A Computer Simulation Method for a Six-Tooth Annular Three-Dimensional Braided Structure

Abstract

The present invention is mainly applied to the technical field of six-tooth annular three-dimensional braiding forming, and mainly provides a simulation prediction algorithm for a six-tooth annular three-dimensional braiding structure. The main feature of the method is to digitalize and parameterize the braiding process through machine simulation, and to perform digital simulation of the braiding model structure by establishing various types of matrix databases and calling and calculating them by a computer. The method includes the following steps: Step 1, determining the coordinate position of the yarn carrier; Step 2, generating the initial yarn trajectory; Step 3, optimizing the yarn trajectory characteristics; Step 4, adding mechanical tightening to the yarn trajectory coordinates; Step 5, materializing the yarn. The simulation structure obtained by the present invention has a very high accuracy through experimental comparison, and can predict the fiber structure between yarns, which plays an important role in the prediction of the microscopic structure, structure simulation and performance prediction of braided materials.

Description

Technical Field

[0001] The present invention is mainly applied to the technical field of six-tooth annular three-dimensional braiding forming technology, and mainly provides a simulation prediction algorithm for a six-tooth annular three-dimensional braiding structure. Background Art

[0002] Due to the requirements of modern industries such as aerospace and automotive for lightweighting, composite materials have gradually replaced metal materials. As an advanced composite material, three-dimensional braided composite materials have received great attention due to their superior designability, good integrity, and excellent mechanical properties. Compared with unidirectional fiber composite materials, laminates, and fiber-wound composite materials, it has great advantages. Three-dimensional braided composite materials not only have the advantages of high specific stiffness, high specific strength and density, and strong corrosion resistance, but also have better impact resistance, fatigue resistance, higher damage tolerance, and no interlaminar delamination. In fiber-wound and 2D braided composite materials, cracks tend to propagate at the interface between fibers and the matrix and delaminate. However, the fiber intersection structure in 3D braided composite materials plays a crack arrest role in the 3D direction. To explore and design this special fiber structure, it is necessary to perform simulation prediction on the microstructure of the braided preform.

[0003] Due to the particularity of the 3D braided fabric structure, the geometric modeling and structural simulation of the internal structure of the 3D braided fabric play an important role in predicting the mechanical properties of 3D braided composite materials. The current structural simulation method is based on a rectangular or circular flat knitting machine, and the interweaving of yarns is controlled by a switch. This allows independent movement between the bevel gears and the yarn guides, and its process trajectory model can be established mathematically. However, in actual industrial applications, large-sized braided preforms need to be woven, and the planar shape of the knitting machine used is annular or rectangular annular. Therefore, it is necessary to perform digital simulation on the knitting model structure of the annular structure knitting machine.

[0004] For this reason, a computer simulation method for a six-tooth annular three-dimensional braiding structure is provided. Summary of the Invention

[0005] Aiming at the fact that the existing simulation methods cannot meet the requirements of computer digital simulation, a computer structural simulation method for six-tooth annular three-dimensional braiding is disclosed.

[0006] The present invention is implemented as follows. First, fiber parameters, yarn carrier parameters, and dial parameters are determined. The fiber parameters include fiber width and the number of fibers. The yarn carrier parameters include the number of yarn carriers and the yarn carrier numbers. The dial parameters include the rotation angle and the dial numbers.

[0007] The knitting process is digitalized and parameterized through machine simulation, and digital simulation of the knitting model structure is performed by means of computer calculation. This simulation method includes the following steps:

[0008] Step 1. Determine the coordinate positions of the yarn carriers. Based on the positions of the yarn carriers and the dial of the machine, establish a grid to divide the coordinate system of the yarn carrier positions. The distance between adjacent x and y coordinate axes is set to a / 2. With an arbitrary position as the center point of the dial, the yarn carriers are distributed around the center point of the dial at the vertices of a regular hexagon, and the initial coordinate positions of the yarn carriers are determined.

[0009] Step 2. Generate the initial yarn trajectory. Establish a database of the yarn carrier drive unit matrix, the yarn carrier center matrix, and the yarn carrier rotation matrix through the machine simulation method. According to the set knitting rules, call the corresponding database and perform computer operations to obtain the yarn carrier path structure corresponding to the coordinate positions of the yarn carriers.

[0010] Step 3. Optimize the characteristics of the yarn trajectory. Use the cubic B-spline curve to optimize, and optimize the yarn carrier trajectory with geometric right-angle connections into a flexible smooth continuous curve, which is the path structure of the yarn (fiber).

