Orientation of a center plane of a tapered feature 2

[Burunduk]

A designer applied perpendicularity feature control frame with the leader pointing to a centerline representing the center plane of an internal taper feature (a "pocket" with symmetrical non-parallel opposed surfaces). I don't consider this specification valid according to ASME Y14.5-2009 but I'm struggling to provide a good explanation of why perpendicularity shouldn't be used this way. The one use of perpendicularity I know when it is applied on a virtual, derived geometry (as opposed to an actual surface) is when a center plane/axis of a feature of size is controlled. It doesn't seem right in the context of a tapered feature, not associated with a size dimension - but I can't form a good argument why. A valid point is that a center plane can be derived from a tapered feature (for example, a datum plane derived from tapered datum feature), and I suppose that a way to evaluate the derived plane orientation relative to a DRF can be found. I need your help, please.

 

[chez311]

Rejecting a UAME based on the possibility of the simulator to contract further after completing the process is rejecting it based on some mechanical behavior related to the process of the simulation, not to the theory of dimensioning and tolerancing.

Accepting a UAME based on the requirement of a physical simulator of a certain truncation which does not match the feature in question to "contract" to make proper contact with a part is "based on some mechanical behavior related to the process of the simulation, not to the theory of dimensioning and tolerancing". The jaws may be contracting relative to each other, however as pylfrm noted previously all the simulator is actually doing is simulating a different part of the cone - hence why a fully formed conical simulator requires no such "contraction".

(A) If the chosen simulator has a different truncation height or is a fully formed cone no such "contraction" is necessary. The requirement of your truncated simulator to contract to make sufficient contact with the part is either something which supports your argument or irrelevant due to it being "based on some mechanical behavior related to the process of the simulation, not to the theory of dimensioning and tolerancing". It cannot be both.

Figure (1) in your sketch shows that if the simulator's small end is larger than 20.1 (middle image) or 19.9 (right side image) it will have to contract to fully contain the feature.

Please refer to my (A) above. In reality any discussion of a truncated simulator is an artifact of physical simulation. The envelope under discussion would extend infinitely, and would therefore be a fully formed cone. No amount of "expansion/contraction" of the envelope would be necessary to simulate a truncated conical feature of any configuration.

Figure (2) shows 2 different fully acceptable simulation results, identical ones. No need to choose among them

If both are acceptable (or presumably anything in between) then this means there is no minimum or maximum. You've just proven my point.

If you prefer to call the apex and axis of a 180° "cone" indistinguishable rather than ambiguous then so be it. I'd rather call it imaginary (made up). If you look at a black surface you can imagine that there is a black ink mark on it, which may be there and may not. If you make a truncated cone into a nonzero size cylinder by folding the included angle about a fixed size truncation at least the axis doesn't disappear. You may disagree but I find the apex less important. When you construct a conical feature on a CAD program by creating a "revolute" you need to define the feature outline and an axis of revolution. The apex simply results from the geometry you create.

I don't really see the point in throwing around terms like "made up" and "imaginary" when discussing theoretical geometric constructs, unless it is to simply discredit me by using words with connotations that imply my assertions are not based in reality. A plane of zero thickness, a line (or axis) of zero width, or point of zero size are all "imaginary" - there is no true physical analog. When either of us talks about any of these geometric concepts we are discussing things which are "imaginary".

I'm not sure discussing CAD conventions is entirely productive either. A conical feature can also be produced by the "loft" function connecting a circular base and a point, or even the "extrude" function and specifying a taper angle.

Its interesting to note that most basic definitions out there of a cone is some variation of "a shape which has a flat base and tapers to a point" without any discussion of an axis. I think the definition from wolfram alpha offers a little more nuance:

"A (finite, circular) conical surface is a ruled surface created by fixing one end of a line segment at a point (known as the vertex or apex of the cone) and sweeping the other around the circumference of a fixed circle (known as the base)"

The definition of a single, unique axis arises from the base being a shape with rotational symmetry. One could also create a non-symmetric conical shape from a base being some other non-symmetric shape which is swept around instead of a circle - say a D-shape (circle with a flat on one side). In that case one unique axis would not be able to be clearly defined.

"A conical feature has by default a conical boundary." this us what I tend to think too, but what is the shape of the boundary of a hex screw head?

A conical feature defined like Y14.5-2009 fig 4-45 has a conical boundary, absolutely yes.

A hex feature defined in a similar manner (ie: profile tolerance which applies to the entire hex - say with an all-around leader) would also have a hex boundary.

I hope you will also consider responding to the question at the end of my 17 Dec 19 03:44 post

Could you provide some examples of surfaces (or sets of surfaces) that you would say do not have UAMEs?

I too am interested in your answer to this.

 

[Burunduk]

chez311,
I'm not necessarily talking about a physical simulator. Can't a theoretical simulator be finite? Think of a finite theoretical conical surface with boundaries - a virtual envelope with truncation and a base roughly the same distance apart (slightly longer) as they are at the actually produced feature. It can be scaled up or scaled down to contain the feature. I never said it must. I say that if it can, it has what it takes to be UAME per the standard. "In reality any discussion of a truncated simulator is an artifact of physical simulation." - why?

Minimum/maximum can be related to the range of sizes of circular element containing the feature:
Actual produced feature (external conical) #1: 29.8 - 49.75 "minimum contracted"
Actual produced feature (external conical) #2: 30.1 - 50.33 "minimum contracted"

Certainly didn't intend to discredit your assertions by the use of words "imaginary" and "made up", my apologies if I made it look that way. I guess I did a poor job at conveying my point: using your own words the axis and apex for a 180° "cone" are "indistinguishable". For a 0° "truncated cone" at least the axis is distinguishable. The lack of an apex is what differentiates it from an "official" cone per the definitions you quoted but at least it is still without a doubt a surface of revolution (same "family" as the cone). A plane surface can only be "imagined" as a surface of revolution if you "make" a random normal to be an axis and it's intersection point with the plane - an apex. It is certainly not "a shape which has a flat base and tapers to a point", either. Hope this communicates my idea in a more appropriate manner.

