I suppose it is not so simple when you take tolerances into account. When I do this, I draw the thing out and the most methodical way possible. I use absolute coordinates for everything. Each individual arthithmetic operation is simple. There are just lots of them.
After that, it is primarily a matter of understanding the drawings and the tolerances.
Tolerance analysis can be as simple as looking at dimensions, tolerances, part datums, and assembly functional datums. Or you could use one of the many modern statistical analysis tools. I would also suggest using excel to do your stats and other math functions.
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Heckler
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I have found Excel to be useful in analyzing tolerances, just to reduce the probability of arithmetic errors.
I have not found a general formal technique that would allow unskilled labor to pick numbers off drawings and plug them into Excel.
I set up a few cells for each feature or problem space boundary to be evaluated, and label them so I can remember which is which and so I can maybe re-use the block for a similar situation in the future.
I have so far not evolved a block that can usually be copied without modification. If there exists a system of tolerancing that would enable such an activity, I haven't stumbled onto it.
Statistical techniques may be useful for characterizing the behavior of a factory, but they are not real useful to a guy who is trying to adjust a machine setup.
My experience with Statistical methods is extensive but to be affective the entire business/manufacturing process needs to buy into the concept otherwise the loop can't be closed.
I think you have to start by assigning reasonable tolerances to each dimension. You have to have an idea how the part is made and what a typical shop is capable of holding. Whether a diameter is to be machined or ground will tell you that you are restricted to say .005 or .0005 inches. You would not put .001 tolerance on a hole that a bolt goes through, as it would have to be reamed, and you would not want to hold it location much tighter than plus/minus .005. So with two dimensions controlling the location, you need .010 clearance right from the start (maybe not exactly .010), plus a couple more thou so the bolt will go through, and then add on your normal drilling tolerance. No tolerance stackup needed.
In an assembly involving several dimensions, add up all the tolerances and then adjust any clearances, gaps, or fits to accommodate this. I think a worst case stackup is a little extreme and a statistical one might be more realistic, but there is some argument here.
If you're using traditional +/- tolerances, a complete tolerance stackup isn't practically possible. Such tolerancing doesn't include effects of perpendicularity of holes, shape/form of holes, and a number of other factors, and these can have an immense impact. I've tried it on a chain of less than a dozen items, and it didn't yield anything realistic even if I included lots of gross assumptions about manufacturing capability.
If you're using GD&T, you can do a tolerance stack-up. It's a combination of graphical and mathematical work that accounts for worst cases (e.g. smallest dowel in the largest hole)of size, location, form, etc. It is quite comprehensive. This will give you the worst-case scenarios, not the probable case. Typically people will have some heart problems when they see how bad things could be, and rationalize that it never has been that bad, so the analysis is garbage. If you have hard statistical data on the manufacturing capabilities, you can greatly improve the results by including them in the calculation. There are a number of CAD analysis packages that do this, and you can always do it manually (that way you understand the process and are less likely to overlook something). My suggestion would be to take a good course from someone like Tec-Ease and work at it manually.
You can really drive yourself nuts trying to account for every feature that in some extreme case might not be square with the rest of the world. If you have a lot of drawings to do with dozens of dimensions on each, you might not ever finish the job anyway so the stackups would not matter very much in the end (seen that happen lots of times).
One case from my own experience: we had an assembly of several parts that had been made for many years but suddenly one day could not be put together. Management called out the Tiger Team and the logical decision was that it was a design error. I was picked to do a stack up, but all I did was a quick worse case plus/minus stackup and found nothing wrong. Unacceptable answer. They gave it to another guy who added in all the concentricities, parallels, perpendiculars, and probably more, but still could not explain it. When they were done blaming engineering, it occurred to them to measure the parts. All were within spec but one which was something like an eighth inch off.
