Ok, it appears that he doesn’t actually want a knurling effect, rather a large diamond grid lightly engraved on the surface of the tube. so After much messing about with felt tip pens and cardboard tubes:
…what we’re after in engineering terms – I think – are effectively two intersecting twin start threads, one left-hand, one right-hand. The starts offset 90 degrees.
So I think I was on the right lines with the 2mm pitch thread.
Thinking is – no power, use the hand wheel and light cuts.
1) Turn the first thread as normal, right to left.
2) Then do the second thread, right to left, but turning the chuck the opposite direction with the tool upside down.
3) Then what? The next normal thread (ie the other start for step 1) needs to start exactly 180 degrees from the first. How do you do this while accounting for backlash etc?
Assuming this is done ok, the final spiral would be as per 2), turned opposite direction and starting 180 degrees from 2).
I think from the tube experiments that if the start points are not exactly 90 degrees apart, we’ll get asymmetric diamonds.
Any ideas?