[0011] Step 4. Yarn trajectory coordinate + mechanical tightening. Tighten the coordinates of the yarn trajectory by simultaneously pulling in the distances between adjacent x and y coordinates and increasing the distances between adjacent points on the z-axis, and pull in the distances between the yarns. Through coordinate rotation, perform mechanical analysis on adjacent points to establish a fiber tension model.

[0012] Step 5. Yarn materialization. Establish a Tubelike solid function to perform solid modeling on the yarn.

[0013] Furthermore, when digitizing and parameterizing the knitting process through machine simulation, each bevel gear is simplified into a regular hexagon, and the vertex of each regular hexagon is a yarn rack. The movement of a single gear driving the yarn rack can be regarded as the transformation of the vertex positions of the regular hexagon. Establish a single dial matrix database, designated as the C(nr) matrix.

[0014]

[0015] In this matrix, the value of the letter "Yk" represents the position vector matrix of the kth yarn guide, the element with a value of 0 represents the position without a yarn nozzle configuration, the element nr represents the nth of the 60° gear rotation angles, and the positive or negative value of nr is shown in Table 1, which determines the rotation direction of the bevel gear. When the value of r is positive, it represents the configuration position where the yarn nozzle rotates clockwise.

[0016] When the value of r is negative, it represents the configuration position where the yarn nozzle rotates counterclockwise; when the value of r is 0, the configuration position of the yarn guide remains unchanged. The rotation transformation characteristic matrix R(θ) can calculate the rotation position matrix of a single yarn carrier.

[0017] Furthermore, assume double-layer weaving is carried out. The center of the dial is set as the H matrix, and a parametric model of the overall structure of the six-tooth annular three-dimensional weaving structure is established for the machine-computer. A database of the center position matrix of the dial is established:

[0018]

[0019] Let the overall coordinate matrix be (M, N). The extraction function of the center coordinates and matrix of the corner wheel is:

[0020] M_1 = zeros(M, N);

[0021] M_2 = zeros(M, N);

[0022] M_3 = zeros(M, N);

[0023] M_4 = zeros(M, N);

[0024] The rotation characteristic matrix D(θ) for two-dimensional rotation around an arbitrary point is obtained:

[0025]

[0026] The x_Yarn function is introduced as the position coordinate function of the yarn. Then m is the number of fibers, n is the number of weaving steps, and the coordinates of the initial yarn points are:

[0027]

[0028] Let the coordinate position transformation function in the Z direction be z_Yarn = h.

[0029] Furthermore, in step two, according to the corresponding weaving parameters, the corresponding database is called, and then the fiber width, the number of yarn carriers, the yarn carrier numbers, and the weaving parameters of the rotation angle required by the designer are input to construct the structure of the yarn / fiber path, obtaining the trajectory diagram of the yarn carrier. Then, the cubic B-spline curve optimization function is introduced, representing the i-th curve, and the relationship of the yarn trajectory is obtained:

[0030]

[0031] Furthermore, a Tubelike entity function is established. Assume: [Xgrid, Ygrid, Zgrid] = TubeLike(xd, yd, zd, r), where r is the fiber radius. Since the fiber is composed of the connection of points, the angle vector t is introduced and the first-order difference function is used for continuous processing to make the fiber a smooth curve; t = linspace(0, 2*pi, 30)'

[0032]

[0033]

[0034]

[0035] Then, calculate the cosine of the angle between the normal and the positive direction of the coordinate axis, and the negative value of the sine of the angle between the normal and the positive direction of the coordinate axis:

[0036] d1 = sqrt(dx.^2 + dy.^2)

[0037]

[0038] d2 = sqrt(dx.^2 + dy.^2 + dz.^2)

[0039]

[0040] Then, the mesh data Xgrid, Ygrid, and Zgrid of the three-dimensional pipe-shaped geometric body are calculated:

[0041]

[0042] Compared with the prior art, the computer simulation method for the six-tooth annular three-dimensional braided structure provided by the present invention calculates the coordinate position of each point through computer according to machine simulation, and constructs the simulation calculation of the yarn carrier and the yarn trajectory by using the geometric structure formed by connecting adjacent points. After adding the TubeLike entity function, the structural relationship between different yarn trajectories is ensured to remain unchanged, and a braided model with a real braiding effect is calculated. The simulation structure obtained by the present invention has a high accuracy through experimental comparison, and can predict the fiber structure between yarns, which plays an important role in the prediction of the microscopic structure, structural simulation, and performance prediction of braided materials. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 It is a logical relationship flow chart of a computer simulation algorithm for predicting a six-tooth annular three-dimensional braided structure;

