Topology preserving fitting of trimmed NURBS CAD models to deformed solids

Abstract

With Manufacturing 4.0 and digital twins becoming prevalent, leveraging data from different sources, serial numbers, and lifecycle stages for quantitative evaluation is crucial to improve manufacturing. However, inconsistent geometries between as-built and as-designed parts cause difficulties in inspection using data obtained from various modalities. To address this issue, in this work, we create a framework for mapping between the as-designed CAD representation and the as-built part using surface measurements. The main challenges are to capture the correspondence between entities while maintaining topological consistency with the design and eliminating the gaps between connected surfaces. These challenges are even more pronounced when handling complex multi-surface parts with trimmed surfaces and large-scale deformations. Our framework uses the standard mathematical representation of surface geometry in CAD, i.e., the non-uniform rational B-splines (NURBS). We deform the as-designed CAD model using constrained optimization to match the surface measurements of the as-built part. To preserve the topology  (the interconnectivity of its surfaces) and obtain a gap-free connection between adjacent surfaces, we formulate new optimization constraints that keep the edge consistent in the geometric space. We test our framework on multiple CAD models that have trimmed NURBS surfaces. This research enables accurate mapping of metrology data from the actual part to the corresponding CAD model, enabling applications such as in-situ monitoring, defect localization, and control of manufacturing processes.