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# In worst case, the flatness is...5

## In worst case, the flatness is...

D. Definitely.

### RE: In worst case, the flatness is...

0.25 is probably what the quiz question is seeking as the answer. This is from 0.2 traced in one direction (perhaps downward) and a possible 0.05 in the other direction (perhaps upward).
But that notion of straightness in a certain direction is somewhat flawed, because the direction to trace is based on stabilizing the part in a certain orientation (read: datum). Tagging the FCF to a certain view isn't enough.

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

### RE: In worst case, the flatness is...

(OP)
The quiz originated when I'm reading a book says: a feature can have different straightness values specified in different views. Then I’m thinking what the flatness will be in this case, so I’m seeking the answer, thanks for all of your valuable replies and comments.

Dave: Would you pls kindly adv. flatness value if you say D Definitely.
Capnhook: Would you pls kindly adv. how you get the value 42.

Thanks

Season

### RE: In worst case, the flatness is...

CH has the correct explanation - I just preferred to hold off on what looked like an academic question.

I've never gotten the interest in trying to interpret one control in terms of other controls, particularly ones that don't perform the same function, such as in this case. Much like speculating as to which makes for a better chisel, a hammer or a vise? I guess as a quiz it is meant to determine if the user knows the difference.

You need to read HHGTTG** to understand how 42 can be the correct answer to almost any question, subject to having a good understanding of what the question means. You'll also need a towel and a package of peanuts.

**Google can find the reference for this.

### RE: In worst case, the flatness is...

#### Quote:

Here is the same model with straightness of 0 in any cross-section.
CH, I'm not sure that I see that second sketch as having perfect straightness in any cross-section. Do you mean in any cross-section of a given view? Or perfect straightness in all directions?

Because having perfect straightness in all directions would seem to be equivalent to perfect flatness.

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

### RE: In worst case, the flatness is...

J-P,

Take a deck of cards and give it a twist. Each card edge remains straight and, twisted correctly, each section perpendicular is also straight.

### RE: In worst case, the flatness is...

Dave -- of course, but that deck of card is not straight in all directions. Only in the directions that the cards lay.
Thus my point.

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

### RE: In worst case, the flatness is...

@ Belanger:

Straightness control itself applies separately in given view:

S specified in front view applies to cross-section parallel to front plane.

S specified in side view applies to cross-section parallel to side plane.

There is no such thing like Straightness "all-over"

"For every expert there is an equal and opposite expert"
Arthur C. Clarke Profiles of the future

### RE: In worst case, the flatness is...

Fine -- I'll buy that. But I'm curious if anyone caught my point above:
You say "S specified in front view" (or side view). How do we align those sampled lines? Parallel to the face of the part that we see? Or the back face? This is perhaps an inherent problem with the entire idea.

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

### RE: In worst case, the flatness is...

The lack of stringent rules concerning the orientation of a part with respect to view-dependent tolerances within Y14.5 means that straightness is something of a fiction for anything but round items where orientation of the part is not material to creating a boundary simulator. At least the trig works to minimize the effects of minor orientation changes.

What's left to the imagination is that, for a given setup, there is a good chance the line segment of interest will not be the complete width or length of the part. It isn't clear if the entire deviation is applicable to the fractional segment or if it is reduced to some proportion of the overall width/length.

This shape has a lot of perfect straightness: http://mathworld.wolfram.com/One-SheetedHyperboloi... Straightness is critical to the creation of the shape, but it is unclear it's a target for a straightness control.

### RE: In worst case, the flatness is...

Vishal2015 (Mechanical):

What does it mean by 'Straightness is maintained in X and Y Direction in zero'?

### RE: In worst case, the flatness is...

It's a typo and badly worded. Deviation of straightness in X and Y directions is zero. IOW looking at constant X component the surface parallel to the YZ plane is straight. Likewise for the constant Y component parallel to the XZ plane.

### RE: In worst case, the flatness is...

That's right 3DDave.

Deviation of straightness in X direction is zero as well as in Y direction is also zero

### RE: In worst case, the flatness is...

The correct answer is that there is no flatness control contained within straightness, so answer d (or none of the above, or whatever). See Vishal2015's graphic to see why.

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

### RE: In worst case, the flatness is...

The correct answer is 0.6 (assuming that Rule #1 governs the drawing).

Vishal's graphic is great because it clearly shows that straigthness tolerance specified in two orthogonal directions does not control flatness of a surface, but the graphic does not and I believe never meant to prove the correct answer was different than 0.6.

Side note regarding 3DDave's point about "lack of stringent rules concerning the orientation of a part with respect to view-dependent tolerances within Y14.5". ISO solved that dillemma quite reasonably by introducing Intersection Plane concept in ISO 1101:2012. The attached figures show 3D annotation case, but the concept can be applied to traditional 2D drawings as well.

http://files.engineering.com/getfile.aspx?folder=9...

### RE: In worst case, the flatness is...

Naww - it's really constrained by the limits of size. If the bottom surface is perfectly flat then the entire size tolerance can go into variation in the top surface, the worst of which will see 0.6 units of out-of-plane behavior. Depending on the fitting algorithm it might come out as a bit more if the software picks a plane that is not parallel to the bottom surface as the reference plane.

The trick to the question is noting that the individual straightness tolerances do not limit the flatness; their inclusion is misleading with respect to flatness control.

