How to account for bonus tolerance in traditional +/- stack-up spreadsheet using statistical methods 1

[jonathan8388]

Hello everybody,

I am looking for some help from somebody who is very familiar with statistical tolerancing for a question that I have. It is a long winded question, so please bear with me. I work in the aerospace industry in rocket propulsion as a design engineer. I am currently working on the tolerance analysis for portions of our motor design and have been using both the "Dimensioning and Tolerancing Handbook" by Drake, and "Mechanical Tolerance stackup and Analysis" by Fischer extensively for my work. I am currently doing the work in excel under a traditional +/- tolerancing technique, which has been pretty simple for the most part. There are a few stackups that I am encountering with 15+ contributors that yield extremely large variations in gaps in worst case, so I began experimenting with statistical tolerancing using the RSS method for a few select gaps. This has also been pretty simple for most dimensions, but I am having trouble figuring out the right way to factor MMC or LMC modifiers into the +/- stackup report for the statistical work.
Both the "Dimensioning and Tolerancing Handbook" and "Mechanical Tolerance stackup and Analysis" texts show how to account for the MMC and LMC modifiers in a +/- spreadsheet format, but the problem I am having is that they conflict each other, which effects the final RSS tolerance. As a general example, let's say I have a hole with the following dimensions that I need to add into a stackup spreadsheet:

Nominal Diameter: 1.000"
Diameter Size Tol: +/- 0.100"
Positional Tol: 0.05" @ MMC

The book by Fischer will split these tolerances into three different lines in the spreadsheet: one for the hole size tolerance (+/- 0.100"), one for the positional tolerance @ MMC (+/- 0.05") and one for the bonus tolerance ( +/- .200") and use these three separate tolerances to compute an RSS.

The Dimensioning and Tolerancing handbook, however, states that you need to first find the Resultant condition (in this example, 1.35"), find the Virtual condition (in this example, .85"). Then, find the midpoint of these two and convert to an equal +/- tolerance, which would be 1.10" +/-.250". This book states that this 1.10" +/-.250" is what actually needs to be used in the spreadsheet. If use this single .250" tolerance in an RSS and compare this to the way Fischers book does it (breaking it out into three separate tolerances), I get the same worst case, but I get different statistical values for the total assembly gap tolerance.

Does anybody know the right way to account for this bonus tolerance in an RSS analysis? Should I split things up in the stackup like Fischer does, or should I combine into one line like the Dimensioning and Tolerancing handbook does?


Regards,
Jonathan

 

[Belanger]

Not to throw a pole into the spokes of your bicycle, but a purist might say that RSS isn't really trustworthy with something like bonus tolerance. This is because one of the assumptions necessary for RSS is that it be applied to things where the component variables are independent (other assumptions: a capable process, with normal distribution, centered on the mean, etc.).

The whole notion of bonus tolerance is that it is tied to another variable: the size of the hole.

Having said that, it makes me think that the method in Drake's book might be better because it lumps the bonus idea into the other dimension, rather than factoring it out separately. I'll noodle it some more, but interested to hear what others might think.

John-Paul Belanger
Certified Sr. GD&T Professional
Geometric Learning Systems

 

[3DDave]

Too bad the VSA guys got bought by Seimens. They did their analysis using the Monte Carlo method, which eliminates the need to have to reason the process out; just set up the geometry equations and the expected distributions and randomize away.

Drake has criticized this approach for not giving the same answer every time, as if a factory run of parts will net the same answer as his method produces. It would be bias to say the Fisher's method is better as I haven't really seen it and I did like working with him on a large project before he really got his company going.

When I did such analysis I soon discovered that the analysis didn't matter unless the manufacturing process was characterized. For example, the odds of a hole diameter varying much in size, even if the tolerance is large, are small. Position will vary depending on setup and temperature fluctuations in the shop, and it won't be circular. Without feedback the results are pretty much a guess.

If you can convince the powers that be that this analysis is worthwhile, then go for VSA. It has two big advantages - one, it does the grunt work for you, but more important, it generates C code as an intermediate and you can inspect that code to see exactly what it's up to. In this case, what they would do** is allocate a random value to the diameter (within size tolerance) then use what remained as a limit on the position tolerance for the axis, then use what remains for the orientation of the axis. The then generate the transform for points on the surface of the hole which are then measured against other varied geometry.

The best part was being able to insert any distribution and drive other systems to generate tolerance aware results from otherwise unvarying programs. For example, one could use the tolerance model of an engine assembly to drive a combustion analysis that is based on compression ratio and determine operating efficiency variation as a result of manufacturing variation.

