operation cnc

[Jonathan]

OK but surely it depends on the speed you need.

Yes, if it's sufficient and the motors can drive it at that speed you're fine. But that's the other issue, you will need significantly more torque from the motors to obtain the same feed-rate/acceleration as with the 16mm screw since it is not a linear relationship, power 4 in fact, so for a given acceleration you need (20/16)^4=2.44 times the torque. So if at the speed/acceleration you would have run the machine on with the 16mm screw you have that much spare torque then it would be fine with 20mm, but it's a shame because you would definitely have got better feedrates with the 1610 screw and it's added an unnecessary risk.

For a 1500mm 2005 screw the critical speed is about 1200 rpm with the standard bearing arrangement, so 1200*5=6m/min feedrate.
For 1610, same length etc, it's about 1000rpm, so 1000*10=10m/min feedrate.

From experience the formula used here seems to be conservative, so that is probably enough assuming the motors you have can actually output enough power to achieve that feedrate.

Plus you get greater mechanical advantage with a smaller lead?

True, but you can use the pulleys to get whatever mechanical advantage (i.e. ratio) you want, so it's a bit of a moot point.