Examples of surfaces that do not have UAMEs: plane surfaces, surfaces like these. Basically, all surfaces that neither have rotational symmetry nor can be cross-sectioned perpendicularly to some kind of definable center (plane/axis/intersection line between planes) to produce 2D outlines with symmetrically opposed line elements.

My feeling is that there was a tendency to include cones into the feature of size category even before irregular features of size were introduced in 2009. I am still not saying for sure that they are. Just wondering why not. No thoughts at all to share about my link concerning countersinks?

 

[Burunduk]

Just to make sure:

Figure (2) shows 2 different fully acceptable simulation results, identical ones. No need to choose among them

If both are acceptable (or presumably anything in between) then this means there is no minimum or maximum. You've just proven my point.

I hope you realize that when I talk about a "range of sizes" along a simulator that contains the feature I am referring to the circular elements along the "used" portion of the simulator - the extent which makes contact with any portion of the actual surface. I do not consider the diameters at the unused portions of the simulator (that just hang in the air or surround other features). This is why in your figure (2) the simulations are identical (same "minimum contracted" range).

 

[chez311]

I'm not necessarily talking about a physical simulator. Can't a theoretical simulator be finite? Think of a finite theoretical conical surface with boundaries - a virtual envelope with truncation and a base roughly the same distance apart (slightly longer) as they are at the actually produced feature.

The extent of a datum feature simulator should be sufficient to cover the entire datum feature. Beyond that, extent is irrelevant. That's why it's simpler to consider simulators as having infinite extent.

I see no reason it should be for a conical feature considered in isolation. The requirement for a simulator of finite extent is a physical necessity not a theoretical one. If the simulator/envelope needs to be at least as long as the surface of the feature, why not treat it as infinite? Pylfrm just addressed this as well.

I hope you realize that when I talk about a "range of sizes" along a simulator that contains the feature I am referring to the circular elements along the "used" portion of the simulator - the extent which makes contact with any portion of the actual surface.

I don't follow this logic. Are you saying that a fixed, fully formed conical simulator would be at its minimum or maximum depending on where it contacts the feature? Seems tenuous at best. If the simulator for two different variations of a feature is the same, then it is no more minimum or maximum.

using your own words the axis and apex for a 180° "cone" are "indistinguishable". For a 0° "truncated cone" at least the axis is distinguishable.

I initially said essentially there are infinite possible apexes and axes for a planar feature/180 degree cone. I used the word "indistinguishable" to differentiate infinite possibilities from what you called "disappearing".

I just showed an example of a non-symmetrical conical shape which would have an infinite number of possible axes and would not have rotational symmetry. Would you say this is no longer a conical shape or no longer has anything in common with regular cone because it does not have a single defined axis? I would say it is still conical, just not a regular cone. Symmetry which lends itself to a clearly defined axis is a property of a special case of cones (or other geometry), but not necessarily an integral requirement.

The definition of a single, unique axis arises from the base being a shape with rotational symmetry. One could also create a non-symmetric conical shape from a base being some other non-symmetric shape which is swept around instead of a circle - say a D-shape (circle with a flat on one side). In that case one unique axis would not be able to be clearly defined.

Your assertion about whether the axis or apex is more important feels much like a "chicken or egg" scenario - however in this way in light of my above case, it seems that the axis is a derived property and that conical shapes are possible which have an infinite number of possible axes. The existence of a vertex establishes a fundamental difference between a conical shape and a cylindrical one.

A plane surface can only be "imagined" as a surface of revolution if you "make" a random normal to be an axis and it's intersection point with the plane - an apex. It is certainly not "a shape which has a flat base and tapers to a point", either.

Sure it is. It just so happens that taper is 180 degrees so that the point/apex lies on the same plane as the base. This revolved surface does not have to be so abstract as you might imply - is it not possible to take a line segment and rotate it around a point (apex)? The resulting surface would be planar, and has no volume (or infinite volume?) so I understand anyone's issues with calling such a surface a cone however such a shape is still possible.

Basically, all surfaces that neither have rotational symmetry nor can be cross-sectioned perpendicularly to some kind of definable center (plane/axis/intersection line between planes) to produce 2D outlines with symmetrically opposed line elements.

Irregular non-symmetric features do not have a single defined/unique center plane/axis, is any possible axis/plane acceptable for sectioning in that case?

Can you also more specifically define "symmetrically opposed line elements" ? I'm not sure why the focus on symmetry, no kind of symmetry is a requisite for having a UAME - neither in the standard's definition nor geometrically. Additionally datum feature A in Y14.5-2009 fig 4-33 has no directly (or symmetrically) opposed elements and yet certainly has a UAME.

My feeling is that there was a tendency to include cones into the feature of size category even before irregular features of size were introduced in 2009. I am still not saying for sure that they are. Just wondering why not. No thoughts at all to share about my link concerning countersinks?

Where do you see such tendency? Its been 62 years since the inception of the Y14.5 family of standards. Now in its 7th incarnation, I see no example of cones being treated as a FOS in the standard - irregular or otherwise. The only evidence I've seen presented is a very generous reading of the definition of IFOSb.

The example you provided is only evidence of one person's interpretation, not of any conformance to the standard. Without an accompanying note on how simulation should occur I would say the specification as shown is an improperly applied position tolerance to a non FOS. Such a callout may "work" for a non-critical countersink as any variation or ambiguity in how the countersink is measured/simulated may have minimal impact on function but that does not make it correct. I think you'll also find that due to the way countersinks are typically produced the biggest source of variation is their depth (ie: with a form tool in the same operation as the mating holes) and relatively accurate countersinks can be accomplished with minimal effort. Even if applied by hand the form tool will self-center.

"expert" or "professional literature" does not equate to infallible.

 

[Burunduk]

envelope, actual mating: this envelope is outside the material. A similar perfect feature(s) counterpart of smallest size that can be contracted about an external feature(s) or largest size that can be expanded within an internal feature(s) so that it coincides with the surface(s) at the highest points.

