Discrete path planning of carbon fiber patch placement with complex surface

Abstract

At present, carbon fiber automatic placement technology is mainly applicable to the preform of large and complex components, while the preform of small size and large curvature carbon fiber components mainly relies on manual placement, which has the problems of high labor cost, slow speed, and low repeatability. In order to realize the automatic placement of carbon fiber components with large curvature and small size, this article adopts the carbon fiber patch placement method to make the preforms. By combining the surface subdivision method and the finite element optimization method of carbon fiber patch placement angle, a discrete path planning method of robotic carbon fiber patch is proposed. This method divides the complex surface into surface fragments with similar curvature and normal angle, which can effectively reduce the wrinkles in the process of carbon fiber patch placement and improve the utilization of carbon fiber patch. At the same time, the stiffness optimization design of carbon fiber patch composite preforming is realized by combining the finite element optimization method of placement angle. The helmet surface was selected as the research object of carbon fiber placement path planning, and the path planning of helmet surface placement was carried out, and the simulation tests of helmet placement in different regions and overall placement were compared. It was found that the stiffness of carbon fiber patches placed in different regions of the helmet surface was better than that of the overall placement.

Keywords

Carbon fiber patch surface subdivision path planning placement

Fiber-reinforced composites have excellent properties such as high specific strength, high specific stiffness, good toughness and easy customization, outstanding advantages such as structural-functional integration and design-manufacturing integration, and easy forming into large components, which have wide applications in aerospace, high-speed rail transportation, wind power generation and other industrial fields.¹ The use of carbon fiber prepregs has been steadily increasing in recent years to save energy consumption, for example, the latest Boeing 787 Dreamliner uses more than 50% of composite materials in its structural components.

At present, the automatic placement methods for preparing carbon fiber composite components are divided into automatic tape placement (ATL) and automatic filament placement (AFP). Due to the high cost, slow speed, high scrap rate, and low repeatability of the manual placement process, automatic fiber placement technology has become an important technical means to replace manual carbon fiber placement. ATL technology^2,3 is suitable for processing large flat parts and cannot complete operations such as complex curved surfaces with variable thickness and reinforcement. If the curvature of the fiber layup path is too large, it is easy to produce tearing and folding defects. Therefore, tape lay-up forming is mostly used for forming small curvature parts such as large panels and wings. AFP technology^4,5 is an advanced composite material manufacturing technology, which can realize the reinforcement fiber laying along the specified complex curve, and can automatically control the number of prepreg fiber bundles to change the fiber laying width. AFP equipment has a very complex structure and is usually more suitable for processing complex components with large curvature.

The above analysis shows that the existing composite molding process still has difficulties in relation to low cost, high performance, and accurate manufacturing of small size and large curvature feature parts. In 2017, the German automation company Cevotec proposed a new preparation method of carbon fiber preforming system, which is the carbon fiber patch placement (FPP) technology,^6,7 enabling the transfer, heating, and placement of carbon fiber patches on the mold surface by a robot with a dedicated end effector. Carbon FPP can be used to create complex fiber preforms, such as aerospace gears with concave and convex surfaces, right-angled edges, and flexible placement of small parts with large curvature. A wide range of materials can be applied, including carbon fiber, glass fiber, and aramid fiber.

