When I was an apprentice in the tool room we used to do this, as I remember it we used a copper rod in the drill press, the end of which we smeared with lapping compound and with the drill running we made overlapping patterns of the end on the part we were decorating. Getting the spacing even is tricky, as is using the correct grade of compound for the material being finished and using a constant pressure and time at each spot.
Check it out on the web, this was fifty years ago and a bit foggy in the memory.
Edit, I see that wooden dowels are used instead of the copper rod we used, you can see that the center of the swirl is just about erased by the adjacent swirls, if you can see the center too much the pattern is not so good.