Help! How to handle Unequal Bilateral Tolerance using RSS/MRSS method? 4

[Buck61]

Help! I posted the following question last week and basically got nowhere- please submit solid approach/solution only.

Best Regards,
Buck61

Hi,
I need to know how to go about using an unequal bilateral tolerance when calculating total variation using the RSS tolerance analysis method.
All RSS examples I have seen use uniform bilateral tolerances.

A text I have at work "Dimensional Management" (by Mark Curtis c2002) which includes a section on modified MSRR (pg 166) where he uses a correction factor of K = 1.4 x RSS and 1.7 x RSS. However, as shown, you must multiply K by the RSS previously calculated using uniform bilateral tolerances.
??
I appreciate your respective input,
Buck

 

[drawoh]

Buck61,

Let's try to agree on terminology here.

Nominal size: original intended size.

Maximum size: largest size allowed by tolerance.

Median size: size exactly half way between max and min.

Minimum size: smallest size allowed by tolerance.

Tolerance: exactly half the distance between max and min, or the exact distance between nominal and either max or min.

For example, we have a 40mm shaft and hole designed as an ANSI RC6 fit. For the shaft, we call up Ø40e8, which is equivalent to Ø40-0.06/-0.09.

Nominal 40
Maximum 39.94
Median 39.925
Minimum 39.91
Tolerance: ±0.015

Regardless of how someone applies tolerances to a part, you can calculate the maximum, nominal and minimum dimension, and the tolerance, as noted above.

An unequal, bilateral tolerance is a formatting technique that has no bearing on how you interpret your tolerance. The only problem I have with this is that I do not see a relationship between your tolerance, and your anticipated standard deviation of your inspected parts.

JHG

 

[KENAT]

http://www.eng-tips.com/threadminder.cfm?pid=1103

may be a better place to look if drawoh answer doesn't meet your desires.

I'd have thought converting to symmetrical just for calculations sake may work.

As to the first line of this post, given that we aren't being paid to help you, I suggest you may want to rephrase your request.

Posting guidelines faq731-376

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(probably not aimed specifically at you)
What is Engineering anyway: faq1088-1484​

 

[Buck61]

I do apologize for the way the posting came out- it was not intentional.
Thank you drawoh and Kenat for your very helpful inputs!

Best Regards,
Buck61

 

[btrueblood]

FWIW, to file under "more information than you probably wanted":

The RSS method works (i.e. correctly predicts the 1-sigma distribution of assembly stackup tolerances) when the distribution of actual part dimensions is rectangular within the tolerance band, i.e. the part dimensions are randomly distributed between the tolerance limits. I can't prove that thesis other than to point you at the Monte Carlo method, where you can show that it works. For other distributions of errors, a common one being a gaussian distribution of errors (i.e. the parts show a bell-shaped curve of dimensions with nominal at or near the center of the tolerance), the RSS method will tend to overpredict the 1-sigma distribution of actual tolerance accumulations.

While what Drawoh says is strictly true per the dimensioning and tolerancing standards, modern statistical control methods (correctly applied) can and do produce dimensional variations of actual parts better modelled as Gaussian or quasi-Gaussian distributions. Using a biaxial tolerance (e.g. XXX +YYY -ZZZ) indicates to an SPC type that you want the median distribution of the parts at XXX, not halfway between +YYY and -ZZZ.

Similar overprediction by the RSS method occurs when considering vector sums of errors, e.g. 2-D bolt patterns, or mating of circular/cylindrical parts where the rotation/clocking of non-concentricities is not controlled.

For anything more complicated than a 1-D stackup of simple +/- toleranced parts, consider doing a Monte Carlo analysis. Consider doing it just for fun, if you like playing with math. Monte Carlo is just a fancy term for what amounts to using random numbers (most spreadsheets and math computation programs have random number routines built-in) to simulate possible distributions of errors and how they will stack up. There are methods to take random numbers and generate various distributions (Gaussian, triangular, trapezoidal) from them, look in a good math or statistics handbook. Or ask here, and I'll post at least the quasi-Gaussian method. If nothing else, it will bore Kenat to tears.