Automated production of composite preforms is generally based on computer aided design (CAD) and computer aided manufacturing (CAM) technologies to generate automatic placement paths. Many studies have been conducted on the path design of composite parts, which are mainly divided into directional and non-directional paths, where directional paths refer to path trajectories with a fixed reference direction, and non-directional ones on the contrary. Many studies have shown that variable angle path design methods can improve the mechanical properties of composite structures.⁸^–¹⁰ These include reduction of stress concentration,¹¹ improvement of structural strength,¹² and improvement of buckling resistance.¹³^–¹⁶ Shirinzadeh et al.¹⁷^–²⁰ took open-surface components as the main object of study, divided the trajectories into initial and offset trajectories according to the wire laying process, listed the methods for generating the initial trajectories, the continuous equidistant offset of the trajectories, and the boundary problems arising in the offset, and gave the solutions. Schueler et al.²¹ proposed to preset a curve outside the surface and then orient the projection to the surface to form an initial path. After continuous offset, a curve cluster is formed to cover the entire surface. When calculating the offset points, the chord length approximating the arc length is used. The calculation is simple and efficient, and it is applicable to flat components with small curvature. Blom et al.²² introduced the basic principle of common angle configuration in the traditional wire laying method when optimizing the design of cylindrical component layers. Foong²³ investigated a path generation scheme based on process planning and force conditions using an open surface as the object of study. Since the layup is not limited by the “natural path,” the layup method can freely steer the path according to the force conditions to take full advantage of the mechanical properties of the fiber material, and therefore the direction is variable. Many scientists have done a lot of theoretical and experimental research, Tosh et al.^24,25 proposed non-directional curved wire layup paths, the principal stress method and the load path method, respectively, which are both used to increase the structural strength by changing the layup direction, and were experimentally verified with perforated laminates and C-beams. Gliesche et al.²⁶ also took the perforated laminates as the research object, and planned the wire layup path according to the finite element analysis results, which greatly increased the fracture strength. Legrand et al.²⁷ introduced the genetic algorithm in the planning of the lay-up path. Setoodeh et al.²⁸ took the minimum flexibility (deformation) as the objective and compared the greatly improved component performance of rectangular laminates under the variable stiffness condition (continuously changing lay-up angle) with that under the constant stiffness condition (fixed angle). Crosky et al.²⁹ used the principal stress method, the load path method, and the genetic algorithm to design the wire path, and conducted experimental research on perforated composite plates. Blom et al.³⁰ studied the performance of flat members under the condition of rotating path laying and the path generation method of tapered members under the conditions of geodesic, fixed angle, fixed curvature, and linear change angle. Lopes et al.³¹ took laminates as the research object and proved the advantages of curved wire layup over straight wire layup in component strength through experiments. In the optimization design of composite lay-up, Parnas et al.³² analyzed the force conditions by establishing a triangular finite element mesh from two aspects of placement angle and placement thickness, and then optimized the design of the components to improve the strength of the components while reducing the weight of the structure, which is a significant improvement over the previous optimization design methods.

From the above literature analysis, it can be seen that there are many research studies on the automatic placement of continuous trajectories of carbon fiber composites, mainly on the directional and non-directional continuous placement paths, but there are few reports on the carbon FPP method and path planning. In this article, we propose a discrete robot carbon fiber patch path planning method based on the carbon FPP method, combining point cloud surface subdivision and stiffness optimization method, obtaining robot placement space points through surface subdivision and secondary subdivision, obtaining placement angle through finite element optimization method, and completing the optimized path of carbon fiber automatic patching robot, which can provide robot carbon fiber automatic patch path planning method. It can provide reference values for the robot carbon fiber automatic placement path planning method.

Carbon fiber patch automatic placement path planning

Carbon FPP principle and mathematical model

The carbon fiber placement system mainly consists of industrial robot, flexible end effector, carbon fiber patch, placement mold, and floating force control device, where the flexible end effector is made of high temperature resistant foam and vacuum generator, as shown in Figure 1. In the placement process, the robot adsorbs and transfers the carbon fiber prepreg patch to the top of the mold placement point normal by the flexible end-effector, and after the z-axis direction of the robot end-effector is aligned with the mold placement point normal, the carbon fiber patch is attached to the mold surface. The adaptive deformation of the flexible end effector is more conducive to mapping the carbon fiber patch to the mold surface. After the placement is completed, the robot starts the next cycle until all points are completed.

Figure 1.

Composition of carbon fiber patch placement system.

Carbon fiber patch is a regular tape prepreg. During the process of placing the carbon fiber patch on the mold surface with a robot, in addition to aligning the center point of the patch with the placement space of the mold, it is also necessary to locate the main direction of the carbon fiber patch material. In the process of placement, the change of the main direction of the patch material will affect the stiffness of the whole component. Carbon fiber prepreg patch material belongs to orthogonal anisotropic material, and its main direction is often inconsistent with the established object coordinate axis direction in the process of preform molding, the change of placement angle under the object coordinate system will affect the change of its stiffness matrix in the component.

