A method of polar fabric modeling

Abstract

This invention discloses a modeling method for polar fabrics. This method not only captures the unique spatial topological features of radial divergence and circumferential closure inherent in polar fabrics, establishing a microscopic model of the annular polar fabric in a cylindrical coordinate system that couples the sinusoidal undulations and random distribution characteristics of the yarns, accurately representing the interweaving structure of the circumferential and radial yarns; it can also establish a quasi-fiber-scale model to realistically simulate the random arrangement and spatial compression effect of the individual fiber filaments within the yarn. This modeling method, spanning both microscopic and quasi-fiber scales, effectively improves upon the shortcomings of traditional modeling. It eliminates the problem of treating yarns as homogeneous entities and ignoring the true structure of fiber entanglement, leading to distorted stress distribution in simulations. This significantly improves the prediction accuracy of the fabric's microscopic damage mechanism and provides theoretical support for optimizing automated yarn weaving processes and predicting the mechanical properties of polar fabrics.

Description

Technical Field

[0001] This invention belongs to the field of textile composite material modeling technology, and specifically relates to a method for modeling polar fabrics. Background Technology

[0002] Polar fabrics are high-performance textile structures woven from circumferential and radial yarns. They have excellent circumferential rotational load-bearing capacity and can be used as composite material reinforcements in high-end composite equipment such as aero-engine rotor components and flywheel energy storage components. They have broad application prospects in the aerospace and high-end manufacturing fields.

[0003] Parametric modeling is a key technology in the digital design of composite materials. By constructing multi-scale structural models, it effectively correlates the microscopic structural features of materials with their macroscopic mechanical properties, providing crucial support for material performance prediction, weaving and molding process optimization, and cost control. It is a vital foundation for promoting the high-performance and large-scale application of composite materials. Specifically, the mesoscale model characterizes the interlacing morphology, arrangement density, and spatial configuration characteristics of yarn layers, while the quasi-fiber scale model reconstructs the actual path and microscopic structural features of individual fibers. Together, they form a key support for the refined modeling and performance analysis of polar fabrics. For polar fabrics, establishing accurate parametric modeling methods covering both mesoscale and quasi-fiber scales is a core prerequisite for achieving structural performance prediction, weaving process optimization, and automated production.

[0004] However, existing modeling methods for composite reinforced fabrics are mostly designed for conventional fabric structures such as plain weave, twill weave, or three-dimensional woven fabrics. These methods typically assume yarns are arranged along straight or regular curved paths, making it difficult to adapt to the non-uniform interweaving and polar coordinate distribution of circumferential and radial yarns in polar fabrics. Furthermore, existing modeling methods generally remain at a single scale: one type focuses on simplified geometric descriptions at the macroscopic or yarn level, lacking modeling tools capable of accurately representing the yarn interweaving morphology in polar fabrics at the microscopic scale; another type is limited to the microstructural analysis of conventional fabrics, failing to reconstruct the three-dimensional fiber paths and their structural characteristics resulting from polar coordinate distribution in polar fabrics at the quasi-fiber scale. These shortcomings prevent existing models from meeting the refined modeling needs of polar fabrics in structural design, performance prediction, and weaving process parameter optimization, making related design and production processes heavily reliant on experience. Therefore, there is an urgent need to propose a parametric modeling method for polar fabrics at the microscale and fiber level. This method can parametrically describe the yarn-level structural features and fiber-level path features respectively, while establishing a correspondence with the process parameters of polar fabrics. This will improve the accuracy, versatility, and support capability for automated production of polar fabric modeling, and provide predictions for the mechanical properties of polar fabrics. Summary of the Invention

[0005] To address the shortcomings of existing technologies, the purpose of this invention is to provide a method for modeling polar fabrics at a microscale.

[0006] Another objective of this invention is to provide a modeling method for a quasi-fiber scale model of polar fabrics;

[0007] The objective of this invention is achieved through the following technical solution.

[0008] A method for modeling a microscale model of polar fabrics includes the following steps:

[0009] S1. Assume a circular polar fabric. The polar fabric is woven from M circumferential yarns, 2*W radial yarns and W*2*(N-1) parallel weft yarns. Each circumferential yarn is circular. The M circumferential yarns are arranged in concentric circles. The circumferential yarns form a sine wave along their circumference. Each radial yarn is arranged along the radial direction of the polar fabric. The 2*W radial yarns are divided into W yarn groups. Each yarn group includes 2 parallel and adjacent radial yarns.

[0010] W yarn groups are uniformly distributed on the polar fabric, and the part between any two adjacent yarn groups is a fan-shaped representative volume unit, and the included angle between any two adjacent yarn groups is S.

[0011] Establish a cylindrical coordinate system, and take the center of the polar fabric as the origin of the cylindrical coordinate system. The polar angle range of a sector representative volume unit in the polar fabric is [0,S]. Divide the sector representative volume unit corresponding to the polar angle range [0,S] of the cylindrical coordinate system along its angle bisector to obtain two mirror-symmetric sector rings. Each sector ring is a sector sub-unit. Let the sector sub-unit with the polar angle in [0,S / 2] be the starting sub-unit.

[0012] Establish a Cartesian coordinate system, with the center of the polar fabric as the origin of the Cartesian coordinate system, and the straight line with a polar angle of 0 in the cylindrical coordinate system as the X-axis of the Cartesian coordinate system. The Z-axis of the Cartesian coordinate system and the cylindrical coordinate system coincide and are in the same positive direction. The parallel yarns in the starting sub-unit are evenly distributed, and all the parallel yarns in the starting sub-unit are parallel to the X-axis of the Cartesian coordinate system. The radial yarns in the starting sub-unit are parallel to the X-axis.

