Thermal Correction of a 40 H7/g6 Fit
A batch of 40 mm nominal steel shafts and bores is machined and measured on the shop floor at 34 °C. The drawing calls for a 40 H7/g6 fit: hole H7 = +0.025/0 mm, shaft g6 = −0.009/−0.025 mm. A digital micrometer with 0.001 mm resolution reads a shaft at 39.978 mm; a bore gauge reads the mating hole at 40.012 mm. Both instruments were zeroed on a 40 mm setting ring at 20 °C and have a stated uncertainty of ±0.004 mm. The steel expansion coefficient is 11.7 × 10⁻⁶ /°C. The inspector wants to accept the parts because both readings are inside the drawing limits. The assembly is a locating fit that must have a clearance between 0.005 mm and 0.045 mm at 20 °C. The parts will run at 20 °C.
1. Correct the measured values to 20 °C and decide whether the shaft and hole conform to the drawing.
Read the worked answer
Temperature difference = 34 − 20 = 14 °C. Thermal expansion of a 40 mm steel dimension = 11.7 × 10⁻⁶ × 40 × 14 = 0.00655 mm. At 34 °C the parts are larger than at 20 °C, so subtract this from each reading. Corrected shaft = 39.978 − 0.00655 = 39.9715 mm. Corrected hole = 40.012 − 0.00655 = 40.0055 mm. Shaft g6 limits are 40 − 0.009 = 39.991 mm maximum and 40 − 0.025 = 39.975 mm minimum. The corrected shaft is below the minimum by 0.0035 mm, so it does not conform. Hole H7 limits are 40.000 to 40.025 mm; the corrected hole is within limits. The inspector's raw readings are misleading because they include thermal growth.
2. Calculate the clearance at 20 °C and discuss whether the nonconforming shaft can still be accepted for assembly.
Read the worked answer
Corrected clearance = hole − shaft = 40.0055 − 39.9715 = 0.0340 mm. The required assembly clearance is 0.005 to 0.045 mm, so the actual clearance is within the functional range. However, the shaft violates its drawing size limit. The measurement uncertainty is ±0.004 mm, and the shaft is only 0.0035 mm below the lower limit, so the result is within the uncertainty band. That makes it a borderline reject, not a clear functional failure. The correct action is to re-measure at 20 °C with calibrated instruments, using a guard band, and confirm the size. If the shaft is confirmed undersize, it should be rejected or accepted only by a documented engineering concession; the assembly clearance alone does not make the part conform to the drawing.
3. Explain why zeroing the instruments at 20 °C does not remove the need for temperature correction, and state one additional check for the bore gauge.
Read the worked answer
Zeroing at 20 °C establishes the instrument reference, but the workpiece at 34 °C is physically larger. The micrometer or bore gauge reads the expanded workpiece, so the indicated size includes thermal growth relative to 20 °C. The setting ring compensates the instrument scale, not the part temperature. For the bore gauge, check its calibration against the setting ring at the same temperature as the measurement and confirm that the gauge head has had time to reach thermal equilibrium with the bore. A bore gauge can also read small if the head is not square to the bore axis or if the bore is tapered. Re-measure the hole at two depths and two directions to confirm roundness and cylindricity before making the acceptance decision.