A densification method for fiber curve placement path with unsteady offset vector

Abstract

The present invention belongs to the technical field of fiber curve laying path densification, and proposes a non-steady offset vector fiber curve laying path densification method, including: first, pre-processing the model of the fiber reinforced composite material core mold; then, taking the reference path of the fiber curve laying on the core mold surface as a reference, fully considering the relationship between the core mold boundary and the reference path, establishing a non-steady offset vector fiber curve laying path densification algorithm, through which the key nodes selected on the reference path are offset in different directions and step sizes to obtain the key nodes of the offset path, and using the curve fitting method to obtain a continuous fiber curve laying path, generating a global full laying path of the core mold. The present invention is suitable for the path densification of any open surface core mold, and has important theoretical significance and practical value for realizing the actual engineering application of fiber reinforced composite materials.

Description

Technical Field

[0001] The present invention relates to the technical field of fiber curve placement path densification, and in particular to a method for densifying a fiber curve placement path with a non-steady offset vector. Background Art

[0002] The fiber placement equipment for fiber-reinforced composite materials usually uses multiple fiber bundles to be laid simultaneously. In engineering practice, it is only necessary to plan the center path of the actual laying, and use the fiber curve laying reference path on the surface of the mandrel as a reference to perform path densification on the surface of the mandrel. However, the traditional parallel or translational path densification methods are essentially to use fixed-step offset or fixed-direction offset to obtain an offset path, thereby achieving full path laying. However, the densified paths obtained by such methods have defects such as fiber overlap, gaps, or excessive curvature changes. In addition, because the traditional method does not consider the laying boundary of the mandrel surface, the offset path exceeds or does not reach the mandrel boundary, and a fully covered full-laying path cannot be obtained, and the path densification problem of the curved mandrel is not further explored.

[0003] Therefore, there is an urgent need for a fiber curve placement path densification method that is efficient, adaptable, and can achieve uniform spacing distribution and sufficient coverage, so as to provide a full-laying path distribution solution for the actual engineering manufacturing of fiber-reinforced composites. Summary of the invention

[0004] The purpose of the present invention is to provide a method for densifying the path of non-steady offset vector fiber curve placement, which can solve the technical problems of small application range, uneven distribution of densified path spacing and insufficient coverage of traditional path densification methods.

[0005] The present invention solves the technical problem and adopts the following technical solution:

[0006] A method for densifying a fiber curve placement path with an unsteady offset vector comprises the following steps:

[0007] S1. Preprocessing the fiber reinforced composite material core mold;

[0008] S2. Establish an algorithm for densifying the fiber curve placement path with an unsteady offset vector. Through this algorithm, the key nodes selected on the reference path are offset in different directions and step sizes to obtain the key nodes of the offset path. The curve fitting method is then used to obtain a continuous fiber curve placement path to generate a global full-placement path for the core mold.

[0009] As a further optimization, the model preprocessing of the fiber reinforced composite material core mold includes the following steps:

[0010] S101, establishing a three-dimensional model in finite element software ABAQUS, dividing the quadrilateral unit grid, and extracting unit node information and core mold boundary node information through the INP file;

[0011] S102. Reconstruct the core model surface in MATLAB, and use linear interpolation to obtain a set of interpolation points of the boundary curve.

[0012] As a further optimization, the fiber curve placement path densification algorithm using the unsteady offset vector offsets the key nodes selected on the reference path in different directions and step sizes to obtain the key nodes of the offset path, and uses a curve fitting method to obtain a continuous fiber curve placement path to generate a full placement path for the core mold, including the following steps:

[0013] S201, setting the parallel spacing h of the microelement curve segments between the two paths, the number of offset paths s and the number of key nodes n, and performing path densification on the core mold on one side of the reference path;

[0014] S202, according to the number of key nodes n, obtain the key node set Q of the reference path S by taking points at equal distances;

[0015] S203, according to the relationship between the reference path and the core model boundary, solve each key node Q i (i=1,2,…,n) offset vector;

[0016] S204, offset the key nodes on the reference path on the core mold surface according to the offset vector to obtain the offset path S k The key node set

[0017] S205, determine the kth bias path S k Whether the two end points reach the core mold boundary, if they reach the boundary, no processing is performed, if they do not reach the boundary, the path extension method is used to process and obtain a new bias path S k The key node set is obtained by fitting the key nodes using the curve fitting method to generate a continuous bias path S k ;

[0018] S206, using the bias path S k To solve the next bias path for reference, the bias path S k As the new reference path S, update the number of key nodes n;

[0019] S207 , judging whether the path densification termination condition is met, if k>s is not met, repeating S202 to S207 , otherwise terminating the path densification.