### RE: In worst case, the flatness is...

Dave,
The bottom surface does not have to be perfectly flat to allow the top surface to be 0.6 units out-of-plane. It may even have 0.6 of flatness error.

### RE: In worst case, the flatness is...

pmarc - you are correct.

### RE: In worst case, the flatness is...

Why 30mm dimension is subject to rule 1? Does not have opposing and parallel elements for its entire width, right? Might be governed by rule 1 in some portions/ area, but does it make it regular feature of size or not?
So, flatness of the upper surface is controled by rule 1 only to a certain degree. Am I right or I am entirelly walking in the weeds?

This question qualifies to be in the GDTP certification exam, because from 3 qualified professionals you get 3 different answers😉😂

### RE: In worst case, the flatness is...

Not totally up to speed on the 2009 std. Did something change relative to “flatness”?

You can now measure flatness (straightness of line elements) from an opposing surface?

Also straightness of a line element is a refinement of the limits of size. (not applied to an axis or median plane in this example).

A way to measure flatness (straightness) is to lay the surface in consideration on a surface table with a dial indicator that penetrates the surface table. NOT from laying the opposing surface on the surface table. Flatness (straightness of line elements) is relative to the surface itself, NOT another surface. This eliminates the “size tolerance.” (In this case)

IMO the flatness is limited to the max 0.2 straightness callout. The 0.05 straightness will fall within that not added to it.
1. The surface is inspected to be within limits of size
2. The surface is inspected for straight line elements across the length to a 2D tolerance zone of parallel line
elements 0.20 apart.
3. The surface is rotated 90 degrees and is inspected to 2D tolerance zone of parallel line elements 0.50 apart.
(how does the 0.05 zone not fall within the 0.20 zone geometrically ?)

How is any surface element greater than a 0.2 tolerance?

I would answer "B" to the question.

### RE: In worst case, the flatness is...

SeasonLee,

Please don’t let us killing each other

### RE: In worst case, the flatness is...

(OP)
greenimi

I'm seeking for the correct answer, pls see what I posted at 17 Jul 15 22:34

#### Quote (SeasonLee)

The quiz originated when I'm reading a book says: a feature can have different straightness values specified in different views. Then I’m thinking what the flatness will be in this case, so I’m seeking the answer, thanks for all of your valuable replies and comments.

Season

### RE: In worst case, the flatness is...

greenimi,

From the 2009 standard...

5.3
Form tolerances critical to function and interchangeability
are specified where the tolerances of size do not
provide sufficient control
.
A tolerance of form may be
specified where no tolerance of size is given (e.g., in the
control of flatness after assembly of the parts). A form
tolerance specifies a zone within which the considered
feature, its line elements, its derived median line, or its
derived median plane must be contained.

Straightness could be used for example on a corrugated surface.
If it where along the corrugations, then I could see the profile of the
corrugation limited by its size tolerance; the longitudinal elements would
be controlled by straightness. (90deg to the profile of the corrugation -
"one" straightness control).
If the peaks of the corrugation (tangencies) were laid on a surface plate,
then the straightness is controlling the "flatness" to a degree.

That is not the example from the OP

In this example we have a planar surface with two straightness controls.
Straightness must be less than the size limits or what use is it for a planar surface.
The lesser value (0.05) would need to lie within the (0.2) tolerance.
At any line element within the 0.2 tolerance there is a crossing tolerance zone
90 degrees which is 0.05. I can not see how any element in the 0.05 zone could be
"added" to the 0.2 tolerance. Therefore it must lie within the 0.2 straightness geometrically.
( cant see it any other way from where I am sitting)

To me the straightness control for a planar surface would be limiting the curvature, waviness, or taper of the planar surface,
in a direction. Cant think of why I would use 2 staightness controls in reality. Just would use a flatness control.

Seems like a thought provoking question to consider multiple straightness controls as effecting flatness within
the limits of size.

my 2 cents

### RE: In worst case, the flatness is...

Dtmbiz,

I agree with what you said, but we have to understand what the standard requires and does not require. After we understand the theory, we can apply such of said theory in some sort of practical way.

I can see that the straightness of each element is controlled to 0.2 in one direction and in 0.05 in the other. However, I don’t see why the 30mm size dimension is a regular feature of size (at least not the entire surface) hence why is subject to rule#1. Each longitudinal element of the surface must lie between two parallel lines 0.05 apart in one direction and 0.2 apart in the other direction. That is my understanding of the theory.

Therefore, my opinion is that each elements could be misaligned to infinity since it is not subject to rule#1. And therefore, the relative "locations" of the "filaments" to each other are not limited by that envelope (Rule #1) requirement.

What am I missing?

As I stated before: if I am wrong won’t be the first time.

### RE: In worst case, the flatness is...

greenimi,

What may have been throwing me off track in my last post was that “the question” asks about a “flatness” control while the "FCS are straightness controls". Mixing 2D and 3D tolerance zones.

Limits of size and orientation controls, etc do control flatness to a degree, however actual flatness is not measured from opposing surfaces. The question is more or less a “gotcha” question IMO. The question is asking to derive information from 2D tolerance zones to determine a 3D tolerance zone value. Flatness is not measured from an opposing surface, where straightness can be. What is the question actually “trying to get at”?

What we do know is that both straightness controls are each less than the size limit tolerance and they should be.

