Using a Novel Process-Near Mechanical-Deflection-Based Spreading Test Rig for a Systematic Experimental Analysis of Carbon Fiber Rovings Spreading Process

Abstract

Unidirectional (UD) fiber-reinforced thermoplastic tapes provide excellent specific mechanical properties; thus, they are being increasingly used for the targeted local reinforcement of plastic components in lightweight construction applications. An essential step in the production of UD tapes is fiber spreading, the aim of which is to expand fiber rovings from an initial width to a defined final width. Using a test rig under realistic conditions, we systematically investigated the factors that influence fiber spreading by deflection. Carbon-fiber rovings with various numbers of filaments were guided over deflection rods, and roving width before and after spreading was recorded with cameras. A full design of experiments (DoE) plan was set up, in which (i) the number of rods, (ii) rod diameter, (iii) immersion depth of the rod, and (iv) take-off speed of the fiber roving were systematically varied. We statistically evaluated the results of the experiments and found that the main factors that influenced the response variables investigated were number of rods and rod diameter, followed by immersion depth. We also observed that a higher number of filaments in the roving led to more complexity and greater variability. Our results can be used to optimize the spreading configuration in the production of UD tapes.

1. Introduction

Composites are materials that are manufactured by combining various constituent materials to achieve synergistic properties. They are used in numerous industries [1] and play a crucial role in modern technology. Composites consist of at least two different materials, each of which contributes, with its unique properties, to the overall performance. Thus, the advantages of each individual material can be exploited while minimizing their disadvantages [2].

In 2022, 12.7 million tons of fiber-reinforced plastics were produced worldwide, of which 2.8 million tons were made in Europe, where 41.8% (1.2 million tons) of the annual production is attributed to thermoset composites and 58.2% (1.6 million tons) to thermoplastic composites [3]. In contrast to thermosets, in which the molecular chains cross-link chemically during curing, thermoplastic composites exhibit only physical entanglement of the molecular chains and can therefore be remelted and then reshaped and processed into complex structures [4,5]. Components made of thermoplastic composites can also be welded, which increases design flexibility [6]. Thermoplastic composites exhibit excellent solvent resistance, high fracture and impact resistance, and unlimited shelf life, and can be stored at a low cost [7]. They are, to some extent, mechanically recyclable [8], and their manufacturing processes allow for a high degree of automation [6,7,8,9,10,11]. One disadvantage of thermoplastics is their comparatively high viscosity, which requires high processing temperatures and makes it difficult to impregnate the fibers. In fiber-reinforced plastics, a basic distinction is made between short, long, and continuous (endless) fibers.

In order to achieve the European Union’s Green Deal climate goal of climate neutrality by 2050 or a 55% reduction in greenhouse gas emissions by 2030, efficient solutions are needed in the transport sector, particularly in aviation and the automotive industry [12]. Using fiber-reinforced plastics in place of traditional materials reduces pollutant emissions by decreasing component weight while maintaining the mechanical properties required [8,13,14,15]. In unidirectional fiber-reinforced thermoplastic tapes (UD tapes), unidirectionally aligned reinforcing fibers are embedded within a polymer matrix. Due to their specific mechanical properties, UD tapes are used increasingly in applications that require light weight. Depending on the load case of the component, UD tapes are stacked in a specific layer structure and formed into a laminate, which can then be processed further. This combination fulfills the stiffness and strength requirements of the component at a significantly lower component weight [9,11].

UD tapes are produced in a continuous process where (i) fiber rovings pulled from a creel must be (ii) spread before (iii) impregnation with polymer melt (e.g., via a die). The tape must then be (iv) calibrated to the required thickness, (v) cooled and (vi) wound onto a spool. Figure 1 illustrates this process.

