Application of graph theory for preventing carriers’ collisions in variable path braiding machines

Braided preforms are now used for structural composite parts. They have made their way into the aeronautic and the automotive sectors. With the development of variable carriers’ paths braiding machines, the braid geometry can now be tailored to specific needs and be fabricated to a near net shape of the final product. However, the carrier’s path variability brings complexity to the manufacturing process: carriers can collide with each other while braiding the desired structure. Manual trial and error is still needed to program a collision-free braiding process, which is time and resource consuming. We proposed a method, based on graph theory, to automatically prevent collisions during the braiding process. This method can be applied onto variable carriers’ paths braiding machines. To do so, the bedplate of the braiding machine is modeled as a graph. Faces represent horngears and edges represent carriers’ path. Vertices can represent one of the following three: a horngear’s slot, a track intersection, or possible stationary carrier’s position. A collision is prevented by delaying the displacement of one or more carriers. A prevention algorithm is presented, which prescribe a delay to each carrier in order to achieve a collision-free process. To demonstrate the algorithm, a case study is carried out on a 3D textile printing braiding machine. The algorithm offers an automatic and efficient method to prevent collisions in variable carriers’ paths braiding machines.