Dowels specified in inches, measured with the wrong micrometer
A batch of 60 dowel pins is turned from EN8 bar to a drawing size of Ø 0.5000 in, tolerance +0.0005 in / −0.0000 in, surface finish Ra 0.4 µm. The shop floor is at 34 °C; the inspection room and the micrometer were calibrated at 20 °C. Take α = 11.7 × 10⁻⁶ /K for steel. The only instruments available are: a 0–25 mm outside micrometer with 0.01 mm graduations; a 0–1 in micrometer reading to 0.001 in; a vernier caliper with 0.02 mm least count; and a digital caliper whose data sheet quotes ±0.02 mm accuracy. Inspection uses the metric micrometer, records each pin to the nearest 0.01 mm, and passes every pin that reads between 12.69 mm and 12.71 mm. Seven pins were rejected, and three of those were re-polished to size.
1. Convert the drawing limits to millimetres and judge whether the instrument choice and the accept band used by inspection are correct.
Read the worked answer
Conversion. 0.5000 in × 25.4 = 12.7000 mm. 0.0005 in × 25.4 = 0.0127 mm, so the limits are 12.7000 / 12.7127 mm - a tolerance band of only 12.7 µm.
Rule of ten. The measuring resolution should be about one tenth of the tolerance, i.e. ≤ 1.27 µm. Compare:
- metric micrometer, 0.01 mm = 10 µm resolution: unusable (resolution is nearly the whole tolerance band);
- 0.001 in micrometer = 0.0254 mm = 25.4 µm: worse than the metric one;
- vernier caliper 0.02 mm and digital caliper ±0.02 mm accuracy: far outside the band.
Accept band. The band actually used, 12.69–12.71 mm, is 20 µm wide instead of 12.7 µm and is wrongly positioned: it accepts pins up to 10 µm below the low limit (they will not assemble as an interference dowel should) and it rejects good pins between 12.710 and 12.7127 mm. Both are wrong, and the reject count is therefore not a measure of the process.
Action: re-inspect with a 0.001 mm micrometer or a comparator setting master before scrapping anything.
2. Quantify the temperature effect and say what should be done about it.
Read the worked answer
ΔL = L α ΔT = 12.7 × 11.7 × 10⁻⁶ × (34 − 20) = 2.08 × 10⁻³ mm = 2.08 µm.
That is 2.08/12.7 ≈ 16% of the tolerance band, so it cannot be ignored on a 12.7 µm band: a pin reading 12.7100 mm at 34 °C is about 12.7079 mm at 20 °C.
Nuance that decides the action. Expansion only cancels between workpiece and gauge if both are at the same temperature. If the micrometer has been in the 34 °C shop long enough, its screw has grown too and much of the error cancels for a steel part; if the pin comes straight off the lathe (often 40–50 °C) and is gauged immediately, the error is real and larger than 2 µm.
Recommendation: never gauge a warm part. Soak the pins and the micrometer on a steel plate in the inspection room for at least 30 minutes, gauge at 20 ± 2 °C, and only then apply the batch decision. Measuring at the machine and passing parts on a 0.01 mm micrometer is the real fault here, not the 2 µm itself.
3. Calculate the rejection and scrap percentages and comment on what these figures mean.
Read the worked answer
- Rejected at final inspection: 7/60 = 11.67%
- Re-worked and recovered: 3/60 = 5.0%
- Scrapped: (7 − 3)/60 = 4/60 = 6.67%
For a simple turned dowel with a stable process, roughly 7% scrap against a 12.7 µm band is plausible but high, and it would normally be attacked with an SPC chart on the pitch of the machine.
Here, however, the figure is meaningless: the parts were sorted with a 10 µm resolution micrometer against a 12.7 µm band, so most of the 7 rejects are measurement decisions, not manufacturing defects. Before any process change, re-sort the 7 rejected pins plus a sample of the 53 accepted ones with a 0.001 mm micrometer at 20 °C. If the true capability is good, most of the rejects return to the batch and the real scrap figure drops; if a genuine size drift exists, the machine offset - not the operator - is the thing to adjust.