A method and system for modeling a solid rocket motor case

Abstract

The application discloses a solid rocket engine shell modeling method and system, and relates to the technical field of solid rocket engines. The method comprises the following steps: obtaining the coordinates of the thickness growth starting points of the H+1th winding layer according to the coordinates of the thickness growth starting points of the Hth winding layer, the normal line slope of the curve between two adjacent thickness growth starting points, and the thickness of the Hth winding layer; obtaining the contour curve by adopting B-spline curve fitting; repeating the steps until H reaches a preset value; for the contour curve of any winding layer within the conversion radius, a straight line Y=k*X+(y0-k*x0) with a slope of tanθ is used to replace the contour curve of the winding layer; and constructing a solid rocket engine shell model according to the contour curves and the straight lines. The application can accurately and quickly establish a solid rocket engine shell model.

Description

Technical Field

[0001] This invention relates to the field of solid rocket motor technology, and in particular to a method and system for modeling solid rocket motor casings. Background Technology

[0002] Carbon fiber reinforced resin matrix composites (CFRPs) are widely used in aerospace, energy, and automotive fields due to their high specific modulus and high specific strength. Composite fiber-wound pressure vessels, as a crucial energy storage device, are widely used in solid rockets, aircraft, marine vessels, and automobiles. Using fiber winding technology as the molding process for composite pressure vessels has enabled the shell to meet the requirements of lightweight design and high internal pressure, achieving both large-scale construction and low cost.

[0003] Currently, the main design methods for solid rocket motor casing winding layups are mesh theory and the finite element method (FEM). Accurate modeling of the designed layup method is a prerequisite for the accuracy of finite element analysis results. Due to the varying angles and thicknesses of the winding layers in the pressure vessel head section, pressure vessel modeling is difficult and complex, and there is no good method to achieve both accurate and rapid model creation. For simulation engineers, such modeling processes are extremely time-consuming, especially for special model structures requiring iterative calculations, which can significantly hinder product design and development progress and prolong product update cycles.

[0004] Based on the constructed solid rocket motor shell model, burst pressure analysis and damage analysis can be performed to study the damage and failure modes of the shell. Most existing shell simulation analyses employ manual modeling methods for solid rocket motor shells. This method is not only time-consuming but also produces models with very low accuracy, showing significant dimensional discrepancies with the actual wound shell products. The paper "Rapid Modeling Method and Verification Analysis of Solid Rocket Motor Composite Shells Based on ABAQUS" proposes a rapid modeling method for solid rocket motor composite shells based on ABAQUS. This method relies on external winding software to generate winding data files, then reads these files to find thickness growth points, and models the solid rocket motor shell in ABAQUS (ABAQUS simulation software). The model accuracy depends on the modeling accuracy of the external winding software and cannot accurately predict the winding layer thickness near the polar holes. The solid rocket motor shell model established by this method has a large error in winding layer thickness compared to reality, fails to consider actual process conditions, and has low model accuracy.

[0005] In summary, given the current problems of long modeling time and low accuracy in solid rocket motor casings, it is particularly important to develop a method for accurately and quickly building solid rocket motor casing models. Summary of the Invention

[0006] The purpose of this invention is to provide a method and system for modeling solid rocket motor casings, which can accurately and quickly establish solid rocket motor casing models.

[0007] To achieve the above objectives, the present invention provides the following solution:

[0008] A method for modeling a solid rocket motor casing, the method comprising:

[0009] Step S1: Obtain the coordinates of the starting points of the growth of each thickness of the H-th winding layer in the end cap segment; where H is a positive integer and the initial value of H is 1;

[0010] Step S2: For any two adjacent thickness growth start points of the Hth winding layer of the end cap segment, obtain the normal slope of the curve between the two adjacent thickness growth start points based on the coordinates of the two adjacent thickness growth start points.

[0011] Step S3: Based on the coordinates of the growth start points of each thickness of the Hth winding layer in the end cap segment, the slope of the normal line between two adjacent growth start points of the Hth winding layer in the end cap segment, and the thickness of the Hth winding layer in the end cap segment, obtain the coordinates of the growth start points of each thickness of the (H+1)th winding layer in the end cap segment; wherein, the (H+1)th winding layer covers the Hth winding layer; the number of growth start points of the (H+1)th winding layer is the same as the number of growth start points of the Hth winding layer; the thickness of the Hth winding layer in the end cap segment is obtained using a cubic spline thickness prediction method.

[0012] Step S4: Fit the coordinates of the growth start points of each thickness of the H+1 winding layer of the end cap segment using a B-spline curve to obtain the contour curve of the H+1 winding layer of the end cap segment.

[0013] Step S5: Determine if H is less than a preset value; if yes, set H = H + 1 and return to step S1; if no, obtain the conversion radius and conversion angle; the conversion radius is the radius of the parallel circle at the position of the polar hole h times the bandwidth; where h is a positive integer greater than or equal to 2.

[0014] Step S6: For any winding layer profile curve within the conversion radius, replace the winding layer profile curve with a straight line with a slope of tanθ; the equation of the straight line with a slope of tanθ is Y = k*X + (y0 - k*x0); where (x0, y0) are the coordinates of the thickness growth start point on the winding layer profile curve at the conversion radius, θ is the conversion angle, k is the slope, k = tanθ, Y represents the dependent variable, and X represents the independent variable;

[0015] Step S7: Construct a solid rocket motor casing model based on the contour curves of each winding layer of the end cap section and the straight lines with a slope of tanθ within the conversion radius.

[0016] Optionally, the step of obtaining the coordinates of the starting points for the growth of each thickness of the Hth winding layer of the end cap segment further includes:

[0017] Obtain the core model created in the ABAQUS simulation software;

[0018] Obtain the contour curve selected along the outer contour of the core mold model;

[0019] Based on the contour curve selected along the outer contour of the core mold model, the coordinates of the starting points for the growth of each thickness of the first winding layer of the end cap segment are obtained.

