I have created a ring by making a flat cylinder and then boolean-ing out a smaller, flat cylinder from the inside. I have long since applied the boolean (including from several other cutouts as can be seen). I have also extruded some details as can be seen near the front of the ring in the picture. This is for a 3D printing project and when I first created those cylinders long ago I thought this would be enough facets, but now I have found that once it is printed, the facets can still be seen in the model.
I have tried the smoothing tool, several different smoothing modifiers, subdivisions, etc. Most smoothing efforts seem to smooth everything on the model, but I want to keep the crisp edges on the XY plane (top and bottom of the ring) and smooth the edges to make a finer cylinder (more on the Z plane). How do I smooth just what is selected here to make a cleaner arc and not anything else?