Acceptance decision on a hot batch of Ø25 h7 shafts
A batch of 60 ground shafts, nominal Ø25 h7 (0.000/+0.021 mm), is inspected by a trainee in a room where the thermometer reads 34 °C and there is no air conditioning; the reference temperature is 20 °C. The shafts come straight from the cylindrical grinder, where coolant is at 38 °C, and are measured within two minutes. The 0–25 mm outside micrometer used has a calibration sticker dated 14 months ago; when closed on its zero standard at 34 °C it reads +0.002 mm. Results: 14 shafts read 25.020 to 25.023 mm, the rest read 25.004 to 25.014 mm. The trainee wants to accept all of them because a vernier caliper also reads about 25.02 mm on the largest shaft. The supervisor argues that the micrometer 'reads high', so everything should be accepted. The drawing calls for 25 h7 and the customer requires gauge R&R below 30 % of tolerance.
1. Correct the readings for zero error and thermal expansion, and state which shafts, if any, breach the tolerance.
Read the worked answer
Two corrections are needed before comparing with 0/+0.021 mm.
- Zero error: the micrometer reads +0.002 mm when closed, so all readings are 0.002 mm high; subtract 0.002 mm.
- Temperature: steel expands about 11.5 × 10⁻⁶ per °C. A part measured at roughly 34–38 °C, say 36 °C, is 16 °C above the 20 °C reference, so the correction over 25 mm is 25 × 11.5 × 10⁻⁶ × 16 ≈ 0.0046 mm. The part will be smaller when it cools, so subtract this as well. Total correction ≈ 0.0066 mm.
Applying it:
- Largest shaft 25.023 mm − 0.0066 ≈ 25.0164 mm: inside the 25.021 mm upper limit.
- 25.020 mm − 0.0066 ≈ 25.0134 mm: inside.
- Smallest 25.004 mm − 0.0066 ≈ 24.9974 mm: below the 25.000 mm lower limit, i.e. undersize.
So on corrected figures the group reading 25.004–25.006 mm is suspect undersize. However, a correction is not a measurement: with expansion, zero drift and an overdue calibration, uncertainty is comparable to the 21 µm tolerance band. All borderline parts must be soaked at 20 °C for at least 12 h and re-measured with a calibrated instrument before a decision.
2. Evaluate the instrument choice and calibration status, and state what must be done before the batch can be released.
Read the worked answer
Instrument suitability:
- The tolerance band is 21 µm. A 0–25 mm micrometer with 0.001 mm resolution and about ±2 µm uncertainty is fit for purpose; a vernier caliper with 0.02 mm resolution has uncertainty of roughly ±20–30 µm, which is of the same order as the whole tolerance. The caliper reading cannot support acceptance or rejection.
- The calibration sticker is 14 months old and the zero has drifted by 2 µm. The instrument's status is unknown, so every result from it is unverified evidence, not a measurement result.
Before release:
- Quarantine the batch and send the micrometer for calibration; obtain the as-found report to judge how many earlier results are invalid.
- Re-measure after temperature soak at 20 °C, using a calibrated micrometer and a setting standard, with at least two operators and repeat readings on 10 parts.
- Run a gauge R&R study; if the result exceeds 30 % of the 21 µm tolerance, improve the gauge, fixturing or training before releasing.
- Record the temperature at measurement on the inspection report and segregate undersize parts for concession or scrap.
- Fix the process cause: parts should cool before inspection, and the inspection room needs temperature control for h7 work.