Worst-case

Worst-case tolerance analysis is the traditional type of tolerance stackup calculation. The individual variables are placed at their tolerance limits in order to make the measurement as large or as small as possible. The worst-case model does not consider the distribution of the individual variables, but rather that those variables do not exceed their respective specified limits. This model predicts the maximum expected variation of the measurement. Designing to worst-case tolerance requirements guarantees 100 percent of the parts will assemble and function properly, regardless of the actual component variation. The major drawback is that the worst-case model often requires very tight individual component tolerances. The obvious result is expensive manufacturing and inspection processes and/or high scrap rates. Worst-case tolerancing is often required by the customer for critical mechanical interfaces and spare part replacement interfaces. When worst-case tolerancing is not a contract requirement, properly applied statistical tolerancing can ensure acceptable assembly yields with increased component tolerances and lower fabrication costs.

Statistical variation

The statistical variation analysis model takes advantage of the principles of statistics to relax the component tolerances without sacrificing quality. Each component's variation is modeled as a statistical distribution and these distributions are summed to predict the distribution of the assembly measurement. Thus, statistical variation analysis predicts a distribution that describes the assembly variation, not the extreme values of that variation. This analysis model provides increased design flexibility by allowing the designer to design to any quality level, not just 100 percent.

There are two chief methods for performing the statistical analysis. In one, the expected distributions are modified in accordance with the relevant geometric multipliers within tolerance limits and then combined using mathematical operations to provide a composite of the distributions. The geometric multipliers are generated by making small deltas to the nominal dimensions. The immediate value to this method is that the output is smooth, but it fails to account for geometric misalignment allowed for by the tolerances; if a size dimension is placed between two parallel surfaces, it is assumed the surfaces will remain parallel, even though the tolerance does not require this. Because the CAD engine performs the variation sensitivity analysis, there is no output available to drive secondary programs such as stress analysis.

In the other, the variations are simulated by allowing random changes to geometry, constrained by expected distributions within allowed tolerances with the resulting parts assembled, and then measurements of critical places are recorded as if in an actual manufacturing environment. The collected data is analyzed to find a fit with a known distribution and mean and standard deviations derived from them. The immediate value to this method is that the output represents what is acceptable, even when that is from imperfect geometry and, because it uses recorded data to perform its analysis, it is possible to include actual factory inspection data into the analysis to see the effect of proposed changes on real data. In addition, because the engine for the analysis is performing the variation internally, not based on CAD regeneration, it is possible to link the variation engine output to another program. For example, a rectangular bar may vary in width and thickness; the variation engine could output those numbers to a stress program which passes back peak stress as a result and the dimensional variation be used to determine likely stress variations. The disadvantage is that each run is unique, so there will be variation from analysis to analysis for the output distribution and mean, just like would come from a factory.

While no official engineering standard covers the process or format of tolerance analysis and stackups, these are essential components of good product design. Tolerance stackups should be used as part of the mechanical design process, both as a predictive and a problem-solving tool. The methods used to conduct a tolerance stackup depend somewhat upon the engineering dimensioning and tolerancing standards that are referenced in the engineering documentation, such as American Society of Mechanical Engineers (ASME) Y14.5, ASME Y14.41, or the relevant ISO dimensioning and tolerancing standards. Understanding the tolerances, concepts and boundaries created by these standards is vital to performing accurate calculations.

Tolerance stackups serve engineers by:

• helping them study dimensional relationships within an assembly.
• giving designers a means of calculating part tolerances.
• helping engineers compare design proposals.
• helping designers produce complete drawings.