The constitutive model of carbon fiber composite is:

σ = E_{c} \cdot ε

(1)

where σ is the stress matrix; ε is the strain matrix; E_c is the material stiffness matrix. As carbon fiber prepreg is a typical orthotropic material, there are:

E_{C} = E_{s}^{- 1} = [\begin{matrix} \frac{1}{E_{1}} & - \frac{v_{12}}{E_{2}} & - \frac{v_{13}}{E_{3}} \\ - \frac{v_{21}}{E_{1}} & \frac{1}{E_{2}} & - \frac{v_{23}}{E_{3}} \\ - \frac{v_{31}}{E_{1}} & - \frac{v_{32}}{E_{2}} & \frac{1}{E_{3}} \\ \frac{1}{G_{23}} \\ \frac{1}{G_{31}} \\ \frac{1}{G_{12}} \end{matrix}]

(2)

where, the material stiffness matrix is expressed by the engineering elastic constant, where E₁, E₂, E₃ are the principal tensile modulus of the material, and G₂₃, G₃₁, G₁₂ are the shear modulus; v₁₂, v₂₁, v₁₃, v₃₁, v₂₃ and v₃₂ are Poisson's ratios. Combined with the rotation transformation formula of stress and strain, the material stiffness matrix of any orientation is obtained as follows

\begin{array}{l} E_{C} = R_{σ}^{- 1} E_{C} R_{ε}^{- 1} = \\ {[\begin{matrix} \cos^{2} θ & \sin^{2} θ & 2 \cos θ \sin θ \\ \sin θ & \cos^{2} θ & - 2 \cos θ \sin θ \\ 1 \\ \cos θ & - \sin θ \\ \sin θ & \cos θ \\ - \cos θ \sin θ & - 2 \cos θ \sin θ & \cos^{2} θ - \sin^{2} θ \end{matrix}]}^{- 1} \end{array}

\cdot E_{C} \cdot \begin{array}{l} {[\begin{matrix} \cos^{2} θ & \sin^{2} θ & - \cos θ \sin θ \\ \sin θ & \cos^{2} θ & \cos θ \sin θ \\ 1 \\ \cos θ & - \sin θ \\ - \sin θ & \cos θ \\ 2 \cos θ \sin θ & - 2 \cos θ \sin θ & \cos^{2} θ \end{matrix}]}^{- 1} \end{array}

(3)

The placement diagram is shown in Figure 2. Firstly, the carbon fiber patch position is described in the object coordinate system, and after the carbon fiber patch to object coordinate system position conversion, the carbon fiber position is further converted in the base coordinate system. Finally, the final posture of the robot's work placement point is obtained, and the specific transformation is shown in equations 1–5.

Figure 2.

Schematic diagram of carbon fiber patch placement.

Since the angle of the main direction of the carbon fiber patch will affect the stiffness of the carbon fiber structure, the position and orientation information of the carbon fiber patch should be considered in the placement process. The mapping transformation relationship between the base coordinate system, object coordinate system, and fiber patch material coordinate system is established to mathematically describe the carbon fiber placement. The schematic diagram of its placement is shown in Figure 2. First, the position and attitude of the carbon fiber patch are described in the object coordinate system. After completing the position and attitude transformation of carbon fiber patch in the object coordinate system, we further perform the position and attitude transformation of carbon fiber in the base coordinate system. Finally, the final position and attitude of the robot work placement point are obtained, and the specific conversion is shown in equations 4–8:

{}^{B}P = {}_{C}^{B}T^{C} P

(4)

{}^{A}P = {}_{B}^{A}T^{B} P

(5)

{}^{A}P = {}_{B}^{A}T_{C}^{B} T^{C} P

(6)

{}_{C}^{A}T = {}_{B}^{A}T_{C}^{B} T

(7)

{}_{C}^{A}T = [\begin{array}{l} {}_{B}^{A}R_{C}^{B} R_{B}^{A} & {}_{B}^{A}R {}^{B}P_{CORG} + {}^{A}P_{BORG} \\ 000 & 1 \end{array}]

(8)

where ^CP is the vector in the fiber patch material coordinate, ^BP is the expression of vector ^CP in the object coordinate system, T is the homogeneous transformation matrix, R is the rotation matrix, ^BP_CORG and ^AP_BORG are the vector expression from the origin of the fiber patch material coordinate system to the origin of the object coordinate system and the vector expression from the origin of the object coordinate system to the origin of the base coordinate system, respectively.