We do know that straightness controls are used to refine form more than the size limit.

Knowing those facts, I can not believe that the “flatness question” answer can be equal to the size tolerance of 0.6.

If a grid of parallel line element zones at 0.2mm apart are laid length ways and are separated by ‘some distance’ (in theory there are an infinite number of line elements) from the front face to the back face; and the same is done at 90 degrees with the 0.05mm tolerance; and there is a simultaneous requirement in the controls that I see; now we have "a 3D grid" (topography map) that no element of the surface can violate and still be an acceptable feature.

That grid has a max tolerance of 0.2mm. How than can the flatness possibly be the size limit tolerance of 0.6mm??
I am actually leaning more toward 0.05 max flatness if as the ASME Y14.5 definition the "flatness" is measured relative to the surface itself and not the opposing surface as in the picture of the example question.

The distance from a minimum point of one "line element" to a max point of another line element spaced longitudinally could be 0.6 from one “line element” to another; the size limit. That is for just 1 of the 2 straightness callouts. However you have 2 callouts that the “line elements” must meet simultaneously.

Now we have a “question” regarding “flatness” a 3D tolerance zone relating to straightness controls witch are 2D tolerance zones, AND they are measured differently according to ASME Y14.5.

The only way that I can see to even try to equate the two is to look at the 3D tolerance of the accumulative straightness grid.

Rule #1 only applies at MMC. The straightness control applies relative to high and low points within the limits of size.

### RE: In worst case, the flatness is...

dtmbiz,

Quote:"attempting to show my point regarding simultaneous requirement with diagram"

I don't know how the simultaneous requirements comes to play in this conversation. What the form error straightness versus flatness has to do with the simultaneous requirement?

Quote: "The distance from a minimum point of one "line element" to a max point of another line element spaced longitudinally could be 0.6 from one “line element” to another; the size limit"

I agree here, but only if rule#1 is in effect, but does it? That would be my main question!

Is the 30mm dimension subject to rule#1?

If yes, why yes?
If no, why no?
If yes and no, why yes and no?

### RE: In worst case, the flatness is...

greenimi,

Quote: "The distance from a minimum point of one "line element" to a max point of another line element spaced longitudinally could be 0.6 from one “line element” to another; the size limit"

true if only 1 control : straightness 0.2
NOT true with 2 controls : straightness 0.2 + straightness 0.05

The longitudinal line elements must also be included as points in a given
plane with the width line element 0.05 straightness.

Consider for example:
A logitudinal element close to the farside of the surface has a high point at the high limit and then it runs within a 0.2 tolerance zone oriented parallel from the surface dimensioned from.

Another logitudinal element close to the nearside of the surface has a low point at the low limit and then it runs within a 0.2 tolerance zone oriented parallel from the surface dimensioned from.

The first line element can only be lower at any point 0.2 from its high point
The second line element can only rise higher at any point 0.2 from it low point.

That would mean that at the closest points possible with in their respective 0.2 straightness tolerance zones, they would be 0.2 apart. (limit tol 0.6 minus 2X 0.2 tol zones).

For this example those two points (high point of first line element & low point of second line element) are in the same plane across the width.

Now measure the part in the same setup at 90 degrees (across the width) to the 0.05 tolerance zone, oriented parallel to the bottom surface and please, explain to me how those two line elements are contained in the same 0.05 tolerance zone.
They are at best 0.2 apart in this example.

Or else show me "geometricaly with dimensions" how this is possible as others are claiming ?

### RE: In worst case, the flatness is...

dtmbiz -

Take a pack of cards and shift the deck a bit. The straightness along the long sides of the cards remains -0- no matter how they are shifted. The straightness across the depth of the deck can be -0- even if the pile of cards is shifted very far to one side. The size tolerance controls the minimum size of the box the shifted pack might go back into without realigning the cards.

CH posted a picture http://files.engineering.com/getfile.aspx?folder=7...

The main flaw in your diagram is that straightness zones are not restricted to being parallel to any datum, so the sloped line should have a zone essentially aligned to the slope. http://files.engineering.com/getfile.aspx?folder=2...

tl;dr straightness has no parallelism requirement.

3DDave,

### RE: In worst case, the flatness is...

I've already agreed that CH is correct - near the start of this thread.

### RE: In worst case, the flatness is...

0.6 if the dimension is subject to rule 1
But it is subject to rule 1?

If not what would be the new answer?

### RE: In worst case, the flatness is...

(OP)
Here is the reply from one expert of Tec-Ease:

"The question on flatness with respect to the feature of size 30+/-0.3 indicated on the quiz.

According to Rule #1, this part must fit within an envelope of 30.3 and any two point measurement may not be less than 29.7. If the part passes these size checks, the top and bottom surfaces as well as the derived median plane must be flat within 0.6. Therefore, the stated straightness tolerances would be refinements per the standard."

"Per the standard as I have stated in my response the flatness would be 0.6.
If your question is with respect to the straightness tolerances. Then as I have also stated in my response the flatness must be fall within each of the straightness tolerances for the indicated surfaces, and the size of the feature must fall within the size tolerance. I hope this helps."

Season

### RE: In worst case, the flatness is...

Okay I understand.
I agree that for all practical purpose that flatness would be 0.6. Let’s get that out of the way.
Now from a theoretical point of view:

It is weird to disagree with such as authority (Tec-Ease experts), but I would say that the rule#1 is limited only to *a* section of the surface. What I mean?