A finite simulator for an AME should be good enough because the only meaningful length of the simulator is the one that has the potential to contact the feature's high points, in other words, the "working" portion of the simulator depends on the length of the feature. The rest of the simulator's extent is just there to make sure that the entire feature is contained - so it is more of a technical "just-in-case" thing, what I would call "a physical necessity", rather than a theory-based requirement. Since the "empty" portions of the simulator do nothing, no need for infinite simulators. A theoretical finite conical simulator for a truncated cone can be exactly as long as the actual produced feature and it can be seen as an envelope that is able to contract/expand because each circular element along it has size. I think this logic is easy to follow.

Depending on how it's dimensioned, the conical D-shaped feature can potentially be considered an irregular feature of size type (b), having a conical actual mating envelope. The flat part can be treated as an interruption, similarly to how longitudinal flats that interrupt a cylindrical feature do not prevent it from being an irregular feature of size type (a) having a cylindrical AME.

As I mentioned Taper is defined in Y14.5 as the change of size for a unit length so really there is no such thing as a "180° taper" unless you want to treat it as an infinite change in size along zero length, which is what I would call "tenuous at best". The fact that you can portray a plane created as revolved surface (around a point, not axis by the way) is not more relevant than the description of a cylindrical feature created by changing the included angle of a truncated cone from any value to zero while keeping one of the ends at a constant diameter.

Irregular non-symmetric features do not have a single defined/unique center plane/axis, is any possible axis/plane acceptable for sectioning in that case?

Can you also more specifically define "symmetrically opposed line elements" ? I'm not sure why the focus on symmetry, no kind of symmetry is a requisite for having a UAME - neither in the standard's definition nor geometrically.

It is true that among irregular features of size there are non-symmetric examples such as the irregular shaped pocket in fig. 8-19. Which by the way, do not have one unique size dimension either, yet are fully compatible with the IFOS type (b) definition. The examples of non-FOS which I brought up do not include these. Basically, I referred to features that can not be described as neither "internal" not "external", just surfaces that do not connect back to themselves. I think the image in the link from my previous post makes it quite clear.

Where do you see such tendency?

The book preview I linked to is one example, based on the 1994 standard. I might be wrong but my guess is that similar practices are among the triggers for the introduction of IFOS back in 2009. The countersink example doesn't seems to be only one person's interpretation, either. See the replies in thread thread1103-110073, or thread1103-255441. I am sure there are more on this subject with similar ideas explained. I guess what you can read there is not as questionable as it was prior to the 2009 version.

Another source that might be of interest is this article by Al Neumann and Scott Neumann of Technical Consultants Inc.
An Exerpt:
"In the new standard, a hex, square, cone, or other similar type of features can used as a feature of size and even as a datum feature as long as they are properly related with profile or other geometric controls. This small change was really needed and opens the door to many possibilities, especially in plastics and sheet-metal parts."

 

[pylfrm]

I do not see in Y14.5 2009 where the AME concept is used for any geometric control other than position tolerance and form controls.

It's nothing specific to the profile tolerance. It's about the datum feature reference. See paras. 4.5.1(c), 4.11.4(a), 4.11.4(b), 4.11.4(c), 4.11.12, 4.11.13, and possibly others.


Burunduk,

For a feature that has a UAME and a fully-defined true profile, would you say that the UAME is always an isotropically scaled version of the true profile of the feature? Is that what you take "similar perfect feature(s) counterpart" to mean in the AME definitions?

Fig. 4-3 doesn't tell us exactly what datums should be derived from a feature with this specific shape but it would be reasonable to assume that the datums should be 2 center planes and one datum line at the intersection of these two datum planes. The two perpendicular datum planes would center the true profile and the related tolerance zone in 2 directions.

You're saying the symmetry planes of the UAME would be coincident with the symmetry planes of the true profile, right?

The profile tolerance in fig. 4-44 controls not only the form of the surface but also the size of each circular element at a known distance from the apex, thus the range of the non-uniform size of the entire produced feature along its physical length.

That sounds like a roundabout way of describing form. What are you saying is the difference? Do you think it would be possible to have a feature with perfect form that does not meet the profile tolerance?

This a link to a book preview that discusses the application of position tolerance to countersinks. Page 89, figures 8-49, 8-51. I posted it in the thread opened by dtmbiz but no one responded, so I repost it here too. What opinions on this? Example of bad practice promoted in professional literature?

The figures you mention have MMC position tolerances, so they don't seem very relevant to the discussion here.

I didn't verify, but I assume this book is based on ASME Y14.5M-1994. Some of the relevant definitions are significantly different in that version.


pylfrm

 

[Burunduk]

For a feature that has a UAME and a fully-defined true profile, would you say that the UAME is always an isotropically scaled version of the true profile of the feature? Is that what you take "similar perfect feature(s) counterpart" to mean in the AME definitions?

Considering the standard's definition of true profile - no, not always. Only in the special case where the true profile is unrelated to any datums, i.e. when the FCF for the profile control the tolerance zone of which is constrained to the true profile doesn't reference any datum features.

You're saying the symmetry planes of the UAME would be coincident with the symmetry planes of the true profile, right?

Yes, but this doesn't define the UAME, it defines the true profile. The "unrelated AME" is literally unrelated - doesn't recognize anything in space but the feature it simulates. The final UAME envelope will have dimensions proportionally dependent on the basic dimensions defined for the feature but if this can be considered as an association with the true profile, the proportional dimensions are where this remote association ends. Again: no offsets, progressions, etc. relative to anything but the feature are derivative from the definition of the UAME.

That sounds like a roundabout way of describing form. What are you saying is the difference? Do you think it would be possible to have a feature with perfect form that does not meet the profile tolerance?

Even in the case of a conical feature that is only controlled by a profile tolerance, there is an imposed size control for every individual cross section of the feature, without size requirements for specific cross sections. Often there are directly toleranced size dimensions applied too, they can be used to control limits of size in a given location relative to the apex, not necessarily to other features.

The figures you mention have MMC position tolerances, so they don't seem very relevant to the discussion here.

They certainly are very relevant. Applying position control on a feature is recognizing the feature as a feature of size, regardless of the control is RFS (involving UAME) or otherwise MMC/LMC (uninvolving UAME). If anything that scheme became proper after irregular features of size were added in 2009, aimed at expanding the FOS concept to features not characterized by a single size dimension.

I didn't verify, but I assume this book is based on ASME Y14.5M-1994. Some of the relevant definitions are significantly different in that version.

