Had a round 5" laminated steel laying around and decided to make a pipe center....
For the axle, used a drill chuck arbor MT02 to JT4. Machined Jacobs taper to 25mm the internal diameter of my bearing.
The bearing used is from a car front wheel. It's a double row angular contact ball bearing. It can handle axial and radial loads, It's preloaded (no free play), has good seal and it is cheap. The one I used has 25mm internal diameter, 55mm external and 45mm long.
Machined the 5" steel with 4 jaw chuck since this is the biggest I have. First back side was made with bearing case. Pressed bearing and axle. So, I machined most of the taper (35º).
***Now comes the odd part***
For the two finishing pass, I mounted the pipe center in tailstock and driven it by a threaded bar (see pics) This way I ensured best concentricity.