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Mathematical definition: multiple datum feature-primary on a cylindrical surfaces

Mathematical definition: multiple datum feature-primary on a cylindrical surfaces

Mathematical definition: multiple datum feature-primary on a cylindrical surfaces

(OP)
What is the mathematical definition of A-B as multiple datum feature?

I do understand what is the axis of UAME for datum feature A and how to determine that. The same for datum feature B, but what is the axis of A-B (compound) and how to determine/ explain what means? –see fig. 4-25 /2009






RE: Mathematical definition: multiple datum feature-primary on a cylindrical surfaces

If you understand how to get a datum axis from a single datum feature (from the UAME), then it's almost the same for the combined datum features. It's a single datum axis derived from the smallest pair of coaxial circumscribed cylinders. Digest that sentence and I think that's what you're looking for.

John-Paul Belanger
Certified Sr. GD&T Professional
Geometric Learning Systems

RE: Mathematical definition: multiple datum feature-primary on a cylindrical surfaces

aniiben,

I don't think the ASME standards have a mathematically rigorous and general explanation for datums established from multiple features of size.

Quote (Belanger)

It's a single datum axis derived from the smallest pair of coaxial circumscribed cylinders.
What does "smallest pair" mean? Should the sum of the diameters be minimized? Should the diameter difference be held fixed at 5? How would the answer differ if the two features had unequal total size tolerances?

pylfrm

RE: Mathematical definition: multiple datum feature-primary on a cylindrical surfaces

pylfrm -- The two circumscribed cylinders don't have to be of equal size, or size tolerance. But they must stay coaxial. ("Sum of the diameters"? Not sure why this would even enter the picture.)

And the "smallest pair" means that the two must close down until each makes high-point contact with the actual part. So differing size tolerances would not matter; just close down until your grab each diameter. But you have to close down while always keeping these envelopes coaxial.

John-Paul Belanger
Certified Sr. GD&T Professional
Geometric Learning Systems

RE: Mathematical definition: multiple datum feature-primary on a cylindrical surfaces

I think pylfrm is asking for the "how"...

Equal rate of closing? Absolute rate? Percentage of the total allowed variation per unit time? 2thumbsup

If two cylindrical datum features have different nominal sizes and different tolerances, is the clamped-up position truly determinate in the fixture? If there's no prescribed "how", there are going to be multiple possibilities.

RE: Mathematical definition: multiple datum feature-primary on a cylindrical surfaces

Quote (Nescius)

If there's no prescribed "how", there are going to be multiple possibilities.

Yep, that's basically the point I was trying to make. Given OP's use of the word 'mathematical', I suspect they may be wondering along the same lines.

pylfrm

RE: Mathematical definition: multiple datum feature-primary on a cylindrical surfaces

I couldn't find it in the history of my replies, but I am pretty sure I posted attached figure before in this forum. It shows how ISO deals with the problem. The figure comes from ISO 5459:2011, and although does not solve all the problems that could potentially happen during datum axis derivation/simulation (especially when hard gaging is used to simulate datum features), it offers much more math details comparing to what has been given in ASME.

http://files.engineering.com/getfile.aspx?folder=a...

RE: Mathematical definition: multiple datum feature-primary on a cylindrical surfaces

pmarc,

Interesting approach. It seems fairly robust at first glance. Always good to learn about the ISO side of things, so thank you for posting that.

pylfrm

RE: Mathematical definition: multiple datum feature-primary on a cylindrical surfaces

(OP)
Thank you pmarc,
That is very helpful.
And since some parts with the above A-B callout are measured on CMM which use by default ISO language then your posting is even more relevant to me.

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