Whenever a standard geometric elements is
measured using more points than the minimum number of probing points,
scattered values are obtained. These scattered values are an indication of
the quality of the measurement and of the part.
However, at the same time, the standard
geometric element has been overdetermined, since it was probed using more
points than mathematically necessary. This is why a suitable substitute
element must be calculated using a so-called fit algorithms.
Various algorithms are available, which are best explained using
the example of a "circle":
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| The fit algorithm according to Gauss simply calculates a circle which lies as
accurately as possible "in the middle" of all measured points.
In the Gauss algorithm, all points have equal weight.
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The
fit algorithm called "circumscribed circle" calculates a circle
such that all measured points are inside the circle, and the circle is as
small as possible.
This algorithm is usually used for determining the geometric
data of shafts when pair dimensions are checked. |
The
fit algorithm
called "inscribed circle" calculates a circle such that all measured
points are outside the circle, and the circle is as large as possible.
This algorithm is usually used for determining the geometric
data of bores when pair dimensions are checked.
Attention: The center
of the circumscribed circle is in a different place than the center
of the inscribed circle. |
The
fit algorithm called "minimum zone circle" calculates two circles
such that one is outside all points and the other one inside all points but
that both have the same center. Then the distance of the two circles (the
difference in diameters, shown on the picture in red) is the form deviation.
The minimum zone circle (Chebychev circle)
is then the middle circle of these two circles.
This algorithm is used almost exclusively for the calculation
of form errors. |
