Mathematische Beschreibung von gekrümmten Oberflächen für die Anwendung in der Koordinaten-Meßtechnik

Abstract

Measuring workpieces with curved surfaces using coordinate measuring machines requires a suitable calculator-internal representation of the nominal shape of the workpiece according to the drawing. It is necessary for controlling the measuring process as well as for acquiring, including the correction of the dislocation due to the probe ball, and for processing the measurement data, i.e. for the alignment, the actual-nominal-comparison and for the documentation of the results. Main part of the measurement data processing is the location of the measured points relative to the nominal shape. This yields an essential requirement on the type of the representation. During extensive investigations, an implicit representation of the nominal "shape by an equation F(x1, x2, x3) = 0 proved to be profitable. In the following a suitable approach of the mapping F is given and analyzed. A particular problem when processing measurement data is the calculator-internal alignment of the work-piece. This can be described by a transformation T of the coordinate system due to the workpiece. As shown below, T can be computed by solving a nonlinear system of equations involving an approach for the distance between measured points and nominal shape which is based on the implicit representation of the. © 1983 CIRP.