[0013] S2, construct the path equations for the centerlines of the M circumferential yarns. The path equation for the centerline of the m-th circumferential yarn along the direction from the inner arc edge of the starting sub-unit to the outer arc edge is as follows:

[0014]

[0015] in, Let m be the radius of the center line of the m-th circumferential yarn. , The inner diameter of the starting subunit. The distance between the center lines of adjacent circumferential yarns in the starting subunit. The polar angle in cylindrical coordinates;

[0016] Let Z be the Z-axis coordinate of the centerline of the m-th circumferential yarn in the cylindrical coordinate system; To determine the vertical distance from the peak of the sine wave formed by the centerline of the circumferential yarn to the polar coordinate plane, one radial yarn and N-1 parallel weft yarns in the initial sub-unit are both considered as transverse yarns. The distance between the center lines of any two adjacent transverse yarns in the starting sub-unit; the center lines of the transverse yarns form a sine wave;

[0017] S3, Construct the path equations for the centerlines of the N transverse yarns within the initial sub-unit. Following the direction of increasing Y-axis in the Cartesian coordinate system, the path equation for the centerline of the nth transverse yarn is as follows:

[0018]

[0019] Let n be the X-axis coordinate of the centerline of the nth transverse yarn in the Cartesian coordinate system. , Let Y be the Y-axis coordinate of the centerline of the nth transverse yarn in the Cartesian coordinate system. The outer diameter of the starting sub-unit;

[0020] The number of transverse yarns interwoven with the m-th circumferential yarn : ;according to as well as Determine the starting point of each transverse yarn, where the starting point of the nth transverse yarn is connected to the circumferential yarn of the nth transverse yarn. The endpoints of all transverse yarns are connected to the Mth circumferential yarn;

[0021] For the first The radius of the center line of the circumferential yarn;

[0022] The center line of the nth transverse yarn is located at the x-axis coordinate of The Z-axis coordinate in the Cartesian coordinate system The vertical distance from the peak of the sine wave formed by the centerline of the transverse yarn to the xy-coordinate plane in the Cartesian coordinate system. Let n be the number of antinodes in the sine wave formed by the centerline of the nth transverse yarn; the X-axis coordinate of the centerline of the nth transverse yarn is... The point at time is located on the sine wave formed by the center line. One antinode segment;

[0023] The center line of the nth transverse yarn The angular frequency corresponding to each antinode segment;

[0024] S4, using the angle bisector of the representative sector volume unit as the axis of symmetry, mirrors the paths of the center lines of the M circumferential yarns corresponding to the starting sub-unit in S2 to generate the polar angle. The path of the center line of the M circumferential yarns corresponding to the sector subunit, and the combined polar angle. and polar angle The paths of the center lines of the M circumferential yarns corresponding to the two sector sub-units are obtained to obtain the paths of the center lines of the M circumferential yarns of the representative sector volume unit;

[0025] Using the angle bisector of the representative volume element in the sector as the axis of symmetry, the paths of the center lines of the N transverse yarns corresponding to the initial sub-unit in S3 are mirrored to generate the polar angle. The paths of the center lines of the N transverse yarns corresponding to the sector-shaped subunit are merged into polar angles. and polar angle The paths of the center lines of the N transverse yarns corresponding to the two sector sub-units are obtained to obtain the paths of the center lines of the 2N transverse yarns of the representative volume unit of the sector.

[0026] S5, make both the single transverse yarn cross section and the single circumferential yarn cross section elliptical, sweep the circumferential yarn cross section along the path of the center line of the circumferential yarn to generate the circumferential yarn solid, sweep the transverse yarn cross section along the path of the center line of the transverse yarn to generate the transverse yarn solid, and obtain a three-dimensional solid of a fan-shaped representative volume unit with a polar angle range of [0,S].

[0027] S6. Using the Z-axis of the cylindrical coordinate system where the three-dimensional entity of the sector-shaped representative volume unit is located as the rotation reference axis, the three-dimensional entity is arranged around the rotation reference axis in full circumference, and the three-dimensional entities of adjacent sector-shaped representative volume units are in contact to generate a microscale model of polar fabric.

[0028] In this technical solution, , .

[0029] In the above technical solutions, =0.2~0.4mm.

[0030] In the above technical solutions, =0.2~0.4mm.

[0031] In the above technical solutions, .

[0032] In the above technical solutions, , The center line of the nth transverse yarn The length of each antinode segment projected onto the xy coordinate plane.

[0033] In the above technical solution, when hour, , The center line of the nth transverse yarn Minimum X-axis coordinate of each antinode segment , For the first The radius of the center line of the circumferential yarn; The center line of the nth transverse yarn Minimum X-axis coordinate of each antinode segment , For the first The radius of the center line of the circumferential yarn;

[0034] when hour, , The center line of the nth transverse yarn The minimum X-axis coordinate of each antinode segment.

[0035] A method for modeling a quasi-fiber-scale model of polar fabrics includes: treating transverse yarns and circumferential yarns as yarns, and constructing K fiber monofilaments within each yarn in the micro-scale model of the polar fabric. The construction method includes:

[0036] Step 1: Take the radial yarn section and the circumferential yarn section as the yarn section respectively, define a single yarn as consisting of K fiber filaments, and let the cross section of each fiber filament be a circular cross section with a radius of R.

[0037] Determine the coordinates of the center of the cross-section of the K fiber filaments in a single yarn: Set a set of center points, which includes the coordinates of the center of the cross-section of the K fiber filaments.

[0038] Step 2: Using the assembly function of the modeling software, construct the K fiber monofilaments in each yarn based on the coordinates of the center of the cross-section of the K fiber monofilaments corresponding to the center point set.

