Modeling method of fiber-grade two-dimensional circular braided fabric
By obtaining the geometric parameters of fiber-level two-dimensional circular braids and performing matrix transformation, the problem of unsatisfactory braided fabric modeling and simulation in the prior art is solved, efficient braided fabric modeling and simulation are achieved, and design and simulation flexibility and convenience are improved.
Patent Information
- Application Number
- CN202411817696.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-11
- Publication Date
- 2025-03-18
AI Technical Summary
In the prior art, fiber-level two-dimensional circular braids are difficult to model or simulate or simulate the simulation effect, and the model construction efficiency is ineffective.
By obtaining the geometric parameters of the fiber-level two-dimensional circular braid, a linear equation of a single fiber is established, and a single fiber bundle is generated through translation and rotation operations, and the fiber bundle is then transformed into a sinusoidal braided yarn, and finally a model of the two-dimensional circular braid is constructed through matrix transformation.
It realizes efficient modeling and simulation of fiber-level two-dimensional circular braids, improves the flexibility and simulation convenience of braided fabric design, and can accurately capture factors such as the number of cross-sectional fibers, internal and external transfer, distribution, twist and twist direction in the fiber bundle. It is suitable for developing new braided products or completing personalized customization.
Smart Images
Figure CN119647137A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of braided fabric modeling, and specifically relates to a modeling method for a fiber-level two-dimensional circular braided fabric. Background Art
[0002] With the rapid development of high-tech industries such as aerospace, new energy, ocean, biomedicine, communication information, and military industry, the market's requirements for fiber material performance are increasing, which has promoted the research and development of new fibers. As a result, a large number of high-performance fibers with good comprehensive performance have been born, such as aromatic polyamide fibers, polyarylate fibers, ultra-high molecular weight polyethylene fibers, polyimide fibers, etc. These high-performance fiber braids are widely used in space exploration, lightweight structural design of new spacecraft, and other fields with their advantages of light weight, high strength, high modulus, wear resistance, strong designability, and easy processing, and have successfully replaced traditional metal braided structural parts.
[0003] From a microscopic perspective, the performance of high-performance fiber braids is directly affected by their internal braiding structure. Braids are composed of interwoven braided yarns, and each braided yarn is composed of thousands of fibers. These fibers remain relatively stable when there is no external force; but when external force is applied, the fibers will undergo relative displacement, and then appear in a variety of arrangements such as parallel, staggered or spiral. These different arrangements directly affect the interaction forces between fibers, such as friction and adhesion, and thus affect the mechanical properties of the braided yarn and the entire braid. Therefore, it is very necessary to establish an accurate and convenient micro-geometric model. Through accurate model construction, the behavior of fibers at the microscopic level under different conditions can be simulated, providing guidance for the design of new braided products and the optimization of existing products. With the advancement of science and technology, researchers are paying more and more attention to the influence of material microstructure on macrostructure. As the basic component unit of a variety of materials, the properties of fibers directly determine the application performance of the braided products in the fields of aerospace, automobiles, sports equipment, etc. Researchers can optimize the design to meet specific application requirements by deeply understanding the microstructure of braids, which is of great significance for describing the discrete internal structure of three-dimensional braids and predicting and optimizing material properties. Summary of the invention
[0004] The present invention proposes a modeling method for a fiber-level two-dimensional circular braid, which aims to partially or completely solve the technical problems in the prior art that fiber-level two-dimensional circular braids are difficult to model and simulate, or the modeling and simulation effects are unsatisfactory, or the model building efficiency is low. The technical solution of the present invention is as follows:
[0005] A modeling method for a fiber-level two-dimensional circular braid, comprising:
[0006] Step S100: according to the weaving structure of the fiber-level two-dimensional circular braid, geometric parameters of the fiber-level two-dimensional circular braid are obtained, the geometric parameters including twist pitch h, fiber radius r, total number of single fibers m, twist degree A, fiber amplitude a, braid radius R, and total number of braided yarns n;
[0007] Step S200: Modeling a single fiber bundle: establishing a linear equation of a single fiber, translating the single fiber along the X-axis to obtain the first single fiber, rotating the first single fiber around the Z-axis by 2π / m, 4π / m, ..., 2πk / m, ..., 2π(m-1) / m to respectively form the second single fiber, the third single fiber, ..., the kth single fiber, ..., the mth single fiber; the first single fiber, the second single fiber, the third single fiber, ..., the kth single fiber, ..., the mth single fiber form a single fiber bundle, wherein k=1, 2, ..., m;
[0008] Step S300: Modeling a single sinusoidal braided yarn: using a single fiber bundle as a single braided yarn, and transforming the single braided yarn into a single sinusoidal braided yarn;
[0009] Step S400: Modeling a two-dimensional circular braided fabric: translating a single sinusoidal braiding yarn along the X-axis to obtain the first braiding yarn, rotating the first braiding yarn around the Z-axis by 2π / n, 4π / n, ..., 2πi / n, ..., 2π(n-1) / n to form the second braiding yarn, the third braiding yarn, ..., the i-th braiding yarn, ..., the n-th braiding yarn respectively; twisting or untwisting the first braiding yarn, the second braiding yarn, the third braiding yarn, ..., the i-th braiding yarn, ..., the n-th braiding yarn; rotating and interweaving the first braiding yarn, the second braiding yarn, the third braiding yarn, ..., the i-th braiding yarn, ..., the n-th braiding yarn around the Z-axis to form a braided fabric, wherein i is the number of the braiding yarn, i=1, 2, 3, ..., n.
