Motor and Ball Screw Formula

Assuming you're using a servo motor(electric DC), the two factors that must be considered are the moment (torque, force X perpendicular distance) applied at the ball screw and velocity. If the load is too heavy, the drive will overload trying to move it. If it's marginal, the velocity will cause the motor to overtravel and it loses it "home position". It gets very technical, but in a nutshell, that's the idea. If a more technical answer is required, let me know. Hope that gets you started.

ok thats good but do you think you can break it down just a little. im a little lost

Let us say the ball drive makes 4 turns in one inch and you need to lift 100 pounds 12 inches in 4 second, or 48 turns total at 12 turns/second or 720 RPM

you have done 12 x 100 = 1200 footpounds of work in 4 sec = 300 fp/second.

1 HP is 550 foot pounds per second, so your 100% efficient motor need to be rated at 0.54 HP at 1800 rpm and must be geared to 720 rpm in some manner.

All this is 100% efficient. A real motor will not be 100% efficient and the gears will lose energy, so 75% is a design number.