A trajectory line-based method for cutting and spreading of a laying material sheet

Abstract

The application discloses a kind of based on trajectory line's laying sheet cutting and unfolding method, including five steps of five steps of pre-processing, expansion processing, expansion error analysis, obtaining optimal solution, expansion graphic output, it is suitable for the cutting and unfolding of one-way prepreg laying sheet of non-developable surface workpiece.It is set as the target to obtain the least laying sheet number within the limit of prepreg deformation, the precision of expansion result is controlled by setting the limit deformation of prepreg and expansion error analysis, if the precision is lower, the initial expansion number of sheet can be adjusted to be unfolded again, the optimal solution is obtained using genetic algorithm, the laying efficiency is maximized on the premise of guaranteeing laying quality.The application uses laying trajectory line as "sheet center line", can maximize guarantee the continuity of fiber and the fiber angle requirement of laying, and prepreg is not forced in vertical fiber direction, so that deformation in expansion process all occurs in fiber direction, avoids defect in vertical fiber direction when laying.

Description

Technical Field

[0001] This invention belongs to the field of composite material laying and molding, specifically relating to a method for cutting and unfolding laying material sheets based on trajectory lines. Background Technology

[0002] Advanced resin-based composite materials possess excellent properties such as lightweight, high strength, high modulus, fatigue resistance, corrosion resistance, good designability, and processability, making them ideal aerospace structural materials. They are widely used in aerospace, automotive manufacturing, shipbuilding, wind power, and related fields. Currently, the application of automated tape and fiber layup in the aerospace field is relatively mature. However, due to component structure and cost considerations, many parts still require manual layup. For the layup process, the cutting and unfolding of the layup sheets remains a key factor affecting the quality of the molded parts.

[0003] Most current surface development methods are designed for isotropic materials, requiring the material to have the same deformation capacity in all directions during development. These methods are not suitable for composite materials. Research on the development of unidirectional prepregs for composite materials is limited. Carbon fiber unidirectional prepregs are typical anisotropic materials, exhibiting significant differences in mechanical properties along the fiber direction and perpendicular to the fiber direction. The direction perpendicular to the fiber cannot withstand tensile forces during layup; even small stretches can cause splitting or gap defects, affecting part quality. Furthermore, tensile deformation along the fiber direction is extremely limited.

[0004] Traditional methods for cutting and unfolding curved surfaces involve the lofting method, which is based on descriptive geometry and consists of two steps: lofting and unfolding. The first step is to draw the lofting diagram of the curved surface to a certain scale; the second step is to calculate the product blank drawing, i.e., the unfolded drawing, based on the lofting diagram and the experience of the workers. For unfolding non-developable curved surfaces, the commonly used method in engineering is to attach kraft paper to the surface of the three-dimensional product and then piece the kraft paper together to obtain a two-dimensional planar drawing. These two methods are not only inefficient and labor-intensive, but also produce low-precision two-dimensional planar drawings. The results largely depend on the worker's experience and skill level, and the unfolding accuracy is even lower for complex curved surfaces. Furthermore, problems exist such as mismatch between the fiber direction of the prepreg sheet and the cutting seam, interruption of continuous fiber load-bearing, and a large number of sheets of varying sizes. Currently, the design of digital fabric sheet cutting schemes in China relies on the imported software Fibersim. However, the cutting and unfolding schemes provided by Fibersim software disrupt fiber continuity, reducing the mechanical properties of the fibers and their composites. Moreover, the imported software is expensive, significantly increasing production costs. Summary of the Invention

[0005] To address the aforementioned problems, this invention discloses a method for cutting and unfolding paving sheets based on trajectory lines. This invention achieves digital cutting and unfolding design of paving sheets for non-developable curved surfaces, accurately unfolding paving sheets with different angles and performing error analysis. For unsatisfactory results, the cutting scheme can be readjusted, finding the unfolding scheme with the fewest unfolded sheets within the maximum allowable deformation of the paving sheet.

[0006] A method for cutting and unfolding paving sheets based on trajectory lines includes the following specific steps:

[0007] S1: Pre-development processing. Pre-development processing is the preparatory work for development. In this step, the surface to be developed is divided into surface pieces. This mainly includes generating the laying trajectory line, i.e., the "center line of the material piece", determining the initial number of material piece divisions n, and generating the material piece cutting edge line.

