Is a diameter the distance between two points? Or is a diameter the average circle diameter?

(This tip is compliant only with ISO – ISO 14600-2:1999)

Recently, following a failure, I was asked the question: what is a diameter?

A problem was found of parts not mating. When re-measured, the results were different from the values in the original measurement report. After examination, it was discovered that the values reported in the original measurement for the diameter requirement were the average (Least Squares) circle size, and in the repeat measurement, distances were measured between opposing points, and that was the reason for the difference. The supplier claimed that “That is the way to measure by CMM, and no special control requirements have been given…” Hence the question, what is a diameter?

It is important to remember that according to the latest approach of ISO, a drawing is a specification of requirements applied to the finished part! The drawing specifies what should be, and not how to produce or how to check it (unless otherwise stated explicitly).

And regarding the Question – What is a Diameter?
According to ISO, the default definition, unless otherwise specified, is:
“Diameter is the length of a straight line connecting two points, in a section perpendicular to the axis of a circular body, which passes through the center of the cross section.”
In other words, real distances should be reported, not average values!!!

It therefore follows that the claim “that is the way to measure by CMM” is unsatisfactory, and the value that was reported is not the value required!!!
In addition, the definition of a diameter contains two requirements, which are not simple; the standard provides a solution on how to find them:

• diameter shall be measured perpendicular to the axis! – a real part is does not have a perfect form; it has a center line, it has no axis (a theoretical straight line).
• The length of the straight line connecting the points, which passes through the center of the circle! – the section line is not a perfect circle, so what is the center?

The following illustrations show how a cylinder diameter is defined according to ISO GPS standards:

• What is the axis to which the measurement is perpendicular?
• What is the center through which the measurement must pass?

In Figure 1, the blue surface represents a sample of a cylinder envelope. The numbered elements are:

1. An average (LSQ – Least Squares) cylinder of sampling points from the real envelope of the feature.
2. The axis of the average cylinder (the cylinder is a theoretical geometric form, so its axis is straight).
3. Section planes perpendicular to the axis of the average (LSQ) cylinder.
4. The average (LSQ) circle.

Figure 1

Figure 2 shows a section perpendicular to the axis, and the numbered elements are:

Figure 2

1.  The section line of the measurements in a section plane perpendicular to the axis.
2.  The average (LSQ) circle of the points, in the section plane.
3.  The dimensions of the diameter are the distances between opposing points, with the straight line connecting them passing through the center of the LSQ circle in the cross section.

It is important to note that the average (LSQ) circle center in the cross section is not necessarily on the axis of the average cylinder.
The average cylinder is used to define the measuring direction.
The average circle in the cross section is used to find the center of the cross section.
The maximum and minimum dimensions must be reported (verify that there is no deviation in the envelope from the dimension’s defined tolerance).

In summary

The default definition in ISO for a diameter dimension is the real distance between two points in a section perpendicular to the axis that passes through the center of the cross section.
If we want a different definition, it must be noted explicitly!!!

Specifying a standard in the drawing defines the rules according to which the drawing should be interpreted, and prevents disputes!!!

Questions? Ideas? Suggestions?
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