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

## Tolerance Analysis and Tolerance Allocation: Is There a Difference?

When **only two** parts are assembled, we usually do not talk about tolerance analysis. In this case, the dimensioning must be such that the parts always fit. If there are more than two parts in the assembly, tolerance analysis can be useful. However, there is no hard and fast rule. Even in mass production, for example, tolerance analysis can be useful in a two-part assembly. Tolerance analysis is actually a **generic term**. It can be divided into:

- the analysis of actual dimensions of
**manufactured parts**; - tolerance
**allocation**, deriving tolerance specifications on technical drawings.

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

## Choosing Optimal Tolerances

As a mechanical designer, you want **optimal tolerances** on your drawings. Tolerances that are large enough for a low price and small enough to ensure a good fit of the assembly. Tolerance stack-up analysis is an excellent tool for deriving these optimal tolerances. Tolerance analysis **focuses on the simple** question: do all the parts fit? And, as a designer, you will always have cost in mind.

## Step Plan Tolerance Stack-up Analysis

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

**First**you determine which dimension in the assembly you want to analyze, the so called the**critical dimension**.- Then you determine the
**specification**for that critical dimension. - Next, you build the
**chain of tolerances**that affect the critical dimension. - Next, you
**sum**all the tolerances in the chain. - Finally, you
**compare**the derived sum to the specification in step 2. Take action if the specification is not met.

## Statistical or Worst-Case Stack-Up

At each step, there may be questions that are difficult to answer. For example, must the specification in step 2 always be met under all circumstances? And what is the margin? In Step 3, there may be a mechanical adjustment or there may be moving parts in the assembly. Step 4 is whether to do a worst-case analysis or a statistical analysis. What is the distribution of dimensional variation and how do you statistically add up these tolerances? What seemed like a relatively simple question can turn into a complex analysis. In the next post I will discuss these steps in more detail.

## Tolerance Stack-up Analysis Expertise

Jaap Vink of Vink System Design & Analysis has great expertise in tolerance budgeting and **stack-up analysis** and has done several projects in this area. As a guest lecturer for Mikrocentrum, I have given a three-day course on tolerance analysis for several years.