Hot Inspection Room and an H7 Bearing Bore
Forty bearing housings have a bore specified Ø30.000 to Ø30.021 mm (H7). The inspection room has no air conditioning and reads 31 °C; the machine shop where the parts were cut reads 26 °C. The inspector uses a 25–50 mm inside micrometer, zeroed on a 30 mm setting ring that is stored in the same inspection room. Six parts read 30.019, 30.021, 30.024, 30.020, 30.023 and 30.018 mm. The three parts over 30.021 mm have been segregated. The drawing also calls for cylindricity of 0.005 mm, and the bore is 45 mm long, so the micrometer is being rocked to find the maximum diameter. The customer requires gauge R&R below 10 % of tolerance for critical bores; the tolerance width is 0.021 mm. The production supervisor argues that everything is about 5 µm bigger because of the heat and wants all parts accepted.
1. Evaluate the supervisor's thermal argument quantitatively. Does a 31 °C inspection room make the parts read 5 µm large? Show the calculation and state the one thermal effect that genuinely matters here.
Read the worked answer
- Expansion of a 30 mm steel bore over 11 °C: 30 × 11.5 × 10⁻⁶ × 11 = 0.0038 mm (3.8 µm). So the supervisor has found a real number.
- But the setting ring sits in the same room, is the same material, and grows the same 3.8 µm. The micrometer is zeroed on the ring, so the ring growth is built into the zero. The comparison of bore to ring cancels the expansion to first order; the residual is only the material mismatch between ring and part, which for steel on steel is effectively zero.
- The reading therefore still represents the 20 °C size within roughly 0.2 µm. The parts are genuinely 2–3 µm over, not thermally inflated.
- The effect that does matter: a part carried in from the 26 °C shop and measured immediately is 5 °C cooler than the ring. Error = 30 × 11.5 × 10⁻⁶ × 5 = 0.0017 mm (1.7 µm), and it makes the part read small, not large. On a 21 µm tolerance that is 8 % of the band and must be controlled.
Conclusion: the heat does not excuse the oversize parts. If anything, parts measured straight from the shop are being accepted when they are slightly larger than the reading.
2. Decide the disposition of the six parts. Include the gauge R&R allowance of 10 % of tolerance and explain why the two-point micrometer cannot sign off the cylindricity callout.
Read the worked answer
- R&R allowance = 10 % × 0.021 mm = 0.0021 mm (2.1 µm). Any decision within 2.1 µm of a limit is not defensible without re-measurement.
- 30.024 mm: 3 µm over the upper limit, beyond the R&R allowance. Reject or rework to a target such as 30.012 mm to leave margin.
- 30.023 mm: 2 µm over, inside the uncertainty band. Re-measure before deciding; do not scrap on one reading.
- 30.021 mm: exactly at the limit. Accept only if a repeat measurement at controlled temperature confirms it is not above; hone to 30.015 mm to be safe.
- 30.019 and 30.020 mm: 1–2 µm below the limit, acceptable only if re-measured with a known-capability gauge; realistically they are fine.
- 30.018 mm: clearly inside; check the lower limit is 30.000, which it is.
A two-point inside micrometer finds one diameter per position. It cannot detect out-of-roundness (three-lobed bores are invisible to two-point measurement), taper along the 45 mm length, or a barrel shape. The 0.005 mm cylindricity callout needs a bore gauge or air gauge at three sections and two planes, or a CMM. Rocking to find the maximum also biases the reading large, which is another reason to re-measure rather than argue.
3. Propose the measurement-system and process changes that would prevent a repeat, covering temperature, gauge capability, and the instrument choice for this feature.
Read the worked answer
- Let parts soak. Bring parts to the inspection room and hold them long enough to equalise, or record part temperature and apply a correction. A 5 °C difference is 1.7 µm on this bore.
- Calibrate against the ring at use temperature. Keep the ring with the micrometer, log the calibration date, and check the micrometer zero at the start of each session.
- Run a proper gauge R&R: 3 operators × 10 parts × 3 trials, reported against the 0.021 mm tolerance. If it exceeds 10 %, replace the inside micrometer with a three-point bore gauge or a setting-ring-based bore gauge.
- Choose the right instrument for the callout: a two-point micrometer can confirm size but not cylindricity. Add a bore gauge at three sections for the 0.005 mm requirement.
- SPC: plot bore size per lot so a drift is caught before parts are at the limit.
- Bring the bore target to about 30.012 mm so normal tool wear does not push parts over the limit.
- Record shop and inspection room temperatures on the inspection sheet.
- Feed the results back to the machinist for tool offset correction rather than sorting at the end of the batch.