GD&T/Perpendicularity

[[Ja...]]

I have a theoretical question regarding GD&T and how the CMM interprets perpendicularity in a particular case.

(A) Assume a perpendicularity callout on a cylinder to a plane. The value for perpendicularity is the diameter of the related actual mating envelope of the axis, correct? I understand that the software can constrain a cylinder to the datum and contract/expand until making contact, and thus determine the value.

(B) If we consider perpendicularity in terms of projection of the cylinder axis, we can see how, mathematically speaking, perpendicularity is a particular flavor of position. Assume the cylinder is being measured perpendicular to the XY-plane. Project the cylinder axis onto the ZX-plane and the YZ-plane, forming angles A1 and A2, respectively. Let the cylinder be of height h. Then, we have that the deviation in X from one axis endpoint to the other is dx = h*tan(A1) and deviation in Y is dy = h*tan(A2). Project the axis onto the XY-plane, where we have that the distance between endpoints is sqrt(dx^2 + dy^2). This is simply a position calculation without the factor of 2 in front because we are measuring the entire width of the diametral zone, instead of the radial positional error. Thus, perpendicularity is a "refinement" of position.

(C) The above points have assumed that we have an axis that is straight, but not necessarily perpendicular. Assume that we measure three sections of the cylinder and form a curved axis. This will surely affect the way of calculation. Assume that the second point of the axis is much farther along Y than the other two. When projecting onto the YZ-plane, how does the software determine A2? Surely it cannot just measure endpoint to endpoint. Does it least squares the projection points? Does it simply perform a contraction/expansion algorithm? Does it matter which evaluation method you have chosen for the feature?

[[Da...]]

Once the cylinder is checked , Calypso produces a PERFECT cylinder in its place. The perfect cylinder is used for the calculation. Calypso cannot project form errors because they are completely unpredictable. It can't assume that a bend in the axis will continue at the same rate as the historic data. Cylinder , Cone, and plane are 3d features that have to be handled this way. A good thing to know if you're arguing with a machinist or engineers that are checking things from a surface plate.

[[Br...]]

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1. A perpendicularity tolerance in this case would be a cylindrical tolerance zone that is perfectly perpendicular to the Datum
reference.
2. The axis of the feature (at RFS) is what must fall within this tolerance zone. The Axis in this case would be produced by the
Unrelated Actual Mating Envelope (UAME). If it were the RAME, then there would never be any error because that
would make the axis perfectly perpendicular to the datum, and thus always falling within the cylindrical tolerance zone.

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I love the way you think Jacob. When you say Perpendicularity is a refinement of position, that is absolutely correct though the way you got there is interesting. GD&T trainers usually like to break down all the types of geometric tolerances into 4 major characteristics.

1. Size
2. Form
3. Orientation
4. Location

From there you can sort of categorize each of geometric tolerances by which of these 4 characteristics they control. So a perpendicularity tolerance controls Orientation. A Position tolerance controls Location and Orientation. So as you can see both geometric tolerances share one of these Characteristics--Orientation. So by dropping a perpendicularity tolerance with a position tolerance you will be able to give a tighter control to the orientation of the particular feature of size than what is already available from the position tolerance, thus, as you said, a refinement of the position tolerance.

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I think you are misunderstanding what an "Axis" is as defined in ASME Y14.5-2009. The Feature Axis is the axis of the unrelated actual mating envelope of the feature. This means the axis is a perfectly straight line. There is no "curve" as you put it, to an Axis. It sounds like what you are confusing it with is what is called a Derived Median Line, which is what would be evaluated in things like a Concentricity tolerance or Straightness tolerance. Now this also I believe is a major difference between ISO and Y14.5. With ISO the derived median line is evaluated for things like perpendicularity and Position as opposed to what ASME refers to as the Axis. That is why Calypso has the option to select one or the other for you evaluation when you create the characteristic.

So to finally answer your question, "how is Calypso calculating perpendicularity?". It depends on what option you have selected. If you select the derived median line option, It will look at all the median points of each circle section and then the height at wich the maximum point is determined will be output. I you have the "P" button selected it will be an axis and simply output the distance from min to max. I don't know If the evaluation method affects the derived median line calculation. I would probably use LSQ for that (that's what the cookbook recommends as well). But per ASME, you need to create that UAME either by OuterTangential, or MaxInscribe/MInCircumscibed.

[[Ja...]]

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Thanks Dave,

That makes sense that the software cannot, nor should it, extrapolate beyond the data that it measures directly. It is good to know for shop discussions, and I would guess that I would just have to take more levels/points to closer match what the plate says. Efficiency would be sacrificed temporarily, but a point would be proven.

[[Ja...]]

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Brett,

My line of thinking was incorrect per Y14.5-2009. I was referring to the RAME of the axis itself, not of the feature. This is not defined per ASME because an actual mating envelope doesn't apply to an axis, but rather to a feature. It worked as a visualization tool for me to think of the measured perpendicularity "error" as the size of the RAME of the axis, not of the feature.

You are absolutely correct in that I was misunderstanding the axis. Technically, I was considering a derived median line. I would like to get involved with ISO, because I am trying to understand Position, and thus Perpendicularity, in terms of the derived median line. I guess that was the whole point of this post, and it sounds like ISO may have some answers. I am also trying to think of things in a mathematical sense, but I may be overcomplicating it. The way that Calypso evaluates the characteristic was just made much simpler with your explanation.

Thank you.

[[An...]]

