Comparison of Point Measurement Strategies and Mathematical Algorithms for Evaluation in Contact Measurement of a Spherical Surface on a CMM

This paper compares different point measurement strategies for spherical surfaces using a coordinate measuring machine. A total of 77 points were measured using the Sphere, Touch Point, Space Point, and Mid Point strategies, and approximately 2200 points were measured by scanning the surface with eight circles. Three probe configurations with different probe tip diameters were used for the measurements. The acquired data were processed with Calypso software, and the results for sphere diameters and centers were verified using the LSQ algorithms with the Kåsa and Newton methods, as well as Chebyshev fitting. Spherical shell half-widths and Root Mean Square Errors were used to evaluate accuracy. The results show that the sensor with rprobe=2.500557 mm provides the smallest deviation from the certified value for both diameter and center position. The deviations remain smaller than the maximum permissible error of length measurement E0,MPE. The scanning strategy does not consistently provide better results for either the diameter or the sphere center compared to point measurement. The results of the LSQ method in Calypso correspond to those obtained by the Kåsa/Newton methods (with results identical at the μm scales), while the Calypso Minimum Feature evaluation method corresponds to the Chebyshev fit.