Total positional tolerance at material condition

Total positional tolerance at material condition (Hole)

Suppose the Ø 1.005 / 1.010 hole is inspected and there are six parts with different ID dimensions. Their actual sizes checked with run out methods give that their actual axis is to be .006” over and up from the true position even though they have different actual ID’s. We want to know which part is within true position tolerance at MMC. Parts to be acceptable require some calculation when is used the run out method.

            In GD&T, maximum material condition (MMC) refers to a hole that contains the greatest amount of material.
            To understand and memorize simply and logically the concept, I suppose that you have a part designed as a square with one hole in the center, Ø 1.005 / 1.010 . You have produced just 5 parts and measured their holes. The hole of part #1 is on the low side of its tolerance Ø 1.005" and the hole of part #5 is on high side of its tolerance Ø 1.010". Here is the question:

Which part will weigh more and which part will weigh less?

The MMC size of a hole is smallest size, or the Lower Specification Limit Ø 1.005". As the size of the hole departs from the MMC size toward the LMC size a bonus tolerance is gained. The bonus tolerance is the difference between the actual size of the hole and the MMC size of the hole which is the LSL which in our case is Ø 1.005". For a shaft is the opposite, because the MMC size of a feature is the Largest shaft, and the calculation starts from the Upper Specification Limit (USL) minus the actual size of the shaft. The MMC is used to tolerance parts the parts that fit together but do not move to each other.

There is also the opposite of MMC. It,is the concept of LMC (the Least Material Condition), which is the largest hole and the smallest shaft. For the hole the bonus tolerance at LMC is the difference between actual size of the hole and the Upper Specification Limit (USL) which is Ø 1.010" if the true position is required at LMC. Usually it is used to not have a loose-fitting with mating part.

Picture 1

                                                         
So, when we make the part the center(axis) of the hole (circle) varies. What is important is what is the actual distance of the center of the hole to the datumes -A- and -B-. The basic distances give the true position of the hole to the datumes -A- and -B-. So, we need to know the distance between the actual center of the hole we made to the center coordinates of the hole where it is supposed to be (true position) given as basic distances. By applying the Pythagorean Theorem we can calculate it and find out that distance which is in fact a radius from the trueposition point of view (Circle zone or cylindrical zone). To get the diameter of the actual cylindrical zone of the actual hole location, because the true position as required as a diameter, we need to multiply the radius times two.

So the actual center of the hole is positioned in a circle that has a diameter of .016”. The True Position Tolerance is only .003” but there is an MMC modifier. With these data we still do not know if the trueposition is within tolerance or not. The following formulas are used to calculate the bonus tolerance and total positional tolerance:

Bonus = Actual feature of size-MMC
Total positional tolerance= Bonus + Geometric tolerance

We have 6 parts in which the hole is produced at:

1. Part#1 Ø 1.005
2. Part#2 Ø 1.006
3. Part#3 Ø 1.007
4. Part#4 Ø 1.008
5. Part#5 Ø 1.009
6. Part#6 Ø 1.010

Calculating the bonus and the total positional tolerance for all samples:

As you can see, in our example in the picture 1, when the center of of the hole (axis) has a deviation .006" in X and Y direction, even the parts have bonus tolerances they are out of the specification because the calculated Total Position Tolerances have a max of .008”, which is < .016" actual true position of the hole calculated by applying the Pythagorean Theorem.

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