Machine Design #97: Allocate Tolerance by Function — Tight Where It Matters, Open Where It Can
Functional tolerance allocation must preserve function, manufacturability, inspectability, cost, and serviceability when the boundary changes.
Function before a number
Write the input, expected result, acceptance limit, failure symptom, and measurement method before choosing a thickness, tolerance, datum, or hole pattern. Assign an owner to every value and change.
Core checks
- Functional characteristic and acceptance limit: record value, source, method, owner, and pass/fail evidence.
- Stack contributors and datum scheme: record value, source, method, owner, and pass/fail evidence.
- Process capability and supplier risk: record value, source, method, owner, and pass/fail evidence.
- Worst-case versus statistical allocation: record value, source, method, owner, and pass/fail evidence.
- Inspection effort and measurement uncertainty: record value, source, method, owner, and pass/fail evidence.
- Cost, change, and reallocation rule: record value, source, method, owner, and pass/fail evidence.
| Failure mode | Symptom | Verification |
|---|
| Function not defined | Over-tight or weak design | Rebuild the functional stack |
| Datum not real | Inspection and assembly disagree | Try the real fixture |
| Documents out of sync | Correct number, wrong revision | Baseline every reference |
Tolerance stacking: two ways to add up, two different answers
Before allocating tolerances to individual parts, you have to know what they add up to. There are two ways to add them, for two different situations.
Worst case: add the tolerances directly. Suppose an assembly has five parts in series, each at plus or minus 0.1 mm. The worst case is all five deviating the same way: 5 x 0.1 = plus or minus 0.5 mm. This is absolutely safe but pessimistic — the probability of all five deviating to their maximum in the same direction is very small.
Statistical (root sum square): take the square root of the sum of the squares. With the same example: the square root of (5 x 0.1 squared) is about plus or minus 0.22 mm, less than half the worst-case figure.
| Which method | When |
|---|
| Worst case | Low volume, safety matters, the consequence of one bad assembly is severe, or the process is not under statistical control |
| Statistical | High volume, a stable process with data to prove it, accepting a very small fraction outside the range |
The crucial point: statistical stacking is only legitimate when you hold process capability data from the supplier. Using it because the number looks nicer is fooling yourself.
Three allocation approaches, chosen by circumstance
| Approach | How it works | Suits |
|---|
| Equal split | Every link in the chain gets an equal share | Nothing known about the process; a starting point |
| By process capability | Links the shop can hold tightly get the tighter share | The capability of each operation or supplier is known |
| By cost | Tighten where it is cheap, open up where it is expensive | It is known which link jumps in price for one more grade |
In practice the second and third go together: tighten the link the shop already holds tightly at low cost, and open up the link that would need a different machining method to achieve.
Cheaper than tightening tolerances: remove links and allow adjustment
Before tightening each link, try these two directions — they are usually much cheaper:
- Reduce the number of links in the chain. Combine two parts into one, or locate the whole assembly from
one common part instead of locating in series. Every link removed takes its whole tolerance share out of the total.
- Allow one controlled adjustment. A shim, an adjusting screw, a slot with a clearly stated tolerance. A
controlled adjustment is quite different from "let the fitter tweak it" — it has a range, a way to measure and an acceptance criterion.
Any feature not in the functional chain should take the general tolerance in the drawing corner rather than an individual value. See also Manufacturing Engineering #05 — the tolerance you write decides the machining price.
Budgeting the tolerance: do not tighten every part equally
When an assembly has a total allowable tolerance (say the fit clearance must stay within 0.2 mm), the real question is how to split that 0.2 mm across the parts. Split it wrong and either the assembly fails, or the cost climbs because you tightened parts that never needed to be tight.
Three common ways to split:
- Equal split: an equal share to each part. Simple, but usually wasteful, because some parts hold a
tight tolerance cheaply and others are expensive.
- Split by process capability: parts that hold tight cheaply carry the bigger share; hard parts
(thin walls, soft material, long parts) get the loose share.
- Split by cost: put the tight tolerance on the part that is cheapest to hold tight, loosen the
expensive one.
