Orientation Density Function of Ply yarn

Assuming that the individual fibers in a ply yarn have the form of a doubly wound helix, we simulate the paths of the individual fibers in the yarn. We show the fiber paths as a function of the fiber position in the single yarn, the number of twists of the single yarn and the ply yarn, and the direction of twist for the single yarn and the ply yarn. We also calculate the orientation angle, the orientation density function, and the mean of orientation angle in a ply yarn in order to predict the mechanical properties of ply yarn.