Interpreting a Shaft Drawing with Conflicting Tolerances
A student is given a detail drawing of a stepped shaft. The overall length is dimensioned as 120 ±0.2 mm. A chain of dimensions along the same axis reads 45 ±0.1 mm, 50 ±0.1 mm and a remaining length that is not dimensioned directly. A separate note on the drawing states "all dimensions in mm, unless otherwise stated" and a general tolerance block reads "±0.3 for untoleranced dimensions." The student measures a finished part with a vernier caliper: overall length 120.35 mm, and the 45 mm step measures 44.95 mm. The student is unsure whether the part is acceptable and asks whether the caliper reading is trustworthy.
1. Work out the implied remaining length and its tolerance from the chain of dimensions, and explain why dimensioning both an overall length and a full chain is a drawing problem.
Read the worked answer
The chain covers 45 + 50 = 95 mm of the 120 mm overall length, so the remaining length is:
120 − 95 = 25 mm
Its tolerance comes from combining the tolerances: worst case the overall is 120 ±0.2 and the chain segments are 45 ±0.1 and 50 ±0.1. The remaining length is therefore 25 mm with a worst-case spread of ±(0.2 + 0.1 + 0.1) = ±0.4 mm, i.e. 24.6 to 25.4 mm.
The drawing is over-constrained: giving both an overall dimension and every segment means the last segment is determined by the others but not stated, and its tolerance is inherited rather than chosen. A drafter should either dimension the overall and one reference segment, or dimension the full chain and leave the overall as a reference (bracketed) dimension. Over-dimensioning invites arguments at inspection about which dimension governs.
2. Assess whether the measured part is acceptable, and state which measurement is the concern.
Read the worked answer
Check each measured feature against its stated tolerance:
- Overall length: 120.35 mm against 120 ±0.2 mm → upper limit is 120.20 mm. 120.35 mm is out of tolerance by 0.15 mm.
- 45 mm step: 44.95 mm against 45 ±0.1 mm → limits 44.90 to 45.10 mm. 44.95 mm is within tolerance.
So the part fails on overall length, not on the step. Note that the 25 mm remaining length would then be 120.35 − 44.95 − 50 = 25.40 mm, which sits right at the inherited upper limit - another sign the chain is over-constrained.
Before scrapping, the student should confirm the measurement, because a single caliper reading near a limit is not conclusive.
3. Explain why a single vernier caliper reading may not be trustworthy here, and what the student should do to confirm the result.
Read the worked answer
A vernier caliper has resolution typically 0.02 mm and accuracy worse than that, so a reading 0.15 mm outside a limit is plausible but should be confirmed. Sources of error include:
- Zero error - the jaws may not close to zero; check and apply correction.
- Parallax and reading error on the vernier scale.
- Measurement force and jaw tilt - calipers are easily skewed on a cylindrical shaft, giving a chord rather than a diameter or a slightly long reading.
- Temperature - a warm part from machining expands; measure at room temperature.
- Worn or damaged jaws on a workshop caliper.
To confirm, the student should re-zero the caliper, take three readings at different orientations (rotate the shaft 120° between readings), and compare with a micrometer (resolution 0.01 mm) for the critical overall length. If the micrometer agrees the part is oversize, record it as non-conforming rather than reworking on the strength of one caliper reading.