Tolerance Stack-Up Analysis for Plastic Assemblies

Two molded parts that each meet their drawing can still fail to assemble. This is not a manufacturing failure; it is a stack-up failure. The dimensions that matter in an assembly are the sum of several individually acceptable deviations, plus the sources of variation that never appear on a drawing at all: shrinkage, tooling wear, warp, and assembly shift. Stack-up analysis is how you find the problem before the tool is cut rather than after the first build.

Figure 1. Dimension chain from part datum to assembly shift with worst-case and statistical formulas.

The two methods you need

Worst-case analysis sums every contributor at its limit in the same direction:

`` Assembly clearance (worst case) = Nominal gap − Σ (each tolerance at its limit) ``

It answers a simple question: if every part in the assembly happens to be at the worst permissible extreme, does it still fit? This is the correct method for safety-related assemblies, for low-volume production where statistical mixing is unlikely, and for any assembly that must work on the very first build.

Statistical (root-sum-square) analysis treats the contributors as independent random variables:

`` Total variation (RSS) = √(t1² + t2² + t3² + ... + tn²) ``

RSS reflects reality better at high volume, where extremes rarely coincide. It gives a much smaller predicted variation than worst-case, which allows looser tolerances and lower cost. Its validity depends on the assumption that each contributor is centered and normally distributed — an assumption that molded parts with asymmetric warp violate.

A defensible approach is to run both. Use worst-case to check that the assembly cannot fail catastrophically, and RSS to understand the expected production variation and to justify the tolerances you have chosen.

Contributors that drawings do not show

This is where most stack-up analyses on molded parts go wrong. The drawing tolerances are not the whole story.

• Mold shrinkage variation. Each material and each wall thickness has a shrinkage range. The same nominal dimension on parts from two different wall thicknesses will not match, even from the same tool.
• Tooling wear. Over a mold's life, cavity dimensions move. A freshly cut cavity and a cavity with two million shots behind it are different parts. Plan the stack-up against the worn condition, not the new one, or plan a tool refurbishment into the schedule.
• Warp and post-mold shrinkage. A part can meet its dimensions in the fixture and drift after ejection. Glass-filled parts and parts with uneven walls are especially prone to this, and semi-crystalline resins continue to shrink for days.
• Datum selection and fixturing. The datum scheme in the drawing determines how dimensions are measured. If the mold defines features from a different datum than the drawing, the measured variation will not match the predicted variation.
• Assembly shift. Screw bosses, snap fits and press fits move the parts relative to one another under load. The modeled position is not the assembled position.
• Process variation between machines. Two presses producing the same part can hold different process windows, and therefore produce slightly different dimensions.

Building the analysis

1. Define the assembly requirement. State exactly what must be true: a gap, an interference, a flush condition, a force. Vague requirements produce meaningless analyses.
2. Draw the chain. Trace the dimension path from the datum of one part, through the interface, to the critical feature on the other part. Every link is a contributor.
3. List contributors with their tolerances and distributions. Include drawing tolerances, shrinkage ranges, wear allowances and assembly shift. Mark which ones you control and which you do not.
4. Decide the direction of each contributor. Stack-up analysis is direction-dependent. A tolerance that helps in one build direction hurts in the other.
5. Run worst-case and RSS. Compare the results with the requirement.
6. Identify the dominant contributors. In most assemblies two or three contributors dominate the total. Fixing those is where the cost reduction is.
7. Iterate on the design, not just on the tolerances. Changing a datum, adding a compliant feature or moving a locating feature often costs less than tightening three tolerances.

Design strategies that absorb variation

Once the analysis shows a problem, the cheapest fixes are usually geometric.

• Use compliant features. Snap fits, spring tabs and crush ribs tolerate variation because they deflect. A rigid butt joint has to be dimensioned exactly.
• Choose the right locating scheme. One point of location plus one point of alignment plus one point of restraint is more forgiving than a fully constrained pattern of tight fits.
• Provide generous clearance in non-critical interfaces. Tight a non-functional gap only when there is a reason; cosmetic tightness often costs more than it is worth.
• Size for the stack, not the nominal. Design clearance into the interface so the worst case still has margin.
• Tighten only the functional dimensions. A drawing where every dimension is tight costs more and behaves no better than one where the critical characteristic is identified and controlled.
• Design for adjustable assembly where the product allows it: a slotted hole, a captured insert or a clip that can accommodate build variation in the field.

Working with the mold shop

The stack-up analysis is only useful if it turns into tooling decisions.

• Give the mold shop the tolerance on the dimension that matters and tell them it is a stack-up contributor. Dimension the mold from an agreed datum.
• Discuss shrinkage explicitly, including whether the analysis assumes nominal or worst-case shrinkage.
• Agree a cavity dimension monitoring plan so wear is visible before it becomes an assembly failure.
• Where the analysis shows a tight cavity, consider a sample and correction loop during tooling rather than a single cut.
• Record the assumed wear allowance in the tooling documentation so a future refurbishment targets the right dimension.

Figure 2. Quick reference: the key checks and reference values from this guide.

Checklist for a stack-up analysis

• State the assembly requirement in measurable terms
• Trace the full dimension chain and list every contributor
• Include shrinkage, warp, tooling wear and assembly shift, not only drawing tolerances
• Run both worst-case and statistical (RSS) analyses
• Check worst-case in both build directions
• Identify the two or three dominant contributors
• Solve with design geometry before tightening tolerances
• Use compliant features and a forgiving locating scheme
• Agree datums and shrinkage assumptions with the mold shop
• Record wear allowances and a cavity monitoring plan

An assembly that fits on the bench and fails in production was almost always analyzed only at nominal. Treating shrinkage, wear and assembly shift as first-class contributors is what turns a stack-up study into a design decision.