[0020] As a further optimization, the offset vector described in step S203 is divided into a plane offset vector and a curved surface offset vector according to the type of the core mold surface.

[0021] As a further optimization, the direction of the plane offset vector is solved as follows:

[0022] Solve the unit direction vector XL of the tangent line of the core mold boundary at the first and last points of the reference path s and XL d , and use it as the offset unit direction vector of the first and last points;

[0023] Calculate the offset unit direction vector XL of the first and last points of the reference path s and XL d Angle

[0024] Determine the offset vector angle of adjacent nodes on the reference path

[0025] As a further optimization, the process of solving the modulus length of the plane offset vector is as follows:

[0026] Calculate the tangent vectors of the key nodes of the reference path with the offset unit direction vector XL i Angle

[0027]

[0028] Determine the offset vectors of key nodes on the fiber reference path Length of mold

[0029] As a further optimization, the direction of the surface offset vector is solved as follows:

[0030] Based on the surface boundary information, the unit direction vector L of the tangent line at the first and last points of the reference path is solved s and L d , and use it as the offset unit direction vector of the first and last points;

[0031] The offset unit direction vector L s and L d Project onto the reference plane and solve for the offset projection unit direction vector and

[0032] Project the unit direction vector according to the bias and Solve the angle between adjacent projection direction vectors in, θ is the bias projection unit direction vector and The angle between

[0033] Projection point of the key node of the reference path in the reference plane is the starting point of the projection unit direction vector, and determines the projection unit direction vector of each point Inversely calculate the offset unit direction vector L of the key node of the reference path on the surface i .

[0034] As a further optimization, the process of solving the modulus length of the surface offset vector is as follows:

[0035] Solve the tangent vector τ of the key node of the reference path i and the offset unit direction vector L i Angle

[0036]

[0037] Offset vector X of the key node of the reference path i The modulus length is solved as follows:

[0038] As a further optimization, the path extension method described in step S205 includes:

[0039] The offset path whose path endpoint does not reach the boundary is processed, and the interpolation point set of the boundary is traversed to make the line segment formed by the interpolation point and the path endpoint meet the fiber laying angle information of the previous offset path at this position, ensuring that the shape characteristics of the offset path remain unchanged, and it is supplemented as the endpoint of the offset path.

[0040] As a further optimization, the curve fitting method described in step S205 is a NURBS curve fitting method.

[0041] The beneficial effects of the present invention are as follows: through the above-mentioned method for densifying the fiber curve placement path using a non-steady offset vector, the curve is straightened based on the differential idea, and the key nodes on the reference path are moved along their corresponding offset vectors with reference to the reference path, and the boundary conditions of the shape of the core mold of the fiber reinforced composite material structure are fully considered. A path extension method is given to obtain the supplementary points of the offset path curve, and the offset points are fitted into a continuous fiber curve placement path using a cubic NURBS curve fitting method to obtain a full-paving path with uniform spacing distribution, retaining the original reference path shape characteristics, and fully covering the entire core mold surface, thereby making up for the shortcomings of the translation method and the parallel method path densification methods. Therefore, the present invention has universality and high efficiency in planning the fiber curve placement reference path of any open surface core mold, and has important theoretical significance and application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1It is a flow chart of a method for densifying a placement path of an unsteady offset vector fiber curve in Embodiment 1 and Embodiment 2 of the present invention;

[0043] Figure 2 This is a schematic diagram of the solution principle of the unsteady offset vector of the plane square plate core model in the first embodiment of the present invention;

[0044] Figure 3 a) is a distribution diagram of the planar square plate core mold in the first embodiment of the present invention, Figure 3 b) is a finite element model distribution diagram of the plane square plate core mold in the first embodiment of the present invention, Figure 3 c) is a microscopic fiber laying angle distribution diagram of the flat square plate core mold in Example 1 of the present invention;

[0045] Figure 4 Schematic diagram of the reference path of the planar square plate core mold in the first embodiment of the present invention;

[0046] Figure 5 1 is a schematic diagram of a full paving path of a planar square plate core mold before the path is extended in the first embodiment of the present invention;

[0047] Figure 6 Schematic diagram of the full paving path after the plane square plate core mold path is extended in the first embodiment of the present invention;