Would you say that per the 1994 standard, non-FOS can be controlled for position when modified MMC?

 

[pylfrm]

For a feature that has a UAME and a fully-defined true profile, would you say that the UAME is always an isotropically scaled version of the true profile of the feature? Is that what you take "similar perfect feature(s) counterpart" to mean in the AME definitions?

Considering the standard's definition of true profile - no, not always. Only in the special case where the true profile is unrelated to any datums, i.e. when the FCF for the profile control the tolerance zone of which is constrained to the true profile doesn't reference any datum features.

I suspect the intended meaning of my question didn't quite make it through here. Let me phrase it another way:

For a feature that has a UAME and a fully-defined true profile, would you say that the UAME is always similar (in this sense, except excluding reflection) to the true profile of the feature?

Even in the case of a conical feature that is only controlled by a profile tolerance, there is an imposed size control for every individual cross section of the feature, without size requirements for specific cross sections.

I still don't understand what distinction you're saying exists between this and form control. If a feature with perfect form will always satisfy a tolerance, that means the tolerance does not control anything other than form.

Would you say that per the 1994 standard, non-FOS can be controlled for position when modified MMC?

ASME Y14.5M-1994 para. 5.2(b) leaves the door open by saying "considered feature", not "feature of size" like para. 5.2(a) does. Perhaps the door is closed by some other statement, but I don't know offhand. The more important question (as far as drawing interpretation is concerned) is whether such a tolerance has a well-defined meaning. I would have to investigate further to attempt to answer that. I rarely use the 1994 standard, so I'm not sure when or if that will happen.


pylfrm

 

[Burunduk]

For a feature that has a UAME and a fully-defined true profile, would you say that the UAME is always similar (in this sense, except excluding reflection) to the true profile of the feature?

Yes, I would. Important parts of that concept in the context of our discussion:

"possibly with additional translation, rotation and reflection. This means that either object can be rescaled, repositioned, and reflected, so as to coincide precisely with the other object."

Basically, it comes down to what I said earlier: the same shape and proportional dimensions. Since there is no organized location and orientation relationship between the similar (per the referenced definition) geometries, considering a "uniform offset" from the true profile serves no purpose.

I still don't understand what distinction you're saying exists between this and form control. If a feature with perfect form will always satisfy a tolerance, that means the tolerance does not control anything other than form.

I think I know where the difficulty to recognize the size control aspect of that profile control originates: the lack of a single size dimension describing the entire feature. For some reason, this problem only occurs with tapered features. Perhaps it is because of an abstract approach to the concepts that automatically makes everything theoretical infinite, with the infinite length extruding in the same direction along which size changes. For the internal pocket in fig. 8-19, would you say that because there is no single size dimension, the composite profile tolerance controls only the form of the feature but not the size? I suppose not. Similarily for a truncated cone, there is no single size dimension and size is dependent on where exactly it is being measured, but a tolerance zone limited between coaxial cones can control the size of a finite feature with it's ends (which are also the ends of the tolerance zone) located at fixed distances from the apex.

 

[pylfrm]

For a feature that has a UAME and a fully-defined true profile, would you say that the UAME is always similar (in this sense, except excluding reflection) to the true profile of the feature?

Yes, I would.

All right.

Consider a feature where the true profile is defined to be two internal cylindrical surfaces of diameter 10 mm, with parallel axes separated by 90 mm. First of all, do you agree that this is a fully-defined true profile?

Now consider a part where this feature is produced as two internal cylindrical surfaces of diameter 10.1 mm, with parallel axes separated by 90 mm. Imagine two holes through a plate of roughly 50 mm thickness, perpendicular to its flat surfaces. By your interpretation, I believe the UAME would be two cylindrical surfaces of diameter 10.01 mm, with parallel axes separated by 90.09 mm. The scale factor of the UAME would be 1.001 relative to the true profile. Do you agree?

Alternately, consider a part where this feature is produced as two internal cylindrical surfaces of diameter 9.9 mm, with parallel axes separated by 90 mm. Again, imagine two holes through a plate of roughly 50 mm thickness, perpendicular to its flat surfaces. By your interpretation, I believe a UAME would not exist. The scale factor would need to be 0.99 or less for a single surface of the UAME to fit within a single hole, but that would leave a gap of 79.2 mm or less between the envelope surfaces. The corresponding wall thickness on the part is 80.1 mm, so there's no way for both envelope surfaces to fit within both holes simultaneously. Do you agree?

I think I know where the difficulty to recognize the size control aspect of that profile control originates: the lack of a single size dimension describing the entire feature.

That is certainly not the reason for me.

For the internal pocket in fig. 8-19, would you say that because there is no single size dimension, the composite profile tolerance controls only the form of the feature but not the size? I suppose not.

I would not.


pylfrm

 

[Burunduk]

Pylfrm,

Good point about the two holes IFOS. I wasn't cautious and I shouldn't have said "always". I had your example from fig. 8-20 in mind and how it also applies to other continuous shapes such as in fig. 8-19. If I was presented with a 2 holes case I would say the UAME is two cylinders of simultaneously adjustable diameters always equal, with their axes spaced the basic distance apart. That is because these are two separate features treated as one, with no surface continuity between them. If two separate features such as in fig. 8-21 are used as a single IFOS the fixed distance would be between their centroids, and each (sub)envelope would be the scaled down/up version of the basically defined shape as described earlier, they would be fixed in orientation to each other and equal in dimensions, the two of them as a group being the UAME. Do you have any objections to this description? Again I wouldn't say that the envelope(s) should have a defined spatial relationship with the true profile.
The relationship would end at the UAME being the scaled up/down version of the true profile and maintaining the same basically defined distance between separate features treated as one. Anything else would imply that the "unrelated actual mating envelope" is not really "unrelated".

 

[chez311]

A theoretical finite conical simulator for a truncated cone can be exactly as long as the actual produced feature and it can be seen as an envelope that is able to contract/expand because each circular element along it has size.

I see no reason to consider a theoretical simulator as anything other than infinite. It is the simplest interpretation, and does not involve factors which are secondary to verification of the surface of interest for a primary datum feature considered by itself ie: how much and where the truncation happens. Such truncation can and should be evaluated when conformance of these secondary features is considered relative to the conical surface.

