Suppose that you went through your tolerance analysis step plan and made a tolerance chain. The only thing to do now is to add up all tolerances. This seems easy enough but there are a few questions to consider:
- What to do with asymmetrical tolerances?
- Do you perform a worst-case analysis or (3) a statistical analysis?
- When does the stack-up meets its specification?
1 Convert Asymmetrical Tolerances
To start with the first item: asymmetrical (or limit) tolerances are always converted into symmetrical (or equal bilateral) tolerances. So a dimension A t1/t2 is converted into B +/-t. For example: 12 +0.2/0 becomes 12.1 +/-0.1. The reason behind this is that working with symmetrical tolerances:
- is less work;
- is less error prone;
- makes it easy to perform a statistical analysis.
Working with symmetrical tolerances is less work because you only have to make one stack-up instead of two. With asymmetrical tolerances you have to make a stack-up in the positive direction and one in the negative direction. You easily make a mistake by putting a tolerance in the positive chain while it belongs in the negative chain (and vice versa). And if you want to perform a statistical analysis you still have to take into account the mean value and the symmetrical tolerance.
The conclusion at question 1 is: always convert asymmetrical tolerances into 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 their maximum or minimum allowed value. And that the deviations have the most unfavorable combination regardless of the improbability. In other words: worst-case. The worst-case tolerance analysis is now simple. Just add up all tolerances in the chain, often called a linear sum. To make it clear you put everything 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 a worst-case analysis is that it is easy to do. The disadvantage is that you account for a very improbable combination of realized dimensions: the maximum allowed deviation in a worst-case combination. Therefore the tolerance specifications must be unnecessary tight and become more expensive then necessary.
In a next article you will read more about performing a statistical tolerance analysis (3) and read about the criteria for deciding if the stack-up meets its requirements (4).