[0010] Optionally, step S200 includes:
[0011] Step S201: Establish a straight line equation L0 of a single fiber. The straight line equation L0 is:
[0012] L0=[0,0,ht / 2π,1] T (1)
[0013] Wherein, π is the circumference of a circle, t is an equation parameter, and the dimensionless parameter t=π / 8*(j-1) is defined, j is the number of points on a single fiber, j=1, 2, ..., +∞ integers, and T is a vector transpose symbol;
[0014] Step S202: translating a single fiber along the X-axis by a distance of 2r to obtain the first single fiber. The single fiber translation matrix T1 is:
[0015]
[0016] Step S203: The first single fiber is rotated around the Z axis by 2π / m, 4π / m, ..., 2πk / m, ..., 2π(m-1) / m to form the second single fiber, the third single fiber, ..., the kth single fiber, ..., the mth single fiber respectively; the first single fiber, the second single fiber, the third single fiber, ..., the kth single fiber, ..., the mth single fiber form a single fiber bundle, and the fiber rotation matrix α1 of the kth single fiber rotating around the z axis is:
[0017]
[0018] Optionally, step S300 includes: taking a single fiber bundle as a single braiding yarn, and transforming the single braiding yarn into a single sinusoidal braiding yarn, wherein the transformation matrix T2 is:
[0019]
[0020] Optionally, step S400 includes:
[0021] Step S401: A single sinusoidal braiding yarn is translated along the X-axis by a distance R to obtain the first braiding yarn. The braiding yarn translation matrix T3 is:
[0022]
[0023] Step S402: The first braiding yarn is rotated around the Z axis by 2π / m, 4π / m, ..., 2πi / m, ..., 2π(n-1) / n to form the second braiding yarn, the third braiding yarn, ..., the i-th braiding yarn, ..., the n-th braiding yarn respectively; the fiber rotation matrix α3 of the first braiding yarn, the second braiding yarn, the third braiding yarn, ..., the i-th braiding yarn, ..., the n-th braiding yarn, and the i-th braiding yarn rotating around the z axis is:
[0024]
[0025] Step S403: twisting or not twisting the first braiding yarn, the second braiding yarn, the third braiding yarn, ..., the i-th braiding yarn, ..., the n-th braiding yarn;
[0026] Step S404: Rotate the first braiding yarn, the second braiding yarn, the third braiding yarn, ..., the ith braiding yarn, ..., the nth braiding yarn around the Z axis so that the first braiding yarn, the second braiding yarn, the third braiding yarn, ..., the ith braiding yarn, ..., the nth braiding yarn are interwoven, and the interwoven matrix α4 is:
[0027]
[0028] Step S405: The first braiding yarn, the second braiding yarn, the third braiding yarn, ..., the ith braiding yarn, ..., the nth braiding yarn after interweaving are translated to obtain a braided fabric. The translation matrix T4 is:
[0029]
[0030] Optionally, in step S403, a portion of the first braiding yarn, the second braiding yarn, the third braiding yarn, ..., the ith braiding yarn, ..., and the nth braiding yarn is twisted counterclockwise, and another portion of the first braiding yarn, the second braiding yarn, the third braiding yarn, ..., the ith braiding yarn, ..., and the nth braiding yarn is twisted clockwise, and the braided fabric includes Z-twisted braided yarns and S-twisted braided yarns, and the twist matrix α of the ith braiding yarn is 21 for:
[0031]
[0032] Among them, A is not equal to 0.
[0033] Optionally, in step S403, the first braiding yarn, the second braiding yarn, the third braiding yarn, ..., the ith braiding yarn, ..., the nth braiding yarn are all twisted counterclockwise, and when the braided fabric only includes Z-twisted braiding yarns, the twisting matrix α of the first braiding yarn, the second braiding yarn, the third braiding yarn, ..., the ith braiding yarn, ..., the nth braiding yarn is 22 Both are:
[0034]
[0035] Among them, A is not equal to 0.
[0036] Optionally, in step S403, the first braiding yarn, the second braiding yarn, the third braiding yarn, ..., the ith braiding yarn, ..., the nth braiding yarn are all twisted counterclockwise, and when the braided fabric only includes S-twisted braiding yarns, the twisting matrix α of the first braiding yarn, the second braiding yarn, the third braiding yarn, ..., the ith braiding yarn, ..., the nth braiding yarn is 23 Both are:
[0037]
[0038] Among them, A is not equal to 0.
