# Measurerement vs. theoretical element: Theory of metrology and my confusion

Discussion in 'Sampling, Standards and Inspection' started by 00253, Sep 22, 2019.

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1. ### 00253New Member

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I have recently joined a small quality department in a starting company. We try to do as many measurements as possible on CMM. Last week, we measured a diameter on a series of pieces, many of which turned out to be nonconforming. There was no circularity check in the part drawing, so we only found out later when analyzing that the pieces were clamped too hard during machining and got elliptical (aluminum alloy).

It was Friday (brains fried) and we found ourselves baffled at this realization:
When you measure a diameter with a caliper, you repeat the measurement at different positions in relation to the circumference ("at angles") and average it. This is a direct measurement (is it?) which can also reveal an issue with the circularity. But then, through a train of thought, imagine that that circularity is completely out of bounds — the shape of the hole is a mess, and you still perform the measurements, and average them. Question #1: How does the measured "diameter" relate to the theoretical element of circle? How to interpret the measured diameter? You could be measuring a square hole and the circumference could come out fine. I can't get my head over it. This issue stands even if you would describe the hole that's to be measured as "circular enough". Diameter is a property of a circle, and you're measuring a real linear dimension that doesn't relate to any REAL circle.

Question #2: How does this translate to CMM? You measure some points on the """circumference""" and use something like the smallest squares method to find the approximate circle. Again, how does the diameter of this theoretical circle relate to the real thing?

We do have a "general" tolerances that apply to unquoted dimensions and an acceptable circularity is actually defined, but that's not the issue here.

I'm sorry if I'm being too dense. We realized that we may be overthinking the whole thing, but then again, we would like to get this straight, more so because we don't have too much training in theoretical metrology. We were thinking — when we measure a diameter, should we also evaluate the related circularity? Is there any literature you guys would recommend to get me out of this Lovecraftian madness? Thank you for your time...

2. ### Andy NicholsModeratorStaff Member

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Welcome: Can I ask is the blueprint using some type of GD&T like ASME Y14.5 or similar? If not, then engineering might need to go back to some basics, first.

Is roundness and/or cylindricity called out? Or is it "assumed" that the form of the round feature should fall within the general tolerance of size of the feature. A clip from the way the feature is drawn might help, nevertheless:

When using calipers, you are hoping the part isn't oval, isn't eccentric and isn't also tapered in form. When making cmm measurements, as you say, making multiple touches helps since you are getting closer and closer to a "mean" circle, which becomes closer to the true dimension. This then becomes limited to the time it takes etc.

However, depending on WHERE you measure the feature the influences of taper/cylindricity etc come into play. The number of touches comes from a limitation of some touch probes' internal mechanisms and the way they work. A "scanning" touch probe, such as Renishaw "Revo" gives a true(r) value.

Last edited: Sep 23, 2019
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3. ### Bev DModeratorStaff Member

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We should never average these types of measurements. the Customer never experiences the average.
The drawing should call out the necessary dimension based on the use of the part. If it doesn't contact your Customer to find out the best way.

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4. ### _Zeno_Member

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Have you ever seen a print that identified how a diameter should be evaluated (ie: gaussian least squares, maximum inscribed, minimum circumscribed, inner tangential, outer tangential, etc)? Forty year in quality and I haven't. Furthermore, when the customer is queried about what's appropriate for their application, most have been unable to provide any guidance.

5. ### Bev DModeratorStaff Member

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Note that I said the drawing should and those who are true to GD&T would do it. I have seen it properly dimensioned on drawings, although not as often as I'd like.
as for the issues with the Customer not knowing the intent that - is in my experience - because I was talking to a 'check the box' supplier quality engineer and not someone who actually knew what the part was intended to do. Sometimes I could figure it out just knowing what the part was.

Those real constraints are not an excuse to measure the parts any old way. and averaging is definitely not the way to go. I would also add that a good contract review is intended to iron these things out as how things are measured has a direct effect on cost.

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