[0020] Optionally, obtaining the normal slope of the curve between the growth start points of two adjacent thicknesses of the H-th winding layer of the end cap segment based on the coordinates of the growth start points of two adjacent thicknesses specifically includes:

[0021] Using the formula k2=-(y i+1 -y i ) / (x i+1 -x i ) Calculate the normal slope of the curve between the growth start points of two adjacent thicknesses of the H-th winding layer in the end cap segment; where k2 is the normal slope of the curve between the growth start points of two adjacent thicknesses of the H-th winding layer in the end cap segment, (x i y i (x) represents the coordinates of the starting point of the growth of the Hth winding layer thickness in the end cap segment. i+1 y i+1 ) represents the coordinates of the thickness growth start point adjacent to the thickness growth start point of the Hth winding layer of the end cap segment.

[0022] Optionally, obtaining the coordinates of the growth start points of each thickness of the (H+1)th winding layer of the end cap segment based on the coordinates of the growth start points of each thickness of the Hth winding layer of the end cap segment, the slope of the normal line of the curve between two adjacent growth start points of the Hth winding layer of the end cap segment, and the thickness of the Hth winding layer of the end cap segment specifically includes:

[0023] When k2 is positive, use the formula X = x i +t*sin(arctan(k2)) and Y=y i +t*cos(arctan(k2)) calculates the coordinates of the starting point of the growth of the H+1th winding layer thickness of the end cap segment;

[0024] When k2 is negative, use the formula X = x i -t*sin(arctan(k2)) and Y=y i-t*cos(arctan(k2)) calculates the coordinates of the starting point of the growth of the H+1th winding layer thickness of the end cap segment; where t is the thickness of the Hth winding layer of the end cap segment, and (X, Y) are the coordinates of the starting point of the growth of the H+1th winding layer thickness of the end cap segment.

[0025] Optionally, the method further includes:

[0026] The end cap section is reinforced by winding or carbon cloth reinforcement.

[0027] The present invention also provides the following solutions:

[0028] A solid rocket motor casing modeling system, the system comprising:

[0029] The thickness growth start point coordinate acquisition module is used to acquire the coordinates of the thickness growth start points of each H-th winding layer of the end cap segment; where H is a positive integer and the initial value of H is 1;

[0030] The module for obtaining the normal slope of the curve between thickness growth start points is used to obtain the normal slope of the curve between any two adjacent thickness growth start points of the Hth winding layer of the end cap segment, based on the coordinates of the two adjacent thickness growth start points.

[0031] The module for obtaining the coordinates of the starting point of the next winding layer thickness growth is used to obtain the coordinates of the starting points of the thickness growth of each of the Hth winding layers in the end cap segment based on the coordinates of the starting points of each thickness growth of the Hth winding layer in the end cap segment, the slope of the normal line between two adjacent starting points of the thickness growth of the Hth winding layer in the end cap segment, and the thickness of the Hth winding layer in the end cap segment; wherein, the H+1th winding layer covers the Hth winding layer; the number of starting points of the thickness growth of the H+1th winding layer is the same as the number of starting points of the thickness growth of the Hth winding layer; the thickness of the Hth winding layer in the end cap segment is obtained using a cubic spline thickness prediction method.

[0032] The B-spline curve fitting module is used to fit the coordinates of the growth start points of each thickness of the H+1 winding layer of the end cap segment using B-spline curves to obtain the contour curve of the H+1 winding layer of the end cap segment.

[0033] The judgment module is used to determine whether H is less than a preset value; if yes, then set H = H + 1 and return the coordinate acquisition module of the thickness growth starting point; if no, then acquire the conversion radius and conversion angle; the conversion radius is the radius of the parallel circle at the position of the polar hole h times the bandwidth; where h is a positive integer greater than or equal to 2;

[0034] The straight line replacement module is used to replace the contour curve of any winding layer within the conversion radius with a straight line with a slope of tanθ; the equation of the straight line with a slope of tanθ is Y=k*X+(y0-k*x0); where (x0, y0) are the coordinates of the thickness growth start point on the contour curve of the winding layer at the conversion radius, θ is the conversion angle, k is the slope, k=tanθ, Y represents the dependent variable, and X represents the independent variable;

[0035] The solid rocket motor casing model construction module is used to construct a solid rocket motor casing model based on the contour curves of each winding layer of the end cap section and the straight lines with a slope of tanθ within the conversion radius.

[0036] Optionally, the system further includes:

[0037] The core model acquisition module is used to acquire the core model created in the ABAQUS simulation software.

[0038] The core mold model outer contour curve acquisition module is used to acquire the contour curve selected along the outer contour of the core mold model;

[0039] The module for obtaining the coordinates of the starting point of the first winding layer thickness growth is used to obtain the coordinates of the starting points of each thickness growth of the first winding layer of the end cap segment based on the contour curve selected along the outer contour of the mandrel model.

[0040] Optionally, the module for obtaining the normal slope of the curve between the thickness growth initiation points specifically includes:

[0041] The unit for calculating the slope of the normal curve between the thickness growth initiation points is used to apply the formula k2=-(y i+1 -y i ) / (x i+1 -x i ) Calculate the normal slope of the curve between the growth start points of two adjacent thicknesses of the H-th winding layer in the end cap segment; where k2 is the normal slope of the curve between the growth start points of two adjacent thicknesses of the H-th winding layer in the end cap segment, (x i y i (x) represents the coordinates of the starting point of the growth of the Hth winding layer thickness in the end cap segment. i+1 y i+1 ) represents the coordinates of the thickness growth start point adjacent to the thickness growth start point of the Hth winding layer of the end cap segment.

[0042] Optionally, the module for obtaining the coordinates of the starting point of the next winding layer thickness growth specifically includes:

[0043] k2 is the coordinate calculation unit for the starting point of the next winding layer thickness growth when k2 is positive. It is used when k2 is positive, using the formula X = x i+t*sin(arctan(k2)) and Y=y i +t*cos(arctan(k2)) calculates the coordinates of the starting point of the growth of the H+1th winding layer thickness of the end cap segment;

[0044] When k2 is negative, this is the coordinate calculation unit for the starting point of the next winding layer thickness growth. It is used when k2 is negative, using the formula X = x i -t*sin(arctan(k2)) and Y=y i -t*cos(arctan(k2)) calculates the coordinates of the starting point of the growth of the H+1th winding layer thickness of the end cap segment; where t is the thickness of the Hth winding layer of the end cap segment, and (X, Y) are the coordinates of the starting point of the growth of the H+1th winding layer thickness of the end cap segment.