The rule#1 is restricted/ applicable to regular feature of size, right?

Is the 30mm dimension regular feature of size, per Y14.5?

I would argue NO.

Because does not have a set of two opposed parallel surfaces. It has but not for its entire length. So it is regular for only a portion of its entire surface. So rule#1 would be applicable only for a limited surface. (the portion that has OPPOSING and PARALLEL surfaces)

So if the OP would ask what would the max flatness for the bottom surface I would agree that is 0.6. But for the top surface, since again, it is not subject to rule#1 (again because it is not regular feature of size) I would say it is not limited to 0.6.
Anyone see my point?

### RE: In worst case, the flatness is...

3DDave,

Yup, blew that theory up (:
The error of my thinking was that the tolerance zones were oriented
parallel to the surface measured from. That was alot a grief for me
over simple orientation of the tolerance zones. I hope you just mentioned
that and it wasnt further up in thread. oiveh!
No wonder I have never used straightness of a line controls on a planar surface.
Cant think of why I would.
I really do like profile of surf and line much better.

greenimi,

The ole' ; is it a feature of size or not a feature of size?

Similarly this comes of with partial cylindrical features (not closed)
that do not have a full diameter.

A 100 mm cube has all edges with varying and mixed blends and chamfers
with a wide range of sizes (just to setup that no opposing surface is
exactly to the same extent).

Are there any features of size contained in the cube?

Maybe a new thread on features of size? and then again, maybe not (:

### RE: In worst case, the flatness is...

#### Quote:

Maybe a new thread on features of size? and then again, maybe not (:
Yes, that would be nice to see. I can't believe this question has played out as long as it has. (My 2 cents)

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

### RE: In worst case, the flatness is...

Wouldn't be easier to answer my concerns/ issue here, in this thread, because there is related with the flatness.
If the rule#1 is not active or in effect, then the flatness wouldn't be controlled to 0.6, right? would be a different answer.

So, it is or is not ?
No hard feelings, if I am wrong I am fine with it.

### RE: In worst case, the flatness is...

From ASME Y14.5-2009:

1.3.32 Feature of size
feature of size: encompasses two types: regular and irregular. See paras. 1.3.32.1 and 1.3.32.2.

1.3.32.2 Irregular Feature of Size. irregular feature of size: the two types of irregular features of size are as follows:
(a) a directly toleranced feature or collection of features that may contain or be contained by actual mating envelope that is a sphere, cylinder, or pair of parallel planes
...

So, everything that fits between two parallel planes may be used as a feature of size. Have I answered your concern enough?

"For every expert there is an equal and opposite expert"
Arthur C. Clarke Profiles of the future

### RE: In worst case, the flatness is...

So, if it is an irregular feature of size--as you stated above--, it is not subject to rule#1 !!

If it is not subject to rule#1 then the max flatness will not be controlled to 0.6 max, right?

Same standard as above (ASME- Y14.5-2009)

2.7 LIMITS OF SIZE
Unless otherwise specified, the limits of size of a feature
prescribe the extent within which variations of geometric
form, as well as size, are allowed. This control
applies solely to individual regular features of size as.......

2.7.1 Variations of Form (Rule #1: Envelope Principle)

The form of an individual regular feature of size is
controlled by its limits of size to the extent prescribed in
the following paragraphs and illustrated in Fig. 2-6.

### RE: In worst case, the flatness is...

What's a big deal, your part still has "two opposed parallel elements", so it falls under "regular" as well.

I was just trying to show how far today's definition of FOS was stretched.

"For every expert there is an equal and opposite expert"
Arthur C. Clarke Profiles of the future

### RE: In worst case, the flatness is...

I would say has two opposed parallel elements but only for a portion of the surfaces we are talking about (the flatness in question is for the entire surface), so the rule# 1 is only for a portion / area of the surface in question and not for its entire length/ width.

Do you see my point?

### RE: In worst case, the flatness is...

No, I don't.

If envelope principle applies, envelope encompasses the entire feature, not the part of it

"For every expert there is an equal and opposite expert"
Arthur C. Clarke Profiles of the future

### RE: In worst case, the flatness is...

Quote: "If envelope principle applies, envelope encompasses the entire feature, not the part of it "

My question: Where does it say that?

Probably you will answer:" where does it say that does not encompasses the entire feature?"

And my answer would be in "two opposed parallel elements"

Not the entire feature has OPPOSED and parallel elements.

### RE: In worst case, the flatness is...

CH -- I think greenimi is asking this; see my graphic: Would you say that the flatness of the entire bottom surface is limited to 1 mm (based on the height tol) because the "envelope" goes across top and bottom?

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

### RE: In worst case, the flatness is...

Let’s say/assume that the step in the J-P Belanger example is dimensioned to 7 ± 0.4 mm.

The question is what would be the maximum flatness allowed for the bottom surface?
1mm? 0.8mm? other combination?

### RE: In worst case, the flatness is...

Belanger and greenimi,

Allow me to counter your questions with very simple yes-or-no question:

By your own logic, does Rule 1 apply to the part on the picture?

"For every expert there is an equal and opposite expert"
Arthur C. Clarke Profiles of the future

Yes.

