Mathematical modeling of braiding yarn trajectories for variable cross-section mandrels of equal-coverage

Abstract

The braiding coverage is very important to the forming quality, especially its mechanical properties. To address the issue of constant coverage on rotating surfaces with variable cross-section mandrels, a modeling method for yarn trajectories with equal coverage rates is proposed in this research. The novel equal-coverage theory model takes into account the effect of variation of mandrel radius on the braiding angle, establishes the relationship between the braiding angle and the variation of braiding radius, and solves for the traction speed. The yarn trajectory is calculated by MATLAB and the traction speed based on the variations in the braiding angle and radius is computed as well. The resulting trajectories are input in NX.11 to construct a variable cross-section mandrel model with equal coverage rates. Comparing the simulation model with actual braided materials shows that the errors in the braiding angle and coverage rate are within ± 5° and 3 %, verifying the feasibility of the proposed method. The results will provide theoretical guidance and basis for further control of braiding quality.