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DERIVED MEDIAN LINE should mean: DERIVED MEDIAN POINT CLOUD

[[SH...]]

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I suggest you to refer James D Meadows GD&T book,it a good book according to my experience. He is ASME member. Reading directly a ASME standard is a hard nut to crack.....

[[An...]]

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DERIVED MEDIAN LINE should mean: DERIVED MEDIAN POINT CLOUD

[[Br...]]

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Derived Median Line is the term in ASME.(If I'm not mistaken, ISO GPS just calls it a median line.) A point cloud is typically referred to as a collection of points in 3D space. I suppose one might say a derived median line is composed of a could of derived median points. But the official term is Derived Median Line, and it is important we get our terms right because they have very specific definitions.

ASME Y14.5-2009 para 1.3.31

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.

Here's an example of an application of Derived Median Line from Y14.5



Here is an example from Alex Krulikowski's Fundamentals of Geometric Dimensioning and Tolerancing

[[An...]]

Just my point of view.
See attached.

Contribution_20_12_2019.pdf

[[Ja...]]

Andreas,

Where is this point cloud viewpoint coming from? A circular cross section will produce one circle whose one center point depends on how it is evaluated. Are you considering all possible centers by changing evaluation settings? Are you associating one cross section with more than one center point? If so, why?

[[Me...]]

I think he is highlighting that the Y14.5 standard is not clear as to how the center point of each cross section is to be established. Changing the evaluation method is going to produce a different center point.

[[An...]]

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Yes,but:
One cross section with many MEDIAN POINTS.

Example:
A cylinder with 500 surface points yield 250 median points.
Connecting all these median points of one cross section would yield an unregular closed shape.
Putting all seven shapes together creates an amount that I call
the DERIVED MEDIAN POINT CLOUD.
The target of calculation now is getting the minimum circumscribed cylinder
that includes this cloud.
This cylinder is constrained in location and direction to the datum of Concentricity.
The diameter of this cylinder is the result of Concentricity.

In this context,the term DERIVED MEDIAN LINE makes no sense.

[[Ja...]]

Andreas,

Y14.5-2009 Fig. 7-60 is essentially what you are referring to. I learn something new every day. I would argue that "derived median point cloud" is not defined per Y14.5, but I understand why you are calling it that. It appears to me, at first glance, that this line of thinking really only applies when discussing concentricity as it is defined in 7.6.4.1. The topic of this conversation was really about Perpendicularity/Position.
It seems that you are just refining what Brett said when he said a derived median line would be used for concentricity which is an interesting catch.

If Concentricity, defined this way, is truly different than Position (as is stated in the note after 7.6.4.1) then how did ASME get away with eliminating Concentricity in 2018? I haven't dug deep enough I guess....

[[An...]]

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Yes! But:
I would strongly doubt the correctness of the texts in figures 5-2 and 10-2.
In spite of all linguistic infirmity.
Give me the time to argue.

[[An...]]

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It also applies when regarding Fig.5-2 (straightness)

[[Ja...]]

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Just ordered his text per Y14.5-2018. Thanks for the recommendation!

[[Ja...]]

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I don't see that in 5-2. It just refers to the derived median line, which is as Brett stated: the line formed by the center points of all cross sections. This is just one definition after another.

You are correct in that there is an exception when it comes to Concentricity and, now that I dig deeper, Symmetry in the 2009 standard. That exception is viewing things as a "point cloud" as you define it. After 2009, however, that whole viewpoint seems to disappear. One of the reasons why may be made clear by looking at Fig. 7-65 and 7-66. I think the intent is the same, but with the Positional tolerance we have the added benefit of the ability to control the orientation of the slot to the primary datum in one shot.

[[An...]]

OK J.C.

Do me one favour and explain:
What is the difference between a "Center Line" and a "Median Line"?

[[Br...]]

You are right Andreas, Concentricity controls all the derived mid points, whereas straightness is the median line that comes from the individual cross sections.So there is a difference. But I want to be clear, what Jacob is asking about and what Calypso is evaluating is the Derived median line. It takes cross sectional points at each measured circular level to evaluate. All this information is available in the Calypso operating instructions PDF.

DML 2.JPGDML 1.JPG

[[Ja...]]

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I never used the term "Center Line", but as is defined in Y14.5 the derived median line is the line formed by the center points of all of the cross sections of the feature.

Take a cross section of a cylindrical feature. You will have X number of points. Perform a mathematical fitting algorithm on those X points. You will have one center that corresponds to that particular cross section. Repeat for Y number of cross sections. Now construct a line from those Y points. That is your derived median line.

[[An...]]

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Sorry! I would not agree with that!

Straightness_1.pdf

[[Br...]]

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It is different because it uses the median points vs. position that controls the Axis or mid plane of a feature at RFS. Concentricity was eliminated because it is a worthless tolerance that is usually misused. There are better options that will better apply to functionality of a part through tolerances like position or runout. If Concentricity is truly needed, in cases such as dynamic balancing, a note should be put on the drawing.

[[Br...]]

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My goodness it's nearly a handrawn picture, get over it. Alex Kruilikowski is a commitee member of Y14.5 I assure you he believes the cross sections are perp to the UAME axis. Especially because he says it in the quote I provided in that picture.

[[An...]]

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I used it all day long.Every cylinder measurement creates a center line:
X-coordinate
Y-coordinate
Z-coordinate
Angle a1
Angle a2
Length
Evaluation: Least Squares (MCC/MIC/Min)

The Median Point in my understanding:
The symmetry point of two opposing surface points.