[0048] Figure 7 This is a schematic diagram of the solution principle of the unsteady offset vector of the concave-convex surface core mold in the second embodiment of the present invention;

[0049] Figure 8 a) is a distribution diagram of the concave-convex curved surface core mold in the second embodiment of the present invention, Figure 8 b) is a finite element model distribution diagram of the two concave and convex surface core molds in the embodiment of the present invention, Figure 8 c) is a microscopic fiber laying angle distribution diagram of the concave-convex curved surface core mold in Example 2 of the present invention;

[0050] Fig. 9 Schematic diagram of the reference path of the concave-convex curved surface core mold in the second embodiment of the present invention;

[0051] Fig.10 This is a schematic diagram of the full paving path of the concave-convex curved surface core mold path before extension in the second embodiment of the present invention;

[0052] Fig.11 It is a schematic diagram of the full paving path after the concave-convex curved surface core mold path is extended in the second embodiment of the present invention. DETAILED DESCRIPTION

[0053] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings here can be arranged and designed in various different configurations.

[0054] Embodiment 1

[0055] See also Figure 1 This embodiment provides a method for densifying the path of an unsteady offset vector fiber curve placement. This embodiment is used for a plane square plate core mold. The method includes the following steps:

[0056] S1. Preprocessing the fiber reinforced composite material core mold;

[0057] S2. Establish an algorithm for densifying the fiber curve placement path with an unsteady offset vector. Through this algorithm, the key nodes selected on the reference path are offset in different directions and step sizes to obtain the key nodes of the offset path. The curve fitting method is then used to obtain a continuous fiber curve placement path to generate a global full-placement path for the core mold.

[0058] Specifically, in this embodiment, the model preprocessing of the fiber reinforced composite material core mold may include the following steps:

[0059] S101, establishing a three-dimensional model (plane square plate model) in the finite element software ABAQUS, dividing the quadrilateral unit grid, and extracting the unit node information and the core mold boundary node information through the INP file;

[0060] S102. Reconstruct the core model surface in MATLAB, and use linear interpolation to obtain a set of interpolation points of the boundary curve.

[0061] It should be pointed out that, in this embodiment, the fiber curve placement path densification algorithm using the unsteady offset vector offsets the key nodes selected on the reference path in different directions and step sizes to obtain the key nodes of the offset path, and uses the curve fitting method to obtain a continuous fiber curve placement path to generate a global full placement path for the core mold, which may include the following steps:

[0062] S201, setting initial parameters, namely: the parallel spacing h of the micro-element curve segments between the two paths, the number of offset paths s and the number of key nodes n, and then performing path densification on the core mold on one side of the reference path; specifically, in this embodiment, the parallel spacing is h=2, the path densification is first performed on the left side of the reference path, the number of offset paths is s=11, and the number of key nodes n=31;

[0063] S202, according to the number of key nodes n, obtain the reference path S by taking points at equal distances p The key node set Q p ;

[0064] S203, according to the relationship between the reference path and the core mold boundary, solve each key node The offset vector

[0065]

[0066] S204, offset the key nodes on the reference path on the core mold surface according to the offset vector to obtain the offset path The key node set

[0067] S205: Determine the kth bias path Whether the two end points reach the core mold boundary, if they reach the boundary, no processing is performed, if they do not reach the boundary, the path continuation method is used to process and obtain a new bias path The key nodes are set, and the curve fitting method is used to fit the key nodes to generate a continuous bias path

[0068] S206, using the bias path To solve the next offset path for reference, set the offset path As the new reference path S p , update the number of key nodes n;

[0069] S207 , judging whether the path densification termination condition is met, if k>s is not met, repeating S202 to S207 , otherwise terminating the path densification.

[0070] See also Figure 2 The offset vector in step S203 of this embodiment is a plane offset vector, and the direction of the plane offset vector is solved as follows:

[0071] 1) Solve the unit direction vector XL of the tangent line of the core mold boundary at the first and last points of the reference path s and XL d , and use it as the offset unit direction vector of the first and last points;

[0072] 2) Calculate the unit direction vector XL of the first and last points of the reference path s and XL d Angle

[0073]

[0074] 3) Determine the offset vector angle of adjacent nodes on the reference path

[0075] The process of solving the modulus length of the plane offset vector is as follows:

[0076] 1) Calculate the tangent vector of the key node of the reference path with the offset unit direction vector XL i Angle

[0077]

[0078] 2) Determine the offset vector of the key node on the fiber reference path Length of mold

[0079] It should be pointed out that the path extension method described in step S205 of this embodiment may include: processing the offset path whose path endpoint has not reached the boundary, traversing the interpolation point set of the boundary, so that the line segment formed by the interpolation point and the path endpoint satisfies the fiber laying angle information of the previous offset path at this position, ensuring that the shape characteristics of the offset path remain unchanged, and supplementing it as the endpoint of the offset path; the curve fitting method may be a NURBS curve fitting method.

