Calculating TP of datum pattern?

[Einzel]

Given the attached example, how would the true position tolerance be calculated on the pair of thru holes? Is it simply the error in their linear basic distance or does it have to do with their three dimensional forms (i.e. perpendicularity as well)? And a follow-up: where would the alignment be located for any other feature when referencing these two datums? Would it be the centroid between the two holes using the line between them as a skew direction?

 

[greenimi]

What would be the mating components (pins/ studs, screws) that goes inside these holes?
Could you, please, provide the mating components sizes and tolerances?
Position in general includes perpendicularity along with mutual relationship between the holes, so no concern here.

 

[Burunduk]

Assuming drawing standard ASME Y14.5:

Is it simply the error in their linear basic distance or does it have to do with their three dimensional forms (i.e. perpendicularity as well)?

The position tolerance controls both their mutual location (distance) and orientation perpendicular to datum A (and parallelism to each other). This is preferably achieved by the surface interpretation of the MMC position control (virtual condition boundaries that must not be violated).
But first, the two holes need size tolerance, which is not specified.

And a follow-up: where would the alignment be located for any other feature when referencing these two datums?

The 2 holes as datum feature B establish two datum axes. Assuming that the controls of other features on the part reference the |A|B| datum reference frame, 3 perpendicular planes of the DRF are established. One of them is datum plane A. The other 2 intersect at any of the 2 datum axes. One of them is also coincident with the axis of the other hole.

 

[Woosang]

One of them is datum plane A. The other 2 intersect at any of the 2 datum axes. One of them is also coincident with the axis of the other hole.

Burunduk,

Your interpretation of DRF looks that the origin of DRF is located at the axis of either one of the hole.
But, shouldn't the DRF be located in between the two holes, similar to pattern of holes as datum feature in Figure 7-18 of Y14.5-2018?

 

[Burunduk]

Woosang,
I think the DRF can be established the same way as in fig. 4-9 of Y14.5-2009. Imagine that the position control for the holes that reference |A|B|C| was in reference to |A|B-C| instead, I think it would be a very similar case to the OP.

Edit: just in case the above might be misleading for someone, the equivalence between the |A|B|C| and |A|B-C| for fig. 4-9 which I mentioned is only in the way the final established datum reference frame (three planes as measurement origin) looks like (ie where it is located and how it is oriented). There is no equivalence in the order of engagement of each datum feature simulator with the part, and not in the role of each datum feature in constraining degrees of freedom.

 

[Einzel]

The tolerance was excluded as I was trying to get a spatial explanation, primarily (and also cause I forgot to add it to this example). I was mainly concerned to know if the holes were measured as 3D features rather than the usual 2D circle on a base plane as I'm more used to. My understanding of the true position output was normally to a third plane located equally between the two holes of Datum B so that each hole would have (essentially) the same true position error, which I believe is what Woosang is saying?

 

[Burunduk]

As a matter of fact, practically, the location of the origin of measurement does not matter that much. It can be on the true position axis of one of the holes or right in the middle of the distance between them.
Suppose that there is a third hole somewhere controlled for position with reference to |A|B|. What you measure as the position error is the deviation of the feature axis from true position (in terms of axis interpretation). The exact coordinates of that true position (the center of the tolerance zone) do not matter because what you check is conformance to a cylindrical tolerance zone, not the values of linear distances from the origin.

 

[chez311]

Einzel/Woosang,

The "location" of the origin and DRF is really less important (and if you ask me quite arbitrary) than the constraint of DOF relative to said DRF and relationship between datum features and their associated simulators. If a particular origin is desired it can be specified, but really as long as your measurements are taken from a consistent reference it matters little.

Given the attached example, how would the true position tolerance be calculated on the pair of thru holes? Is it simply the error in their linear basic distance or does it have to do with their three dimensional forms (i.e. perpendicularity as well)?

I was mainly concerned to know if the holes were measured as 3D features rather than the usual 2D circle on a base plane as I'm more used to.

Note - assuming you're going by the newer ASME standards (Y14.5-2009+) "true position" now refers to the theoretically exact location of a feature, to be defined with basic dimensions. "Position tolerance" is the proper terminology when referring to the tolerance of position. Additionally there can be no "error" in a feature's basic dimension(s) - by definition basic dimensions are theoretically exact. The position tolerance defines a tolerance zone (related to your datum features with basic dimensions) which allows a certain amount of variation (position error) in the feature(s) of interest but we would no longer use the term "basic dimension" to describe this variation/error.

Position is a 3D control if applied to a 3D FOS (ie: hole or boss) and controls a combination of orientation (perpendicularity) and location. If one wanted to apply position to only a single 2D element it would have to be specified as such. Unfortunately what you are probably used to, hence the question, is that many CMM setups only sample a feature at a single z-height which does not take into account orientation (perpendicularity) error - I would consider this improper and would personally push for a minimum of 2x z-heights (3x where feasible or more on critical/tight tolerance/high length to width ratio features). Unfortunately the reality of the situation is that many people do not do this.

 

[Einzel]

I probably should've phrased my error sentence differently. I meant error *from* the basic. i.e. the measured distance is 9.8 then each hole would have a ToP of 0.2.

And I was used to a 2D ToP in the past mostly because our software, controllers, and machines were so aged that asking for more was a large task. Also the prints being used were 30+ years old. Thank you for the clarification.

 

[chez311]

I meant error *from* the basic. i.e. the measured distance is 9.8 then each hole would have a ToP of 0.2.

Simply measuring the distance between as produced feature axes makes a few assumptions that may or may not be reasonable depending on the tolerances involved and the configuration of the features. First it assumes perfect orientation and form. Second, it falls apart (and/or gets unnecessarily complicated) pretty quickly when a pattern of more than two features is considered.

