I had to make a threaded sleeve to protect the threads on a threaded shaft. In my case to protect the threads of a rifle barrel to which a muzzle brake is attached. The thread protector I made is knurled on the outside, and with an internal thread, in this case 9/16"-24tpi.
Whenever I make a part that has internal thread, over 1/2", I like to cut 95% of the thread on the lathe, then finish it off with a tap. In my case, I do not have a 9/16-24 tap, so I had to do all the thread on the lathe. Its easy enough to check the progress of the threading operation if you have a short male section: see if it screws all the way in, if not, remove another thou and test again. But I had to test the internal thread by trying to screw on the 24" rifle barrel, which to say the least is awkward, and you can easily damage the male threads on the barrel. So I get to the point that it seems to be fine, without screwing the barrel all the way on. I had already knurled the part, and thinking the internal thread of the protector sleeve was proper, I cut off the part. Deburred the inside with a wire brush attached to my cordless drill, and proceeded to thread the new sleeve onto the barrel threads. Of course, it only threads on about half way nicely and then gets tight. You can't force it: stainless on stainless, it will gall and weld itself together. So now what? I have to open the threads just a tad to make it thread easily all the way on. I can't work on the male threads, because the muzzle brake threads on perfectly. I've used many techniques in the past successfully. So 1st try: a wooden dowel coated with grinding paste. Screw the part onto the wooden dowel, in and out. The dowel should be as large as the major diameter of the thread or slightly larger. This usually works well if it just needs a smidgen. Not this time. 2nd try: find a smaller tap with the same pitch, in my case 7/16"-24, place the tap in the threaded sleeve, and roll the part, just like rolling dough. Of course being carefully that the tap threads are nestled in part threads, and test often. This worked perfect.