Research status of simulation modeling technology for the 3D braiding process

Abstract

Three-dimensional (3D) braiding has excellent mechanical properties due to its unique spatial organization, in which simulation modeling of the braiding process is a key technology to study the complex spatial structure of 3D braided fabrics. The paper first summarizes the research methods of 3D braiding simulation modeling technology in recent years; second, it focuses on the analysis of numerical method modeling based on geometric dynamics, geometric modeling based on the braiding process, and modeling based on the finite-element method; then, based on the existing technology and application status quo, it sums up the advantages and shortcomings of the current 3D braiding process simulation modeling technology; and, finally, it describes the challenges and opportunities of the 3D braiding simulation modeling technology. The future development direction of the three modeling methods and the new idea of mutual coupling of the three methods are proposed and future development prospects are described. The paper provides technical support for the simulation modeling of the braiding process in 3D braiding technology.

Keywords

three-dimensional braiding simulation modeling braiding process numerical methods geometric modeling finite-element analysis

Three-dimensional (3D) braided composites have provided significant improvements in the specific strength and specific modulus of materials owing to its overall complex yarn interwoven structure and improved interlayer connection strength over other laminated materials,¹ and has received widespread attention from all walks of life due to this and many other advantages, such as good structural integrity and designability.^2,3 3D braiding is a braiding method in which yarns are interlaced in three dimensions to form a continuous, interconnected fiber web. This method allows the yarns to be interlaced in three directions, axial, radial, and circumferential, without the need to stack individual layers. This results in a single fabric with cohesion that is reinforced with fibers in all three dimensions is known as a 3D braid. It has become an important structural material in the aerospace, energy, major strategic equipment, rail transport, automotive industry, carbon/carbon composites, urban infrastructure, biomedical, sporting goods, and other fields.⁴ 3D braided structures exhibit superior strength due to the interlocking nature of the fibers, resulting in a more-even distribution of stresses throughout the material. 3D braiding is capable of producing complex shapes and structures that are difficult or impossible to achieve with conventional weaving or knitting. However, the technology and machinery required for 3D braiding is complex, and the initial setup of the process can be very time-consuming, especially for new designs that require extensive testing and validation. With the rapid development of computer technology to promote the progress of simulation technology, 3D braiding process simulation modeling technology can be used to predict the braiding and forming process, which can be efficient and reasonable for manufacturing 3D braided composite materials. 3D braiding process simulation modeling technology provides technical support to ensure the excellent performance of 3D braided composites.

Due to the excellent performance of 3D braided composites, many scholars have researched 3D braiding technology and published reviews of related research. In terms of 3D braiding equipment and the 3D braiding process, Bilisik⁵ reviewed the development of 3D braided precast structures, 3D braiding technology and methods, pointed out the limitations of the current 3D braided composites performance, and proposed that the multi-axis 3D braiding technology should be developed in the direction of automation, but the text lacks a summary of the research on the design of the braiding process as well as the methods of simulation and modeling of the braiding process. Li et al.⁶ discussed the braiding equipment and braiding process, mainly introducing different types of braiding machines, working principles, and a variety of braiding structures, summarized the research hotspots of 3D braiding technology and the future 3D braiding equipment needs to solve the engineering problems; however, the text did not address the long period of the design of the braiding process, the lack of simulation modeling methods, and other issues. Li et al.⁷ reviewed the development of 3D braiding technology from the aspects of 3D fabrics, braiding technology, braiding equipment, etc., and stated that the future research direction should ensure the performance of braided composites while realizing the automation of 3D braiding, but how to design the braiding process and how to simulate the braiding process were not discussed in the paper. In terms of analyzing the relationship between the fine structure and mechanical properties of 3D braided composites, Han et al.⁸ reviewed the two aspects of 3D braided composites braiding process and the fine structure of braided composites, briefly introduced the braiding method, equipment, and the exploration of the braiding method and the research process, and sorted out the modeling methods of the fine structure of braided composites as well as the direction of the future research on the fine structure. However, the design of the braiding process affects the fine structure of the braided composites, and the simulation of the braiding process is particularly critical, and the simulation of the braiding process is not mentioned in the paper. Gu et al.⁹ reviewed the research related to the structural mechanical modeling of 3D braided composites in recent decades, including the modeling of fiber tilt model, multi-cell model, and numerical element method, which are divided into three categories, namely, mechanical equivalent model, cell geometric model, and yarn geometric model, and reviewed and discussed the mechanical properties of 3D braided composites, and proposed that the interrelationships between the modeling of braided structures and other factors that may affect the mechanical characteristics of braided composites should be further explored. Chen et al.¹⁰ reviewed the braided structure effect, mechanical response, and failure mechanism of 3D braided composites under different strain rates through experimental and simulation analysis methods. The damage evolution and stress propagation of 3D braided composites were explained from macroscopic and microscopic perspectives through finite-element modeling methods. Although the finite-element modeling methods were mentioned in the paper, it lacked a comprehensive analysis of the simulation technology methods for the 3D braiding process. However, the paper does not mention the relationship between the simulation modeling of the braiding process and the modeling of the braided structure. It is proposed that the interrelationships between the modeling of braided structures and other factors that may affect the mechanical characteristics of braided composites should be further explored. The above review summarizes the mechanical property analysis of 3D braiding equipment, 3D braiding process, and microstructure of braided composites, and proposed the future development direction of 3D braiding equipment, process, and microstructure mechanical analysis of braided composites. However, the research on the braiding process of 3D braided composites is less mentioned, and there is a lack of analyses and summaries of 3D braiding process simulation technology, which makes it necessary to analyze and explore the methods of 3D braiding process simulation modeling.

