Analysis of Circular Braiding Process, Part 2: Mechanics Analysis of the Circular Braiding Process and Experiment

Abstract

The final structure of a braid is a consequence of force interactions among yarns in the convergent zone. In Part 1, the influence of friction forces on the final braided structure was discussed via kinematic analysis. A transformation from a 3-D cone to a 2-D plane was made for the mechanics analysis. A mechanics model is proposed in this paper to determine the braid angle by considering interlacing forces. Equilibrium equations for the braiding process are deduced. A Newton-Raphson method is used to solve the nonlinear algebraic equation set. Experiments have been conducted to produce braids at different machine speeds and with different tensions, and reveal that the mechanics model is potentially a better predictor of final braid structure than the kinematic analysis.

A yarn interaction model for circular braiding

“…Zhang et al [4,5] reported that the discrepancy between kinematic models and experiments increases with the friction and the number of spools. They modeled the axisymmetrical braiding process with a cylindrical mandrel and a 64-carrier machine.…”

Theoretical and experimental study of braid pattern in mandrels with arbitrary cross-sections

“…Equations (10) and (11) are the general solutions of the differential equation (9). Using these equations, the braid angle of every point on the mandrel's crosssection can be determined by setting the appropriate boundary conditions.…”

“…Using these equations, the braid angle of every point on the mandrel's crosssection can be determined by setting the appropriate boundary conditions. Solving equation (11) involves the use of powerful mathematical software such as Wolfram Mathematica or Maple, and ultimately leads to an excessively long and complicated solution. So for easier and quicker determination of braid angle, differential equation 9is solved numerically by the Euler method.…”

“…9 on 2D braid geometry reported that braid angle and braid diameter are the parameters that may noticeably affect the cover factor. In a series of studies by Zhang et al., 10,11 the inter-yarn friction in the convergence zone was modeled based on a modified yarn trajectory. As for the sliding of the yarns on the mandrel, a model was developed by Kessels 12 to explain and predict this particular phenomenon.…”

“…As for the sliding of the yarns on the mandrel, a model was developed by Kessels 12 to explain and predict this particular phenomenon. The vectorial models explaining the positioning of the yarns on the mandrel were later developed by Kessels and Akkerman 11 and Michaeli et al 13 These researchers modeled the braid as a set of points, defined their positions with the help of vectors, and finally used a computer-assisted incremental approach for analysis. Rawal 14,15 proposed a number of equations for mapping the yarn paths on circular cylinder, circular cone, and square prism structures among others.…”