Carbon fiber patch surface wrinkle control model

In the process of placing the carbon fiber patch to the surface mold, the formation of wrinkles will affect the structural and mechanical properties of the carbon fiber products, and the wrinkles are caused by the deformation of the carbon fiber patch material exceeding the permissible deformation limit.³³ Therefore, it is necessary to consider the influence factors of wrinkles in the process of placement to reduce the generation of wrinkles.

Due to its many advantages, NURBS is often used as a mathematical method to define the geometric shape of industrial products. Suppose that the complex surface studied is a smooth surface P (u, v), and its NURBS surface representation method is as follows:

P (u, v) = \frac{\sum_{i = 0}^{n} \sum_{j = 0}^{m} B_{i, k} (u) B_{j, l} (v) ω_{i, j} d_{i, j}}{\sum_{i = 0}^{n} \sum_{j = 0}^{m} B_{i, k} (u) B_{j, l} (v) ω_{i, j}} F = {s^{'}}_{u} \cdot {s^{'}}_{v}

(9)

where: u, v are parameter variables; D_i,j (i = 0, 1, … , n; j = 0, 1, … , m) are control vertices in a topological rectangular array to form a control grid; ω_i,j (i = 0, 1, … , n; j = 0, 1, … , m) is the corresponding weight factor. B_i,k (u) (i = 0, 1, … , n), B_j,l (v) (j = 0,1, … , m) are the normalized B-spline basis functions of degree k along the u direction and degree l along the v direction respectively, which are determined by the node vectors U and V in the u and v directions according to the de Boor Cox recursive formula:

The unit normal vector of any point on the surface is $n = \frac{{s^{'}}_{u} \times {s^{'}}_{v}}{| {s^{'}}_{u} \times {s^{'}}_{v} |} = \frac{{s^{'}}_{u} \times s^{'}_{v}}{\sqrt{E G - F^{2}}}$ , where ${s^{'}}_{u} = \frac{\partial P (u, v)}{\partial u}, {s^{'}}_{v} = \frac{\partial P (u, v)}{\partial v}, {s^{″}}_{u v} = \frac{\partial P (u, v)}{\partial u \partial v}, {s^{″}}_{u u} = \frac{\partial P (u, v)}{\partial u \partial u}, {s^{″}}_{v v} = \frac{\partial P (u, v)}{\partial v \partial v};$ where $E = {s^{'}}_{u} \cdot {s^{'}}_{u}, F = {s^{'}}_{u} \cdot {s^{'}}_{v}, G = {s^{'}}_{v} \cdot {s^{'}}_{v}$ is the first basic quantity. Where $L = n \cdot {s^{″}}_{u u}, M = n \cdot {s^{″}}_{u v}, N = n \cdot {s^{″}}_{v v}$ is the second basic quantity.

Assume that d = du: dv is the principal direction of surface P (u, v) at point c, and k_n is the normal curvature along the principal direction. According to the principal curvature equation:

| \begin{array}{l} L - k_{n} E & M - k_{n} F \\ M - k_{n} F & N - k_{n} G \end{array} | = 0

(10)

The calculation results are as follows:

H = \frac{k_{\max} + k_{\min}}{2} = \frac{E N - 2 F M + G L}{2 (E G - F^{2})}

(11)

K = k_{\max} k_{\min} = \frac{L N - M^{2}}{E G - F^{2}}

(12)

where H is the mean curvature of this point, K is the Gaussian curvature, k_min and k_max are the two principal curvatures of a point on the surface, where

k_{\max} = H + \sqrt{H^{2} - K}, k_{\min} = H - \sqrt{H^{2} - K}

From a geometric point of view, increasing the traction width or path curvature will leads to an increase in wrinkle amplitude.³⁴ Based on Gutowsky's mapping corollary for fiber sheets and differential geometry theory, Zhang et al.³⁵ deduced that the minimum deformation of the carbon fiber tape when laid along the geodesic path is:

