Evaluation of roundness tolerance zone using measurements performed on manufactured parts: A probabilistic approach

In the verification of the compliance with dimensional and geometrical specifications of manufactured parts, the features are frequently sampled using Coordinate Measuring Machines. The evaluation of roundness tolerance zone by using measurements performed on cylindrical work pieces is specifically dealt with. Once a finite set of points is sampled, a fitting method is adopted to estimate the parameters of the reference circle. In particular, three different methods are considered, i.e. the usual Least Squares method, the so called Probabilistic Method, and the standardized Minimum Zone method. In order to have complete information on the reference features, knowledge of their uncertainty is required. Two uncertainty evaluation techniques are examined, i.e. a theoretical approach and the bootstrap method. Then, a new procedure based on the calculation of the probability density function of the width of roundness tolerance zone is developed. The practical application to the actual measurement of circular features on cylindrical holes allows to understand the differences between the results obtained with the presented approaches. Finally, the advantages of the probabilistic approach are highlighted.