[0039] Optionally, in step S403, the first braiding yarn, the second braiding yarn, the third braiding yarn, ..., the ith braiding yarn, ..., the nth braiding yarn are all untwisted to serve as a single braiding yarn, and the untwisted matrix is:
[0040]
[0041] Optionally, when the braid includes Z-twisted braided yarn and S-twisted braided yarn, the fiber curve equation L1(i,k) of the k-th single fiber of the i-th braided yarn in the braid is:
[0042] L1(i,k)=T4*α4*α3*T3*T2*α 21 *α1*T1*L0=M*L0(10-1) where the overall transformation matrix M1 is:
[0043] M1=T4*α4*α3*T3*T2*α 21 *α1*T1(11-1)
[0044] Optionally, when the braided fabric includes only Z-twisted braided yarns, the fiber curve equation L2(i,k) of the k-th single fiber of the i-th braided yarn in the braided fabric is:
[0045] L2(i,k)=T4*α4*α3*T3*T2*α 22 *α1*T1*L0=M*L0(10-2) where the overall transformation matrix M2 is:
[0046] M2=T4*α4*α3*T3*T2*α 22 *α1*T1(11-2)
[0047] Alternatively, in step S400, when the braided fabric includes only S-twisted braided yarns, the fiber curve equation L3(i,k) of the k-th single fiber of the i-th braided yarn in the braided fabric is:
[0048] L3(i,k)=T4*α4*α3*T3*T2*α 23 *α1*T1*L0=M*L0(10-2) where the overall transformation matrix M3 is:
[0049] M3=T4*α4*α3*T3*T2*α 23 *α1*T1(11-3)
[0050] Alternatively, when the braided fabric includes no twist, the fiber curve equation L4(i,k) of the kth single fiber of the i-th braided yarn in the braided fabric is:
[0051] L4(i,k)=T4*α4*α3*T3*T2*α 24 *α1*T1*L0=M*L0(10-4) where the overall transformation matrix M4 is:
[0052] M4=T4*α4*α3*T3*T2*α 24 *α1*T1(11-4) Compared with the prior art, the beneficial effects of the present invention are as follows:
[0053] (1) In the present invention, by changing geometric parameters (such as twist pitch h, fiber radius r, total number of single fibers m, twist degree A, fiber amplitude a, braid radius R, total number of braided yarns n, etc.), the modeling method of fiber-level two-dimensional circular braid can be used to simulate the texture and structure of the fiber-level two-dimensional circular braid. The modeling method of fiber-level two-dimensional circular braid has good universality, effectively improves the flexibility of braid design and the convenience of simulation, and is also suitable for developing new braid products or completing personalized customized braids.
[0054] (2) In the present invention, the modeling method of fiber-level two-dimensional circular braided fabrics can obtain the spline curve of the two-dimensional circular braided structure based on matrix transformation. By changing the geometric parameters, the appearance and structure of different braided fabrics can be modeled and simulated. The modeling and simulation of braided fabrics including Z-twist braided yarn and S-twist braided yarn, the modeling and simulation of braided fabrics including Z-twist braided yarn, the modeling and simulation of braided fabrics including S-twist braided yarn and the modeling and simulation of braided fabrics including untwisted braided yarn are completed. The factors such as the number of fibers in the cross section of the fiber bundle, internal and external transfer, distribution, twist and twist direction are captured more accurately, which lays a foundation for researchers to simulate and analyze different braiding parameters (such as fiber type, fiber density, etc.) and mechanical properties analysis of braided fabrics, and has important theoretical significance for subsequent mechanical modeling, force analysis, failure mechanism analysis, etc. of braided fabrics;
[0055] (3) In the present invention application, a modeling method for fiber-level two-dimensional circular braids is used to improve the scientificity and accuracy of the design and production of two-dimensional circular braids, so that the two-dimensional circular braid products can be visualized and digitized, and the feasibility of weaving on a machine can be directly predicted, which completely replaces the existing products that need to complete sample proofing and manufacturing before weaving on a machine and verifying the color effect, saving the cycle of repeated design and proofing. Applying the modeling technology of fiber-level two-dimensional circular braids to the production process of two-dimensional circular braid products can not only reduce production costs and shorten the design and production cycle of products, but also effectively solve the problem of three-dimensional modeling of braids, greatly improving the competitiveness of enterprises, and has good technical and market application value. BRIEF DESCRIPTION OF THE DRAWINGS
[0056] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings required for use in the description of the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.
[0057] Figure 1 Schematic diagram of the process for modeling a single fiber bundle ( Figure 1(a) is a spatial schematic diagram of a single fiber. Figure 1 (b) is a schematic diagram of a single fiber after translation transformation. Figure 1 (c) is a schematic diagram of a single fiber bundle);
[0058] Figure 2 It is a schematic diagram of a single sinusoidal braided yarn;
[0059] Figure 3 Schematic diagram of twisted braided yarn ( Figure 3 (a) is a schematic diagram of Z-twisted braided yarn. Figure 3 (b) is a schematic diagram of S-twisted braided yarn);
[0060] Figure 4 It is a schematic diagram of untwisted braided yarn;
[0061] Figure 5 Schematic diagram of the translation and rotation transformation of a single sinusoidal braided yarn ( Figure 5 (a) is a schematic diagram of a single sinusoidal braided yarn after translation transformation. Figure 5 (b) is a partial structural diagram of the first braiding yarn, the second braiding yarn, the third braiding yarn, ..., the i-th braiding yarn, ..., the n-th braiding yarn, Figure 5 (c) is a schematic diagram of the overall structure of the first braiding yarn, the second braiding yarn, the third braiding yarn, ..., the i-th braiding yarn, ..., the n-th braiding yarn);
[0062] Figure 6 Schematic diagram of modeling and simulation of braided fabrics ( Figure 6 (a) is a schematic diagram of the structure of the modeling simulation of the braided fabric including Z-twisted braided yarn and S-twisted braided yarn. Figure 6 (b) is a schematic diagram of the structure of the modeling simulation of the braided fabric including only Z-twisted braided yarns. Figure 6 (c) is a schematic diagram of the structure of the braided fabric modeling simulation including only S-twisted braided yarns. Figure 6 (d) is a structural schematic diagram of the modeling simulation of a braided fabric including only untwisted braided yarns); DETAILED DESCRIPTION
[0063] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all of the embodiments; based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.
[0064] In the description of the present invention, it should be understood that the terms "upper", "lower", "front", "back", "left", "right", "top", "bottom", "inside", "outside" and the like indicating directions or positional relationships are based on the directions or positional relationships shown in the drawings, and are 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 direction, be constructed and operated in a specific direction, and therefore cannot be understood as a limitation on the present invention. In order to make the purpose, technical solution and advantages of the present invention clearer, the implementation methods of the present invention will be further described in detail below in conjunction with the drawings.
