Specification of Task

A magnet ring is specified by two circular contours of given diameter: the outer one and the inner one (the hole). The following dimensions to be measured were specified by our industrial partner, a Polish producer of magnet rings (Polfer, Warsaw):

1.

The maximum outer diameter, $D_{max}$.

2.

The minimum outer diameter, $D_{min}$.

3.

The maximum inner diameter, $d_{max}$.

4.

The minimum inner diameter, $d_{min}$.

5.

The ovality of the outer contour, $O_{D}$, defined as the maximum difference between diameters separated by $90^\circ$.

6.

The ovality of the inner contour, $O_{d}$, defined as $O_{D}$, but for the inner contour.

7.

Non-concentricity $N_{cnc}$, defined as the distance between the centroids of the two contours.

8.

Non-circularity of the outer contour $N_{cir}$, defined as

$$N_{cir} = \frac{4 \sum_{i}\vert A_i\vert}{\pi D^2_{av}}$$ (3)

where $D_{av}$ is the average diameter of the outer contour, $\vert A_i\vert$ the (absolute) area differences between the circle of diameter $D_{av}$ and the outer contour, as explained in figure 15. (The circle is centered on the centroid of the outer contour.)

  

Figure: To the definition of $N_{cir}$.