[0080] In actual application, in this embodiment, after the path densification on one side of the reference path is completed, the path densification is performed on the right side area of ​​the reference path in the same way; specifically, in this embodiment, the number of offset paths in the right side area of ​​the reference path is s=14, and the number of key nodes is n=31.

[0081] Figure 3 middle, Figure 3 a) shows the distribution diagram of the plane square plate core mold in this embodiment, 3b) shows the distribution diagram of the finite element model in this embodiment, 3c) shows the distribution diagram of the microscopic fiber laying angle in this embodiment, wherein the microscopic fiber laying angle range is [0°, 90°], Figure 4 The reference path curve of the plane square plate core mold is shown. Its change trend is consistent with the orientation of the fiber laying angle and carries the fiber laying angle information. Figure 5 The full paving path obtained by using the unsteady offset vector fiber curve placement path densification algorithm is shown. Figure 3 The microscopic fiber laying angle distribution diagram in the figure shows that its changing trend meets the customary fiber laying angle distribution, but there is a defect in the mandrel boundary area that fails to reach the mandrel edge. Therefore, the path extension method is used to extend the offset path to make the extension curve transition smooth and smooth, and obtain a full laying path with uniform spacing distribution and sufficient coverage. Figure 6 .

[0082] Therefore, this embodiment takes the reference path of the plane square plate core mold as a reference, fully considers the boundary of the plane core mold, and corrects the offset path with the path extension method, thereby obtaining a full-paving path with uniform spacing distribution and sufficient coverage, avoiding the defects of gaps, overlaps, and excessive changes in path curvature that exist in traditional path densification methods, and obtaining a full-paving path that is highly consistent with the microscopic fiber laying angle distribution law, giving full play to the axial mechanical properties of the fiber, and providing a full-paving path distribution scheme for the fiber curve laying of fiber-reinforced composite materials. Taking the plane square plate core mold of the fiber curve laying reference path as an embodiment, the effectiveness of the path densification method for the plane square plate core mold is proved.

[0083] Embodiment 2

[0084] See also Figure 1 This embodiment provides a method for densifying a non-steady offset vector fiber curve placement path. This embodiment is used for a concave-convex curved surface core mold. The method includes the following steps:

[0085] S1. Preprocessing the fiber reinforced composite material core mold;

[0086] S2. Establish an algorithm for densifying the fiber curve placement path with an unsteady offset vector. Through this algorithm, the key nodes selected on the reference path are offset in different directions and step sizes to obtain the key nodes of the offset path. The curve fitting method is then used to obtain a continuous fiber curve placement path to generate a global full-placement path for the core mold.

[0087] Correspondingly, in step S1 of this embodiment, the model preprocessing of the fiber reinforced composite core mold includes: establishing a concave and convex surface shell model in the finite element software ABAQUS, and dividing the quadrilateral unit grid, extracting the unit node information and the core mold boundary node information through the INP file, reconstructing the core model surface in MATLAB, and using the linear interpolation method to obtain the interpolation point set of the boundary curve.

[0088] Step S2 includes the following specific steps:

[0089] S201, setting initial parameters, namely: the parallel spacing h of the microelement curve segments between the two paths, the number s of the offset paths and the number n of the key nodes, and performing path densification on the core mold on one side of the reference path;

[0090] Specifically, in this embodiment, the parallel spacing is h=2, the path densification is first performed on the left area of ​​the reference path, the number of offset paths is s=25, and the number of key nodes is n=45.

[0091] S202, according to the number of key nodes n, obtain the reference path S by taking points at equal distances J The key node set Q J ;

[0092] S303, solve each key node according to the relationship between the reference path and the core mold boundary The offset vector X i (i=1,2,…,n);

[0093] S204, offset the key nodes on the reference path on the core mold surface according to the offset vector to obtain the offset path The key node set

[0094] S205: Determine the kth bias path Whether the two end points reach the core mold boundary, if they reach the boundary, no processing is performed, if they do not reach the boundary, the path continuation method is used to process and obtain a new bias path Finally, the key nodes are fitted by the cubic NURBS curve fitting method to generate a continuous bias path

[0095] S206, using the bias path To solve the next offset path for reference, set the offset path As the new reference path S J ;

[0096] S207 , judging the termination condition of path densification, if k>s is not satisfied, repeating S302 to S307 , otherwise, terminating the path densification.

