Taper turning: set-over and compound angle

Taper turning is the production of a conical surface by gradually reducing the diameter along the length of the job.

Methods

• Compound rest swivelled to half the taper angle (short, steep tapers).
• Tailstock set-over (long, gentle tapers between centres).
• Taper attachment (guide bar) on the back of the lathe (accurate, long tapers).
• Form tool (very short tapers) and combination of feeds in a CNC machine.

(a) Tailstock set-over

Given D = 60 mm, d = 40 mm, taper length l = 200 mm, total length L = 300 mm.

$$\begin{aligned} S &= \frac{D-d}{2}\times\frac{L}{l} \\ &= \frac{60-40}{2}\times\frac{300}{200} \\ &= 10 \times 1.5 = 15\ \text{mm} \end{aligned}$$

Here L is the total length of the job between centres. The tailstock is moved sideways by 15 mm (its direction decides which end is larger), and the carriage then feeds parallel to the bed.

(b) Compound-slide angle

Half taper angle $\alpha$:

$$\tan\alpha = \frac{D-d}{2l} = \frac{60-40}{2\times 200} = 0.05$$ $$\alpha = \tan^{-1}(0.05) = 2.86^\circ$$

The compound rest is swivelled to 2.86° from the axis (full included taper 5.72°). Taper = (D - d)/l = 20/200 = 1 in 10.

Answer: (a) tailstock set-over = 15 mm; (b) compound rest angle = 2.86°.