[0065] A modeling and simulation method for a fiber-level two-dimensional circular braid, comprising:
[0066] Step S100: according to the weaving structure of the fiber-level two-dimensional circular braid, geometric parameters of the fiber-level two-dimensional circular braid are obtained, the geometric parameters including twist pitch h, fiber radius r, total number of single fibers m, twist degree A, fiber amplitude a, braid radius R, and total number of braided yarns n;
[0067] In some embodiments, the two-dimensional circular braids are generally diamond, regular, and Hergless. The diamond structure is also called a 1×1 braided structure, in which yarns in opposite directions cross every other bundle. Regular, Hergless, and square structures are also called 2×2 braided structures and 3×3 braided structures, respectively.
[0068] In some embodiments, taking a fiber-level 2×2 two-dimensional circular braid as an example, the geometric parameters of the two-dimensional circular braid include twist pitch h=2, fiber radius r=1, total number of single fibers m=6, twist degree A=1, fiber amplitude a=3, braid radius R=6, and total number of braided yarns n=12.
[0069] Step S200: Modeling a single fiber bundle: establishing a linear equation of a single fiber, translating the single fiber along the X-axis to obtain the first single fiber, rotating the first single fiber around the Z-axis by 2π / m, 4π / m, ..., 2πk / m, ..., 2π(m-1) / m to respectively form the second single fiber, the third single fiber, ..., the kth single fiber, ..., the mth single fiber, respectively, the first single fiber, the second single fiber, the third single fiber, ..., the kth single fiber, ..., the mth single fiber form a single fiber bundle, wherein k=1, 2, ..., m;
[0070] like Figure 1 As shown, specifically, step S200 includes:
[0071] Step S201: Establish a straight line equation L0 of a single fiber. The straight line equation L0 is:
[0072] L0=[0,0,ht / 2π,1]T (1)
[0073] Among them, h is the twist pitch, π is the circumference of a circle, t is the equation parameter, and the dimensionless parameter t=π / 8*(j-1) is defined. j is the number of points on a single fiber, and j=1, 2, ..., +∞ integers. By using j to describe t, the number of points on the fiber can be refined. T is the vector transpose symbol.
[0074] In some embodiments, Figure 1 (a) is a spatial schematic diagram of a single fiber. The number of points j on a single fiber is 30. The linear equation of a single fiber can be established by equation (1): L0 = [0, 0, 30 / 8, 1] T .
[0075] Step S202: translating a single fiber along the X-axis by a distance of 2r to obtain the first single fiber. The single fiber translation matrix T1 is:
[0076]
[0077] In some embodiments, Figure 1 (b) is a schematic diagram of a single fiber after translation transformation, r = 1, and the single fiber is translated along the X axis by a distance of 2 to obtain the first single fiber through formula (2). The single fiber translation matrix T1 is:
[0078]
[0079] Step S203: The first single fiber is rotated around the Z axis by 2π / m, 4π / m, ..., 2πk / m, ..., 2π(m-1) / m to form the second single fiber, the third single fiber, ..., the kth single fiber, ..., the mth single fiber respectively. The first single fiber, the second single fiber, the third single fiber, ..., the kth single fiber, ..., the mth single fiber form a single fiber bundle. The fiber rotation matrix α1 of the kth single fiber rotating around the z axis is:
[0080]
[0081] Among them, k = 1, 2,…, m.
[0082] In some embodiments, Figure 1(c) is a schematic diagram of the structure of a single fiber bundle, m = 6, and the single fiber is rotated around the Z axis by π / 3, 2π / 3, π, 4π / 3, and 5π / 3 respectively by formula (3), so as to form the uniformly distributed second single fiber, third single fiber, fourth single fiber, fifth single fiber, sixth single fiber, first single fiber, second single fiber, third single fiber, fourth single fiber, fifth single fiber, and sixth single fiber, a total of 6 single fibers, and the 6 single fibers are combined to form a single fiber bundle. The fiber rotation matrix α1 of the kth single fiber rotated around the z axis is:
[0083]
[0084] In the formula, k = 1, 2, 3, 3, 4, 5, 6.
[0085] Therefore, in step S200, first, in the modeling of a single fiber, the linear equation L0 uses the relationship between the dimensionless parameter t and the number of points j to accurately describe the morphology of a single fiber, laying the foundation for the subsequent accurate construction of a fiber bundle; in addition, the translation operation can conveniently generate the first single fiber according to the set distance 2r with the help of the translation matrix T1, so that the construction process of a single fiber bundle can proceed in an orderly manner; the rotation operation around the Z axis and the corresponding rotation matrix generate multiple single fibers through a specific angle rule and form a single fiber bundle (for example, a single fiber bundle obtained when m=6); in addition, the single fiber bundle modeling method can effectively simulate the fiber bundle structure composed of fibers of different twists and different numbers, which is of great significance for studying the distribution of mechanical properties and changes in optical properties of fiber bundles, and can help scientific researchers to deeply understand the relationship between the internal structure of fiber materials and macroscopic properties, thereby providing powerful modeling technology support for fiber material research and development, performance optimization, etc. in the fields of textiles and materials science.