[0045] Optionally, the system further includes:

[0046] The head section reinforcement module is used to reinforce the head section by winding or carbon cloth.

[0047] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0048] The solid rocket motor casing modeling method and system disclosed in this invention eliminates the need to read winding data generated by external winding software to obtain the coordinates of the thickness growth start points of each winding layer. Considering actual process conditions, it sequentially calculates the coordinates of the thickness growth start points of each winding layer based on the outer contour of the mandrel model in ABAQUS, enabling rapid modeling. This avoids the problem of large discrepancies between the winding layer thickness and the actual thickness, resulting in low model accuracy, caused by reading winding data generated by external winding software. Furthermore, by using a radius transformation method—that is, replacing the contour curve of any winding layer within the transformation radius with a straight line Y = k*X + (y0 - k*x0) with a slope of tanθ—the actual winding layer thickness near the end cap section's pole hole is accurately predicted. This avoids the problem that cubic spline thickness prediction formulas cannot accurately predict the actual winding layer thickness near the pole hole. Therefore, it can accurately and quickly establish a solid rocket motor casing model, solving the problems of long modeling time and low accuracy in current solid rocket motor casing modeling methods. Attached Figure Description

[0049] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0050] Figure 1 Flowchart of Example 1 of the method for modeling solid rocket motor casing;

[0051] Figure 2 This is a flowchart illustrating the principle of the parametric rapid modeling method based on shell head reinforcement design of the present invention.

[0052] Figure 3 A schematic diagram of fibers wound around a composite material shell end cap;

[0053] Figure 4 This is a schematic diagram of the conversion radius and conversion angle;

[0054] Figure 5 This is a schematic diagram illustrating the increase in the thickness of the winding layer in the end cap section;

[0055] Figure 6 This is a preview of the sketch.

[0056] Figure 7 This is a schematic diagram of the principle of a B-spline smooth curve.

[0057] Figure 8 This is a schematic diagram of the spline vertex control principle.

[0058] Figure 9 A rendering of the shell model head section created by the rapid modeling system of this invention;

[0059] Figure 10 This is a detailed view of the head section of the shell model of the present invention;

[0060] Figure 11 This is a GUI interface diagram of the rapid modeling system of the present invention. Detailed Implementation

[0061] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0062] The purpose of this invention is to provide a method and system for modeling solid rocket motor casings, which can accurately and quickly establish solid rocket motor casing models.

[0063] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0064] Example 1

[0065] Figure 1This is a flowchart of an embodiment of the solid rocket motor casing modeling method of the present invention. Figure 1 As shown, this embodiment provides a method for modeling a solid rocket motor casing, including the following steps:

[0066] Step S1: Obtain the coordinates of the starting points of the growth of each thickness of the H-th winding layer of the end cap segment; where H is a positive integer and the initial value of H is 1.

[0067] The process preceding step S1 also includes:

[0068] Obtain the core model created in the ABAQUS simulation software.

[0069] Obtain the contour curve selected along the outer contour of the core mold model.

[0070] Based on the contour curve selected along the outer contour of the mandrel model, the coordinates of the starting points for the growth of each thickness of the first winding layer of the end cap section are obtained.

[0071] Step S2: For any two adjacent thickness growth start points of the H-th winding layer of the end cap segment, obtain the normal slope of the curve between the two adjacent thickness growth start points based on the coordinates of the two adjacent thickness growth start points.

[0072] Step S2 specifically includes:

[0073] Using the formula k2=-(y i+1 -y i ) / (x i+1 -x i ) Calculate the normal slope of the curve between the growth start points of two adjacent thicknesses of the H-th winding layer in the end cap segment; where k2 is the normal slope of the curve between the growth start points of two adjacent thicknesses of the H-th winding layer in the end cap segment, (x i y i (x) represents the coordinates of the starting point of the growth of the Hth winding layer thickness in the end cap segment. i+1 y i+1 ) represents the coordinates of the thickness growth start point adjacent to the thickness growth start point of the Hth winding layer of the end cap segment.

[0074] Step S3: Based on the coordinates of the growth start points of each thickness of the Hth winding layer in the end cap segment, the slope of the normal line between two adjacent growth start points of the Hth winding layer in the end cap segment, and the thickness of the Hth winding layer in the end cap segment, obtain the coordinates of the growth start points of each thickness of the (H+1)th winding layer in the end cap segment; wherein, the (H+1)th winding layer covers the Hth winding layer; the number of growth start points of the (H+1)th winding layer is the same as the number of growth start points of the Hth winding layer; the thickness of the Hth winding layer in the end cap segment is obtained using the cubic spline thickness prediction method.

[0075] Step S3 specifically includes:

[0076] When k2 is positive, use the formula X = x i +t*sin(arctan(k2)) and Y=y i The formula +t*cos(arctan(k2)) calculates the coordinates of the starting point of the growth of the H+1th winding layer thickness of the end cap segment; where t is the thickness of the Hth winding layer of the end cap segment, and (X, Y) are the coordinates of the starting point of the growth of the H+1th winding layer thickness of the end cap segment.

[0077] When k2 is negative, use the formula X = x i -t*sin(arctan(k2)) and Y=y i -t*cos(arctan(k2)) calculates the coordinates of the starting point of the growth of the H+1th winding layer thickness of the end cap segment; where t is the thickness of the Hth winding layer of the end cap segment, and (X, Y) are the coordinates of the starting point of the growth of the H+1th winding layer thickness of the end cap segment.

[0078] Step S4: Fit the coordinates of the starting points of the growth of each thickness of the H+1 winding layer of the end cap segment using a B-spline curve to obtain the contour curve of the H+1 winding layer of the end cap segment.