A key process step in the production of UD tapes is the spreading of the fiber rovings. A perfectly spread and homogeneous fiber carpet is crucial for achieving complete fiber impregnation and thus high-quality tapes. Various spreading techniques can be used to spread fiber rovings from their initial shape to the desired width: (i) mechanical, (ii) electrostatic, (iii) pneumatic/vacuum, (iv) vibration, or (v) acoustic techniques. Mechanical fiber spreading seeks to achieve a uniform distribution of fiber bundles by stretching, deflecting, or combing them. For this purpose, cylindrical or concave spreading rods are used that can be connected individually or in series and arranged linearly or in a circle. The surface of the spreading elements is smooth or equipped with combs/needles [16,17,18,19,20,21]. In electrostatic fiber spreading, the filaments of a fiber bundle are separated by applying a voltage to one or more electrodes over which the bundles are pulled [22,23,24,25,26]. In pneumatic/vacuum fiber spreading, fiber bundles are spread using fluid–mechanical effects, such as the Bernoulli and Venturi effects. For this purpose, the fluid (usually air) is sucked in or out via dies along or across the fiber direction. Air dies for high-velocity air jets or V-shaped dies are commonly employed. Alternatively, the air is extracted in vacuum chambers. To increase the efficiency of these pneumatic systems, they are sometimes used in combination with mechanical devices, such as rollers or combs [27,28,29,30,31,32,33,34,35]. The technology required for fiber spreading by means of vibration is similar to that of mechanical spreading, but one or more spreading rods are made to vibrate perpendicularly to the fiber direction to improve spreading [36,37,38]. In acoustic fiber spreading, sound energy is used to make a gaseous medium (air) vibrate. This vibrational energy of the medium is transferred to the fiber bundle, which causes the fibers to spread [39,40]. Although several different spreading techniques exist, only a few systematic scientific studies on the spreading behavior of fiber rovings can be found in the literature.

As early as 1996, Wilson [41] investigated the lateral spreading of polyamide fiber rovings and cotton yarns during mechanical spreading by deflection. He developed a simple mathematical model for estimating the spreading width when using a single spreader rod. Irfan [42] extended this theory to include the use of glass-fiber rovings and an estimation of the spreading width at a second spreader rod. Both models were validated experimentally in simple setups that are not applicable in practice: Wilson carried out purely static experiments in which the roving was under tension, while Irfan investigated the spreading behavior by pulling the roving cyclically under tension over spreader rods and then releasing the tension. In both cases, force was applied by attaching a weight. Krützmann [43] proposed a machine learning approach to reducing fluctuations in roving quality in which a supervised process model trained on real data and a process control model were used to select suitable spreader rod positions; the results confirmed the added value of adaptive, model-based spreading. Newell [28] reported on carbon fiber spreading using the Venturi principle: with the help of pinch rollers and two Venturi distributors, he was able to achieve a homogeneous fiber distribution. Chen [29] developed a 3D model of a pneumatic fiber distributor. He compared numerical and experimental results and established both qualitative and quantitative agreement.

While all the aforementioned spreading techniques have the same aim of spreading fiber bundles homogeneously and evenly, they differ in the process engineering efforts involved. Spreading by means of mechanical deflection, as shown schematically in Figure 2, is the simplest method and works on the following principle [44]: as the fiber bundle is guided over a horizontal rod, the arrangement of the individual filaments within the bundle results in different radii at its inner and outer sides ($R_1$ and $R_2$). This, in turn. increases the arc radius of the section in contact with the rod in the radial direction. Since the length of the individual filaments of the rigid glass or carbon fibers does not change, the tension in the outer (upper filament layer) fibers increases. To relax the fiber tension, the outer filaments move towards the center and displace the bottom filaments, which causes both the spreading of the roving and a reduction in bundle height.

This work systematically investigated the factors that influence fiber spreading by mechanical deflection. A novel test rig was developed and used to simulate spreading in a continuous production process under realistic conditions. Unlike in previous studies, this test rig was designed to measure both the input and output widths of the same roving sections before and after spreading, and thus allowed for a direct comparison and quantification of spreading performance. Systematic experimental tests following a design of experiments (DoE) plan were conducted to investigate the influences of the number of rods, rod diameter, immersion depth and take-off speed on spreading. The results were then analyzed using statistical methods.

2. Materials and Methods

2.1. Materials

Three carbon-fiber rovings that differed in the number of filaments (24 K or 60 K) and in sizing (see

Table 1. Fiber types studied.

Fiber	Company	Fiber Type	Filaments	Sizing
E23	Teijin (Wuppertal, Germany)	Tenax-E STS40 E23	24 K	Epoxy
F13	Teijin (Wuppertal, Germany)	Tenax-E STS40 F11	24 K	Polyurethane
TRH	Mitsubishi Chemical (Irvine, CA, USA)	Pyrofil TRH50 60M	60 K	Epoxy

) were investigated.

2.2. Equipment

A novel test rig, the main components of which are illustrated in Figure 3a, was developed and employed to investigate the main factors that influence fiber spreading. A single roving was unwound from a spool by means of a winder at a controlled take-off speed and then pulled through a spreading configuration that comprised a variable number of spreading rods with defined diameters. The horizontal and vertical distances between the spreader rods could be adjusted individually to alter the relative positions of the rods and thus the resulting wrap angles. The initial and final widths of the roving were recorded by two line-scan cameras mounted before and after spreading to determine initial and spread widths and enable direct comparisons of the same roving area before and after spreading. Two monochrome NECTA N4K-3 (Alkeria, Cascina, Italy) line-scan cameras from Alkeria equipped with AMS DR4K3.5 sensors (AMS AG, Graz, Austria) with 1 × 4096 pixels and a pixel size of 3.5 µm were used. Ricoh FL-BC7528 lenses (Ricoh Imaging Company, Tokyo, Japan) with a minimum working distance of 250 mm and a focal length of 75 mm were mounted on the cameras. A Baumer rotary encoder (Baumer GmbH, Friedberg, Germany) mounted on a 30 mm diameter roller was used to match the recording frequencies of the line-scan cameras to the roving take-off speed. The number of encoder ticks was set based on the pixel width in the transverse direction to ensure that there was no distortion and that $∆x=∆y$ applied to all pixels, where $∆x$ and $∆y$ correspond to the length information of a pixel in the longitudinal and transverse directions, respectively. Load cells recorded the force applied to the roving before and after spreading.

To guarantee that both cameras captured the same section of the roving, they were synchronized by means of a Python script. The recording scheme is illustrated in Figure 3b. Recording started at the infeed camera; the encoders of both cameras were set to zero (1), and the infeed width was recorded over a defined roving length (2)–(3). Concurrently, the encoder ticks were counted and compared to the current roving length between the cameras. Once the encoder ticks corresponded to the current length of the roving, the second camera commenced recording (4) until the same roving length had been recorded (5).

2.3. Procedure

For all experiments, a roving length of 94.25 mm (one encoder revolution) was recorded precisely before the first and after the last spreader rods. The images collected were then binarized using a Python (version: 3.12.0) script and fed to an edge-detection algorithm that calculated the actual mean roving width. For this purpose, the camera position was first calibrated to determine the width of a pixel: a calibration strip with a defined width was recorded, and the number of pixels over the defined width was determined using the IC Measure software (version: 2.0.0.286). The calibration procedure was repeated whenever the camera position changed. To determine the accuracy of the camera calibration, the camera position was changed several times and the calibration process repeated to determine the deviation in the width measurement caused by calibration (see Section 3.1).

2.4. Experimental Design

Using the Stat-Ease 360 software (version: 22.0.6 64-bit), a full-factorial DoE, that included four factors with two levels—resulting in $2^4=16$ runs—was created. The following factors were chosen: (i) rod diameter, (ii) number of rods, (iii) immersion depth, and (iv) take-off speed. The former two are categorical and the latter two numerical factors.

Table 2. Factors in the DoE plan.

Factor	Name	Units	Type	Minimum	Maximum
A	Rod diameter	mm	Categorical	15	45
B	Number of rods	-	Categorical	3	7
C	Immersion depth	mm	Numerical	20	40
D	Take-off speed	m/min	Numerical	1	5

summarizes the factors and their respective level values. To check for the linearity of the relationships, five center points were added for which the numerical factors were defined as the midpoints between minima and maxima. Since no “center point” could be defined for the categorical factors, we duplicated the center points of the numerical factors for all four combinations of the two categorical factors. This increased the total number of center points to 20, but ensured that the center points also accounted for variation in the categorical factors. The complete experimental design of 36 runs is presented in

Table A1. Full-factorial experimental design for fibers E23, F13 and TRH.

Std	Run	Factor 1 A: Rod Diameter	Factor 2 B: Number of Rods	Factor 3 C: Immersion Depth	Factor 4 D: Take-Off Speed
		(mm)	-	(mm)	(m/min)
8	1	45	7	40	1
16	2	45	7	40	5
5	3	15	5	40	1
14	4	45	5	40	5
7	5	15	7	40	1
25	6	15	5	30	3
32	7	45	7	30	3
29	8	15	5	30	3
17	9	15	5	30	3
12	10	45	7	20	5
26	11	45	5	30	3
31	12	15	7	30	3
18	13	45	5	30	3
30	14	45	5	30	3
21	15	15	5	30	3
36	16	45	7	30	3
24	17	45	7	30	3
10	18	45	5	20	5
2	19	45	5	20	1
11	20	15	7	20	5
9	21	15	5	20	5
35	22	15	7	30	3
1	23	15	5	20	1
33	24	15	5	30	3
27	25	15	7	30	3
3	26	15	7	20	1
22	27	45	5	30	3
13	28	15	5	40	5
4	29	45	7	20	1
15	30	15	7	40	5
6	31	45	5	40	1
34	32	45	5	30	3
19	33	15	7	30	3
20	34	45	7	30	3
28	35	45	7	30	3
23	36	15	7	30	3

in Appendix A.

The responses of the factorial design included the final width, spread ratio, and force, as listed in

Table 3. Responses in the DoE plan.

Response	Name	Units
R1	Final width	mm
R2	Spread ratio	-
R3	Force	N

. The final width is the width of the fiber roving after spreading and is the most practically important target variable. The spread ratio is intended to eliminate effects caused by input width variations and was defined as the ratio between initial and final roving widths, $w_{initial}$ and $w_{final}$, respectively:

$$R2={\displaystyle \frac{W_{initial}}{W_{final}}}.$$

(1)

To determine the spread ratio correctly, the exact same roving section was used for a comparison before and after spreading. The force, which should be as low as possible to minimize fiber damage, describes the total force acting on the roving during the spreading process.

For the statistical analysis of the results, both Pareto charts and interaction diagrams were created using State Ease 360 statistical software to illustrate which factors influence each response variable. For the Pareto charts, State Ease 360 calculates the lower limit of the t-value based on the standard t-critical value used for single-effect tests in statistical models. The t-critical value is derived from the t-distribution for a given level of significance (α) and the degrees of freedom of the model. This value serves as a threshold for assessing the significance of an effect. A central feature of the calculation in State Ease 360 is the dynamic adjustment of the t-value thresholds. This is performed iteratively as the terms in the model change. Adding or removing terms changes the degrees of freedom of the model and thus the distribution on which the calculation of the critical t-value is based. In this way, the program ensures that statistical tests are consistent and accurately matched to the current model specification. An interaction plot, in contrast, visually represents how multiple factors influence a response variable, highlighting both main effects and interactions. Parallel lines indicate additive effects, where factors act independently, while non-parallel or crossing lines reveal interactions, showing that the effect of one factor depends on another. The strength of effects and interactions can be qualitatively inferred from the slopes and spacing of the lines. Steeper slopes or large gaps between lines often indicate significant effects.

3. Results and Discussion

This section presents the results of the experimental trials conducted in this work. We first discuss the repeatability of the calibration process of the measuring system and then present data that demonstrate the variations in the input width of the fiber rovings. Finally, the results of the full factorial tests are evaluated for each fiber.

3.1. Repeatability of the Calibration Process

To determine the measurement accuracy of the camera, a 30 mm wide calibration strip was measured ten times, and the position of the camera changed between measurements. The results are shown in Figure 4. The widths measured ranged from 29.92 mm to 30.48 mm. The relative error with respect to the width of the calibration strip was between 0.27% and 1.6%. The average relative error was 0.71%, which indicates that calibration introduced no significant error.

3.2. Variation in Input Width of Fiber Roving

Commercially available fiber tows commonly show variations in roving width during unwinding that are caused by folded and twisted roving sections. During roving production, the winding tensions applied differ between beginning and end of the winding process, which causes variations in roving shape [44].

In preliminary experiments, the input width of each roving was determined 175 times, as shown in Figure 5a. For the two 24K fibers, the minimum and maximum input widths were 6.42 mm and 10.92 mm for fiber E23, and 4.43 mm and 10.59 mm for fiber F13. For the 60K fiber, input widths ranged from 7.07 mm to 10.59 mm. The standard deviations (2) from the mean were 0.65 mm, 0.99 mm, and 2.08 mm for E23, F13, and TRH, respectively. The standard deviation was calculated by

$$\sigma ={\displaystyle \frac{1}{N}}\sqrt{{\displaystyle {\sum }_{i=1}^N}{(x_i-\mu )}^2},$$

(2)

where $N$, $x_i,$ and $\mu$ are the number of samples, the measured value, and the mean value of all measured values, respectively.

Figure 5b presents the results of the measurements in the form of a whisker box plot, which illustrates both central tendencies and scattering. Fibers E23 and F13 show a similar dispersion of input widths, and the central tendencies of both groups are close to each other. For E23, the median and the mean are 9.36 mm, which indicates a symmetrical (standard) data distribution. Most of the measurements are concentrated within a narrow range (between 9.04 mm and 9.8 mm), as indicated by the small IQR and short whiskers. Low outliers are measurements with significantly smaller input widths. Fiber F13, which has the same number of filaments and diameter as E23, shows a different behavior. Here, the median and the mean of 8.11 mm are significantly lower than for E23. The data distribution within the IQR is much broader, ranging from 7.35 mm to 8.83 mm. This suggests that the sizing had an influence on the input width.

The TRH fiber, with 60,000 filaments, shows significantly wider scattering of the measured values than E23 and F13. The median of 13.22 mm indicates a larger average input width. The width of the IQR and the length of the whiskers are also larger for TRH, which indicates greater variability in input width. For TRH, 50% of the data measured were between 11.88 mm and 14.52 mm. This greater variability was due to the higher number of filaments. Further, compared to the 24K fibers, the roving was in many cases already partially collapsed at the edges when it was unwound from the spool, which significantly affected its input width. A summary of the statistical parameters of the input width measurement is given in

Table 4. Characteristic statistical values of the input widths of the three fiber types.

Fiber	Median	Mean	Standard Deviation	1. Quartile (25%)	3. Quartile (75%)	IQR	Min	Max	Number of Outliers
	(mm)	(mm)	(mm)	(mm)	(mm)	(mm)	(mm)	(mm)	-
E23	9.36	9.36	0.65	9.04	9.80	0.76	6.42	10.92	3
F13	8.11	8.11	0.99	7.35	8.83	1.48	4.43	10.59	1
TRH	13.22	12.92	2.08	11.88	14.52	2.63	7.07	16.64	3

. Overall, the data show that the groups with fewer filaments (E23 and F13) had greater consistency in input width, while the group with more filaments (TRH) had greater variability and more outliers. This may indicate that additional measures are needed to stabilize the spread ratio during the experimental process.

3.3. Main Factors That Influence Fiber Spreading

A full factorial experimental design was used to identify and analyze the main factors that influence fiber spreading due to deflection. This type of design allows for a systematic investigation of the effects of, and the interactions between, the various parameters, thus facilitating a deeper understanding of what influences fiber spreading. The results for each fiber type are presented below.

3.3.1. Final Width

The factors that affected the final width (R1, Table 3) are shown in Figure 6 in the form of Pareto charts, in which the t-value indicates whether the main effect or the interaction has a strong influence on the response variable. For all fiber types, the main influencing factor was the number of rods (B), while the take-off speed of the roving (D) had no relevant impact on the final width. The former result can be explained by the increased number of deflections: with each deflection, the roving widens as the tension difference between the inner and outer filaments is balanced. Since the speed does not change the tension difference between the filaments at the inner and outer radii of the roving, the take-off speed is not expected to affect the final width. The immersion depth (C) and the interaction AB between the rod diameter (A) and number of rods (B) also had a relevant impact. Overall, the t-values of the influencing factors were significantly higher for type E23 than for the other two types.

For fiber E23, all influencing factors (except take-off speed) showed a positive effect on the final width. In other words, on average, across all experiments, the final width grew with increasing factor levels. However, the interaction diagram in Figure 7a illustrates a strong positive interaction, AB. While the rod diameter did not influence the final width when the number of rods was low, the width grew dramatically with rising rod diameter for high rod numbers. The measured center points are scattered symmetrically around the center point predicted by the regression model. Similarly, for each categorical factor, the analysis of repeatability showed the symmetrical scattering of the center points around the linear model. An analysis of variance (ANOVA) at the 5% level of significance showed that, with p-values less than 0.001, both the rod diameter and number of rods were highly significant, while immersion depth and the interaction AB yielded p-values of 0.0009 and 0.0006. The coefficient of determination $R^2$ was 0.8965, and the adjusted coefficient of determination $R_{adj}^2$ was 0.8806; the small difference between these two values indicates that there was no overfitting. Residuals are the difference between each measured output value and its model prediction. The residual plots showed no trends or patterns for the E23 fiber data, which suggests that the residuals were independent and not correlated. Similarly, the probability plot for the residuals showed that the data points roughly followed a straight line; in other words, there were no outliers, and the model order was good.

Fiber F13 behaved slightly differently: on average across, all experiments, both the number of rods (B) and immersion depth (C) had a positive effect on the final width, while the rod diameter (A) and take-off speed (D) showed no effect. It is possible that the effect of the rod diameter (A) was lost due to the scatter of the initial width, and therefore we do not see a significant effect compared to the other two fiber types. Figure 7b illustrates that, on average, and compared to the number of rods, the rod diameter appears to have had only a minor influence on the final width. However, analysis of the positive interaction AB showed a different result: for a small rod diameter, the positive effect of the number of rods was negligible within the error margins; with rising rod diameter, in contrast, the width decreased at a low number of rods, but grew dramatically at a high number of rods. With a p-value of 0.2945, the ANOVA thus identified the rod diameter alone as being insignificant to the final width, although it played an important role when analyzed in conjunction with the number of rods. Significant p-values, in contrast, were found for immersion depth (C), interaction AB, and number of rods (B), with 0.0425, 0.0349, and 0.0008, respectively. The coefficient of determination for the fiber F13 regression model was only 0.7832 and the adjusted value 0.7345, which may have been the result of greater natural scattering, missing model terms that were omitted due to slightly too high p-values, or unknown experimental disturbances. Again, the residuals of the data points are normally distributed, and the residual plots show no significant trends.

Fiber TRH behaved similarly to fiber E23. Again, the number of rods (B) was the main influencing factor, with a positive effect on the final width. Immersion depth (C) and rod diameter (A) also showed a positive influence, while the take-off speed (D) was not relevant. However, unlike for the previous two fiber types, the ANOVA (α = 0.05) showed that rod diameter, immersion depth, and interaction AB had no significant effect on the final width, with p-values of 0.2598, 0.0620 and 0.2008, respectively. Only the number of rods (B) significantly impacted the final width, with a p-value of 0.008. In the case of the TRH fiber, at 0.6580, the coefficient of determination $R^2$ was low, and the adjusted coefficient of determination was only 0.6033, which indicates poorer model prediction. The main reason for this may be the large variations in the TRH fiber input width, which also caused scattering of the output widths, despite constant settings. We calculated the relative standard deviation (RSD; Equation (3)) as a measure of data scattering, obtaining values of 4.73%, 5.15%, and 5.85% for the E23, F13, and TRH fibers.

$$RSD={\displaystyle \frac{\sigma }{\overline{x}}}·100\%,$$

(3)

where $\sigma$ and $\overline{x}$ are the standard deviation and the mean value. The RSD values obtained also correlate with the respective $R^2$ values of 0.8965, 0.7832 and 0.6580. The TRH data residuals are normally distributed, as are those of the other fiber types, and no trends are identifiable in the residuals.

3.3.2. Spread Ratio

For all fiber types, the spread ratio (R2, Table 3) is dominated by the number of rods (B) and the rod diameter (A), as illustrated by the Pareto diagram in Figure 8. In addition, the following differences were observed: for fiber E23 (Figure 8a), both interaction AB and immersion depth (C) affected the spread ratio, while for fiber F13 (Figure 8b), the immersion depth had an impact. Fiber TRH (Figure 8c) exhibited interaction AB effects, but was not influenced by immersion depth.

Analogously to the final width, the take-off speed (D) had no influence on the spread ratio for any of the fiber types. In general, the remaining influencing factors had a positive effect on the spread ratio. As can be seen in Figure 9, the spread ratio for the factorial point replicates is scattered, and the same applies to the measurement data for the center point replicates. Further, Figure 9 illustrates a positive interaction AB for fibers E23 and TRH. For both levels of the rod diameter, the spread ratio increased with the increasing number of rods. This effect was, again, particularly pronounced for a large rod diameter. Figure 9b shows that the rod diameter and the number of rods affected the spreading ratio for fiber F13, but—given the parallel lines—there was no interaction between these two factors.

The ANOVA showed that rod diameter and number of rods were highly significant factors for all three fibers (p-value < 0.0001). For E23 and F13, immersion depth was also significant, with p-values of 0.0480 and 0.0022 for E23 and F13, respectively. TRH also showed a highly significant interaction AB (p < 0.0001), and this interaction was also significant for E23. The model accuracy for the E23 and F13 fibers was 0.8590 and 0.8433, and the adjusted coefficients of determination were 0.8373 and 0.8259, respectively, indicating reasonable model accuracy without overfitting. In the case of the TRH fiber, the model quality was 0.8555 and the adjusted value was 0.8382. However, the input width varied considerably for this type, and the normal distribution of the residuals was S-shaped, which indicates a non-normally distributed data set. The residuals as a function of the run exhibited some outliers. Runs 1, 22, 25, 29, 34, 36 were therefore excluded from the analysis, which resulted in the normal distribution of the data. Closer examination revealed (see Appendix A Table A1) that the outliers occurred only when seven rods were used. This can be attributed to the TRH fiber, with its 60,000 filaments being much wider than the two 24K fibers, and the roving therefore sometimes folding up when being wound onto the spool, which would have reduced its width considerably. Further, the seven rods spread the roving and gave rise to variations in the spread ratio.

The relative standard deviations for the E23, F13 and TRH fibers were 5.47%, 5.92% and 3.48%, respectively, corresponding to model qualities of 0.8590, 0.8433 and 0.8555.

