How to calculate tolerances of a part?

There are 2 methods to calculate tolerances. They are

  1. Stackup
  2. RMS (Root Mean Square)

What are tolerances?

Tolerances are deviations from the specified dimensions. In the real world of mass production, it is very hard and futile to create parts to the exact dimension.

Let’s say you want a pencil 100mm long. But it is very hard to make a pencil that is exactly 100mm long. So you tell me that you are satisfied with a pencil whose length lies in the range of 99mm and 101mm. The 2mm in between 99mm and 101mm is called tolerance. It is represented as 100±1mm in the manufacturing world.

Tolerance calculations are very important in the field of engineering. Here, we are talking about physical tolerances in the field of mechanical engineering. There are other tolerances also: like material composition tolerance, tolerances in temperature and humidity etc. Tolerances coexist with dimensions, everywhere.

Many factors contribute to tolerance in parts. A minor change in ambient temperature can influence cooling rates of injection molds. This difference might lead to slightly smaller or bigger sizes of features.

Why are tolerances important?

Tolerances form one of the most important parameter in mass production. Close watch is kept on tolerance fluctuations in parts/components. Too much fluctuation and an eventual deviation from the specified levels would have adverse impact on part quality, part failure and eventual safety problems. There are also numerous statistical tools employed just to evaluate these fluctuations.

Right setting and control of tolerance can lead to improvement in part quality along with reduction of costs.

How do I set tolerances?

Tolerance settings are directly related to part costs. A tighter setting would lead to increase in part costs. This is because to achieve the result, the factory making the product would have a higher rejection rate. Apart from that, the part might also have to go through extra processes using specialised equipment to achieve the dimensions.

Setting tolerances has to done after consulting standards as well as after talking to the factory that would be making the product. This is because the factory might not always be be capable of maintaining the general tolerances that you might be referring to. It is better to clarify this well in advance and choose a factory accordingly.

Here is the PDF file of IS2012 which is the BIS standard for general tolerances.

How do I calculate the effective tolerance between two points in a part?

As mentioned above, there are 2 methods.

  1. Stackup
  2. RMS (Root Mean Square)

Stack Up Analysis

Let’s say you have the following part at hand.

As you can see, A is the ‘Product Datum’. It is the 0 point of the part and most major features are dimensioned from the product datum. It is a very important part.

Now let’s say you need to find the tolerance of the face E with reference to face A (Product Datum).

The maximum tolerance of E with reference to A would be (0.2+0.4+0.1+0.1). This is because A-B will expand by 0.2mm, B-C will expand by 0.4mm, C-D will expand by 0.1mm and D-E will expand by 0.1mm. Therefore the maximum expansion will be (0.2+0.4+0.1+0.1). Same thing for contractions.

This is stackup analysis. Make sure that the dimensions are in the straight line though. If some dimensions in between are not in line, resolve them into the directions and do the same thing.

Stackup analysis shows us the absolute worst case tolerance. If the part is made according to specification, there is no way the length from A-E would exceed (5+10+2+3)±(0.2+0.4+0.1+0.1).

For all critical parts that pertain to regulation or safety, do a stackup analysis. It is not pretty when safety or regulatory problems happen.

Root Mean Square Analysis

Unlike Stackup Analysis, Root Mean Square helps us estimate the tolerance range with the highest frequency. This is assuming normal distribution while design which means that you assume that most of the results will concentrate around the nominal dimension (in Poisson distribution chart).

For Root Mean Square analysis, take all the dimensions (make sure they are in the same direction. If not, resolve it).

0.1      0.1       0.4       0.2

Square the values

0.01     0.01     0.16     0.04

Add the values up

0.01+0.01+0.16+0.04 = 0.22

Now find the square root of the sum.

sqrt(0.22) = 0.469

0.469mm would be the RMS tolerance.

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