Tolerance Stack-Up on a Pump Housing
A student team is designing an aluminium pump housing that clamps a 20 mm bearing into a bore. The bore is machined to 20.00 +0.05/0.00 mm. The bearing outer diameter is specified 19.98 +0.00/-0.02 mm. The housing wall is 6 mm, and the clamp bolt passes through a clearance hole of 8.4 +0.2/0.0 mm into a tapped hole with positional tolerance of 0.3 mm diameter at maximum material condition. The team's first prototype used a 20.00 mm reamed bore and the bearing was a light press fit, but in service the housing cracked at the bore edge after 200 hours. The workshop can hold +/-0.02 mm on a CNC mill but only +/-0.1 mm on the manual drill for the clearance hole. The team wants to move to production with 500 units.
1. Analyse the fit between the bore and the bearing and explain whether the specified tolerances are appropriate.
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Worst-case fit analysis:
- Largest bore = 20.05 mm; smallest bearing = 19.96 mm → clearance = 0.09 mm (loose).
- Smallest bore = 20.00 mm; largest bearing = 19.98 mm → clearance = 0.02 mm (tight but still clearance).
So the specified tolerance band never produces interference - the fit ranges from 0.02 to 0.09 mm clearance. This is a clearance fit, not the light press fit the team observed in the prototype, where a nominal 20.00 bore with a nominal 19.98 bearing gave 0.02 mm clearance but manufacturing variation was not controlled.
The cracking at the bore edge is more likely caused by the press fit the prototype actually had (interference inducing hoop stress in a thin 6 mm wall) combined with stress concentration at the bore edge, not by the specified clearance fit. A 6 mm aluminium wall around a 20 mm bore gives a wall-to-bore ratio of 0.3, which is thin; an interference fit there generates high hoop stress.
Conclusion: the specified tolerances are appropriate for a clearance fit and would prevent the cracking seen in the prototype, provided production actually holds them. The team should not reintroduce a press fit without thickening the wall or adding a retaining feature (e.g. circlip or shoulder).
2. Assess whether the production process can meet the tolerances and recommend changes for the 500-unit run.
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Bore: +/-0.02 mm on the CNC mill can hold a 0.05 mm total band, so the bore tolerance is achievable, but only with a boring or reaming operation after milling - a drilled hole will not hold it. The process plan must specify bore-then-ream and in-process gauging at a sampling rate (e.g. first-off and every 25th part) because 500 units is enough for tool wear to drift the bore.
Clearance hole: the manual drill holds only +/-0.1 mm, which is a 0.2 mm band. The specified 8.4 +0.2/0.0 is a 0.2 mm band, so it is just achievable on the manual drill at its limit - risky at 500 units. Two options:
- Move the clearance hole to the CNC (drill and interpolate) to hold the tolerance comfortably.
- Loosen the clearance hole and rely on the positional tolerance at MMC to guarantee assembly.
The positional tolerance of 0.3 mm at MMC on the tapped hole, combined with a fixed fastener condition, means the clearance hole must provide enough float. Fixed-fastener rule: clearance = positional tolerance + fastener diameter allowance. With an 8 mm bolt, an 8.4 mm hole gives 0.4 mm total float, 0.2 mm radial, which barely covers the 0.3 mm positional tolerance (0.15 mm radial) plus drill error. Recommendation: enlarge the clearance hole to 8.8 mm or move it to CNC, and specify a functional gauge to check the pattern on a sample. Document the process capability (Cpk) before full production.