[0079] Step S5: Determine if H is less than the preset value; if yes, let H = H + 1 and return to step S1; if no, obtain the conversion radius and conversion angle; the conversion radius is the radius of the parallel circle at the position of the polar hole h times the bandwidth; where h is a positive integer greater than or equal to 2.

[0080] Step S6: For any winding layer profile curve within the conversion radius, replace the winding layer profile curve with a straight line with a slope of tanθ; the equation of the straight line with a slope of tanθ is Y=k*X+(y0-k*x0); where (x0, y0) are the coordinates of the thickness growth start point on the winding layer profile curve at the conversion radius, θ is the conversion angle, k is the slope, k=tanθ, Y represents the dependent variable, and X represents the independent variable.

[0081] Step S7: Construct a solid rocket motor casing model based on the contour curves of each winding layer of the head section and the straight lines with a slope of tanθ within the conversion radius.

[0082] This solid rocket motor casing modeling method also includes:

[0083] The end cap section is reinforced by winding or carbon cloth reinforcement.

[0084] The technical solution of the present invention is illustrated below with a specific embodiment:

[0085] The solid rocket motor casing modeling method of this invention is a rapid modeling method for solid rocket motor casings based on secondary development of Abaqus (ABAQUS). Figure 2 This is a schematic diagram of the rapid modeling method for solid rocket motor casing based on Abaqus secondary development according to the present invention, as shown below. Figure 2 As shown, the rapid modeling method for solid rocket motor casing based on Abaqus secondary development of this invention mainly includes the following steps:

[0086] Step 1: Create a mandrel model in ABAQUS (ABAQUS simulation software), and select a contour curve along the outer contour of the mandrel (mandrel model) as the mandrel feature set. Based on the mandrel feature set, the coordinates of the growth start points of each thickness of the first winding layer of the end cap segment can be obtained.

[0087] Step 2: Calculate the thickness t of the fiber winding layer in the end cap section of each layer (spiral winding layer) in the layup scheme. The thickness of the fiber winding layer within two bandwidths (twice the bandwidth) of the end cap section is predicted using a cubic spline thickness prediction formula. The principle formula is as follows:

[0088] When fibers are wound around the composite shell end cap, such as Figure 3 As shown, the yarn is wound from the bobbin section to the pole hole, tangent to the pole hole circle, forming a complete winding layer. From yarn tape A to yarn tape B, the thickness of all the yarns within this range on the end cap is superimposed, with severe thickness accumulation at a wide bandwidth position of the pole hole.

[0089] Considering that the fiber volume in the cylinder section is equal to the fiber volume at the pole hole, a cubic spline function is used to predict the fiber thickness of the fiber-wound composite shell end cap. The expression for the cubic spline function in the range [r0, R] is given as follows:

[0090] t(r i )=m1×r i 0 +m2×r i 1 +m3×r i 2 +m4×r i 3

[0091] Where R is the radius of the shell cylinder; t(r i ) represents the thickness of the winding layer in the end cap section; r i Let r be the radius of the parallel circle at the winding position, i.e., the radius of the parallel circle corresponding to the i-th thickness growth point on the end cap. i 0 r i 1 r i 2 r i 3 In this context, 0, 1, 2, and 3 are exponents; a cubic spline function is a cubic equation in one variable; m i(i = 1, 2, 3, 4) are coefficients, obtained according to the following conditions: (1) The number of yarns at the pole hole position is equal to the number of yarns in the bobbin section; (2) The thickness at the two bandwidths satisfies the constraint condition, that is, the thickness value at the two bandwidths is equal to the cubic spline function value; (3) The end cap thickness curve is continuous at two bandwidths from the pole hole; (4) The fiber volume V within the two bandwidths is... consat Keeping the values ​​unchanged, the results are as follows:

[0092]

[0093]

[0094]

[0095] Among them, r0, r b r 2b These represent the radius of the polar aperture, the radius of the parallel circle at one bandwidth, and the radius of the parallel circle at two bandwidths, respectively. R The number of single layers of spiral winding for the cylinder section, m R n is the number of yarn pieces in the bobbin section, n0 is the number of single layers wound at the pole hole, m0 is the number of yarn pieces at the pole hole, and t is the number of yarn pieces in the bobbin section. R t represents the thickness of the spiral wound layer in the cylinder section (the thickness of the wound layer in the cylinder section). p Let α0 be the thickness of a single layer of the spiral winding layer, b be the width of the winding yarn, and r represent the integral over r.

[0096] At locations outside the two bandwidths, based on the continuous winding of the fibers, it can be determined that the total amount of fibers at each parallel circle of the end cap is the same as the total amount of fibers wound around the cylinder. From this, the thickness formula at each parallel circle can be derived:

[0097]

[0098] Where r and the above r i They are the same variable; n R m is the number of spiral winding layers in the cylinder section. R n is the number of yarn pieces passing through the equatorial circle; n0 is the number of layers wound at the pole hole; m0 is the number of yarn pieces at the pole hole; w is the yarn width; t p This refers to the thickness of a single layer of the yarn (the thickness of a single layer of the spiral winding layer).

[0099] If the thickness within two bandwidths differs significantly from the actual process conditions due to manufacturing factors, a conversion radius R can be introduced. f Within the conversion radius, users can define the winding layer termination method by adjusting the winding layer elevation angle θ (i.e., conversion angle θ). The fiber termination method can be defined according to the actual process conditions. Specific implementation methods are as follows:

[0100] The contour curve of the winding layer within the conversion radius is replaced by a straight line with the slope of:

[0101] k = tanθ

[0102] The equation of the line is:

[0103] Y = k*X + (y0 - k*x0)

[0104] Where x0 and y0 are the radii (transformation radii) of the parallel circle R. f The coordinates of the thickness growth point (thickness growth start point) on the corresponding winding layer contour are shown below. A schematic diagram of the transformation radius and transformation angle is shown in the figure. Figure 4 As shown.