### RE: In worst case, the flatness is...

CH: Nice try that is virtually same question I asked (you just changed the picture, essentially), so I'll be interested in your answer.

I will offer this: Our current discussion seems to revolve around a very specific detail within Rule #1: Paragraph 2.7.1 clearly states that it applies to a regular FOS (and thus not to an irregular FOS).

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

### RE: In worst case, the flatness is...

Nice try J-P,

So, yes or no?

"For every expert there is an equal and opposite expert"
Arthur C. Clarke Profiles of the future

### RE: In worst case, the flatness is...

See my post from 15:51 today. Wouldn't you say that my Q came first? So I'll await your answer on my graphic.

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

### RE: In worst case, the flatness is...

Well, I'll rise above the fray to tip my hand. I think the ASME standard really needs to clarify the definition of a regular FOS to say "directly opposed elements" rather than "opposed elements."
Anyhow, a purist would say that on my picture the bottom surface's flatness is 1 mm -- only for that small area that stays directly below the top ledge. (The remainder of the surface would be held flat within the tolerance on the height of the longer shelf, which isn't currently shown over on the right side.)
Similarly, it could be said that on your picture, CH, the bottom surface's flatness is held to within the size tolerance of the main part, except for the imaginary circle that sits under the hole's location, since that area isn't a regular FOS derived from the main part's size.
Having said that, I don't know anyone who would really cling to such a nitpicky view. We'd all probably agree with greenimi and say "yes" to your question. But we've exposed a need for clarification in Y14.5.

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

### RE: In worst case, the flatness is...

J-P Belanger,
Amen. Thank you for reinforcing my point.
Also I would say that for the first picture CH posted - the one with a hole- for all practical purposes my answer is still yes. But for the second picture CH posted for the same practical purposes I would vote for No.
I agree that the standard would be better if the proposed definition is clarified with that addition or similar one.
Where we draw the line between first CH picture and the second one - again in the real world - I don't know.
Maybe we also have to think how the features ACT in assembly not only if they have direct opposing elements or not. Just a thought.

### RE: In worst case, the flatness is...

My initial answer is looking better all the time.

### RE: In worst case, the flatness is...

#### Quote (greenimi)

Where we draw the line between first CH picture and the second one - again in the real world - I don't know.

Could you drive the line between part in OP, and the part with the simple (small) chamfer? Which size chamfer has to be to start worrying?

Standard does not provide exact numbers, ratios, percentages necessary for feature to be considered. Nevertheless, occasionally it provides a clue.

For example in Para. 4.8 abot datum features it says: ..."However, a datum feature should be accessible on the part and of sufficient size to permit its use"

They are steering away from using word "fixture" but they are clearly stating that feature must be big enough to grab on it.

In this line of thought, I believe 30+/-0.3 dimension is a regular feature of size because it is "sufficient".

And little bit of historical perspective.

in 1982 FOS was "set of two plane parallel surfaces"

in 1994 it was "set of two opposed elements or opposed parallel surfaces"

and in 2009 "set of two opposed parallel elements or opposed parallel surfaces"

Nowhere standard says that said "elements" must be exact copies of each other, so I safely assume they may be "sufficient"

You can devise "go-no go" gauge to check size 30 and it will work. When assembled with mating parts it will act as feature of size (imagine it being a spacer of certain size), etc., etc.

The truth is, you cannot always hide behind the standard and avoid making decisions all together.

It is your responsibility to draw the line. If you believe the drawing may be misinterpreted, it is your job to add control (flatness?) to clarify.

In this sense, OP has purely academic interest.

Still, if I remember correctly, when answering "multiple questions" you are supposed to pick the answer as close to what you believe is correct as possible.

Given that part in question is very close to be regular feature of size, I believe the answer will be very close to 0.6, so I chose answer "C"

"For every expert there is an equal and opposite expert"
Arthur C. Clarke Profiles of the future

### RE: In worst case, the flatness is...

CH,

If you read my post from September 11, 2015 at 11:39 see what I said:
Copy-paste:
"Okay I understand.
I agree that for all practical purpose that flatness would be 0.6. Let’s get that out of the way.
Now from a theoretical point of view................""

And from here the discussion starts on what standard requires and what standard does not require.......

Quote:"In this sense, OP has purely academic interest."
I agree. what's is why I have driven the discussion from the theoretical point of view. Therefore, from the theoretical point of view ....... the correct answer is.................. fill the blanks

### RE: In worst case, the flatness is...

From theoretical point of view straightness does not control flatness (also something that I said long ago)

"For every expert there is an equal and opposite expert"
Arthur C. Clarke Profiles of the future

### RE: In worst case, the flatness is...

Quote:"From theoretical point of view straightness does not control flatness (also something that I said long ago) "

Nobody said it does.

The OP asked a question based on existing skecth / print requirements. The OP's question was what is the worst case flatness of a certain surface. AND that certain surface happened to be controlled by 2 straightness callouts. Nothing to do --directly-- with the straightness requirements.

### RE: In worst case, the flatness is...

The OP drawing contained straightness requirements and directly toleranced dimension.

We have agreed that straightness does not control flatness.

We have agreed that for practical purpose we can assume the flatness will be controlled by the amount of dimensional tolerance, that is 0.6

What it it, that we did not agree about?