I would say that instead the "physical necessity" of a physical simulator of a certain length is an approximation of an infinite theoretical simulator. If you take the "expansion of circular elements" as well as the "working length" to be properties which support your position, one could consider a planar simulator of a certain area, consisting of circular elements of a certain size (or at least one circular element which describes its outer limit - say if we consider the end face of a cylindrical part), which must increase in area to accommodate a planar feature with a larger area and larger circular elements (or larger single outer element). Would you say this behavior is inherently or truly "expansion" in the same manner as a cylindrical simulator and is it notably different than consideration of a fixed simulator of infinite extent? I would say all you have accomplished is simulating a larger (or different) portion of the infinite theoretical planar simulator.

If you think my planar simulator has no physical analog - consider the flat portions (top or bottom) of the jaws of your truncated conical simulator. These would move with the jaws and the "working portion" would consist of circular elements (or at least an outer circular element) of increasing/decreasing size depending on where the jaws are in relation to one another. You might say this is indeed contrived and it can be identically simulated by a fixed planar simulator, to which I would respond that that is precisely my point.

The flat part can be treated as an interruption, similarly to how longitudinal flats that interrupt a cylindrical feature do not prevent it from being an irregular feature of size type (a) having a cylindrical AME.

I of course meant the entire surface including the irregularity. A D-shaped feature of constant cross-section with a profile tolerance surrounding the entire D-shape including the flat would be an IFOSb not an IFOSa. The UAME would be D-shaped.

The flat would be considered along with the rest of the conical shape. You've sort of skirted around my question - you have intimated the importance of a single defined axis, however such a shape would not have a single defined axis and could not be created by revolving a fixed profile around a single axis. Do you believe it no longer has anything in common with a regular cone?

As I mentioned Taper is defined in Y14.5 as the change of size for a unit length so really there is no such thing as a "180° taper" unless you want to treat it as an infinite change in size along zero length, which is what I would call "tenuous at best"

You have literally just described the slope of a vertical line. The slope of a horizontal line is 0/infinity = 0 and the slope of a vertical line is infinity/0 = undefined. You're free to argue that one of the basic tenants of linear algebra is "tenuous" however you've got at least several hundred years of mathematics to contend with on that point. Are you also saying that theres no such thing as a 180 degree angle?

One could also simplify this as "for every incremental diametrical change in size, there is zero change in axial length." It might not make any sense to specify a feature like this - but theoretically/geometrically it is possible, and the geometry it would describe is planar.

The fact that you can portray a plane created as revolved surface (around a point, not axis by the way) is not more relevant than the description of a cylindrical feature created by changing the included angle of a truncated cone from any value to zero while keeping one of the ends at a constant diameter.

But thats exactly the POINT. Its the ability to at least conceptualize the existence of a point/vertex for the former which makes it relevant. For the latter it is not possible - therefore not relevant.

As I said before a single defined axis is not even necessary. A line segment (or line or ray) connecting a point (vertex) and a profile which is swept around said profile is all thats necessary to create a conical shape - regular or irregular. Though a single defined axis can be derived from a regular cone.

Basically, all surfaces that neither have rotational symmetry nor can be cross-sectioned perpendicularly to some kind of definable center (plane/axis/intersection line between planes) to produce 2D outlines with symmetrically opposed line elements.

It is true that among irregular features of size there are non-symmetric examples such as the irregular shaped pocket in fig. 8-19. Which by the way, do not have one unique size dimension either, yet are fully compatible with the IFOS type (b) definition. The examples of non-FOS which I brought up do not include these.

You provided a description of what you would not consider a FOS which would seem to include non-symmetric examples such as 8-19 (no rotational symmetry, no definable center plane/axis) so I asked for clarification on that description. The example you provided does not clear up this discrepancy, nor does the introduction of other terms/descriptions which provide more questions than answers ("neither 'internal' not 'external'" and "surfaces that do not connect back to themselves").

The only thing I gather from your example is that you do not believe 2D/3D approximately sinusoidal shapes to be FOS. I am not clear on your reasoning or how that coincides with your initial description while allowing for non-symmetric examples such as 8-19.

I might be wrong but my guess is that similar practices are among the triggers for the introduction of IFOS back in 2009.

There are no examples in 2009 or the new 2018 of cones as a FOS except again by a generous interpretation of IFOSb. In fact in 2018 there are direct references in the definition for IFOSa and IFOSb to example figures - none of which are remotely conical/tapered.

What I see in the articles/examples you provided is a number of people with the desire to treat conical/tapered features as just another FOS and try mightily to stuff it into that box - and understandably so as the ability to derive a distinct axis from a regular cone is too tempting to ignore. The fundamental differences are summarily ignored.

The fact is these fundamental differences should not be ignored, and try as they might it does not belong in that box. Cones/tapers ARE fundamentally different and should be treated accordingly. Realistically I believe they deserve their own category and treatment (pmarc mentioned in the other thread that in ISO there are "features of angular size").

I think I know where the difficulty to recognize the size control aspect of that profile control originates: the lack of a single size dimension describing the entire feature. For some reason, this problem only occurs with tapered features.

There is no "difficulty to recognize" - profile of a cone considered by itself does not control "size" in any sense of the definition. Y14.5-2009 fig 4-45 if the conical feature has perfect form as pylfrm mentioned it will always satisfy the 0.02 profile tolerance. Where is the size control?

For the internal pocket in fig. 8-19, would you say that because there is no single size dimension, the composite profile tolerance controls only the form of the feature but not the size? I suppose not.

The control of size is not relegated to the use of a single size dimension. Profile control of the irregular pocket in Y14.5-2009 fig 8-19 certainly controls both form and size.

 

[pylfrm]

If two separate features such as in fig. 8-21 are used as a single IFOS the fixed distance would be between their centroids, and each (sub)envelope would be the scaled down/up version of the basically defined shape as described earlier, they would be fixed in orientation to each other and equal in dimensions, the two of them as a group being the UAME. Do you have any objections to this description?