This paper reviews the research on simulation modeling technology of the 3D braiding process. First, the research progress of the three main simulation modeling methods, such as numerical method modeling based on geometric dynamics, geometric modeling based on braiding process, and finite-element method modeling are reviewed; second, the hot issues and solutions of the current research of the three methods are analyzed and contrasted; and, finally, the strengths and weaknesses of the three methods are discussed and the directions of future development and the problems that need to be solved are presented, and new ideas on the mutual coupling of the three research methods are proposed. The work of this paper can provide some theoretical references for related researchers to fully understand the current research status in this field.

Simulation modeling methodology

The research methods of 3D braiding process simulation modeling technology are mainly divided into three categories. The first category is based on the numerical method of geometric dynamics modeling, which can provide detailed information on the state and performance of braided composites. The second category is based on the geometric modeling of the textile process, which can simulate and analyze the important parameters such as the yarn and the trajectory of yarn carriers in the process of braiding. The last category is based on the finite-element method, which can more accurately simulate the behavior and response of braided composites. These three methods are closely related and complementary to each other in the simulation modeling of the 3D braiding process and jointly promote the development of 3D braiding technology.

Numerical modeling of geometric dynamics

The numerical modeling method based on geometric dynamics (shown in Figure 1) is to establish a geometric dynamics model of the 3D braiding process by analyzing the interweaving of the yarns and the interaction between the yarns and the mandrels and to analyze the influence of the 3D braiding process on the geometric structure of the 3D braided composites. Geometric dynamics¹¹ is the systematic study of trajectories, velocities, accelerations, and other kinematic properties, of objects in space, and the representation of these motions on geometric figures, which is often combined with differential equations and dynamical system theories to describe the motion characteristics of various mechanical and dynamical systems.

Before Zhang et al.¹² analyzed the yarn motion, the “straight yarn assumption” was made, which means that all yarns in the convergence zone are straight. Each yarn starts at the bobbin and ends at the mandrel in the tangential direction. As shown in Figure 2, P₁P₂ is a straight yarn in the convergence zone and the braiding angle α/2 is the angle between P₁P₂ and P₂P₃. From this, the braiding angle can be deduced as

\frac{α}{2} = \tan^{- 1} \frac{P_{1} P_{2}}{P_{2} P_{3}} = \tan^{- 1} \frac{\sqrt{R_{S}^{2} - R_{m}^{2}}}{H}

(1)

where R_m (D_m) and R_s (D_s) are mandrel and spool radii (diameters), respectively, and H is the distance between spool plane and fell plane.

The braid angle determines the helical length L:

L = \frac{π D_{m}}{\sin \frac{α}{2}}

(2)

Since the other yarns in the braiding process are just repeating the same motion at different positions, only one yarn needs to be analyzed, and the yarn motion can be considered as the vector sum of the circumferential and axial motions as shown in Figure 3:

V_{M i} = V_{τ} + V_{a}

(3)

where M_i (i = 1 in Figure 3) is a certain fixed point on a yarn, V_τ is the circular velocity vector, and V_a is the axial velocity vector along the yarn; each are discussed in the following.

Next, Zhang et al.¹³ simplified the convergence zone during the braiding motion into a cone as shown in Figure 4. The yarn A O in Figure 4 was divided into k elements, and equilibrium analysis was performed at each interweaving point. As shown in Figure 5, the tension and normal force on the yarn after it has been straightened reveal the true length of the yarn. Here T_m is the mandrel side tension and T_s is the yarn tension. The interleaving point and normal force are denoted as A_i and N_i, respectively, where i is from 1 to k. The interleaving angle θ_i is the angle between the axial tension of the yarn and the plane of unfolding, which is necessary for the determination of the normal force: θ_i is a parameter determined on the basis of the diameter of the yarn and the distance d_i. To analyze the yarn A O, Figure 6 shows the force acting on one of the interweaving points, point i, of the yarn A O. Thus there are three equilibrium equations and one friction equation in the x, y, and z directions. Here ζ_i denotes the angle between the force and the friction force, C₁ denotes the coefficient of friction, and C₂ denotes the friction index:

F_{x} = - T_{i} \cos α_{i} + T_{i + 1} \cos α_{i + 1} - F_{i} \sin ζ_{i} = 0

(4)

F_{y} = T_{i} \sin α_{i} - T_{i + 1} \sin α_{i + 1} - F_{i} \cos ζ_{i} = 0

(5)

