Optimal gear combination with the same ratio

Question

Summary: In a gear train, with given target ratio and configuration (eg. number of gears and how many compound gear steps are involved), what are the considerations when trying to select the optimal size (number of teeth) of the gears?

Full story: I have a small lathe with manually adjustable gear train for the power feed. Manual means that I have a selection of gears to choose from and I can decide which 3 or 4 of them to install to achieve the required final ratio. There are three shafts altogether, out of which the driver shaft and the driven leadscrew have fixed position and the middle one is adjustable (this can accommodate a single idler gear or two as a compound).

Now I basically understand how to calculate the gear ratios that are needed, but I have many gears and I can achieve the same final ratio by several different configurations. For the sake of the argument, please ignore that some of the theoretical configurations might be physically impossible to fit.

Example: My leadscrew has a pitch of 1.5mm, and say I would like to cut a 0.75mm pitch thread, so I need a 2:1 gear ratio. With 3 gears, the size of the idler in the middle does not affect the ratio so I can use (driver/idler/driven) 20/X/40, 30/X/60, 40/X/80, the idler being anything between 20 to 80 teeth as long as I can fit it. In a similar fashion, with 4 gears where the idlers are compound on the same shaft, I can use something like 20/30/60/80 or even 20/80/60/30 to achieve required final ratio.

Obviously some of the configurations are more optimal than others considering stresses, wear, and maybe for other reasons. I would like to know if some basic thumb rules can be used like "more teeth are the better due to stress distribution" and "try to avoid great differences in number of teeth". Another issue is that the gears have actually been made of different materials, most being POM but some aluminum and the smallest ones with 20 teeth are from steel. I have a feeling that the differences in strength might affect this for a greater extent than the differences in teeth.

Answer 1

Generally you want more than 24 teeth in a gear to avoid having an undercut tooth profile, if you're using off the shelf 20 degree gears. Spur gears you also want to have at most a 5:1 ratio between teeth. Your smaller gear (pinion) should be of a harder material than it's mating gear. If possible have the greatest common factor between the number of teeth be 1, this way every tooth on the gear will encounter every tooth on the pinion and wear will be more even than if the same pairs of teeth mesh every time.

Answer 2

Probably the best option should be select the least used gear (this is what I would have done in this case).

I know the multiple gear system (i've operated a lathe in the past) and there's some gears that I've never used (and neither my predecessor). So if you're using the geartrain the best option is to use some gear less usable (and with less wear) for other configurations.

Later when you need to make your gear (too much wear). You want to create a new gear with better material and you'll select the oposite (the most interchangeable gear for all your common applications).

About the forces involved, I'm not to sure but if the gear is between two other gears shouldn't be too different.