Why do I get a taper when turning?

[irving2008]

I've been practicing machining the ends of my leadscrews using a sacrificial bit of 12mm threaded rod. I am having problems with surface finish and a small amount of taper.

I don't have a steady so have been taking very fine cuts using a brazed tip tool (like the 12mm one in the photo but a 16mm to fit the lathe).

I thought that any movement of the workpiece away from the tool, due to lack of a steady or movement in the spindle bearings, would result in an oversize at the end, and on/under-size nearer the chuck. In fact the reverse is true, the taper being .05 - .07mm in about 30mm.

I've checked the topslide movement relative to a test bar and the topslide runs parallel to the bar within .02mm over a 100mm length. Also the run-out of a test bar in my newly ground chuck jaws is less than 0.02mm over the same length.

If the workpiece was canted in the chuck am I right in my belief that that should not result in a taper, although the machined end would be off centre relative to the rest of the workpiece?

Should I be worried about this level of error, given the age of the machine (90-ish years)?

I am aware there is some movement in the slides, with end float and backlash, and I am assuming this is the main culprit for the somewhat rough surface finish, however slowly I take the feed, although the spindle speed is only 160rpm (I think, I've not measured it accurately yet).

This is clearly too low for such a small diameter workpiece... I need to change the drive pulley arrangement to give me a higher top speed (700rpm?) so I can bring it down if need be with the VFD (and backgear for threading)