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MMC & Tolerance Stacks For Beginners!
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👶 Meme Of The Week
🙋♂️ Interview Practice Question of the Week
Two components need to fit inside of a bracket (as pictured). Nominally, there is clearance. However, being the wonderfully diligent and talented engineer you are, you know that not all parts are manufactured nominally. Will the parts fit together?
Perform a tolerance stack given the following component drawings to assembly tolerance of the parts at RSS limits.
✅ The Answer
This question is a classic, and tests a skill that you will need to know in any mass production design role. Tolerance stacks are a fundamental skill in a mechanical engineer’s arsenal, and very useful in quantifying clearances, gaps, and general fitments.
First off, what is a tolerance stack, and why do we need it?
For better or for worse, we’re not scientists. We are paid to build things in a cost effective manner. As such, we have to deal with tolerances and manufacturing. Therefore the actual parts will not be the exact size as the CAD. When looking to see if the pieces above will fit together, we have a few options, practically speaking.
We can make the teal C shaped piece taller, expanding the MMC of our assembly. This will not only increase the clearance for assembly, but also the material, weight, shipping and manufacturing costs.
Another option would be to crack down on those tolerances; make the components flatter! Hone, lap, grind, and inspect them. Toss out parts not meeting specifications. As you might have guessed, this is also expensive as it impacts yield and throughput.
We can cut down on the part thickness to increase that clearance? This would likely increase manufacturing cost, decrease stiffness and increase likelihood of yielding, but if you want to run the sims on if all that strength is needed, this is an option. When approaching the simulations team to ask for that, just be sure you have looked into other options first and have proper justification for why it’s needed.
Run a tolerance analysis! (Also known as a TA or tolerance stack)
This is a relatively easy way to quantify what that gap will look like in general use cases. One fundamental problem with all of the other strategies, is that you still have no way of knowing how much is enough? You have intuition and guesswork, but…
A) It’s your job to do this. Leave the guessing out if you don’t need it. At every level of every organization, someone is cutting corners. Our job is to figure out exactly how much of that corner to cut!
B) In more complicated assemblies with multiple axes of concern and going through and across more parts, your guess probably won’t be worth much.
So how do we do a tolerance stack?
When I was first asked to do a tolerance stack, the way my manager described it was as an ant crawling along all the parts adding the tolerances through each interface until it reaches the same point again. In many ways, that’s actually pretty much all there is to it (granted it would have helped if he had been more specific, especially for a 3D stack with 6 components and 20+ tolerances but c’est la vie). Let’s dive into the details:
The first thing I like to do is mark the gap/clearance/fit that I am trying to analyze. For us, it’s the following gap:
Based on the drawing, it appears that the part has a nominal clearance of 0.2 mm. Given the tolerance on the teal gap is +/- 0.1, and the red component has a thickness with tolerance +/- 0.05 and the yellow component has a thickness with tolerance +/- 0.10, a quick glance tells us that if each of these components is at the worst case tolerance specification (MMC), the components will not assemble. The gap will be 6.10 while the two parts will have combined thickness 3.05 + 3.10 = 6.15. That, is the reason we check RSS (root sum square - look this up if unfamiliar) tolerances as well! Though not as conservative as the worst case, if we make some generally reasonable assumptions, we can greatly reduce the conservativeness of our estimation for the required gap (resulting in reduced cost).
The most important assumption we are making, and one which we must ensure is in fact true, is that each tolerance we include follows a normal distribution, and in this case, is mean centered. That is to say, that if we look at 100 parts, the majority of them will be centered around the nominal value following a gaussian curve. If there are as many parts at the nominal spec as there are at the bounds, we cannot apply this approach and should instead opt for a Monte Carlo.
A simple RSS tolerance analysis of thickness tolerances alone would give the following:
RSS = ((0.10^2)+(0.05^2)+(0.10^2))^0.5 = 0.15 mm
Given that we have 0.2 mm of nominal clearance, this means that we should actually be fine! An easy way to conceptualize this, is that everything goes wrong in the worst case. But, if we’re looking at RSS tolerances, if something goes wrong in one direction, it’s just as likely something will go wrong in the other direction, cancelling it out! For that reason, RSS tolerances may be smaller than we initially expect. Note that it is still common to add some buffer on top of RSS tolerances if we are able to, given lack of complete knowledge of the validity of the input assumptions (a vendor may say they are hitting a 3 +/- 0.1 mm, but what if the actual distribution is 3.09 +/- 0.01 mm? They technically aren’t out of specification, but your beautiful tolerance stack is now invalid).
There are different levels of fidelity / conservative estimation when it comes to tolerance stacks. The “quick and dirty” tolerance stack for this assembly showed that we have 0.05 mm of clearance. If we’re interested in the detailed analysis (which is likely overly conservative), we need pretend we’re an ant.
Below, each interface is identified.
Many people start with identifying each waypoint on the graphic, though I tend to go through the interfaces in my head and write down
In the end, you may have to then get real world data on thickness and tolerances and use the standard deviation instead of the drawing tolerances. For high volume applications, use +/- 6 sigmas, this will result in a defect rate of 3.4 PPM (parts per million). For lower volume applications, determine the acceptable failure rate and apply the proper number of standard deviations to your RSS calculations to find if clearance needs to be increased or is acceptable as is.