Lathe router - video

[Jon]

Lathe router. By Paul's Garage Projects. 3:52 video:

[Toolmaker51]

Technically didn't get 'smaller' the radius didn't change, it collapsed, about 1/3rd width of cutter. An easy step alleviates this.
Open bore undersize.
Drill and tap for clamp bolts.
Saw the parting line, use some kind of fixture for a very straight and square cut.
Insert fasteners and tighten with a couple strips of business card or paper for about 0.010 max.
Chuck carefully and finish bore to size. The paper shim will keep the bore 'open' to allow easy insertion while remaining very round to clamp on body, the clamp screws will pull a large portion of the bore into shape and conform to what is being clamped.

This works with single or double split clamps. Double split works no matter shim thickness used and engages intended diameter with higher yet percentage of contact. They also accommodate obstructions by separating. Important sometimes to not impart undue pressure on stators, bearings, other rotating parts. Only feature differences; mill mating faces, mark the housing so those remain matched when bored and assembled, no matter how many times it's used.
Clamps I've made are drilled through, tapped deep as possible. Blind holes invite jammed fasteners, being hard to clear of chips.
Preference is spotfacing both sides for socket screws and nuts to skip tapping altogether. A cap screw and nut, or a long set screw and two nuts are far easier to replace than a stripped hole.