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.