Description And Arithmetical Realization Of Permutation Of Three-dimensional Track-and-Column Braiding Procedure

Advanced composites with 3-D braided preforms have been greatly developed as new pattern materials with a unique advantage since the early 1980s. In braiding process all yarns are braided at the same time while each yarn moves with a determinated rule and then interweaves together as a whole fabrics. The characteristic of good profile modeling design of the braided structure makes it particularly suitable for conforming to surfaces of varying cross-sectional shapes such as rectangle-shape and U-shape structures. It has been showed that advanced composites with 3-D braided preforms as reinforcements are widely applied for air materials, spacecrafts, weaponry, automobiles, sports and medical apparatus, as they are of excellent performances, including light mass, through-thickness reinforcement to prevent delamination, high damage tolerrance, higher intensity, structural integrity, design flexibility, and precision etc. The research of braiding technique for preforms is vitally important because preforms are the frameworks of composites. Among all kinds of braiding techniques,track-and-column braiding is a very popular technique.In detail, braiding lattice-array is made of braiding main-array and boundary-array . Lattice-array is abstracted as mathematic collection and braiding pattern as set mapping. In case of the numbers of lattice for bothsides of boundary-array must be equal for every row and every column, permutation can accurately express every movement of pace of carriers, so that braiding process is converted to permutation process.With braiding process, firstly define braiding process parameters , set braiding patterns in theory , based on theories of mathematic set and permutation , establish model of lattice-array and braiding pattern in order to translate braiding process to mathematic operation so as to prove accurateness of theoretical braiding pattern through computer simulation.By use of matlab programme, realize the computering of braiding permutation process and solve the calculating problem of important braiding parameters.Summarizing this paper, track-and-column braiding process are systematically studied , which are essential to the braiding design of preforms. What's more, this paper offers some new ideas and means for further research.