关键词: 六角形三维编织, 管状织物, 虚拟编织, 二维平铺网格图, Matlab

Abstract: The hexagonal three-dimensional (3D) braiding machine has become a research hotspot in 3D braiding field because it can carry more yarns and adapt to more flexible braiding process. However, the development of hexagonal 3D braiding technology is less mature at present, and the way to verify the braiding process through physical sample faces the problems of high cost and long development cycle. Therefore, a three-dimensional virtual modeling method of tubular braiding based on two-dimensional(2D) tiled grid model was proposed in this paper, which could be used for rapid verification and development of braiding process. 
First, the two-dimensional tiled grid model of tubular braiding and its rotation matrix and interweaving matrix were defined, and the corresponding relationship between tiled grid and yarn's interwoven form was established both graphically and numerically. Second, according to the characteristics of braiding machine with regular hexagonal chassis layout, an oblique coordinate system for the hexagonal chassis and a polar coordinate system for the chassis unit were established. Combining with information on braiding process transformations, an iterative formula for the trajectory of the carrier was proposed and used to calculate the xy coordinates of each carrier on the chassis at the same time. Adding the drawing distance of the yarn over the mandrel as z coordinate, the spatial motion position of the yarn in the cartesian coordinate system of the chassis could be obtained. Then the spatial position of the yarn in the cartesian coordinate system of the braiding was obtained by the coordinate system transformation from the chassis' to the braiding's. Third, by expanding the braiding from 3D to 2D along the circumference, the interweaving relationship of yarns on three dimensions was transformed into the intersecting relationship on the plane. By application of the chassis interweaving layer, the interwoven form of each yarn in the crossing segment was obtained by judging the interweaving relationship between the intra-layer and inter-layer interactions of the carrier. Based on the relationship between the switch step angle and the number of yarn's twisting knot, the interwoven form of each in the twisting segment was deduced. Fourth, an example was given to illustrate how the obtained yarn interweaving information was written into the rotational matrix and the interleaving matrix. The two-dimensional tiled grid diagram of that tubular braiding was obtained from the two matrixes and then converted into the 3d model of the braiding by applying Matlab commands. The correctness and effectiveness of the modeling method in this paper were further verified by the same structural comparison between the real and the virtual braiding of the tubular braid. A two-dimensional tiled grid model of tubular braiding was firstly proposed in this paper. And then the following research work was carried out, which mainly included the calculation of yarn motion trajectory, the analysis and judgment of yarn interweaving information, the acquisition of the 2D tiled grid model and its 3D modelling by Matlab. Finally, the correctness and feasibility of the 3D virtual braiding modeling method were verified by example analysis. That can realize the rapid development of hexagonal braiding process.
Virtual braiding technology has been studied deeply in the field of fixed-track braiding, and some virtual braiding simulation software has been successfully developed, such as Texmind Braider Software and Herzog software. However, the research in the field of hexagonal 3D virtual braiding is relatively immature. The yarn motion model based on oblique-polar coordinate system of the chassis proposed in this paper can be generally adopted in hexagonal 3D virtual braiding modeling, and is beneficial to the development of hexagonal 3D virtual braiding application software.

Key words: hexagonal three-dimensional braiding, tubular braiding, virtual braiding, two-dimensional tiled grid diagram, Matlab