Geometrical modelling and control of a triaxial braiding machine for producing 3D preforms

Braiding is a relatively less explored textile process for producing composite preforms. Biaxial braids can be produced as hoses and subsequently be draped over different three-dimensional surfaces. However, triaxial braids are relatively stable structures and should be produced to the desired shape during the braiding process. This is achieved by over-braiding on mandrels that either form part of the finished composite or removed before the moulding process. Triaxial braided composites have superior mechanical properties due to fibre orientations along three directions.Geometry of a braided structure depends on the number of yarn carriers, rotational speed of the carriers, take-up speed and the effective perimeter of the cross-section of a mandrel. In the present work, a VRML based geometrical visualisation tool has been developed to simulate a braid structure on any predefined mandrel geometry, and using a predefined yarn cross-section. Braid angles, cover factors and yarn volume fractions can be computed from these simulations. A triaxial braiding machine has been developed with an independent servo control of the carrier movement and the take-up mechanism; geometrical simulation is used as an input to the control system to continuously vary the braid structure along the length of a mandrel. Flexible tooling is important for rapid product development. A flexible mandrel has been developed that can be mechanically adjusted to change the cross-section and the taper. This system enables rapid development of braided preforms.     

Process simulation and fabrication of advanced multi-step three-dimensional braided preforms

The fundamentals of multi-step braiding for the fabrication of three-dimensional fibre preforms for composites have been studied. To facilitate the understanding of the complex multi-step braiding processes, a computer simulation algorithm has been developed. The simulation acts as a tool to allow the identification of individual yarn paths, number and location of yarn groups, and braid geometry. It was found that individual control of the rows and columns of yarn carriers on a Cartesian braiding bed allows for the fabrication of advanced multi-step braids; the micro-structural possibilities of three-dimensional braids are thus greatly extended. Some basic relationships of the braiding parameters have been identified. It has been concluded that the traditional four-step and two-step braidings are special cases of multi-step braidings. To verify the feasibility of the structures, experimental investigations have also been carried out. Innovative braid architectures have been designed and fabricated using a prototype multi-step braiding machine.     

三维四步方形编织结构的几何建模

研究三维复合材料的编织结构是分析这种材料力学性能的前提。从三维编织工艺和实际的编织过程出发,针对方形编织结构提出了一种单元几何模型。该模型以携纱器循环一周返回到起始位置所形成的纱线编织结构作为单元,保证了纤维束的连续性和材料整体结构的完整性。对每根纱线,选取它在编织体各个区域内合适的控制点,过这些控制点拟合成三次样条曲线,以此模拟纱线的空间结构中心线。最后得到纱线和编织体的结构。     

Characterization and comparative study of three-dimensional braided hybrid composites

Cartesian three-dimensional braiding as a method of preforming for hybrid composites has been investigated. The fundamental case of a two-sided hybrid 3-D braid was chosen. Hybrid preforms, along with a corresponding set of non-hybrid preforms for control, were fabricated using a Cartesian braiding method. The preforms were consolidated through a Resin Transfer Molding process and prepared for characterization and mechanical testing. Characterization of the braided hybrid composite specimens included yarn packing and deformation within an assumed unit cell, and measurement of constituent tow fiber volume fraction using digital image analysis. A comparison study of the elastic performance of Kevlar/epoxy and carbon/Kevlar hybrid composites was carried out. The tension test results show a near-linear stress-strain relationship for both specimen types within the range of the applied load. The tensile modulus for the carbon/epoxy and hybrid composite were found to be 41 GPa and 74 GPa, respectively. In addition, the Poisson ratio of near unity for both specimen types strongly suggests a fiber dominated material response. The difference in hybrid composite transverse strain due to the differing constituent fiberous materials is found to be appreciable. It is believed that this discrepancy in Poisson contraction, between the carbon and Kevlar sides of the specimens, causes the propagation of transverse cracks [primarily within the carbon tows] and ultimately leads to catastrophic composite failure. Composite ultimate strength and strain to failure were found to be 793 MPa and 1.9% for the Kevlar/epoxy sample and 896 MPa and 1.1% for the carbon/Kevlar hybrid.     

The effect of yarn distortion on the mechanical properties of 3D four-directional braided composites

A representative volume cell (RVC) is chosen to analyze the mechanical properties of 3D (3 dimensions) four-directional braided composites. Owing to braid yarns (an assembly of fibers) squeezing against each other in the braided composites, the braid yarns are distorted. Based on geometrical characteristics of the braided composites, cross-section of each braid yarn is supposed to be an octagon and divided into seven regions in the RVC. The distortion characteristics of yarns are considered in each region. Elastic properties of each region obtained by stochastic function theory are introduced into finite element model to calculate the mechanical properties of the RVC. The influences of yarn distortion on the stiffness and strength of the braided composites are obtained and discussed.     

