The Sinking Shelf: Tolerances in a Flat-Pack Display Unit
A student is building a flat-pack retail display shelf from 12 mm MDF for a school exhibition. The design uses interlocking slots: the vertical panels have 12.4 mm slots so the horizontal shelves slide in with a friction fit. The student cut all six horizontal shelves from the same sheet with a CNC router, whose kerf and bit runout produce a consistent +0.3 mm oversize on every slot and shelf tab. During dry assembly the first three shelves fit snugly, but the fourth shelf jams and the fifth will not enter at all. The student has 9 hours of workshop time left, a 2400 x 1200 mm sheet of spare MDF, and an assessment deadline in five days. The brief requires the unit to be demountable at least four times without tools.
1. Diagnose why the fit degrades progressively across identical parts, and explain what this tells you about the student's quality-control approach.
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The parts are nominally identical but not actually interchangeable. A consistent +0.3 mm oversize on every slot and tab means each joint is slightly tight; the first three shelves seat only because the student is forcing them, which compresses the MDF edges and slightly deforms the slots. Each insertion removes a little material and changes the geometry, so by the fourth shelf the accumulated interference exceeds the available clearance and the joint seizes. The fifth fails outright because the cumulative distortion has closed the slot.
The deeper issue is that the student is using trial assembly as the only inspection step. There is no measurement of the actual slot width against the intended 12.4 mm, no check of the router's output on a test coupon, and no tolerance budget. A 12.4 mm slot for a 12 mm shelf nominally gives 0.4 mm clearance, but a +0.3 mm oversize on the tab consumes most of that, leaving about 0.1 mm per side before any distortion. The correct control is to cut a test joint first, measure it, and adjust the toolpath offset before cutting the full run. Progressive failure across supposedly identical parts is a signal of interference fit, not random error, and should have been caught at the coupon stage.
2. Recommend a recovery plan that meets the demountable-four-times requirement within the remaining time, justifying your trade-offs.
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The current interference fit cannot satisfy the brief: a joint that needs force to assemble will not survive four tool-free cycles, and MDF edges will crumble each time. Recovery should prioritise function over finish because the deadline is fixed and the spare sheet is limited.
First, stop assembling the remaining shelves and measure the actual slot and tab widths on the failed parts. Second, re-cut the vertical panels only, from the spare sheet, with a revised slot width of about 12.9-13.0 mm to give roughly 0.4-0.5 mm clearance per side after the observed +0.3 mm oversize. Keep the existing shelves, since their tabs are already within the new clearance. Third, add a simple locking detail, such as a through-dowel or a wedge, so the unit is demountable without tools and does not rely on friction alone.
The trade-off is that re-cutting the verticals uses perhaps 40 percent of the spare sheet and around 3 hours of the 9 available, leaving time for a full four-cycle assembly test and finishing. Re-cutting every part would be safer but would consume the sheet and the schedule. The revised design is slightly looser and may look less refined, but it is honest about the tolerance reality and demonstrably meets the brief.