[0039] In step 1, the method for obtaining the coordinates of the center of the cross-section of the fiber monofilament corresponding to the K fiber monofilaments in the center point set includes:

[0040] Step 11, the method for obtaining the coordinates of the center of the cross-section of the first fiber filament in the center point set includes: establishing a local Cartesian coordinate system with the center point of the yarn cross-section as the origin. The x-axis of the local Cartesian coordinate system is parallel to the major axis of the ellipse formed by the yarn cross-section, and the y-axis of the local Cartesian coordinate system is parallel to the minor axis of the ellipse formed by the yarn cross-section. Using the Monte Carlo method, a center coordinate (x', y') that satisfies the first constraint condition in the local Cartesian coordinate system is randomly generated within the rectangular envelope region bounded by the yarn cross-section. The center coordinate (x', y') is then assigned to the center point set. The first constraint condition is as follows:

[0041] Where, if the yarn is a transverse yarn, then a=a1, b=b1; if the yarn is a circular yarn, then a=a2, b=b2.

[0042] Step 12, setting each integer from 2 to K to i, the method for obtaining the coordinates of the center of the cross-section of the i-th fiber monofilament in the center point set includes: using the Monte Carlo method to randomly generate a coordinate point that satisfies the second constraint condition in the local Cartesian coordinate system within a rectangular envelope region bounded by the yarn cross-section ( , If the coordinate point ( , If the distance between the coordinates of a point and the center of the cross-section of each fiber monofilament in the current center point set satisfies the following condition, then the coordinate point ( , (To be included in the set of center points)

[0043] ;

[0044] in, Coordinates ( , ) and the current center point set The Euclidean distance between the coordinates of the centers of the cross-sections of the corresponding fiber monofilaments; 1 to Given any integer, iterate through... , This represents the number of coordinates of the center of the cross-section of the fiber monofilament corresponding to the current center point set; Coordinates ( , The corresponding fiber monofilament cross-sectional radius; For the current center point set, the first The coordinates of the center of the cross-section of a single fiber filament correspond to the radius of the cross-section of that single fiber filament; and All in [R min ,Rmax Randomly selected from [ ]; Tol is the non-contact judgment tolerance between fiber monofilaments;

[0045] The second constraint is as follows:

[0046] Wherein, if the yarn is a transverse yarn, then a=a1, b=b1; if the yarn is a circular yarn, then a=a2, b=b2.

[0047] In the above technical solutions, .

[0048] In the above technical solution, the R of each fiber monofilament is in R min ~R max The value is randomly selected from R, or a constant value R is set for R. H , where R min R is the minimum radius of the cross-section of a single fiber filament. max R is the maximum radius of the cross-section of a single fiber filament. min <R max .

[0049] The beneficial effects of this invention are as follows:

[0050] (1) The polar fabric modeling method of the present invention can not only capture the unique spatial topological features of radial divergence and circumferential closure of polar fabrics, but also establish a micro-scale model of annular polar fabrics with coupled yarn sinusoidal fluctuations and random distribution characteristics in a cylindrical coordinate system, accurately characterizing the interlacing structure of circumferential and radial yarns; it can also establish a quasi-fiber scale model to realistically simulate the random arrangement and spatial compression effect of fiber monofilaments inside the yarn. This modeling method that spans the micro-scale and quasi-fiber scale can effectively improve the defects of traditional modeling, eliminate the problem of distorting the stress distribution obtained by simulation by equating yarns to homogenized entities and ignoring the real structure of fiber entanglement in traditional models, and significantly improve the prediction accuracy of the micro-damage mechanism of fabrics. It can provide theoretical support for the optimization of automated yarn production process and the prediction of mechanical properties of polar fabrics, and has extremely high industrial transformation value, especially suitable for the design and production of high-performance polar fabrics for aero-engine rotor components and flywheel energy storage components.

[0051] (2) The polar fabric modeling method of the present invention only requires inputting a small number of geometric parameters to quickly complete the model construction; in addition, the process parameters, such as adjusting h1, h2, etc., can be modified. , , , This invention enables fully automated reconstruction of polar fabrics from macroscopic weaving schemes to microscopic and quasi-fiber scale structures. Compared with traditional manual modeling or non-parametric methods, this invention significantly shortens the modeling cycle of polar fabrics, providing support for rapid iteration of fabric structures and large-scale scheme selection. Attached Figure Description

[0052] Figure 1 This is a schematic diagram of a polar fabric structure;

[0053] Figure 2 This is a schematic diagram of a representative volume unit structure of a single sector shape according to the present invention;

[0054] Figure 3 (a) is a schematic diagram of the Z-direction trend of the center line of a single circumferential yarn in this invention. Figure 3 (b) is the Z-direction path curve of the centerline of the circumferential yarn;

[0055] Figure 4 (a) is a schematic diagram of the Z-direction trend of the centerline of a single radial yarn in this invention. Figure 4 (b) is the Z-direction path curve of the centerline of the radial yarn;

[0056] Figure 5 The flowchart for generating the sequence of center circles of cross sections corresponding to K fiber monofilaments in a single yarn consists of three parts: (a), (b), and (c).

[0057] Figure 6 (a) is the stress cloud diagram of the finite element model simulation of the polar fabric composite rotor of Embodiment 3 of the present invention. Figure 6 (b) is a simulated stress cloud diagram of a single representative volume element in a sector.

