Analysis of 2D and 3D circular braiding processes: Modeling the interaction between the process parameters and the pre-form architecture

• Analytical modeling of braiding processes adapted to complex shaped mandrels.
• Modeling using differential geometry approach (parametered curves).
• Analysis of manufacturing process during transitory process run.
• Mathematical description of the positioning of the braiding front.

This paper focuses on the modeling of a 2D and 3D circular braiding process to establish the adapted relationships between the architecture of the complex-shaped braids and the process parameters by considering the transitory and steady-state process stages. The modeling approach is based on differential geometry. We describe the trajectory of a strand of yarn as a parameterized curve on an elementary surface of the mandrel, which is described geometrically by two radii of curvature of the reference system. The developed analytical relationships allow us to take into account such transitory or steady-state process-run phenomena as the motion of the braiding front, the slippage on the mandrel and the relaxation of the yarn. The model is successfully compared to other analytical models found in the literature. Additionally, we validate the model for the case of 2D and 3D circular braiding processes run in the transitory stage.