Compaction pressure distribution and pressure uniformity of segmented rollers for automated fiber placement

Abstract

For automated fiber placement onto molds with complex surfaces, uneven compaction pressure distribution limits tows number in a single sequence and affects layup quality. Compaction roller has a direct influence on the pressure distribution, but the relationship between the two has not been widely explored. In this paper, the segmented compaction roller is used, and a theoretical model of compaction pressure distribution for layup onto general surfaces is established by analyzing the contact between the roller and prepreg layers, followed by experimental validation. Based on the model, single-point pressure uniformity and whole-path pressure uniformity are proposed to quantitatively evaluate the pressure distribution. Furthermore, pressure distribution and pressure uniformity of segmented roller and common roller are compared, as well as the influence of the two pressure distribution on layup quality. The results show that the established model can predict pressure distribution and provide a basis for analyzing layup defects, and segmented rollers apply evener compaction pressure and help to improve layup quality.

Keywords

Automated fiber placement compaction pressure distribution compaction pressure uniformity segmented compaction roller

Introduction

In the past few decades, advanced composite materials have been increasingly used in aerospace industry and many other fields due to their higher specific strength, better corrosion resistance and improved mechanical properties over mental materials.^1,2 Automated tape laying (ATL) and automated fiber placement (AFP) are important technologies to manufacture composite structures, and the latter is especially suitable for manufacturing structures with complex curved surfaces.³ In AFP, each tow is driven individually and laid onto the mold surface or previous layers under a controlled tension using a numerical controlled robotic system. The tensioned tows coming from spools are fed through the AFP head to the compaction roller, which provides a required compaction force to make tows adhere to the mold or previous layers.^4,5

Compaction force is one of the most important process parameters for AFP, and many studies have shown that appropriate compaction force helps to improve prepreg tack levels and layup quality.^6–11 However, little attention has been paid to the compaction pressure (the force per unit area on prepreg layers, unit: Pa), which is more essential than compaction force (unit: N). At present, most of the researches on AFP process were carried out on flat mold, in which case the compaction pressure distribution is relatively even. However, for layup onto complex surfaces, which is where AFP is particularly suitable, the uneven deformation of the compaction rollers leads to uneven pressure distribution^12–14 and further leads to uneven tack levels and layup defects.^14–18 Therefore it is not enough to study the compaction force alone, but also the compaction pressure and carry out quantitative evaluation of it.

The compaction pressure is mainly influenced by three factors: the mold surface, the compaction force, and the roller structural parameters. Among them, the mold surface has already been determined before AFP and cannot be adjusted. Most studies improve the layup quality by changing the compaction force, while the effect of roller structure has not received enough attention. Bakhshi and Hojjati⁶ studied the pressure distribution of five different compaction rollers in the case of placement on flat mold, and they concluded that pressure distribution plays a crucial role in achieving good layup quality. Chu et al.¹⁹ modeled compaction pressure distribution by finite element method and analyzed the effect of roller deformation on layup quality. Cheng et al.¹⁶ analyzed the effect of the roller attitude on the fiber pull-up by means of differential geometry. Jiang et al.^12,14 modeled the pressure distribution under the common compaction rollers in AFP and optimized the roller structure. They concluded that the pressure distribution can be improved by reducing the hardness and width and increasing the outer radius of the rollers.

However, common rollers have difficulty in achieving ideal pressure distribution for layup onto complex surfaces due to their structural limitation. In recent years, a type of roller with ingenious structural form—segmented compaction roller—has been gradually applied. As shown in Figure 1, segmented roller consists of several narrow segments, each segment able to move up or down and retreat individually to conform the surface of mold.^20,21 Besides, each segment is covered with a flexible rubber cover and individually subjected to an air pressure load. Denkena et al.²² used segmented compaction roller in their research and pointed out its structural characteristics, but did not analyze it in detail. The existing studies still lack quantitative analysis of the pressure distribution under segmented roller and the adaptability of segmented roller to mold.

Figure 1.

(a) Common compaction roller (b) segmented compaction roller.

On the basis of our previous work on common roller,¹⁴ a study on the segmented roller and compaction pressure uniformity is carried out. In this paper, a theoretical model is established to calculate compaction pressure distribution under segmented roller for layup onto general surfaces and validated by the following experiment. Based on the model, single-point pressure uniformity and whole-path pressure uniformity are proposed to quantitatively evaluate the pressure distribution. Furthermore, the pressure distribution, pressure uniformity, and layup quality of segmented roller and common roller are compared. The results show that the established model can be used to predict pressure distribution under segmented roller. Moreover, segmented rollers apply evener compaction pressure and can eliminate layup defects caused by insufficient pressure under common rollers.

Modeling and experimental validation of compaction pressure distribution under segmented rollers

Contact analysis of segmented roller and mold with general surfaces

The compaction pressure is essentially the contact pressure between roller, layers, and mold. However, due to the complexity of AFP, it is difficult to obtain an accurate analytical solution for the pressure distribution. The mold surface is an irregular 3D surface without function expressions, and the rubber cover of the compaction roller is characterized as hyperelastic and exhibits large deformation. Therefore, the following simplifications are made to simplify the problem and obtain an approximate solution.

(i) The compaction roller basically maintains a low speed and uniform rolling in AFP; then the rolling process can be considered as a static press process at each path point.

(ii) Each segment of the segmented roller is relatively thin, but when multiple segments are placed side by side, the two sides of each segment are in close contact during deformation, as shown in Figure 2(a). Moreover, the part where the deformation occurs is concentrated in a small area at the bottom. Therefore, except for the outer side of the two outer segments, the segmented roller can be regarded as a plane strain case.

(iii) The following analytical method was used. Since the main focus is on pressure, preliminary results are first obtained using the qualitative analysis method in contact mechanics²³ and Gaussian theory²⁴, without considering friction and shear for the time being. The results are then corrected by finite element simulations considering friction and shear.

Figure 2.

(a) Profile of the rubber cover deformation of the segmented roller (b) the placement of segmented roller onto mold with a general surface S.

Under lubricated conditions and uniform deformation between contact surfaces, the stress–strain relationship can be predicted by Gaussian theory,²⁴ as shown in the first two equations in equation (1). Ignoring ε³, the simplified stress–strain relationship shown in the third equation in equation (1) can be obtained. And for non-uniform deformation, Young’s modulus E in equation (1) needs to be replaced with the effective compression modulus E_C to modify Gaussian theory, as shown in equation (2)²⁴

{\begin{cases} σ = \frac{E (λ^{- 2} - λ)}{3} \\ λ = 1 - ε \\ \Rightarrow σ = \frac{E}{3} [\frac{3 ε - 3 ε^{2} + ε^{3}}{{(1 - ε)}^{2}}] \approx \frac{E ε}{1 - ε} \end{cases}

(1)

{\begin{cases} E_{C} = E (I + K M^{j}) \\ σ = \frac{E_{C} ε}{1 - ε} \end{cases}

(2)

where M is the shape factor, that is, the ratio of the area to which the force is applied to the force-free area. And I, K, j are coefficients related to the shape, hardness, and material proportioning of the rubber. However, the second equation of equation (2) is an empirical formula, and coefficients values are unknown for rubber cover of compaction roller. The value of E_C will be given in Calculation method of EC and k by other method.

Figure 2(b) shows the placement of the segmented roller onto mold with a general surface S. The segmented roller is composed of n segments (generally n < 16). The width of each segment is L₀, and the total width L = nL₀. Suppose the current prepreg layer is the i^th layer, S_i is the surface of the i^th layer, and l is a path of the i^th layer. Take any path point p on path l for analysis; then the following spatial rectangular coordinate system is established: the coordinate origin O is located at p, the x-axis is the tangential direction of path l at point p, and the z-axis is the outer normal direction of surface S_i at p.

Since each segment can rotate and move up or down independently and is subject to the same air pressure load, the contact between each segment and prepreg layers can be analyzed separately. Take any radial cross section y = y_c of the m^th (m =1, 2, ..., n) segment for analysis, as Figure 2(b) and Figure 3 shows. Σ_m is the contact zone between the m^th segment and layers, l_m is the center line of the m^th segment, R is the outer radius of the rubber cover, and r is the inner radius. F₀ is the compaction force of each segment, and the total compaction force F = nF₀. F₀ and F are perpendicular to surface S_i at path point p, that is, they are parallel to z-axis. h is the thickness of all layers, and h = ih₀, where h₀ is the thickness of a single layer.

Figure 3.

Contact analysis of the m^th segment in cross section y = y_c (a) deformation and contact stress of roller and layers (b) actual contour of the roller after deformation.

After applying F₀, the original surface S_i of the i^th layer is deformed to S_i^′. For the time being, assume that the contour of the roller remains circular. Take any point A on the original contour of the roller for analysis. A moves to point A₁(x_A1, y_A1, z_A1) along the radius direction after deformation, and A₁ is on the deformed surface S_i^′ of the i^th layer. Therefore, the compression stress σ_A1 at A₁ can be obtained, as shown in equation (3)

{\begin{cases} ε_{A 1} = \frac{R - d_{A 1}}{R - r} \\ σ_{A 1} = \frac{E_{C} ε_{A 1}}{1 - ε_{A 1}} \end{cases}

(3)

where d_A1 is the distance between A₁ and the center line l_m, ε_A1 is the compression strain at A₁. Moreover, the projection of ε_A1 on the normal direction of S_i^′ is the compaction pressure p_A1 to be obtained, as shown in equation (4)

p_{A 1} = σ_{A 1} \cos α_{A 1}

(4)

where α_A1 is the angle between σ_A1 and p_A1. Then calculate σ_z-A1, the projection of σ_A1 along z-axis. Integrate σ_z over the contact zone Σ_m, and the result is equal to F₀, as shown in equation (5), where β_A1 is the angle between σ_A1 and σ_z-A1

{\begin{cases} σ_{z - A 1} = σ_{A 1} \cos β_{A 1} \\ \iint_{Σ_{m}} σ_{z} d S = F_{0} \end{cases}

(5)

Moreover, only radial strain was analyzed previously, while circumferential strain and the presence of friction lead to a change in the contact width, as shown in Figure 3(b). To solve this problem, a scaling factor k is introduced, and move point A₁ along surface S_i^′ on cross section y = y_c to point A₂. The coordinate relationship between points A₁ and A₂ is shown in equation (6)

{\begin{cases} x_{A 2} = x_{A 1} / k \\ y_{A 2} = y_{A 1} \\ {S^{'}}_{i} (x_{A 2}, y_{A 2}, z_{A 2}) = 0 \end{cases}

(6)

After the above analysis of the deformation of the roller, the next step is to obtain the deformed surface S_i^′ of the i^th layer. The mold surface S is known, and the original surface S_i of the i^th layer can be obtained by thickening S by h = ih₀, where h₀ is the thickness of a single layer. After being subjected to compaction pressure, S_i deforms to S_i^′. Since the in-plane modulus of the layers is much higher than the out-plane modulus, only the deformation in the layers thickness direction is considered. Take any point C on surface S_i in cross section y = y_c to analyze, as shown in Figure 3(a), and the deformed point C₁ on S_i^′ can be obtained as follows

{\begin{cases} Δ h_{C} = E_{3} i h_{0} p_{C} d S_{C} \\ x_{C 1} = {\begin{cases} x_{C} - Δ h_{C} \sin γ_{C}, \vec{t} \cdot \vec{i} \geq 0 \\ x_{C} + Δ h_{C} \sin γ_{C}, \vec{t} \cdot \vec{i} < 0 \end{cases} \\ y_{C 1} = y_{C} \\ z_{C 1} = z_{C} - Δ h_{C} \cos γ_{C} \end{cases}

(7)

where Δh_C is the deformation of point C in the direction of layer thickness, p_C is the compaction pressure at C, γ_C is the angle between p and z-axis, and dS_C is a small area around point C. E₃ is the out-of-plane modulus of layers.

\vec{t}

is the vector pointing to the direction of the outer normal of S_i, and

\vec{i}

pointing to the positive direction of x-axis. Thus, the relationship between the original surface S_i and the deformed surface S_i^′ is established.

The pressure distribution under the m^th segment is obtained by combining equations (5)–(7). Repeat this analysis for all segments to obtain the entire pressure distribution around a certain path point. And repeat this process for all path points to obtain pressure distribution of the entire layup process.

Calculation method of E_C and k

In this section, the effective compression modulus E_C and the scaling factor k are determined by combining finite element simulation with MATLAB function fitting. A two-dimensional finite element model of the contact between segmented roller and flat mold is established in ABAQUS. The inner radius r, the outer radius R, and the hardness H of the rubber cover is set to 40 mm, 45 mm, and 55 HA. The element type of the rubber cover is set to CPE4RH and that of the mold and the sleeve is CPE4R.

