Circularity - definition

[pmarc]

Circularity as stated in paragraph 5.4.3(a) of Y14.5-2009 is:
"[...] a condition of a surface where for a feature other than sphere, all points of the surface intersected by any plane perpendicular to an axis or spine (curved line) are equidistant from that axis or spine."

Take a simple cylinder, but produced with maximum possible (within limits of size) derived median line straightness error and imagine that this cylinder is perfectly round in each cross-section. My question is following: in the light of cited definition, will this as-produced cylinder be treated as perfectly circular or not? What do you, guys, think?

 

[Belanger]

Your post says that "this cylinder is perfectly round in each cross-section," so I'm not sure what you mean -- you've essentially said that it already conforms. Are you getting at something to do with how the cross-sections are taken?

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

http://www.gdtseminars.com

 

[pmarc]

J-P,
Yes, I am getting at something that especially has something to do with the relationship between cylinder's surface and the axis of the element.

Imagine that I somehow manufactured a perfectly round and straight pin and I bent it in subsequent operation, so there is a certain amount of straightness error, but the pin stays round. Would that pin be measured perfectly circular according to the definition?

 

[ALK35]

pmarc,

By definition, I would say it sure would. Circularity is each line element sperately, unlike if there were a straighness (on the FOS) or cylindricity callout on that cylinder.

 

[axym]

pmarc,

I would say that the bent part would meet the definition of perfectly circular. The cutting planes for the circular elements must all be normal to a spine. The spine can be a curved line, and the choice of spine is completely arbitrary.

The spine does not need to have any particular relationship to the axis of the cylinder, but the axis would generally be a decent first approximation of the optimal spine. The derived median line would be an even better approximation.

Evan Janeshewski

Axymetrix Quality Engineering Inc.

http://www.axymetrix.ca

 

[pmarc]

Evan,
Based on which statement from the standard you claim that cutting planes must be all normal to a spine? From Circularity definition I rather conclude that cutting planes for a cylinder must be perpendicular to an axis of the cylinder (which according to 1.3.28 definition is an axis of unrelated actual mating envelope unless otherwise specified) and normal to spine for features other than cylinders (like sine wave for example). I guess this is crucial thing to solve my problem. If you convince me that the cutting planes for a cylinder are always normal to actual spine, I will have no further questions.

 

[axym]

pmarc,

The Circularity definition is a bit of a can of worms, so I'm not sure that you're going to get the definitive answer you're looking for.

I got the part about the cutting planes being normal to a spine from Y14.5.1M-1994 6.4.3 (a):

"A circularity tolerance specifies that all points of each circular element of the surface must lie in some zone bounded by two concentric circles whose radii differ by the specified tolerance. Circular elements are obtained by taking cross-sections perpendicular to some spine. For a sphere, the spine is 0-dimensional (a point), and for a cylinder or cone the spine is 1-dimensional (a simple, non self intersecting, tangent-continuous curve). The concentric circles defining the circularity zone are centered on, and in a plane perpendicular to, the spine."

One could argue that the 5.1 idea of taking cross sections perpendicular to a curved spine comes out of nowhere, and does not logically follow the way that circularity was defined in Y14.5M-1994. This was "for a feature other than a sphere, all points of the surface intersected by any plane perpendicular to an axis are equidistant from that axis". The issue is clouded by the inconsistent use of the term "axis" in Y14.5M-1994. In most contexts, the term "axis" refers to the axis of the AME and is by definition perfectly straight. But Straightness was defined as "a condition where an element of a surface, or an axis, is a straight line". So the term "axis" was also occasionally misapplied to refer to a line that can be curved.

I agree that the reference to the spine (curved line) in the Y14.5-2009 definition didn't solve the problem. It isn't clear whether the spine refers to the as-designed center geometry of the feature or the curve defining the cross sections on an as-produced feature.

Functionally, I think it makes sense that the Circularity cross-sections follow the curvature of the as-produced feature. Otherwise, Circularity would end up indirectly controlling the straightness of the feature - the cylinder you described in the OP would have imperfect Circularity because it was bent, not because the cross sections were not circular. But the definitions in Y14.5-2009 don't give us a rigorous path to that result.

Evan Janeshewski

Axymetrix Quality Engineering Inc.

http://www.axymetrix.ca

 

[pmarc]

Evan,
Thanks for reply.
I also think that functionally it makes more sense that the Circularity cross-sections follow the as-produced curvature of the feature, however Y14.5-2009 definition does not help at all to get to this conclusion. The term "axis" may suggest, or actually (in absence of any additional comment) is implying, that it is the axis of the AME, thus my question. I was also aware of Y14.5.1 interpretation of Circularity - question is, whether other Y14.5 users will ever look to that interpretation when applying or especially inspecting Circularity.

And last but not least, assuming that I agreed for Circularity cross-sections being perpendicular to a spine and not to axis of the AME, how should Circularity inspection look like? If I use dial indicator to check as-produced banana-shape cylinder, should the orientation of the indicator relative to inspected surface change at each cross-section? How should I technically find/determine actual spine at all? Any ideas?

 

[Belanger]

I don't see much of an issue here. The standard says nothing about a "cylinder," just about a plane which must be perpendicular to the axis (or spine) at the various points.
Consider a radiator hose -- we can check its circularity, but we'd have to adjust the planes as we move along the (as-produced) axis.

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

http://www.gdtseminars.com