---
title: "Thread errors and effect of pitch error"
subject: "Metrology"
chapter: 12
key: "semester_3/metrology:screw-thread-errors-and-pitch-effect"
source: https://www.bctengineer.com/q/semester_3/metrology/screw-thread-errors-and-pitch-effect
site: BCT Engineering
---

# Thread errors and effect of pitch error

Metrology · Chapter 12: Measurement of Screw Threads

- Asked in: year not given, 3+5 marks
- Video: [Screw Thread Errors - Screw Thread Measurements - Metrology and Quality Engineering](https://www.youtube.com/watch?v=m9ELHtth7pI) — Ekeeda
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/metrology/screw-thread-errors-and-pitch-effect
- Whole chapter: https://www.bctengineer.com/md/semester_3/metrology/chapter-12

## Question

(a) List the errors that may occur in a screw thread and explain their effect on the fit. (b) A 60 degree metric screw thread has a pitch error of $+0.03$ mm. Find the increase in the virtual (functional) effective diameter. If the measured effective diameter of the bolt is 18.350 mm, find the virtual effective diameter. What is the value if the thread is a $55^\circ$ Whitworth thread?

## Answer

#### (a) Errors in threads
1. **Pitch errors:** progressive (the pitch increases or decreases uniformly), periodic (the error repeats every revolution, e.g. due to an eccentric lead screw), drunken thread (the helix is irregular within each turn), and irregular.
2. **Flank angle errors:** the thread angle is incorrect, or one flank is inclined differently from the other.
3. **Major and minor diameter errors:** wrong depth and root form.
4. **Effective (pitch) diameter errors:** the diameter at which the thread width and the gap width are equal is wrong.

**Effect:** a pitch error or an angle error makes the bolt (external thread) behave as if it had a larger effective diameter, so it may not assemble with the nut (internal thread). Contact then occurs only at a few points on the flanks, so the load-carrying area drops, and the thread wears quickly and can strip. To compensate, the effective diameter of the bolt must be reduced (or that of the nut increased), which uses up part of the tolerance.

#### (b) Numerical
Because of a pitch error $\delta P$, the flanks of the bolt and nut interfere. The bolt behaves as if its effective diameter were larger, so the virtual (functional) effective diameter is increased by

$$
\delta E = \delta P\,\cot\frac{\alpha}{2}
$$

For $\alpha = 60^\circ$: $\cot 30^\circ = 1.732$

$$
\delta E = 1.732 \times 0.03 = 0.052\ \text{mm}
$$

Virtual effective diameter $= 18.350 + 0.052 = 18.402$ mm.

For Whitworth ($\alpha = 55^\circ$): $\cot 27.5^\circ = 1.921$

$$
\delta E = 1.921 \times 0.03 = 0.0576\ \text{mm}, \quad E_{virtual} = 18.350 + 0.058 = 18.408\ \text{mm}
$$

**Answer: increase = 0.052 mm (metric), virtual effective diameter = 18.402 mm; for Whitworth 0.058 mm (18.408 mm).**

## Check yourself

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

1. Why can a bolt with pitch error fail to assemble with its nut?
   A. The pitch error reduces the effective diameter of the bolt
   B. The pitch error makes the bolt act as if it has a larger effective diameter
   C. The major diameter becomes smaller
   D. The nut becomes harder than the bolt
   Answer: B. The flanks ride over each other, so the bolt behaves as larger; its effective diameter must be reduced to compensate. (Key point: Effect of pitch error)

2. The increase in virtual effective diameter due to pitch error dP is:
   A. dE = dP tan(alpha/2)
   B. dE = dP sin(alpha)
   C. dE = dP cot(alpha/2)
   D. dE = dP / cot(alpha)
   Answer: C. Pitch error is converted into an equivalent diameter change using dP cot(alpha/2). (Key point: Formula)

3. For a 60 degree thread with dP = 0.03 mm and measured E = 18.350 mm, what is the virtual effective diameter?
   A. 18.380 mm
   B. 18.350 mm
   C. 18.298 mm
   D. 18.402 mm
   Answer: D. dE = 1.732 x 0.03 = 0.052; virtual E = 18.350 + 0.052 = 18.402 mm. (Key point: Metric thread numerical)

4. How does the correction for a 55 degree Whitworth thread compare with 60 degree for the same pitch error?
   A. Larger: 0.058 mm because cot 27.5 deg = 1.921
   B. Smaller: 0.052 mm
   C. Same: 0.052 mm
   D. Zero since Whitworth has no pitch error effect
   Answer: A. cot(27.5 deg) = 1.921 > cot(30 deg) = 1.732, giving 0.0576 mm and a virtual diameter of 18.408 mm. (Key point: Whitworth)

## Related in Metrology

- [Measuring thread pitch, angle and diameters](https://www.bctengineer.com/question.md?key=semester_3%2Fmetrology%3Atoolmaker-microscope-thread-measurement) — Metrology, chapter 12
- [Effective diameter by three-wire method](https://www.bctengineer.com/question.md?key=semester_3%2Fmetrology%3Athree-wire-method-effective-diameter) — Metrology, chapter 12
- [Error propagation and effect of averaging](https://www.bctengineer.com/question.md?key=semester_3%2Fmetrology%3Aerror-propagation-and-averaging) — Metrology, chapter 2
- [Limits of a 40 H7/g6 hole-shaft fit](https://www.bctengineer.com/question.md?key=semester_3%2Fmetrology%3Afit-40-h7-g6-calculation) — Metrology, chapter 9

## Related in other subjects

- [Screw jack with square thread](https://www.bctengineer.com/question.md?key=semester_7%2Fmachine_design_ii%3Ascrew-jack-square-thread-numerical) — Machine Design II, chapter 8
- [Screw thread production and change gears](https://www.bctengineer.com/question.md?key=semester_4%2Fmanufacturing_and_production_processes%3Ascrew-thread-manufacturing-change-gears) — Manufacturing and Production Processes, chapter 11
- [Box deodar column, 60 mm planks, 350 kN](https://www.bctengineer.com/question.md?key=semester_6%2Fdesign_of_steel_and_timber_structure%3Atimber-box-column-deodar-5m-350kn) — Design of Steel and Timber Structure, chapter 11
- [Greatest bolt force, 100 kN at 500 mm](https://www.bctengineer.com/question.md?key=semester_6%2Fdesign_of_steel_and_timber_structure%3Abolt-force-shaft-100kn-500mm) — Design of Steel and Timber Structure, chapter 4