The Mooney–Rivlin model, which is widely used for modeling the deformation of hyperelastic materials in the case of small and medium deformations, is used as the constitutive model of the rubber cover. The material parameters of each part are listed in Table 1. Since the stiffness of the mold and sleeve is much greater than that of the rubber cover, they are constrained as “rigid body” to improve computational efficiency. And the friction coefficient between the rubber cover and mold is set to 0.357.²⁶ Concentrated forces from 1 N to 7 N (i.e., F₀/L₀, the compaction force per unit width of the roller) are applied to the center of the sleeve in turn.

Table 1.

Material parameters of each part in the finite element model.²⁵.

Part	Material	E (MPa)	μ	C₀₁ (MPa)	C₁₀ (MPa)
Mold	Steel	2.1×10⁵	0.3	—	—
Sleeve	Steel	2.1×10⁵	0.3	—	—
Rubber cover	Silicon rubber (55 HA)	—	—	0.1	0.4

The simulation result is shown in Figure 4(a). The CPRESS (contact pressure) of each element node of the mold surface is extracted to obtain a set of data about the pressure p and x-coordinates. And d₀, distance from the center line l_m to the mold surface after the roller deformation, is also extracted.

Figure 4.

(a) Simulation result of compaction pressure on flat mold (F₀/L₀ = 5 N/mm); (b) fitting result of compaction pressure distribution; (c) simulation results and predicted results.

One the other hand, according to the theoretical model in Contact analysis of segmented roller and mold with general surfaces, function expression of pressure distribution on flat mold is derived, as shown in equation (8)

{\begin{cases} ε (k x) = \frac{R - \sqrt{d_{0}^{2} + {(k x)}^{2}}}{R - r} \\ p (x) = \frac{E_{C} ε (k x)}{1 - ε (k x)} \frac{d_{0}}{\sqrt{d_{0}^{2} + {(k x)}^{2}}} \end{cases}

(8)

Except for E_C and k, other unknowns in equation (8) can be obtained from the simulation results. Then E_C and k are fitted according to the functional form of equation (8) using MATLAB function fitting tool, and the fitting result is shown in Figure 4(b). It can be seen that the simulation result and the fitting result have good similarity.

Furthermore, according to equation (2), E_C and k are related to the inner radius r, outer radius R, hardness H, and compaction force F₀. For the segmented rollers with r = 40 mm, R = 45 mm and H = 55 HA, the fitting results of E_C and k are listed in Table 2. After obtaining the discrete E_C and k data, linear interpolation method is used to obtain the E_C and k in each d₀ interval. And the comparison of the FE results and predicted results for intermediate values of F₀/L₀ is shown in Figure 4(c). It can be seen that the two results also have good similarity. Moreover, for other roller sizes and hardness, the corresponding values of E_C and k can be obtained similarly.

Table 2.

F₀/L₀ and the corresponding E_C and k.

Compaction force per unit width of the roller (F₀/L₀, N/mm)	d₀ (mm)	E_C(MPa)	k
1	44.88	8.30	0.93
2	44.82	8.78	0.89
3	44.78	9.29	0.87
4	44.74	9.72	0.86
5	44.71	10.12	0.85
6	44.68	10.46	0.84
7	44.65	10.78	0.83

Case of calculating pressure distribution under segmented roller

Based on the established model, calculate the compaction pressure distribution around five path points P₁ ∼ P₅ of a 3D surface, as shown in Figure 5(a). The length and width of the mold are 280 mm and 130 mm, respectively. The thickness h₀ of a single layer is set to 0.125 mm, and the layers number is 3; thus, the total thickness of the three layers h is 0.375 mm. Then, the third layer surface S₃ is obtained by thickening the mold surface S by 0.375 mm. {O_M} is the mold coordinate system. And the surface S₃ at P₁, P₂, and P₃ is convex and at P₄ and P₅ is concave. Porcupine curvature radius of S₃ is obtained by CATIA, as shown in Figure 5(b). The out-of-plane modulus E₃ of prepreg is 5.3 MPa. The segmented roller has 11 segments. Each segment has a width L₀ = 11 mm, and the total width L = 121 mm. The inner radius r, outer radius R, and hardness H are the same as those in Calculation method of EC and k. The compaction force F₀ for each segment is set to 25 N, corresponding to the total compaction force F of 275 N.

Figure 5.

(a) The curved mold and the surface of the third prepreg layer; (b) porcupine curvature radius of the third layer surface S₃.

