A yarn interaction model for circular braiding

Abstract

Machine control data for the automation of the circular braiding process has been generated using previously published mathematical models that neglect yarn interaction. This resulted in a significant deviation from the required braid angle at mandrel cross-sectional changes, likely caused by an incorrect convergence zone length, in turn caused by this neglect. Therefore the objective is to use a new model that includes the yarn interaction, assuming an axisymmetrical biaxial process with a cylindrical mandrel and Coulomb friction. Experimental validation with carbon yarns and a 144 carrier machine confirms a convergence zone length decrease of 25% with respect to a model without yarn interaction for the case analyzed, matching the model prediction using a coefficient of friction of around 0.3.

Mechanical analytical modelling of non-axisymmetric overbraiding

“…Two major works have been published using this approach: Zhang et al proposed in Zhang et al 5,6 a method assuming a conical convergence zone and van Ravenhorst and Akkermann proposed a method considering a non-developable convergence zone. 7 In these two methods, frictional effects are implemented which increases the accuracy of the process modelling compared to the kinematic models. However, the models stay limited to axisymmetric braiding configurations.…”

“…However, the models stay limited to axisymmetric braiding configurations. Regarding the computation method, due to the set of equations that must be solved, the method used in literature [5][6][7] are respectively the Newton-Raphson method and a non-linear optimization method and can be thus classified as numerical. A third approach is the mechanical modelling which is based on the use of finite element interacting with each other after applying the proper boundary conditions.…”

“…Similarly, L y and L z are respectively the distances between the fell point and the spool in the y-direction and z-direction. Equations ( 5) and ( 6) impose the moment equilibrium at the fell point of the yarn in the xy-and xz-planes and equation (7), projected in the three directions of space, imposes the force equilibrium in the x-, y-, and z-directions. Equations ( 5) to (7) are written in the general case in which the yarn-yarn interaction forces F !…”

Prediction method for offset compensation on three-dimensional mandrel with spatial irregular shape

“…van Ravenhorst et al. [5] proposed a new yarn interaction model to simulate yarn interaction behavior. Won-Jin et al.…”

Modeling and analysis of the carrier arrangement in three-dimensional circular braiding

“…The model focused on the geometrical parameters and the varying horn gear speed. Ravenhorst and Akkerman 7 proposed a yarn interaction model that could simulate the yarn interaction behavior in 3D circular braiding. Ma et al.…”