Trajectory optimization for automated tape placement on triangular mesh surfaces considering gap requirements

Automated tape placement (ATP) is an important automated process adopted for the fabrication of large composite components. Trajectory planning is the key link of ATP, which directly affects the precision and efficiency of the layup process, and the quality of final products. Presently, most existing trajectory optimization methods for ATP focus on smooth surfaces. Nevertheless, as commercial CAD/CAM software generally uses NURBS (Non-uniform Rational B-Splines) for modelling, the difficulty of finding the solution and the low efficiency associated with the calculation process are inevitable. The discrete methods provide alternatives for designing layup trajectories, whereas their accuracy is seldom analyzed. Furthermore, a path optimization algorithm for eliminating gap problems while preventing wrinkles on discrete models is rarely reported. In this paper, the adjustment of layup trajectories for ATP is considered on triangular meshes. Firstly, the triangular mesh is reconstructed as a Nagata patch to recover the original geometry with good accuracy. Then, a numerical method for tracing desired paths on the Nagata patch set is provided, and the computation efficiency is validated. Next, two optimization methodologies are proposed to improve the layup of composite tapes while avoiding wrinkles. Finally, the presented two strategies are examined on a discrete hyperbolic surface and a discrete freeform surface, and some of the results are delivered.