Micrometer zero error and an argument over rejected pins
A bicycle-parts job shop must inspect a lot of 500 hardened steel pins, nominal diameter 12.000 mm with a tolerance of ±0.020 mm. The inspector uses a 0-25 mm outside micrometer with 0.01 mm graduations, one division on the thimble. Before starting, the micrometer is closed on its anvils and reads 0.02 mm. The inspector measures 30 pins in the workshop at 34 °C ambient; the pins came from an air-conditioned store at 22 °C an hour earlier. Readings are recorded without correction and the lot is rejected because 12 of the 30 readings lie between 12.025 and 12.035 mm. The production supervisor argues that the micrometer is "only 0.01 mm accurate" and that the rejections are meaningless. The shop has a vernier caliper (0.02 mm), the micrometer, and a dial indicator with a granite surface plate and a 12 mm slip gauge set.
1. Apply the zero-error correction to the disputed readings and decide whether the rejections stand.
Read the worked answer
With the anvils closed and clean the micrometer reads 0.02 mm, so the instrument over-reads by 0.02 mm: true size = indicated − 0.02 mm.
The disputed readings 12.025 to 12.035 mm become 12.005 to 12.015 mm, all inside the limits of 11.980 to 12.020 mm. The 12 rejections are therefore invalid and the parts are good - provided the 0.02 mm is a genuine zero error and not dirt or a worn measuring face. Clean the anvils with a lint-free cloth and re-check twice before accepting that figure.
Note the scale of the problem: the tolerance band is only 40 µm wide, so a 20 µm systematic error uses up half of it. That is why zeroing against a slip gauge, not merely closing the anvils, must be part of the routine before every batch. The lot should be re-inspected after correction, and the inspector's records should show the correction applied.
2. Evaluate the temperature argument quantitatively. Is thermal expansion a credible explanation for the reported rejections?
Read the worked answer
Δd = α L ΔT = 11.5 × 10⁻⁶ × 12 × (34 − 22) = 11.5 × 10⁻⁶ × 12 × 12 = 0.00166 mm ≈ 1.7 µm.
That is about 4% of the 40 µm tolerance band, smaller than the micrometer's own 10 µm resolution and far smaller than the 20 µm zero error. The steel micrometer frame also expands, and the two effects partly cancel in any case. Thermal expansion cannot explain the reported rejections - the zero error does.
Where temperature does matter: long handling of warm pins with bare hands, measuring straight after grinding when coolant and grinding heat are still in the part, and comparing against a 20 °C slip gauge while the pin is at 34 °C. Practical rule: let parts soak at inspection temperature, handle with tongs or gloves, and record part and room temperatures so any dispute is settled with numbers rather than opinion.
3. Recommend the correct measuring method for the 500-piece lot, and state whether the available instruments are adequate. What other controls belong in the inspection routine?
Read the worked answer
The micrometer's 0.01 mm graduation is 10 µm, i.e. 25% of the 40 µm tolerance - marginal under the rule of ten (resolution should be about one-tenth of tolerance). The vernier caliper at 0.02 mm is half the tolerance band and is not acceptable for this job.
Recommendation: use a comparator - a 0.001 mm dial indicator on a granite surface plate, set against a wrung 12 mm slip-gauge stack. Each pin passes under the stylus in seconds with 1 µm resolution, giving a go/no-go decision without thimble-reading errors. Keep the micrometer for setting the comparator and for refereeing borderline parts, using the ratchet or friction thimble for consistent force.
Other controls: fix the measuring points (two diameters at 90°, three axial positions) and record them; verify the comparator setting at the start, middle and end of the lot; keep calibration records for every instrument; and use a proper sampling plan for 500 pieces rather than 30 random pins. A gauge R&R check with two inspectors on ten pins would show whether the method, not the parts, is the real source of variation.