If every part in your assembly passed inspection but the assembly still does not close, you almost certainly have a tolerance stack-up problem. A stack-up is the accumulation of allowed deviations along a chain of dimensions: each part is individually within spec, but the deviations land in the same direction and the total exceeds the clearance you designed. Tolerance stack-up analysis is the calculation that catches this on paper, before you cut steel — you add up the chain of dimensions that controls a critical gap and check whether the worst legal combination still fits.
What a dimension chain actually is
A dimension chain is the sequence of features that determines the distance between two points you care about. Take the gap between a lid and a housing. That gap is not controlled by one dimension — it is controlled by the housing wall thickness, the depth of the recess, the boss height, the thickness of the gasket, the screw head height, and the position of the mounting hole. Six dimensions, six tolerances, one gap.
This is the difference between checking a part and checking a system. A part inspection asks "is this feature within its stated limits?" A stack-up asks "can all of these features simultaneously sit at their limits and still let the product exist?" Those are different questions, and only the second one predicts whether assembly line workers will be reaching for a hammer.
Two ways to run the numbers
Choosing the method is the central decision in any stack-up, because it directly sets how expensive your parts will be and how many assemblies will fail on the line.
- Worst-case (arithmetic) stack: add every tolerance at its maximum, all pushing the same direction. Conservative and absolutely safe — if the worst-case number fits, nothing can fail to assemble. The cost is that long chains force very tight individual tolerances, and tight tolerances get expensive fast.
- Statistical (RSS) stack: assume deviations distribute around nominal and combine them as the root sum of squares. The predicted range is dramatically narrower than worst case, which lets you loosen individual tolerances. The tradeoff is that a small fraction of assemblies will fall outside the range and need rework or selective fitting.
- Sensitivity analysis: rank each dimension by how much it contributes to the total spread. Usually two or three dimensions dominate. Tighten only those and leave the rest generous — this is where the real cost savings live.
- Monte Carlo simulation: for chains involving angles, curved interfaces, or non-linear motion, sample thousands of random parts in software instead of hand-summing. Necessary whenever the geometry is not a simple straight-line addition.
A practical rule: use worst-case for anything safety-critical or anything you cannot rework, and statistical for cosmetic gaps and high-volume consumer assemblies where a small rework rate is cheaper than tight tooling.
Why the assembly doesn't close: the usual suspects
In practice a handful of causes account for most failed closures.
- Nobody ran the stack. Each engineer specified a reasonable tolerance for their own part and no one summed the chain.
- Chained datums. Dimensions referenced part-to-part-to-part instead of all referenced from a single functional datum, so errors compound instead of staying independent. Correct datum strategy is the whole point of GD&T; linear plus-minus dimensioning quietly hides this problem.
- Process shrink treated as a tolerance. Molded parts shrink, and shrink varies with wall thickness and fill. If your model was scaled for nominal shrink but the walls are uneven, real parts drift off nominal in ways the drawing never described — see wall thickness for injection molded parts.
- Warpage counted as zero. A flat part is an assumption, not a fact. Warp, sink, and post-mold relaxation all add to the chain and rarely appear in the calculation. Many of these show up in the catalog of injection molding defects.
- Fastener and bearing float ignored. A screw in a clearance hole can sit anywhere in that hole. That float belongs in the stack.
- The prototype lied. The first units were machined or printed and happened to land near nominal, so the fit felt fine. Printed parts have completely different deviation behavior — compare 3D printing tolerances against molded tolerances before you trust a printed fit.
Fixing a stack without making every part expensive
The instinct after a failed assembly is to tighten everything. That is the most costly possible response. Better moves, roughly in order of preference:
- Shorten the chain. Fewer parts between the two controlled points means fewer tolerances to accumulate. Combining two parts into one removes an entire interface from the calculation.
- Re-datum. Reference the critical features from the same datum on the same part so their relationship is controlled directly rather than through intermediaries.
- Design in adjustment. A slot instead of a hole, a shim, a floating bracket, or an elastic element absorbs accumulated error for pennies. One deliberate adjustment feature can replace three tightened tolerances.
- Widen the target. If the required gap is a cosmetic preference rather than a functional requirement, changing the requirement is free.
- Tighten selectively. Only after the above, and only on the dimensions the sensitivity analysis flagged as dominant.
- Reshape the interface. Compliant features such as ribs, tapers, and lead-ins let parts self-align. This is why snap-fit geometry normally includes generous lead-in angles.
When to run the analysis
Run a first pass as soon as the architecture is set and the part split is known — long before drawings are finished. Repeat it after every significant geometry change, and once more as part of the design for manufacturing review before tooling is released. The calculation itself is inexpensive engineering time. Discovering the problem after a mold is cut means mold rework, a new sample run, and weeks of schedule — the most expensive way to learn arithmetic.
One habit worth adopting: write the critical stacks down as a short list of controlled gaps with their target, method, and result, and keep it with the drawing package. It gives your contract manufacturer a clear statement of what actually matters, which is far more useful than a drawing covered in uniformly tight tolerances.
If parts that pass inspection are not going together, or you want the critical stacks checked before a tool is cut, Projects House runs tolerance analysis as a standard part of mechanical design. Send us your assembly through the contact form and we will review the chains that matter.