One factor not considered in Y14.5.1 et al, is the concept of epsilon, which is found elsewhere in mathematics. It represents the smallest noticeable delta. Those results that are less than epsilon away from the ideal value are considered equal to the ideal value.
I suspect that small amounts of curvature are easily detected for sufficiently small epsilon based on the above local size definition. Whether that epsilon is important to most or not is immaterial to the definition.
There is also the inspection tolerance problem that was poorly handled in the gaging standard. The precision of the inspection equipment needs to be in proportion to the desired approach to the dimensional boundary, not to the tolerances applied to the features.
If it's important that a dimensional limit not be exceeded it doesn't matter how large the target is but how close to the edge of the target the acceptable measurement is. Look at photo-finishes for horse racing. Horses are big and the length of the track is pretty big too, but the measurement technique is such as to discern very small differences.
Pmarc's assessment is correct as usual. The ISO definition adds additional constraints, to make the local sizes fully defined.
There is another aspect of the local size definitions that comes into play when form error is present:
The first graphic is one interpretation of "any individual distance at any cross section". I've tried to indicate the diameters at which the surface is directly opposed. Note that these diameters do not pass through a common point - each one is independent of the others. This would be straightforward with a 2-point measuring device (mic) but difficult and time-consuming with a CMM.
The second graphic illustrates the ISO definition that pmarc described. Each 2-point diameter passes through the center of the least squares circle. Note that the surfaces are not directly opposed at these diameters. This would be difficult with a 2-point measuring device but straightforward with a CMM.
The two methods clearly give different results, and the difference would correspond to the relative magnitude of the form error.
So, reading through the debates, I'd like to add another hypothetical monkey wrench/question into the works.
Assuming the dimensions are in millimeters, 30 +/- 0.3 would allow a manufacturer to use potentially use 1.1875" stock, assuming the material requirement allowed for such a standard size (29.7 mm -30.3 mm = 1.1693 INCH - 1.1929 INCH), and that the tolerances for that standard size still fell within the design intent on the drawing. If thats the case, then would Rule #1 still be applicable, as stock material provided in the as-finished state is exempt from Rule #1? Or do we always assume Rule #1 is in effect unless we explicitly state that the material comes from a raw stock sizing?
Nobody is forcing manufacturer to use unfinished stock size, so unless the drawing explicitly states "stock" (which it doesn't), the question is irrelevant.
"For every expert there is an equal and opposite expert"
Arthur C. Clarke Profiles of the future
2.7.2 Form Control Does Not Apply (Exceptions to
Rule #1)
The control of geometric form prescribed by limits of
size does not apply to the following:
(a) stock, such as bars, sheets, tubing, structural
shapes, and other items produced to established industry
or government standards that prescribe limits for
straightness, flatness, and other geometric characteristics.
Unless geometric tolerances are specified on the
drawing of a part made from these items, standards for
these items govern the surfaces that remain in the asfurnished
condition on the finished part.
(b) parts subject to free-state variation in the unrestrained
condition. See para. 5.5.
It appears that you are aware of the previous post exception regarding Rule #1 and stock based on your question.
Stock should be also be identified as such as mentioned below.
(a) Each dimension shall have a tolerance, except for
those dimensions specifically identified as reference, maximum,
minimum, or stock (commercial stock size). The
tolerance may be applied directly to the dimension (or
indirectly in the case of basic dimensions), indicated by
a general note, or located in a supplementary block of the
drawing format. See ASME Y14.1 and ASME Y14.1M.
What is your question regarding the OP flatness question considering straightness (or not considering straightness) regarding this thread? (to me, the lengthy thread with tangent topics obscures your question)
