A measured surface is never flat. To serve as a datum, for example for the position of a hole, it is associated with an ideal plane. How this is done was newly defined in ISO 5459:2024: older measurement programs often still use the previous default. The example in this article is measured by tactile probing, with a stylus ball on a coordinate measuring machine.
On the left you can switch between the current standard ISO 5459:2024 and the withdrawn 2011 edition. On the right you set the association criteria. To get started, play the sequence with the “Burr” profile and switch between [GE] and [CE] in step 4.
At the edges of the extracted line there are often no prominent peaks to place the straight lines on. The convex hull drops steeply there and distorts the evaluation. The angle of the placed straight lines is therefore limited.
The basis is the Gaussian line of the extracted line, the range δ of the deviations from it and the size D of the feature. D is the largest distance between two points of the projected area: in the section it is the length of the line, for a rectangular plane the diagonal. A placed straight line may tilt by at most 4·δ/D rad relative to the Gaussian line. Only for unusually large form deviations over a small extent, where 4·δ/D exceeds 0.1 rad, does the standard fix the angle at 0.1 rad (5.73°).
Three fictitious examples: the first two show a typical surface, the third a small surface where the cap of 0.1 rad applies.
The straight line is limited to 0.002 rad, that is a drop of 10 µm over 5 mm. At the edge the filtered line lies 10 µm above the extracted line.
The tilt stays below the limit. The hull follows the edge unchanged, and at the edge the filtered line lies on the extracted line.
The straight line is limited to 0.1 rad, that is a drop of 20 µm over 0.2 mm. At the edge the filtered line lies 10 µm above the extracted line. Such surfaces are hardly suitable as datums; the standard advises against this case.
The skin model is the real (that is, non-ideal) surface of the part as the measuring instrument captures it: with waviness, roughness and form deviation. A datum on this surface, however, must be ideal, otherwise neither a coordinate system can be built on it nor a tolerance zone aligned to it.
A section through the skin model gives a line that stands in for the part surface in the graphic. To this line we associate a straight line, which stands in for an ideal plane.
Two steps are needed before the ideal line can be associated. The stylus ball captures the surface and rides on the crests, narrow grooves stay out of reach: a mechanical, morphological filter. Then follows the filter defined in the standard, in our example [EM]. Only on the filtered feature is the association carried out. An association always requires an objective function and a constraint.
G, Gaussian: The sum of the squared distances of all points is minimal. Every point counts equally, the orientation of the line is robust against single outliers.
C, minimax (Chebyshev): The largest deviation is minimal. The orientation of the line is therefore determined by the extreme points.
None (M): The line may cut the profile, points lie on both sides.
E, outside the material: The line touches the surface from outside, like a locating face.
I, inside the material: The line lies entirely in the material and touches the lowest points.
Objective function and constraint give the symbols GM, GE, GI, CM, CE and CI. For association without constraint, the line can also be shifted in parallel (material offset, ISO 5459:2024, Table 14): G+ shifts the free Gaussian line outwards until it touches the outermost point, G− inwards. GE and G+ look alike but give different results, as the standard explicitly points out. Whether a drawing needs one of these indications or the default is enough is what we settle in the drawing review.
If the datum section carries only the datum letter, the default of the standard applies. For a single planar datum ISO 5459:2024 newly defines first the filter [EM] and then the association criterion [GE]: of all lines outside the material, the one with the smallest sum of squared deviations. The standard justifies the change to [GE] with the lower sensitivity to edge effects of the datum feature.
For the plane, ISO 5459:2011 specified the minimax line outside the material (CE) at this point. It rests on two high points and, even without a preceding filter, behaves roughly like a plane placed against the part, but causes the problems with outliers at the edges described above.
For the inspection laboratory this means: for every drawing, check which edition applies and which filter and association the measurement program actually computes. If the software only offers “Gaussian, shifted”, that is [G+] and not [GE]. In CMM programming we set the criterion explicitly instead of relying on the software default. With small deviations the results hardly differ; with large ones they can overturn an inspection decision.
In dimensional inspection we document the criterion used in the report so that the result remains traceable.
The association criterion does not belong on the datum indicator at the part. Only the letter appears there. It is indicated in the datum section of the tolerance indicator, in square brackets directly after the datum letter (ISO 5459:2024, Clause 8). Without brackets the default [EM][GE] applies.
Ø 0.1A
Only “A”: datum from the plane with the default filter [EM] and the default association [GE].
Ø 0.1A[GM]“A[GM]”: Gaussian without material constraint.
If an association method is to apply to the whole drawing, it is stated in or near the title block as a drawing-specific default, for example “DS ISO 5459[CB1,5][GM]”. It then applies to every datum unless the datum section says otherwise. Whether these indications on your drawing are appropriate, complete and unambiguous is what we check in the drawing review.