F_{z} = T_{i} \sin θ_{i} + T_{i + 1} \sin θ_{i + 1} - N_{i} = 0

(6)

F_{i} = C_{1} {N_{i}}^{C_{2}}

(7)

Braiding technology was first applied in the aerospace field in the 1980s, when the study of the 3D braiding process was mostly based on repetitive field experiments, which enabled the determination of braiding process parameters. Due to the more cumbersome experimental method, long design cycle, high design cost, etc., Du and Popper¹⁴ first proposed a detailed modeling of the braiding process, through the braiding shape and the mechanical arm extracted mandrel speed associated with other key parameters of the method of predicting the braiding process of the braiding machine, the yarn volume fraction, and other fabric geometric structures, to avoid the experimental method wasting resources. Based on the above research, some scholars have been studying 3D braiding based on the numerical method modeling of geometric dynamics, mainly from the analysis of the interweaving situation between yarns and the analysis of the interaction between yarns and mandrels.

In terms of analyzing the interweaving of yarns, Zhang et al.¹² analyzed the kinematics of the circular braiding process by taking into account the effects of absolute motion, relative sliding, and twisting of yarns in the convergence region to obtain the braiding angle of the 3D mandrel surface, and concluded that the friction between yarns during the braiding process resulted in the slowing down of yarn deposition to the mandrel and the reduction of the braiding angle. Based on the above study, Zhang et al.¹³ also analyzed the geometrical structure and related mechanical properties of braided fabrics and established a mechanical model describing the braiding process considering the inter-yarn friction, which can predict the braiding angle of fabrics more accurately, and concluded that the inter-yarn friction affects the final fabric structure of braided composites. Kessels and Akkerman¹⁵ proposed a braiding angle prediction model for complex biaxial braided precast bodies, which is efficient in predicting the braiding angle of complex mandrels in a 3D braiding process, but neglects the slip phenomenon when yarns are deposited on the surface of the mandrels. Van and Akkerman¹⁶ addressed the problem of the significant deviation of the change in the cross-section of the mandrels to the braiding angle due to the neglect of the interaction between the yarns and analyzed the relationship of the interaction force with the braiding angle for the axisymmetric biaxial braiding process, but did not consider the case of asymmetric biaxial braiding. Ni and Wei¹⁷ determined the mechanical model of the yarns in the braided precast by analyzing the 3D four-step rectangular braided composites, analyzing the interweaving of the yarns as shown in Figure 7, established the basic cellular model of the braided precast as shown in Figure 8, determined the spatial topology of the internal yarns, fitted the trajectories of the yarns by three times spline curves, and finally proposed an improved braided geometrical model. Wang et al.¹⁸ proposed an effective preform boundary reflection (PBR) method to model the yarn motion based on the simplified yarn interweaving motion. Based on the interweaving motion of the yarns, a CAD system that can automatically generate the geometry of 3D braided composites with arbitrary braiding parameters based on the simplified motion model was developed using MATLAB, Visual C++, and SolidWorks.

In conclusion, the geometric dynamics modeling while considering the internal interwoven structure of the yarns can effectively predict the braiding angle as well as plot the yarn trajectory and finally generate the fabric structure. Based on the above study, other important influencing factors such as the interaction force between the yarns need to be considered to make the braiding angle, yarn trajectory, and its fabric structure more accurate during the braiding process.

2. In terms of analyzing the interaction between yarns and mandrels, Nishimoto et al.¹⁹ proposed a prediction method based on the variation of braiding angle over time due to the change of mandrel speed by analyzing the interrelationship between yarns and mandrels, which analyzes the starting stage of 3D braiding and predicts the braiding angle of cylindrical regular mandrels under non-steady-state conditions, but the method does not consider factors such as the interaction of yarns, so the prediction accuracy is not high. Rawal et al.²⁰ developed a geometric model of yarn trajectories on the surface of cylindrical and conical mandrels with rhombic, regular, and triaxial braiding patterns, which modeled 3D braiding for regular mandrels, with less error between the theoretical and actual values of the braiding angle and higher accuracy, and which provided a reference idea for the subsequent 3D braiding of complex mandrels. Gondran et al.²¹ proposed a method for calculating the mandrel extraction velocity profile to achieve the desired braiding angle, which iteratively calculates the velocity profile starting from an approximate model and designing simulations and field experiments for correction based on the yarn–mandrel interaction, which is effective on non-axisymmetric, curved, and variable cross-section mandrels, with small errors in the braiding angle. Imbert et al.²² proposed a new method combining mechanical and geometrical approaches to model the yarn interweaving situation and deposition process in 3D braiding, using the Newton–Raphson method to solve the geometrical and mechanical equilibrium of the whole braided composite material in the convergence zone to obtain an accurate 3D braiding model. The model is designed for 3D braiding of irregular mandrels but does not take into account the complexity of industrial production and ignores factors such as interactions between yarns under external interference conditions. Meng et al.²³ studied the relationship between the mandrel movement process and the yarn according to the 3D mandrel structure parameters as shown in Figure 9, under the consideration of yarn tension perturbation, a real-time prediction of the offset under the complex mandrel is proposed and an accurate trajectory is generated after offset compensation, which effectively puts the braiding angle error under control, and the theoretical braiding angle, and the comparison of braiding angle before and after compensation are shown in Figure 10. Li et al.²⁴ proposed a trajectory-solving method based on dual robots cooperatively clamping the mandrel, which can solve the braiding problem of large-size shaped structural mandrels. Meanwhile, a yarn trajectory prediction model for the dual robots’ trajectory was established, which can accurately predict the shaped structural mandrels, improve the braiding efficiency, and enhance the mechanical properties of the braided composites under the same conditions. In conclusion, by studying the relationship between the movement of the core axes for modeling, the yarn trajectory can be visualized and the trajectory error can be reduced, and the complex core axes should be analyzed based on this study to realize the visualization of the yarn trajectory on any core axes.

Based on the above research, although the numerical method based on geometric dynamics can simulate and model the braiding process to obtain the prediction results quickly, most scholars only consider the interweaving relationship between yarns or the interaction between yarns and mandrels, and the assumption conditions of modeling have a large deviation from the actual production conditions, so it is not possible to simulate the actual production process. As a result, the model established by the numerical method based on geometric dynamics has a large error with the actual production data, and there is an urgent need for a new method to solve the problem of the large error between the realistic numerical model and the actual production data of the 3D braiding process modeling.

Geometric modeling of the braiding process

The geometric modeling method based on the braiding process (shown in Figure 11) to establish a simulation model of the 3D braiding process by analyzing the braiding process parameters, braiding method, yarn trajectory paths, and other factors, and to analyze the influence of the 3D braiding process on the geometric structure of the braided composites. According to the 3D braiding process parameters, the programming method is used to simulate the whole process of braiding, obtain the spatial coordinate points of the fiber bundle trajectory, and import all the coordinate points into the computer-aided design (CAD) software to carry out the 3D visual solid modeling of the overall 3D braided structure. This is also a new type of modeling approach that many scholars are exploring. Currently, it is mainly researched from the three aspects of predicting the fabric structure by fitting the yarn trajectory, simulating the direction of the braiding process, and analyzing the motion law of the yarn carrier to deduce the fabric structure.

Aspects of yarn trajectory fitting for predicting fabric structure

Kostar and Chou²⁵ developed an algorithm for the simulation of braided composite structures in a Cartesian coordinate system through the fundamentals of multistep braiding used for the fabrication of 3D braided composites, which identifies the individual yarn paths, the number and location of yarn groups, and the braided composite geometries, which can be used for fabrication of a variety of 3D braided composite structures, and the methodology has enabled the microscopic The structural possibilities of 3D braided composites have been greatly expanded. Liao and Adanur²⁶ developed a CAD model to describe the external and internal geometries of 3D circular braided layers to simplify the design process of the braiding process. A 3D trajectory was used to represent the yarn shape, which takes into account the structural characteristics of the braid and the finite dimensions of the fibers and simulates the fabric more accurately. Shao et al.²⁷ obtained a simulation method for designing and realizing 3D longitudinal and transversal step braiding composites by simulating the braiding motion through a computer and fitting the yarn trajectories with Bezier curves according to the basic braiding principle of 3D longitudinal and transversal step braiding, by describing the braiding diagram in a braiding manner and converting the braiding process into the form of mathematical substitution operation. Deng et al.²⁸ took four-step rectangular 3D braided composites as an example, based on the analysis of 3D four-step braiding motion law as well as the yarn motion law, to solve the geometric simulation problem of 3D braided composites. The mathematical model between the braiding process parameter and the geometric structure was established, and then UG was used as the 3D display platform and MATLAB was used as the control core, to realize the 3D pre-modeled entity geometric simulation. Yang et al.²⁹ proposed a simpler method of mapping the yarn motion model based on the law of yarn motion in the 3D four-step braiding process and simulation analysis, meanwhile, they developed a CAD system for analyzing the 3D rectangular braided preforms, and re-developed Solidworks software for geometric structure simulation using VC++. Xiao et al.³⁰ studied the four-step 3D braiding motion law, by fitting the spatial coordinates of the yarn, designing the static model algorithm of the yarn entity, and, finally, establishing the static model of the yarn entity, which realizes the motion simulation in the process of braiding. Zhang and Yan³¹ deduced the algorithm of four-step braiding according to the braiding parameters, obtained the specific process parameters of the braided body, and then used MATLAB to write a script to track the movement of the yarn carrier, determine the spatial position coordinates of the yarn movement and store them in a matrix, write a B uniform spline curve script and import the spatial yarn position points in CATIA software and generate the spline curve to realize the simulation of the 3D four-step braiding as well as rectangular braiding. Simulation of braiding and modeling of rectangular and circular braiding. Li et al.³² established the yarn trajectory as well as the fabric structure in MATLAB by analyzing the fabric surface, fitted the yarn trajectory using B-spline curves, and optimized the model based on the coordinate transformation algorithm, and the fabric model was optimized as shown in Figure 12, which establishes a more precise circular hexagonal fabric structure.