[0008] S2: Unfolding process. Based on the layup trajectory, the original surface is approximated by a ruled surface for unfolding. For any part, the layup trajectory line is a curve on the surface of the part. There must exist a developable surface along the trajectory line that is tangent to the surface of the part. This developable surface is used to replace the original surface for unfolding.

[0009] S3: Unfolding Error Analysis. This involves performing local deformation analysis and overall error analysis based on edge length and unfolded area on the unfolded results.

[0010] S4: Obtain the optimal solution. Set the unfolding objective to obtain the minimum number of paving sheets within the allowable deformation range of the prepreg to improve paving efficiency. Use a genetic algorithm to obtain the optimal solution.

[0011] S5: Expand the graphic output. Considering the file types the machine can recognize during material cutting, the expanded graphic will be output as a DXF or DWG file.

[0012] Furthermore, in step S1, the layup trajectory is used as the centerline of the surface sheet to be unfolded. The layup trajectory is generated using the fixed-angle method. The fixed-angle method lays the sheet at a fixed angle according to the layup direction requirements, ensuring that the planned trajectory perfectly matches the designed fiber angle. The characteristic of the fixed-angle method is that the trajectory always maintains a fixed angular relationship with the selected reference direction, allowing for precise control of the actual layup angle.

[0013] Furthermore, in step S1, the initial number of unfolded material sheets n is first determined, and then the workpiece surface is divided into n parts using trajectory lines. Then, a center line is generated between adjacent trajectory lines as the material sheet cutting edge line, and the workpiece surface is divided into surface sheets to be unfolded using the material sheet cutting edge line.

[0014] Furthermore, the ruled surface approximation unfolding method based on the laying trajectory in step S2 starts from one end of the "sheet centerline". Points are drawn at intervals of "unfolding point spacing" d. The normal plane of the "sheet centerline" is drawn through the point and intersects with the surface to be unfolded to obtain an intersection line. Adjacent intersection lines will divide the surface into a "small rectangle" to form a rectangular band. Unfolding this rectangular band, the "sheet centerline", i.e., the trajectory line, is unfolded into a straight line without deformation. The intersection line is perpendicular to the "sheet centerline". On the unfolded "sheet centerline", each intersection line is unfolded sequentially according to the original length of the surface of the intersection line. Finally, the endpoints on the left and right sides of the intersection line are connected with NURBS curves to obtain the unfolded plane.

[0015] Furthermore, the local deformation analysis in step S3 is to evaluate the accuracy of the curved surface sheet unfolded in step S2, ensuring the accuracy of the boundary position and preventing defects such as wrinkles, gaps, and overlaps when the planar sheet is laid onto the curved mold. Specifically, the local deformation analysis analyzes the deformation of the "small rectangles" into which the curved surface sheet is divided along the trajectory line. Deformation during the unfolding process occurs along the fiber direction, and the local deformation analysis focuses on the fiber direction. The difference between the length of the left and right sides of the "small rectangle" and the length of its centerline is the deformation value. The length of the centerline of the "small rectangle" is the unfolding point spacing d. Let the length of the left side of the "small rectangle" be l. Li The left side is l long Ri 'i' is the number of the 'small rectangle', and 'E' is the length deformation on the left. Li The calculation formula is: Right side deformation E Ri The calculation formula is:

[0016] Furthermore, the overall error analysis based on edge length and unfolded area in step S3 is to help users grasp the unfolding accuracy from a macroscopic perspective, thereby improving the algorithm efficiency of obtaining the optimal solution using the genetic algorithm in step S4, and helping users quickly find the optimal number of unfolded pieces. The overall error analysis includes overall error analysis based on edge length and unfolded area, with edge length error E... L This involves analyzing the changes in the cut edge before and after unfolding, and the calculation formula is as follows: L' is the length of the trimmed edge after unfolding, and L is the length of the trimmed edge of the surface before unfolding; area error E S This is used to measure the difference between the surface area before unfolding and the surface area after unfolding. The calculation formula is as follows: S' is the area of ​​the unfolded plane, and S is the area of ​​the unwound curved surface.