[0058] Figure 7 (a) is a schematic diagram of the polar fabric composite rotor of Comparative Example 1 of the present invention. Figure 7 (b) is a magnified schematic diagram of the inner hole of the rotor of polar fabric composite material. Detailed Implementation

[0059] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0060] Example 1

[0061] A method for modeling a microscale model of polar fabrics includes the following steps:

[0062] S1, as Figure 1 As shown, suppose a circular polar fabric is woven from M circumferential yarns, 2*W radial yarns and W*2*(N-1) parallel weft yarns. Each circumferential yarn is circular, and the M circumferential yarns are arranged in concentric circles. The circumferential yarns form a sine wave along their circumference. Each radial yarn is arranged along the radial direction of the polar fabric. The 2*W radial yarns are divided into W yarn groups, and each yarn group includes 2 parallel and adjacent radial yarns.

[0063] W yarn groups are uniformly distributed on the polar fabric, and the portion between any two adjacent yarn groups is a sector-shaped representative volume unit (i.e., there are W sector-shaped representative volume units in the polar fabric), and the included angle between any two adjacent yarn groups is S.

[0064] Establish a cylindrical coordinate system, with the center of the polar fabric as the origin. A representative sector volume element in the polar fabric corresponds to a polar angle range of [0, S] in the cylindrical coordinate system (the unit of polar angle is rad). Divide the representative sector volume element corresponding to the polar angle range [0, S] along its angle bisector to obtain two mirror-symmetric sector rings. Each sector ring serves as a sector sub-unit, as shown below. Figure 2 As shown, the number of parallel yarns in each sector subunit is N-1, and the sector subunit with polar angle in [0, S / 2] is taken as the starting subunit;

[0065] Establish a Cartesian coordinate system, with the center of the polar fabric as the origin of the Cartesian coordinate system, and the straight line with a polar angle of 0 in the cylindrical coordinate system as the X-axis of the Cartesian coordinate system. The Z-axis of the Cartesian coordinate system and the cylindrical coordinate system coincide and are in the same positive direction. The parallel yarns in the starting sub-unit are evenly distributed, and all the parallel yarns in the starting sub-unit are parallel to the X-axis of the Cartesian coordinate system. The radial yarns in the starting sub-unit are parallel to the X-axis.

[0066] S2, construct the path equations for the centerlines of the M circumferential yarns. The path equation for the centerline of the m-th circumferential yarn along the direction from the inner arc edge of the starting sub-unit to the outer arc edge is as follows:

[0067]

[0068] in, Let m be the radius of the center line of the m-th circumferential yarn. , The inner diameter of the starting subunit. The distance between the center lines of adjacent circumferential yarns in the starting subunit. The polar angle in the cylindrical coordinate system (in this embodiment, the independent variable) is... Divide into 20*W equal parts. );

[0069] In this embodiment, a value of 0.5 is set to ensure that when m=1, the center line of the first circumferential yarn will not fall on the inner arc of the original starting subunit;

[0070] like Figure 3 As shown in (b), Let Z be the Z-axis coordinate of the centerline of the m-th circumferential yarn in the cylindrical coordinate system; The vertical distance from the peak of the sine wave formed by the centerline of the circumferential yarn to the polar coordinate plane. =0.2~0.4mm, The first phase factor (used to constrain the alternating up-and-down undulation of the centerlines of adjacent circumferential yarns in space); one radial yarn and N-1 parallel weft yarns in the starting sub-unit are both treated as transverse yarns. The distance between the center lines of any two adjacent transverse yarns in the starting sub-unit; the center lines of the transverse yarns form a sine wave;

[0071] S3, Construct the path equations for the centerlines of the N transverse yarns within the initial sub-unit. Following the direction of increasing Y-axis in the Cartesian coordinate system, the path equation for the centerline of the nth transverse yarn is as follows:

[0072]

[0073] Let n be the X-axis coordinate of the centerline of the nth transverse yarn in the Cartesian coordinate system. , Let Y be the Y-axis coordinate of the centerline of the nth transverse yarn in the Cartesian coordinate system. The outer diameter of the starting sub-unit;

[0074] The number of transverse yarns interwoven with the m-th circumferential yarn : ;according to as well as Determine the starting point of each transverse yarn, where the starting point of the nth transverse yarn is connected to the circumferential yarn of the nth transverse yarn. The endpoints of all transverse yarns are connected to the Mth circumferential yarn;

[0075] For the first The radius of the center line of the circumferential yarn; in this embodiment, it is set to 0.5 to ensure that when n=1, the center line of the first transverse yarn in the starting sub-unit will not fall on the X-axis;

[0076] like Figure 4 As shown in (b), The center line of the nth transverse yarn is located at the x-axis coordinate of The Z-axis coordinate in the Cartesian coordinate system The vertical distance from the peak of the sine wave formed by the centerline of the transverse yarn to the xy-coordinate plane in the Cartesian coordinate system. =0.2~0.4mm; The number of antinodes in the sine wave formed by the centerline of the nth transverse yarn; The X-axis coordinate of the center line of the nth transverse yarn is: The point at time is located on the sine wave formed by the center line. One antinode segment; The second phase factor (used to constrain the centerline of the nth transverse yarn to alternately undulate up and down in space);

[0077] The center line of the nth transverse yarn The angular frequency corresponding to each antinode segment , The center line of the nth transverse yarn The length of each antinode segment projected onto the xy coordinate plane;

[0078] when hour, , The center line of the nth transverse yarn Minimum X-axis coordinate of each antinode segment , For the first The radius of the center line of the circumferential yarn; The center line of the nth transverse yarn Minimum X-axis coordinate of each antinode segment , For the first The radius of the center line of the circumferential yarn;

[0079] when hour, , The center line of the nth transverse yarn Minimum X-axis coordinate of each antinode segment;

[0080] S4, using the angle bisector of the representative sector volume unit as the axis of symmetry, mirrors the paths of the center lines of the M circumferential yarns corresponding to the starting sub-unit in S2 to generate the polar angle. The path of the center line of the M circumferential yarns corresponding to the sector subunit, and the combined polar angle. and polar angle The paths of the center lines of the M circumferential yarns corresponding to the two sector sub-units are obtained to obtain the paths of the center lines of the M circumferential yarns of the representative sector volume unit (in cylindrical coordinate system).

