Originally Posted by
109jb
That link is for calculating the force produced by an ACME screw. The OP has ballscrews which are much more efficient. Here is a calculator for ballscrews. For efficiency, a ballscrew is about 90% efficient.
My G0704 has the 570 oz-in steppers on all axes and has proven sufficient in X and Y but I would like a bit more on Z due to drilling forces. The ballscrew calculator says a 570 oz-in motor on a 0.196" (5mm) lead screw at 90% efficiency will give 1027 pounds of linear force. Using your 180 pound cutting force requirement there is a healthy margin. However, for a stepper design, the desired rapid speed may be the driver for motor sizing. This is because stepper torque drops off with increasing RPM and there will be a speed where the stepper will stall. For the 570 oz-in motors I can rapid reliably at about 150 IPM with double spring preload ball nuts. With single ball nuts that speed is closer to 200 IPM