[0017] Furthermore, in step S4, the optimal solution is obtained by setting the objective as minimizing the number of prepreg sheets within the allowable deformation range of the prepreg, and using a genetic algorithm to obtain the optimal solution. The specific algorithm steps are as follows:

[0018] Step 1: First, set the initial number of unfolded sheets n according to the curvature of the workpiece surface.

[0019] Step 2: Perform pre-processing on the surface of the part to generate a laying trajectory line as the center line of the material sheet. Generate a center line between adjacent trajectory lines as the cutting edge line of the material sheet to divide the surface into surface pieces to be unfolded.

[0020] Step 3: The surface patch to be unfolded is unfolded and deformed using the ruled surface approximation optimization unfolding method based on the laying trajectory line of the present invention.

[0021] Step 4: Determine the overall error E L and E S Does it exceed the deformation limit ε? max If the deformation limit ε is exceeded max If the number of unfolded sheets becomes n+1, then return to Step 2; if the deformation limit ε is not exceeded. max Then proceed to step 5 of the program.

[0022] Step 5: Determine the local deformation amount E Li and E Ri Is it greater than the deformation limit ε? max If it is greater than the deformation limit ε max If the number of unfolded sheets becomes n+1, then return to Step 2; if it is less than the deformation limit ε max Then execute program Step 6.

[0023] Step 6: Determine whether the local deformation is greater than 0.9 times the deformation limit ε. max If yes, output the unfolded result; otherwise, the number of unfolded pieces becomes n-1, and return to Step 2. Note that if the result after this loop exceeds the deformation limit ε, the output will be lost. max If so, then the previous expansion result will be output.

[0024] The beneficial effects of this invention are as follows:

[0025] 1. This invention uses the trajectory line as the center line of the unfolded material sheet. This method takes into account the characteristics of the unidirectional prepreg of the raw material and can maximize the continuity of the fiber and the laying angle requirements.

[0026] 2. The unfolding method proposed in this invention unfolds the prepreg along its original length in the direction perpendicular to the fiber, ensuring that the prepreg is not subjected to force in the direction perpendicular to the fiber. This ensures that the deformation during the unfolding process occurs in the fiber direction, avoiding splitting or gap defects in the direction perpendicular to the fiber during laying, which would affect the quality of the parts.

[0027] 3. This invention takes into account the relationship between unfolding accuracy and laying efficiency after unfolding. The unfolding target is set to obtain the minimum number of laying sheets within the allowable deformation range of the prepreg, which can maximize laying efficiency while ensuring laying quality.

[0028] 4. The prepreg deformation limit ε of the present invention max The unfolding method of the present invention can be set by the user, so it has good adaptability to different prepregs. Attached Figure Description

[0029] Figure 1 This is a schematic diagram of generating the wire-laying trajectory using the fixed-angle method;

[0030] Figure 2 This is a schematic diagram showing the division of the ruled surfaces of the paving sheet for the component;

[0031] Figure 3 It is a unfolded diagram of the lining sheet for the component;

[0032] Figure 4 This is a schematic diagram of localized deformation analysis;

[0033] Figure 5 This is the flowchart of the algorithm for obtaining the optimal solution. Detailed Implementation

[0034] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. It should be noted that the terms "front," "rear," "left," "right," "up," and "down" used in the following description refer to directions in the accompanying drawings, and the terms "inner" and "outer" refer to directions toward or away from the geometric center of a specific component, respectively.

[0035] Taking an elliptical rotating component, such as an aircraft auxiliary fuel tank, as an example, the process for cutting and unfolding the paving material is as follows:

[0036] S1: Pre-processing for expansion.

[0037] S1-1: First, generate a fixed-angle laying trajectory in the plane, such as... Figure 1 As shown, P is a point on the surface. A plane Σ, the osculating plane of the surface, is drawn through P. n is the normal vector of point P, m is a vector in the reference direction outside the plane, t is the projection of m onto plane Σ, l is the direction vector of the trajectory, the angle between l and m is a fixed angle α, the angle between t and m is β, and the angle between t and l within plane Σ is θ. From spatial geometric relations, we know that cosα = cosβ × cosθ. The fixed angle α is known, therefore: After obtaining the direction of the trajectory, a straight line with a spacing of d between trajectory points is projected onto the surface along the direction vector l of the trajectory to obtain the next paving trajectory point. This process is repeated until all trajectory points are obtained. Finally, NURBS curves are used to fit all trajectory points to obtain the complete paving trajectory line.

