Freeform surfaces have been widely used in various industries. The quality of a freeform surface highly depends on its correct geometry that is defined by profile tolerance. Freeform surface inspection is the process to check the geometry of a manufactured surface against the required tolerance zone through the following steps: acquisition of measurement points on the surface, alignment of measurement points with the ideal design surface through localization, reconstruction of a continuous model of surface, and comparison of the reconstructed surface with the design surface and its tolerance. This research focuses on the prediction and reduction of uncertainties of the reconstructed surface. Simulations and experiments have been conducted to show the effectiveness of the developed methods.
Robust methods have been developed for both rough localization and fine localization processes. For rough localization, distance constraints among points are used in addition to curvature constraints to improve robustness of the method. For fine localization, a model is developed to predict uncertainties of the finely localized measurement points based on the input uncertainties and uncertainties introduced in the localization process. The optimal location and orientation of the design coordinate system are also identified to improve the robustness of fine localization process by minimizing uncertainties of the localized measurement points.
B-spline surface reconstruction from scattered data points is conducted and an accurate model is developed to predict uncertainties of surface reconstruction process. First the variances of the B-spline surface’s control points are estimated statistically, and then the variances of control points are propagated to the variances of points on the B-spline surface. To improve the accuracy of uncertainty prediction at any location, variances of the control points in all three Cartesian directions are considered.
In this research, a method is developed to estimate the accumulated uncertainties of any location on the reconstructed model of manufactured surface considering different uncertainty sources in measurement, localization, and surface reconstruction processes. The variation boundaries of the reconstructed surface can be obtained based on the estimated uncertainties and the desired confidence level. The obtained variation boundaries are then compared against the required tolerance zone for surface inspection.