The Bore That Read Good for the Wrong Reason
The finish bore on a 6061 aluminum housing is Ø50.000/50.025 mm. A machinist checks the first article with a two-point bore gauge zeroed on a 50.000 mm steel setting ring and reads 50.009 mm - inside tolerance. The part left the machine four minutes earlier; the shop is at 27.5 °C, the coolant is at 24 °C, and the steel ring has been sitting in the shop for two days. The gauge has never been through a GR&R study, and three readings by two operators on the same bore spread 0.006 mm. The drawing is dimensioned at 20 °C. α(aluminum) ≈ 23 µm/m·°C; α(steel) ≈ 11.5 µm/m·°C.
1. What is the part's size at 20 °C, and do you accept it on this reading?
Read the worked answer
Work the comparator math, both bodies at 27.5 °C (ΔT = 7.5 °C).
- Ring bore at 27.5 °C: 50.000 × (1 + 11.5e-6 × 7.5) = 50.000 + 0.0043 = 50.0043 mm
- A comparator displays ring nominal plus the difference: display = 50.000 + (part − ring) → part at 27.5 °C = 50.009 − 50.000 + 50.0043 = 50.0133 mm
- Correct the part to 20 °C: 50.0133 − (50 × 23e-6 × 7.5) = 50.0133 − 0.0086 = ≈50.0047 mm
Verdict: the part is ~50.005 mm at 20 °C - inside 50.000/50.025. But the reading of 50.009 is not the part size, and the fact that it happened to land in tolerance is luck.
Key insight: the aluminum part and the steel master grow by different amounts (0.0086 vs 0.0043 mm), so a warm aluminum part checked against a warm steel master over-reads. The correction is not a single CTE term; it is the differential. If the ring had been the same material, the two effects would nearly cancel.
2. You have a 0.006 mm operator spread on a 0.025 mm tolerance. How does that change your decision-making, and what do you do about it?
Read the worked answer
0.006 / 0.025 = 24% of tolerance from repeatability alone - conditional at best.
Consequences:
- A part reading within 0.006 mm of either limit cannot be dispositioned on one reading. You need a guard band: accept only inside roughly 50.000 + 0.006 to 50.025 − 0.006 until the gauge is studied.
- The gauge may not have the resolution/discrimination for the job (rule of thumb: the measuring increment should be ≤ 1/10 of tolerance, i.e. ≤ 0.0025 mm here), and a two-point bore gauge on a lobed bore also carries form error.
Actions:
- Run a proper GR&R (3 operators × 10 parts × 3 trials). Target ≤10% of tolerance; 10–30% is conditionally acceptable only with a documented guard band and a better alternative in work.
- Move to a bore micrometer, air gauge, or an in-process gauging head with a digital readout of 0.001 mm; qualify it against a certified ring at the same temperature as the parts.
- Write the measurement method, temperature, soak time, and decision rule onto the inspection plan so every operator applies the same rule.
3. What process controls would you add so that this argument does not repeat on every first article?
Read the worked answer
Control temperature, control soak, control the master - in that order.
- Soak: parts must reach 20 ± 1 °C before final gauging - a 50 mm aluminum part needs hours, not minutes. Either a temperature-controlled inspection room with a documented minimum soak, or measure hot with a written, signed correction (as computed above) and a part-temperature probe reading at the bore.
- Master: the setting ring must be certified, in date, and at the same temperature as the gauge and (as closely as practical) the part. Record the ring ID and calibration date on the inspection sheet.
- Coolant/process: hold coolant temperature near ambient so parts do not come off the machine 3.5 °C above shop air; a chiller or a settling tank costs far less than scrapping a lot on a thermal argument.
- Feedback loop: log the corrected size against machine offsets so the operator is adjusting to the 20 °C number, not the shop-temperature number. Otherwise the machine gets offset in the wrong direction and a good process drifts out of tolerance overnight.
- Capability: with 0.025 mm tolerance and a ±0.003 mm measurement, keep Cpk above 1.33 or the measurement argument will keep recurring at the limits.