---
title: "Taper turning: set-over and compound angle"
subject: "Workshop Technology"
chapter: 6
key: "semester_2/workshop_technology:taper-turning-setover-numerical"
source: https://www.bctengineer.com/q/semester_2/workshop_technology/taper-turning-setover-numerical
site: BCT Engineering
---

# Taper turning: set-over and compound angle

Workshop Technology · Chapter 6: General Machining Processes “Chip-forming”

- Asked in: year not given, 3+5 marks
- Video: [Taper turning methods| Taper turning by compound  rest method| Taper turning operation on lathe m/c](https://www.youtube.com/watch?v=g4qHlSoISJ0) — PK Classes
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_2/workshop_technology/taper-turning-setover-numerical
- Whole chapter: https://www.bctengineer.com/md/semester_2/workshop_technology/chapter-6

## Question

Define taper turning. List methods of taper turning on a lathe. A job is to be turned to a taper from 60 mm diameter to 40 mm diameter over a length of 200 mm on a bar of total length 300 mm. Calculate (a) the tailstock set-over and (b) the compound-slide angle if the taper is cut by swivelling the compound rest.

## Short answer

Taper turning produces a conical diameter. Methods: compound rest swivel, tailstock set-over, taper attachment, form tool. For D=60 mm, d=40 mm, taper length 200 mm, total length 300 mm: tailstock set-over = (60-40)/2 × 300/200 = 15 mm; compound rest angle = arctan((60-40)/(2×200)) = 2.86°.

## Answer

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.

| Item | Value |
|---|---|
| Taper | 1 in 10 |
| Half angle | 2.86° |
| Set-over | 15 mm |

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

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Which method suits long, gentle tapers between centres?
   A. Compound rest swivelling
   B. Tailstock set-over
   C. Form tool
   D. Facing
   Answer: B. Tailstock set-over is used for long gentle tapers; the compound rest suits short steep tapers. (Key point: Methods of taper turning)

2. For D = 60, d = 40, taper length 200 mm and total length 300 mm, the set-over S = (D-d)/2 x L/l is
   A. 10 mm
   B. 15 mm
   C. 20 mm
   D. 30 mm
   Answer: B. S = 10 x 300/200 = 15 mm. (Key point: Set-over formula)

3. The compound rest is swivelled to the half taper angle, tan(alpha) = (D-d)/(2l) =
   A. 0.10, giving 5.71°
   B. 0.05, giving 2.86°
   C. 0.05, giving 5.72°
   D. 0.20, giving 11.3°
   Answer: B. tan(alpha) = 20/400 = 0.05, so alpha = 2.86°; the full included angle is 5.72°. (Key point: Compound slide angle)

4. In the set-over formula, L is
   A. The length of the tapered part only
   B. The total length of the job between centres
   C. The diameter of the bar
   D. The tailstock travel
   Answer: B. L is the total length between centres; l is only the tapered length. (Key point: Meaning of L in set-over)

## Related in Workshop Technology

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