A recirculating ball screw uses a series of balls between the threads of the nuts and the threads of the screw. These balls create a rolling (rather than sliding) contact between the screw and nut, making for very efficient power transmission. The rolling balls, however, eventually pop out one end of the nut and need a recirculation tube to shuttle them back to the other end of the nut.

This is a working version that shows off how a recirculation ball screw works. It uses 6mm dia. airsoft BB's for the balls, but nut and screw are 3D printed. The transparent view of the nut above shows the spiral ball path and the internal recirculating tube.

The screw is a little funky in that I flatted one side for printing. This creates gaps in the thread, but the gaps don't interfere with the ball recirculation, and only minimally reduce the load capacity.

Printing
Print in PLA. I used 0.2mm layers, which is fine for the nut, but with the screw printed sideways, it will be smoother with 0.15 or even 0.1mm layers. All parts print without supports. You do need a well tuned printer that prints with no elephant's foot.

Assembly
Getting all the balls in place innut. the nut along with the screw is a little tricky. There is a loading port in the side of the nut. Hold the nut in a vise horizontally, with the loading port facing up. Insert the screw into the nut, holding it horizontal and more or less centered in the nut. Start inserting 6mm dia, balls in through the loading port rotating the screw slightly as you add balls to get the balls distributed along the internal thread. You should be able to add a total of 28 balls. Next insert the little plug piece into the loading port. It should press in place, but if it seems a little loose, just cover it with a small piece of tape.

Now you should be able to press on the screw with quite a bit of force while rotating it and watch the balls circulating along the thread and through the recirculation tube. Be careful not to run the not off the end of the screw, or you will have balls everywhere!