A roundness evaluation algorithm with reduced fitting uncertainty of CMM measurement data *

This paper presents a novel algorithm for evaluating roundness from discrete coordinate data measured by a coordinate measuring machine (CMM). The main feature of this algorithm is the concept and quantification of profile confidence level, which is used to reduce the uncertainty associated with fitting the sampled data points in the determination of the roundness zone. This algorithm starts by characterizing the deterministic profile of a circular feature. After the deterministic profile is obtained, the normally distributed fitted residuals are available and regarded as random errors. With the established random errors, the roundness zone corresponding to a satisfactory profile confidence level can be determined. Extensive experimental data analysis has been carried out to validate the unique advantage of the present algorithm: if the circular deterministic profile is characterized correctly, the evaluated roundness values are consistent under different sample sizes and/or sampling locations. Also, these consistent roundness values are very close to the minimum-zone solution of a large sample size, which often provides a good approximation to the true roundness value. The present algorithm is thus deemed robust and able to reliably evaluate roundness with a relatively small number of data points.