 

[KENAT]

You just reminded me why I stick with worst case most of the time.

Posting guidelines faq731-376

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(probably not aimed specifically at you)
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[btrueblood]

Sorry, Kenat, I know. FWIW, I have used the above mentioned Monte Carlo methods exactly once in 20 years to do something that made an impact on how the world works. We added about .003" to a bolt pattern tolerance zone allowance, which reduced some machining costs and eliminated a regularly recurring MRB action.

Then, about a year or two later participated in a redesign that eliminated the bolt pattern entirely.

 

[drawoh]

btrueblood,

Where are you getting your standard deviation from? Statistical methods ought to work, if you know this.

So many people out there fire the drawing up in CAD and apply the default tolerances. If I draw up a welded aluminium tube frame, and apply ±.005" tolerances all over it, what you are using for standard deviation? Even if the person preparing the drawings is compentent and professional, the drawing reflects the requirement, not the capabilities of the fabricator.

JHG

 

[btrueblood]

Drawoh,

You get it from actual measurements of sampled parts. Good shops are doing that for you these days, as part of statistical process control procedures.

The only time RSS is useful is in predicting the statistical probability of a given set of parts mating up to within some limits. Yes, you will have parts that won't, but with a big enough sample and good measurements, you can predict how many won't.

The example I gave was for a set of parts that mated on various cylindrical features, several of which had no fixed clocking. I was able to show, via statistical techniques, that a mis-position of the bolt pattern could be acceptable (to better than a 3 sigma limit) provided the parts were assembled with the rotate-able bits randomly oriented in re clocking. It worked, and we built about 750 or 1000 units with that tolerancing scheme with no rejections, which is well within what the statistics predicted.

For interest, the overal distribution of alignment errors amounted to a gamma distribution, i.e. there is zero probability of perfect alignment...

You are correct, as I said earlier, about how drawings are interpreted per ANSI standards. That limits how much any designer or preparer of drawings should rely on statistical techniques, because you can't predict the distribution of actual part dimensions (you can only assume a rectangular distribution, and we all know what happens when you ass-ume). Some day they may update that standard to account for SPC controls, but I doubt it.

 

[loughnane]

Standard practice to determine the standard deviation seems to be dividing RSS by 3. (which equates to a CPK of 1.00).

The monte carlo method is useful, but only as useful as the statistical distribution it is based on. If it is based on a normal distrubtion it will approach a true normal distribution as the number of samples approaches infiniti. If it is a rectangular distribution, it will approach that.

All Monte Carlo does is provides a little dose of reality. It is a 'simulation' and not a statistical calculation



Chris Loughnane - Product Design

http://www.pdnotebook.com

http://www.twitter.com/DesignNotebook

 

[drawoh]

loughnane,

You are assuming that the error is caused by variation from machine pass to machine pass.

Error could be caused by someone misreading a print or a machine control. A production machine might drift with time due to tool wear or due to a slipping friction contact.

Once I have inspected a production run, I have the mean and the standard deviation. I can draw the curve out and satisfy myself that it is a normal curve.

If my new design will be fabricated by the same process, I can use your data with some confidence. This allows me to try to predict how my new design will work. In the absence of inspection data, my drawing tolerances have to be treated as rectangular distribution.

JHG

 

[loughnane]

drawoh

True, my assumption assumes normal distribution (a pretty solid assumption, but still not always the case). I take no account of someone misreading a print (i tend to focus on injection molding as opposed to custom machining, which I guess I have exposed).

As for tool wear, I've seen it assumed (again with 'normally distrubted 'volume injection molded parts) that the mean actually shifts over time, sometimes as much as a 1.5sigma.

Treating your drawing tolerances as rectangular in absence of inspection data is very conservative is it not? I tend to use the normal distribution assumption even in early design work to ensure that the mechanism i am developing is even feasible. However, once we get the first shots off the tool, we use those real tolerances (normal or not) to drive the fine tuning of the mechanism.