Here are a few objections:
[ul]
[li]ASME Y14.5-2009 does not contain the word "centroid", and I don't recall seeing anything indicating that the concept might apply.[/li]
[li]The location of the centroid depends on what portion of the surface is considered. No rules are provided for making this determination.[/li]
[li]The result depends on how the overall feature is divided up into separate portions to be scaled individually. No rules are provided for how to do this.[/li]
[li]Your description does not cover cases where the overall feature is divided up into portions which are not all identical.[/li][/ul]

Again I wouldn't say that the envelope(s) should have a defined spatial relationship with the true profile.

If the UAME is used as a primary datum feature simulator, such a relationship must be defined.

There may also be a de facto spatial relationship between the UAME and true profile based on how the UAME is defined, even if it's not explicitly part of the definition. It's convenient for this to be the same relationship as the one used for a primary datum feature reference.

The relationship would end at the UAME being the scaled up/down version of the true profile and maintaining the same basically defined distance between separate features treated as one. Anything else would imply that the "unrelated actual mating envelope" is not really "unrelated".

In this context, "unrelated" means that the relationship between the UAME and the actual part is unconstrained except by contact between the envelope and the corresponding surface on the actual part. A relationship between the UAME and an otherwise unconstrained true profile does not conflict with this.


pylfrm

 

[Burunduk]

What I see in the articles/examples you provided is a number of people with the desire to treat conical/tapered features as just another FOS and try mightily to stuff it into that box

If you read the entire article which I linked to you might have noticed this:
"what follows are the views of someone who has been a member on the ASME Y14.5 subcommittee for the past 25 years."
Based on this I am not considering the author as someone that "tries mightily" to stuff cones into the box of IFOS; there is a high probability that he took part in creating that box, or at least is well aware of the intentions of the people who created it and has a pretty good idea of what fits in that box.

I see no reason to consider a theoretical simulator as anything other than infinite.

I think that a good reference for the required length of a theoretical simulator is the length of a tolerance zone. UAME simulators are used to simulate a feature axis that needs to be positioned within a tolerance zone. Y14.5 requires tolerance zones to apply to the full extent of the feature but not beyond that. If all tolerance zones and derived feature axes would be required to be infinite there would be no meaning to concepts such as a projected tolerance zone, and it would be virtually impossible to conform to a position tolerance for a considered hole from the aspect of orientation as the allowed angular error for the derived axis would be zero, regardless of the hole depth/length of the surface. A finite simulator for a conical feature can more easily be described as potentially being able to be "expanded" or "contracted" as these words are part of the AME definition, but even if a fully formed fixed cone is used as a simulator for a truncated cone, I wouldn't make an issue out of it, because the definition doesn't specify in no uncertain terms what "expanded" or "contracted" means.

The difference between the planar "adjustable" simulator you described and a conical adjustable simulator is that the conical adjustable simulator can make sense even if it is potentially replaceable by a fixed simulator. Diameters along the simulator can be related to specific theoretical values derivative from the drawing. I don't see how diameters of circular elements on a planar feature can have any meaning.

You provided a description of what you would not consider a FOS which would seem to include non-symmetric examples such as 8-19 (no rotational symmetry, no definable center plane/axis) so I asked for clarification on that description. The example you provided does not clear up this discrepancy, nor does the introduction of other terms/descriptions which provide more questions than answers ("neither 'internal' not 'external'" and "surfaces that do not connect back to themselves").

Split the part from fig. 8-19 right in the middle of it. You will get 2 separate parts each with a portion of the original internal feature. The original pocket was a feature of size. Each of the split portions of it is not, and they represent my view on how a non-planar non-FOS looks like. I am pretty sure you get the idea, and if the terms I used fail to describe it properly, you probably can come up with a better definition of your own for this type of features.

There is no "difficulty to recognize" - profile of a cone considered by itself does not control "size" in any sense of the definition. Y14.5-2009 fig 4-45 if the conical feature has perfect form as pylfrm mentioned it will always satisfy the 0.02 profile tolerance. Where is the size control?

A cylindrical theoretical feature has size because all circular elements along it have size - identical size. You say that a profile control for a conical feature doesn't control size. Does it mean that the circular elements along a cone don't have size, or does it mean that any circular element along the feature can be produced at any random size and still conform to the drawing specification? To clarify what I mean: can the conical feature from fig. 4-45 be produced with the theoretically smallest circular element at 50mm diameter as produced, the theoretically largest element at 80mm diameter as produced, and a 49.5mm diameter circular element somewhere in between, and be within the profile tolerance?

Again I wouldn't say that the envelope(s) should have a defined spatial relationship with the true profile.

If the UAME is used as a primary datum feature simulator, such a relationship must be defined.

If the two holes you brought up as an example in your previous post are defined with basic spacing between axes and a directly toleranced diameter for each one, there is no defined true profile. Therefore the relationship with it cannot be defined for the UAME. My assertion about centroids was an attempt at an extension of the principle of two adjustable cylinders with fixed basic spacing for more complex features such as in fig. 8-19. I really don't see how definition of a centroid for a theoretical feature can be problematic and what rules are missing. If my use of the term "centroid" is inaccurate in the context of what we are discussing, consider a geometrical center for each (sub)feature from fig. 8-19, for which proportional expansion of the (sub)feature would result in uniform enlargement of distances from every point on the (sub)feature to the said geometrical center. An equivalent concept can be applied for (sub)features that differ from each other by shape and/or dimensions. (Edit: The erased part is irrelevant because I no longer think there might be any issue with the use of the term "centroid".)

Happy New Year

 

[Burunduk]

I of course meant the entire surface including the irregularity. A D-shaped feature of constant cross-section with a profile tolerance surrounding the entire D-shape including the flat would be an IFOSb not an IFOSa. The UAME would be D-shaped.

The flat would be considered along with the rest of the conical shape. You've sort of skirted around my question - you have intimated the importance of a single defined axis, however such a shape would not have a single defined axis and could not be created by revolving a fixed profile around a single axis. Do you believe it no longer has anything in common with a regular cone?

Forgot to address this: If the entire shape including the flat is controlled with a single all around profile tolerance then indeed it is type (b). It doesn't have a defined axis but neither do other irregular features of size such as in fig. 8-19. A geometrical center can still be found.