[0097] Specifically, the offset vector described in step S203 in this embodiment is a surface offset vector, and its solution principle is shown in Figure 7 , for the curve offset vector, the direction of the surface offset vector is solved as follows:

[0098] 1) Based on the surface boundary information, solve the unit direction vector L of the tangent at the first and last points of the reference path s and L d , and use it as the offset unit direction vector of the first and last points;

[0099] 2) Offset the unit direction vector L s and L d Project onto the reference plane and solve for the offset projection unit direction vector and

[0100] 3) Based on the bias projection unit direction vector and Solve the angle between adjacent projection direction vectors in, θ is the bias projection unit direction vector and The angle between

[0101] 4) Projection points of the key nodes of the reference path in the reference plane is the starting point of the projection unit direction vector, and determines the projection unit direction vector of each point Inversely calculate the offset unit direction vector L of the key node of the reference path on the surface i .

[0102] In addition, the process of solving the modulus length of the surface offset vector is as follows:

[0103] 1) Solve the tangent vector τ of the key node of the reference path i and the offset unit direction vector L i Angle

[0104]

[0105] 2) Offset vector X of the key node of the reference path i The modulus length is solved as follows:

[0106] Correspondingly, the path extension method described in step S205 of this embodiment is to process the offset path whose path endpoint has not reached the boundary, traverse the interpolation point set of the boundary, and make the line segment formed by the interpolation point and the path endpoint satisfy the fiber laying angle information of the previous offset path at this position, ensure that the shape characteristics of the offset path remain unchanged, and supplement it as the endpoint of the offset path; the curve fitting method is also a NURBS curve fitting method.

[0107] In this embodiment, after the path densification on one side of the reference path is completed, the path densification is performed on the right side area of ​​the reference path in the same way; specifically, in this embodiment, the number of offset paths in the right side area of ​​the reference path is s=10, and the number of key nodes is n=45.

[0108] Figure 8 middle, Figure 8 a) shows the distribution diagram of the concave-convex curved surface core mold in this embodiment, Figure 8 b) shows the finite element model distribution diagram in this embodiment, Figure 8 c) shows the distribution diagram of the microscopic fiber laying angle in this embodiment, wherein the microscopic fiber laying angle value range is [0°, 90°], Fig. 9 The reference path curve of the concave-convex curved mandrel is shown, and its variation trend is highly consistent with the microscopic fiber laying angle distribution on the mandrel surface. Fig.10 The full paving path obtained by using the unsteady offset vector fiber curve placement path densification algorithm is shown. Figure 8The distribution diagram of the microscopic fiber laying angle in the figure shows that its changing trend is consistent with the distribution law of the microscopic fiber laying angle. In view of the defect that the boundary area of ​​the mandrel does not reach the edge of the mandrel, the path extension method is used to extend the offset path to make the transition between the curves smooth and smooth, and obtain a full laying path with uniform spacing distribution and sufficient coverage. Fig.11 .

[0109] Therefore, the above method of this embodiment uses the reference path of the concave-convex curved surface core mold as a reference, fully considers the boundary of the concave-convex curved surface core mold, and corrects the offset path with the path extension method, thereby obtaining a full-paving path with uniform spacing distribution and sufficient coverage. It not only avoids the defects of gaps, overlaps, and excessive changes in path curvature that exist in traditional path densification methods, but also enables the path densification method to be implemented on the curved surface structure, thereby obtaining a full-paving path that is highly consistent with the distribution law of the microscopic fiber laying angle, giving full play to the axial mechanical properties of the fiber, and providing a full-paving path distribution scheme for the curved fiber laying of fiber reinforced composite materials. Taking the concave-convex curved surface core mold of the reference path for the curved fiber laying as an embodiment, the effectiveness and universality of the path densification method are proved.

