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I had this properly explained to me a couple summers ago in a Curve Refresher coarse by a trainer, but can someone explain to me again why the number we get for a profile is essential the worst deviated nominal point doubled?

This is extremely hard to explain to our operators because it isn't clearly defined in the Y14.5 2009 standard about the overall result for profile.
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It's actually quite interesting. ASME Y14.5.1-1994, "the math standard", Par 6.5 (c) states

"For both unilateral and bilateral profile tolerances two actual values are necessarily calculated: one for surface variations in the positive direction and one for the negative direction. For each direction, the actual value of profile is the smallest intermediate tolerance to which the surface conforms. Note that no single actual value may be calculated for comparison to the tolerance value in the feature control frame, except in the case of unilateral profile tolerances."

Thus, per ASME Y14.5(.1) you cannot use one value (worst deviation doubled) as an actual profile value. It appears that CMM software does this as a way to spit out one result, but that is incorrect per ASME. Maybe there is something different when working to ISO? I'd be interested to find out.
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Didn't think of that, good catch. It is interesting to pinpoint where this 2xMax idea came from though and whether it is valid in ISO.
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I had a particular part where my results were disputed, so I reported the single number(worst x 2) and the min max(both were negative). Using your example, I believe they used the worst (.01) and reported the profile good because it was less than the .012 tolerance. Finally gave up on that argument. Clearly demonstrated in your example, the .01 violates the .006 PER SIDE tolerance zone. Thanks, I may steal this example.
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I rarely work with ISO but if memory serves me I believe that ASME reports the worst deviation doubled and ISO reports the Min/Max. IMO, you should always report min/max regardless of the standard. The doubled worst deviation reporting does nothing for a machinist and/or analysis and you can report a number that is within the tolerance value but fails because the deviation exceeds the min/max in one direction on a profile with unequal distribution.

So yeah, 2 results is the way to go IMO.
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I've reported the one result method for 15 years now and never once had a problem explaining the issue to operators. That's how they taught us in training and until today I didn't even know that Min/Max was an option. But I might be a tad more helpful than others because if I get a profile out, I'll print out a graph to show what's going on or i'll give basic reference dimensions if they're on the print.
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I like reporting the deviation from basic as well, as a reference to the operator, so he/she can see what's really happening.
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My reasoning has always been to think of reporting of the profile callout as being a zone callout much like true position is.
Reporting twice the deviation maintains the same unit of measure as is used in the call out.

If you have a zone that is 0.1 then either side of the zone is only 0.05.

If the result was not doubled, then 0.051 result would be out of tolerance on a 0.1 call out.

The other problem with reporting profile is that depending on the curvature of the geometry that is being measured, even a plus or minus result is not necessarily going to be able to demonstrate what is going on with the surface.

Consider if you have a part where the profile of the part extends around the entire periphery of a part and is tied to a bore through the center as its main locational datum. Now let us assume the profile was machined with the location off by some amount in one axis.

The result would be a profile that had an equivalent plus stock on one side and minus stock on the other. Depending on the part geometry, it could get even more confusing as it is possible there are other issues with the profile besides the ones caused by location.

Due to these factors I find it is generally not very helpful to report min / max values. In cases where the machinist or engineer is attempting to get a better understanding of what is going on I find it is far more helpful to either provide a graphic that shows the profile if using a line profile or use cad evaluation in the case of a surface profile. This gives a much better visual representation of what is actually going on rather than relying on a min max value which can just inject further confusion into things.
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I think you should always report more than just the one profile number. We had an issue where we were not permitted to report items on the CMM report that were not on the print. We were reporting only profile. With Calypso doubling the result on profile, the tooling engineer was making adjustment in the amount of what the profile was. Only to find out it didn't change. What was happening was the shift put the profile out in the opposite direction by the same amount. The tooling guy didn't know this. The inspector didn't know either. So reporting more than just the profile is extremely helpful especially when trouble shooting.
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Quick update - I just read that ASME Y14.5.1 - 2020(?) will be the new revision of the math standard. Supposedly, in the new rev, there will be a new definition regarding the "Actual Value" of a Profile tolerance. Keep an eye out...
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