"For every expert there is an equal and opposite expert"
Arthur C. Clarke Profiles of the future

### RE: In worst case, the flatness is...

We agreed that from 10000 miles high, the answer is 0.6.

Someone who is really detailed oriented might say:
Wait, not so fast!

Now , when we really get into the details ( and an engineer should) of this particular part or question, part with the configuration as shown, we found that we disagree where rule#1 is applicable (what area/ portion of this surface, what is covered and what is not covered).

As I stated before, we have to understand the theory, what the standard requires and does not require, before we have some hope to apply such of said theory in any sort of practical way.

### RE: In worst case, the flatness is...

greenimi

For the sake of discussion, let’s say the surface is not an FOS.

That surface must lie within the size limits.

What would you expect the "Flatness" to be ?

PS
ASME is applied to achieve requirements for real parts.

What does theoretical have to do with your argument?

Curious...

### RE: In worst case, the flatness is...

If the feature is not FOS you SHOULD define it with profile. Period.

Direct toleranced dimensions (aka ±) work very well (robust product definition, unambiguous requirements, only one legal interpretation of the functional requirements, whatever you want to say) for FOS and not much else.

### RE: In worst case, the flatness is...

There is no theory, because GD&T is not science. It's a rule-book written by people barely understanding math.

Re-read the statement from 1.3.32.1: "set of two opposed parallel elements OR opposed parallel surfaces"

Can you visualize parallel elements that are NOT parallel surfaces?

"For every expert there is an equal and opposite expert"
Arthur C. Clarke Profiles of the future

### RE: In worst case, the flatness is...

Hi All,

Interesting debate.

One problem I always had with the description of size in Y14.5 is the emphasis on the "size also controls form" idea. The first sentence in the Limits of Size section states "Unless otherwise specified, the limits of size of a feature prescribe the extent within which variations of geometric form, as well as size, are allowed". This would naturally lead one to believe that size controls form. But the "size controls form" idea is not a rule, and does not bring in specific form controls. For the width example in the OP, the size tolerance does not impose a flatness tolerance of 0.6 on each surface. The form control from a size tolerance is indirect, and is a consequence of two specific geometric requirements:

1. The feature must conform to the Rule #1 boundary (a boundary of perfect form and MMC size)
2. The feature's actual local sizes (opposed point distances) must all be within the size limits.

When these two requirements are applied to regular features of size whose points are all opposed, then the "indirect form control" concept works. If we look at the possible as-produced surfaces that meet both requirements, we see that the form error of the surface cannot be larger than the size tolerance.

But if the requirements are applied to features whose points are not all opposed, then things change. In other words, if the feature has points that do not have a corresponding opposed point. This may be by design, as in the parts with partially opposed widths that have been discussed (or cylinders with a blind hole on one side). This may also be a symptom of the as-produced part, where a cylinder with a nominally perpendicular end face is produced with a tilted end face. In either case, we get some non-opposed points. What do we do with those?

I don't think that the problem is deciding whether or not Rule #1 applies. The problem is with the definition of actual local size. In Y14.5-2009, actual local size is defined as "the measured value of any individual distance at any cross section of a feature of size". There are several problems with this definition (this discussion could fill another thread), but the main one for this thread is the idea of a "distance". This can't deal with non-opposed points. In the places where the points are not opposed, we can't define the actual local size. What is a distance when there is only one point? So the unopposed sections of the surface can pretty much do anything within the Rule #1 boundary, and we don't get the indirect control of form. To appreciate what type of control the actual local sizes apply, imagine measuring the size of the feature using a micrometer with pointed anvils. All you can measure are sets of opposed points. If the surface has areas that are not opposed, you can't measure those areas. It's as simple as that.

So what do we do with those areas that are not opposed? Strictly speaking, the form in those areas is not controlled. In most cases, this does not cause a practical concern. If the unopposed areas are relatively small as in CH's part with the blind hole, we probably assume that the surface is continuous enough that there won't be significant local deviations in the non-opposed areas. If the unopposed areas are relatively large as in CH's part with the rectangular cavity, we might not assume this. Where do we draw the line? There are no rules - this is where "practical considerations" come in. As CH alluded to, it comes down to risk management. It is up to the designer to decide whether to go with just the size tolerance or to add additional controls (if they feel that the size tolerance would allow undesirable outcomes that have a significant chance of occurring).

Evan Janeshewski

Axymetrix Quality Engineering Inc.
www.axymetrix.ca

### RE: In worst case, the flatness is...

Evan, great post!!

And I am glad we pushed this thread so far (we wouldn’t have Evan’s input otherwise)

Definitely worth the 70 replies.

### RE: In worst case, the flatness is...

Thank you Evan,

It is very true that in real life we never have perfectly opposing features. Does it mean Rule 1 should never apply?

There is no way standard will eventually provide strict rules for every possible part. There always will be space for making personal decision.

OP example didn't ask what control is better to use. The question was, how bad part can we get with controls already there.

Since nothing ever is 100% perfect, "none of the above" is (almost) always technically correct.

0.6 was good, reliable guess. Sometimes creators of exercise books don't really dig as deep as we think. That's another moment to be taken into consideration.

All together it was great discussion, but I think it's getting too long.

Question to Season: HAVE YOU FINALLY FOUND THE ANSWER IN THE END OF THE BOOK?