ε = L (u = \frac{w}{2}) - L (u = 0) = − \frac{w^{2}}{8} \int_{0}^{L} K (φ, v) \sqrt{G (φ, v)} d v

(13)

where ε is the minimum deformation, 0 ≤ φ ≤ W/2, and K(φ, v) is the Gaussian curvature of the surface at the point P(φ, v); g(φ, v) is the first basic of fundamental quantities of the mold surface of the surface at the point P(φ, v).

Since the deformation of the prepreg tape is greatest at the boundary, the wrinkle is more likely to occur near the tape boundary, and $η$ denotes the limit of slip of the fibers at the prepreg tape boundary with respect to the center fiber. When the prepreg tape type, the placement process parameters (e.g. prepreg tape heating temperature, mold temperature, placement pressure) and the surface mold are given, the value of $η$ is only affected by the length and width of the prepreg tape and can be expressed as:

η = L η_{i} (W)

(14)

where η_i denotes the limit of slip of the boundary fiber relative to the central fiber per unit length.

The wrinkle generation condition is given by:

ε_{2} < - L η_{i} (W)

(15)

Whether the surface of the mold with positive Gaussian curvature is wrinkled in the process of laying the fiber tape is judged according to:

\frac{W^{2}}{η i (W)} \leq \frac{8}{K_{\max}}

(16)

Whether the surface of the mold with negative Gaussian curvature is wrinkled in the process of laying the fiber tape is judged according to:

\frac{W^{2}}{η i (W)} \leq \frac{8}{K_{\min}}

(17)

Whether the complex mold surface consisting of positive and negative Gaussian curvature regions is wrinkled during the laying of fiber tape is judged based on:

\frac{W^{2}}{η i (W)} \leq \min (\frac{8}{K_{1}}, - \frac{8}{K_{2}}, - \frac{8}{K_{3}}) = \min (\frac{8}{K_{1}}, - \frac{8}{K_{3}})

(18)

where K₁ represents the maximum Gaussian curvature in the positive Gaussian curvature area. K₂ and K₃ represents the maximum and minimum Gaussian curvature in the negative Gaussian curvature area respectively.

Based on the above criteria, the width W of the carbon fiber patch without wrinkles can be obtained. It can be seen from equation 13 that the width of the carbon fiber patch cannot exceed W, otherwise the carbon fiber patch will exceed the allowable deformation limit, resulting in wrinkles. In addition, in the process of carbon FPP, the change accumulation and integration step of the Gaussian curvature of the surface of equation 13 will also affect the deformation of the carbon fiber. In this article, a discrete carbon FPP method is used to fabricate carbon fiber components. The length of carbon fiber patch is discrete, and the effect of the length of the carbon fiber patch on the wrinkle can be ignored. For the curvature variation the cluster segmentation method is used to cluster the regions with similar curvature to reduce the influence of curvature on the wrinkle.

Point cloud surface segmentation and placement path planning algorithm

Through the above analysis, it can be seen that the wrinkles in the process of carbon FPP and the direction of carbon FPP are two important factors affecting the mechanical properties of carbon fiber patch components. In order to obtain carbon fiber patch components with better mechanical properties, it is necessary to reduce the generation of wrinkles and select a better patch placement angle in the process of carbon FPP.

In order to obtain fragmentation with similar curvatures, based on the three-dimensional (3D) point cloud model of the geometric mold, this article uses the point cloud region growth segmentation algorithm to divide the complex surface point cloud data into multiple simple fragmentation regions with similar curvatures and smooth surfaces, so that in the process of carbon FPP, the carbon fiber patch will not have large wrinkles due to excessive curvature changes. In order to obtain the space placement points, it is necessary to divide the segmented 3D area point cloud data into two-dimensional (2D) parameter domain carbon fiber sheets. The width of carbon fiber patches is determined by equations 16–18 above. By subdividing different segmentation areas of the 3D point cloud into 2D parametric plane rectangles, the center point of a 2D plane rectangle is obtained, and the mapping of this point in 3D space is the robot placement point. Finally, the 3D space coordinates and normal vector of the placement point are obtained.

