NOT RECOMMENDED: Basic Steel Barrel Trimmers / Pen Mills
... But here is how I used them ... I have two of the Rockler barrel trimmers, the ones with six cutting edges. I sharpened them with diamond paddles. Eventually the individual cutting edges reach the point where they can't be sharpened evenly, so I bought the second set, which wore out quickly enough, too.
The proper way to sharpen them is flatten the flat faces, the ones that are parallel to the center shaft. Sharpen each face with the diamond hone using exactly the same pressure, number of strokes, etc. The fewer the number of strokes the better. DO NOT sharpen or touch the angled faces or the tips!
NOT RECOMMENDED solution described above:
https://www.rockler.com/barrel-cleaner-pen-mill-kit
https://www.rockler.com/double-sided-diamond-hone (Metal substrate, more durable. The ones I chose.)
https://www.rockler.com/diamond-hone-sharpening-set (Plastic substrate, not durable. I did not choose these.)
I will be giving away the Rockler barrel trimmer / pen mills for our club's next auction or to a beginning (begging?) local pen turner.
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RECOMMENDED: Sanding Jig on the Lathe
The proper solution is to buy or build a sanding jig for your lathe. Rick Harrell makes and sells good ones here:
https://www.penturners.org/threads/custom-made-penturning-tools-accessories.92501/
(search for "sanding")
Someday I will get around to building my own.
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MY CURRENT SOLUTION: Woodpeckers Pen Mill Set
I bought the Woodpecker's pen mill and have not looked back. They are expensive, but they work very well. They stay sharp no matter the pen blank material. Someday the carbide tips will be easy to replace when they finally get dull. I bought the 5 piece set from this page:
https://www.woodpeck.com/ultra-shear-pen-mill-inserts.html
I hope this helps.