In summary, the method of yarn trajectory fitting to predict the fabric structure is mainly through the analysis of braiding parameters and mathematically represented, the yarn trajectory is visualized in spatial position coordinates, and, finally, the trajectory is fitted to form the fabric structure. Among the described processes, adding a B-spline curve and other methods in the process of yarn trajectory fitting can reduce the error of yarn trajectory. Based on the above study, factors such as interactions between yarns should be considered to improve the modeling accuracy.

Simulation aspects based on the braiding process

Na et al.³³ developed a mathematical model for predicting the braiding pattern on arbitrarily shaped mandrels based on the parameters of the braiding process. The model contains the basic requirements for forming the braiding pattern. The minimum path condition was also introduced to reflect the braiding process parameters more strictly. The model predicts the braiding pattern on the mandrel within a suitable accuracy range and provides an effective means of designing braided composites. Swery et al.³⁴ predicted the manufacturing process of braided composite parts using a complete simulation process chain to predict the braiding results for braiding using various braiding process parameters. Yang et al.³⁵ simulated the entire process of braiding a yarn bundle based on the actual four-step braiding process from fiber twisting to yarn bundle braiding and established the relationship between braiding parameters and the structure of braided composites, which will help to improve the preparation process of braided composites. Wang et al.³⁶ proposed a method for the simulation of braiding machine motion and the generation of geometric models of yarn braiding structure. For the motion simulation of a traditional circular braiding machine, a compact geometric modeling method for yarn braiding structure was proposed. Ding et al.³⁷ proposed a MATLAB-based computer-aided braiding method for the hexagonal 3D braided stent, which plans and determines the interweaving method of yarns on the mandrel through the chassis paths of the hexagonal braiding process as shown in Figures 13 and 14. At the same time, MATLAB was used to calculate the interweaving order and interweaving mode of the yarns in each section, and the 3D solid model of the stent with different braiding processes was constructed as shown in Figure 15. Liao et al.³⁸ proposed a virtual braiding method and investigated the effects of 3D braiding process parameters (including starting yarn angle and tension) on the structure of braided composites. Decreasing the yarn angle or increasing the yarn tension leads to a tighter structure of the braided composites, which is beneficial for the analysis of the structure of the 3D braided composites as well as the design of the 3D braiding process. In conclusion, the method of fabric modeling by combining the virtual braiding technology with the braiding process can realize the rapid design of the 3D braiding process and fabric structure modeling. Wang et al.³⁹ explored the structure of a prefabricated body based on a triangular braiding process, developed the braiding process software based on Python language and CATIA, and established the parametric geometric model of a prefabricated body.

However, this method does not consider the interaction between yarns and whether the on-site production meets the conditions of this method, so the future development direction should consider the above factors while modeling and improving the accuracy of the fabric structure.

Analyzing the laws of motion of yarn carriers to derive fabric structures

Tada et al.⁴⁰ studied the braiding structure of coupled rectangular braided layers and its structural parameters, investigated the process of braiding composites with various cross-sections, and proposed a design method for arranging the yarn carrier gears and determining the paths of the carriers as well as the number of carriers. Kyosev⁴¹ designed algorithms for simulating the machine configurations as well as calculating the paths of the carriers and developed a program for simulating the movement of the braiding machine by inputting the process parameters. Kim⁴² developed a circular braiding simulator that can simulate any number of corner wheels and calculate complex paths of multi-layer interlocking braided yarns based on the relative motion between the corner wheels and the spindle, which can be done on a mandrel of arbitrary contour. Kyosev⁴³ proposed a modeling algorithm related to a 3D braiding machine in which the corner wheels of the braiding machine have independent actuation switches to produce fabrics with complex cross-sections and the fabric structure can be changed during the production process. Mei et al.⁴⁴ proposed a method for modeling the process as well as the topological yarn structure relationships of 3D rotary braided composites and developed an algorithm for the automatic design of yarn interleaving in braided composites by tracking the carrier paths with a machine control code, where the carrier paths are characterized by computable switching configuration matrices, which is used to establish, without considering the volume of yarns, the lattice-like ideal yarn topology, which provides a potential method for the exploration of braided structures, as well as guidance for the control of rotary braiders. Next, Mei et al.⁴⁵ further investigated the effect of the yarn-carrier configuration on fabric structure and found that the difference in the number of yarn carriers in a certain yarn-carrying path led to different interweaving densities of yarns, which resulted in different yarn topologies and, meanwhile, the addition of axial yarns during the braiding process was able to eliminate the effect of the larger size of the internal crystalline cells and the lower volume fraction of the fibers due to the number of carriers, and the results provide a reference for new braiding methods. Based on the hexagonal 3D braiding process, Lv et al.⁴⁶ analyzed the motion law of the yarn carrier during the braiding process, wrote an algorithm using MATLAB to convert the motor control matrix it reads into the coordinates of the spatial trajectory points of the braided yarn, fitted the trajectory of the yarn motion using B-spline curves, and then optimized the yarn cross-section and the length of the node to obtain a structural yarn model that can well reflect the real braiding samples. Yang et al.⁴⁷ deduced the running path of the yarn carrier based on the movement law of the second-generation hexagonal braiding corner wheel and the conversion device and wrote a coding program to simulate the travel path of the yarn carrier. The spatial path of yarn movement is obtained by calculating the distance traveled in the braiding axial direction, and the spatial path is optimized by using the B-spline method, and, finally, the function is used for the solidification simulation, which realizes the visualization of fine structure. Li et al.⁴⁸ established the relationship between braiding parameters and honeycomb geometric parameters according to the basic principles of 3D braiding and the braiding process, based on the principle of the four-step method of 3D braiding, the interweaving state of yarns can be changed by controlling the movement of the yarn carrier, thus controlling the separation and combination of the braided composites, which results in the formation of a 3D braided honeycomb fabric, and the braided parameters and fabric structure were created using a machine simulation approach The flow of the process is shown in Figure 16. Li et al.⁴⁹ proposed an algorithm that can simply and effectively calculate the relationship model between braiding parameters and fiber structure to track the yarn carrier trajectory through machine simulation of Eulerian rotation matrix operations, while yarn volume was taken into account and shrinkage factor was introduced to optimize the yarn trajectory to predict the real fabric structure. In summary, the path of the yarn carrier is set according to the angle wheel, the reversing device, and the movement mode of the yarn carrier, the path is digitized, and the spatial coordinates of the yarn are expressed through the relationship between the mandrel and the yarn, and, finally, the virtual braided fabric is generated. The modeling method can meet the needs of the plant, but with more specific problems for analysis, there are greater limitations, so the future direction of the development of this method should be to meet the needs of any braiding modeling at the same time as ensuring the accuracy of the modeling.