 

[pylfrm]

If the two holes you brought up as an example in your previous post are defined with basic spacing between axes and a directly toleranced diameter for each one, there is no defined true profile. Therefore the relationship with it cannot be defined for the UAME.

The diameter of the cylindrical surfaces was part of the true profile definition I provided for that example. If you want a more general statement, replace "true profile" with "basic geometry". That would include both true profile and true position.

I really don't see how definition of a centroid for a theoretical feature can be problematic and what rules are missing.

Consider a feature where the true profile is defined as follows:

planar surface at x = 1 with outward-pointing normal vector ( 1, 0, 0)
planar surface at x = 3 with outward-pointing normal vector (-1, 0, 0)
planar surface at x = 4 with outward-pointing normal vector ( 1, 0, 0)
planar surface at x = 7 with outward-pointing normal vector (-1, 0, 0)​

To apply your UAME interpretation, a rule would be needed to answer the following question:
[ul]
[li]Should this feature be divided up into separate portions to be scaled individually?[/li][/ul]

If the answer to the first question is "yes", rules would be needed to answer the following additional questions:
[ul]
[li]How should the feature be divided up? Slots of width 2 and 3? A slot of width 6 and a tab of width 1? Some other way?[/li]
[li]Should the centroids be determined based on infinite surfaces? Based on the nominal extent of the surfaces? Some other way?[/li]
[li]What should be the relationship between the scale factors used for the separate portions of the feature?[/li][/ul]


pylfrm

 

[Burunduk]

If you want a more general statement, replace "true profile" with "basic geometry". That would include both true profile and true position.

If by "basic geometry" you mean form(s) or mutual position or both, defined by the basic dimensions that are specified for the feature(s) in the drawing but not related to any datums, then we are along the same lines. For features defined with basic dimensions that specify the form, that basic geometry can be considered as the geometry being scaled to produce the UAME. I definitely disagree that an infinite expansion/contraction or "infinite offset" as was described, from the said basic geometry to the simulator or feature surfaces is possible under any realistic circumstances.

If I consider the 4 surfaces you described in isolation, with the specified directions of material (outward normal directions), as a single irregular feature of size used as a primary datum feature, then these are 2 slot features of widths 2mm and 3mm treated as one. The simulator of the actual mating envelope (primary RMB datum feature simulator) is two expanding tabs with their center planes at a fixed distance of 3.5 mm apart. It's the mating envelope simply because nothing else can mate with this feature. For more complex features the place of center planes can be taken by lines passing through the centroids of the subfeatures (the centroid is a point). The direction of the line is the direction of the feature's extrusion.

Based on this the answers to your questions are:
"Should this feature be divided up into separate portions to be scaled individually?" - yes.

"How should the feature be divided up? Slots of width 2 and 3? A slot of width 6 and a tab of width 1? Some other way?" - this was answered above.

"Should the centroids be determined based on infinite surfaces? Based on the nominal extent of the surfaces? Some other way?"
Based on the information provided, only center planes are relevant. The extent doesn't matter in this case.

"What should be the relationship between the scale factors used for the separate portions of the feature?" - they should be identical. each tab should stop its expansion when it is constrained by the high points of the slot surfaces.

 

[pylfrm]

If by "basic geometry" you mean form(s) or mutual position or both, defined by the basic dimensions that are specified for the feature(s) in the drawing but not related to any datums, then we are along the same lines.

I think that's pretty close to what I mean by "basic geometry", although I'd say it's partially defined by the basic dimensions and partially defined by the pictorial representation on the drawing.

What do you mean by "we are along the same lines"?

Based on this the answers to your questions are:
"Should this feature be divided up into separate portions to be scaled individually?" - yes.

"How should the feature be divided up? Slots of width 2 and 3? A slot of width 6 and a tab of width 1? Some other way?" - this was answered above.

I was mainly interested in general rules that you would use to answer these or similar questions for any considered feature.

"Should the centroids be determined based on infinite surfaces? Based on the nominal extent of the surfaces? Some other way?"
Based on the information provided, only center planes are relevant. The extent doesn't matter in this case.

I thought the centroid concept was intended to be a generalization that could be used on all features, but I suppose I misunderstood.

Perhaps you can imagine a modified version of ASME Y14.5-2009 Fig. 8-21 where the surface opposite datum feature A is at an angle. Would that shift the centroids toward the thicker part of the plate?

"What should be the relationship between the scale factors used for the separate portions of the feature?" - they should be identical. each tab should stop its expansion when it is constrained by the high points of the slot surfaces.

That constraint would depend on how much the other tab has already expanded. More detailed rules would be required here.


I suppose most of the above isn't particularly relevant for a single conical surface, so I'll try to get back to that subject.

Consider the following scenario:
A projected RFS position tolerance of diameter 0.2 is applied to an external feature. Its datum feature references fully constrain all six degrees of freedom. In some arbitrary coordinate system, the true position axis of the feature is defined to be x = y = 0 and the tolerance zone extent is defined to be 10 <= z <= 20. The actual feature surface is represented by a large number of well-distributed points with known locations in the same coordinate system. The actual feature is somehow known to satisfy the position tolerance.

If the feature is nominally cylindrical, the UAME can be determined as follows:
Consider the infinite set of all candidate UAME axes that satisfy the position tolerance. For each of these, determine the normal distance from the axis to each point on the actual feature surface. The axis that produces the smallest maximum distance is the UAME axis, and that distance is the UAME radius.

Can you provide a description of a procedure to determine your proposed UAME if the feature is nominally conical with a specified direction of taper and basic included angle?


pylfrm

 

[Burunduk]

I think that's pretty close to what I mean by "basic geometry", although I'd say it's partially defined by the basic dimensions and partially defined by the pictorial representation on the drawing.

What do you mean by "we are along the same lines"?

Of course, I meant basic dimensions + the outline of the feature as shown on the drawing, defining the form. I didn't mean a list of basic dimensions of unspecified geometry. What I meant to say is that my view on the matter of "basic geometry" and its implementation in the context of our discussion seems to be along the same lines as yours. Nevertheless, I must emphasize again that if the scaling of this basic geometry (where applicable*) to produce the UAME is treated as "uniform offset", this "uniform offset" towards the material of the feature can never become infinite or unlimited under any realistic circumstances. *For collections of features toleranced with +/- sizes, position, and dimensioned with basic spacing, the said scaling is not applicable because the basic spacing ("basic geometry") shouldn't be scaled.

