Component Tolerance Stack Up In Assembly

Every dimension on an assembly drawing is a nominal value with a tolerance, and the clearance that decides whether the product fits together is the difference between two or more of those dimensions. Whether the parts still fit when each dimension sits at its own limit is the question a tolerance stack up answers, and it is asked most often about the gap between two tall components, the alignment of a connector with a panel opening, and the seating of a board inside its enclosure.

This article explains what a stack up does, how the worst case and statistical methods differ, where the contributing tolerances actually come from, and how to allocate a budget that the process can hold.

What A Stack Up Answers

The method starts by identifying a resultant dimension, which is the clearance or the alignment that the product needs, and then expressing it as a sum of contributing dimensions. A connector position, for example, is the sum of the board outline position, the pad position relative to the outline, the component body and lead tolerance, and the placement accuracy of the machine. Each contributor has a nominal value and a tolerance, so the resultant has a nominal value and a tolerance as well.

Clearance is also one sided, which is a point that is easy to miss. The gap is either positive or negative, and only the negative side is a failure, so the designer cares about the tail of the distribution on one side rather than about the spread in both directions. That is why a stack up that reports a symmetric plus or minus figure for a clearance is only half the answer.

A tolerance is a permission rather than a description of what the process does, and the distinction matters when the result is interpreted. A stack up built from drawing tolerances describes the worst case the drawings allow, while the parts that arrive describe the distribution the process actually produces. Where a process is centred and comfortably inside its limits, the drawing limit is rarely approached and the statistical method is realistic. Where a process runs near one limit, or drifts during a run, the drawing limit is reached often and the same analysis will underpredict the failures.

It is also worth separating dimensions that affect fit from those that affect function. A clearance between a connector and a panel opening is a fit dimension, and going slightly negative means the part does not assemble, which is visible immediately. A dimension that sets an electrical parameter, such as the gap between a pad and a plane, affects function rather than fit, and a small excursion may appear only as a change in impedance or in leakage current. The two kinds of dimension need different confidence levels, and a single blanket tolerance hides that difference.

Worst Case And Statistical Methods

The worst case method adds the absolute values of the contributors, which guarantees that the assembly fits even if every part is at its limit in the least favourable direction. It is simple and it is safe, but it is expensive, because ten contributors of plus or minus a tenth of a millimetre add up to a whole millimetre of clearance that may never be needed in practice.

The statistical method treats each tolerance as a limit on a distribution, typically three standard deviations, and combines the standard deviations as the square root of the sum of squares. The same ten contributors then produce a combined spread of about three tenths of a millimetre rather than one millimetre. The method is only valid when the contributors are independent, centred on nominal, and stable, and it fails when several dimensions come from the same process step or when a process drifts. The common practice is worst case for a handful of contributors and a statistical method for a larger number, with a safety factor applied to the result.

Where The Tolerances Come From

A contributor list is worth building once and reusing. The component body and lead tolerances come from the data sheet and are taken at their maximum and minimum, not at the typical value that the sales drawing shows. Placement accuracy combines the repeatability of the machine with its absolute accuracy and with the vision alignment, and each of those has its own figure. On the board side the pad position relative to the outline, the drilled hole position, and the dimensional change of the laminate during lamination all contribute.

Some of those contributors are correlated, and treating them as independent overstates the statistical result. The pad pattern and the solder mask come from the same artwork, so they move together, and a laminate that shrinks uniformly moves every feature on the panel in the same direction. Two components placed in one pass on the same machine share a common offset, which cancels when the clearance between them is the quantity of interest. Deciding which contributors are truly independent is the part of the analysis that requires engineering judgement rather than arithmetic.

Designing Clearance That Survives

Once the budget exists, the question is where to tighten it. Tightening a machine accuracy or a component tolerance usually costs money on every unit, while changing the design to increase the nominal gap costs nothing per unit, so the cheapest move is nearly always to move the features apart rather than to demand a better process. Where the gap cannot be increased, dimensional chains should be shortened, because every removed contributor removes its tolerance from the sum.

Dimensioning from a single datum is the other habit worth adopting. A chain of dimensions, each measured from the previous feature, accumulates tolerance along its length, whereas a set of dimensions taken from one reference does not. One sided tolerances are also useful where the physical requirement is one sided, because specifying a minimum clearance without an upper limit leaves the fabricator free to work on the side that does not matter.

Documenting And Verifying The Result

The stack up should live in a spreadsheet next to the assembly drawing, with each contributor, its source, and its tolerance visible, so that any change can be re-evaluated quickly. When a component changes supplier, when the laminate changes, or when a placement machine is replaced, the relevant line changes and the resultant is recalculated. A stack up that exists only as a calculation on one drawing revision is of little use later.

Verification is a measurement, not a calculation. The resultant dimension is measured on first articles and on a sample from production, and the spread is compared with the prediction. If the measured spread is wider than predicted, one of the contributors is larger than assumed or the distribution is not centred. The related geometry rules are described under pad design standards and board outline and mounting design, and the assembly side under placement order and pad positioning.

FAQ

Is the statistical method always acceptable in place of worst case? No. It is acceptable when the contributors are independent, centred, and stable, and it should be avoided for small counts or where several dimensions come from the same process step.

Which tolerance should be tightened first? Usually the one with the largest contribution to the resultant spread, or the one that is cheapest to change. Moving a component in the layout is normally cheaper than buying a more accurate machine.

How is a stack up verified? By measuring the resultant dimension on first articles and on a production sample and comparing the observed spread with the predicted one, then repeating the check after any process or supplier change.