Since the profiles of most aerospace components are often irregular surfaces without specific function pressions, the function integral in equation (5) needs to be replaced by a numerical integral. Triangular meshing is performed on surface S₃ and the center points of each triangular mesh are extracted. After that, calculate the product of the pressure at each center point and the area s_i of each corresponding mesh, sum all the results, and the value is equal to F₀, as shown in equation (9)

{\begin{cases} ε_{i k} = \frac{R - d_{i k}}{R - r} \\ p_{i} = \frac{E_{C} ε_{i k}}{1 - ε_{i k}} \cos α_{i k} \\ \sum p_{i} s_{i} \cos β_{i k} = F_{0} \end{cases}

(9)

where p_i is the compaction pressure of the center of each triangular mesh. The algorithm for calculation compaction pressure distribution under segmented compaction roller is shown in Figure 6. Step 1 is to get the required inputs of the mold. In Loop 1, c is the distance from the roller axis to the path point. Bisection method is adopted to change the value of c within the range of inner diameter r and outer diameter R until the deviation e between the sum of σ_z·s_i of each triangular mesh and the set compaction force is within the error range. The value of e is set to be F/100, and n is the number of segments. When calculating pressure distribution under each segment, the layer surface S₃ is divided into several sections along y-axis, and the spacing of each section is set as 1 mm. Calculate the minimum distance between S₃ in the adjacent section and the axis of the corresponding segment. Then this distance is substituted into the interpolation function to get the corresponding E_C and k of the section. And the pressure distribution under one segment can be obtained.

Figure 6.

Flow chart of the algorithm for calculation compaction pressure distribution under segmented compaction roller.

Moreover, pressure distribution around each path point is obtained in Loop 2, as shown in Figure 7(a). {O_M} is the mold coordinate system, and {P_i} (i = 1, 2, ..., 5) is the coordinate system at each path point. It should be noted that in order to be consistent with the experiment in Experimental validation, the z-axis of {P_i} is in the same direction as the z-axis of {O_M}, not along the normal vector of the surface.

Figure 7.

(a) Theoretical calculation results of compaction pressure distribution under segmented roller around path points P₁ ∼ P₅; (b) pressure distribution under segmented roller along the whole path l.

And calculate pressure distribution along the whole path in Loop 3. Since each mesh will undergo a pressure rise from zero to maximum and back down to zero in AFP process, the average pressure of each mesh is taken as the pressure along the whole path, as shown in equation (10). n_P is the number of path points, and the value is taken to be 480

{\begin{cases} p_{i - Σ} = \sum_{j = 1}^{n_{P}} p_{i - j} \\ p_{i - aver} = \frac{p_{i - Σ}}{{n^{'}}_{P}} \end{cases}

(10)

where p_i-j (j = 1, 2, ..., n_P) is the pressure on mesh i when calculating pressure around the j^th path point, and p_i-Σ is the sum of the n_P pressures on mesh i. n_P’ is the number of p_i-j that are greater than 0, and p_i-aver is the average pressure on mesh i. The final calculation results are shown in Figure 7(b). It is worth noting that the center of the pressure distribution is not necessarily at the path point, which is related to the direction of the applied compaction force and the shape of the mold surface. By the way, it takes 5.21 s to obtain the pressure results for all 480 path points as shown in Figure 7(b), with an average time of about 11 ms for one path point. The CPU of the computer used is AMD Ryzen 7 5800H, and the software used is MATLAB.

Experimental validation

Experimental setup and materials

In order to validate the established model, an experiment was carried out to measure the compaction pressure distribution. Figure 8(a) shows the experimental setup and a curved mold, which is the same as the one shown in Figure 5. The mold was fixed on the rigid plate of the experimental setup, and the plate can be moved along the guide rails according to control program. The structural parameters of the segmented roller are the same as those in Case of calculating pressure distribution under segmented roller. The gaspipe fittings on both sides of the roller are connected to pneumatic circuit, and the applied compaction force can be adjusted by controlling the compressed air pressure.

Figure 8.

(a) Experiment setup of fiber placement; (b) measurement principle of pressure measurement film; (c) the relationship between pressure and color density; (d) fitting result of the relationship between color density and gray scale.

