Hopefully I can simplify a response here. There are two things you need to consider.
One is the resolution of your system. Say you have a stepper system and are resolving one step. That is the minimal rotation on the screw is one step and for grins we will say that equals 1.8 degs on the motor shaft. The motor then turns that shaft that much or an amount determined by a drive ratio. In any event lets say the leadscrew shaft turns 1.8 degrees, you should now be able to see that a machine with a high TPI count will move the motor less than one with a lower TPI count. The pitch of the lead screw determines (in part) the resolution of the system or it impacts the overall ratio of the system.
Another issue is the torgue being applied. A screw is nothing more than an inclined plane wraped around a rod. A high TPI leadscrew has a mechanical advantage that is greater than a low TPI leadscrew. At least in theory, at some point the balls become so small that mechanical advantage can be difficult to realize.
All that being said you are other wise right in that the CNC control should be able to adjust for any lead you may have on the leadscrew. There is an issue with resolution though if you go the wrong way, the CNC can not resolve at the work piece less than the mechanical system allows for. This applies equally to stepper based systems and resolver/encoder based systems. In a feed back system the CNC has a set number of "pulses" that can be seen per revolution of the leadscrew shaft. So if you have 1000 counts per revolution, the circle of revolution gets divided up into 1000 parts. With the overall system ratio (including the leasdscrew TPI) you can determine real world mechanical resolution.
So the leadscrew TPI works in conjunction with the rest of the ratios in the system to determine the distance moved per count. <<<<<<That is it in a nut shell>>>>>>
As a rough guide though, I generally want systems to resolve better than the mechanical accuracy needed. Of course like all things in life there are a lot of opinions here. But if you want to maintain accuracy of 0.001" you should set your system up to resolve below that, with 0.00025" resolution being good. That is one fourth the desired resolution. I've seen and worked on systems that go well beyond that though.
I hope that my geting ot the nutshell hasn't put you to sleep.
Dave |