Borderline 50 h6 shaft measurement in a hot workshop
A 50 mm diameter shaft, tolerance 50 h6 (0/−0.016 mm), is turned and brought to the inspection bench. The workshop is at 31 °C and the shaft has been there for two hours. The micrometer has a zero error: with the anvils closed it reads +0.003 mm. Three readings at one section are 49.987, 49.989 and 49.986 mm. The micrometer and shaft are both steel, coefficient of linear expansion 11.5 × 10−6 /°C, and the drawing is interpreted at 20 °C. The inspector’s calibration certificate gives an uncertainty of ±0.002 mm for the micrometer over this range. The production manager wants the shaft accepted because “it is within a couple of microns”. A go/no-go gauge is not available.
1. Using the readings and calibration data, determine the size at 20 °C as best you can and state whether the shaft conforms to 50 h6 (0/−0.016 mm). Explain how the zero error and the common steel temperature affect your calculation.
Read the worked answer
Average reading = (49.987 + 49.989 + 49.986) / 3 = 49.98733 mm. The micrometer reads +0.003 mm at zero, so subtract 0.003 mm: 49.98433 mm.
The temperature correction needs care. If only the shaft is corrected, the expansion is αLΔT = 11.5 × 10−6 × 50 × 11 = 0.0063 mm, giving 49.9780 mm. But the micrometer frame and screw are also steel at the same 31 °C. To first order, the micrometer scale expands by the same factor as the shaft, so the scale reading already compensates for the shaft expansion. The corrected size is therefore about 49.9843 mm, not 49.978 mm.
The 50 h6 limits are 50.000 mm and 49.984 mm. The corrected result is only 0.0003 mm above the lower limit, which is far smaller than the ±0.002 mm measurement uncertainty. The shaft is therefore borderline and cannot be declared conforming on this evidence. A controlled re-measurement at 20 °C is required.
2. The production manager argues that the shaft is “within a couple of microns” and should be accepted. Give a reasoned response, including the risks of accepting it.
Read the worked answer
The tolerance zone is only 0.016 mm wide, and the measurement uncertainty alone is ±0.002 mm. The measured value sits about 0.0003 mm from the lower limit, so the “couple of microns” is the uncertainty, not a safe margin. In addition, only one section has been measured; ovality, taper and surface finish have not been assessed, and the shaft may not have reached thermal equilibrium.
Accepting a borderline undersize shaft risks a loose fit in a bearing or gear. That can lead to creep, fretting, noise and heat, and the problem may only appear after the machine is in service. The correct response is to re-measure in a controlled 20 ± 1 °C environment after stabilisation, using a calibrated micrometer zeroed on a 50 mm gauge block at the same temperature. Measure at three sections and two directions, record the maximum and minimum, and compare the actual fit with the mating part if the result is still within 0.002 mm of the limit.
3. Describe a practical inspection method to settle the question without a go/no-go gauge.
Read the worked answer
Move the shaft to an inspection area at 20 ± 1 °C and allow at least two hours for stabilisation. Clean the shaft and micrometer anvils. Zero the micrometer on a calibrated 50 mm gauge block that has been at the same temperature; record the residual zero error. Measure at three sections along the shaft and in two perpendicular directions at each section, using the friction thimble consistently.
Calculate the average, maximum and minimum diameters and the out-of-round and taper. Include the calibration uncertainty and the zero error in the report. If the result is still within 0.002 mm of a limit, use a comparator or a coordinate measuring machine, or check the actual fit with the mating bearing or gear. Do not release the shaft on a single reading at the tolerance boundary. Record the method, temperature, instrument identification and all readings.