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# How to find Unrelated Acutal Mating Envelope of a FOS?

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## How to find Unrelated Acutal Mating Envelope of a FOS?

(OP)
Guys,
I am curious your opinion on how would you find unrelated actual mating envelope (UAME) of a feature of size with a method different than usage of a "best-fit" gage for the measured feature. Let's say I want to use CMM for this.

UAME and its axis or centerplane (depending on the type of a FOS) is needed for verification of position of a feature of size for instance. The concept is also needed when parallelism, perpendicularity or angularity tolerance is applied to an axis or a centerplane of FOS.

How would you approach for position control when a typical cylindrical hole in a plate, nominally perpendicular to a flat surface (primary datum feature), was inclined in reality?

### RE: How to find Unrelated Acutal Mating Envelope of a FOS?

Let us first establish that no-one can find "the infinitely definitive" UAME size of a feature. The measured value will always be an estimation attained with a finite set of points and subset of imperfect tools.

Let us also establish that assumptions regarding form and orientation used to moderate the finite set of points will have a proportionally negative effect on the estimated value as their validity deminishes.

That said: The best insrument I have seen as yet to extract these measured parameters is a dedicated cylindricity measuring tool i.e. Mahr or Taylor Hobson, that can scan spirally in a bore very precisely and do a post measurement analysis for numerous geometry parameters.

Typically: on a CMM if the operator assumes that the bore is straight, round, and common size... but he/she is not so sure about the perpendicularity of the deep bore... he/she will make the size and location measurement (mid depth in the bore) to moderate the difference he/she may find at the ends.

Some might check both ends of a bore to verify the location deep and shallow, some may include the middle, it all depends how deep the bore is... how much time it takes to inspect, and what the assumptions are.

Paul

### RE: How to find Unrelated Acutal Mating Envelope of a FOS?

Like any other measurement, it comes down to 2 things:
A physical gage, such as an expanding mandrel (for a hole), or
A numerically derived measurement, such as a CMM (it sounds like that's the option you were interested in, so I would agree with Paul here)

UAME is supposed to be a very frequent measurement, since it's an integral part or Rule #1! So I would think it isn't very esoteric.  (Pmarc, you mentioned that it would be needed to check position or perpedicularity, but I would disagree and say that those measurements are the related AME. Straightness and flatness on a FOS would be looking for the UAME.)

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

### RE: How to find Unrelated Acutal Mating Envelope of a FOS?

(OP)
Paul, J-P,
Thanks for your responses and of course I wouldn't be myself if I didn't have any comments:

1. Paul, I agree with what you said about the influence of finite number of probing points on the accuracy of measurements. Actually I agree with other things too. The problem I see is that in my opinion the routine you called "typical" is based on operator's assumptions and relies on simplifications which sometimes might not be correct and will not reflect the actual geometry of the toleranced FOS well enough. I understand that reality very often (maybe even always) forces an operator to find a compromise between the accuracy of measurements and a time needed for inspection, but by starting this thread I was rather thinking if someone could give one clear, precise and mathematically correct method of finding UAME of FOS.

2. J-P, I would say that term 'UAME' is integral for Y14.5-2009 standard and logically it should be a very frequent measurement but I am afraid in reality it means nothing to inspectors. What is even worse, Y14.5.1M-1994 is not giving any support on how to deal with UAME (I hope updated version will be more specific on this). Theoretically it is a very useful concept, but as long as it is not sanctioned anywhere how to correctly establish its size and orientation, it is a pure theory. I would like to see an inspection report showing that the position of an axis of UAME of cylindrical hole was verified and not the position of calculated center points of top and bottom of the hole. As you probably remember there was a discussion in the past about the inspection of Rule#1 - whether it is verified on the shop floor or not. The reality shows that even if it is checked it happens very, very rarely. And I am tempted to say the same about UAME.

3. J-P, position and perpendicularity contols (applied to FOS) aim to check if axis or centerplane of FOS is within a tolerance zone, right? According to the definitions given in 1.3.28 and 1.3.29 of Y14.5-2009, axis and centerplane are 'elements' established from feature's unrelated actual mating envelope. For position example see fig. 7-8 which clearly shows that the axis of UAME has to be within specified tolerance zone. The tolerance zone is located and oriented relative to DRF, but the verification is done on axis derived from UAME. Regarding perpendicularity control: although chapter 6, "Tolerances of Orientation", does not show in any figure feature's UAME, it uses terms 'feature axis' and 'feature center plane'. Again according to 1.3.28 and 1.3.29 it means that orientation of axis or centeplance of UAME has to be verified (unless otherwise specified). Maybe I misinterpreted your response, but this is what I meant in my original post.

### RE: How to find Unrelated Acutal Mating Envelope of a FOS?

Yes, for ASME Rule #1 should be integral to every size inspection (with the appropriate exceptions, such as nonrigid parts, etc.).  Whether it's actually done or not is a different discussion. Obviously, we somehow make parts that work, and Rule #1 is there for a reason!