In your case there might be some fitting required since not all DOF are constrained (and especially so since its specified MMC) in the position tolerance for the 2X holes but below should give you an idea of how those assumptions come into play. On the left is the situation you described with two features of perfect orientation for which the assumption is valid. On the right is two features with orientation error for which the assumption is not valid and the measured distance "between the features" would give an incorrect result. The "distance between axes" measurement shown is if the measurement is done with the 2D measurement you describe (1x z-height sampling).

Note this is shown in terms of the axis interpretation, as you have specified MMC controls the axis of the feature can be evaluated but the surface interpretation takes precedence - however only calculating actual value of the surface interpretation just tells you essentially how close you are to violating virtual condition. This is good for a pass/fail check but tells you little information about the process so very often instead the axis is used during measurement. It can with some creativity, and I outlined what I thought might be an acceptable approach in the thread (

https://www.eng-tips.com/viewthread.cfm?qid=460445).

 

[Woosang]

Burundak/chez311,

As a matter of fact, practically, the location of the origin of measurement does not matter that much. It can be on the true position axis of one of the holes or right in the middle of the distance between them.

The "location" of the origin and DRF is really less important (and if you ask me quite arbitrary) than the constraint of DOF relative to said DRF and relationship between datum features and their associated simulators. If a particular origin is desired it can be specified, but really as long as your measurements are taken from a consistent reference it matters little.

As both of you said, I understand that the location of DRF origin in this case may not affect on determining the functionality of the features.
But often there is argument between CMM guys on where to put their coordinate system.
Because, if the origin is at one of the hole axis, that hole is never out of tolerance, while if the origin is in the middle between the two holes, that's not the case.

If one has to have only one interpretation regarding location of DRF origin, what would you say?

 

[chez311]

Woosang,

Whatever origin you choose should be fixed in relation to the theoretical simulator geometry. What you described can happen regardless of where the chosen origin is if you both use only a 2D single Z height sample as well as do not attempt a best fit for both (or all) features in the pattern which attempts to find the minimum position error. This is a result of the free (unconstrained) DOF in situations like OPs.

For example on the figure I shared on (15 Jan 20 21:46) on the left (perfect orientation) if you assume the simulator for the hole on the left should be coaxial with the as produced hole it will show zero position error while the hole on the right will show 0.4 - minimizing both will result in the variation shown of 0.2 for both. For the case on the right (both holes have orientation error) it does not matter how the geometry is optimized in relation to the simulators - both holes will always have nonzero position error, the caveat being if only a single z-height 2D sample is taken. In that case optimization/best-fit will result in both holes showing 0 position error - which of course can be shown to be incorrect when the 3D geometry is considered and shows the issues with such simplified measurement.

 

[3DDave]

Any reference to a datum feature with an MMB OR LMB modifier that is established using MMB has the potential for an infinite number of relevant locations that can be derived from the actual features. Since this example does not include any reference, there is no use in guessing what that derivation might be.

 

[Burunduk]

Because, if the origin is at one of the hole axis, that hole is never out of tolerance, while if the origin is in the middle between the two holes, that's not the case.

Two important things should be clarified:

1. The holes are not controlled for position relative to the |A|B| DRF, they are controlled relative to the |A| DRF, which a single plane.
The position tolerance of the holes and their position error is not related to the origin (DRF) established from datum features A and B, which is the origin that was asked about in the OP: "where would the alignment be located for any other feature when referencing these two datums?"

2. If an origin for measurements of other features (not shown in the posted figure) is chosen at the true position of one of the holes - it doesn't mean that it is coincident with the actual produced hole axis (and as chez311 noted, it can't be, unless the hole is produced with perfect orientation). It is coincident with the center axis of the datum feature simulator. Since the discussion is in the context if CMM measurement, I don't know how beneficial it is to consider the datum feature simulator, so it can be looked at as the true position of that datum feature hole - which is generally speaking the theoretical location and orientation axis of that hole. For the true position in this case (related to the position tolerance of the holes), only the orientation is defined relative to the datum as datum feature A doesn't constrain translational degrees of freedom in the relevant directions. So the two true position axes should have a fixed spacing between them but are not required to have a specific location (as a pattern), to the referenced datum. Again: the control is all about orientation and spacing and nothing else.

 

[Woosang]

the control is all about orientation and spacing and nothing else.

Thanks Burunduk, you are correct. My previous wording you quoted was totally wrong.

But I still doudt that the location of origin may matter in CMM measurement, if the other features are toleranced referencing two holes as datum feature B like in OP's case - e.g. side surfaces have profile tolerance with A|B.
When I have free time, I will make some simulation with 3D models and get back.

 

[chez311]

Since the discussion is in the context if CMM measurement, I don't know how beneficial it is to consider the datum feature simulator, so it can be looked at as the true position of that datum feature hole - which is generally speaking the theoretical location and orientation axis of that hole.

I would agree. I am used to speaking in terms of simulators, but you could pretty much replace anywhere I have mentioned "simulator" with "true position" if that fits the paradigm better since of course by definition, unless otherwise modified, your simulator is located at true position.

One could also think in terms of the RAME, since the tolerance specified is MMC and maximization* of the RAME of both holes would result in minimization* of the actual value for position error of both holes:

actual value = size_MMC - size_RAME

*Edit - minimization of the actual value being the "most negative" ie: the more negative the more clearance to VC. A hole offset to the maximum extent allowed by the position tolerance will have a surface interpretation actual value which is positive and equal to the position tolerance in the FCF (t_0). A hole at MMC and perfect position will have an actual value of zero, and at LMC and perfect position will have an actual value of size_MMC - size_LMC