[0081] Using the angle bisector of the representative volume element in the sector as the axis of symmetry, the paths of the center lines of the N transverse yarns corresponding to the initial sub-unit in S3 are mirrored to generate the polar angle. The paths of the center lines of the N transverse yarns corresponding to the sector-shaped subunit are merged into polar angles. and polar angle The paths of the center lines of the N transverse yarns corresponding to the two sector sub-units are used to obtain the paths of the center lines of the 2N transverse yarns of the representative sector volume unit (in Cartesian coordinates).

[0082] S5, such as Figure 3 of (a), Figure 4 As shown in (a), both the cross-section of a single transverse yarn and the cross-section of a single circumferential yarn are elliptical. The major axis of the transverse yarn cross-section corresponding to the ellipse is a1, and the minor axis is b1; the major axis of the circumferential yarn cross-section corresponding to the ellipse is a2, and the minor axis is b2. The circumferential yarn cross-section is swept along the path of the center line of the circumferential yarn to generate a circumferential yarn solid. The transverse yarn cross-section is swept along the path of the center line of the transverse yarn to generate a transverse yarn solid. Thus, a three-dimensional solid of a sector-shaped representative volume unit with a polar angle range of [0, S] is obtained (during the sweeping process, the normal direction of the transverse yarn cross-section is consistent with the path of the center line of the corresponding transverse yarn, and the normal direction of the circumferential yarn cross-section is consistent with the tangent direction of the path of the center line of the corresponding circumferential yarn).

[0083] S6. Using the Z-axis of the cylindrical coordinate system where the three-dimensional entity of the sector-shaped representative volume unit is located as the rotation reference axis, the three-dimensional entity is arranged around the rotation reference axis (in the counterclockwise direction) in a full circle (circumferential direction arrangement), and the three-dimensional entities of adjacent sector-shaped representative volume units are in close contact (i.e., without gaps or overlaps), generating a microscale model of polar fabric.

[0084] In this technical solution, , .

[0085] Example 2

[0086] A method for modeling a quasi-fiber-scale model of polar fabrics, which treats transverse yarns and circumferential yarns as yarns respectively, also includes constructing K fiber monofilaments within each yarn in the three-dimensional entity of Example 1. The construction method includes:

[0087] Step 1: The radial and circumferential yarn cross-sections are respectively used as yarn cross-sections (elliptical). A single yarn is defined as consisting of K fiber filaments (K controls the fineness of the quasi-fiber scale model; in this embodiment, K=50). The cross-section of each fiber filament is a circular cross-section with a radius of R. The radius of R for each fiber filament is within the range of R... min ~R max Randomly selected value (R) min R is the minimum radius of the cross-section of a single fiber filament. max R is the maximum radius of the cross-section of a single fiber filament; min <R max (This can be used to simulate the random distribution characteristics of the cross-sectional diameter of a fiber monofilament), or R can be set to a constant value R. H In this embodiment, the R of each fiber monofilament is in R min ~R max Randomly selected values, R min =0.01mm, R max =0.03mm;

[0088] Determine the coordinates of the center of the cross-section of the K fiber filaments within a single yarn: Set a set of center points, which includes the coordinates of the center of the cross-section of the K fiber filaments (i.e., K coordinates).

[0089] Methods for obtaining the coordinates of the center of the cross-section of the fiber monofilament corresponding to the K fiber monofilaments in the center point set include:

[0090] Step 11, the method for obtaining the coordinates of the center of the cross-section of the first fiber filament in the set of center points includes: such as Figure 5 As shown, a local Cartesian coordinate system is established with the center point of the yarn cross-section as the origin. The x-axis of the local Cartesian coordinate system is parallel to the major axis of the ellipse formed by the yarn cross-section, and the y-axis of the local Cartesian coordinate system is parallel to the minor axis of the ellipse formed by the yarn cross-section. Using the Monte Carlo method, a circle center coordinate (x', y') that satisfies the first constraint condition in the local Cartesian coordinate system is randomly generated within the rectangular envelope region bounded by the yarn cross-section. The circle center coordinate (x', y') is then assigned to the circle center point set. The first constraint condition is as follows:

[0091] Where, if the yarn is a transverse yarn, then a=a1, b=b1; if the yarn is a circular yarn, then a=a2, b=b2.

[0092] Step 12, setting each integer from 2 to K to i, the method for obtaining the coordinates of the center of the cross-section of the i-th fiber monofilament in the center point set includes: using the Monte Carlo method to randomly generate a coordinate point that satisfies the second constraint condition in the local Cartesian coordinate system within a rectangular envelope region bounded by the yarn cross-section ( , If the coordinate point ( , If the distance between the coordinates of a point and the center of the cross-section of each fiber monofilament in the current center point set satisfies the following condition, then the coordinate point ( , (To be included in the set of center points)

[0093] ;

[0094] in, Coordinates ( , ) and the current center point set The Euclidean distance between the coordinates of the centers of the cross-sections of the corresponding fiber monofilaments; 1 to Given any integer, iterate through... , This represents the number of coordinates of the center of the cross-section of the fiber monofilament corresponding to the current center point set; Coordinates ( , The corresponding fiber monofilament cross-sectional radius; For the current center point set, the first The coordinates of the center of the cross-section of a single fiber filament correspond to the radius of the cross-section of that single fiber filament; and All in [R min ,R max Randomly selected from []; Tol is the non-contact judgment tolerance between fiber monofilaments (fiber monofilaments generated within a single yarn do not interfere with each other in physical space; setting the non-contact judgment tolerance Tol can effectively solve the geometric interference and model generation failure problems caused by extremely small spacing under high fiber filling rate). In this embodiment, Tol is 0.0001 mm.