**It's been a while, but I think this was the order of evaluation.

 

[jonathan8388]

John,
Thank you for the input. The way Drake's book did it is where I was leaning towards. Only because his method gave a more "conservative" RSS (larger tolerance band) by grouping the tolerances into one term instead of parsing them out like Fischer does. If you find anything else in your noodling, please let me know.

Dave,
I have actually been working on an effort in my company to get some type of variation software for our complex problems. I have used 3DCS at a previous company and I was very pleased with the software, so I was starting to pitching that. I am not sure how VSA compares, but I will also look into it. We use a lot of Siemens products already (such as Team Center and NX) so maybe that is another good option in lieu of 3DCS. Unfortunately things move at a sloths pace where I work, so I am stuck doing spreadsheet analysis for the foreseeable future. We are also working on better defining our process capabilities which is taking time. So it seems we have a long way to go in order to even use the software to its full potential in the event that we get it soon enough. We used to tolerance to worst-case all of the time, but suffered the blow of so many NCRs because tolerances were too tight in order to meet the worst-case requirements. In my current time frame, I don't know what options I have other than to do some statistical spreadsheet analysis to open up tolerances, or just do a redesign to make it easier to hit worst case for all of my gaps.


-Jonathan

 

[weavedreamer]

Combines the geometric tolerance, bonus, and shift summing them into one unit to use under RSS.
[ul]
[li]A premise used in statistical stacks is that all tolerance are independent.[/li]

[li]Bonus and shift tolerances are dependent variables.[/li]

[li]Therefore, bonus and shift tolerances must be converted into independent variables in a statistical stack.[/li]
[/ul]

 

[ljones]

3DDAVE,

When you say VSA does the grunt work for you, does that mean it converts bonus and shift tolerances to independent variables?
I have not used VSA and is interested how it prefers the RSS inputs. Where I work we are expected to input bonus and shift tolerances as separate lines in our stack sheet. Also we do not use RSS tolerance values that are less than 5 dims. Comments?

 

[3DDave]

VSA simulates actual part variations, so there is no separate 'bonus,' only the size and allowable shift for that size. This is used to generate suitable geometric outputs. The direction and amount of shift is random with the amount of shift limited to a range of 0 to the allowable shift for that size. It's perfectly possible for a large hole to be located at true position; it is unlikely for a large hole to be at the limit including the 'bonus.' The result is a distribution of sizes and shifts and from that one can examine the results to make a prediction about acceptable product rates.

You can do the same in Excel; have a stack on each line and pick the values based on random numbers. Create 10,000 lines or whatever represents a typical quantity and then fit a distribution to the output. Coming up with equations that allow rotation is the ugly; generating those equations and supplying the randomization was the VSA grunt work.

 

[brfischer]

Hi There
Bryan Fischer here. A friend told me about this conversation about how to model additional tolerance (bonus tolerance) in tolerance stackups. Obviously, for worst-case, it doesn’t matter if a geometric tolerance and bonus tolerance are combined or entered separately in a tolerance stackup.

A + B + C = (A + B) + C = A + (B + C) = …

However, in a complex function like RSS, the result is different.

A^2 + B^2 + C^2 ≠ (A + B)^2 + C^2 (unless A and/or B are zero)

Method 1 A^2 + B^2 + C^2
Method 2 (A + B)^2 + C^2

There are compelling arguments and reasons to model a tolerance stackup both ways.

To argue in favor of Method 1, bonus tolerance is driven by a separate variable, the size of the as-produced hole, and as such, it should be modeled as a separate variable from the location error. It is extremely likely that the variation of the size of an as-produced hole and the variation of its location are independent variables, especially in parts with drilled holes, and as such, should be modeled separately. I’ve had strong arguments from experienced analysts in favor of this approach.

To argue in favor of Method 2, bonus tolerance is an extension/expansion of the allowable location error, and as such should be modeled as the same variable. In the end, there is only one variable, e.g. the positional tolerance zone with a variable boundary. I’ve had strong arguments from experienced analysts in favor if this approach.

We solve this problem by allowing the user to model the tolerance stackup either way depending on their view of their situation. In our Tolerance Stackup Software Toolset, which is an extension of the forms shown in my book, by default the software groups the bonus tolerance with the value on the line above it before squaring. By default, our Toolset uses Method 2. If the user doesn’t want bonus to be grouped with the geometric tolerance, they can omit the term “bonus” and the software squares each value separately (Method 1).

I hope this helps. Take care.

 

[brfischer]

I forgot to mention. Regardless of which method you choose, the reason you should show bonus tolerance on a separate line is so you and your team can see the effect of the MMC or LMC modifier. There is more information in the report. For example, seeing that an MMC modifier adds .01 variation to a tolerance stackup that has .005 interference should help the designer understand that RFS would be better in that case.