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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: Is There a Difference?

If only two parts are mounted on each other then we usually do not talk about tolerance analysis. In that case the dimensioning must be such that the parts always fit. With more than two parts in the assembly, tolerance analysis can come in handy. Although there is no fixed rule for this. Even in mass production, for example, tolerance analysis can be useful in a composition of only two parts. The word tolerance analysis is actually a generic term. The discipline can be divided into:

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

Thus, the first is about an analysis of the production process and its possible adjustment. The second is about the design of the product. In this article I want to talk about tolerance allocation. But I’ll stick with the commonly used term tolerance analysis anyway.

## Choosing 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. Tolerance analysis focuses mainly on the simplified question: do all the parts fit? And as a designer, you will of course always keep an eye on the cost.

## Step Plan Tolerance Stack-up Analysis

A tolerance stack-up analysis consists of a number of basic steps. A brief summary can be found below.

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 Stack-Up

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. As a guest lecturer for Mikrocentrum I have given a three-day course on tolerance analysis for several years.