"Lloyd E. Sponenburgh" lloydspinsidemindspring.com fired this volley in
. 3.70:

Then you can also shoulder the piece so the bearings have
something to press against in pre-load.

I should have said "...bearings on both ends", and the shouldering is
only required on one end, the nut provides the other "shoulder".

But the shaft must fit the inner race diameter with a snug sliding fit or
a bit tighter if you have a press and mandrel to put it on. You're not
likely to get that fit with merchant stock steel sized to the nominal
dimension you want.

LLoyd