Tc 9-524 fundamentals of machine tools

L1 = Length of taper
For example, the amount of tailstock offset required to
machine a bar 36 inches (3 feet) in length for a distance of 18
inches (1.5 feet) when the large diameter is 1 3/4 (1 .750)
inches and the small diameter is 1 1/2 (1.5) inches is
calculated as follows
OFFSET 
= L X (D-d)-
2XL1
OFFSET =36 X (1.750 - 1.5)
36
OFFSET =36 X 0.25
36
OFFSET = 9/36
OFFSET = 0.25 inch
7-37

---

TC 9-524
Therefore, the tailstock would be offset (toward the
operator) 0.25 inch to machine the required taper.
Metric tapers can also be calculated for taper turning by
using the offset tailstock method. Metric tapers are expressed
as a ratio of 1 mm per unit of length. Figure 7-66 shows how
the work would taper 1 mm in a distance of 20 mm. This
taper would then be given as a ratio of 1:20 and would be
annotated on small diameter (d) will be 1 mm greater (d + ).
Refer to the following formula for calculating the dimensions
of a metric taper. If the small diameter (d), the unit length of
taper (k), and the total length of taper (1) are known, then the
large diameter (D) may be calculated. The large diameter (D)
will be equal to the small diameter plus the amount of taper.
The amount of taper for the unit length (k) is (d + 1) - (d).
Therefore, the amount of taper per millimeter of unit length
= (l/k). The total amount of taper will be the taper per
millimeter (l/k) multiplied by the total length of taper (l).
For example, to calculate for the large diameter D for a 1:30
taper having a small diameter of 10 mm and a length of 60
mm, do the following:
Since the taper is the ratio 1:30, then (k)= 30, since 30 is the
unit of length.
Tailstock offset is calculated as follows: