Research on the kinematic trajectory of hexagonal annular three-dimensional braided forming process

Three-dimensional (3D) braided composites have garnered significant attention in aerospace, automotive, and marine applications due to their exceptional structural integrity and mechanical performance. However, the kinematic complexity inherent in braiding processes has significantly impeded accurate trajectory prediction and process optimization. This study presents a comprehensive investigation of the kinematic trajectory of hexagonal annular three-dimensional braided forming process through an integrated multi-body dynamics and analytical modeling framework. A novel virtual prototype mathematical model incorporating realistic operational conditions including collision forces, friction effects, and inertial dynamics was established to accurately predict yarn carrier trajectories. Simultaneously, a complementary analytical trajectory prediction algorithm was developed using kinematic equations, providing theoretical validation for the numerical simulation results. The proposed "compartmentalized classification" braiding process enhances traditional two-step methods by maintaining horn gear density while increasing layer configurations, thereby improving braiding efficiency by up to 33% in multi-layer applications. The mathematical framework establishes quantitative relationships between horn gear layer configuration, gear quantity, and yarn carrier capacity, providing a theoretical foundation for scalable braiding system design. Systematic trajectory prediction algorithms validated against simulations demonstrate that consideration of realistic force conditions significantly influences predicted yarn carrier trajectories, particularly during acceleration, deceleration, and direction transition phases. The velocity profiles reveal that yarn carriers maintain consistent speed magnitudes with irregular fluctuations during horn gear transitions, while collision forces stabilize at approximately 8 N, ensuring consistent yarn tension and uniform braiding patterns. The integrated framework provides fundamental understanding of the dynamic mechanisms governing the braiding process and offers a robust theoretical basis for the precise control and optimization of complex three-dimensional braided structures with tailored mechanical properties.