[0038] S1-2: Determine the initial number of sheet divisions n based on the curvature of the aircraft auxiliary fuel tank and the fiber direction, and generate n trajectory lines. Use the trajectory lines to divide the surface of the workpiece into n parts.

[0039] S1-3: Generate the material cutting edge line. Generate a center line between adjacent trajectory lines as the material cutting edge line. Starting from the endpoints of two adjacent trajectory lines, connect the two endpoints on the curved surface to form a curve and obtain the midpoint of the curve. Take two more points on the two trajectory lines at a 10mm interval, connect the two points to form a curve, and obtain the midpoint of the curve. Repeat this process until the other endpoint of the trajectory line. Then, fit these midpoints with a NURBS curve to obtain the material cutting edge line.

[0040] S2: Unfolding the surface patch. For the elliptical rotating part of an aircraft auxiliary fuel tank, the laying trajectory is a curve on the part's surface. Along the trajectory, there must exist a developable surface tangent to the part's surface. This developable surface replaces the original surface for unfolding.

[0041] like Figure 2 As shown, starting from one end of the trajectory line, a normal plane is drawn through endpoint P1. This normal plane intersects the surface patch to be unfolded, resulting in curve Γ1. Let the distance between unfolding points be d. A second unfolding point P2 is drawn on the trajectory line at a distance d from endpoint P1. A normal plane is drawn through point P2, and this normal plane intersects the surface patch to be unfolded, resulting in curve Γ2. This process is repeated until the other endpoint of the trajectory line, resulting in points P3, P4, ..., P... n And curves Γ3, Γ4...Γ n The surface patch to be unfolded is formed by curves Γ1, Γ2...Γ n Divide into n-1 small "rectangles" to form a rectangular strip.

[0042] The surface to be unfolded is divided into rectangular strips, which are then unfolded using ruled surfaces. This paper uses cylindrical surfaces to approximate the surface to be unfolded, such as... Figure 3 As shown, first unfold the trajectory line without distortion into a straight line, and then find the corresponding unfolded points P1', P2'...P on the unfolded trajectory line. n ', due to curves Γ1, Γ2……Γ n At points P1, P2...P on the trajectory line n On the normal plane, therefore, after expansion, curves Γ1, Γ2...Γ are formed. n Still perpendicular to the trajectory line, curves Γ1, Γ2...Γ nare unfolded without length deformation along the curved surface into curves Γ1′, Γ2′……Γ n ′, finally, the endpoints on the same side of the curves Γ1′, Γ2′……Γ n ′ are connected with NURBS curves to obtain the trimming edge of the blank, and the bridging surface is used to obtain the developed plane.

[0043] S3: Development error analysis.

[0044] The deformation during the development process all occurs in the fiber direction, so the analysis of development error and deformation is also focused on the fiber direction. As Figure 4 shown, deformation analysis is performed on each small "rectangle" divided in section 3.3.1, the endpoints of the curves Γ1, Γ2……Γ n are M1N1, M2N2……M n N n , the midpoints are P1, P2……P n , the developed point spacing d is the length of the curve P1P2. If the curve P1M1 < P2M2, a line segment P2M equal in length to P1M1 is drawn on the curve P2M2 11 , connect M1M 11 ; if P1M1 > P2M2, a line segment P1M equal in length to P2M2 is drawn on the curve P1M1 11 , connect M2M 11 . At this time, M1M 11 or M2M 11 is the side length of the left side of the small "rectangle" M1N1N2M2, which has a difference from the developed point spacing d, and this difference is the deformation after development. Let M1M 11 (or M2M 11 ) be l L1 , then the deformation E on the left side of the small "rectangle" M1N1N2M2 L1 is: Similarly, the deformation E on the right side of the small "rectangle" M1N1N2M2 R1 is analyzed in the same way. By analogy, until the last small "rectangle" M n-1 N n-1 N n M n is completely analyzed. After development, the left and right side lengths of the small "rectangle" are both the developed point spacing d. If the deformation is a positive number, it indicates that the fibers in this region will be stretched after development; if the deformation is a negative number, it indicates that the fibers in this region will be compressed, and wrinkles may occur in this region.