Pressure measurement film (model: LLLW, ultra super low pressure), supplied by FUJIFILM Corporation, was used to obtain the pressure distribution and accurate contact area under the roller. The film is composed of two polyester bases, one coated with a color-forming layer and the other with a color-developing layer, as shown in Figure 8(b). Both of the two bases are 90 μm thick. Place the coated side against each other, and when pressure applied, the two coatings react and produce red color in the color-developing layer. The color density corresponds to the value of the pressure, as well as ambient temperature and humidity. The relationship between color density and pressure is shown in Figure 8(c). Select one of the five curves in Figure 8(c) to use according to ambient temperature and humidity. Since the color density is hard to quantify and read, it is converted into gray scale and a curve of the relationship between them is fitted, as shown in Figure 8(d). Combining Figures 8(c) and (d), the correspondence between gray scale and pressure can be obtained.

Experimental procedure and results

Three prepreg layers were placed on the mold by hand before the experiment, and the prepreg used is AC531/CCF800H unidirectional carbon/epoxy tow with a width of 6.35 mm and a thickness of 0.125 mm. Then, prepare five pieces of pressure measurement films with the size of 130 mm ×30 mm, and laid one piece on one of the path points P₁∼ P₅. Adjust the air pressure in the pneumatic circuit to 0.45 MPa, corresponding to the total compaction force of 275 N. The ambient temperature was kept at 15°C with a relative humidity of (65 ± 2)%.

Control the servo motor of the experimental setup to make the mold move along the guide rails. And when the mold moves to the target path point, stop the servo motor and open the pneumatic valve connecting the roller to make the compressed air into the roller. After that, the roller applies a total force of 275 N to the mold, as shown in Figure 9(a). Then, the color density around the five path points is obtained, as shown in Figure 9(b). According to the ambient temperature and humidity, choose Curve C in Figure 8(c), then convert the color density into pressure distribution, and the results are shown in Figure 9(c). And the comparison between the theoretical results and experimental results of average pressure along x-axis is shown in Figure 10.

Figure 9.

(a) Experiment of measuring compaction pressure distribution under segmented roller; (b) color density on pressure measurement films around path points P₁∼ P₅; (c) experimental results of pressure distribution under segmented roller; (d) manufacturing error of the segmented roller.

Figure 10.

Comparison between the calculation results and experimental results of average pressure along x-axis.

Form Figure 7(a), Figure 9(c) and Figure 10, it can be seen that the theoretical results and experimental results are relatively similar, from the viewpoint of the contact area and pressure distribution. The difference between the two results may be caused by the following reasons.

(i) The gaps and overlaps of the prepreg layers cause obvious pressure fluctuations in the experimental results. However, layup defects are ignored in the theoretical model to simplify AFP process.

(ii) The outer surface of rubber cover of one segment is uneven, and the segments are not close to each other but have a small gap (see Figure 9(d)), that is, the manufacturing error of the roller leads to less than ideal experimental results.

(iii) The pressure measurement film itself has an error of 0.06 MPa.

Considering the above experimental errors, the established model can be considered effective.

Analysis of compaction pressure uniformity

Calculation pressure distribution under common roller

To further understand the characteristics of segmented roller, pressure distribution under common roller is also calculated according to the model proposed by Jiang et al.,¹⁴ and the results are shown in Figure 11(a). The inner radius, outer radius, hardness, and width of the common roller are 21 mm, 42.5 mm, 45 HA, and 126 mm, respectively, and the compaction force is set as 700 N. The reason for choosing 700 N is that the average pressure and maximum pressure of the common roller under 700 N are close to that of the segmented roller under 275 N, and that would be a fair comparison. Similarly, equation (10) is used to calculate the pressure distribution along the whole path, as shown in Figure 11(b).

Figure 11.

(a) Calculation results of pressure distribution under common roller according to the model proposed in Reference 14; (b) pressure distribution under segmented roller along the whole path l.

Then, the same experiment was carried out for the common roller, as shown in Figure 12. Comparing Figure 7 and Figure 11, in general, the common roller has a larger contact area along roller radial direction (i.e., path direction), but the pressure distribution along roller axis is not ideal. At point P₃, both the two rollers achieve good pressure distribution. However, at P₁ and P₂, nearly half of the area under the common roller is not subjected to pressure. And at P₄ and P₅, the pressure in the central area below the roller is very small, as the two points are located in a concave position. This means that in real AFP, the tack levels will be weak at the zones where the compaction pressure is low. And for placement onto surfaces with small curvature radii, it is necessary to reduce the tows number in a single sequence to prevent defects, which will reduce placement efficiency.

