This paper presents algorithms for estimating the minimum volume bounding box based on a three-dimensional point set measured by a coordinate measuring machine. A new algorithm, which calculates the minimum volume with high accuracy and reduced number of computations, is developed. The algorithm is based on the convex hull operation and established theories about a minimum bounding box circumscribing a convex polyhedron. The new algorithm includes a pre-processing operation that removes convex polyhedron faces located near the edges of the measured object. As showed in the paper, the solution of the minimum bonding box is not based on faces located near the edges; therefore, we can save computation time by excluding them from the convex polyhedron data set. The algorithms have been demonstrated on physical objects measured by a coordinate measuring machine, and on theoretical 3D models. The results show that the algorithm can be used when high accuracy is required, for example in calibration of reference standards.
The paper proposes the kernel probability density function approach to estimate the distribution of measurements on a part which is measured in a coordinate measuring machine (CMM). The study is based on the experimental data derived from internal cylinder measurements. The distribution free model suggested by Wilks was used as a reference for the selection of the sample size. Three cross sections of a cylinder were measured regarding to this reference. The work defines the minimum required sample size for obtaining at least 0.95 proportion of radius variation for particular studied cylindrical part with 95% confidence level.
This paper investigates the possibility for reduction of sample size for inspection of two-point diameters with a coordinate measuring machine, by use of statistical methods. The statistical methods implement the parametric and nonparametric statistic. As confirmed by the simulation results it is possible to keep the 95% confidence level with a relatively small data sample. A low sample size would be especially important for an operative online dimension inspection with CNC machine and immediate correction of a suspected part.
The paper analyses methods for outlier detection in dimensional measurement. The cross sections of an internal cylinder were inspected by CMM (coordinate measuring machine), and received data sets were employed for further investigation. The efficiency of Rosner’s and Grubbs’ methods for excluding outliers from the measuring data had been estimated. The method of Rosner had been defined as the most effective for this case study. The simulation results were confirmed by experimental verification.
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