[0105] The cubic spline thickness prediction formula is well known in the art, and this invention uses this formula to predict the thickness of the end cap section. Generally speaking, the cubic spline thickness prediction formula cannot accurately predict the actual thickness (winding layer thickness) near the polar hole. Since existing end cap thickness prediction methods, such as the cubic spline thickness prediction method, cannot accurately predict the winding layer thickness near the polar hole, this invention adds a new polar hole thickness processing method, namely, using the conversion radius to predict the end cap section thickness.

[0106] Since most existing formulas for predicting the thickness of the winding layer in the shell end section are difficult to accurately predict, this invention proposes the concept of a conversion radius. Within the conversion radius, users can define the winding layer termination method by adjusting the elevation angle (winding layer elevation angle), so that the fiber thickness near the pole hole is closer to the actual process conditions. Users can adjust the thickness of the winding layer near the shell pole hole based on their own work experience, which can more closely resemble the actual shell product.

[0107] Step 2 is a cyclical step. All spiral windings in the layup scheme need to go through Step 2, where the thickness of the end section of each spiral winding layer in the layup scheme is calculated.

[0108] Step 3: Draw the outer contour curve of the layup based on the calculated thickness t of the end cap section winding layer in Step 2. Using the outer contour curve of the mandrel, employ the ABAQUS secondary development Python language to obtain the coordinates and curvature of the thickness growth start points (generally more than 60) of the end cap section winding layer thickness growth on the mandrel's outer contour curve (the purpose is to be able to draw the outer contour curve of the next fiber winding layer on the mandrel's outer contour). Increase the winding layer thickness in the direction perpendicular to the thickness growth start point curve, such as... Figure 5 As shown, the formula for increasing thickness is as follows:

[0109] k2=-(y i+1 -y i ) / (x i+1 -xi )

[0110] Where k2 is the normal slope of the curve (the slope of the normal line between the growth start points of two adjacent thicknesses of the winding layer), (x i+1 ,y i+1 ), (x i ,y i ) represents the coordinates of the starting point for adjacent thickness growth.

[0111] When k2 is positive, the coordinates of the starting point for the growth of the next winding layer thickness are obtained as follows:

[0112] X = x i +t*sin(arctan(k2))

[0113] Y = y i +t*cos(arctan(k2))

[0114] Where t is the thickness of the winding layer.

[0115] When k2 is negative, the coordinates of the starting point for the growth of the next winding layer thickness are obtained as follows:

[0116] X = x i -t*sin(arctan(k2))

[0117] Y = y i -t*cos(arctan(k2))

[0118] The starting point of the next layer thickness growth is fitted using a B-spline curve to obtain the outer contour of the next winding layer. The drawing method for subsequent winding layers is similar, resulting in... Figure 6 The sketch shown, Figure 6 The image shows a preview of the sketch when the angle is 0 degrees (i.e., a 0-degree straight line).

[0119] The equation of the B-spline curve is:

[0120]

[0121] Among them, c i (i = 0, 1, ..., n) are the control vertices, N i,k (u)(i=0,1,...,n) is a k-degree normalized B-spline basis function, with the highest degree being k. The basis function is expressed as follows:

[0122]

[0123] Where, N i,k In (u), the subscript i represents the sequence number, and the subscript k represents the order. For example, to determine the i-th k-th B-spline N... i,k(u), we need to find u i u i+1 ,…,u i+k+1 Here, [u] i ,u i+k+1 Defined as N i,k The support interval of (u). The coordinates of the corresponding u-value on the B-spline curve can be calculated using the above formula.

[0124] The principle of B-spline smooth curves is as follows: Figure 7 As shown, Figure 7 The principle of B-spline data processing is illustrated.

[0125] k-th order B-spline N i,k (u) is a B-spline of degree k-1 N i,k-1 (u) and N i+1,k-1 (u) Calculate the desired result recursively, and then proceed recursively in sequence. The coefficients of the basis function combination are respectively and The denominators of these two coefficients are the k-1 degree B-spline N. i,k The length of the support interval (u) is the parameter u, which represents the length of the support interval of the i-th k-th B-spline [u]. i ,u i+k+1 The length of the two parts.

[0126] When two nodes are at the same position, the combination coefficients in the recursive formula may have both numerator and denominator of 0 in a special case. In this case, the coefficients can be set to 0.

[0127] The curve (i.e.) Figure 8 The curve in the interval [u] i ,u i+k+1 A point p(u) in the equation is formed by k+1 vertices c. j (j = ik, i - k + 1, ..., i) and the basis functions determine the vertex, which is independent of other vertices, such as Figure 8 As shown. Moving the i-th control vertex will at most affect the interval (u i ,u i+k+1 The B-spline function has an impact on local curves on the B-spline, but it does not affect B-spline curves in other intervals. Therefore, the higher the order, the smoother the data points fitted by the B-spline function, but the greater the computational cost of the recursive function.

[0128] The i-th k-th B-spline N i,k The support interval of (u) is [u i ,u i+k+1 The order k of the B-spline is related to the left endpoint u of the support interval. i The subscript is irrelevant and is related to the right endpoint u of the support interval. i+k+1This indicates that the number of node intervals in the support interval is related to the order k, and the k-th degree B-spline curve contains k+1 node intervals. Therefore, at any point u on the parameter u-axis, there are at most k+1 non-zero k-th degree B-spline N. j,k (u), where j is (ik, i-k+1, ..., i), and all other k-order B-splines in this interval are 0. By the definition of a B-spline, a B-spline curve exhibits locality; a point on a k-order B-spline curve within its domain is connected to at most k+1 vertices c. j It is relevant but does not affect other vertices.

[0129] The B-spline curve equation is well known in the art. This invention uses the B-spline curve equation for fitting to obtain the contour curve of the winding layer of the end cap segment. The formulas and the meanings of the parameters mentioned in the above introduction of the B-spline curve are all well known in the art, and therefore will not be repeated.

[0130] Step 3 is a cyclical step, outlining the outer contour curve of each layer in the layup scheme.