Figure 12.

(a) Experiment of measuring compaction pressure distribution under common roller; (b) color density on the pressure measurement films around path points P₁∼ P₅; (c) experimental results of pressure distribution under common roller.

For the segmented roller, even at the large curvature positions of P₁, P₂, P₄, and P₅, the pressure along roller axis is evener, which means the pressure difference between different tows is smaller. The main reason for this is that segmented rollers have stronger deformation capacity, and evener pressure distribution can be achieved through the independent move of each segment.

Single-point pressure uniformity u_sp

The uneven compaction pressure distribution leads to insufficient or even no pressure on some prepreg tows and may further cause undesired layup quality. Therefore, pressure uniformity is proposed to quantify the even degree of the pressure along roller axis. Moreover, the pressure uniformity is divided into two aspects: single-point pressure uniformity u_sp and whole-path pressure uniformity u_wp. u_sp characterizes the pressure uniformity around each path point, while u_wp the pressure uniformity along the whole path.

Considering that there are three possible methods to select data points for calculating single-point pressure uniformity u_sp, the pressure distribution around point P₃ under common roller is taken as an example to illustrate, as shown in Figure 13. The first method is that the data points are selected from the entire contact zone between the roller and the layers (Figure 13(a)), the second are selected from a straight line directly below the roller axis (Figure 13(b)). And the third are taken from the maximum pressure in each roller radial section and these points will form a curve (Figure 13(c)).

Figure 13.

Three methods to select data points for calculating single-point pressure uniformity: (a) select from the entire contact zone; (b) select from a straight line below the roller axis; (c) select from the maximum pressure in each roller radial section.

As compaction roller keeps moving along predefined paths in AFP, the pressure distribution in roller axial direction is much more important than that in roller radial direction (the path direction). On the one hand, the pressure difference in the radial direction will be compensated with the movement of the roller. On the other, pressure distribution along roller axis represents the differences of tack levels between different tows and has a greater effect on layup quality. Moreover, each point of layers undergoes a pressure rise from zero to maximum and back down to zero in AFP process. Therefore, on a comprehensive consideration, the third selection method is the most appropriate way to calculate u_sp.

On the basis of the pressure distribution, the maximum pressure p_i-max in each roller radial section is extracted, and the standard deviation of all p_i-max is used to represent the dispersion degree of pressure distribution. Then, the standard deviation after normalization is subtracted from one to obtain the expression for the single-point pressure uniformity u_sp within the range of 0–1, as shown in equation (11). The more u_sp tends 1, the smaller the pressure difference between different tows, which represents the better pressure distribution

{\begin{cases} p_{aver}^{sp} = \frac{\sum_{i = 1}^{j} p_{i - \max}}{j} \\ u_{sp} = 1 - \sqrt{\frac{1}{j} \sum_{i = 1}^{j} {(\frac{p_{i - \max} - p_{aver}^{sp}}{p_{aver}^{s p}})}^{2}} \end{cases}

(11)

u_sp of path points P₁ ∼ P₅ for the common roller and segmented roller is then calculated, as shown in Figure 14(a). The u_sp of the segmented roller at the five path points is higher than that of the common roller, especially at P₁ and P₂ where the curvature radius of surface S₃ at the path point is small. Moreover, even if the curvature radii are similar (such as P₁ and P₅), the u_sp of the same roller still differs considerably, which may be related to whether the mold is convex or concave at that point (the mold at P₁, P₂ and P₃ is convex, at P₄ and P₅ is concave).

Figure 14.

(a) Single-point pressure uniformity u_sp and whole-path pressure uniformity u_wp of common roller and segmented roller around path points P₁∼ P₅; (b) The position of the data points used to calculate u_wp.

Whole-path pressure uniformity u_wp

On the basis of pressure distribution along the whole path, whole-path pressure uniformity u_wp is proposed to represent the pressure uniformity along the whole path, as shown in equation (12), where p_i-aver is the average pressure on mesh i. The whole-path uniformity is the uniformity across roller width and layup path l at the same time. And as shown in Figure 14(b), the points surrounded by the purple box are used to calculate u_wp

{\begin{cases} p_{aver}^{wp} = \frac{\sum_{i = 1}^{k} p_{i - aver}}{k} \\ u_{wp} = 1 - \sqrt{\frac{1}{k} \sum_{i = 1}^{k} {(\frac{p_{i - a v e r} - p_{aver}^{wp}}{p_{aver}^{wp}})}^{2}} \end{cases}

