I have a slow-speed drill press which seems quite solid, the play is minimal. Normally, it does not cause problems. This conical bit:
when applied to this 8 mm hole:
is an exception: the bit jumps and squeaks loudly, the machine resonates. As seen in the image, it is impossible to make an even chamfer. I was thinking about filling the hole with a 3d-printed plastic cylinder with a small pilot hole, but I am not sure it it would help, given that the material is a hard stainless steel. It is fastened in a 4.5 kg vice which can move freely, so that the bit position can be adjusted. The vice seems to be stable, despite the vibration.
How to make an even chamfer? Its angle of 45 deg is important.