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There are many variables which can cause taper in a turned part. To test spindle runout, chuck drill rod or similar and indicate from the tool post.
The reason why you have a taper is because the material is sticking out 2 inches. The material is springing away from the tool. As you get closer to the headstock the material doesn't deflect like at the 2.0 inch mark. You didn't mention the diameter of the material or the finished dia. of the part. Tool & billet deflection is common.
These Lathes are very accurate and you also didn't mention if you have a center into the end of the part. You may need to spot drill and use either a live center or dead center held in the tailstock. Do you have a Live Center or dead Center?? This would help eliminate the taper you are experiencing.
I use a PC 50 lathe which turns a slight taper (wider by
0.0018" at 2" out from the headstock). Is there a way to adjust
the headstock? I took the cover off and the prismatic shape of the front
way is built into the headstock so that's not obviously adjustable short of
scraping. I tried shimming the far end of the bed like you would level to
adjust twist in the bed of a conventional floor mounted horizontal engine
lathe. That didn't change anything and I suspect it just slightly
deformed the sheet metal holding the bed. Any ideas on this? I
admit that the error is pretty small but I sometimes make little optical mounts
that slide together and they and I are happier when things are cylindrical.