In summary, although the current research on the 3D simulation of the 3D braiding process has been effective, the three methods still have problems that need to be solved. The method of modeling by simulating the braiding process lacks the analysis of internal structural interactions, which leads to errors in the prediction results. The method of deducing fabric structure by analyzing the motion law of the yarn carrier is mainly aimed at simulating specific local problems because the motion of the yarn carrier is controlled by the track of the braiding machine itself, so the method does not apply to the simulation modeling of all 3D braiding processes. The method of fabric structure prediction by yarn trajectory fitting has a higher computational cost, but the prediction result is accurate, which is one of the better prediction results among the three methods. However, the yarn prediction is more idealized, which ignores the actual production process, and it is possible to combine the law of motion of the yarn-carrying machine with the fitting of yarn trajectory to carry out 3D virtual braiding, which can improve the prediction result accuracy as well as realize the designability of fabrics.

Finite-element technique modeling methods

Modeling based on the finite-element method (as shown in Figure 17) takes into account the braiding of braided composites with complex mandrels while taking into account several neglected factors in the numerical method, such as the forces between the yarn and the guiding ring. Combining the above considerations, the 3D braiding model is finally established. The finite-element method⁵⁰ is an effective solution method for solving mathematical problems, and its basic solution idea is to divide the computational domain into a finite number of non-overlapping units. Within each cell, some suitable nodes are selected as the interpolation points of the solution function, the forces acting on the cell are equivalent to the nodes, and the variables in the differential equations are rewritten as linear expressions consisting of the node values of each variable or its derivatives with the selected interpolation function, that is, the interpolation function is used to approximate the substitution, and with the help of the variational principle or the weighted residual method, the differential equations are discretized to be solved.

Research on the finite-element method for the 3D braiding process has benefited from the rapid development of computer technology in recent years, and the current research mainly focuses on the establishment of a single-cell model for the fine structural characteristics of fabrics, the solid model reflecting the internal structure of fabrics, and the simulation of the braiding process, etc. This paper mainly focuses on the simulation modeling of the braiding process, so it summarizes the finite-element technology in simulating the braiding process. Due to the iterative updating of finite-element technology, it is possible to calculate the trajectory of yarn under geometric and mechanical constraints in the 3D braiding process. Pickett et al.⁵¹ used a finite-element method for simple regular cross-sections to predict the yarn paths and the fine structure of the final braided layer and proposed a method to use explicit finite-element techniques to perform a complete simulation chain for the braiding of braided composites and the prediction of the mechanical properties of the final composites, as well as the prediction of the mechanical stiffness of the final composites. Hans et al.⁵² proposed a method to simulate the braiding process utilizing finite-element techniques. This method involves analyzing a generic shape of braided composites, defining the boundary conditions of the braiding mandrel, extracting the corresponding braiding process parameters, and employing the necessary friction coefficient as an input parameter through both simulation experiments and field tests. The validity of the proposed method has been verified through rigorous simulation and field experiments. Swery et al.³⁴ predicted the properties of braided composites obtained from the braiding process based on a complete simulation of the process chain, which contains the prediction of the geometrical morphology of the braided composites obtained from 3D braiding and the prediction of the permeability of the composite cell geometries, which saves on the manufacturing costs by investigating the relationship between the geometrical structure of the composite preform and the permeability of the different regions, as well as by the complete simulation of the process chain. Wang et al.⁵³ to solve the problem of the inability of the ordinary braiding machine to use the closed annular shaft mandrel for continuous braiding, adopted a finite-element method to simulate the braiding process, reflecting the yarn trajectory of the prefabricated body, whose braiding angle can be realized by projection and surface flattening with a higher degree of accuracy, and obtained an effective method for predicting braiding angle. Zhou et al.⁵⁴ used a truss-cell-based simulation method to simulate the 3D four-way braiding process on a macroscopic scale using the finite-element method to obtain the spatial trajectory of the yarns during the braiding process and establish the relationship between the braiding parameters and the structure of the braided composites, and the overall simulation results are shown in Figure 18. Li et al.⁵⁵ proposed an optimization algorithm for the complex features of the mandrel surface and reconstructed the mandrel mesh to achieve the fast calculation of the parameters in the braiding process, as well as the prediction of the quality of the braiding angle, coverage, etc., which substantially reduced the design cycle of the braiding process.