The placement angle of carbon fiber is obtained by using the finite element optimization method, with the stiffness as the optimization goal, and the angle of each carbon fiber placement layer as the design variable. The stiffness is optimized to obtain the optimal placement angle of carbon fiber patch. The algorithm flow of placement path is shown in Figure 3, and the specific description is as follows:

Figure 3.

Flow chart of placement point algorithm.

Denoising and downsampling the 3D point cloud data of the acquired mold surface (in order to improve the calculation efficiency).

The region growing segmentation algorithm is used for the preprocessed point cloud data to segment the region within a certain curvature range and the normal vector angle range, so as to realize the segmentation of complex surfaces into smooth and similar surface fragments.

The regions segmented in the previous step are projected in the 2D parameter plane respectively, and the projection plane is selected according to the maximum area obtained in the projection plane for each segmented region, and the secondary segmentation is carried out in the 2D parameter plane based on the shape of the patch to obtain the parameters of the center position of the patch. Where the width of the carbon fiber patch is determined by equations 16–18 previously mentioned.

Inverse mapping the obtained 2D planar position parameters to 3D point cloud space to obtain the spatial position and normal vector of the patch center points. In order to reduce the errors caused by multiple projections and surface fitting, the search algorithm is used to obtain the 3D spatial coordinate information, and the 3D spatial point index is found by Euclidean distance to obtain the 3D point position information. The search method is as follows:

c_{index} = \min [{(a - a_{c})}^{2} + {(b - b_{c})}^{2}]

(19)

where, a_c and b_c are the 2D plane coordinates of the center point of the patch, a and b are the plane coordinates of the point cloud to be searched, and c_index is the 3D spatial coordinates to be searched.

5. Based on the stiffness optimization design, the placement angles of the carbon fiber patches of each placement layer are obtained.

Helmet example

Helmet surface placement point acquisition

The carbon fiber helmet is a complex non-developable surface with multiple surface combinations, and this section takes the helmet as the research object for path planning of the carbon FPP process. Since the obtained point cloud contains noise and the initial point cloud data is large, pre-processing of the original point cloud data is required. Noise reduction and downsampling are performed on the helmet surface point cloud data, as shown in Figures 4 –7, to obtain higher computational accuracy and computational efficiency.

Figure 4.

Original point cloud.

Figure 5.

Point cloud noise reduction.

Figure 6.

Point cloud normal vector calculation.

Figure 7.

Point cloud downsampling processing.

In order to reduce the wrinkles generated during the placement of carbon fiber patches, a point cloud region growth segmentation algorithm was used to segment the helmet surfaces, and finally three surface segments with similar curvature were obtained. The segmentation results are shown in Figure 8.

Figure 8.

Surface segmentation.

After completing the segmentation of the helmet surface area, it is necessary to project each segmented area into 2D plane space and perform the secondary patch size division, and take the center position of each patch as the robot placement point position after the division (as shown in Figure 9), and reverse project it into 3D coordinate space to obtain the placement point position for the robot to place the carbon fiber patch, as shown in Figure 10.

Figure 9.

Patch secondary division.

Figure 10.

Carbon fiber patch space placement point position.

Helmet sub-regional patch placement angle acquisition

The placement angle of carbon fiber patch prepreg tape is an important factor affecting the stiffness of carbon fiber components. In this article, carbon fiber patch adopts unidirectional prepreg tape, and the placement angle of carbon fiber in the main direction will affect the stiffness of the carbon fiber helmet. In order to obtain the optimized stiffness to resist the damage to the human body caused by the deformation of the helmet under external loads, this section takes the stiffness of the carbon fiber helmet as the optimization goal, and the stiffness index is the maximum deformation. The smaller the maximum deformation, the better the stiffness. With the placement angle of each layer of carbon fiber as the design variable, the stiffness is optimized to obtain the optimal placement angle of carbon fiber prepreg.

