Study On The Law Of Three-Dimensional Rectangle Braiding

One of the main features of 3-D braiding composite is performance designable. It requires that 3-D preforms should be braided according to compatible unit cell structure, cross-sectional shape and size. 3-D braiding is an effective tool to fabricate 3-D textile performs and the track and column braiding is one of the most active technology. During braiding, the movement of braiding carriers determines the unit cell structure and the shape of cross-section of the preform. This thesis studies the relationship between the braiding pattern and the movement of braiding carriers. The objective is to develop a method to obtain an expecting braiding pattern for the purpose of possible performance designable requirements.To form 3-D braided preforms with given yarn orientation and interlacing architecture, the free end of the braiding yarns should be moved in a platform in a given order with the other end of the braiding yarns will form interlacing at a position above the braiding platform. Track and column braiding is one of the effective 3-D braiding techniques. By driving braiding carriers along tracks arranged in rows and columns in the braiding platform, various braiding patterns can be obtained. The key issue of the braiding technique is to control the movement of the braiding carriers. Therefore, the law of braiding, tracks in the braiding platform and the arrangement of braiding carriers are three fundamental elements in 3- D braiding. To braid a 3-D preform with a desired braiding architecture, a law governing the braiding process is essential, by which the movement of the braiding carriers is determined.A braiding plan to describe the track and column braiding is introduced in this thesis. Some concepts such as lattice array, main array, side array, Z-array, H-array and stepping array are defined. The braiding plan is consisted of a lattice array and a stepping array, by which the essential factors of the track and column braiding are represented. Filled with different colors or symbols, the lattice array can represent the initial arrangement of the braiding platform, including the positions of braiding and non-braiding carriers, the cross-section of 3-D perform, and etc. The stepping array is consisted of a Z-array and a H-array representing movement of carriers in the column direction and row direction, respectively. This digitalized representation of the braiding plan will facilitate the study of the braiding processing.The correct configuration of the braiding platform and the initial arrangement of braiding carriers on the braiding tracks are discussed. The lattice array is composed of a main array and surrounding side arrays. The number of columns in the side arrays on both side of any row in the main array must be equal. Similarly, the number of rows in the side arrays on both side of any column in the main array must also be equal. But the number of columns (or rows) of different rows (or columns) in the side arrays is unnecessary to be the same. In practice, when considering the versatility of a braiding platform, a lattice should be so built array that the number of columns inthe side arrays row-wise is equal, so as the number of rows in the side arrays column-wise. But the number of the columns and that of rows could be arranged differently. In the thesis, the position of braiding carriers in the braiding platform is decided mathematically. To conduct out track and column braiding, there must not be any blank element in the main array. In other words, the main array must be filled with braiding carriers fully. Before braiding, there must be braiding carriers in the side arrays, and the numbers of carriers must not be less than the number of columns (or rows) in the side arrays row-wise (or column-wise). When braiding a profiled 3-D preform, a rectangular lattice array that can locate the total number of the braiding carriers is used, in which the braiding carriers are arranged to form the profiled cross-section and the non-braiding carriers are arranged to transfer driving motion.Mathematically, the latti...