I didn't have a copy of Y14.5 handy when I wrote my first response, but I wasn't really doubting you. The standard does indeed use that term UAME for some of those explanations.

But I think it boils down to this:  If you are using the "axis" interpretation to explain a position tolerance (or perpendicularity) then the UAME is the right language to use.  But if you are using the boundary idea to explain the concept, then the Related AME is all that matters! So I was just taking a shortcut to say that there's no need to really find the UAME for position.  (But there sure is a need for Rule #1.)

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

### RE: How to find Unrelated Acutal Mating Envelope of a FOS?

(OP)
J-P,
I agree that related AME is the key concept when using 'boundary' (surface) interpretation of the callout and there is no need for an axis of UAME in such cases.

The problem is that 'boundary' interpretation can work only if (M) or (L) modifier has been specified after a tolerance value within FCF. For geometrical tolerances applied at RFS basis "axis/centerplane" interpretation is the only concept we have.

### RE: How to find Unrelated Acutal Mating Envelope of a FOS?

pmarc,

I'm not sure I see the problem.  In 2009, the definition of AME  is "a perfect feature counterpart of smallest size that can be contracted about an external feature or largest size that can be expanded within an internal feature so that it coincides with the surface at the highest points".  It then goes on to say that the UAME is not constrained to any datums.

For a nominally cylindrical hole, the UAME would be the maximum inscribed cylinder.  If the hole is tilted, then the UAME will also be tilted.

Extracting the UAME from a given cylindrical surface may not always be easy, but the goal is clear.  If the inspector tries to find the UAME by just measuring points at two nominally oriented cross sections at the top and bottom of the hole, then there will probably be measurement error.

Other complications could come in if we look deep enough.  If the actual cylindrical surface was tapered, so that a best fit gage pin would rock inside the hole, then there will be numerous "candidate" UAME's.  Also, the extent of the UAME axis for a position or orientation measurement is not always clearly defined.  The axis of the UAME in Figure 1-1 is clearly defined, but the feature is curved and it is not clear where to "cut off" the axis for comparison to a position or orientation tolerance zone.

Evan Janeshewski

Axymetrix Quality Engineering Inc.
www.axymetrix.ca

### RE: How to find Unrelated Acutal Mating Envelope of a FOS?

(OP)
Evan,
That is why I said Y14.5 and Y14.5.1 do not support inspectors in their search for UAME and its axis - assuming one is willing to search for it.

### RE: How to find Unrelated Acutal Mating Envelope of a FOS?

Pmarc, I think Related AME is still applicable even for the RFS condition (even though it's not mentioned on p. 108-109 of the standard).

The difference is that the worst-case boundary for the MMC examples that you mention are a constant boundary (VC).  But there is still a boundary in the RFS condition; it's not a constant, however.  But the Related AME idea still works, doesn't it?

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

### RE: How to find Unrelated Acutal Mating Envelope of a FOS?

(OP)
J-P,
Just a short question first - how would you define the size of the boundary in RFS condition? Let's say we are considering a flat plate with a hole of diameter 10.0-10.2 with positional callout |pos|ø 0.4|A|B|C|. A, B and C are typical flat surfaces of the part.

### RE: How to find Unrelated Acutal Mating Envelope of a FOS?

First, the size of the hole must be checked.  This involves two steps: a two-point check to verify the actual local size at various depths, and then a boundary check for Rule #1 (this is, of course, the infamous UAME).

Then to check position, we have some sort of expanding cylindrical device that is perpendicular to datum A and fixed from B and C. As it expands, it will stop when it hits the high point of the hole's inner surface.  This is by definition the Related AME.  (This is the main answer to the question in your last post.)

Now I think we could simply compare this RAME to the UAME. The difference in those two numbers must be 0.4 or less.

So the UAME is still part of the picture, but since it was already determined in the size check, it doesn't need to be directly derived for the position check ... that is where the RAME comes in.

I'm thinking this out as I type, so feel free to poke holes in it!

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

### RE: How to find Unrelated Acutal Mating Envelope of a FOS?

(OP)
J-P, the reason I asked you how to define (calculate) size of a boundary of the RFS condition was, as you already noticed, to point out that even if we wanted to use RAME concept we would still need to involve UAME into play. You just simply assumed that UAME will be known by checking Rule #1 requirement. But that was actually the clue of my original question: how to find this UAME with CMM for instance.

If the actual hole's surface is more or less cylindrical, regardless whether it is tilted or not, probing in sufficient number of points for obtaining a cloud of points and extracting the UAME from it should be enough. But what if the surface is tapered, as Evan mentioned? In such case there are many potential UAME's that will fit into observed shape. Which is correct? Where is a document that specifies correct methodology?

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