Cutting thin-wall tubing on a lathe

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I need to make about 10 metal sleeves from 2.5mm OD thin-wall brass tubing. I made a custom travelling rest to support the tubing, so I can position my parting tool right where the tubing exits the rest (see photo below).

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The hole is just a little larger than the tubing. My question is about the height of my parting blade. For this kind of situation is it best to have the blade slightly high, low, or dead-center on the tubing?

One refinement I'm thinking about is making a piece with a V groove in it, to support the tubing a little better. The piece would be run up to the tubing and fixed with a couple of screws. I _could_ mill a step in my vertical block, but I have some other plans for this thing once I'm done making my brass sleeves.

BTW I initially just positioned my parting tool very close to the chuck jaws but its 3-point grip didn't provide enough support for the tubing -- the ends of the tubing became deformed. These sleeves need to slip over a small post and there isn't much clearance. I was forced to ream out the ends of the tubing, not easy to do with a .250" long piece of 2.5mm tubing. That got old pretty quickly.
 
I would think that slightly low position would be preferred. IIRC, brass seems to like a negative rake. For pieces that small, I would use a support rod inside the tubing. With a sliding fit, the parting tool will quit as soon as it contacts the rod and the parted tube can be slid off. Turn a shoulder on the rod so it can be slid back to allow cleanup of the remaining tubing.
 
I know you are asking about "cutting on a lathe", but do you really need the lathe? Jeweler's saw would make short work of that.
 
Use a tool as thin as possible, I used to part S/S needle tubing, held it in a collet and used a bit more like a knife than a parting tool, did the parting right up against the collet, made them by the thousands.
 
If you need more support, consider making a tube (bushing) that is a slip fit over your brass tube and modify your existing support so the OD will not spin in it. Lube the outside of your brass tube so it runs freely, and extend the new support tube far enough to get your cutoff blade right up against the support tube. This will prevent your brass tube from flexing from the cutting pressure.

A friend uses a slitting saw for a parting tool. He made a holder for his QCTP. This allows using a much narrower tool.
 
I do it differently. I cut the pieces slightly longer on the vertical bandsaw then "face" them to size in the lathe.
This is a case where you can remove and replace the part without runout concerns, mostly
 
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I ended up attaching a second block to the back side of my travelling rest I drilled a hole in it, same size as the one in the rest. Then milled off .070" to produce a slot for my parting blade. In use the tubing passes through both holes so it's well-supported on both sides.

Making-do with the stuff I had on hand.
 
I like your solution . Tubing can be difficult to work.

I found this 1/8” wall x 6” or 7” OD acrylic to be pretty challenging. There is a piece of 1.775” steel as a mandrel, then centering disks plus 2” pvc pipe stacaked up and pushed hard against the chuck jaws (the tailstock center is in a close fitting sleeve to support the bar and it also provides the push to compress the pvc stack up). Then I can cut both ends in the same set up (the ends need to be parallel to each other, all 4 tubes have to be near the same length (about +/- 0.002” tolerance and as “square to the tube axis as can get it”). Miserably easy to chip.
 

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