Bob La Londe wrote:

Ballscrews and ball nuts are a type of screw and nut. Doesn't answer
the basic premise. More TPI and high step rate or less and lower step
rate.
OK, the basic problem is that stepper torque falls off rapidly with
increasing speed. At some point, the available torque is less than the
drag (friction plus machining forces) and the stepper starts to lose
steps. To REALLY know what is going on, you have to get manufacturer's
data charts on the torque vs. speed for the specific motor, drive and
power supply voltage. This is the reason why so many setups use a
stepper with a 1:1 drive ratio to the leadscrew. If it weren't for this
loss of torque, you could use lots of reduction as is often used with
servo motors, where the torque is pretty much flat across the speed range.

Once you have a chart of torque vs. speed, you can then figure linear
force that can be delivered at a specific IPM feedrate. You can then
compare what happens at 1:1 or at 2:1 reduction. Probably, in most
cases, you will find that the belt reduction doesn't buy you anything
except at standstill. When you near that motor speed where the supply
voltage limits the drive, then the reduction will actually hurt you, you
will get more torque to the screw without reduction.

Jon