[0086] Step S300: Modeling a single sinusoidal braided yarn: a single fiber bundle is used as a single braided yarn, and the single braided yarn is transformed into a single sinusoidal braided yarn;
[0087] Specifically, step S300 includes: taking a single fiber bundle as a single braiding yarn, and transforming the single braiding yarn into a single sinusoidal braiding yarn, wherein the transformation matrix T2 is:
[0088]
[0089] In some embodiments, the fiber amplitude a=3, and the transformation matrix T2 is:
[0090]
[0091] Therefore, in step S300, firstly, a single fiber bundle is used as a single braiding yarn, and the transformation matrix T2 can be used to effectively convert it into a sinusoidal curve according to the set fiber amplitude a, which helps to simulate the bending deformation of the woven fabric during actual use or stress, and can provide a powerful model basis for studying the relationship between the geometric morphology changes and mechanical properties of the woven fabric; in addition, the modeling method of a single sinusoidal braiding yarn can flexibly construct various types of braiding yarn models to meet the needs of different braided fabric structure and performance research, and has important application value in the research and development, design and quality control of textile materials.
[0092] Step S400: Modeling a two-dimensional circular braided fabric: translate a single sinusoidal braiding yarn along the X-axis to obtain the first braiding yarn, rotate the first braiding yarn around the Z-axis by 2π / n, 4π / n, …, 2πi / n, …, 2π(n-1) / n to form the second braiding yarn, the third braiding yarn, …, the i-th braiding yarn, …, the n-th braiding yarn, respectively, rotate and interweave the first braiding yarn, the second braiding yarn, the third braiding yarn, …, the i-th braiding yarn, …, the n-th braiding yarn around the Z-axis to form a braided fabric.
[0093] Specifically, step S400 includes:
[0094] Step S401: A single sinusoidal braiding yarn is translated along the X-axis by a distance R to obtain the first braiding yarn. The braiding yarn translation matrix T3 is:
[0095]
[0096] In some embodiments, Figure 5 As shown in (a), a single sinusoidal braided yarn is translated along the X-axis by a distance R (R=6, i.e., the translation distance is 6) to obtain the first braided yarn. The braided yarn translation matrix T3 is:
[0097]
[0098] Step S402: The first braiding yarn is rotated 2π / n, 4π / n,…, 2πi / n,…, 2π(n-1) / n around the Z axis to respectively form the second braiding yarn, the third braiding yarn,…, the i-th braiding yarn,…, the n-th braiding yarn, the first braiding yarn, the second braiding yarn, the third braiding yarn,…, the i-th braiding yarn,…, the n-th braiding yarn, the fiber rotation matrix α3 of the i-th braiding yarn rotated around the z axis is:.
[0099]
[0100] In some embodiments, Figure 5 Middle (b), Figure 5As shown in (c), the partial and overall schematic diagrams of the first braiding yarn, the second braiding yarn, the third braiding yarn, ..., the i-th braiding yarn, ..., the n-th braiding yarn, the fiber rotation matrix α3 of the i-th braiding yarn rotating around the z-axis is:
[0101]
[0102] Step S403: twisting or not twisting the first braiding yarn, the second braiding yarn, the third braiding yarn, ..., the i-th braiding yarn, ..., the n-th braiding yarn;
[0103] In some embodiments, the twisting degree A=1, the first braiding yarn, the second braiding yarn, the third braiding yarn, ..., the i-th braiding yarn, ..., a portion of the braiding yarns in the n-th braiding yarn are twisted counterclockwise, the first braiding yarn, the second braiding yarn, the third braiding yarn, ..., the i-th braiding yarn, ..., another portion of the braiding yarns in the n-th braiding yarn are twisted clockwise, the braided fabric includes Z-twisted braiding yarns and S-twisted braiding yarns, and the twist matrix α of the i-th braiding yarn 21 for:
[0104]
[0105] In some embodiments, the twist degree A=1, Figure 3 (a) is a schematic diagram of the structure of Z-twisted braided yarns. The first braided yarn, the second braided yarn, the third braided yarn, ..., the i-th braided yarn, ..., the n-th braided yarn are all twisted counterclockwise. When the braided fabric only includes Z-twisted braided yarns, the twist matrix α of the first braided yarn, the second braided yarn, the third braided yarn, ..., the i-th braided yarn, ..., the n-th braided yarn 23 Both are:
[0106]
[0107] In some embodiments, the twist degree A=1, Figure 3 (b) is a schematic diagram of the structure of S-twisted braided yarns. The first braided yarn, the second braided yarn, the third braided yarn, ..., the i-th braided yarn, ..., the n-th braided yarn are all twisted counterclockwise. When the braided fabric only includes S-twisted braided yarns, the twist matrix α of the first braided yarn, the second braided yarn, the third braided yarn, ..., the i-th braided yarn, ..., the n-th braided yarn 23 Both are:
[0108]
[0109] In some embodiments, Figure 4is a schematic diagram of untwisted braided yarns. The first braided yarn, the second braided yarn, the third braided yarn, ..., the i-th braided yarn, ..., the n-th braided yarn are all untwisted as braided yarns. The untwisted matrix is:
[0110]
[0111] Step S404: Rotate the first braiding yarn, the second braiding yarn, the third braiding yarn, ..., the ith braiding yarn, ..., the nth braiding yarn around the Z axis so that the first braiding yarn, the second braiding yarn, the third braiding yarn, ..., the ith braiding yarn, ..., the nth braiding yarn are interwoven, and the interwoven matrix α4 is:
[0112]
[0113] In some embodiments, the total number of braided yarns n=12, and the corresponding interlacing matrix α4 is:
[0114]
[0115] Step S405: The first braiding yarn, the second braiding yarn, the third braiding yarn, ..., the ith braiding yarn, ..., the nth braiding yarn after interweaving are translated to obtain a braided fabric. The translation matrix T4 is:
[0116]
[0117] In some embodiments, the twist pitch h=2, and the translation matrix T4 is:
[0118]
[0119] Therefore, in step S400, first, in the translation operation, the translation distance of a single sinusoidal braiding yarn along the X-axis can be accurately determined with the help of the braiding yarn translation matrix T3, so as to obtain the first braiding yarn with accurate position, which provides a stable and precise starting condition for the construction of subsequent braided fabrics and ensures the controllability and repeatability of the entire modeling process; in addition, the rotation operation around the Z-axis uses the fiber rotation matrix α3 to generate multiple braiding yarns through a specific angle sequence, and can flexibly adjust the number n of braiding yarns to simulate circular braids of different densities and structural complexities. The rotation angle setting can evenly distribute the braiding yarns, which is conducive to constructing a regular structure. The model of a braided fabric with uniform mechanical properties is of great significance for studying the performance of the braided fabric in different force directions; in addition, the use of twisted matrix / untwisted matrix, interlaced matrix and translation matrix enables each braiding yarn to adjust the shape and position of the braided fabric, and interweave with each other according to the design requirements, truly restoring the interlaced structure of the yarn inside the two-dimensional circular braided fabric, which not only helps in the subsequent in-depth analysis of the microscopic properties such as the internal stress distribution and friction characteristics of the braided fabric, but also can provide a basis for optimizing the braiding process parameters, so as to improve the macroscopic properties such as the strength, toughness and durability of the braided fabric, and provides strong technical support for the product development, performance prediction and structural optimization of braided fabrics.
