Suppose you have gone through your tolerance analysis step plan and created a tolerance chain. Now all you have to do is add up all the tolerances. This seems simple enough, but there are a few issues to consider:
- What do you do with asymmetric tolerances?
- Do you perform a worst-case analysis or:
- a statistical analysis?
- When does the stack-up meet its specification?
1 Convert Asymmetrical Tolerances
To start with the first pont: asymmetric (or limit) tolerances are always converted into symmetric (or equal bilateral) tolerances. Thus, a dimension A t1/t2 is converted into B +/-t. For example: 12 +0.2/0 becomes 12.1 +/-0.1. The reason for this is that working with symmetric tolerances is:
- is less work;
- is less prone to error;
- makes it easier to perform a statistical analysis.
Working with symmetric tolerances is less work because you only have to make one stack-up instead of two. With asymmetrical tolerances, you have to make one stack-up in the positive direction and one in the negative direction. It is easy to make a mistake by putting a tolerance in the positive chain when it belongs in the negative chain (and vice versa). And if you want to do a statistical analysis you still have to take into account the mean and the symmetric tolerance.
The conclusion to question 1 is: Always convert asymmetrical tolerances to symmetrical tolerances.
2 Worst-case Summation
In a worst-case tolerance analysis, you assume that each dimension in the tolerance chain will be made at its maximum or minimum allowed value. And that the variances will have the most unfavorable combination, regardless of how unlikely it is. In other words, worst-case. Worst-case tolerance analysis is now simple. Just add up all the tolerances in the chain, often called a linear sum. To make it clear, put it all in a table. Example:
| Part | Nominal dimension | +/- Tolerance |
|---|---|---|
| A | 12.5 | 0.2 |
| B | -16.0 | 0.1 |
| C | 3.0 | 0.3 |
| D | 5.7 | 0.2 |
| ——- + | ——- + | |
| Total | 5.2 | 0.8 |
Conclusion: the critical dimension is 5.2 +/- 0.8.
The advantage of worst-case analysis is that it is easy to do. The disadvantage is that you are considering a very unlikely combination of realized dimensions: the maximum allowable deviation in a worst-case combination. Therefore, tolerance specifications must be unnecessary tight and more expensive than necessary.
In the next article you will learn more about performing a statistical tolerance analysis (3) and read about the criteria for deciding if the stack-up meets its requirements (4).