[0131] Step 4: Based on the requirements for the shell explosion location, it is generally required that the shell explodes within the cylinder. However, due to the shell's own structure and other reasons, the strength at the end cap is usually relatively weak, requiring end cap reinforcement. Depending on the actual reinforcement process, two rapid modeling reinforcement methods are needed: winding reinforcement and carbon fiber reinforcement. Users need to choose one of the two reinforcement methods based on the actual process. When winding reinforcement is selected, the thickness of the reinforcement layer is calculated using the thickness prediction formula in Step 2. When carbon fiber reinforcement is used, the thickness of the reinforcement layer is uniformly distributed in the end cap section, and the thickness value of the carbon fiber reinforcement layer is a given parameter; this thickness does not need to be calculated by the user. The winding contour drawing method for both reinforcement methods is the same as in Step 3 (after obtaining the reinforcement thickness, the drawing method in Step 3 is used to reinforce the end cap).

[0132] Step 4, head reinforcement, refers to the addition of layers when the strength of the shell head section is insufficient. The specific order needs to be determined according to the process conditions, and it is generally added between two helical winding layers. The solid rocket motor shell modeling method of this invention is a parametric rapid modeling method based on shell head reinforcement design. It utilizes the secondary development function of ABAQUS to achieve rapid modeling of the solid rocket motor shell, and uses B-spline fitting to fit the outer contour curve of the winding layer, making the outer contour of the winding layer closer to the actual process conditions, and enabling precise reinforcement of the head according to actual needs. The principle flowchart of the parametric rapid modeling method based on shell head reinforcement design of this invention is as follows: Figure 2 As shown.

[0133] Step 5: Divide the head portion of each layer of the winding model into more than 60 parts. After the division is completed, write code to assign material properties to each part.

[0134] After the single-layer winding layer modeling is completed, step 5, the cutting, is performed.

[0135] Step 6: If the winding method described in the layup scheme has been modeled, proceed to Step 7; if the winding method described in the layup scheme has not been modeled, continue from Step 2.

[0136] Step 7: Assemble each of the constructed winding layers to update the outer contour of the shell. Using Python, an ABAQUS rapid modeling script is written to model the outer contour of the mandrel sequentially according to the layup sequence given in the layup scheme (steps 1 to 5 are the modeling process for a single winding layer; step 7 assembles each of the constructed winding layers to update the outer contour of the shell and obtain the final shell model). This updates the model's contour, and B-spline curves are used to smooth surfaces with uneven thickness, resulting in the final shell model (solid rocket motor shell model). The effect diagram of the head section of the shell model established by the rapid modeling system of this invention is shown below. Figure 9 As shown, the details of the head section of the shell model are displayed as follows. Figure 10 As shown. After the final shell model is built, a GUI visualization interface is developed to create parameter interfaces for the modeling scripts, such as... Figure 11 As shown. Figure 11 In the above, the number of end cap slices corresponds to the number of thickness growth points mentioned above; the end cap conversion angle corresponds to the elevation angle of the winding layer within the aforementioned conversion radius; and the winding layer modeling parameters correspond to the layup scheme.

[0137] The shell model constructed by this invention can be used for burst pressure analysis and damage analysis to study the damage and failure modes of the shell.

[0138] To address the various problems existing in the current modeling process of solid rocket motor shells (including manual modeling and modeling by reading data from external winding software), this invention utilizes the secondary development capabilities of Abaqus to achieve rapid modeling of solid rocket motor shells, significantly reducing the preprocessing steps for simulation analysis and possessing important engineering practical significance for the design of composite pressure vessels. This invention also develops modeling methods for various winding patterns, enabling accurate modeling even for complex shells. The solid rocket motor shell modeling method of this invention can rapidly model according to user-designed layup schemes, achieving modeling of various fiber winding layup schemes, such as helical winding, circumferential winding, head reinforcement, enlarged hole winding, non-geodesic helical winding, and non-geodesic enlarged hole winding, without relying on external winding software to generate winding data, thus reducing dependence on external winding software. Existing technologies rely on external winding software to generate winding data, which is then read into Abaqus for modeling. Since the model accuracy depends on the modeling accuracy of the external winding software, it cannot accurately predict the winding layer thickness near the polar holes. This invention does not read external data files to find thickness growth points; instead, it obtains these points based on the outer contour of the mandrel model in Abaqus. Compared to existing technologies that rely on data from external winding software, resulting in significant errors in winding layer thickness, this invention considers actual process conditions, improving model accuracy and solving the problems of long modeling time and low accuracy in solid rocket motor casings. This significantly reduces research time costs and has important reference value for aerospace engine design and development.

[0139] Example 2

[0140] In order to implement the method corresponding to Embodiment 1 above and achieve the corresponding functions and technical effects, a solid rocket motor casing modeling system is provided below, which includes the following modules:

[0141] The core model acquisition module is used to acquire the core model created in the ABAQUS simulation software.

[0142] The core mold model outer contour curve acquisition module is used to acquire the contour curve selected along the outer contour of the core mold model.

[0143] The module for obtaining the coordinates of the starting point of the first winding layer thickness growth is used to obtain the coordinates of the starting points of each thickness growth of the first winding layer in the end cap segment based on the contour curve selected along the outer contour of the mandrel model.

[0144] The thickness growth start point coordinate acquisition module is used to acquire the coordinates of the thickness growth start points of each H-th winding layer of the end cap segment; where H is a positive integer and the initial value of H is 1.

[0145] The module for obtaining the normal slope of the curve between thickness growth start points is used to obtain the normal slope of the curve between any two adjacent thickness growth start points of the H-th winding layer of the end cap segment, based on the coordinates of the two adjacent thickness growth start points.

[0146] The module for obtaining the coordinates of the starting point of the next winding layer thickness growth is used to obtain the coordinates of the starting points of the thickness growth of each of the Hth winding layers in the end cap segment based on the coordinates of the starting points of each thickness growth of the Hth winding layer in the end cap segment, the slope of the normal of the curve between two adjacent starting points of the thickness growth of the Hth winding layer in the end cap segment, and the thickness of the Hth winding layer in the end cap segment; wherein, the H+1th winding layer covers the Hth winding layer; the number of starting points of the thickness growth of the H+1th winding layer is the same as the number of starting points of the thickness growth of the Hth winding layer; the thickness of the Hth winding layer in the end cap segment is obtained by using the cubic spline thickness prediction method.