The cost-tolerance curve
Machining cost rises fast as the tolerance tightens, not linearly: halving the tolerance often more than doubles the cost, because you change method (milling to grinding, grinding to lapping) and add inspection. So before you write a tight number, ask whether the function truly needs it, or whether you are tightening out of habit.
When the total tolerance is too tight to split across separate parts:
- Select fit: measure, then pair a large part with a small one so they cancel, instead of tightening
both. Used widely on piston-and-bore and graded ball bearings.
- An adjustment feature: an adjusting screw or a shim absorbs the error, letting the remaining parts
hold an economical tolerance.
Choosing select fit or an adjustment feature is a trade: cheaper to machine but more work at assembly and at spares replacement. Decide early, do not scramble when the assembly fails to meet spec.
MINATA release checklist
- [ ] Function, boundary, and failure symptom are written.
- [ ] Datums, ownership, process, and mistake-proofing are clear.
- [ ] Six topic checks have evidence and pass/fail limits.
- [ ] Manufacturing, assembly, inspection, and maintenance were tried.
- [ ] Revision, supplier, material, and configuration records agree.
Good engineering is an explicit chain that survives manufacture, operation, maintenance, and change. For functional tolerance allocation, evidence that function and variation remain reliable is the MINATA standard.
Frequently asked questions
Worst case or statistical stacking?
Worst case for low volume, where safety matters, or where there is no process data. Statistical stacking for high volume with data proving the process is stable. Choosing the statistical method because it gives a more comfortable number is fooling yourself.
For five parts each at plus or minus 0.1 mm, what is the total?
Worst case is plus or minus 0.5 mm (direct addition). Statistically it is about plus or minus 0.22 mm (the root sum of the squares). The two differ by more than a factor of two, so choosing the method is a design decision, not a minor technical detail.
Is it safer to tighten every dimension?
No. Tightening across the board raises cost, inspection time and scrap without adding function. The correct approach is to find the tolerance chain leading to the characteristic that must be guaranteed, then tighten only the links actually in that chain.
Is allowing an adjustment a sign of sloppy design?
Not if the adjustment is controlled: it has a range, a measuring method and an acceptance criterion. What is sloppy is letting the fitter tweak it with nothing on the drawing — because then the second machine differs from the first.
Is removing parts from the chain really cheaper?
Usually cheaper than tightening tolerances, because every link removed takes its whole contribution out of the total error while also removing a part to buy, to inspect and to assemble. Worth trying before deciding to tighten each link.
Frequently asked questions, continued
Should I split the tolerance equally across every part in the chain?
Usually not. An equal split is simple but wasteful, because each part has different difficulty and cost. Put the tight share on the parts that are easy and cheap to hold, loosen the hard or expensive ones.
Why does tightening a tolerance raise cost so fast?
Because machining cost is not linear: halving the tolerance often more than doubles the cost, since you change method (milling to grinding, grinding to lapping) and add inspection. Tighten only when the function truly needs it.
When do I use select fit instead of tightening everything?
When the total tolerance is too tight to split economically across separate parts. Measure, then pair a large part with a small one so they cancel (piston-and-bore, graded bearings). The trade is extra measuring and pairing at assembly and at replacement.
A quick table for the shop floor
Tolerance allocation is easier when the situation, the way it is given and the purpose are lined up:
| Situation | How to give or control it | Purpose |
|---|
| Locating features | Tight, along the functional chain | Guarantee the relative position |
| Non-functional surfaces | An economical machining tolerance | Do not raise cost needlessly |
| An adjustment step | Leave a shim or a controlled gap | Absorb assembly variation |
A worked case
Do not split the tolerance evenly across every dimension. Start from the clearance or offset allowed at the output, build the tolerance stack-up, then allocate it by process capability and by how much each step contributes.
Conclusion
Allocate Tolerance by Function is not paperwork done to make a file look tidy. It is how intent becomes a result that can be manufactured, assembled and measured repeatedly. A good drawing does not need the designer standing beside it to explain it; the structure of the information has to do that work.
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