I've been running some production parts in my shop- and for those that aren't familiar with my frayed-shoestring-budget garage shop, one of my machines is a small Logan 11" lathe converted to CNC using a Centroid Acorn system.
I've been having some issues with variable tolerances and random tapers, in a straight OD turn. Only up to about .002" max, so it's by no means critical to the part, but it still annoys me.
The taper issue I suspected came at least in part from a worn tailstock, that due to the length of the part, needs to be extended out about 2/3rds of its range, just to be able to reach the part. I got tired of using "cut and try" to dial in the tailstock alignment, so I decided to fall back to the old tried-and-true "two collars" test bar method.
Just to be clear, I don't claim to have come up with or invented any of this.

I can't recall when or where I saw this specific idea, but it's been a good long time- easily twenty years or more. And of course a version of it is briefly mentioned in SouthBend's
How To Run A Lathe back in 1941.
Anyway, I started with a chunk of Home Depot 5/8" allthread, and a set of matching nuts.
The allthread I cut into two pieces, one about six or seven inches long, and another about a foot long. Each of these I faced, chamfered and gave a nice deep centerdrill to both ends:
The short one for the job at hand (nominally a 6" workpiece) and the longer one for later use, since I need to double-check the alignment of the big Springfield tailstock.
For a set of collars, I dug a chunk of 1-1/2" aluminum round stock out of my junk bin, and drilled it out to 5/8".
As the little lathe doesn't part heavy rod well, I simply bandsawed two thick rings off.
Those got chucked up, faced and slightly beveled:
Then it was a simple matter of clamping the two discs more or less at either end of the rod, and snugging them down.
Some people have used plain washers, or cut discs from 1/4" plate, etc. You can use anything you want- diameter wise, material wise, thickness wise. I simply recommend aluminum as it's easier to cut, and to make them thickish (as opposed to just a washer, say) simply to make it easier to measure.
This method is, I think, an improvement over the solid machined bar, simply becasue it's easier to make, and a little more "reusable". If the discs, through repeated re-truing, get too small, just swap them.
Then again, most typical home shop types will only use something like this a few times at most, so no worries either way.
Now, I don't have a dog drive plate, so here's the older'n me trick: Just chuck up a random chunk of mild steel, and turn a 60-degree point in it. As long as you don't take it out of the chuck, regardless of how worn or eccentric your chuck is, the point will be accurate and concentric to the spindle's axis of rotation.
Then, simply attach your favorite drive dog, mount the bar up between the centers, and rest the dog-leg on one of the chuck jaws.
After that, simply take a light skim cut of the disc nearest the chuck. You don't have to take much off, just enough you know the disc is now round and centered.
Then, flip the bar end-for-end, and take a skim cut on the other disc.
In this case, we're just getting the discs to round and concentric- you want them close, but the final cut will be next.
Now, take another fine skim cut...
Then flip it end for end again,
and without moving the cross slide or compound, take a final skim cut on the other disc. Theoretically, the two discs should be not only the exact same size, but also exactly concentric with the drilled centers.
Now, measure the two discs to be sure;
According to my Mitutoyo 1-2" mic with a tenths vernier, both were exactly 1.4835".
Now, with it still in place, I could plunk my dial indicator in place, and move the cross slide 'til it zeroes.
Again,
without moving the cross slide, I moved the carriage to indicate the other disc- which appears to be .001" off center. (Towards the operator.)
With a little care and light use of the tailstock adjusters, I was able to zero it, or at least, very close to it.
Now, in order to move over to the Logan, I needed that headstock center. I don't need to spin the rod this time, so no need for a dog or driver, but I still needed the accurate center. I know the 3-jaw is a couple of thou out, so I switched back to the collet assembly, and re-turned the point:
Moving that same point and collet over to the Logan, I chucked it all up, making sure to check the tailstock with the barrel extended about as far as it needs to in use for this particular part. I then moved the indicator over (the tool center height on both machines is the same) and while it's hard to tell, I 'zeroed' it at the 6:00 position.
I did that so there was minimal preload on the tip, and it could just 'walk up' on the other disc- I wouldn't have to pull on the stem to get it past the edge.
This time the tailstock was .002" off, with everything snugged and locked.
And it was about here I found another problem: There appears to be a LOT of slop in the X-axis ballscrew. According to the indicator, and the MPG dial on the Centroid remote, I could run the slide in to zero the dial, but backing it out, I could dial in 7-8 thou before the needle started to move.
Clearly the X-axis ballscrew was either not that great to begin with (most likely- I was buying cheap Import parts) or has worn rapidly (also not unlikely, again cheap import stuff.)
I may have to tear this thing down and see if I can't find a better quality replacement screw. Or one of the imports with the double ballnut...
In the meantime, I dialed in the tailstock as best I could...
And added an old manual machinists' trick to the program. The 'conversational' programming has it's own built-in tool retract between passes- and it's not that much. So I edited the program to add another .100" to the retract- in the hopes that would take some of the slop out of the motion as it moves the tool back into the work.
After that I ran about two dozen pieces. Less taper, but still about .002" part-to-part variance on the overall sizes. Probably the best I'm going to get until I can do something about that ballscrew (if that is indeed the problem...)
Stand by, more to come.
Doc.