The area divided by the point cloud on the helmet surface above was modeled in the Workbench platform applying the ACP module according to the composite modeling method. The material epoxy carbon unidirectional (UD) (230 GPa) prepreg was used (its material properties are shown in Table 1). The initial placement angle of each carbon fiber layer was 0 degrees (the reference direction is the angle between the fiber placement direction and the x-axis of the helmet center point) and the fiber thickness of each layer was 0.2 mm. Apply static load on the top of the helmet in the workbench static module, and the deformation simulation results of the helmet are shown in Figure 11(a), with the maximum deformation of 7.81 mm.

Table 1.

Material characteristics of epoxy carbon UD

Density (kgm^–3)	Young's modulus in x direction (Mpa)	Young's modulus in y direction (Mpa)	Young's modulus in z direction (Mpa)	xy Poisson's ratio	yz Poisson's ratio	xz Poisson's ratio
1490	1.21E+05	8600	8600	0.27	0.4	0.27

Figure 11.

Deformation results of regional placement. (a) Subregional placement of unoptimized deformation; (b) deformation of candidate group 1 for regional placement optimization; (c) deformation of candidate group 2 for regional placement optimization and (d) deformation of candidate group 3 for regional placement optimization.

Taking the stiffness of the carbon fiber helmet as the optimization goal, and the placement angle of each layer of carbon fiber in the helmet fragment area as the design variable, the stiffness was optimized, and the optimal placement angle of each layer of carbon fiber prepreg in the fragment area was obtained. The optimal space filling design method was used to optimize the simulation experiment design. The simulation was carried out according to the experimental combination of placement angles of each layer of carbon fiber patch in each fragment area, and the obtained results were fitted with quadric surface response using genetic algorithm.

After obtaining the response surface model, a multi-objective genetic algorithm was used to optimize the maximum deformation, and three groups of optimization candidate placement combination parameters were obtained. The candidate parameters were brought into the statics model for verification to obtain the deformation results as shown in Table 2. Compared with the helmet modeling with 0° placement angle in each subregion, the maximum total deformation after optimization is reduced to 5.49 mm (as shown in Figure 11).

Table 2.

Combination of candidate parameters for regional optimization

Sub-region 1 placement angle (°)	Sub-region 2 placement angle (°)	Sub-region 3 placement angle (°)	Maximum total deformation (mm)
(0°/0°/0°/0°)	(0°/0°/0°/0°)	(0°/0°/0°/0°)	7.81
(–81.8/12.5/–86.9/–89.9)	(–83.6/–76.0/82.8/85.7)	(–13.0/52.4/–38.6/–3.9)	5.80
(78.2/23.4/–86.3/–87.9)	(–88.7/–83.2/–75.1/88.7)	(–13.5/56.8/–40.4/–3.0)	5.56
(–72.8/22.9/–87.6/–88.9)	(–87.3/–89.8/–77.2/88.8)	(–10.8/52.3/–36.2/–6.4)	5.49

Helmet overall placement angle optimization

In order to compare the difference between the mechanical properties of the surface sub-regional patch placement and the overall patch placement, the same optimization method as in the section on helmet sub-regional patch placement angle acquisition is used in this section, the whole surface area of the helmet is modeled according to the composite material modeling method, the material is epoxy carbon UD (230 GPa) prepreg, the initial placement angle of each layer of carbon fiber is 0 degrees placement (the reference direction is the angle between the fiber placement direction and the x-axis of the helmet center point), a total of four layers were posted, the thickness of each fiber layer was 0.2 mm. A static load was applied on the top of the helmet in the workbench static module. The deformation simulation result of the helmet is shown in Figure 12(a), with the maximum deformation of 8.80 mm. The optimized candidate parameters are brought into the static mechanical model for verification, and the deformation results are shown in Table 3. Compared with the whole helmet surface area, the maximum total deformation after optimization is reduced to 6.54 mm (as shown in Figure 12).

Figure 12.

Overall placement deformation results. (a) Unoptimized deformation in overall placement (b) deformation of global placement optimization candidate group 1; (c) deformation of global placement optimization candidate group 2 and (d) deformation of global placement optimization candidate group 3.

Table 3.