"For every expert there is an equal and opposite expert"
Arthur C. Clarke Profiles of the future

### RE: In worst case, the flatness is...

greenimi

The OP question was regarding the max flatness considering the straightness of planar line elements controls.

The apparent answer is the size limits control the flatness.

Considering the possibilities of surface curvature that is possible within the size limits
I cant possibly see how straightness of planar line elements would be useful for a planar surface. Dont want to make the thread longer... thats just me.

#### Quote (If the feature is not FOS you SHOULD define it with profile. Period)

That is your "opinion". Dont know how you can claim "should".
(over 70 comments on a limit dimension. you missed the "points of view"?)

A parallelism control could work just as well IMO. (if there was a datum to reference)

However, back to the question / example. The example is obviously incomplete.
It does not reflect comprehensive functionality with just the example shown.
It was a question to consider "flatness".

You never answered my question on what effect this question regarding flatness would differ if the limit dimension is not relatve to a FOS. No rule #1; then what?

### RE: In worst case, the flatness is...

greenimi,

I'm glad that the thread is getting to some interesting outcomes. Your questions tend to make us dig deep and extract the subtle details. Keep in mind that the writers of GD&T textbooks and exercise books (and even standards) can only get into the intricacies to a certain extent, without losing most of their audience. People want things to be simple and easy, not complicated and difficult. I know from experience that it is much easier to make money glossing over these subtleties than it is addressing them. I'll stop there before I get into a self-righteous, bitter rant ;^).

CH,

I would say that Rule #1 still applies, even with features that are not perfectly opposed. Assessing the feature's conformance to a boundary is straightforward, even if the feature has unopposed areas.

Again, to me the difficulty lies in the actual local size. It's an old, shop-worn tolerancing tool that serves well for parts that one wants to be able to inspect with a caliper or mic. But for this tool to work, certain conditions have to be in place (such as opposed geometry, and form error that is relatively small). When these conditions are not satisfied, it breaks down and becomes ambiguous. It's just not as robust as zone-based geometric tolerances.

Evan Janeshewski

Axymetrix Quality Engineering Inc.
www.axymetrix.ca

### RE: In worst case, the flatness is...

Dtmbiz,
The fact the straightness requirement is there or not is irrelevant for the question asked by the OP. And yes, the size limits control the flatness and “straightness does not control flatness”

Quote: “That is your "opinion". Dont know how you can claim "should"”
Of course, IT IS my opinion. But looks like I was not entirely far off in the weeds by bringing it up.

Quote:” You never answered my question on what effect this question regarding flatness would differ if the limit dimension is not relatve to a FOS. No rule #1; then what?”

If it is not relative to a FOS (and specially regular FOS), then rule#1 does not apply and the flatness could be controlled indirectly by others controls zone based geometric tolernaces (and not a non-based tolernaces) :
You can use profile to locate the surface, or even composite profile and the flatness would be indirectly controlled there.
You can also use directly flatness, but should be a refinement of the location control and the orientation control. I am sure you know, you locate first and then orient and then refine the form if it is still needed.

Evan,
Quote: “……actual local size is defined as "the measured value of any individual distance at any cross section of a feature of size". There are several problems with this definition (this discussion could fill another thread), but the main one for this thread is the idea of a "distance"…………

That is why the math standard Y14.5.1 moved toward the LMC sphere concept.
Concept not very developed in Y14.5 (at least not yet) .

Probably in the very near future. By the way do you know if the math standard will get a new revision soon or nothing in sight?

### RE: In worst case, the flatness is...

There are a number of articles on math interpretations that preceded the issue of the Y14.5.1, but Google seems to find none since. Voeckler should have generated a new chapter before proposing the out-of-order datum evaluation scheme that got dropped in place. Or the committee should have tabled the new scheme until that math section was generated to match.

### RE: In worst case, the flatness is...

greenimi,

Thank you for your time to directly respond.
You have explained your interest in FOS and Rule #1.

Agreed regarding other geometric controls are available along with fundamentals
and rules for consideration, however the question was regarding the example as shown.

This thread went to some areas of interest at a deeper level.
(dont they all or at least most? - rhetorical)

### RE: In worst case, the flatness is...

greenimi,

A new revision of the Y14.5.1 mathematical definition standard is currently in development. I am hoping that it will be released in 2016.

I'm not sure what will happen with the definition of actual local size - to me, this is one of the most difficult problems in GD&T. There is not even agreement on the meaning of the current definition in Y14.5 applied to cylinders, as "any individual distance at any cross section" is interpreted differently by different people. Some interpret it as a distance extracted from 2 opposed points (as one would measure with a mic), and some interpret it as a diameter extracted from a cross-sectional circular element. Unfortunately, the standard contains text supporting both interpretations and no figures that clarify the meaning (only side views are shown, obscuring what is really happening within a given cross section). So we don't even know for sure whether a cross section of a cylindrical feature has one actual local size or many. The committee is in a difficult position, because it is now impossible to choose one or the other without contradicting past practices in some way. The Y14.5.1M-1994 mathematical definitions standard created a novel definition based on an LMC sphere, but this has been largely ignored in industry (partly because it conflicts with the idea of 2-point opposed diameters, and partly because the mathematical definitions standard was itself largely ignored).

The fact that there are camps favoring different interpretations makes it likely that different types of local size are needed for different applications. The ISO GPS standards define several different types of size, but so far Y14.5 has not embraced this approach.