[0044] Figure 2 It is a parametric model diagram of a unit structure machine - computer of a six-tooth annular three-dimensional braided structure;

[0045] Figure 3 It is a parametric model diagram of an overall structure machine - computer of a six-tooth annular three-dimensional braided structure;

[0046] Figure 4 It is the relationship between the yarn carrier trajectory and the yarn trajectory;

[0047] Figure 5 It is the yarn trajectory path before and after the optimization of the B-spline curve;

[0048] Figure 6Coordinate transformation fiber mechanics tightening geometric model;

[0049] Figure 7 Tubelike solid function yarn solid model;

[0050] Figure 8 Comparison between the experimental woven surface topography and the simulated woven structure surface topography;

[0051] Figure 9 Comparison between the industrial CT scan surface topography and the simulation results. Detailed implementation mode

[0052] In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0053] The implementation of the present invention will be described in detail below with reference to specific embodiments.

[0054] A computer simulation method for a six-tooth annular three-dimensional woven structure, according to Figure 1 The logical relationship flowchart:

[0055] Among them, the fiber parameters include fiber width and fiber number, the carrier parameters include the number of carriers and the carrier number, and the dial parameters include the rotation angle and the dial number;

[0056] The fiber path structure consists of the weaving step length, the number of weaving times, the design requirements, the weaving process and the cross-sectional shape;

[0057] Through the fiber path structure, B-spline curve optimization, establishment of a woven structure model and optimization of the force analysis path are carried out.

[0058] By means of machine simulation, the weaving process is digitalized and parameterized, and digital simulation of the woven model structure is carried out by means of computer calculation. This simulation method includes the following steps:

[0059] Step 1: Determine the coordinate position of the carrier. According to the position configuration of the carrier and the dial of the machine, a grid is established to divide the carrier position coordinate system. The distance between adjacent x and y coordinate axes is set to a / 2. Taking any position as the center point of the dial, the carriers are distributed around the center point of the dial at the vertices of a regular hexagon to determine the initial coordinate position of the carrier;

[0060] Step 2: Generate the initial yarn trajectory. By means of machine simulation, a database of the carrier drive unit matrix, the carrier center matrix and the carrier rotation matrix is established. According to the set weaving rules, the corresponding database is called to perform computer operations to obtain the carrier path structure corresponding to the coordinate position of the carrier;

[0061] Step 3: Optimize the yarn trajectory characteristics. Use cubic B-spline curves for optimization to transform the carrier trajectory with geometric right-angle connections into a flexible, smooth and continuous curve, which is the path structure of the yarn (fiber).

[0062] Step 4: Coordinate tightening of the yarn trajectory + mechanical tightening. Tighten the coordinates of the yarn trajectory by simultaneously reducing the distance between adjacent x and y coordinates and increasing the distance between adjacent points on the z-axis, reducing the distance between the yarns. Through coordinate rotation, perform mechanical analysis on adjacent points to establish a fiber tension model.

[0063] Step 5: Substantiate the yarn. Establish a Tubelike solid function to perform solid modeling on the yarn.

[0064] First, through machine simulation, parameterize the unit structure. Simplify each horn gear into a regular hexagon, and each vertex of the hexagon is a yarn rack. The movement of a single gear driving the yarn rack can be regarded as the transformation of the vertex position of the regular hexagon. See Figure 2 Establish a single dial matrix database, denoted as the C(nr) matrix. The value of the letter "Yk" represents the position vector matrix of the kth yarn guide.

[0065] In this matrix, the element with a value of 0 represents the position without a yarn nozzle configuration. The value of the element nr represents the nth of the 60° gear rotation angle. The positive or negative value of nr is shown in Table 1, which determines the rotation direction of the horn gear. When the r value is positive, it represents the configuration position where the yarn nozzle rotates clockwise; when the r value is negative, it represents the configuration position where the yarn nozzle rotates counterclockwise; when the r value is 0, the configuration position of the yarn guide remains unchanged. The rotation transformation characteristic matrix R(θ) can calculate the rotation position matrix of a single yarn carrier.

[0066]

[0067]

[0068]

[0069] See Figure 3 Taking double-layer weaving as an example, set the center of the dial as the H matrix, and establish a machine-computer parameterized model for the overall structure of the six-tooth ring three-dimensional weaving structure, and establish a database for the position matrix of the dial center.

