---
title: "Lathe operations, taper turning and turning calculations"
subject: "Manufacturing and Production Processes"
chapter: 7
key: "semester_4/manufacturing_and_production_processes:lathe-operations-taper-turning-numerical"
source: https://www.bctengineer.com/q/semester_4/manufacturing_and_production_processes/lathe-operations-taper-turning-numerical
site: BCT Engineering
---

# Lathe operations, taper turning and turning calculations

Manufacturing and Production Processes · Chapter 7: Material Removal Processes: “ Chip-forming”

- Asked in: year not given, 4+4 marks
- Video: [All Lathe Machine Operations: Turning, Facing, Taper Turning, Boring, Knurling, Tapping, Forming](https://www.youtube.com/watch?v=km6ickQglVY) — Shubham Kola
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/manufacturing_and_production_processes/lathe-operations-taper-turning-numerical
- Whole chapter: https://www.bctengineer.com/md/semester_4/manufacturing_and_production_processes/chapter-7

## Question

(a) List the main operations performed on a centre lathe and explain any three methods of taper turning. (b) A bar of 60 mm diameter is turned on a lathe at 500 rpm with a feed of 0.2 mm/rev and a depth of cut of 2.5 mm. The specific cutting energy of the material is 2.5 J/mm$^3$. Determine the cutting speed, the material removal rate, the cutting power and the time to turn a length of 300 mm. Also, a taper is to be turned from 60 mm to 40 mm diameter over a length of 200 mm; find the compound rest setting and the tailstock offset if the whole bar length is 300 mm.

## Short answer

Lathe operations include turning, facing, taper turning, threading, drilling. Taper methods: compound rest swivelled to half angle, tailstock offset for long tapers, taper attachment. Numerical: V = 94.2 m/min, MRR = 47.1 cm³/min, power = 1.96 kW, time = 3 min; compound rest 2.86°, tailstock offset 15 mm.

## Answer

#### (a) Lathe operations and taper turning

The **centre lathe** holds the work between centres or in a chuck and the tool moves along or across the axis. Operations: plain (straight) turning, facing, step turning, chamfering, grooving, parting-off, taper turning, form turning, thread cutting, drilling, boring, reaming, knurling.

**Methods of taper turning**

1. **Compound rest:** the top slide is swivelled to half the taper angle and fed by hand. Suitable for short, steep tapers (angle up to about 45 degree).
2. **Tailstock set-over:** the tailstock is shifted sideways so that the work axis is inclined to the bed. Used for long gentle tapers; the centres are mismatched, which spoils the centre holes.
   Offset is given by $S = \frac{D-d}{2}\cdot\frac{L}{l}$ (L = bar length, l = length of taper).
3. **Taper turning attachment:** a guide bar at the set angle moves the cross slide automatically while the carriage travels. Gives accurate, long tapers without disturbing the centres.
4. **Form tool:** a tool shaped to the taper is plunged in; short tapers only.

#### (b) Numerical

**Cutting speed**

$$
V = \frac{\pi D N}{1000} = \frac{\pi\times60\times500}{1000} = 94.2\ \text{m/min}
$$

**Material removal rate**

$$
MRR = f\,d\,V = 0.2\times 2.5\times 94.2\times1000 = 47\,124\ \text{mm}^3/\text{min} = 785\ \text{mm}^3/\text{s}
$$

**Power**

$$
P = u\times MRR = 2.5\times 785.4 = 1963\ \text{W} \approx 1.96\ \text{kW}
$$

**Machining time**

$$
T_m = \frac{L}{fN} = \frac{300}{0.2\times500} = 3.0\ \text{min}
$$

**Taper**

Half angle for the compound rest:

$$
\tan\theta = \frac{D-d}{2l} = \frac{60-40}{2\times200} = 0.05\;\Rightarrow\;\theta = 2.86^\circ
$$

Tailstock offset for a 300 mm long bar:

$$
S = \frac{D-d}{2}\cdot\frac{L}{l} = \frac{60-40}{2}\times\frac{300}{200} = 15\ \text{mm}
$$

**Answer:** $V = 94.2$ m/min, $MRR = 47.1$ cm$^3$/min, $P = 1.96$ kW, time $= 3$ min; compound rest set at $2.86^\circ$; tailstock offset $= 15$ mm.

## Check yourself

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

1. Which taper turning method suits long gentle tapers without disturbing the centres?
   A. Compound rest
   B. Tailstock set-over
   C. Taper turning attachment
   D. Form tool
   Answer: C. A guide bar moves the cross slide automatically; tailstock set-over mismatches centres, and the compound rest suits short steep tapers. (Key point: Taper methods)

2. How is the compound rest angle found?
   A. tan(theta) = (D - d)/l = 0.1, theta = 5.7 deg
   B. theta = (D - d)/2 = 10 deg
   C. tan(theta) = l/(D - d) = 10
   D. tan(theta) = (D - d)/(2 l) = 0.05, theta = 2.86 deg
   Answer: D. The top slide is set to half the taper angle: (60-40)/(2x200) = 0.05. (Key point: Compound rest setting)

3. What is the tailstock offset for a 300 mm bar?
   A. 15 mm, S = ((D-d)/2)(L/l)
   B. 10 mm, ignoring bar length
   C. 20 mm, using D - d
   D. 6.7 mm, using l/L
   Answer: A. S = 10 x 300/200 = 15 mm. The whole bar length L is used, not only the taper length. (Key point: Tailstock offset)

4. How is turning time found?
   A. T = L f N = 30 000 min
   B. T = L/(f N) = 300/(0.2 x 500) = 3 min
   C. T = L/N = 0.6 min
   D. T = L/f = 1500 min
   Answer: B. Feed per minute is f N = 100 mm/min, so 300 mm takes 3 min. (Key point: Machining time)

## Related in Manufacturing and Production Processes

- [CNC lathe part program with G and M codes](https://www.bctengineer.com/question.md?key=semester_4%2Fmanufacturing_and_production_processes%3Acnc-lathe-part-program-gcode) — Manufacturing and Production Processes, chapter 9
- [Milling, shaper and drilling machine operations](https://www.bctengineer.com/question.md?key=semester_4%2Fmanufacturing_and_production_processes%3Amilling-shaper-drilling-machines-operations) — Manufacturing and Production Processes, chapter 7
- [Orthogonal cutting forces and power numerical](https://www.bctengineer.com/question.md?key=semester_4%2Fmanufacturing_and_production_processes%3Aorthogonal-cutting-forces-power-numerical) — Manufacturing and Production Processes, chapter 7
- [Cutting tool materials and their properties](https://www.bctengineer.com/question.md?key=semester_4%2Fmanufacturing_and_production_processes%3Acutting-tool-materials-characteristics-economics) — Manufacturing and Production Processes, chapter 7

## Related in other subjects

- [Taper turning: set-over and compound angle](https://www.bctengineer.com/question.md?key=semester_2%2Fworkshop_technology%3Ataper-turning-setover-numerical) — Workshop Technology, chapter 6
- [Turning time and metal removal rate](https://www.bctengineer.com/question.md?key=semester_2%2Fworkshop_technology%3Alathe-turning-time-mrr-numerical) — Workshop Technology, chapter 6
- [Classification and main parts of centre lathe](https://www.bctengineer.com/question.md?key=semester_2%2Fworkshop_technology%3Alathe-classification-main-parts) — Workshop Technology, chapter 6
- [Thread cutting on lathe and change gears](https://www.bctengineer.com/question.md?key=semester_2%2Fworkshop_technology%3Alathe-thread-cutting-change-gears) — Workshop Technology, chapter 6