Dimensional Tolerance Stackups other than Worst Case
Dimensional Tolerance Stackups other than Worst Case
(OP)
I seem to recall a method that relies on probability or some percent likelihood of tolerancing parts rather that the worst case max and mins which will not occur.
Does anyone know what this is? Is there some published standard or paper?
Thanks,
Does anyone know what this is? Is there some published standard or paper?
Thanks,





RE: Dimensional Tolerance Stackups other than Worst Case
RE: Dimensional Tolerance Stackups other than Worst Case
In either case, you need to consider whether certain tolerances are coupled, i.e., they move together.
TTFN
RE: Dimensional Tolerance Stackups other than Worst Case
on how many part per 100 or 1000 that you would
consider an acceptable standard based on normal
probability curves. It may have been Erichello's
book on Precision Gearing. I would guess a
.75 percent of allowable tolerance plus and
minus would be acceptable rather than the full
100 percent of tolerance.
RE: Dimensional Tolerance Stackups other than Worst Case
Here is one of 12,500 - odd Google hits...
http://www.variation.com/techlib/ta-2full.html
Cheers
Harry
RE: Dimensional Tolerance Stackups other than Worst Case
TygerDawg
RE: Dimensional Tolerance Stackups other than Worst Case
OD of part = 3.500 +/-.005
ID of bore = 3.513 +.000, -.005
Thanks,
RE: Dimensional Tolerance Stackups other than Worst Case
TOLERANCE MODEL CHARACTERISTICS
Worst Case - Assures 100% assembly acceptance if all parts are within specification. Costly design model. Requires excessively tight component tolerances
Root Sum Square - Assumes Normal distribution and ±3 tolerances. Some fraction of assemblies will not meet specification. May adjust ZASM to obtain desired acceptance fraction. Less costly. Permits looser component tolerances.
Six Sigma Assembly Drift - The same as the Root Sum Square equation with Zp (equal to the number of process standard deviations in each tolerance) replacing Zi.
Six Sigma Component Drift - Most realistic estimates. Accounts for process mean shifts and their long-term affects on assembly distribution.
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RE: Dimensional Tolerance Stackups other than Worst Case
Worst case with your numbers:
max OD of smaller part = 3.505
min ID of larger part = 3.508
So, as long as the parts to made to spec, the min diametral clearance would be .003. Therefore, with in-spec parts, you have 100% chance of the parts fitting together without interference.
In your case, how are the parts inspected? If you're inspecting a sample of the incoming lots, there's a chance the parts might not all be to spec and therefore could cause an intereference. What's your situation?
RE: Dimensional Tolerance Stackups other than Worst Case
Thanks for the reply. I realize the worst case min is .003. All parts are inspected.
What I was looking for was a statistical analysis of the min and max clearance which is not based on worst case. By using a different tolerance range, the max clearance could be reduced.
RE: Dimensional Tolerance Stackups other than Worst Case
Cheers
Greg Locock
Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.
RE: Dimensional Tolerance Stackups other than Worst Case
Apparently "statistical tolerancing" is an ambiguous term for root sum square (RSS), the latter being more descriptive.
farmer2: Assuming your tolerances are normally distributed (which is the best assumption you can make in the absence of further information, because the normal distribution is very common in a majority of physical phenomena), then if you use 0.667 of each tolerance, i.e., x = 0.667(tol1 + tol2 + ... + toln), this gives you 2*sigma standard deviations, which gives you, on the average, a 95.4% certainty for each individual tolerance (not the stack-up).
If you stack two tolerances, what is the probability they'll both be at this 0.667 extreme edge simultaneously? (1-0.9545)^2 = 0.0021. In other words, the certainty is 99.8% that the stack won't exceed 0.667 times the summation of worst-case tolerances. (The certainty is actually even higher, considering that the probability of getting both positive or both negative extreme tolerances simultaneously is actually even lower than 0.0021, but let's not go there since the certainty is already more than high enough for practical purposes.)
So, taking your example, first convert your asymmetric tolerance to a symmetric tolerance; i.e., ID = 3.5105 +/-0.0025, OD = 3.500 +/-0.005. Then, assuming all tolerances are normally distributed, you can say with a 99.8% certainty, gap = (3.5105-3.500) +/-0.667(0.0025+0.005) = 0.0105 +/-0.005. If you stack three or more tolerances, the certainty just increases.
RE: Dimensional Tolerance Stackups other than Worst Case
First I have never used statistical tolerancing. I have used GD&T per ASME Y14.5 off and on for a number of years.
A couple of key points are that as a design entity you always have to make your designs so they fit at worst case. Unless you have a special case at your company where you make every part, how do you control who Purchasing has make your parts? I have always designed parts to always fit at worst case condition and don't have any "outragoues tolerances".
Statistical tolerancing is probably a valid way to do things in theory but in my "real world" it would never work.
RE: Dimensional Tolerance Stackups other than Worst Case
The only problem is that every part becomes the "worst case," and there is almost never a "nominal" case part.
TTFN
RE: Dimensional Tolerance Stackups other than Worst Case
I couldn't do the calcs these days without blowing the dust off a statistics text.
As Greg writes, you need to know the distribution of variations to do either.
RE: Dimensional Tolerance Stackups other than Worst Case
Statistical tolerancing does not have to be put on the drawing for you to use statistics in a "typical case" rather than "worst case" scenario. You can substitute the production stats into the worst-case stack-ups to find a typical case instead. This will quiet those that doubt the "worst case" results as having "never happened, and never will".
A comment was made above about statistical tolerancing being an interesting theory and not being in the "real world". That is true for many companies that do not understand the reason for going this route. Where you don't require that every part-A will fit with every part-B, but that rather eventually every part-A will mate with some part-B, then statistical tolerancing can save you sums of money. Ever had a screw that didn't fit in the first hole that you tried, so you went and tried it in another hole where it did fit, then grabbed another screw from the same batch and fit into the first hole... that's statistical tolerancing at its simplest. Statistical processing is used in making bearings, automobiles, fasteners, electronic components,...
Jim Sykes, P.Eng, GDTP-S
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