Designing gears is somewhat of a mathematical puzzle. You have lots of interconnected factors to play with in hopes of finding the “best” overall solution to the problem. Among the fundamental “variables” is the number of teeth on each component.
As with helix angle, many of our “tribes” have adopted rules on how many teeth can be used in their products. All of these rules are valid in certain circumstances, but may not reflect the full range of possibilities. Back when they were first carved into granite, the rule makers were hoping to save future generations some of the pain they went through discovering what did not work.
Take the typical “low limit” on pinion teeth of 18 for spur gears and 14 for helical gears; if you ever see a severely undercut tooth, you can appreciate what they were trying to avoid. Those rules are not “wrong,” but they simplify the problem in a way that prevents designers from understanding modern manufacturing techniques that allow almost any number of teeth to be made without undercutting.
Before you start typing comments suggesting that I have gone off the deep end, I once had a “desk widget” which featured a ONE-tooth helical pinion driving a fifty-tooth gear. Many things are possible — but not practical; design rules save time but stifle innovation.
Many very successful gear systems employ relatively low numbers of teeth on the pinion. The advent of short lead hobs — generating the tooth profile with a cutting tool having a lower pressure angle than the finished part — made undercutting something that is routinely worked around, rather than avoided. The number of “spaces” factors heavily into grinding cycle times, so there is an economic incentive as well as a bending strength argument for reducing tooth counts.
There is also an excellent counter argument that looks at profile contact ratios and insists upon much higher numbers of teeth. We will cover that in another posting. So to once again paraphrase Mr. Ray Drago’s mantra: the correct answer to “how many teeth?” is “It depends.”