Hi Tony -Happy Thanksgiving!
This is exactly my point. Example: How do you intentionally make a slightly tapered shaft? You intentionally put a horizontal offset in the tailstock. As the piece "wobbles" (so to speak) you will, at the TS end, start out with an interrupted cut which gradually becomes a continuous cut as you get closer to the head. Once you make enough passes, you no longer get an interrupted cut and presto, you have the tapered shaft. The same thing happens when the jaws are not parallel and it's holding the piece at an angle; likewise if the headstock is cocked. If you have a long workpiece and if you use a chuck and if the TS is off-center, you will get a taper at the TS end and closer to the chuck, you will get an inverse bulge. This is because the piece is bending/flexing as it rotates because the chuck jaws are holding it rigidly. It is precisely this reason that the only way to get a true shaft in a manual machine, it to spin between centers with a dog and avoid the chuck altogether. Centers have the desirable trait of being able to hold work in offset axis -and this is why centering holes are cut at 60 degrees -to allow a piece to be held firmly yet, rotate in a plane that's not perpendicular to the endpoints. When you use centers and if the axis is perfectly centered tip-to-tip, you get a perfect shaft (assuming your ways aren't crooked).
Chucks cause all kinds of problems which is why I use high-precision collets when the diameters are under 1-1/8 -and when real accuracy is needed, spin between centers. People like chucks because they're big pieces of metal and look cool but, when you want real accuracy, two simple pointy protrusions and an ugly dog are the way to go.
This case sounds like it could be either unparallel jaws or a cocked headstock. The first place I'd look is the jaws. For a piece just 3-4 inches long, with jaws not square and not center at the TS end, it's very easy to get a taper of 4-5 thou. [Side note: Tapers: I do this all the time because some boat props (the old brass ones) need a very slight taper toward one end. When the desired taper is extreme (more than 4-5 degrees) I use the taper attachment instead].
Also, if a toolbit is slightly high or slightly low by up to several thousandths, it has no perceptible impact on the diameter of the cut. Moving the bit in or out by some amount changes the diameter by 2x same amount but, moving it up or down has no (measurable) impact other than making the finish poor. If you do the geometry of a line that starts out perpendicular to the surface of a circle then, move the line up (so it's still horizontal but no longer perpendicular) by say 10 thou, the delta between the intersection point (the place where the cutting edge would contact) only changes by fractions of a hundred-thousandth -About 2-3 orders of magnitude (less) of what we can even measure.
It's possible though, I'm misreading the symptom but, I thought it was exactly as you mentioned. It's all good. We'll get it sorted out.
Ray
EDITS: First thing in the morning. Had to fix some broken sentences.
Ray, I believe he means after he turns it. Then it should run just as true as the spindle bearings, and with no taper unless there is something wrong. Even a piece chucked crookedly can be trued up by turning. He's not talking about runout, he's talking about taper after he makes a cut.