[0045] The area error is used to measure the difference between the surface area before development and the plane area after development. The edge length error is to analyze the change of the trimming edge before and after development. The calculation formulas of the area error and the edge length error are as follows:

[0046]

[0047]

[0048] Among them, E S For area error, S' is the area of ​​the unfolded plane, S is the area of ​​the surface before unfolding, and E is the area of ​​the surface before unfolding. L L' represents the edge length error, L' represents the length of the trimmed edge after unfolding, and L represents the length of the trimmed edge of the surface before unfolding.

[0049] S4: Obtain the optimal solution.

[0050] The objective is to minimize the number of prepreg sheets within the allowable deformation range of the prepreg to improve laying efficiency. A genetic algorithm is used to obtain the optimal solution. The algorithm flow is as follows: Figure 5 As shown.

[0051] Step 1: First, based on the curvature of the aircraft's auxiliary fuel tank surface, set the initial number of unfolded material sheets n.

[0052] Step 2: Perform pre-processing on the curved surface of the aircraft auxiliary fuel tank to generate a laying trajectory line as the center line of the material sheet. Generate a center line between adjacent trajectory lines as the cutting edge line of the material sheet to divide the curved surface into curved surface sheets to be unfolded.

[0053] Step 3: Use the ruled surface approximation optimization unfolding method based on the laid trajectory line to unfold and deform the surface patch to be unfolded.

[0054] Step 4: Determine the overall error E L and E S Does it exceed the deformation limit ε? max If the deformation limit ε is exceeded max If the number of unfolded sheets becomes n+1, then return to Step 2; if the deformation limit ε is not exceeded. max If so, proceed to step 5 of the procedure.

[0055] Step 5: Determine the local deformation amount E Li and E Ri Is it greater than the deformation limit ε? max If it is greater than the deformation limit ε max If the number of unfolded sheets becomes n+1, then return to Step 2; if it is less than the deformation limit ε max If so, proceed to Step 6 of the program.

[0056] Step 6: Determine whether the local deformation is greater than 0.9 times the deformation limit ε. maxIf yes, output the unfolded result; otherwise, the number of unfolded pieces becomes n-1, and return to Step 2. Note that if the result after this loop exceeds the deformation limit ε, the output will be lost. max If so, then the previous expansion result will be output.

[0057] S5: Expand and output the graphic. Output the expanded graphic as a DXF or DWG file.

[0058] The technical means disclosed in this invention are not limited to those disclosed in the above embodiments, but also include technical solutions composed of any combination of the above technical features.

Claims

1. A method for cutting and unfolding paving sheets based on trajectory lines, characterized in that: The specific steps include the following: S1: Pre-development processing; Pre-development processing is the preparation work for development. In this step, the surface to be developed is divided into surface patches, including generating the laying trajectory line, i.e. "patch center line", determining the initial number of patch divisions n, and generating the patch cutting edge line. S2: Unfolding process; Based on the layup trajectory, the ruled surface is used to approximate the original surface patch for unfolding. For any part, the layup trajectory line is a curve on the surface of the part. Along this trajectory line, there must exist a developable surface that is tangent to the surface of the part. The developable surface is used to replace the original surface for unfolding. S3: Unfolding error analysis; Perform local deformation analysis and overall error analysis based on edge length and unfolded area on the unfolded results; S4: Obtain the optimal solution; the unfolding objective is to obtain the minimum number of paving sheets within the allowable deformation range of the prepreg to improve the paving efficiency. A genetic algorithm is used to obtain the optimal solution. The specific algorithm steps for S4: Obtaining the optimal solution are as follows: Step 1: First, set the initial number of unfolded sheets n according to the curvature of the workpiece surface; Step 2: Perform pre-processing on the surface of the part to generate a laying trajectory line as the center line of the material sheet. Generate a center line between adjacent trajectory lines as the cutting edge line of the material sheet to divide the surface into surface pieces to be unfolded. Step 3: Use the ruled surface approximation optimization unfolding method based on the laid trajectory line to unfold and deform the surface patch to be unfolded; Step 4: Determine the error in edge length and area error Does it exceed the deformation limit? If the deformation limit is exceeded If the number of unfolded sheets becomes n+1, then return to Step 2; if the deformation limit is not exceeded. Then execute program Step 5; Step 5: Determine the amount of local deformation and Is it greater than the deformation limit? If it exceeds the deformation limit If the number of unfolded sheets becomes n+1, then return to Step 2; if it is less than the deformation limit Then execute program Step 6; Step 6: Determine whether the local deformation exceeds 0.9 times the deformation limit. If yes, output the unfolded result; otherwise, the number of unfolded pieces becomes n-1, and return to Step 2. Note that if the result after this loop exceeds the deformation limit... Then output the result of the previous expansion. S5: Expand graphic output; taking into account the file types that the machine can recognize during material cutting, output the expanded graphic as a DXF or DWG file.

