing the load. It is “better” than a spur but not truly helical, either.
Once you have a face contact ratio of 1.0 or more, the standards for a “helical” gear are applied. So why would you want more face contact ratio?
When I started out in 1971, our “family recipe” required a face contact ration of 2.0 or more. Some “experts” thought there was some magic in integral face contact ratio and we put lots of effort into getting as close to 2.0 as possible. Hours of fun were enjoyed debating whether the “magic” would still happen at 1.95, or if the 2.00 had to consider tooth chamfering. You can speculate plenty when there is no funding for research or testing, and no one actually has methods developed for either.
What “evidence” we did have was from noise checks and field reports. Keep in mind that gear quality was lower and most U.S.-produced machinery used through hardened gears. We honestly believed that “initial pitting” was beneficial because it “spread the load out” and would eventually quiet them down. You might laugh now, but our servicemen and sales engineers were trained to repeat the “singing gears are happy gears” mantra.
All of that predates the first issue of Gear Technology, of course, so you would have to really do some old fashioned library time to find out the reasoning behind the change in design philosophy. Suffice it to say, we did not know what we didn’t know and had no reason to change — until “hard gears” completely turned the gear world upside down.