I suppose it's all about one's appetite for risk

Chris Loughnane - Product Design

http://www.pdnotebook.com

http://www.twitter.com/DesignNotebook

 

[btrueblood]

"Standard practice to determine the standard deviation seems to be dividing RSS by 3. (which equates to a CPK of 1.00)."

I wouldn't unless I have data that shows the process has a historical Cpk of 1.0 or less. On new processes, new parts, I'd be more conservative.

"I suppose it's all about one's appetite for risk "

Exactly.

 

[btrueblood]

"If it is based on a normal distrubtion it will approach a true normal distribution as the number of samples approaches infiniti. If it is a rectangular distribution, it will approach that."

Had to re-read that, and I'm not sure I agree.

Rectangularly distributed errors in more than 1 part will produce a distribution that quite closely approximates a Gaussian or normal (i.e. bell shaped curve) distribution.

The classic example is a die (singular of dice). Roll a single standard die, and you (should) get a rectangular distribution of numbers from 1 to 6, i.e. each number occurs with the same frequency, given an arbitrarily large number of rolls.

But, roll two dice and add the numbers? You get a frequency table that very closely matches a Gaussian curve. This (adding two dice rolls) is analogous to choosing two random-length parts and stacking them end to end. So, a rectangular distribution of part dimensions can (when "added" or "stacked") give a normal distribution to the assembly dimension.

 

[loughnane]

"But, roll two dice and add the numbers? You get a frequency table that very closely matches a Gaussian curve. This (adding two dice rolls) is analogous to choosing two random-length parts and stacking them end to end. So, a rectangular distribution of part dimensions can (when "added" or "stacked") give a normal distribution to the assembly dimension. "

Well put. I was wrapped up in thinking about individual dimensions. You are right (which you im sure you know) to say that the stack of rectangular dimensions would approach a normal distribution.

Thinking out loud now... im sure there is a calculation on Wolfram for standard deviation of a rectangular distribution. I wonder if that is the standard deviation you would use to calculate the 'normal distribution of the stack of rectangularly distributed dimensions'

Its 7:17 PM here... im going home.

Chris Loughnane - Product Design

http://www.pdnotebook.com

http://www.twitter.com/DesignNotebook

 

[btrueblood]

Dunno, I don't know Wolfram or MathCad well enough to comment. But I do know that a statistics professor would give you a blank stare to that question - a "standard deviation" is really only defined for a Gaussian or normal distribution. For all other distributions, typically you talk about probabilities, i.e. 95% confidence interval or whatever. For a rectangular distribution, a 95% confidence interval would be .95 times the distribution width or part tolerances, e.g.

 

[loughnane]

http://mathworld.wolfram.com/UniformDistribution.html

I am not 100% on the math either, but was actually made aware of it by my statistics professor.

Chris Loughnane - Product Design

http://www.pdnotebook.com

http://www.twitter.com/_chrisloughnane

 

[btrueblood]

Right, notice the "sigma" term, called the variance or mu2 in their write up, though possibly equivalent in definition mathematically for both distriubtions, does not necessarily have the same properties between the two distributions. I.e. a 3*sigma variance might or might not mean the same thing in terms of probabilites of occurrence from one distribtution to the other, which has implications for things like tolerance stacks where you are effectively looking for the probabilities of additive occurences...and which is where weirder critters like gamma distributions and weibull distributions start to creep in. And the math gets really weird, and you start to look at Monte Carlo methods to get some way to get some meaninful numbers in a relatively straightforward way...

 

[btrueblood]

PS, loughane, notice how it's only me and you talking anymore, and the rest of them have long sinced greyed out and gone away? Glad you are still here and in the discussion, it's the first time in 20 years that somebody actually seemed to know what I was talking about, or cared. I feel so validated now.

 

[btrueblood]

Well, I find myself having to take that last bit back. There was one other engineer who got it, and she was a the time teaching me and a roomful of other enjuneers the basics of Taguchi methods and ANOVA. Smart gal.