How can I be sure that the backlash shown on the control readout is in the ballscrews?
With the machine assembled you can never be absolutely sure but there are ways to improve on sheer guesswork. The encoder (a rotary pulse generator) or a linear scale (a linear pulse generator) feeds signals to the control. A linear scale is mounted directly to the slide and way so bypasses errors in the ballscrew and thrust bearings. An encoder relies on the accuracy of the ball screw and thrust bearings so control manufacturers invariably incorporate an electronic backlash elimination to alleviate any problems. Over compensated electronic backlash elimination can often cause jumping when slide direction changes.