In conclusion, the method of virtual braiding can improve the accuracy of predicting the performance of braided composites by simulating the braiding process through the finite-element technique, and considering the friction coefficient while giving the boundary conditions of the braided mandrels and the related braiding parameters. Based on this method, in the future, factors such as yarn extrusion, bending, torsion, and cross-section change can be taken into account in virtual braiding to improve the prediction accuracy of braided composites. However, the analysis of fabric structure requires the use of multiple software such as solid modeling software, meshing software, and finite-element software, which consumes a great deal of cost. At the same time, the designed fabric structure may not necessarily meet the factory production conditions. This will inevitably cause the existing braiding equipment and technology and fabric structure of the disconnect. Therefore, the finite-element method modeling still needs to be further optimized to meet the current production needs.

Analysis and discussion

The three main research methods of 3D braiding simulation modeling technology are geometric dynamics numerical modeling method, braiding process geometric modeling method, and finite-element modeling method, as shown in Figure 19.

In this paper, we review the advantages and disadvantages of geometric dynamics-based numerical modeling methods, geometric modeling methods based on the braiding process, and modeling based on the finite-element method, and the advantages and disadvantages of each of the three methods are directly compared in Figure 20.

Numerical modeling based on geometric dynamics can quickly predict the results, but the assumptions are too ideal and do not meet the needs of the current production environment. Geometric modeling based on the braiding process can truly reflect the braiding process, but it is mostly a problem-specific analysis and does not achieve a unified modeling to meet the simulation of any braiding process. Modeling based on the finite-element method can accurately describe the complex stress, strain distribution, and interactions between the yarns in the 3D braiding structure. Modeling based on finite-element method can accurately describe the complex stress, strain distribution, and interactions between yarns in 3D braiding structure, but it requires complex mesh division and model building, and the computational cost is large. The three methods have their own advantages and disadvantages, but they can complement each other. In other fields, Dou et al.³ summarized that the structural design should start from the integrated design of “process–structure–property” to improve the material–structure performance matching. Qian et al.⁵⁶ introduced the application of machine learning in the prediction of mechanical properties of textile composites. In the field of metamaterials design, Cui et al.⁵⁷ proposed an intelligent design system for fabricating metamaterials with specified mechanical properties without the need for extensive specialized equipment. Based on the above research ideas, in the aspect of braiding, the integrated fabric design idea of “process–structure–performance” is proposed, and the geometric modeling technology is applied to the finite-element method, which can greatly improve the modeling accuracy, and at the same time, numerical methods are introduced to consider the factors such as the interaction force between the yarns, which can greatly improve the prediction accuracy of the braided composites. Finally, the simulation data are imported into the database, and the machine learning method is used to realize the parametric design of the fabric structure. The coupling of numerical modeling method, geometric modeling method, and finite-element modeling method is shown in Figure 21, which can greatly improve the design efficiency and reduce the production cost by complementing each other’s advantages. An integrated “process–structure–property” braided fabric design optimizes carrier alignment. In the case of multiaxial loading, the orientation and alignment of the yarns help to tune the response of the composite to better withstand the forces. Maximizing material efficiency and reducing dimensional constraints improves the design of 3D braided fabrics. By using this design feature, users can explore a variety of configurations and predict how different yarn positions will affect structural performance under complex multiaxial loading. Ultimately, performance maps can be created to determine the optimal combination of yarn positioning and preformed structures to improve the overall strength and durability of the final product. At the same time, the “process–structure–performance” integrated braided fabric design provides a theoretical basis for 3D braided simulation modeling technology.

To realize the “process–structure–property” integration of braided fabric design, the following problems can be encountered.

At the early stage of design, it is necessary to closely combine various braiding processes with different fabric structures, and obtain the relationship between different braiding process parameters and fabric structure through simulation and experimental verification, which has high design cost, long design cycle, and does not meet the needs of rapid fabric design.

