---
title: "Requirements of machine tool drives"
subject: "Machine Design II"
chapter: 5
key: "semester_7/machine_design_ii:machine-tool-drive-requirements"
source: https://www.bctengineer.com/q/semester_7/machine_design_ii/machine-tool-drive-requirements
site: BCT Engineering
---

# Requirements of machine tool drives

Machine Design II · Chapter 5: System Design

- Asked in: year not given, 6 marks
- Video: [L 04 Features of Machine Tool Drives & Mechanical Drive |Machine Tool Design|Mechanical](https://www.youtube.com/watch?v=zpdEdmTQtG0) — MECHANICAL & AUTOMOBILE ENGINEERING_LJIET
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/machine_design_ii/machine-tool-drive-requirements
- Whole chapter: https://www.bctengineer.com/md/semester_7/machine_design_ii/chapter-5

## Question

Explain the requirements of a machine tool drive. Compare stepped and stepless speed regulation, and explain why spindle speeds are arranged in a geometric progression.

## Short answer

The drive must cover a wide speed range (Rn up to 100), maintain constant power and torque, be rigid, allow fast safe speed changes, and remain compact and stable. Stepped drives offer fixed speeds with high efficiency; stepless drives provide continuous speed but lower efficiency and higher cost. A geometric progression of speeds yields a constant percentage speed loss between steps, so the optimal speed is always close to an available one, and requires fewer gears.

## Answer

A **machine tool drive** transmits power from the motor to the spindle or slide and gives the range of speeds and feeds needed for different materials, tool materials and diameters.

#### Requirements
- Cover the full range of cutting speeds, $v = \pi D N/1000$, for the smallest and largest diameters. The speed ratio $R_n = N_{max}/N_{min}$ is typically 20 to 100 or more.
- Enough **power and torque** at the spindle, constant power over most of the range.
- High **rigidity** and low vibration, accurate running of shafts and gears, low noise.
- Quick, easy change of speed, preferably during running or with levers; safe and simple to operate.
- Compact, economical, easy lubrication and maintenance; minimum number of gears and shafts.
- Stable speed under changing load.

#### Stepped vs stepless
| Point | Stepped (gearbox, cone pulley) | Stepless (variable speed) |
|---|---|---|
| Speeds | Fixed number of speeds | Any speed in the range |
| Examples | Sliding gears, clutch gears, cone pulleys | Variable-frequency motor, hydraulic, friction/pulley variators |
| Efficiency and rigidity | High, positive drive | Lower with friction or belts |
| Cost and complexity | Gears needed but robust | Higher cost for control |
| Use | Lathes, milling machines, drills | CNC machines, grinding, special drives |

#### Why geometric progression
If speeds are chosen as $N_1,\ N_1\varphi,\ N_1\varphi^2, \dots$ the **percentage loss in cutting speed** between steps, $(N_{j+1}-N_j)/N_{j+1} = (\varphi-1)/\varphi$, is the same at every step. The ideal speed for a job is therefore never more than a constant fraction away from an available speed. An arithmetic progression gives a large loss at low speeds and a wasteful closeness at high speeds. The GP also needs fewer gears and fits the standard preferred-number (Renard) series R5, R10, R20, R40 with $\varphi = 1.58, 1.26, 1.12, 1.06$.

## Check yourself

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

1. Why are spindle speeds arranged in geometric progression?
   A. It needs more gears
   B. It gives equal speed differences between steps
   C. It gives the same percentage loss in cutting speed between every pair of steps
   D. It makes the top speed lower
   Answer: C. In a GP the loss (phi - 1)/phi is constant, so the ideal speed is never more than a fixed fraction away from an available one. (Key point: Why geometric progression)

2. What is the drawback of an arithmetic progression of speeds?
   A. It cannot include the top speed
   B. It needs fewer gears
   C. It gives equal percentage losses
   D. It gives a large loss at low speeds and wastefully close speeds at high speeds
   Answer: D. Equal steps are large in percentage terms at low speeds and small at high speeds. (Key point: Arithmetic progression drawback)

3. How does stepless regulation compare with stepped?
   A. Stepless gives any speed in the range, stepped gives a fixed number of speeds with a positive, rigid drive
   B. Stepless has a fixed number of speeds
   C. Stepped can give any speed
   D. Stepless is always cheaper and more rigid
   Answer: A. Stepless drives (variator, VFD) give any speed but cost more and may be less rigid. Gearboxes are robust with fixed speeds. (Key point: Stepped vs stepless)

4. Which standard series has phi = 1.26?
   A. R5
   B. R10
   C. R20
   D. R40
   Answer: B. R5, R10, R20 and R40 have phi = 1.58, 1.26, 1.12 and 1.06. (Key point: Preferred series)

## Related in Machine Design II

- [Six-speed machine tool gearbox design](https://www.bctengineer.com/question.md?key=semester_7%2Fmachine_design_ii%3Amachine-tool-speed-ladder-gear) — Machine Design II, chapter 5
- [Gear ratios of a four-speed car](https://www.bctengineer.com/question.md?key=semester_7%2Fmachine_design_ii%3Aautomobile-gear-ratio-selection) — Machine Design II, chapter 5

## Related in other subjects

- [Induction: sum of geometric progression](https://www.bctengineer.com/question.md?key=semester_4%2Fdiscrete_structure%3Ainduction-geometric-series-sum) — Discrete Structure, chapter 1
- [Time and space mean speed from 20 spot speeds](https://www.bctengineer.com/question.md?key=semester_7%2Ftransportation_engineering_ii%3Aspot-speed-20-observations-travel-time) — Transportation Engineering II, chapter 1
- [Speed control techniques in AC drives](https://www.bctengineer.com/question.md?key=semester_7%2Futilization_of_electrical_energy%3Aac-drive-speed-control-techniques) — Utilization of Electrical Energy, chapter 3
- [Roller chain drive: length, speed and factor of safety](https://www.bctengineer.com/question.md?key=semester_6%2Fmachine_design_i%3Aroller-chain-drive-selection) — Machine Design I, chapter 8