Reality of physical geometry supports the use of opposed points vs random points.
Per Y14.5-94, Section 4.5 Establishing Datums, (4.5.3 and others) "A machine element that is variable in size (such as a chuck, mandrel, vise, or centering device) is used to simulate a true geometric counterpart of the feature and to establish the datum axis or center plane." For a cylindrical feature of size, the true geometric counterpart (TGC) is a perfect cylinder; if the datum feature of size is referenced RFS, then you find the largest inscribed cylinder which makes maximum contact with the wall of the hole. This is repeatable.
While understanding the industry norm of using CMMs of various types, the fact remains that there is a greater inherent error in a CMM-established datum from the raw feature than there is by using a TGC at least as the basis of establishing a CMM datum.
Anyone that has ever done precision metrology on radial elements has seen that a seemingly "perfect" radial segment in fact is composed of multiple radial segments. Using the 3-point method (or 6 or 10, or whatever) to find the center of the arc means that you will end up with multiple arc centers and radial measuremnts. Which, then, do you select? The one closest to what you want, regardless if it is representative of the majority of the feature? Then, add a second set of 3 points to establish the axis of the "cylinder"?
I've tried to illustrate this in the file at the end of this link:
I was at the knife-point of a project where this was a critical factor, costing significant $$s.
I don't dispute that CMMs are useful tools, even necessary in many cases, however I do get rather frustrated at the CMM salesman's mentality / pitch that you just need a few points to simulate a surface adequately to represent its functionality ... and THAT is what ASME GD&T is intended to do ... represent the design intent / functionality. There is considerable ongoing dialog on this site & in other venues as to whether the design intent or manufacturing process or the inspection process is to be predominant in the GD&T application. The standard specifically talks about engineering and omits reference to manufacturing and inspection. Perhaps, in that light, metrology should be focusing on how to achieve the intentions of the design documentation as established with GD&T rather than expecting GD&T to accommodate the inconsistencies of metrology. I recognize that the two aspects are symbiotic in nature, but within the ASME standard, design is paramount. ISO offers the opposite, a GD&T standard that focuses on inspection rather than design intent.
The fact that a center point or axis established by a radial segment without directly opposed points is unrepeatable should guide people to recognize that it is a fundamentally flawed process as far as ensuring design intent. As with any written work (standard or literary), the text itself gives you a substantial part of the knowledge, but you have to extend, combine and contrast ideas to get a full understanding of the content.
OK, I've beaten my head enough for today.
Jim Sykes, P.Eng, GDTP-S
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