[0095] The second constraint is as follows:

[0096] Where, if the yarn is a transverse yarn, then a=a1, b=b1; if the yarn is a circular yarn, then a=a2, b=b2.

[0097] Step 2: Using the assembly function of the modeling software, construct the K fiber monofilaments in each yarn based on the coordinates of the center of the cross-section of the K fiber monofilaments corresponding to the center point set.

[0098] In this embodiment, the translated fiber monofilaments maintain a random cross-sectional distribution while completely following the undulating trend of the yarn path at a microscale.

[0099] Example 3

[0100] A method for modeling a polar fabric composite rotor, based on Example 1, uses transverse yarns and circumferential yarns as yarns respectively, and introduces epoxy resin into the gaps between the yarns of the three-dimensional solid through Boolean operations to construct a finite element model of the polar fabric composite rotor. The relevant parameters are set as follows:

[0101] S is W=10 It is 7.4mm. It is 137.5mm;

[0102] , The number of center lines of the loop yarn within a unit length L (i.e., the loop yarn weaving density). 6 strands / 10mm;

[0103] , The number of centerline yarns in the transverse direction within a unit length L (i.e., the transverse yarn weaving density). It is 5 pieces / 10mm; in this embodiment, L is 10mm;

[0104] h1 is 0.25mm, a1 is 0.7mm, b1 is 0.15mm; h2 is 0.2mm, a2 is 0.55mm, b2 is 0.1mm.

[0105] T800-12K carbon fiber yarn was selected as the transverse yarn, and T800-6K carbon fiber yarn was selected as the circumferential yarn. The material properties of the carbon fiber and the resin in the T800-12K and T800-6K carbon fiber yarns are shown in Table 1 below.

[0106] Table 1

[0107]

[0108] Comparative Example 1

[0109] Using the finite element model of the polar fabric composite rotor in Example 3 as a template, the rotor was actually prepared using existing processes. For details of the preparation method, please refer to: LI Y, LIU A, FU HM, et al. Full-field strain analysis and radial tensile damage mechanisms of polar braided composites[J]. Thin-WalledStructures, 2026, 226: 114883., to obtain the polar fabric composite rotor.

[0110] Finite element analysis was performed on the polar fabric composite rotor finite element model obtained in Example 3 to obtain the simulated failure speed of the polar fabric composite rotor. A macroscopic failure experiment was then conducted on the polar fabric composite rotor obtained in Comparative Example 1 to obtain the actual failure speed of the polar fabric composite rotor. The effectiveness of the microscale modeling method for the polar fabric in Example 1 was verified by comparing the simulated failure speed and the actual failure speed.

[0111] Simulation failure speed acquisition process: Eight-node linear reduced integral hexahedral elements (C3D8R) and four-node tetrahedral elements (C3D4) were selected to perform mesh discretization on the three-dimensional solid and epoxy resin respectively; in order to ensure the continuous and effective transmission of interface load, binding constraints were defined between the outer surface of the three-dimensional solid and the epoxy resin envelope surface, and based on the circumferential cyclic symmetry characteristics of the rotor structure, cyclic symmetry boundary conditions were applied on the circumferential boundaries on both sides of a single three-dimensional solid. Thus, a single three-dimensional solid can be used to equivalently characterize a full-size polar fabric composite rotor structure containing 10 sector-shaped representative volume elements.

[0112] During the solution and analysis phase, a rotational body load around the geometric center axis (Z-axis) is applied to the finite element model in a stepwise acceleration manner to accurately simulate the centrifugal stress state and mechanical response of the polar fabric composite rotor under real service conditions; and the standard statics solver (with built-in convergence criteria) is called to perform static analysis at various speed conditions until the rotor structure is determined to fail and the simulated failure speed is output.

[0113] like Figure 6 As shown, the non-uniform distribution of strain field caused by the difference in the specifications of carbon fiber yarn bundles (12K and 6K) and yarn interlacing can be clearly captured. The stress peak is mainly concentrated at the yarn interlacing position at the edge of the inner hole of the polar fabric composite rotor finite element model. The simulated failure speed is 43400 r / min.

[0114] The actual failure speed was obtained as follows: The polar fabric composite rotor was installed in a vertical high-speed rotor tester. The entire test system was placed in a high vacuum chamber with an ambient temperature of 25±5℃ and a working vacuum level of <10 Pa (to eliminate air resistance and frictional heat effects during high-speed rotation). The polar fabric composite rotor was subjected to rotational testing in a vacuum environment. The speed was gradually increased, with an acceleration of 2000 r / min, until the polar fabric composite rotor failed or experienced significant vibration instability. The experiment was then stopped to obtain the actual failure speed.

[0115] like Figure 7 As shown, the experimental results indicate that when the rotational speed is increased to 40,000 r / min, plastic deformation and microcracks first occur at the edge of the inner hole of the polar fabric composite rotor, resulting in extremely large vibrations during rotation. At this point, the polar fabric composite rotor basically reaches the failure state, and the actual failure speed is 40,000 r / min.

[0116] Due to uncontrollable manufacturing defects such as the random distribution of fibers inside the yarn, yarn extrusion deformation during weaving, and pores in the resin matrix, the failure speed prediction based on the finite element model of the polar fabric composite rotor has certain inherent errors. In this simulation, the actual failure speed and the simulated failure speed have good consistency, with a relative error of only 8.5%, and the overall prediction effect is good. In addition, the macroscopic failure location of the polar fabric composite rotor observed in the above experiment is completely consistent with the stress concentration failure location of the interlacing node of the inner hole extracted based on the finite element model of the polar fabric composite rotor. This proves that the finite element model of the polar fabric composite rotor completely reproduces the radial tensile mechanical response and failure trend of the polar fabric composite rotor in actual testing, and meets the accuracy requirements involved in complex composite material engineering.

