Optimum Z axis steps/mm

I have begun an i3 build. I have been reading an awful lot, but probably not enough. I am planning to use 2 Z axis leadscews and use a pulley/belt configuration with a single nema23 stepper. In selecting rod thread pitch and pulley diameter is there an optimum number of steps per mm I should be shooting for? If it matters, the goal of the machine is to be able to do small, detailed prints.

There's a lot to consider here but the answer is pretty simple...

The motor driver probably does microstepping. Microstepping isn't as precise and torque is lower compared to using the motor's native full steps. In the X and Y axes the extruder moves continuously so the microstepping helps keep the motors running smoothly. In the Z axis you're normally just bumping the X axis up by 50-200 um per layer and then staying there until the layer is finished. That means that precision is important and smooth operation isn't so important, which in turn means it is best to use the motor's native 200 steps per rev in the Z axis (disable the microstepping in the controller/driver, if possible).

Assuming 200 steps per rev and 1:1:1 pulley size ratio (motor, screw 1 and screw 2), if you use 1mm pitch screws, your Z axis steps (layer thickness steps) will be 5 um. That is certainly smaller than you'll ever need- your realistic minimum is more likely to be 100um. If you use a 5mm pitch screw you'll still have steps that are just 25 um. So any screw between 1 and 5mm pitch should be fine. If you want to multiply the motor's torque by reducing the motor pulley size relative to the size of the pulleys on the screws, the step size will become smaller. I would try to use a whole number ratio in the pulley sizes to keep step sizes numerically neat.

As far as I know, all 3DP firmwares use metric units for all calculations. That means it's best to use a metric thread pitch because that will prevent small errors in calculations due to limited precision of the calculations. Moving a whole number of steps per layer is a good thing to do. You can help the situation by slicing to layer thicknesses that allow whole number stepping in your printer. For example, if you use 3mm pitch screws, 1:1:1 pulleys, each step will be 15 um. So slicing for 100um layers would not be a good idea because 100 is not a whole number multiple of 15. Use 105 um instead- that's 7 full motor steps. Likewise, when you design parts to be printed, keep layer thickness in mind and design the part for Z heights that land at whole number layer positions, including hole centers and all horizontal surfaces. This all sounds very picky and most of the time isn't really necessary, but if you want to do precision work you have to think like the printer.

Using a single motor to drive both screws is an excellent choice (I did the same)! One of the good things that comes from that is the ease with which you will be able to do things to the printer/bed/extruder. Instead of having to power the machine up and click through a bunch of menus to use the firmware to move the Z-axis (or go to your computer and do the same) so you can work on the extruder, etc., you can simply pull the belt and know that both screws are being turned equally so you aren't going to have to realign the X axis when you're all done. Believe me, you're going to be making a lot of use of this capability and it will save many hours of tedious waiting and realignment.

Thanks for the excellent response. That is exactly what I needed.