Tensile behaviour of multi-layered braided structures

Multi-layered braided structures are formed as a result of over-braiding the previously formed braids and they are increasingly being used for numerous applications ranging from hoses to energy absorbing composites. In this research work, a series of multi-layered braided structures were prepared on circular braiding machine for obtaining various combinations of braid angles of 30° and 45° in inner and outer layers. Subsequently, the tensile properties of multi-layered braided structures were analysed and it was found that the braid angle in the outer layer has significantly affected the stress–strain behaviour. A simple analytical model for predicting the tensile behaviour of multi-layered braided structures has also been proposed based on the previously developed model of ‘braid-elastic core’ system. A clear distinction has also been made between the helix and braid angles. Furthermore, a comparison has been made between theoretical and experimental values of braid angle, toughness and stress–strain characteristics of multi-layered braided structures.     

Geometric mapping of yarn structures due to shape change in 3-D braided composites

The internal yarn structure in 3-D braided preforms possesses a certain topological character which is unique to the braiding method used. Hence, preforms of different shapes but braided by the same method have topologically similar yarn structures. This unique property offers the possibility that the yarn structure in preform of one shape may be geometrically mapped to that in another shape, and vice versa.

This study discusses a geometric mapping methodology, the objective of which is to obtain the appropriate mapping which analytically links the yarn structures in two preforms of different shapes; if the yarn structure in one preform is known, the yarn structure in the other can be determined by the derived geometric mapping.

Two broad classes of mapping are discussed. The first concerns mapping between two preforms that are braided directly in two different shapes; the second concerns mapping between the initial and final shapes of one single preform which is deformed after braiding. In each case, the mathematical forms of the desired mapping functions are obtained, satisfying the geometric constraints imposed by the internal yarns in the respective preforms. The determined mapping functions are then used to investigate the braidability and/or deformability of the considered preforms. Specifically, limiting windows for the braiding parameters that insure the braidability and/or deformability of the preforms are obtained using the appropriately derived mapping functions.

The 4-step 1 × 1 braiding method is used throughout this paper to illustrate the general mapping procedure; rigorous and explicit geometric relationships are derived leading to mapping functions between preforms of rectangular and curvilinear cross-sections. Numerical examples involving mapping between preforms of rectangular and tubular cross-sections are investigated in detail, along with examination of the preform braidability and/or formability.     

Prediction of the yarn trajectories on complex braided preforms

Braiding can be used to manufacture preforms for resin transfer moulding (RTM). With braiding, many yarns are used, non-geodesic yarn paths are possible, and the interlaced structure of braids provides typical mechanical properties such as high impact strength. Previously, several models were developed to predict the fibre angles on simple, stationary braided preforms, but not for complex, non-axisymmetric preforms. This paper presents a fast and efficient model to predict the fibre angles on complex biaxially braided preforms. The model is verified with experiments on two mandrels and the experimental and numerical results show good agreement.     

矩形组合截面四步法二次三维编织及其空间模型可视化

针对矩形组合截面1×1三维编织, 根据其主体纱和边纱的特点, 在四步法和分组编织的基础上, 通过对2组编织纱线依次进行四步法移动, 实现了矩形组合截面四步法二次三维编织算法。根据此算法, 利用Python脚本语言和GUI工具Tkinter编写了纱线运动模拟程序, 分析了纱线运动规律。对纱线中心线控制点做了3次Beta-Splines样条插值, 利用VTK构建了三维编织物的空间可视化模型, 并允许对该模型进行直观的人机交互操作。      

三维六向编织复合材料弹性性能理论预测

在三维六向编织物纱线运动规律的基础上, 建立了单胞模型, 推导了编织参数之间的数学关系。基于该模型, 采用改进的刚度平均化方法, 导出了三维六向编织复合材料的工程弹性常数, 分析了编织角和纤维体积含量对弹性性能的影响。结果表明, 三维六向编织复合材料具有良好的力学性能, 由于面内纬纱的加入, 使面内的力学性能得到了提高。      