[0117] In summary, the microscale modeling method for polar fabrics proposed in this invention requires only a small number of geometric parameters to quickly complete model construction. While balancing high modeling efficiency and versatility, the simulation calculation accuracy is good, demonstrating that this microscale modeling method for polar fabrics not only meets the requirements of complex composite material engineering design and accurately characterizes the spatial topological properties of polar fabrics, but also exhibits extremely high reliability in predicting composite material performance under complex dynamic loads. It can provide a high-confidence digital auxiliary means for component design optimization and possesses significant industrial transformation value.

[0118] The present invention has been described above by way of example. It should be noted that any simple modifications, alterations or other equivalent substitutions that can be made by those skilled in the art without creative effort without departing from the core of the present invention fall within the protection scope of the present invention.

Claims

1. A method for modeling a microscopic model of polar fabrics, characterized in that, Includes the following steps: S1. Assume a circular polar fabric. The polar fabric is woven from M circumferential yarns, 2*W radial yarns and W*2*(N-1) parallel weft yarns. Each circumferential yarn is circular. The M circumferential yarns are arranged in concentric circles. The circumferential yarns form a sine wave along their circumference. Each radial yarn is arranged along the radial direction of the polar fabric. The 2*W radial yarns are divided into W yarn groups. Each yarn group includes 2 parallel and adjacent radial yarns. W yarn groups are uniformly distributed on the polar fabric, and the part between any two adjacent yarn groups is a fan-shaped representative volume unit, and the included angle between any two adjacent yarn groups is S. Establish a cylindrical coordinate system, and take the center of the polar fabric as the origin of the cylindrical coordinate system. The polar angle range of a sector representative volume unit in the polar fabric is [0,S]. Divide the sector representative volume unit corresponding to the polar angle range [0,S] of the cylindrical coordinate system along its angle bisector to obtain two mirror-symmetric sector rings. Each sector ring is a sector sub-unit. Let the sector sub-unit with the polar angle in [0,S / 2] be the starting sub-unit. Establish a Cartesian coordinate system, with the center of the polar fabric as the origin of the Cartesian coordinate system, and the straight line with a polar angle of 0 in the cylindrical coordinate system as the X-axis of the Cartesian coordinate system. The Z-axis of the Cartesian coordinate system and the cylindrical coordinate system coincide and are in the same positive direction. The parallel yarns in the starting sub-unit are evenly distributed, and all the parallel yarns in the starting sub-unit are parallel to the X-axis of the Cartesian coordinate system. The radial yarns in the starting sub-unit are parallel to the X-axis. S2, construct the path equations for the centerlines of the M circumferential yarns. The path equation for the centerline of the m-th circumferential yarn along the direction from the inner arc edge of the starting sub-unit to the outer arc edge is as follows: in, Let m be the radius of the center line of the m-th circumferential yarn. , The inner diameter of the starting subunit. The distance between the center lines of adjacent circumferential yarns in the starting subunit. The polar angle in cylindrical coordinates; Let Z be the Z-axis coordinate of the centerline of the m-th circumferential yarn in the cylindrical coordinate system; To determine the vertical distance from the peak of the sine wave formed by the centerline of the circumferential yarn to the polar coordinate plane, one radial yarn and N-1 parallel weft yarns in the initial sub-unit are both considered as transverse yarns. The distance between the center lines of any two adjacent transverse yarns in the starting sub-unit; the center lines of the transverse yarns form a sine wave; S3, Construct the path equations for the centerlines of the N transverse yarns within the initial sub-unit. Following the direction of increasing Y-axis in the Cartesian coordinate system, the path equation for the centerline of the nth transverse yarn is as follows: Let n be the X-axis coordinate of the centerline of the nth transverse yarn in the Cartesian coordinate system. , Let Y be the Y-axis coordinate of the centerline of the nth transverse yarn in the Cartesian coordinate system. The outer diameter of the starting sub-unit; The number of transverse yarns interwoven with the m-th circumferential yarn : ;according to as well as Determine the starting point of each transverse yarn, where the starting point of the nth transverse yarn is connected to the circumferential yarn of the nth transverse yarn. The endpoints of all transverse yarns are connected to the Mth circumferential yarn; For the first The radius of the center line of the circumferential yarn; The center line of the nth transverse yarn is located at the x-axis coordinate of The Z-axis coordinate in the Cartesian coordinate system The vertical distance from the peak of the sine wave formed by the centerline of the transverse yarn to the xy-coordinate plane in the Cartesian coordinate system. Let n be the number of antinodes in the sine wave formed by the centerline of the nth transverse yarn; the X-axis coordinate of the centerline of the nth transverse yarn is... The point at time is located on the sine wave formed by the center line. One antinode segment; The center line of the nth transverse yarn The angular frequency corresponding to each antinode segment; S4, using the angle bisector of the representative sector volume unit as the axis of symmetry, mirrors the paths of the center lines of the M circumferential yarns corresponding to the starting sub-unit in S2 to generate the polar angle. The path of the center line of the M circumferential yarns corresponding to the sector subunit, and the combined polar angle. and polar angle The paths of the center lines of the M circumferential yarns corresponding to the two sector sub-units are obtained to obtain the paths of the center lines of the M circumferential yarns of the representative sector volume unit; Using the angle bisector of the representative volume element in the sector as the axis of symmetry, the paths of the center lines of the N transverse yarns corresponding to the initial sub-unit in S3 are mirrored to generate the polar angle. The paths of the center lines of the N transverse yarns corresponding to the sector-shaped subunit are merged into polar angles. and polar angle The paths of the center lines of the N transverse yarns corresponding to the two sector sub-units are obtained to obtain the paths of the center lines of the 2N transverse yarns of the representative volume unit of the sector. S5, make both the single transverse yarn cross section and the single circumferential yarn cross section elliptical, sweep the circumferential yarn cross section along the path of the center line of the circumferential yarn to generate the circumferential yarn solid, sweep the transverse yarn cross section along the path of the center line of the transverse yarn to generate the transverse yarn solid, and obtain a three-dimensional solid of a fan-shaped representative volume unit with a polar angle range of [0,S]. S6. Using the Z-axis of the cylindrical coordinate system where the three-dimensional entity of the sector-shaped representative volume unit is located as the rotation reference axis, the three-dimensional entity is arranged around the rotation reference axis in full circumference, and the three-dimensional entities of adjacent sector-shaped representative volume units are in contact to generate a microscale model of polar fabric.