Evan Janeshewski

Axymetrix Quality Engineering Inc.
www.axymetrix.ca

### RE: In worst case, the flatness is...

Regarding the ISO GPS standard’s approach to the actual local value here is what one of the best experts in the ISO standards said:
Pmarc said: (I know he did not give me the permission to copy and paste and I am very sorry about that, but it is a public site)
Sorry pmarc. If I have to remove this post I will do it without any hesitation.

“Yes, in ISO GPS actual local (two-point) size of a cylindrical FOS is a distance between two points measured in a plane perpendicular to the axis of associated LSQ cylinder, and that distance must be measured across the center of associated LSQ circle.

To me this definition is mathematically consistent, although it does not address all issues. Just one example: picture a pin that is perfectly round yet is bowed to a banana shape. Per ISO definition this feature will not have all actual local sizes identical. Only in one cross section (at the middle of pin's length) they will all be equal, because only in that cross section the surface of the pin will be seen as a perfect circle. In other sections the pin's surface will be seen as an oval/ellipse-like shape, thus lead to different local size measurements. “

### RE: In worst case, the flatness is...

Exactly, how big the difference will be introduced by bananization of a pin?

"For every expert there is an equal and opposite expert"
Arthur C. Clarke Profiles of the future

### RE: In worst case, the flatness is...

One factor not considered in Y14.5.1 et al, is the concept of epsilon, which is found elsewhere in mathematics. It represents the smallest noticeable delta. Those results that are less than epsilon away from the ideal value are considered equal to the ideal value.

I suspect that small amounts of curvature are easily detected for sufficiently small epsilon based on the above local size definition. Whether that epsilon is important to most or not is immaterial to the definition.

There is also the inspection tolerance problem that was poorly handled in the gaging standard. The precision of the inspection equipment needs to be in proportion to the desired approach to the dimensional boundary, not to the tolerances applied to the features.

If it's important that a dimensional limit not be exceeded it doesn't matter how large the target is but how close to the edge of the target the acceptable measurement is. Look at photo-finishes for horse racing. Horses are big and the length of the track is pretty big too, but the measurement technique is such as to discern very small differences.

### RE: In worst case, the flatness is...

greenimi,

Pmarc's assessment is correct as usual. The ISO definition adds additional constraints, to make the local sizes fully defined.

There is another aspect of the local size definitions that comes into play when form error is present:

The first graphic is one interpretation of "any individual distance at any cross section". I've tried to indicate the diameters at which the surface is directly opposed. Note that these diameters do not pass through a common point - each one is independent of the others. This would be straightforward with a 2-point measuring device (mic) but difficult and time-consuming with a CMM.

The second graphic illustrates the ISO definition that pmarc described. Each 2-point diameter passes through the center of the least squares circle. Note that the surfaces are not directly opposed at these diameters. This would be difficult with a 2-point measuring device but straightforward with a CMM.

The two methods clearly give different results, and the difference would correspond to the relative magnitude of the form error.

Evan Janeshewski

Axymetrix Quality Engineering Inc.
www.axymetrix.ca

### RE: In worst case, the flatness is...

So, reading through the debates, I'd like to add another hypothetical monkey wrench/question into the works.

Assuming the dimensions are in millimeters, 30 +/- 0.3 would allow a manufacturer to use potentially use 1.1875" stock, assuming the material requirement allowed for such a standard size (29.7 mm -30.3 mm = 1.1693 INCH - 1.1929 INCH), and that the tolerances for that standard size still fell within the design intent on the drawing. If thats the case, then would Rule #1 still be applicable, as stock material provided in the as-finished state is exempt from Rule #1? Or do we always assume Rule #1 is in effect unless we explicitly state that the material comes from a raw stock sizing?

### RE: In worst case, the flatness is...

Nobody is forcing manufacturer to use unfinished stock size, so unless the drawing explicitly states "stock" (which it doesn't), the question is irrelevant.

"For every expert there is an equal and opposite expert"
Arthur C. Clarke Profiles of the future

### RE: In worst case, the flatness is...

2.7.2 Form Control Does Not Apply (Exceptions to
Rule #1)

The control of geometric form prescribed by limits of
size does not apply to the following:
(a) stock, such as bars, sheets, tubing, structural
shapes, and other items produced to established industry
or government standards that prescribe limits for
straightness, flatness, and other geometric characteristics.
Unless geometric tolerances are specified on the
drawing of a part made from these items, standards for
these items govern the surfaces that remain in the asfurnished
condition on the finished part.
(b) parts subject to free-state variation in the unrestrained
condition. See para. 5.5.

### RE: In worst case, the flatness is...

AMontembeault

It appears that you are aware of the previous post exception regarding Rule #1 and stock based on your question.

Stock should be also be identified as such as mentioned below.

(a) Each dimension shall have a tolerance, except for
those dimensions specifically identified as reference, maximum,
minimum, or stock (commercial stock size)
. The
tolerance may be applied directly to the dimension (or
indirectly in the case of basic dimensions), indicated by
a general note, or located in a supplementary block of the
drawing format. See ASME Y14.1 and ASME Y14.1M.

What is your question regarding the OP flatness question considering straightness (or not considering straightness) regarding this thread? (to me, the lengthy thread with tangent topics obscures your question)

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