I don't have any taper when I turn from the headstock of my 9A in a chuck/collet (what I generally do). Today, I went to turn a 12" long round bar between centers and am getting a slight taper of about .022 over 6-1/2" (on the tailstock end). Diameter is thicker on the headstock side. I have an edge alignment test bar, double checked my tailstock is aligned, and when I run a dial indicator along the test bar, it's consistent within a few thousands over the entire length of the bar. I have about .004" of runout on the tailstock side with my live center.
I don't think it's being caused by tailstock runout, and given the consistent measurements across the test bar, I don't think it's bed wear. Ideas on what else to check? My gib screws and carriage bolt screws/lock are backed out just shy of causing drag. I have ~0.025" backlash in my cross feed, but everything else feels tight.
I'm not aware of any way to lock the cross feed or compound rest...
As much as 0.004", (in my world more than 0.1mm) before you even start, is too much. A good live centre, in a tailstock that is locked gives a fixed point that cannot contribute to taper if it is lined up to the spindle centre. The uncompromising hardball way is use dead centres, and be sure they fit the centre spot holes in the test bar without bottoming on their points.
Next is the headstock. Discover if it has runout. Even if it has some, the error effect it makes is more about cyclic surface finish than taper. A whole 0.022" is because the tail centre is about 0.010" nearer to the tool. Absolutely do as
@Ulma Doctor suggests. Get to know everything about the spindle play.
Turn between dead centres to discover the tail alignment. Sure - folks like to run a dial indicator along the shaft while moving the carriage, but the definitive way is to very carefully use a test bar you make cuts on, and directly measure them. The final cut should be very light, low force kind. Make it up yourself for a test area near the headstock, and another at the tail end, with the space between relieved just deep enough so you can move from the cut at one end to continue the cut at the other end without moving the cross slide out at all. If you can't lock it, then just don't touch it. Leave it at the setting where the tool was cutting with backlash taken up.
Finally, measure the test diameters
with a micrometer! If the taper is still there, adjust the tailstock Y-axis screws.
There can be messed up taper effects if the tail point is not on the correct centre height. Check with the indicator it stays on the line, right up to the tail. At this stage, if there still is a problem, you will have gamed it to the point where your own senses will be giving you clues to the cause.
You want to know the whole deal, like if maybe if your the whole carriage is moving out of a worn area as it approaches the tail, or if there is a bed twist that needs leveling out. I don't say this is what is happening, but I do think you can zero in on the cause.