[0070]

[0071] Let the overall coordinate matrix be (M,N). The extraction function for the center coordinates of the angular wheel and the matrix is: M_1 = zeros(M,N);

[0072] M_2 = zeros(M,N);

[0073] M_3 = zeros(M,N);

[0074] M_4 = zeros(M,N);

[0075] Obtain the rotation feature matrix D(θ) for two-dimensional rotation about an arbitrary point

[0076]

[0077] Introduce the x_Yarn function as the position coordinate function of the yarn. Then m is the number of fibers, and n is the number of knitting steps. The coordinates of the initial yarn points are:

[0078]

[0079] Let the coordinate position transformation function in the Z direction be

[0080] z_Yarn = h;

[0081] See Figure 4 , which is the relationship between the trajectory of the yarn carrier and the yarn trajectory. According to Figure 1 the logical relationship, call the corresponding database according to the corresponding knitting parameters, and then input the knitting parameters such as the fiber width, the number of yarn carriers, the yarn carrier number, and the rotation angle required by the designer to construct the yarn / fiber path, and obtain the trajectory diagram of the yarn carrier. Then introduce the cubic B-spline curve optimization function, representing the i-th curve, to obtain the relationship of the yarn trajectory:

[0082]

[0083] See Figure 5 , assuming that the number of fibers is 120, taking the Figure 3 matrix as an example, perform computer simulation calculations according to the above rules to obtain the yarn trajectory paths before and after the B-spline curve optimization.

[0084] See Figure 6 , in the actual knitting structure, when the fiber is under force, the fiber is straight between the intersection points. Assume that the coordinates of the fiber point are A i+1 , A i-1 , then the center point between the fiber points is A i . When tightening, point A i moves towards the diagonal of the parallelogram formed by A i+1 , A i , A i-1 . The theoretical center line of fiber tightening is the diagonal of the parallelogram, which is the straight line A i+ 1A i-1However, in reality, the fiber is a solid and has its own radius. In order to be closer to the actual fiber mechanical tightening, the position of the fiber entity is reserved. The actual tightening path of the fiber is A i+1 BA i-1 .

[0085] See Figure 7 In order to ensure that the fiber accurately represents the actual shape, a Tubelike entity function is established. It is assumed that: [Xgrid, Ygrid, Zgrid] = TubeLike (xd, yd, zd, r), r is the fiber radius. Since the fiber is composed of lines connecting points, the angle vector t is introduced and the first-order difference function is used for continuous processing to make the fiber a smooth curve.

[0086] t=linspace(0,2*pi,30)'

[0087]

[0088]

[0089]

[0090] Then calculate the cosine of the angle between the normal and the positive axis, and the negative sine of the angle between the normal and the positive axis.

[0091] d1=sqrt(dx.^2+dy.^2)

[0092]

[0093] d2=sqrt(dx.^2+dy.^2+dz.^2)

[0094]

[0095] Then the grid data Xgrid, Ygrid and Zgrid of the three-dimensional pipe geometry are calculated

[0096]

[0097] See Figure 8 , Figure 9 ,After the simulation, experimental verification is carried out to ,comparison between the braided structure samples designed by weaving and ,the simulation structure, and the surface morphology of the braided structure is highly similar to the ,simulated braided structure, and the fiber orientation is basically consistent with the ,structure, which proves the accuracy of the braided structure simulated by this ,method.

[0098] In the accompanying drawings of this embodiment, the same or similar reference numerals correspond to the same or similar components; in the description of the present invention, it should be understood that if there are terms such as "upper", "lower", "left", "right", etc. indicating the orientation or positional relationship, they are based on the orientation or positional relationship shown in the accompanying drawings. This is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation. Therefore, the terms describing the positional relationship in the accompanying drawings are only for illustrative purposes and cannot be construed as a limitation of this patent. For those of ordinary skill in the art, the specific meanings of the above terms can be understood according to specific circumstances.