Braiding Simulation and Prediction of Mechanical Properties

Rotary braiding is a cost effective method to manufacture near net shaped preforms that generally have a closed section and may have an arbitrary shape if braiding is performed over a shaped mandrel. The reinforcement architecture can be varied by the number and spacing of active bobbins, and by the speeds used to ‘take-up’ the braid and move the circumferential bobbins. Analytical methods are available that can reliably predict yarn paths and the final braid meso-structure for simple regular sections, and further analytical methods have been proposed to estimate composite braid elastic mechanical properties. A full simulation chain using the explicit Finite Element (FE) technique is presented for composite braid manufacture and mechanical stiffness prediction of the final composite. First simulation of the braiding process provides detailed information on yarns paths and braid meso-structure, from which Representative Volume Elements (RVE) of the braid may be constructed for analysis of stiffness properties. The techniques are general and can be applied to any braid geometry. A specific problem of meshing the yarn structure and interspersed resin volumes is overcome using conventional solid elements for the yarns and Smooth Particle Hydrodynamics for the resin, with link element to join the two constituents. Details of the background theory, braid simulation methods, meso- model analysis and validation again analytical and test measurements are presented.     

三维五向编织复合材料中纱线截面形状实验分析

采用CCD显微摄像仪获取了树脂基三维五向编织复合材料的一系列截面图像, 分析了编织复合材料内纱线的排列规律及其截面形状的变化。实验结果显示: 沿编织成型方向, 三维五向编织复合材料的不同横截面内纱线的排列方式不同, 且呈周期性变化; 编织纱线的截面形状近似为扁平的凸透镜形; 第5向不动纱的轴线基本保持伸直, 其截面形状沿其轴向近似为扇形和三角形相互过渡变化; 表面编织纱线的排列方式与内部编织纱线的排列有关, 其截面形状近似为椭圆形。     

三维全五向编织复合材料的细观结构分析

针对三维全五向编织复合材料,研究了其四步法编织工艺的实现过程,并详细描述了编织复合材料各控制区域内纱线的空间走向及运动规律,在此基础上建立了能反映三维全五向编织复合材料基本结构的几何单胞模型。通过分析编织物内纱线间的空间挤压关系,设定合理的假设,计算了全五向编织复合材料的纤维体积含量,并分析了纤维体积含量与编织工艺参数之间的关系,为进一步研究该材料的力学性能奠定了基础。     

A yarn interaction model for circular braiding

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.     

二步法方型三维编织复合材料的细观结构

对二步法方型三维编织复合材料的三维五向结构进行了真实的描述与分析。在此基础上划分出边上、角上和内部单元体。通过对复合材料的横截面以及与试件表面成45°的纵切面进行观察,确定出轴纱因受编织纱捆绑挤压产生的形变情况以及轴纱内纤维体积含量。     

Micro-CT Characterization on the Meso-Structure of Three-Dimensional Full Five-Directional Braided Composite

The meso-structure is important in predicting mechanical properties of the three-dimensional (3D) braided composite. In this paper, the internal structure and porosity of three-dimensional full five-directional (3DF5D) braided composite is characterized at mesoscopic scale (the scale of the yarns) using micro-computed tomography (micro-CT) non-destructively. Glass fiber yarns as tracer are added into the sample made of carbon fiber to enhance the contrast in the sectional images. The model of tracer yarns is established with 3D reconstruction method to analyze the cross-section and path of yarns. The porosities are reconstructed and characterized in the end. The results demonstrate that the cross sections of braiding yarns and axial yarns change with the regions and the heights in one pitch of 3DF5D braided composites. The path of braiding yarns are various in the different regions while the axial yarns are always straight. Helical indentations appear on the surfaces of the axial yarns because of the squeeze from braiding yarns. Moreover, the porosities in different shapes and sizes are almost located in the matrix and between the yarns.     

三维方型编织预制件的纱线编织结构

主要研究了四步法1×1 编织预制件的纱线编织结构。采用控制体积单元法和实验观察相结合的方法, 根据携纱器的编织运动规律, 将预制件分为三个区域, 识别了局部单胞模型。在椭圆形横截面假设的基础上, 考虑了编织纱线的填充因子, 建立了编织工艺参数之间的关系。      

Finite Element Analysis of Mechanical Properties of 3D Four-directional Rectangular Braided Composites—Part 2: Validation of the 3D Finite Element Model

In the first part of the work, we have established a new parameterized three-dimensional (3D) finite element model (FEM) which precisely simulated the spatial configuration of the braiding yarns and considered the cross-section deformation as well as the surface contact relationship between the yarns. This paper presents a prediction of the effective elastic properties and the meso-scale mechanical response of 3D braided composites to verify the validation of the FEM. The effects of the braiding parameters on the mechanical properties are investigated in detail. By analyzing the deformation and stress nephogram of the model, a reasonable overall stress field is provided and the results well support the strength prediction. The results indicate it is convenient to predict all the elastic constants of 3D braided composites with different parameters simultaneously using the FEM. Moreover, the FEM can successfully predict the meso-scale mechanical response of 3D braided composites containing periodical structures.