What is Tolerance Analysis?
In this article, I will explain to you what is Tolerance analysis, its need, and broader applications.
Tolerance Analysis
To understand tolerance analysis, first, consider the below picture. We have a tray in which there are 3 boxes stacked together. Also, the dimensions and their tolerances are provided.
As you can see, the trays and the boxes can have a variation in their dimensions in the form of tolerances.
If I ask the question, “How much the tray can vary in its size?”. The answer is easy.
“It can vary from 29.5 to 30.5.”
If I ask, “How much the green box can vary in its size?”. Again the answer is easy.
“It can vary from 7.3 to 7.7.’
Now, comes the prime question, “How much the gap defined by X can vary?”
Now, this requires a little bit of thinking and calculation.
The reason is, the dimension of the gap “X” depends on the dimensions of the tray and the other three boxes. Also, the amount of variation in dimension X depends upon the tolerances of the tray and boxes.
This process of identifying the dimension and tolerance of X is called Tolerance Analysis.
So, here comes the definition of tolerance analysis.
“Tolerance analysis is the process of finding the overall variation in an assembly which is originating from the accumulated variation of the parts that constitute the assembly.”
Requisites for tolerance analysis
A complete definition of all the parts in the assembly along with the assembly methods is needed to perform tolerance analysis.
The dimensions and tolerances with respect to size and position can be well-defined with the help of GD&T.
What can a Tolerance analysis provide?
Let’s consider the below hole and shaft assembly.
Assume that, for optimal performance of the assembly, clearance of at least 0.5 is required between the hole and shaft.
We know that the clearance depicted above depends upon the dimensions and tolerances of the hole and shaft.
By subtracting the minimum size of the shaft(8.5–1 = 7.5) from the maximum size of the hole(10+1 = 11), we can find the maximum value of the clearance = 11– 8.5 = 2.5.
Also, by subtracting the maximum size of the shaft(8.5+1 = 9.5) from the minimum size of the hole(10–1 = 9), we can find the minimum value of the clearance = 9–9.5 = -0.5.
Required clearance range is (0, 0.5).
But, the available clearance range is (-0.5, 2.5).
This means the tolerances of the hole and shaft need to be re-adjusted to arrive at the required clearance range.
By performing tolerance analysis for the above assembly, you can answer the below questions.
How large a hole can get from its nominal so that it can accommodate the shaft and also ensure enough tightness(clearance=0.5)?
How can the designer ensure that the two parts can fit together in assembly?
Will it matter if the shaft is manufactured a little larger?
And so on… with other iterations of the same above questions.
Here, the need to guarantee fit at assembly leads to tolerance analysis. Also, in some cases, the need for interchangeability of parts in the assembly also leads to tolerance analysis.
In short, tolerance analysis ensures that parts fit together at assembly and function well.
Tolerance analysis applications
Tolerance analysis finds its place in all manufacturing industries. From the very small integrated circuit to very large space shuttles.
Take any situation where there is an assembly of components, I bet tolerance analysis is needed there.
Tolerance analysis is part art and part science. You need to practice and gain a lot of experience to become proficient in it. But with the help of standardized tolerance analysis techniques, the complexity in it can be reduced.