[0099] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims

1. A computer simulation method for a six-tooth annular three-dimensional braided structure, characterized in that, First, determine the fiber parameters, yarn carrier parameters, and dial parameters. The fiber parameters include fiber width and fiber number. The yarn carrier parameters include the number of yarn carriers and the yarn carrier number. The dial parameters include the rotation angle and the dial number; Digitalize and parameterize the knitting process through machine simulation, and perform digital simulation of the knitting model structure by means of computer calculation. This simulation method includes the following steps: Step 1: Determine the coordinate positions of the yarn carriers. Establish a grid to divide the coordinate system of the yarn carrier positions according to the positions of the yarn carriers and dials of the machine. Set the distance between adjacent x and y coordinate axes to a / 2. Take any position as the center point of the dial. The yarn carriers are distributed around the center point of the dial at the vertices of a regular hexagon to determine the initial coordinate positions of the yarn carriers; Step 2: Generate the initial yarn trajectory. Establish a database of the yarn carrier drive unit matrix, the yarn carrier center matrix, and the yarn carrier rotation matrix through the machine simulation method. According to the set knitting rules, call the corresponding database and perform computer operations to obtain the yarn carrier path structure corresponding to the coordinate positions of the yarn carriers; Step 3: Optimize the yarn trajectory characteristics. Optimize using the cubic B-spline curve to optimize the yarn carrier trajectory with geometric right-angle connections into a flexible, smooth, and continuous curve, which is the path structure of the yarn; Step 4: Yarn trajectory coordinate + mechanical tightening. Tighten the coordinates of the yarn trajectory by simultaneously shortening the distances between adjacent x and y coordinates and increasing the distances between adjacent points on the z-axis. Shorten the distances between the yarns. Through coordinate rotation, perform mechanical analysis on adjacent points to establish a fiber tension model; Step 5: Yarn solidification. Establish a Tubelike solid function to perform solid modeling of the yarn and optimize the force analysis path through the fiber path structure; Assume double-layer knitting. Set the center of the dial as the H matrix, and establish a machine-computer parameterized model of the overall structure of the six-tooth annular three-dimensional knitting structure. Establish a database of the center position matrix of the dial: ； Let the overall coordinate matrix be (M, N). The extraction function of the center coordinates of the angular wheel and the matrix is: M_1 = zeros(M, N); M_2 = zeros(M, N); M_3 = zeros(M, N); M_4 = zeros(M, N); Obtain the rotation feature matrix for two-dimensional rotation about an arbitrary point : ； Introduce the x_Yarn function as the position coordinate function of the yarn. Then m is the number of fibers, n is the number of knitting steps. The coordinates of the initial yarn points are: ； Let the coordinate position transformation function in the Z direction be z_Yarn = h.

2. A computer simulation method for a six-tooth annular three-dimensional braided structure according to claim 1, characterized in that, When digitizing and parameterizing the knitting process through machine simulation, each horn gear is simplified into a regular hexagon, and the vertex of each regular hexagon is a yarn stand. The movement of a single gear driving the yarn stand can be regarded as the transformation of the vertex position of the regular hexagon. A single dial matrix database is established and set as matrix, ； ； ； In this matrix, the value of the letter "Yk" represents the position vector matrix of the kth yarn guide. The element with a value of 0 represents the position without a yarn nozzle configuration. The value of the element nr represents the nth of the 60° angular gear rotation angles. The positive or negative value of nr is shown in Table 1, which determines the rotation direction of the horn gear. When the value of r is positive, it represents the configuration position where the yarn nozzle rotates clockwise; When the r value is negative, it represents the configured position where the yarn guide rotates counterclockwise; when the r value is 0, the configured position of the yarn guide remains unchanged, and the rotation transformation characteristic matrix , and the rotation position matrix of a single yarn carrier can be calculated.

3. A computer simulation method for a six-tooth annular three-dimensional braided structure according to claim 2, characterized in that In Step 2, call the corresponding database according to the corresponding weaving parameters, and then input the weaving parameters of the fiber width, number of yarn carriers, yarn carrier numbers, and rotation angles required by the designer to construct the structure of the yarn / fiber path, obtain the yarn carrier locus diagram, and then introduce the cubic B-spline curve optimization function, representing the $i$-th curve, to obtain the relationship of the yarn locus: (m ≥ 0) (n ≥ 0).

4. A computer simulation method for a six-tooth annular three-dimensional braided structure according to claim 3, characterized in that, Establish the Tubelike entity function, assuming: $[Xgrid, Ygrid, Zgrid] = TubeLike(xd, yd, zd, r)$, where $r$ is the fiber radius. Since the fiber is composed of the connection of points, introduce the angle vector $t$ and use the first-order difference function for continuous processing to make the fiber a smooth curve; $t = linspace(0, 2*\pi, 30)'$; (x＞0) ； (y＞0) ； (z＞0)； Then calculate the cosine of the angle between the normal and the positive direction of the coordinate axis, and the negative sine of the angle between the normal and the positive direction of the coordinate axis: $d1 = sqrt(dx.^2 + dy.^2)$; ； $d2 = sqrt(dx.^2 + dy.^2 + dz.^2)$; ； Then the grid data $Xgrid$, $Ygrid$, and $Zgrid$ of the three-dimensional tubular geometry are calculated: 。

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