The process of fabric structure verification is characterized by high costs and long lead times for field experiments.

The braiding process is complex, involving yarn tension, braiding density, yarn carrier trajectory, yarn trajectory, and other elements, requiring efficient algorithms for simulation and optimization.

The current braiding process design software is mostly generic, which makes it difficult to meet the design needs of specific braided fabrics.

To solve the above problems, the following solutions are proposed.

The data generated during the simulation and experimental verification of the braiding process parameters and different fabric structures are proposed to be enhanced by data enhancement methods to ensure the effective training of the model and to provide data support for the parametric modeling of fabric structures.

Finite-element analysis can predict different fracture modes such as matrix cracking, fiber breakage, and delamination by simulating stress distribution and material behavior under load. By identifying critical stress points and potential failure mechanisms, simulations can guide the optimization of preformed structures and yarn positioning. Ultimately, an Iterable database is generated to provide a database for the design of integrated braided fabrics.

The yarn tension can be optimized by improving the structure of the yarn carrier device (not discussed in this paper); the braiding density is related to the braiding process parameters, and the algorithm encapsulation through the above-mentioned methods can achieve the optimal design; the trajectory of the yarn carrier can be extracted by recording the position of the carrier at each time through the establishment of a Cartesian coordinate system by the chassis of the braiding machine; and the yarn trajectory can be mapped through the trajectory and the spatial structure relationship of the carrier, and the trajectory mapping can be performed by the data generated during the simulation and experimental validation process to ensure effective training and provide data support for the parametric modeling of the fabric structure. The yarn trajectory can be mapped by the movement trajectory of the yarn carrier and the spatial structure relationship, and it is proposed to fit the yarn trajectory with a three times B-spline curve, which provides the theoretical basis for the simulation modeling of the braiding process.

Taking the main parameters of the braiding process as independent variables (braiding angle, radius of the corner wheel, movement mode of the corner wheel, arrangement of the exchange wheel, position of the yarn carrier, etc.), the overall structure of the design software is established according to the relationship between the parts to meet the design of a variety of braided fabrics, realize the design of a specific fabric, and provide theoretical support for the design software of the braiding process.

Conclusion

The key role of 3D braiding simulation modeling technology in the braiding production process cannot be ignored, which not only solves the traditional slow braiding design and high cost of braiding experiments but also realizes the analysis of the spatial topological relationship of braided composite materials. In recent years, the research results of 3D braiding simulation modeling technology have been effective, but with the use of numerical modeling, geometric modeling, and finite-element method modeling to study 3D braiding simulation modeling technology there are still some problems that need to be solved.

Numerical modeling methods based on geometrical dynamics have limited accuracy and are unable to predict braiding defects directly, often ignoring the effects of factors such as yarn interactions leading to inaccurate results. Numerical modeling methods need to be further investigated and optimized, and important influencing factors such as yarn interactions should be taken into account in the model to improve the prediction accuracy and obtain better predictions of the properties of braided composites.

The modeling complexity of geometric modeling methods based on the braiding process affects the performance of braided composites, and most of the research has been conducted for specific cases, lacking a unified design approach. The geometric modeling approach has a good development prospect in 3D braiding simulation modeling, but it still needs to be further optimized, and it should be investigated how to carry out unified modeling to better reflect the braiding process, realize parametric design, and accurately predict the performance of braided composites, and at the same time, reduce the modeling time and computational cost.

The modeling method based on the finite-element method requires complex mesh delineation and model building, with large computational costs; the accuracy of the finite-element model needs to be experimentally verified and calibrated, which is difficult to experimentally verify. The finite-element modeling method needs to be further optimized to realize the automatic establishment of analytical models, and how to ensure the reduction of computational costs and meet the production conditions while improving the prediction accuracy is the direction of subsequent research.

Braiding technology has developed into an important prefabricated part-forming technology, and the three methods mentioned above have certain difficulties in studying 3D braiding simulation modeling. To reflect all the advantages of the three methods, it is proposed to integrate the above three modeling methods into a new design method of braiding that integrates “process–structure–performance,” applying the modeling method of the braiding process to the finite-element method, and at the same time introducing the numerical method of geometrical dynamics, considering the interaction force between the yarns and other factors. The simulation data are imported into the database, and the machine learning method is used to realize the parametric design of the fabric structure. This improves the design efficiency of braided composites and reduces the production cost. The design method provides a theoretical basis for the automation, digitalization, and intelligence of braided equipment.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: Jiangsu Provincial Science and Technology Plan Project “Research and Development of Key Technologies for Intelligent and High-precision Three-dimensional Braided Prefabricated Equipment” (BE2022061-2); and China National Textile and Apparel Council Science and Technology Guidance Project “Research on Core Technology of Intelligent Braiding Equipment and Production Line for Artificial Blood Vessels” (2021162).

ORCID iDs

Chengxu Yuan

Xin Rong Li

Shijie Zhang

Shun Li

Kui Ma

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