Tolerance Definitions; Concentricity Tolerance; Reference Features; Least Squares Best Fit - HEIDENHAIN ND 1300 Operating Instructions Manual

228
QC-300 Series User's Guide
Tolerances
The following information is supplemental to the tolerance discussions provided earlier in
Chapter 7: Tolerancing.

Concentricity tolerance

The mathematical definition of concentricity is explained in detail in the ASME Y14.5M-1994 standard
and involves "the midpoints of opposing elements" in the determination of actual concentricity. This is not
practical in a discrete point measuring system, so the QC-300 uses the center of the feature (determined by
the best fit) to estimate the concentricity.

Reference Features

When a reference feature is called for in a tolerance definition, the reference feature will nearly always
refer to a datum feature such as a skew line or datum circle. The field is required except for the
MMC / LMC tolerance case.

Least squares best fit

Data is iteratively processed to position a perfect circle within the data cloud in the position that minimizes
the sum of the squared form errors. Form errors are inside and outside the circle.

Maximum inscribed circle

First, a least squares best fit circle is estimated, then the data is iteratively processed to position a perfect
circle through 3 points on the inside of the data cloud. The maximum inscribed circle position encloses the
maximum diameter of the circle by the data cloud. Form errors are outside the circle.

Minimum superscribed circle

First, a least squares best fit circle is estimated, then the data is iteratively processed to position a perfect
circle through a minimum of 2 points on the outside of the data cloud. The minimum superscribed circle
position encloses the data cloud with the minimum circle diameter. Form errors are inside the circle.

ISO (least radial distance)

First, a least squares best fit circle is estimated, then the data is iteratively processed to position a perfect
circle in the location that minimizes the inside and outside form errors. Form errors are inside and outside
the circle.