[0147] The B-spline curve fitting module is used to fit the coordinates of the growth start points of each thickness of the H+1 winding layer of the end cap segment using B-spline curves to obtain the contour curve of the H+1 winding layer of the end cap segment.

[0148] The judgment module is used to determine whether H is less than a preset value; if yes, it sets H = H + 1 and returns the coordinate acquisition module of the thickness growth starting point; if no, it acquires the conversion radius and conversion angle; the conversion radius is the radius of the parallel circle at the position of the polar hole h times the bandwidth; where h is a positive integer greater than or equal to 2.

[0149] The straight line replacement module is used to replace the contour curve of any winding layer within the conversion radius with a straight line with a slope of tanθ. The equation of the straight line with a slope of tanθ is Y=k*X+(y0-k*x0); where (x0, y0) are the coordinates of the thickness growth start point on the contour curve of the winding layer at the conversion radius, θ is the conversion angle, k is the slope, k=tanθ, Y represents the dependent variable, and X represents the independent variable.

[0150] The solid rocket motor casing model construction module is used to construct a solid rocket motor casing model based on the contour curves of each winding layer of the end cap section and the straight lines with a slope of tanθ within the conversion radius.

[0151] Specifically, the module for obtaining the normal slope of the curve between the thickness growth initiation points includes:

[0152] The unit for calculating the slope of the normal curve between the thickness growth initiation points is used to apply the formula k2=-(y i+1 -y i ) / (x i+1 -x i) Calculate the normal slope of the curve between the growth start points of two adjacent thicknesses of the H-th winding layer in the end cap segment; where k2 is the normal slope of the curve between the growth start points of two adjacent thicknesses of the H-th winding layer in the end cap segment, (x i y i (x) represents the coordinates of the starting point of the growth of the Hth winding layer thickness in the end cap segment. i+1 y i+1 ) represents the coordinates of the thickness growth start point adjacent to the thickness growth start point of the Hth winding layer of the end cap segment.

[0153] The module for obtaining the coordinates of the starting point of the next winding layer thickness growth specifically includes:

[0154] k2 is the coordinate calculation unit for the starting point of the next winding layer thickness growth when k2 is positive. It is used when k2 is positive, using the formula X = x i +t*sin(arctan(k2)) and Y=y i The formula +t*cos(arctan(k2)) calculates the coordinates of the starting point of the growth of the H+1th winding layer thickness of the end cap segment; where t is the thickness of the Hth winding layer of the end cap segment, and (X, Y) are the coordinates of the starting point of the growth of the H+1th winding layer thickness of the end cap segment.

[0155] When k2 is negative, this is the coordinate calculation unit for the starting point of the next winding layer thickness growth. It is used when k2 is negative, using the formula X = x i -t*sin(arctan(k2)) and Y=y i -t*cos(arctan(k2)) calculates the coordinates of the starting point of the growth of the H+1th winding layer thickness of the end cap segment; where t is the thickness of the Hth winding layer of the end cap segment, and (X, Y) are the coordinates of the starting point of the growth of the H+1th winding layer thickness of the end cap segment.

[0156] The solid rocket motor casing modeling system also includes:

[0157] The head section reinforcement module is used to reinforce the head section by winding or carbon cloth.

[0158] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant parts can be referred to the method section.

[0159] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A method for modeling the casing of a solid rocket motor, characterized in that, The method includes: Step S1: Obtain the coordinates of the starting points of the growth of each thickness of the H-th winding layer in the end cap segment; where H is a positive integer and the initial value of H is 1; Step S2: For any two adjacent thickness growth start points of the Hth winding layer of the end cap segment, obtain the normal slope of the curve between the two adjacent thickness growth start points based on the coordinates of the two adjacent thickness growth start points. Step S3: Based on the coordinates of the growth start points of each thickness of the Hth winding layer in the end cap segment, the slope of the normal line between two adjacent growth start points of the Hth winding layer in the end cap segment, and the thickness of the Hth winding layer in the end cap segment, obtain the coordinates of the growth start points of each thickness of the (H+1)th winding layer in the end cap segment; wherein, the (H+1)th winding layer covers the Hth winding layer; the number of growth start points of the (H+1)th winding layer is the same as the number of growth start points of the Hth winding layer; the thickness of the Hth winding layer in the end cap segment is obtained using a cubic spline thickness prediction method. Step S4: Fit the coordinates of the growth start points of each thickness of the H+1 winding layer of the end cap segment using a B-spline curve to obtain the contour curve of the H+1 winding layer of the end cap segment. Step S5: Determine if H is less than a preset value; if yes, set H = H + 1 and return to step S1; if no, obtain the conversion radius and conversion angle; the conversion radius is the radius of the parallel circle at the position of the polar hole h times the bandwidth; where h is a positive integer greater than or equal to 2; the conversion angle is the elevation angle of the winding layer within the conversion radius; Step S6: For the contour curve of any winding layer within the conversion radius, use a slope of A straight line replaces the contour curve of the winding layer; the slope is... The equation of the straight line is Y=k X+ Where (x0, y0) are the coordinates of the thickness growth start point on the contour curve of the winding layer at the transformation radius. For the conversion angle, The slope Y represents the dependent variable, and X represents the independent variable; Step S7: Based on the contour curves of each winding layer of the end cap segment and the slopes within the conversion radius, Use straight lines to construct a solid rocket motor casing model; Before obtaining the coordinates of the starting points for the growth of each thickness of the Hth winding layer of the end cap segment, the following steps are also included: Obtain the core model created in the ABAQUS simulation software; Obtain the contour curve selected along the outer contour of the core mold model; Based on the contour curve selected along the outer contour of the core mold model, the coordinates of the starting points for the growth of each thickness of the first winding layer of the end cap segment are obtained.

