Hi Mike ...... Warm welcome to IAP !!! .
All good advice above.
I , SORT OF, do what you are suggesting, if I understand you correctly. . BUT, I don't turn the blanks down to size (not even close) until the tubes are in.
I first turn the blank round, at a diameter of about 0.7 to 0.75 inch diameter.
I cut to the correct length + 0.3", approx.
Square the ends of the blank before drilling. . I do my drilling on the lathe, not with a drill press.
I drill the hole. .
I square the ends of the blanks again, if I think it is necessary.
I mount blank between centers (see below), & turn a LITTLE BIT more off, just to make sure that the blank outer cylinder surface is on the same axis as the hole.
I now trim the blank to the correct length + a few thou on each end.
OK, so now it is time to see how the blank looks with the hardware parts ..... which I think is your main concern.
If you want to do so, you can apply a finish coat or two to this STILL OVERSIZE blank
Sliding in the tube is not necessary. . All you want is to check the appearance of blank next to hardware, right ?
The hole will be big enough for you to insert the hardware ( nib and finial , or whatever you have and whatever you call them ) at both ends .
Have a good look at it and decide whether to proceed or not.
If you decide that it looks good ....... proceed as below . . . . If not, well, just scrap it and go watch the football game . .
But ....... let's be optimistic ....... so, proceed .......
Glue in the tube. . Let the glue dry/cure.
Trim the blank to the exact length ..... at this stage, this means that you only have a few thou to take off at each end to get to the brass tube end.
You are now ready to turn the tube down to its final size and shape, ....... and then apply the finish.
And then you press in the nib and finial (or whatever).
Hope this is clear. . If you have any problem understanding me, just shoot me a question or two.
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I should say that I do not use a mandrel and I do not use bushings.
I use the Turn Between Centers (TBC) method ..... two 60-degree centers ..... fixed center in headstock, live center in tailstock.
The blank (with tube glued in) is held between the two centers. . . I carefully turn the blank down making careful measurements with calipers, until the size is just what I need to match the size of the hardware pieces at each end.
If you want to stick with mandrel and bushings that should be OK also.
I hope this works for you as well as it works for me . . I know that it probably sounds complicated, but it really isn't once you get used to it.