3.3.3. Force

For all three fiber types, the Pareto diagrams of the effects are shown in Figure 10. In contrast to the final width and ratio, all factors from Table 2 had a positive effect on the force (R3, Table 3); this means that the force acting on the roving increased with increasing factor level. Furthermore, depending on the fiber type, various interactions (such as AB, AC, and BC) affected the force acting on the roving.

We found a positive effect on all interactions affecting the roving force. As can be seen in Figure 11, for all fiber types, there was a relatively small increase in stress with increasing number of rods at a small rod diameter. In contrast, a large increase in stress was found at a larger rod diameter. The fiber stresses were in the range of 25 N to 250 N in the experiments. The force on the roving increased with increasing fiber wrap angle (more rods, larger diameter, greater immersion depth) and with increasing take-off speed.

The positive interaction AC in Figure 12a shows an increase in force with increasing immersion depth for a small rod diameter; for a larger rod diameter, the effect of immersion depth becomes negligible as the tension levels equalize. The rod diameter thus had a greater effect on the force than the immersion depth. Figure 12b,c shows small positive effects of the interactions BD and BC for fibers F13 and TRH, respectively. The force thus increased slightly with increasing factor levels.

The ANOVA results for all three fibers (E23, F13 and TRH) showed that rod diameter, number of rods and the interaction AB were highly significant (p < 0.0001) for the force acting on the fiber roving. Immersion depth and take-off speed were also significant for all three fiber types, although at a considerably lower p-value level. The interaction AC for fiber E23 and the interaction BD for fiber F13 reached significant p-values, but with very low F-values of 5.07 and 4.87, respectively, which makes them practically insignificant. The interaction BC with TRH was not significant, with a p-value of 0.0630. The model quality for fiber E23 was very high, with a coefficient of determination $R^2$ of 0.9830 and an adjusted $R^2$ of 0.9787, which indicates accurate predictions of the force applied to the roving. For fiber F13, the model showed the same quality, with the $R^2$ and adjusted $R^2$ both equal to those of E23. The TRH fiber model achieved the highest accuracy, with an $R^2$ of 0.9946 and an adjusted $R^2$ of 0.9932, and thus performed particularly well in predicting force on the roving. That model predictions of the force were better than those of final width and spread ratio can be attributed to the force being independent of the input quality and initial width of the fiber roving.

4. Conclusions

We provided important insights into (i) fiber input width variations, (ii) the factors that influence fiber spreading and (iii) the main parameters that affect the spreading process.

The calibration process was highly repeatable, and the minimal relative error confirms the reliability of the measurement system. Analysis of the input widths showed that fibers with a higher number of filaments (TRH) exhibited greater variability and more outliers than fibers with fewer filaments (E23 and F13). This variability suggests that, in order to ensure consistency, more robust control measures may be required for fibers such as TRH.

The factors that most influenced the propagation of the fibers for all fiber types were the number of rods and rod diameter, followed by the immersion depth. For fibers E23 and F13, an increase in the number of rods or the immersion depth led to a uniform increase in spreading width, while the rod diameter had different effects depending on the fiber type. The interaction between the number of rods and the rod diameter was particularly important for fiber E23, while the interaction had no significant effect for fiber F13. For TRH, the larger number of filaments led to more complexity with higher variability.

The spread ratio analysis confirmed that the number of rods and rod diameter were key influencing factors. The force analysis further highlighted the interactions between these factors. Rod diameter in conjunction with number of rods had a significant effect on the force acting on the roving, as did immersion depth and pull-off speed in specific cases.

This study underlines the importance of key parameters—number of rods, immersion depth, and rod diameter—in achieving any desired spread of fibers. The results provide valuable guidance for optimizing fiber spreading that relies on mechanical deflection, especially for high-filament-count fibers such as TRH, where variability is more pronounced.