2. The solid rocket motor casing modeling method according to claim 1, characterized in that, The step of obtaining the normal slope of the curve between the two adjacent thickness growth start points of the H-th winding layer of the end cap segment based on the coordinates of the two adjacent thickness growth start points specifically includes: Using formula Calculate the slope of the normal curve between the growth start points of two adjacent thicknesses of the H-th winding layer in the end cap segment; where, Let be the slope of the normal curve between the growth start points of two adjacent thicknesses of the H-th winding layer in the end cap segment. , ) represents the coordinates of the starting point of the growth of the Hth winding layer thickness in the end cap segment. , ) represents the coordinates of the thickness growth start point adjacent to the thickness growth start point of the Hth winding layer of the end cap segment.

3. The solid rocket motor casing modeling method according to claim 2, characterized in that, The method of obtaining the coordinates of the growth start points of each thickness of the H+1 winding layer of the end cap segment based on the coordinates of the growth start points of each thickness of the Hth winding layer of the end cap segment, the slope of the normal line of the curve between two adjacent growth start points of the Hth winding layer of the end cap segment, and the thickness of the Hth winding layer of the end cap segment specifically includes: When k2 is positive, use the formula and Calculate the coordinates of the starting point for the growth of the H+1th winding layer thickness in the end cap segment; When k2 is negative, use the formula and Calculate the coordinates of the starting point for the growth of the H+1th winding layer thickness in the end cap segment; where, The thickness of the Hth winding layer in the end cap section is ( , () represents the coordinates of the starting point of the growth of the H+1th winding layer thickness in the end cap segment.

4. The solid rocket motor casing modeling method according to claim 1, characterized in that, The method further includes: The end cap section is reinforced by winding or carbon cloth reinforcement.

5. A solid rocket motor casing modeling system, characterized in that, The system includes: The thickness growth start point coordinate acquisition module is used to acquire the coordinates of the thickness growth start points of each H-th winding layer of the end cap segment; where H is a positive integer and the initial value of H is 1; The module for obtaining the normal slope of the curve between thickness growth start points is used to obtain the normal slope of the curve between any two adjacent thickness growth start points of the Hth winding layer of the end cap segment, based on the coordinates of the two adjacent thickness growth start points. The module for obtaining the coordinates of the starting point of the next winding layer thickness growth is used to obtain the coordinates of the starting points of the thickness growth of each of the Hth winding layers in the end cap segment based on the coordinates of the starting points of each thickness growth of the Hth winding layer in the end cap segment, the slope of the normal line between two adjacent starting points of the thickness growth of the Hth winding layer in the end cap segment, and the thickness of the Hth winding layer in the end cap segment; wherein, the H+1th winding layer covers the Hth winding layer; the number of starting points of the thickness growth of the H+1th winding layer is the same as the number of starting points of the thickness growth of the Hth winding layer; the thickness of the Hth winding layer in the end cap segment is obtained using a cubic spline thickness prediction method. The B-spline curve fitting module is used to fit the coordinates of the growth start points of each thickness of the H+1 winding layer of the end cap segment using B-spline curves to obtain the contour curve of the H+1 winding layer of the end cap segment. The judgment module is used to determine whether H is less than a preset value; if yes, then set H=H+1 and return the coordinate acquisition module of the thickness growth starting point; if no, then acquire the conversion radius and conversion angle; the conversion radius is the radius of the parallel circle at the position of the polar hole h times the bandwidth; where h is a positive integer greater than or equal to 2; the conversion angle is the elevation angle of the winding layer within the conversion radius; The straight line replacement module is used to apply a slope of [value missing] to the contour curve of any winding layer within the conversion radius. A straight line replaces the contour curve of the winding layer; the slope is... The equation of the straight line is Y=k X+ Where (x0, y0) are the coordinates of the thickness growth start point on the contour curve of the winding layer at the transformation radius. For the conversion angle, The slope Y represents the dependent variable, and X represents the independent variable; The solid rocket motor casing model construction module is used to construct models based on the contour curves of each winding layer of the end cap section and the slopes within the transformation radius. Use straight lines to construct a solid rocket motor casing model; The system also includes: The core model acquisition module is used to acquire the core model created in the ABAQUS simulation software. The core mold model outer contour curve acquisition module is used to acquire the contour curve selected along the outer contour of the core mold model; The module for obtaining the coordinates of the starting point of the first winding layer thickness growth is used to obtain the coordinates of the starting points of each thickness growth of the first winding layer of the end cap segment based on the contour curve selected along the outer contour of the mandrel model.

6. The solid rocket motor casing modeling system according to claim 5, characterized in that, The module for obtaining the normal slope of the curve between the thickness growth initiation points specifically includes: The unit for calculating the normal slope of the curve between the thickness growth initiation points is used to apply the formula. Calculate the slope of the normal curve between the growth start points of two adjacent thicknesses of the H-th winding layer in the end cap segment; where, Let be the slope of the normal curve between the growth start points of two adjacent thicknesses of the H-th winding layer in the end cap segment. , ) represents the coordinates of the starting point of the growth of the Hth winding layer thickness in the end cap segment. , ) represents the coordinates of the thickness growth start point adjacent to the thickness growth start point of the Hth winding layer of the end cap segment.

7. The solid rocket motor casing modeling system according to claim 6, characterized in that, The module for obtaining the coordinates of the starting point for the next winding layer thickness growth specifically includes: When k2 is a positive number, it is the coordinate calculation unit for the starting point of the next winding layer thickness growth. This unit is used when k2 is positive, utilizing the formula... and Calculate the coordinates of the starting point for the growth of the H+1th winding layer thickness in the end cap segment; The coordinate calculation unit for the starting point of the next winding layer thickness growth when k2 is negative is used to calculate the coordinates when k2 is negative, using the formula... and Calculate the coordinates of the starting point for the growth of the H+1th winding layer thickness in the end cap segment; where, The thickness of the Hth winding layer in the end cap section is ( , () represents the coordinates of the starting point of the growth of the H+1th winding layer thickness in the end cap segment.

8. The solid rocket motor casing modeling system according to claim 5, characterized in that, The system also includes: The head section reinforcement module is used to reinforce the head section by winding or carbon cloth.

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