maybe it seems need looking for a more complex path , because in the second cycle the diameter of the cylinder already changes for the thickness of the material being rolled (inversely proportional to the thread cutting on the lathe), another possible problem is the material itself, because in theory, A axis or S must make one revolution to move the linear axis for one stepover (material thickness), but as in practice material deviation occurs, I am very skeptical that they can guess the speeds. I used deskproto'' to export gcode for 4 axes with the path ``continues rotary'', where it has the basis of the speed of the linear axis and the stepover, as well as the diameter of the workpiece, so it calculates the speed of the A axis. but this is a hard material and then it is an accurate measure..
www.youtube.com/shorts/OOtRMBdZchk