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**Geometric Dimensioning and Tolerancing**

### Tolerance Stackup Analysis

Tolerance Stack up Analysis. Tolerance analysis is the general term for activities related to the study of accumulated variation in mechanical parts and assemblies. Its methods may be used on other types of systems subject to accumulated variation, such as mechanical and electrical systems. Engineers analyze tolerances for the purpose of evaluating geometric dimensioning and tolerancing (GD&T). Methods include 2D tolerance stacks, 3D Monte Carlo simulations, and datum conversions.

Tolerance stack ups or tolerance stacks are terms used to describe the problem-solving process in mechanical engineering of calculating the effects of the accumulated variation that is allowed by specified dimensions and tolerances. Typically these dimensions and tolerances are specified on an engineering drawing. Arithmetic tolerance stack ups use the worst-case maximum or minimum values of dimensions and tolerances to calculate the maximum and minimum distance (clearance or interference) between two features or parts. Statistical tolerance stack ups evaluate the maximum and minimum values based on the absolute arithmetic calculation combined with some method for establishing likelihood of obtaining the maximum and minimum values, such as Root Sum Square (RSS) or Monte-Carlo methods. In performing a tolerance analysis, there are two fundamentally different analysis tools for predicting Stack up variation: worst-case analysis and statistical analysis.

Worst-case tolerance analysis is the traditional type of tolerance Stack up 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. The statistical variation analysis model takes advantage of the principles of statistics to relax the component tolerances without sacrificing quality. Each componentâ€™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. While no official engineering standard covers the process or format of tolerance analysis and stack ups, these are essential components of good product design. Tolerance stack ups 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 Stack up 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.

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Contributed by Harsh Presh, Pune India