Assessment of the Calculation Methods for Circle Diameter According to Arc Length, Form Deviations, and Instrument Error: A Cosine Function Simulation Approach

Coordinate measuring techniques are essential for determining the diameter and roundness of circular features, yet measurements based on short arc segments remain highly sensitive to form deviations, sampling strategy, and instrument error. With the increasing demands placed on metrology, the choice of suitable data calculation and analysis methods becomes crucial for reliable interpretation of results. This study presents a simulation-based analysis of diameter evaluation for an oval-shaped profile, considering different levels of form deviation, three orientations of the contour peak, and the presence of random measurement error. The analysis includes both complete contours and partial arc segments and evaluates four reference-circle-fitting methods (LSCI, MZCI, MICI, MCCI). The results show that shortening the measured arc increases the influence of local geometric irregularities and random error on the obtained diameter values. The fitting methods behave differently under these conditions: LSCI is strongly affected by the orientation of the deformation peak, while MICI and MCCI provide reliable results only for sufficiently long arcs. MZCI consistently delivers the most stable performance when only fragmentary data are available. These findings indicate that both the choice of reference method and the selection of an adequate arc length are crucial for ensuring reliable and meaningful diameter assessment.