A simpler, cruder, device can be made quickly from a piece of suitable round bar. Here's one I made for 8mm hole size.

Turn the spigot to the appropriate size and a clean area on the parent bar to make future resetting in the 4 jaw chuck easier. Drill a suitable hole, I used M6, the full depth in the spigot and tap using only the taper tap to within about half the width of the part to be held from the shoulder. Make a saw cut down to near the full size bar.

Place the part over the spigot and tighten a square ended bolt in the hole until the part is secure.
I have used the mandrel in the pictures above a few times and it is now just about worn out and will be replaced soon but that is no great problem. I also have a 10mm mandrel to the same design which has also been well used.
The design is not my idea but I can't recall who I got it from, probably off this forum.
Jim