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Need Help! Taper on CNC Lathe

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I've had a takisawa TS-15 for about a month now. I've been getting new tools and running some test parts. I've got an actual part from a friend of mine right now that has pretty tight tolerances (like -0.0000, +0.0005). This isn't all that bad of a problem. This lathe has a lot of cast iron in it and it has box ways - it's built like a locomotive. Additionally, when I run a few parts in a row, the machine repeats very well (not measurable error using mitutoyo calipers). The problem that I'm having is that if I adjust the tool offset on the finishing tool (the same tool finishes the entire OD) I can get some features in spec, but the others are out.

The part is about 2.5 inches long, and has an OD of about 0.5 inches on average. If I adjust the offsets to get the front of the part in spec, the rear of the part is about +0.0025" too large in diameter. This likely means that there is taper in the machine on the order of 3 thou per 3 inches along the Z axis. The machine's manual suggests adjusting some bolts on the head stock to remove taper. I am concerned that there can be several sources of small taper on lathes.

The machine is level, although I am thinking that I could put it out of level on purpose to twist the machine and affect the taper. It could also be the turret that is out? I REALLY don't want to mess with the turret. I also wonder if it has to do with my workholding - although I am using a nice 5C collet chuck (ATS workholding inc) in this case and it all looks pretty darn optimal. Anyone out there deal with this issue before? How did you solve it?

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