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Tolerances become important as soon as you design an assembly of parts. Of course each dimension must be provided with a tolerance. But in an assembly the tolerances become important because all parts must fit. In this article I tacitly will assume that we are dealing with interchangeable parts.

Tolerance Analysis and Tolerance Allocation

We often don’t speak of tolerance stack-up analysis when just two parts are assembled together. Dimensions and tolerances must be such that the parts will always fit. With more than two parts performing a tolerance stack-up analysis can be necessary. This is not a fixed rule though. For instance in mass production even for the assembly of two parts a tolerance stack-up analysis can yield interesting results. A tolerance stack-up analysis can be used for:

  • the analysis of actual dimensions of produced parts;
  • tolerance allocation, deriving tolerance specifications on technical drawings.

In this article I want to speak about tolerance allocation.

Optimal Tolerances

As a mechanical designer you want to put optimal tolerances on your drawings. Tolerances that are big enough for a low price and small enough to ensure a good fit of the assembly. A tolerance stack-up analysis is an excellent tool to derive these optimal tolerances.

Step Plan Tolerance Stack-up Analysis

A tolerance stack-up analysis consists of the following basic steps:

  1. First you determine which dimension in the assembly you want to analyze, the so called critical dimension.
  2. Then you determine the specification for this critical dimension.
  3. Thereafter, you build the chain of tolerances that influences the critical dimension.
  4. Next you add up all tolerances in the chain.
  5. Finally you compare the derived sum with the specification in step 2. Take action when the specification is not met.

Statistical or Worst-Case

In each step there can be difficult to answer questions. Like: must the specification in step 2 always be met under all circumstances? And how big must the margin be? In step 3 there could be a mechanical adjustment or there could be moving parts in the assembly. In step 4 there is the question of performing a worst-case analysis or a statistical analysis. What is the distribution of the dimensional variation and how do you statistically add up these tolerances? What first seemed like a relative simple question can turn into a complex analysis. In a next post I will dive into more detail of these steps.

Tolerance Stack-up Analysis Expertise

Jaap Vink of Vink System Design & Analysis has great expertise in tolerance budgeting and stack-up analysis and has conducted several projects in this field. Besides, I give the Mikrocentrum three-day training course Tolerance Analysis several times a year.

Please feel free to contact me for more information or if you want to do a tolerance stack-up analysis.