[0110] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for densifying the placement path of an unsteady offset vector fiber curve, characterized in that: The steps include: S1. Preprocessing the fiber reinforced composite material core mold; S2. Establish an algorithm for densifying the fiber curve placement path of an unsteady offset vector. By using this algorithm, the key nodes selected on the reference path are offset in different directions and step sizes to obtain the key nodes of the offset path. A curve fitting method is used to obtain a continuous fiber curve placement path to generate a global full placement path for the core mold. The method of using the fiber curve placement path densification algorithm of the unsteady offset vector to offset the key nodes selected on the reference path in different directions and step sizes to obtain the key nodes of the offset path, and using the curve fitting method to obtain the continuous fiber curve placement path to generate the full placement path of the core mold globally includes the following steps: S201, set the parallel spacing of the micro-element curve segments between the two paths h , number of bias paths s and the number of key nodes n , densify the path of the core mold on one side of the reference path; S202, based on the number of key nodes n , obtain the reference path by taking points at equal distances S The key node set Q ; S203, according to the relationship between the reference path and the core mold boundary, solve each key node The offset vector of S204, offset the key nodes on the reference path on the core mold surface according to the offset vector to obtain the offset path S k The key node set ; S205, determine k Bias Path S k Whether the two end points reach the core mold boundary, if they reach the boundary, no processing is performed, if they do not reach the boundary, the path continuation method is used to process and obtain a new bias path S k The key nodes are set, and the curve fitting method is used to fit the key nodes to generate a continuous bias path S k ; S206, using the bias path S k To solve the next offset path for reference, set the offset path S k As the new baseline path S , update the number of key nodes n ; S207: Determine whether the path densification termination condition is met. If not, , then repeat S202 to S207, otherwise terminate the path densification.

2. The method for densifying the placement path of an unsteady offset vector fiber curve according to claim 1, characterized in that: The method of pre-processing the fiber reinforced composite material core mold comprises the following steps: S101, establishing a three-dimensional model in finite element software ABAQUS, dividing the quadrilateral unit grid, and extracting unit node information and core mold boundary node information through the INP file; S102. Reconstruct the core model surface in MATLAB, and use linear interpolation to obtain a set of interpolation points of the boundary curve.

3. The method for densifying the placement path of an unsteady offset vector fiber curve according to claim 1, characterized in that: The offset vector described in step S203 is divided into a plane offset vector and a curved surface offset vector according to the type of the core mold surface.

4. The method for densifying the placement path of an unsteady offset vector fiber curve according to claim 3, characterized in that: The process of solving the direction of the plane offset vector is as follows: Solve the unit direction vector of the tangent line of the core mold boundary at the first and last points of the reference path , and use it as the offset unit direction vector of the first and last points; Calculate the offset unit direction vector of the first and last points of the reference path Angle ; Determine the offset vector angle of adjacent nodes on the reference path .

5. The method for densifying the placement path of an unsteady offset vector fiber curve according to claim 3, characterized in that: The process of solving the modulus length of the plane offset vector is as follows: Calculate the tangent vectors of the key nodes of the reference path With the offset unit direction vector Angle ; Determine the offset vectors of key nodes on the fiber reference path Length of mold .

6. The method for densifying the placement path of an unsteady offset vector fiber curve according to claim 3, characterized in that: The process of solving the direction of the surface offset vector is as follows: Solve the unit direction vector of the tangent line at the first and last points of the reference path based on the surface boundary information , and use it as the offset unit direction vector of the first and last points; Offsets the unit direction vector Project onto the reference plane and solve for the offset projection unit direction vector ; Project the unit direction vector according to the bias Solve the angle between adjacent projection direction vectors ,in, , is the bias projection unit direction vector The angle between Projection point of the key node of the reference path in the reference plane is the starting point of the projection unit direction vector, and determines the projection unit direction vector of each point , inversely calculate the offset unit direction vector of the key node of the reference path on the surface .

7. The method for densifying the placement path of an unsteady offset vector fiber curve according to claim 3, characterized in that: The process of solving the modulus length of the surface offset vector is as follows: Solve the tangent vector of the key node of the reference path With the offset unit direction vector Angle ; Offset vectors of key nodes of the reference path The modulus length is solved as follows: .

8. The method for densifying the placement path of an unsteady offset vector fiber curve according to claim 1, characterized in that: The path extension method described in step S205 includes: The offset path whose path endpoint does not reach the boundary is processed, and the interpolation point set of the boundary is traversed to make the line segment formed by the interpolation point and the path endpoint meet the fiber laying angle information of the previous offset path at this position, ensuring that the shape characteristics of the offset path remain unchanged, and it is supplemented as the endpoint of the offset path.

9. The method for densifying the placement path of an unsteady offset vector fiber curve according to claim 1, characterized in that: The curve fitting method described in step S205 is a NURBS curve fitting method.

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