Tolerances, Fits, and Why Stack-Up Passes Inspection

A drawing dimension without a tolerance is an aspiration. Nothing is made to an exact size, and the tolerance is where the designer says how much the real world is allowed to deviate before the part stops working.

What a tolerance is buying

Tolerances exist because manufacturing has variation and because eliminating variation costs money — steeply. A part held to a tenth of a millimetre and one held to a hundredth are different processes, different machines and often a different supplier.

So a tolerance is a budget decision as much as an engineering one, and the discipline is specifying tight tolerances only where the function actually requires them. A specification that is tight everywhere is usually a specification nobody thought about.

Fits: the useful mental model

Where two parts meet, the relationship between their tolerance bands determines the fit — and the three broad families are worth knowing by behaviour rather than by code.

Clearance fit. The hole is always larger than the shaft, so the parts always assemble and there is always play. Used where parts must slide or rotate, or simply where assembly must be reliable.

Transition fit. Depending where each part falls in its band, the result may be slight clearance or slight interference. Used for location where a part must sit accurately but still be assembled and dismantled.

Interference fit. The shaft is always larger than the hole, so assembly requires force, heating or cooling — and the joint holds by the resulting stress. Used where a part must not move relative to another without a separate fastener.

Working out the resulting clearance or interference range from two tolerance bands is simple arithmetic — largest hole minus smallest shaft for maximum clearance, smallest hole minus largest shaft for the tight end — and it is what you need before committing a drawing.

Stack-up is where assemblies go wrong

The failure that catches people out is not one part being out of tolerance — it is several parts each being comfortably within tolerance and accumulating.

Five parts in a line, each ±0.1 mm, can in the worst case be 0.5 mm out overall. If the assembly needs to hold 0.3 mm, it fails with every component passing inspection, and the inspection reports will all say the parts were fine.

Worst-case stack-up adds the tolerances arithmetically, which is conservative and sometimes unnecessarily so; statistical approaches give a tighter and more realistic answer for volume production. Which method is appropriate is a design decision, and doing neither is the common one.

Datums matter as much as numbers

A tolerance is meaningless without saying what it is measured from. The same nominal dimension referenced from two different faces produces two different parts, and disagreements about datums are a frequent cause of parts that pass inspection and do not fit.

This is what geometric dimensioning and tolerancing exists to make explicit, and it is why a drawing with dimensions but no datum scheme leaves the important decision to whoever happens to set up the machine.

Using it sensibly

Limits arithmetic tells you the range of fits two tolerance bands can produce. It does not know what your parts do, what they are made of, or how they will be measured — and thermal expansion, surface finish and measurement uncertainty all sit outside it.

For anything structural, safety-critical or precision-dependent, the tolerance scheme belongs to the designing engineer. This is a tool for understanding what a drawing is asking for and for checking a fit before you commit to it.

Tolerance costs money, non-linearly

Halving a tolerance rarely doubles the cost; it tends to do considerably worse, because at some point it moves the part to a different process, a different machine, or a different supplier — and adds inspection that was not previously needed.

Which is the practical argument for tolerancing by function rather than by habit. The features that locate, seal or carry load earn tight tolerances; the ones that provide clearance for a spanner do not, and specifying them tightly is money spent for nothing.

Measurement is part of the specification

A tolerance that cannot be measured is not a specification. Every measurement has uncertainty, and a rule of thumb long used in industry is that the measuring equipment should be several times more precise than the tolerance being checked.

Specifying a tolerance tighter than your inspection can resolve produces parts that are accepted or rejected largely by measurement noise, which is worse than a looser tolerance honestly checked.

Temperature, and when it matters

Metals expand measurably, and standard metrology is defined at 20°C for that reason. On most workshop parts the effect is negligible; on a long precision component, or where dissimilar materials are fitted together, it is not.

An aluminium part in a steel housing changes fit noticeably across a working temperature range, because the two expand at quite different rates. Interference fits are frequently made by exploiting exactly that — cooling the shaft or heating the hole to assemble, then letting the temperatures equalise.