Combination of candidate parameters for overall optimization

Overall placement angle (°)	Maximum total deformation (mm)
(0°/0°/0°/0°)	8.80
(–89.9°/89.8°/–89.8°/–85.1°)	6.67
(–89.8°/89.9°/–89.8°/–78.8°)	6.54
(–89.9°/89.8°/–89.6°/–70.8°)	6.56

Comparison of simulation tests between traditional placement and sub-regional angle optimization placement methods

The composite placement was modeled by the ACP module of the workbench platform for the conventional placement angle and placement sequence, and the material was also epoxy carbon UD (230 GPa) prepreg, with four layers of 0.2 mm each. The results of the comparison are shown in Table 4, which shows that the deformation of the components constructed by several groups of conventional placement angles and placement sequences is greater than that of the optimized placement in the sub-area angles.

Table 4.

Simulation test comparison

Placement type	Traditional overall placement				Sub-regional optimal placement
Placement angle and sequence (°)	(0/–45/90/45)	(0/90/90/0)	(–45/45/90/0)	(0/45/90/–45)	Sub-region 1: (–72.8/22.9/–87.6/–88.9)
					Sub-region 2: (–87.3/–89.8/–77.2/88.8)
					Sub-region 3: (–10.8/52.3/–36.2/–6.4)
Maximum deformation (mm)	8.81	5.79	7.23	7.51	5.49

Conclusions

In this article, a discrete robot carbon fiber patch path planning method is proposed by using point cloud processing technology, combining the wrinkle control principle of carbon fiber patch, surface subdivision method, and the finite element optimization method of carbon fiber prepreg patch placement direction. This method can reduce the wrinkles in the carbon FPP process by dividing the surface into similar surfaces and slicing through point cloud segmentation technology. At the same time, the stiffness optimization design of carbon fiber patch composite preform can be realized by combining the finite element optimization method of carbon fiber placement angle. It can provide reference for the automatic forming technology of carbon fiber patch.

Each area of the helmet surface fragment was placed at an angle of 0 degrees. The static load was applied to the top of the helmet in the statics module, and the maximum deformation of the helmet was 7.81 mm. After optimizing the placement angles of each layer in each region, the maximum deformation of the helmet is reduced to 5.49 mm. The optimal combination of the placement angles of the helmet by area is: the placement angles of area 1 are (–72.8°/22.9°/−87.6°/–88.9°), the placement angles of area 2 are (–87.3°/–89.8°/–77.2°/88.8°), and the placement angles of area 3 are (–10.8°/52.3°/–36.2°/–6.4°).

In order to compare the effects of surface segmentation area placement and overall placement on the mechanical properties of the helmet, the overall helmet area was placed at an angle of 0 degrees, and the maximum deformation of the helmet was 8.80 mm when a static load was applied to the top of the helmet in the static module. After optimization of placement angles of each layer, the maximum deformation of the helmet is reduced to 6.54 mm, and the optimal combination of placement angles of the overall helmet is (–89.8°/89.9°/–89.8°/–78.8°). By comparing the simulation of overall helmet placement and segmentation area placement, it was found that the stiffness of the helmet surface segmentation area placement of carbon fiber prepreg sheet was better than the overall placement in both the initial placement with 0 degrees angle and the optimized placement with the optimized angle combination parameters. The deformation of the helmet is smaller than that of the overall helmet after the initial condition and optimization. This also proves the advantages of surface sub-regional placement.

By comparing the simulation tests of conventional placement and sub-regional angle optimal placement, it can be concluded that the deformation of the components constructed by several groups of conventional placement angles and placement sequences is larger than that of sub-regional angle optimal placement. It further explains the advantages of optimizing placement from the perspective of sub-regions.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work financially supported by the Fundamental Research Funds for the Science and Technology Program of Fujian Province (Grant No. 2021H4007), the “Textile Light” Applied Basic Research Program of China National Textile and Apparel Council (Grant No. J202202) and the National Development and Reform Commission Major Technical Equipment Research Project (Grant No. 2102-320905-89-05-514710).

ORCID iDs

Xiaowei Zhang

Xinfu Chi

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