Modeling of braided structures based on secondary helix

Abstract

In this paper, the relationship among primary helix, secondary helix and braiding curve is discussed and it concludes that the braiding curve is the projection of secondary helix on the braiding surface. Based on this conclusion, the equation of braiding curve is derived using Frenet frame. The geometrical models of braided strands are realized by two methods, one is based on the mathematical models; the braiding curves are obtained by their equations directly. The other is based on the projective relationship using SolidWorks™. A projective surface has been built and employed to realize the projection of secondary helix on the helical surface, the braiding curve is obtained by the intersection of projective surface and the helical surface. For both methods, the strands are built by sweeping the cross section along the braiding curve. The modeling methods introduced are not confined by the braiding angle and cross section of strand and could be used to simulate different braided structures.