I cringe every time I read of guys re-aligning their headstocks. It is almost as though the factories are run by such imbeciles that they can do everything except dowel the headstock properly onto the ways.
The assumption of the newbie is that the lathe bed is an immutable frame of reference, as though nothing could possibly affect that massive casting. Well, that is not so. The lathe bed is easily twisted like a licorice twist. It is up to you to untwist it when you set it up. Commonly the lathe position is roughed in with a precision level at two extreme ends of the bed. This gets you in the ballpark.
The final test is the free running mandrel held in the spindle taper or chuck. Now, it is seldom possible to find a perfectly straight shaft 12" long, or if you do have one, to find a chuck that will accurately hold it concentric with the spindle axis. A bit of wobble could skew your analysis if you are not careful.
So typically, one must first ascertain the condition of the chuck. Place a piece of precision ground round in the chuck, and run a dial test indicator on it. Grab the piece or apply leverage to it to deflect it with moderate pressure. If the chuck jaws are in good condition, the piece will consistently spring back to the start reading. If you apply leverage and the piece moves and stays moved, then the chuck jaws are tapered, and gripping (most likely) on the back and looser on the front. I'm assuming that the chuck has been properly mounted and is secure on the spindle nose.
Because the lathe is not yet set up, you don't want to grind the jaws yet. So you have to figure a way to ensure 6 point contact (if using a 3 jaw chuck) of the shaft in the chuck. One way is to use a couple of rings of soft copper wire between the jaws and the test bar. For example, you could strip the insulation off of some solid 14-2 or 12-2 house wire and use that. Form a ring long enough to go round the mandrel. Position one ring in a jaw serration near the back end of the jaw, and the other in a jaw serration near the front of the jaw. Using the jaw serrations makes it easier to hold the wire, but is not a pre-requiste. When you clamp down on the test mandrel, the soft copper will yield, and hopefully, squash enough to actually get 6 points of contact on the test mandrel.
Now the test mandrel can be cut. I would probably use a piece of 1.5" or larger stock, and maybe 6 to 8" long in front of the jaws, and undercut an area, leaving two raised areas on the test bar, about 1/2" wide, one area right at the outermost end, the other right near the jaws. Now, get a sharp finishing tool and take a very light cut on both areas of the test mandrel without permitting any movement of the cross slide or compound. That means you should have already checked the gibs for snug fit in both these areas before the test cut.
Now, using a screw micrometer and not a digital caliper, measure the smoothly turned test areas. If you can't turn the surfaces smooth, then you don't know enough about tool grinding, and you'll need to pause, and go study up
The difference in diameters will reflect the true state of the lathe bed. If the outermost test area is larger than the area nearest the chuck, then the lathe bed is twisted, it is low at the tailstock end, on the operator's side of the machine. Adjust the foot screw or shim that corner of the bed. This is a delicate adjustment, so a screw adjuster is highly recommended.
How much to adjust? It would be proportional to distance. If the lathe bed is 10 times longer than the distance between your test cut areas, then a .002 measured difference might be .010 to .020" elevation of the foot screw. Write down what you did in your adjustment, and take another test cut. Even a newbie should be able to get pretty close in half a dozen trial cuts. The trial cuts are only .002" deep, you don't want to create excessive deflection during the test cuts which will fool you.
The ultimate test is boring a cylinder. While most guys can fiddle and fudge with files and sandpaper on the outside of a piece to bring it in spec, it is a lot of trouble to polish a bore straight and true, . If you bore a hole about 4" deep in a 4" diameter heavy wall pipe, and measure the inside diameter at both ends (with the piece still chucked), and get the same results, the lathe setup is good. Unfortunately, most newbies cannnot accurately measure an ID, but again, using an ID indicator, you should be able to detect taper. Set the dial tip at centerline height, and run it along the back side of the bored hole. Testing in this area will show double the actual alignment error of the lathe bed.
So small errors in taper can be easily corrected by proper adjustment of those ordinary looking screws on the feet of your lathe. Leave the dowel pins in the headstock alone.
Now, you're ready to do the tailstock alignment tests. Do NOT adjust the levelling screws of the lathe bed for tailstock problems. Adjust the push-pull screws in the base of the tailstock itself.
First you get good, then you get fast. Then grouchiness sets in.
(Note: The opinions expressed in this post are my own and are not necessarily those of CNCzone and its management)