I was mainly interested in general rules that you would use to answer these or similar questions for any considered feature.

The only general rules are those in the Y14.5 standard. In the 2009 edition, paragraph 4.17 provides the closest thing to "rules" - with only "may" wording those are probably guidelines rather than rules. I think the part that is most relevant for our discussion is the following, especially the bolded:
"(b) In other applications (such as an irregular shaped feature) where a boundary has been defined using profile tolerancing, a center point, an axis, or a center plane may not be readily definable. See para. 1.3.32.2(b) and Fig. 8-24. MMB and LMB principles may be applied to this type of irregular feature of size. When RMB is applied, the fitting routine may be the same as for a regular feature of size, a specific fitting routine may be defined, or datum targets may be used."

I thought the centroid concept was intended to be a generalization that could be used on all features, but I suppose I misunderstood.

It is a generalization that can be used for collections of closed features treated as a single IFOS: for a pattern of holes there are axes with fixed spacing as defined by basic dimensions, that should be the centers of the UAME simulator components. These axes can be viewed as lines passing through the centroids of the circular outlines of the envelope surfaces. For open features such as slots with their ends open looking for centroid points is not necessary. The fixed spacing of the simulator components should be between center planes. If the slots have closed ends but only their widths are used in the pattern of features of size that is treated as a single IFOS, still no centroid points are necessary and only center planes are relevant for the spacing of simulator/envelope components, just like in the previous case. If the pattern which is treated as IFOS consists of closed slots toleranced with profile all around including the rounded ends, centroids are relevant. The centroids can be for example equally spaced in one direction and aligned with each other in another direction.

Perhaps you can imagine a modified version of ASME Y14.5-2009 Fig. 8-21 where the surface opposite datum feature A is at an angle. Would that shift the centroids toward the thicker part of the plate?

No, it would not. Unlike the center of mass, the centroid is a point derived from a 2D outline of a closed shape. Used for the purposes of application of the basic spacing between UAME components of a single IFOS "multi-feature", It should be determined at any cross section where the entire outline of the "sub-feature" exists, or it can be determined from a projection of the "sub-feature" in the direction of its extrusion. I am talking here only about the theoretical (basic) geometry of course. The theoretical geometry of the feature(s) sets the spacing of the simulator components through the centroids determined from it.

That constraint would depend on how much the other tab has already expanded. More detailed rules would be required here.

Suppose that in fig 4-35 the pins were dimensioned with 5mm diameters, and the datum feature symbol was associated with the specification of "3X dia.5+/-0.1" instead of the circumscribed/inscribed cylinders or the distances. I would say that if that datum feature would be referenced RMB, all 3 holes of the simulator would need to contract simultaneously at an equal rate. If, for example, the spaces between pins were produced very accurately, the largest produced pin would constrain it's part of the simulator first, the second and third would follow according to actual produced size. If the actual spaces between pins were produced less accurate then the spaces could play a role in the order and nature of these constraints; for example, 2 or the 3 of the pins could only make line contact with the holes. Do you have some other interpretation in mind?

Consider the infinite set of all candidate UAME axes that satisfy the position tolerance. For each of these, determine the normal distance from the axis to each point on the actual feature surface. The axis that produces the smallest maximum distance is the UAME axis, and that distance is the UAME radius.

Can you provide a description of a procedure to determine your proposed UAME if the feature is nominally conical with a specified direction of taper and basic included angle?

The only reason why you were able to set a single value for the "smallest maximum distance" is the uniform size imposed by the form of the cylindrical UAME envelope. As you know not all IFOS are like that. Different examples are all IFOS type (b).

Among the infinite collection of candidate conical UAME envelopes the axes of which satisfy the position tolerance, the ultimate UAME envelope is the one that contacts the high points of the feature in a way that minimizes the distances between its own surface and the actual surface of the feature.

 

[pylfrm]

Unlike the center of mass, the centroid is a point derived from a 2D outline of a closed shape. Used for the purposes of application of the basic spacing between UAME components of a single IFOS "multi-feature", It should be determined at any cross section where the entire outline of the "sub-feature" exists, or it can be determined from a projection of the "sub-feature" in the direction of its extrusion.

I assumed you were talking about a centroid of a surface, not of a 2D outline. I see what you mean now though.

Suppose that in fig 4-35 the pins were dimensioned with 5mm diameters, and the datum feature symbol was associated with the specification of "3X dia.5+/-0.1" instead of the circumscribed/inscribed cylinders or the distances. I would say that if that datum feature would be referenced RMB, all 3 holes of the simulator would need to contract simultaneously at an equal rate. If, for example, the spaces between pins were produced very accurately, the largest produced pin would constrain it's part of the simulator first, the second and third would follow according to actual produced size. If the actual spaces between pins were produced less accurate then the spaces could play a role in the order and nature of these constraints; for example, 2 or the 3 of the pins could only make line contact with the holes. Do you have some other interpretation in mind?

Perhaps the simulator surface diameters should be minimized while remaining equal. Perhaps the sum of the simulator surface diameters should be minimized. ASME Y14.5-2009 doesn't really provide a clear answer. The "Means this" portion of Fig. 4-25 just says "smallest pair of coaxial circumscribed cylinders".

the ultimate UAME envelope is the one that contacts the high points of the feature in a way that minimizes the distances between its own surface and the actual surface of the feature.

I think this could be defined more precisely.

The requirement that the envelope "contacts the high points of the feature" leads to the question of which points are high points. I think it would be simpler to replace this with a requirement that no points of the feature violate the envelope. Suitable contact would be ensured by the minimization.

For the minimization, you would need a way to convert "the distances between its own surface and the actual surface of the feature" into a single value to be minimized. Perhaps you would minimize the maximum distance, the sum of the distances, or the sum of the squares of the distances. There are infinite possibilities here, but those three seem particularly worthy of consideration. I suppose it should also be specified that the distances are to be measured normal to the envelope surface.


pylfrm