A lathes whose spindle to lathe bed alignment is off will produce tapered shafts, bores and other unwanted tapers. The taper will be an almost imperceptible one that will foul the fit between two sliding parts. When I refer to cutting tapers, I mean relatively pronounced ones like those on a model cannon barrel, the morse taper on a arbor, the taper on a collet or any other type of locking taper.
Tapers can be cut several different ways depending on the machine available to you. On the SHERLINE lathe, you can do two things. The work, tightly gripped in the head chuck can be turned at an angle to the lathe bed by swiveling the head stock assembly to the required angle. The system is probably the easiest to set up but if the piece is rather long, it can not be supported at the tail end. Only workpieces that are either short or robust enough to withstand flexing against the tool bit can be tapered in this manner. The second method is to use of the compound slide. More on that later. The TAIG does not have a swiveling head stock but the tail stock can be off set off center to enable it to align workpieces at an angle. This also has a problem in that the work purposely tilted can not be held in a conventional rigid chuck but will have to be held between centers and driven by a dog with a hose clamp around the work. Not the most convenient thing to set up. The TAIG does have a pretty good little compound slide that can be used to cut tapers, both long and steep.
To set up a compound slide, you first remove the normal tool post that sits on the cross slide and install the top or compound slide and secure it with its screws or bolts. The angles are set in relation to the long axis of the bed with " 0 " being parallel to the bed. The compound is loosened and swiveled toward the back or the front of the bed 1/2 the total final degrees of the taper or chamfer you are trying to create. If you need a dead center with a 60o point you will need to set the slide to 30o past center toward the rear of the bed. The cutters edge needs to be set at an angle that is less than the compound to provide the needed clearance between the cutter's edge and the tapered surface being machined. The tool is advanced through the cut from the narrow to the widest part of the taper with the compound slide and advanced into the workpiece after each pass with the cross slide.