(12)

Over the whole path, due to the strong deformation ability of segmented roller, the u_wp is higher than that of common roller, but it is not significant. And the u_sp of segmented roller at point P₃, P₄ and P₅ is also not significantly higher than that of common roller. One reason for this is that the mold surface is still relatively simple, and the advantages of segmented rollers can be better highlighted for layup onto complex surfaces. And another reason is that the segmented roller still needs to be optimized. Jiang et al.¹² concluded that decreasing the hardness and increasing the thickness of the cover rubber helps to improve the deformation capacity of common rollers. The hardness and thickness of the rubber cover of the common roller are 45 HA and 21.5 mm, while for that of the segmented roller are 55 HA and 5 mm. Thus, there is still room for further improvement of the structural parameters of the segmented roller.

Additional placement experiment

The pressure uniformity of the common roller at P₁ and P₂ is relatively low, and nearly half of the area under the roller is not subjected to pressure. And at P₄ and P₅, the pressure in the central area below the roller is very small. These above problems may lead to layup defects. In order to investigate the application value of the compaction pressure analysis, 3-tows placement experiments were carried out using the common roller and the segmented roller, as shown in Figure 15(a). The tow’s tension is provided by weights at the end of each tow with a mass of 0.2 kg, corresponding to a tension of 2 N. The placement temperature is provided by a heater, maintained at 35°C, and the placement speed is kept at 15 mm/s. The compaction force is 275 N for the segmented roller and 700 N for the common roller. In addition, the ambient temperature was kept at 15°C with a relative humidity of (65 ± 2)%.

Figure 15.

(a) Additional 3-tows placement experiment; (b) wrinkles appeared after the placement of segmented roller; (c) bridging appeared after the placement of common roller.

The results are shown in Figure 15(b) and (c). For the segmented roller, there are still some wrinkles around path points of P₁ and P₂, as some areas are not subjected to pressure. And for the common roller, obvious bridging appeared due to weak tack level. For these two rollers, the process parameters are almost the same except for the pressure distribution; thus, it can be concluded that the difference of layup quality is mainly caused by the difference of pressure distribution.

Conclusion

In this paper, by analyzing the structural characteristics of segmented compaction roller and the contact stress between roller and prepreg layers, the model of compaction pressure distribution under segmented roller for layup onto general surfaces is established. Two unknown parameters in the model are obtained by combining finite element simulation with MATLAB function fitting. Based on the model, pressure distribution around five path points of a curved surface is obtained. Then, the model is validated by the following pressure measurement experiment. In addition, pressure distribution under the segmented roller and the common roller is compared, and the pressure difference of the segmented roller along roller axis is smaller.

Based on the pressure distribution model, single-point pressure uniformity u_sp and whole-path pressure uniformity u_wp are proposed, and the calculation methods of them are given. Then, u_sp and u_wp for both rollers are calculated. Furthermore, additional placement experiment was carried out to understand the practical value of the established model. In general, the pressure uniformity of the segmented roller is higher than that of the common roller, especially for the mold with large curvature surface. And higher pressure uniformity is beneficial to achieve better layup quality.

The pressure distribution model and the pressure uniformity proposed in this paper provide a basis for analyzing the layup quality from the perspective of compaction pressure distribution. Future work need to be done to optimize the structural parameters of segmented rollers, as well as model layup defects such as wrinkles and bridging based on the obtained compaction pressure.

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) received no financial support for the research, authorship, and/or publication of this article.

ORCID iDs

Yuxiao He

Junxia Jiang

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Compaction pressure distribution and pressure uniformity of segmented rollers for automated fiber placement

Abstract

Keywords

Introduction

Modeling and experimental validation of compaction pressure distribution under segmented rollers

Contact analysis of segmented roller and mold with general surfaces

Calculation method of E C and k

Case of calculating pressure distribution under segmented roller

Experimental validation

Experimental setup and materials

Experimental procedure and results

Analysis of compaction pressure uniformity

Calculation pressure distribution under common roller

Single-point pressure uniformity usp

Whole-path pressure uniformity uwp

Additional placement experiment

Conclusion

Footnotes

Declaration of conflicting interests

Funding

ORCID iDs

References

Calculation method of E_C and k

Single-point pressure uniformity u_sp

Whole-path pressure uniformity u_wp