[0120] In summary, based on the above steps S100, S200, S300, and S400, the fiber curve equation of the kth single fiber of the ith braided yarn in the braid can be obtained accordingly. Using the fiber curve equation of the kth single fiber of the ith braided yarn in the braid, a fiber-level two-dimensional circular braid is obtained by programming modeling and simulation in Visual Studio, such as Figure 6 The three-dimensional simulation results of the fiber-level two-dimensional circular braid are shown.
[0121] Figure 6 (a) is a structural schematic diagram of the modeling and simulation of a braided fabric including Z-twisted braided yarn and S-twisted braided yarn. When the braided fabric includes Z-twisted braided yarn and S-twisted braided yarn, the fiber curve equation L1(i,k) of the kth single fiber of the i-th braided yarn in the braided fabric is:
[0122] L1(i,k)=T4*α4*α3*T3*T2*α 21 *α1*T1*L0=M*L0(10-1) where the overall transformation matrix M1 is:
[0123] M1=T4*α4*α3*T3*T2*α 21 *α1*T1(11-1)
[0124] In the present application, the fiber curve equation L1(i,k) of the kth single fiber of the i-th braided yarn in the woven fabric can describe the morphology of single fibers in the woven fabric including Z-twisted braided yarn and S-twisted braided yarn, and realizes efficient simulation of the fiber orientation changes in the process of two-dimensional circular braiding through a matrix transformation algorithm, which provides a strong basis for optimizing the weaving process of two-dimensional circular braids, thereby improving the quality and performance of two-dimensional circular braids, and has important application value in material design, process improvement and other aspects in the field of textile engineering.
[0125] Figure 6 (b) is a schematic diagram of the structure of the modeling simulation of the woven fabric including only Z-twisted braided yarn. When the woven fabric includes only Z-twisted braided yarn, the fiber curve equation L2(i,k) of the kth single fiber of the i-th braided yarn in the woven fabric is:
[0126] L2(i,k)=T4*α4*α3*T3*T2*α 22 *α1*T1*L0=M*L0(10-2) where the overall transformation matrix M2 is:
[0127] M2=T4*α4*α3*T3*T2*α 22 *α1*T1(11-2)
[0128] In the present invention application, the fiber curve equation L2(i,k) of the kth single fiber of the i-th braided yarn in the braided fabric describes the spatial trajectory of the fiber in the Z-twisted braided yarn, making the microstructure of the two-dimensional circular braided fabric visual. With the help of the fiber curve equation L2(i,k), the mechanical properties and geometric morphology of the two-dimensional circular braided fabric can be predicted, and it can be optimized and adjusted in the product design stage of the two-dimensional circular braided fabric, reducing the trial and error cost in actual research and development and production, and improving the textile industry's research and development and production efficiency in high-performance braided fabrics.
[0129] Figure 6 (c) is a structural schematic diagram of the modeling simulation of a braided fabric including only S-twisted braided yarns. When the braided fabric includes only S-twisted braided yarns, the fiber curve equation L3(i,k) of the kth single fiber of the i-th braided yarn in the braided fabric is:
[0130] L3(i,k)=T4*α4*α3*T3*T2*α 23 *α1*T1*L0=M*L0(10-3) where the overall transformation matrix M3 is:
[0131] M3=T4*α4*α3*T3*T2*α 23 *α1*T1(11-3)
[0132] In the present invention application, the fiber curve equation L3(i,k) of the kth single fiber of the i-th braided yarn in the braid describes the layout direction of multiple fibers in the two-dimensional circular braid including the S-twisted braided yarn, which is conducive to in-depth exploration of the structural characteristics of the S-twisted braided yarn. In textile structure design or process research, the molding process of the two-dimensional circular braid can be accurately simulated based on this fiber curve equation L3(i,k), providing theoretical support for the development of new S-twisted two-dimensional circular braid products.
[0133] Figure 6 (d) is a schematic diagram of the structure of the modeling simulation of the braided fabric including the untwisted braided yarn. When the braided fabric includes no twist, the fiber curve equation L4(i,k) of the kth single fiber of the i-th braided yarn in the braided fabric is:
[0134] L4(i,k)=T4*α4*α3*T3*T2*α 24 *α1*T1*L0=M*L0(10-4) where the overall transformation matrix M4 is:
[0135] M4=T4*α4*α3*T3*T2*α 24 *α1*T1(11-4).
