Prediction of the braid pattern on arbitrary-shaped mandrels using the minimum path condition

A mathematical model is developed to predict the braid pattern (by braiding process) on arbitrary-shaped mandrels considering braiding process parameters. This model includes basic requirements for the braid pattern to be formed, i.e., the braid pattern is formed at a point on the mandrel surface where the line running from the braid point to the yarn carrier on the braiding bed is tangent to the mandrel surface. Additionally, the minimum path condition is incorporated into the mathematical model to reflect braiding process parameters more rigorously. The minimum path condition requires that the braid pattern be formed at a point on the mandrel surface where the total length of the braiding yarn hanging over from the previous braiding point to the yarn carrier is minimized. The new model is implemented to simulate the braid pattern on a conical and a rectangular, acentric mandrel. The simulation results are compared with experiments, demonstrating that the current model is highly suitable for predicting the braid pattern on complex mandrels within reasonable accuracy, thereby providing an effective tool for designing braid composites.