2. The method for cutting and unfolding paving sheets based on trajectory lines according to claim 1, characterized in that: S1: Pre-processing before unfolding. The laying trajectory line is used as the center line of the surface to be unfolded, i.e., the "sheet center line". The laying trajectory line is generated using the fixed angle method. The fixed angle method lays the surface at a fixed angle according to the laying direction requirements. The planned trajectory can fully meet the designed fiber angle. The fixed angle method ensures that the trajectory line always maintains a fixed angle relationship with the selected reference direction, and accurately controls the actual laying angle.

3. The method for cutting and unfolding paving sheets based on trajectory lines according to claim 1, characterized in that: S1: Pre-processing before unfolding. First, determine the initial number of unfolded material pieces n. Then, use trajectory lines to divide the workpiece surface into n parts. Then, generate a center line between adjacent trajectory lines as the material piece cutting edge line. Use the material piece cutting edge line to divide the workpiece surface into surface pieces to be unfolded.

4. The method for cutting and unfolding paving sheets based on trajectory lines according to claim 1, characterized in that: S2: Unfolding process. Based on the laying trajectory, the ruled surface is used to approximate the original curved surface for unfolding. Starting from one end of the "sheet centerline", points are made at intervals of "unfolding point spacing" d. The normal plane of the "sheet centerline" is drawn through the point and intersects with the surface to be unfolded to obtain an intersection line. Adjacent intersection lines will divide the surface into a "small rectangle", forming a rectangular band. Unfold this rectangular band and unfold the "sheet centerline", i.e., the trajectory line, into a straight line without deformation. The intersection line is perpendicular to the "sheet centerline". On the unfolded "sheet centerline", each intersection line is unfolded sequentially according to the original length of the surface of the intersection line. Finally, the endpoints on the left and right sides of the intersection line are connected with NURBS curves to obtain the unfolded plane.

5. The method for cutting and unfolding paving sheets based on trajectory lines according to claim 1, characterized in that: S3: Unfolding Error Analysis. This analysis includes both local deformation analysis and overall error analysis based on edge length and unfolded area. Prepreg Deformation Limits. Input by the user.

6. The method for cutting and unfolding paving sheets based on trajectory lines according to claim 5, characterized in that: Local deformation analysis involves analyzing the deformation of a surface patch divided into "small rectangles" along its trajectory. Deformation during the unfolding process occurs along the fiber direction, and the local deformation analysis focuses on this fiber direction. The difference between the length of the left and right sides of the "small rectangle" and the length of its midline is the deformation value. The length of the midline of the "small rectangle" is the spacing d between the unfolded points. Let the length of the left side of the "small rectangle" be... The left side is [length] 'i' is the number of the "small rectangle", and the length deformation on the left is... The calculation formula is The deformation on the right side The calculation formula is .

7. The method for cutting and unfolding paving sheets based on trajectory lines according to claim 1, characterized in that: The overall error analysis of S3 includes edge length error analysis and unfolded area error analysis. Edge length error... This involves analyzing the changes in the cut edge before and after unfolding, and the calculation formula is as follows: L' is the length of the trimmed edge after unfolding, and L is the length of the trimmed edge of the surface before unfolding; area error This is used to measure the difference between the surface area before unfolding and the surface area after unfolding. The calculation formula is as follows: S' is the area of ​​the unfolded plane, and S is the area of ​​the unwound curved surface.

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