[0136] In the present invention, the fiber curve equation L4(i,k) of the kth single fiber of the i-th braided yarn in the braided fabric describes the curve shape of the single fiber of the untwisted braided yarn, so that the internal structure of the untwisted two-dimensional circular braided fabric can be intuitively presented. Through the precise fiber curve equation L4(i,k), the performance of the untwisted two-dimensional circular braided fabric under different stress and process conditions can be deeply analyzed, providing a quantitative basis for the optimization of the untwisted braiding process.
[0137] Therefore, in the modeling method of fiber-level two-dimensional circular braided fabrics applied for by the present invention, firstly, the spline curve of the two-dimensional circular braided structure can be obtained based on the matrix transformation, and the appearance and structure of different two-dimensional circular braided fabrics can be modeled and simulated by changing the geometric parameters, and the modeling and simulation of braided fabrics including Z-twist braided yarn and S-twist braided yarn, the modeling and simulation of braided fabrics including Z-twist braided yarn, the modeling and simulation of braided fabrics including S-twist braided yarn and the modeling and simulation of braided fabrics including untwisted braided yarn are completed, which can accurately capture factors such as the number of fibers in the cross-section of the fiber bundle, internal and external transfer, distribution, twist and twist direction, etc., lay a foundation for researchers to simulate and analyze different braiding parameters (such as fiber type, fiber density, etc.) and mechanical properties analysis of braided fabrics, and have a great impact on the subsequent mechanical modeling and force analysis of braided fabrics. , failure mechanism analysis, etc. It has important theoretical significance; in addition, the modeling method of fiber-level two-dimensional circular braids improves the scientificity and accuracy of the design and production of two-dimensional circular braids, so that the two-dimensional circular braids products can be visualized and digitized, and the feasibility of weaving on the machine can be directly predicted, which completely replaces the existing products that need to complete sample proofing and manufacturing before weaving on the machine and verifying the color effect, saving the cycle of repeated design and proofing. Applying the modeling technology of fiber-level two-dimensional circular braids to the production process of two-dimensional circular braids can not only reduce production costs and shorten product design and production cycles, but also effectively solve the problem of three-dimensional modeling of braids, greatly improving the competitiveness of enterprises and having good commercial and market application value.
Claims
1. A method for modeling a fiber-level two-dimensional circular braid, comprising: Step S100: according to the weaving structure of the fiber-level two-dimensional circular braid, geometric parameters of the fiber-level two-dimensional circular braid are obtained, the geometric parameters including twist pitch h, fiber radius r, total number of single fibers m, twist degree A, fiber amplitude a, braid radius R, and total number of braided yarns n; Step S200: Modeling a single fiber bundle: establishing a linear equation of a single fiber, translating the single fiber along the X-axis to obtain the first single fiber, rotating the first single fiber around the Z-axis by 2π / m, 4π / m, ..., 2πk / m, ..., 2π(m-1) / m to respectively form the second single fiber, the third single fiber, ..., the kth single fiber, ..., the mth single fiber; the first single fiber, the second single fiber, the third single fiber, ..., the kth single fiber, ..., the mth single fiber form a single fiber bundle, wherein k=1, 2, ..., m; Step S300: Modeling a single sinusoidal braided yarn: using a single fiber bundle as a single braided yarn, and transforming the single braided yarn into a single sinusoidal braided yarn; Step S400: Modeling a two-dimensional circular braided fabric: translating a single sinusoidal braiding yarn along the X-axis to obtain the first braiding yarn, rotating the first braiding yarn around the Z-axis by 2π / n, 4π / n, ..., 2πi / n, ..., 2π(n-1) / n to form the second braiding yarn, the third braiding yarn, ..., the i-th braiding yarn, ..., the n-th braiding yarn respectively; twisting or untwisting the first braiding yarn, the second braiding yarn, the third braiding yarn, ..., the i-th braiding yarn, ..., the n-th braiding yarn; rotating and interweaving the first braiding yarn, the second braiding yarn, the third braiding yarn, ..., the i-th braiding yarn, ..., the n-th braiding yarn around the Z-axis to form a braided fabric, wherein i is the number of the braiding yarn, i=1, 2, 3, ..., n.
