Geometric Partitioning of Complex Surface Measurements

Dimensional inspection of microparts is challenging. Optimized processes, such as microdeep-drawing with tailored tools, even increase the requirements. While the development of fast and precise data acquisition techniques is in progress and various solutions already exist, the geometrical evaluation of measuring data still shows open questions: 1) the evaluation methods for freeform surfaces do not provide information in a form that can be directly used to assess dimensional tolerances; 2) manual association of approximating geometric elements to points is not suited for high inspection rates; and 3) partitioning based on the nominal workpiece coordinate system is affected by alignment uncertainties. An algorithm was developed for the automated evaluation of surface measuring data composed of geometric primitives, such as planes, cylinders, and tori, which combines and optimizes the estimation of geometric parameters together with the automatic partitioning of the measured points. This article presents the extension of this holistic approximation (HA) with root point iteration in order to evaluate more complex geometric elements. The verification of the extended HA for a 2-D combination of lines and an ellipse shows no systematic error and achievable uncertainties below 0.8 μm for the approximated shape parameters of an ellipse for simulated surface data with uniformly distributed noise in the range of 1.0 μm. The validation in comparison with commercial metrology software finally exhibits the full potential of the extended HA. As a result, a fully automatic dimensional evaluation is possible, providing geometric parameters that can directly be compared to nominal specifications and tolerances.