TAPER TURNING
Taper turning falls into three categories, short tapers of relatively obtuse angles generally turned with the top-slide, longer tapers of a more acute angle produced either by setting the tailstock over or by use of a taper turning attachment, and internal tapers.10.1 Short Tapers
Typical examples are chamfers (larger than can be accommodated by a shaped tool), turning 60 degree headstock centers, or turning up blanks for bevel gears. Where the angle is not too critical it is a simple matter to set the angle using the scale on the top-slide base, this should get you within 0.5 of a degree, or a little closer perhaps with care. Where it's essential to achieve greater accuracy it will be necessary to use an accurate protractor (such as a bevel gauge) across the faceplate or cross-slide, and registering on the top-slide. If the body of the slide is not ground square the only option is to withdraw it and use the machined dovetail as a datum surface. When turning tapers of this sort with the top-slide use both hands on the feedscrew handle and try to keep it turning smoothly, you don't want a 'stop-start' situation or the finish and accuracy will suffer. Another typical job is the making of small taper broaches from square silver steel. The maximum size is really governed by the availability of equipment to press them (note: press, not hammer them!) through a pre-drilled hole, using the bench vice or drill press, and this is likely to be about 1/4" unless you happen to own an arbour press. The method is to take a length of square sliver steel about 4" long and machine a gradual taper along about 3" of it's length. The taper should start at the minor diameter of the square (which will be the same size as the pilot hole) and leave sharp corners 3" from the end. Using a threading tool a series of notches are turned to form the cutting lands, the leading face being square to the axis. The tool is then hardened and tempered to dark straw. Use plenty of lubricant and press the broach through the pilot hole in one pass, make quite sure the broach goes in straight or it will break. The result will be a nice square hole of accurate size. I use this method for making small valve handwheels and suchlike.10.2 Long Tapers
Within this classification falls the production of Morse Taper shanks and the like. These require a high degree of accuracy and some discussion of the problems and solutions for producing MT shanks is given in the construction notes for a top-slide setting gauge for turning Morse Tapers . The standard method is to use a commercial shank of known accuracy held between centers as a gauge for setting the top-slide. Setting can be done either using a DTI which will indicate when the slide is parallel with the taper, or by machining a gauge which, when attached to the top-slide, can be pressed against the side of the shank to set the correct cutting angle. I have since successfully used a 'sighting' method whereby the edge of the topslide (which must be machined accurately parallel to the dovetail guides - which is the case with the new Super 7s) is aligned by eye with the edge of the MT blank. This has proved to be quite successful, and the half-dozen times I've tried the method has always resulted in a usable taper shank. The trick is to get the lighting right - an even illumination which is not too bright - and to position the eye vertically such that the finest of knife edges separates the top-slide and the edge of the MT blank. Another method often quoted is to set over the tailstock out of line with the lathe axis. I have several problems with this procedure: firstly, it's difficult to measure with any precision the angle produced in this way, secondly, all turning must be done between centers (which might not be convenient), and lastly, there is the task of re-setting the tailstock to zero so that the lathe can once again turn parallel. All in all, it's probably more trouble than it's worth for routine use. The method is occasionally useful for gradual tapers where the workpiece is of a length near the maximum between-centers capacity of the lathe, but I would bet that it's not often used these days.An alternative to setting over the tailstock is to use an adjustable centre. This device consists of a taper shank to fit the tailstock socket, and a 60 degree point mounted on a sliding bracket which can be moved out of alignment with the lathe axis and locked in position. An improvement on this is to use a small boring head (assuming it will fit the socket) with a center fitted instead of a boring bar, at least this gives some accurate indication of the offset. In both cases it's important that the offset is only horizontal and center height is maintained, ususally more difficult to assess with the boring head as there is no obvious datum surface to rest a square against.
Myford taper turning attachment. The above methods are fine for the occasional production of such tapers, but the real tool for the job is a purpose-built taper turning attachment. This consists of a secondary dovetail slide bolted to the rear of the lathe bed, and to which is attached the rear of the cross-slide by a linkage. To use the slide, the cross-slide feedscrew is disengaged and it is the taper slide that then guides the tool. Myford produce an attachment which has about 10" of travel (6-7" useful capacity), it will operate 15 degrees either side of parallel though the method of setting the angle is a little crude. It has a scale etched on the baseplate, and the dovetail slide is clamped by a simple bolt which is loosened to make adjustments. A more satisfactory solution is to use a fine-threaded screw to move the dovetail slide, and this modification is a feature of the kit design sold by Hemingway . An even better alternative is the design described by Geo.H.Thomas in his book "The Model Engineers Workshop Manual", whereby worm teeth are machined on the end of the dovetail slide, and these are mated with a worm fitted to a bracket. This enables a micrometer collar to be utilised to indicate very fine angular adjustments. With this class of taper tooling the angle required for turning a Morse Taper can be set directly without reference to a commercial taper shank (though this is a good way of calibrating the setup). Without this facility it is useful to set the slide arm accurately with the DTI for common tapers and drill and ream through both the slide arm and base to accept a dowel pin. Inserting the dowel pin will quickly reset the arm to the predetermined angle.
Workpiece should not extend from chuck jaws by more than 3x its diameter 
