Micrometer readings on Ø25 pins in a 34 °C shop
A workshop inspects a batch of 500 ground steel pins, nominal Ø25.000 mm with tolerance +0.000/−0.040 mm, so the limits are 24.960 mm and 25.000 mm. The inspector uses an outside micrometer of 0–25 mm range with 0.01 mm graduation. Checked with the anvils closed and the ratchet used, the barrel reads 0.008 mm. The shop floor is at 34 °C in May, and both the pins and the micrometer have been at that temperature for more than four hours; the drawing and acceptance are defined at 20 °C. The coefficient of thermal expansion of steel is 11.5 × 10⁻⁶ per °C. A sample pin reads 24.986 mm. The customer's report on the previous lot listed three pins outside the limit that the shop had passed, and the shop blames the customer's gauge.
1. Correct the sample reading for zero error and for temperature, and decide whether the pin should be accepted. State the remaining margin.
Read the worked answer
Step 1 - zero error. With the anvils closed the micrometer reads +0.008 mm, i.e. it reads high, so every measurement must be reduced by 0.008 mm: Reading corrected = 24.986 − 0.008 = 24.978 mm.
Step 2 - temperature correction to 20 °C. The pin is at 34 °C, so it is expanded relative to the 20 °C acceptance basis: ΔL = α L ΔT = 11.5 × 10⁻⁶ × 25.000 × (34 − 20) = 11.5 × 10⁻⁶ × 25 × 14 = 0.0040 mm. The pin measured hot is larger than its 20 °C size, so: Size at 20 °C = 24.978 − 0.004 = 24.974 mm.
Decision: the limit band is 24.960–25.000 mm. 24.974 mm lies inside it, so the pin is accepted, but with only 25.000 − 24.974 = 26 µm to the upper limit and 24.974 − 24.960 = 14 µm to the lower limit.
Judgement: 14 µm is less than 1.5 least counts of this micrometer (0.01 mm), and less than the corrections we have just applied (8 µm zero + 4 µm thermal). This pin is accepted, but it is not a comfortable acceptance - the corrections are of the same order as the remaining margin. Any pin correcting to within about 10 µm of a limit should be re-measured at 20 °C or on a comparator against a setting master before release.
2. Assess whether this micrometer is capable of inspecting a 0.040 mm tolerance band, using the rule-of-ten principle and considering the zero error.
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Resolution against tolerance. The rule of ten requires the measuring instrument's resolution to be about one-tenth of the tolerance band: Required resolution ≈ 0.040/10 = 0.004 mm. The micrometer resolution is the 0.01 mm graduation (you can estimate to perhaps 0.002–0.005 mm, but the guaranteed discrimination is 0.01 mm).
Ratio achieved: 0.040/0.010 = 4, i.e. only a 4:1 gauge, not 10:1. This is generally considered marginal-to-inadequate for acceptance of a 40 µm band.
Zero error effect. The 0.008 mm zero error is 20% of the total tolerance band. If uncorrected, it shifts every reading by 8 µm, which is more than half the margin the sample pin had. An uncorrected zero error systematically biases the batch: pins are passed that are really 8 µm oversize, which fits the customer's complaint exactly.
Additional uncertainty sources not yet counted: anvil flatness and parallelism, ratchet force consistency, operator feel, and the 4 µm thermal difference across the batch - together easily 5–10 µm.
Verdict: the gauge is not fit for a 0.040 mm band used as a go/no-go acceptance instrument. Use a digital micrometer of 0.001 mm resolution, or better an indicating comparator set with a gauge block master at 24.980 mm, so the tolerance band is magnified. Additionally: zero-check before each shift, record the zero error, and keep pins and gauge in the inspection room long enough to stabilise near 20 °C.
3. The customer rejected three pins from the previous lot and the shop blames the customer's gauge. Set out a defensible way to resolve the dispute and prevent recurrence.
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The dispute cannot be settled by asserting which gauge is "right"; it must be settled by traceable measurement under agreed conditions.
1. Quarantine and identify. Freeze the disputed pins and their records - which inspector, which gauge, what temperature, what zero error was applied. Without this, the argument becomes opinion.
2. Re-measure under controlled conditions. Bring the pins and both gauges to 20 ± 2 °C for at least four hours (steel pins of 25 mm need a few hours to equilibrate fully, not minutes). Then measure each disputed pin on a calibrated comparator or a 0.001 mm micrometer, with zero set against a gauge block traceable to a national standard.
3. Apply both corrections explicitly - zero error and thermal - and record them. Show the customer the corrected values, not raw readings.
4. Referee gauge by agreement. If disagreement persists, nominate a third-party laboratory or the customer's calibrated gauge as referee, with both parties witnessing. Document the decision in advance so the outcome is binding.
5. Establish gauge capability. Run a simple gauge R&R (two or three operators, ten parts, two trials). For a 0.040 mm band, a gauge contributing more than about 10% of the tolerance is suspect; this shop's 0.01 mm micrometer will almost certainly fail. Replace it with 0.001 mm resolution or a comparator.
6. Fix the routine. Write the inspection instruction to include zero check at shift start, 20 °C soak for precision parts, use of the ratchet, and re-measurement of any part within 10 µm of a limit. That single rule would have caught the three rejected pins before despatch.