2. The modeling method of a fiber-level two-dimensional circular braid according to claim 1, characterized in that: Step S200 includes: Step S201: Establish a straight line equation L0 of a single fiber. The straight line equation L0 is: L0=[0,0,ht / 2π, 1] T (1) Wherein, π is the circumference of a circle, t is an equation parameter, dimensionless parameter t=π / 8*(j-1) is defined, j is the number of points on a single fiber, j=1, 2, ..., +∞ integer, T is the vector transpose symbol; Step S202: translating the single fiber along the X-axis by a distance of 2r to obtain the first single fiber. The single fiber translation matrix T1 is: Step S203: The first single fiber is rotated around the Z axis by 2π / m, 4π / m, ..., 2πk / m, ..., 2π(m-1) / m to form the second single fiber, the third single fiber, ..., the kth single fiber, ..., the mth single fiber respectively; the first single fiber, the second single fiber, the third single fiber, ..., the kth single fiber, ..., the mth single fiber form a single fiber bundle, and the fiber rotation matrix α1 of the kth single fiber rotating around the z axis is:
3. The modeling method of a fiber-level two-dimensional circular braid according to claim 2, characterized in that: Step S300 includes: taking a single fiber bundle as a single braiding yarn, and transforming the single braiding yarn into a single sinusoidal braiding yarn, wherein the transformation matrix T2 is:
4. The modeling method of a fiber-level two-dimensional circular braid according to claim 3, characterized in that: Step S400 includes: Step S401: A single sinusoidal braiding yarn is translated along the X-axis by a distance R to obtain the first braiding yarn. The braiding yarn translation matrix T3 is: Step S402: The first braiding yarn is rotated around the Z axis by 2π / m, 4π / m, ..., 2πi / m, ..., 2π(n-1) / n to form the second braiding yarn, the third braiding yarn, ..., the i-th braiding yarn, ..., the n-th braiding yarn, the first braiding yarn, the second braiding yarn, the third braiding yarn, ..., the i-th braiding yarn, ..., the n-th braiding yarn, and the fiber rotation matrix α3 of the i-th braiding yarn rotated around the z axis is: Step S403: twisting or not twisting the first braiding yarn, the second braiding yarn, the third braiding yarn, ..., the i-th braiding yarn, ..., the n-th braiding yarn; Step S404: Rotate the first braiding yarn, the second braiding yarn, the third braiding yarn, ..., the ith braiding yarn, ..., the nth braiding yarn around the Z axis so that the first braiding yarn, the second braiding yarn, the third braiding yarn, ..., the ith braiding yarn, ..., the nth braiding yarn are interwoven, and the interwoven matrix α4 is: Step S405: The first braided yarn, the second braided yarn, the third braided yarn, ..., the ith braided yarn, ..., the nth braided yarn after interweaving are translated to obtain a braided fabric. The translation matrix T4 is:
5. A method for modeling a fiber-level two-dimensional circular braid according to claim 4, characterized in that: In step S403, a portion of the first braiding yarn, the second braiding yarn, the third braiding yarn, ..., the ith braiding yarn, ..., and the nth braiding yarn is twisted counterclockwise, and another portion of the first braiding yarn, the second braiding yarn, the third braiding yarn, ..., the ith braiding yarn, ..., and the nth braiding yarn is twisted clockwise. The braided fabric includes Z-twisted braiding yarns and S-twisted braiding yarns. The twist matrix α of the ith braiding yarn is 21 for: Among them, A is not equal to 0.
6. A method for modeling a fiber-level two-dimensional circular braid according to claim 4, characterized in that: In step S403, the first braiding yarn, the second braiding yarn, the third braiding yarn, ..., the ith braiding yarn, ..., the nth braiding yarn are all twisted counterclockwise, and when the braided fabric only includes Z-twisted braiding yarns, the twist matrix α of the first braiding yarn, the second braiding yarn, the third braiding yarn, ..., the ith braiding yarn, ..., the nth braiding yarn is 22 Both are: Among them, A is not equal to 0.
7. A method for modeling a fiber-level two-dimensional circular braid according to claim 4, characterized in that: In step S403, the first braiding yarn, the second braiding yarn, the third braiding yarn, ..., the ith braiding yarn, ..., the nth braiding yarn are all twisted counterclockwise, and when the braided fabric only includes S-twisted braiding yarns, the twist matrix α of the first braiding yarn, the second braiding yarn, the third braiding yarn, ..., the ith braiding yarn, ..., the nth braiding yarn is 23 Both are: Among them, A is not equal to 0.
8. The modeling method of a fiber-level two-dimensional circular braid according to claim 4, characterized in that: In step S403, the first braiding yarn, the second braiding yarn, the third braiding yarn, ..., the ith braiding yarn, ..., the nth braiding yarn are all untwisted to serve as a single braiding yarn, and the untwisted matrix is:
9. The modeling method of a fiber-level two-dimensional circular braid according to claim 5, characterized in that: When the braided fabric includes Z-twisted braided yarn and S-twisted braided yarn, the fiber curve equation L1(i,k) of the kth single fiber of the i-th braided yarn in the braided fabric is: L1(i,k)=T4*α4*α3*T3*T2*α 21 *α1*T1*L0=M*L0 (10-1) Among them, the overall transformation matrix M1 is: M1=T4*α4*α3*T3*T2*α 21 *a1*T1 (11-1) 10. A method for modeling a fiber-level two-dimensional circular braid according to claim 6, 7 or 8, characterized in that: When the braided fabric only includes Z-twisted braided yarns, the fiber curve equation L2(i,k) of the kth single fiber of the i-th braided yarn in the braided fabric is: L2(i,k)=T4*α4*α3*T3*T2*α 22 *α1*T1*L0=M*L0 (10-2) Among them, the overall transformation matrix M2 is: M2=T4*α4*α3*T3*T2*α 22 *a1*T1 (11-2) Alternatively, in step S400, when the braided fabric includes only S-twisted braided yarns, the fiber curve equation L3(i,k) of the k-th single fiber of the i-th braided yarn in the braided fabric is: L3(i,k)=T4*α4*α3*T3*T2*α 23 *α1*T1*L0=M*L0 (10-2) Among them, the overall transformation matrix M3 is: M3=T4*α4*α3*T3*T2*α 23 *α1*T1 (11-3) Alternatively, when the braided fabric includes no twist, the fiber curve equation L4(i,k) of the kth single fiber of the i-th braided yarn in the braided fabric is: L4(i,k)=T4*α4*α3*T3*T2*α 24 *α1*T1*L0=M*L0 (10-4) Among them, the overall transformation matrix M4 is: M4=T4*α4*α3*T3*T2*α 24 *α1*T1 (11-4)。