Robust localization to align measured points on the manufactured surface with design surface for freeform surface inspection

• A method is developed for predicting variances of localized measurement points.
• Robust rough localization is conducted by matching various geometric properties.
• Robust fine localization is conducted by selecting the optimal coordinate system.

Inspection of a manufactured freeform surface can be conducted by sampling measurement points on the manufactured surface and comparing the measurement points with the ideal design geometry and its tolerance. Since the measurement coordinate system and design coordinate system are usually different, these measured points should be first aligned with the design surface through localization. In this research, robust localization methods are developed for both rough localization and fine localization processes. For rough localization, some target measurement points are selected and their corresponding points on the design surface are obtained based on similarities in curvatures and distances of these points. Compared with curvatures that are often used in localization, the distances are less sensitive to the errors introduced in manufacturing and measurement processes. In fine localization, uncertainties in the measurement and localization processes are considered to predict the uncertainties of the localized measurement points. The optimal design coordinate system is also selected such that the uncertainties of the localized measurement points can be minimized. Two case studies are provided to demonstrate the effectiveness of the developed methods for freeform surface inspection.