SCREWKING
Tolerance stack-up, and why the screw ends up changing
The short version: every part is inside its tolerance and the assembly still will not go together. Nobody made a mistake — tolerance accumulates. It usually surfaces at trial assembly, and at that point changing the screw is often the quicker, cheaper route — though not always, and the second half of this page is about when it is not.
Every part passes. It still does not fit.
Five parts in a stack, each toleranced at ±0.05 mm. All five ship inside tolerance and all five are good parts. If all five happen to drift the same way, the stack is 0.25 mm off nominal — and across the full range of possible outcomes, 0.50 mm from one extreme to the other.
That is tolerance stack-up. It is not a manufacturing defect; it is what happens whenever several parts sit on the same dimension chain.
The awkward part is that it is invisible in CAD. On screen every part is at nominal and everything fits. It appears when real parts meet.
Two methods, and what each one assumes
aᵢ is the sensitivity coefficient of each dimension in the chain. It can only be dropped on a one-dimensional chain where terms add directly; angles, levers and geometric amplification change it.
| Worst case | RSS (statistical) | |
|---|---|---|
| Formula | Σ|aᵢ|Tᵢ — absolute values summed | √Σ(aᵢTᵢ)² — root sum of squares |
| Assumes | Every part at its limit, all drifting the same way | Inputs independent, stable, near-normal and centred on target, plus a stated mapping from drawing half-tolerance to σ (commonly half-tolerance = 3σ, i.e. Cp = 1.0) |
| Gives | The theoretical boundary of all conforming combinations. If that boundary sits inside the functional limits, every part within the stated tolerances passes this dimensional requirement | An output that can be treated as roughly ±3σ — if those assumptions hold |
| Costs | Tighter tolerances and higher part cost | About 0.27% outside on a two-sided limit (roughly half that if failure is one-sided). A model output, not a defect rate |
| Use when | A single bad assembly is expensive, short runs, or genuine 100% interchangeability | Volume production under statistical process control, where a few outliers can be handled |
Do not treat 0.27% as what RSS delivers. That figure requires every input process to be centred, stable, near-normal and independent, and the drawing half-tolerance genuinely to represent 3σ.
With an off-centre or incapable process the real tail can be far worse than 2,700 ppm. Budgeting 0.27% as an assembly failure rate is the common and expensive misuse of this method. The honest estimate comes from measured mean, sigma and Cpk, not from the formula.
Neither is the correct answer; they are two ways of pricing the same risk. Worst case buys certainty and pays in cost. RSS buys cost and pays by having to manage the tail. And worst case is not simply over-conservative — for safety-critical parts, or where all conforming parts must interchange, it remains the right method.
Found late: what each fix costs
Stack-up problems rarely surface at design review. They surface at trial assembly — and by then the options are these:
| Change | Involves | Schedule |
|---|---|---|
| Housing or structural tooling | Modify or cut a new tool | Months |
| Casting or stamping | Tooling, trials, new first article | Weeks to months |
| Circuit board | Re-layout and re-validation | Weeks |
| Redesign the dimension chain | Everything upstream moves | Longest |
| The screw | Die adjustment or a change of specification | Shortest of these |
So a custom screw is usually not something the customer wanted from the start. It is what happens when the design reaches assembly and the screw is the last degree of freedom that can still move affordably.
When changing the screw is not the cheap route
- The screw is safety-critical, regulated, or already certified. A change means re-qualification
- Shortening reduces thread engagement — stripping risk, or a changed allowance in a blind hole
- Changing head diameter, height or style reduces bearing area — embedment or pull-through
- Changing material, property class, heat treatment, coating or lubrication means re-validating preload, fatigue, corrosion, galvanic behaviour and embrittlement
- A special needs tooling, a minimum order and material procurement — sometimes an upstream part really is easier to move
So the question is not whether changing a screw is cheaper. It is what changing it obliges you to re-verify. A short list makes it cheap. A long one does not.
What a screw can absorb
- Length. The stack drifts one way and the point protrudes after seating; 0.2 mm shorter resolves it. ⚠️ The measurement datum changes with head style — countersunk overall, others under the head. Specify the wrong datum and the change does nothing.
- Head geometry. A head fouling a housing, or head height leaving the surface proud. Usually cheaper than moving the housing — but confirm the bearing area still carries the load.
- Material and finish. The one most often missed, and the one most often misattributed. Friction is not set by the screw's base material. It is a property of the contact system: the thread pair, the bearing face, roughness, coating, lubrication, cleanliness and whether the joint has been tightened before. Change any of those and the torque-to-clamp relationship has to be re-measured on the actual combination, not inferred from a material name.
This bites hardest at small sizes. Below M3 you are outside ISO 16047's reference conditions — which does not mean testing is impossible, but that fixture, sensors and acceptance criteria have to be agreed rather than cited. Published work also reports that the tension of miniature fasteners cannot currently be measured and controlled quantitatively. In this range, change one variable and the whole parameter set has to be re-established.
Prove it on stock before cutting a die
This is what we suggest to customers, and it costs us tooling revenue on purpose: try a stock size first.
- Test the hypothesis. You believe 0.2 mm shorter fixes it — confirm that before committing
- No tooling exposure. If the diagnosis is wrong you have spent one batch, not a die
- Fastest route. Stock ships now; a die change has to be scheduled
Once it is proven, the conversation changes from “does this work” to “can you hold it in production” — which is what tooling is for. A die is a setup cost, not something one order consumes.
Five questions for your next dimension chain
- How many parts sit on this chain, and was it analysed worst case or RSS?
- If RSS — are the processes actually centred and capable, and what mapping from tolerance to σ was assumed?
- How are the outliers handled? Rework or scrap?
- How much of the chain is the screw, and is its tolerance large or small next to the rest?
- If the screw has to absorb the error, how much adjustment is left — and will plating consume it? (M1–M1.4 especially)
References
- Types of Tolerance Stackup Analyses — PTC Creo documentation (states the RSS assumption of Cp = 1.0 with the process mean at the tolerance centre)
- Introduction to Root Sum Squared (RSS) Tolerance Analysis — Five Flute
- NASA — joint testing showing how lubrication of the bearing face shifts the nut factor
- ISO 16047 — Fasteners — Torque/clamp force testing
This page describes methods and trade-offs, not design values for any specific product. Tolerance allocation depends on your chain, your process capability and your acceptance criteria.
Enquiries
Stuck on an assembly you suspect is a stack-up problem? Send the drawing or a sample. We will tell you whether changing the screw can solve it, and what that change would oblige you to re-verify — usually starting from stock.