2. The method for modeling a microscopic model of polar fabrics according to claim 1, characterized in that, ， 。 3. The method for modeling a microscopic model of polar fabrics according to claim 1, characterized in that, =0.2~0.4mm.

4. The method for modeling a microscopic model of polar fabrics according to claim 1, characterized in that, =0.2~0.4mm.

5. The method for modeling a microscopic model of polar fabrics according to claim 1, characterized in that, 。 6. The method for modeling a microscopic model of polar fabrics according to claim 1, characterized in that, , The center line of the nth transverse yarn The length of each antinode segment projected onto the xy coordinate plane.

7. The method for modeling a microscopic model of polar fabrics according to claim 6, characterized in that, when hour, , The center line of the nth transverse yarn Minimum X-axis coordinate of each antinode segment , For the first The radius of the center line of the circumferential yarn; The center line of the nth transverse yarn Minimum X-axis coordinate of each antinode segment , For the first The radius of the center line of the circumferential yarn; when hour, , The center line of the nth transverse yarn The minimum X-axis coordinate of each antinode segment.

8. A method for modeling a quasi-fiber-scale model of polar fabrics, characterized in that, include: Using transverse and circumferential yarns as yarns, K fiber monofilaments are constructed within each yarn in the microscale model of polar fabrics. The microscale model of polar fabrics is derived from the modeling method of the microscale model of polar fabrics described in any one of claims 1 to 7, and the construction method includes: Step 1: Take the radial yarn section and the circumferential yarn section as the yarn section respectively, define a single yarn as consisting of K fiber filaments, and let the cross section of each fiber filament be a circular cross section with a radius of R. Determine the coordinates of the center of the cross-section of the K fiber filaments in a single yarn: Set a set of center points, which includes the coordinates of the center of the cross-section of the K fiber filaments. Step 2: Using the assembly function of the modeling software, construct the K fiber monofilaments in each yarn based on the coordinates of the center of the cross-section of the K fiber monofilaments corresponding to the center point set.

9. The modeling method for quasi-fiber scale models of polar fabrics according to claim 8, characterized in that, In step 1, the method for obtaining the coordinates of the center of the cross-section of the fiber monofilament corresponding to the K fiber monofilaments in the center point set includes: Step 11, the method for obtaining the coordinates of the center of the cross-section of the first fiber filament in the center point set includes: establishing a local Cartesian coordinate system with the center point of the yarn cross-section as the origin. The x-axis of the local Cartesian coordinate system is parallel to the major axis of the ellipse formed by the yarn cross-section, and the y-axis of the local Cartesian coordinate system is parallel to the minor axis of the ellipse formed by the yarn cross-section. Using the Monte Carlo method, a center coordinate (x', y') that satisfies the first constraint condition in the local Cartesian coordinate system is randomly generated within the rectangular envelope region bounded by the yarn cross-section. The center coordinate (x', y') is then assigned to the center point set. The first constraint condition is as follows: Where, if the yarn is a transverse yarn, then a=a1, b=b1; if the yarn is a circular yarn, then a=a2, b=b2. Step 12, setting each integer from 2 to K to i, the method for obtaining the coordinates of the center of the cross-section of the i-th fiber monofilament in the center point set includes: using the Monte Carlo method to randomly generate a coordinate point that satisfies the second constraint condition in the local Cartesian coordinate system within a rectangular envelope region bounded by the yarn cross-section ( , If the coordinate point ( , If the distance between the coordinates of a point and the center of the cross-section of each fiber monofilament in the current center point set satisfies the following condition, then the coordinate point ( , (To be included in the set of center points) ； in, Coordinates ( , ) and the current center point set The Euclidean distance between the coordinates of the centers of the cross-sections of the corresponding fiber monofilaments; 1 to Given any integer, iterate through... , This represents the number of coordinates of the center of the cross-section of the fiber monofilament corresponding to the current center point set; Coordinates ( , The corresponding fiber monofilament cross-sectional radius; For the current center point set, the first The coordinates of the center of the cross-section of a single fiber filament correspond to the radius of the cross-section of that single fiber filament; and All in [R min ,R max Randomly selected from [ ]; Tol is the non-contact judgment tolerance between fiber monofilaments; The second constraint is as follows: Wherein, if the yarn is a transverse yarn, then a=a1, b=b1; if the yarn is a circular yarn, then a=a2, b=b2.

10. The modeling method for quasi-fiber scale models of polar fabrics according to claim 9, characterized in that, The R of each fiber monofilament is in R min ~R max The value is randomly selected from R, or a constant value R is set for R. H , where R min R is the minimum radius of the cross-section of a single fiber filament. max R is the maximum radius of the cross-section of a single fiber filament. min <R max .

Images