Alignment of the mandrel axis has nothing to do with the tailstock. Tailstock is the very last thing to be set up when rebuilding a lathe, simply because is independent of everything else and can be adjusted to suit on its own.
Headstock mandrel needs to be aligned so it is parallel to the bed ways in both the horizontal and vertical planes. Very tricky to do if you have a worn bed with a .005" hollow worn in it at the chuck end where the carriage is most used. But if you reckon your bed is in useable condition, and has been set dead level at both ends, and if your carriage ways and gib are in OK condition, the quick check is to place a 2MT test bar in the headstock spindle with the 6" or 12" long parallel ground section protruding out in the normal area where a turning job would sit. No tailstock is used for this test. A dial indicator mounted on the carriage with the plunger resting on the test bar and the carriage racked back and forth while observing the dial indicator. First done with the dial indicator on the side of the bar, then the top. If the dial indicator reads 0 or within one thou of it all the way along, job's good. If you get a bigger reading, the headstock may need adjusting to suit. (Be sure to check the test bar is running concentrically when rotated before starting the alignment test.
Another way to test headstock mandrel alignment, and a test that should be done after the above anyhow, is to hold a piece of one inch diameter bar in the three jaw chuck, sticking out about six inches, and take a cut along it. Again, no tailstock in place. If the mandrel is aligned, the turned bar will have less than one thou taper over the length of the cut. If the bar turns down tapered, headstock may need adjusting to suit.
Headstock is adjusted by either shimming or scraping in the vertical plane and in the horizontal by using the two clamping screws that are in the front of the headstock at its base, along with shims or scraping the clamped surface of the headstock where it bears against the bed, which necessitates the loosening and tightening of the four headstock hold-down cap screws inside the headstock below the backgear assembly.
Once you have headstock mandrel aligned to the bed axis in this way, THEN you can go on and set the tailstock. Quick and rough way is to put a centre in the headstock mandrel and one in the tailstock and then pinch a thin steel rule between the two. It should stand up vertically and also square across in the horizontal plane if all is aligned well. It is adjusted horizontally by the offsetting screws in the tailstock. If the tailstock is too low, shims can be added between the tailstock body and its base. You can also chekc the alignment of the tailstock quill's number two morse taper with the lathe bed by inserting the MT2 ground test bar into the tailstock taper and running the carraige mounted dial indicator up and down it as was done for the headstock alignment.
There are of course other ways of doing this but this will get you going.
Edited By Hopper on 17/04/2017 11:47:18
Edited By Hopper on 17/04/2017 11:48:35
Edited By Hopper on 17/04/2017 11:51:02