Fig. 2. Examples of Taper Work
Setting Tailstock Center for Taper Turning.—Suppose the tailstock center is to be set for turning part C, [Fig. 2], to a taper of approximately 1 inch per foot. In this case the center would simply be moved toward the front of the machine 1/2 inch, or one-half the required taper per foot, because the total length of the work happens to be just 12 inches. This setting, however, would not be correct for all work requiring a taper of 1 inch per foot, as the adjustment depends not only on the amount of the taper but on the total length of the piece.
Fig. 3. Detail View of Lathe Tailstock
For example, the taper roller B has a taper of 1 inch per foot, but the center, in this case, would be offset less than one-half the taper per foot, because the total length is only 9 inches. For lengths longer or shorter than twelve inches, the taper per inch should be found first; this is then multiplied by the total length of the work (not the length of the taper) which gives the taper for that length, and one-half this taper is the amount to set over the center. For example, the taper per inch of part B equals 1 inch divided by 12 = 1/12 inch. The total length of 9 inches multiplied by 1/12 inch = 3/4 inch, and 1/2 of 3/4 = 3/8, which is the distance that the tailstock center should be offset. In this example if the taper per foot were not known, and only the diameters of the large and small ends of the tapered part were given, the difference between these diameters should first be found (21/2 - 2 = 1/2); this difference should then be divided by the length of the taper (1/2 ÷ 6 = 1/12 inch) to obtain the taper per inch. The taper per inch times the total length represents what the taper would be if it extended throughout the entire length, and one-half of this equals the offset, which is 3/8 inch.
Fig. 4. Taper Plug and Gage