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Tolerance stack-up: every part passes, the assembly fails
Published 2026-09-24
The worst quality problems are the ones with no one to blame. Parts from several suppliers are inspected separately, every one of them is in tolerance, every report is green — and when they are put together the cover will not close, the holes will not line up, the clearance you designed in has vanished. Nobody is wrong, because the fault is not in any part. It is in a chain of tolerances that runs across several drawings and that nobody ever drew. This is about finding that chain, doing the arithmetic on it, and breaking it before the drawings go out.
The parts are fine — the chain nobody drew is not
What an assembly really has to guarantee is usually not a dimension on any single part. It is a quantity that only exists once several parts are together: the gap between a cover and its housing, the alignment of two hole patterns, whether a shaft slides cleanly through three brackets. That quantity appears on no part drawing. It is built, end to end, out of dimensions on several drawings. The string of dimensions that builds it is the tolerance chain; the quantity at the end is the closing dimension.
The deviation of the closing dimension is the sum of the deviations along the chain. Each link only drifts inside its own tolerance, but the links do not necessarily drift in opposite directions — sometimes they all lean the same way. Then a batch that passes piece by piece comes up short as an assembly. Nothing went wrong in machining. The tolerance allocation simply allowed that combination.
So 'every part passes, the assembly fails' is rarely a supplier problem, and rarely an inspection miss. It tells you the tolerances along the chain add up to more than the closing dimension can absorb. The fix lives on the drawings.
Draw the chain first — walk backwards from what you must guarantee
The method is plain. Write down the closing dimension first: what, exactly, has to be true after assembly — a gap no smaller than something, an offset no larger than something, a part that simply has to fit. Then start at one end of it and walk through the real contact faces between parts: this face sits against that part, that part's dimension carries me to the next contact face, and so on to the other end. Every dimension you cross on the way is a link.
Count only real contact. Where a bolt passes through a clearance hole, the parts can shift during assembly, and that link is really the clearance, not the hole spacing on the drawing. Only where a dowel, a spigot or a shoulder pins the parts together do you have a fixed link. A lot of chains come out wrong because a joint that can float was treated as rigid.
When you are done, count the links and check that each one matches exactly one dimension on one drawing. If a link cannot be found on any drawing — because it is split across two dimensions or has to be derived from others — that is the first thing to change. Every link in the chain should be dimensioned directly.
Worst-case or statistical: it depends on volume and on the cost of failure
There are two ways to add up the chain. Worst-case simply sums every tolerance and assumes every part sits at its least favourable limit at once. The result is conservative, but if each part passes, the assembly will always go together. Statistical methods — root-sum-square is the common one — assume the links vary independently and mostly sit near the middle, so extremes rarely coincide. The predicted range is much narrower, which lets you open up every link.
Which one to use is not a maths question; it is a production and risk question. The statistical method rests on assumptions: a large enough batch, stable and centred processes on every link, and no correlation between them. Small batches, pilot runs, one part each from several suppliers, or a link that clearly sits to one side of its band — in all of these the statistical assumptions are weak, and worst-case is the more honest answer.
The other test is what a misfit costs. If a part that will not fit just means picking another from the box, the looser tolerances statistics buys you are a good trade. If a misfit means reworking the whole machine, or the closing dimension governs a seal or something safety-related, design to worst-case. Either method is legitimate, but say on the drawing which one the tolerances were allocated by — otherwise the supplier cannot tell which link genuinely must not move.
When the chain is too long, shorten it — don't tighten every link
When the closing dimension comes out over, the reflex is to tighten every link a grade. That is the most expensive answer: every link now needs a slower process and stricter inspection, and the more links there are, the less tolerance each one gets, until it stops making sense. The better first question is whether the chain can be made shorter.
Each of the moves below either removes links or cuts the chain, rather than spreading the pressure across every part.
| Move | What it does | What it costs |
|---|---|---|
| Put both mating features on the same part | Two links across two parts become one link inside one part | A more complex part, possibly an extra setup |
| Machine mating features in the same setup | Removes the re-location error between two setups | Constrains fixturing and sequence — say so up front |
| Locate with dowels or spigots, not bolt clearance | Turns a floating joint into a defined link | Two more holes and one more assembly step |
| Designate an adjustment link (slots, shims, match-drilling) | One place absorbs the whole chain's deviation at assembly | Assembly labour — weigh it against volume |
| Dimension every mating feature from one datum frame | Stops a second little chain forming inside one part | The datums have to be thought through first |
The links aluminium parts tend to hide
On an extruded-and-machined part there is often a link the machine did not make — the die did: an as-extruded face, a slot width, a wall thickness. Its accuracy is governed by extrusion standards (precision profiles typically to EN 12020, on the order of ±0.1 mm), and tightening the CNC dimensions around it does not improve it. If that link sits in a critical chain, either leave a machining cut at that spot or count its tolerance honestly in the closing dimension.
The second link people miss is the finish. Anodizing and coating both leave a film on mating faces, and if the chain is built from pre-finish dimensions, the closing dimension you calculated describes a state that never exists at assembly. The drawing should say whether each mating dimension applies before or after finishing, and whether mating faces are masked. How much the finish adds depends on the process and film you specify — send the drawing and we will confirm it.
The third is length and temperature. A long part — our profiles run up to 12,000 mm — carries its own bow and twist, and bolting it straight during assembly moves other links with it. Aluminium and steel in the same assembly expand differently, so a clearance that is right at room temperature may not be right in service. You do not always need to put numbers on these, but when you draw the chain, ask of each link: is it still this size in the working condition?
Send the chain with the drawing, and push back when it matters
A supplier who receives a single part drawing can only guarantee that drawing — that is a fact, not an excuse. If the closing dimension decides whether the assembly works, send the assembly drawing, the mating parts, or at the very least one sentence: the clearance these parts must hold once assembled, and which dimensions it runs through. A shop that knows the chain takes extra care on those links, and will offer process moves that break it for you.
On the drawing you can flag the chain dimensions as critical and note which assembly relationship they belong to. Then first-article approval does not have to stop at single parts: agree on an assembly first article, where the parts are actually put together and the closing dimension is checked. A stack of green part reports does not prove the assembly works, and this step is usually the cheapest insurance you can buy.
The other way round: if a supplier proposes opening up one link to bring the price down, push back once — if this link gets looser, who absorbs the margin at the closing dimension? A supplier who can answer is actually looking at your assembly. One who cannot will hand that saving back to you as a part that will not fit. If you are not sure how to break the chain, send us the assembly and we will sort it out with you before the quote.
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