Substitute Geometry of Multidimensional Features

A substitute feature equation (SFE) which is of vital importance in geometric accuracy problems depends on size, position, and orientation deviations (SPODs). To synthesize the equation and evaluate its numerical parameters using CMM measurements, it is necessary to eliminate redundant components from the initial set of SPODs. For this purpose, a linear space of the SPODs transfer functions is considered. A linear basis in this space defines a basic set of the SPODs that are necessary for the workpiece verification procedures: the SFE synthesis followed by the best fitting procedure. The developed algorithms are applied to the geometric accuracy assessments of multidimensional features. The geometric accuracy of the ellipsoid of revolution is simulated. Accuracy assessments, their uncertainty vs. distribution functions, and processing time vs. sample size and the number of the SPODs are evaluated.