Abstract
Abstract. Virtual assembly (VA) is a method for datum definition and quality prediction of assemblies considering local form deviations of relevant geometries. Point clouds of measured objects are registered in order to recreate the objects' hypothetical physical assembly state. By VA, the geometrical verification becomes more accurate and, thus, increasingly function oriented. The VA algorithm is a nonlinear, constrained derivate of the Gaussian best fit algorithm, where outlier points strongly influence the registration result. In order to assess the robustness of the developed algorithm, the propagation of measurement uncertainties through the nonlinear transformation due to VA is studied. The work compares selected propagation methods distinguished from their levels of abstraction. The results reveal larger propagated uncertainties by VA compared to the unconstrained Gaussian best fit.
Highlights
Introduction to measurement uncertainty assessmentA complete statement of a measurement result includes the measurement uncertainty
Due to the contribution of the transformation uncertainty uT to the transformation, the propagated uncertainty UTr increases with an increasing radius r, which can be related by analyzing the visualizations in Fig. 4, where the components uTxr, uTyr, and uTz r increase towards the corners of the analyzed slider
The main contribution to the propagated uncertainty is due to the uncertainty in the transformation parameters uT, which depend on the formulation of the registration problem
Summary
A complete statement of a measurement result includes the measurement uncertainty. The measurement uncertainty is a nonnegative quantity expressing doubt about the measured value, defined as a “parameter, associated with the result of a measurement, that characterizes the dispersion of the values that could reasonably be attributed to the measurand” (ISO/IEC, 2008b). In ISO/IEC (2008a), the main stages of uncertainty assessment are described as formulation, propagation, and summarizing. During formulation, generally the measurand Y is defined, input quantities X are determined, and the measurement model is established as follows: Y = f (X) . A main step is the uncertainty estimation for the input quantities. The Guide to the expression of uncertainty in measurement (GUM) (ISO/IEC, 2008b) reveals two methods for.
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