Two-Stage Optimization of Fluidized-Bed Powder Coating for Continuous Carbon Fiber-Reinforced Polyetheretherketone (CF/PEEK) Towpregs

Abstract

Solvent-free, continuous manufacture of carbon-fiber/poly(ether ether ketone) (CF/PEEK) towpregs via fluidized-bed powder coating requires stable powder fluidization together with controllable coating residence time. A laboratory-scale continuous coating line comprising a creel, guiding/tension rollers, a vibrated fluidized-bed coater, as well as a take-up unit was designed and commissioned. Subsequently, a two-stage optimization and modeling framework was developed. First, PEEK powder fluidization was optimized using a Taguchi L9 design, varying air pressure ($P$), powder weight ($W$), and vibration frequency ($f$); bed expansion ratio ($\epsilon$) and average surface bubble diameter ${(D}_b)$ were measured and ANOVA identified air pressure as the primary contributor to $\epsilon$ (83.4%), establishing a stable operating window. Second, within this window, coating performance was assessed by varying line speed ($V_{line}$) and coating-roller position ($H_r$) in 12 runs and combining them into a geometry-based residence time ($R_t$) for simplified control. Coating quality was quantified based on fiber volume fraction ($Vf$) and composite tensile strength (${\mathsf{\sigma }}_c$) after consolidation. The best condition in the tested range was $Hr=0.5 \mathrm{c}\mathrm{m}$ and $V_{line}=1.5 \mathrm{m}/\mathrm{m}\mathrm{i}\mathrm{n}$ ($R_t=0.54 \mathrm{s}$), achieving 61.5% $Vf$ and 1800.5 MPa tensile strength. The resulting mathematical models predicted $Vf$ and ${\mathsf{\sigma }}_c$ with good accuracy ($R^2\ge 0.92$), supporting parameter selection and process optimization for continuous CF/PEEK towpreg production.

1. Introduction

Global energy demand continues to rise with industrialization and population growth, leading to increased fossil-fuel consumption and greenhouse-gas emissions [1]. This trend strengthens the need for lightweight, high-performance, and recyclable engineering materials to improve energy efficiency and reduce environmental impacts [2]. In transport applications, a 10% reduction in structural weight can reduce fuel consumption by approximately 6–8% [3,4].

Composite materials enable lightweight structures without sacrificing mechanical integrity, offering high specific strength and stiffness as well as good fatigue resistance [5,6,7,8,9]. Within lightweight structural applications, thermoplastic matrices are increasingly preferred due to their recyclability and their compatibility with continuous manufacturing routes. Among high-performance thermoplastics, poly(ether ether ketone) (PEEK) is particularly attractive as a matrix material due to its excellent thermal stability, chemical resistance, and long-term durability. The integration of PEEK’s superior properties into continuous carbon fiber-reinforced thermoplastics (CFRTPs) has resulted in high-performance composites that are gaining increasing attention for aerospace and energy-related components [10,11,12,13,14,15].

A persistent challenge in CFRTP manufacturing is achieving effective fiber–matrix interaction in a process-efficient manner. Although surface modification routes (e.g., plasma treatment, silane coating, chemical functionalization) can improve interfacial bonding, these approaches often require solvent use, multi-step processing and higher operational cost, which limits their environmental and economic sustainability [16,17,18,19,20]. In addition, conventional towpreg/impregnation approaches may involve solvent handling, high-temperature melt processing, or complex multi-stage processing sequences, motivating alternative solvent-free and continuous routes for CF/PEEK towpreg production [15,16,17,18,19,20].

Fluidized-bed powder coating (FBPC) offers an energy-efficient and environmentally favourable option due to its simple process structure and solvent-free operation [20,21]. In FBPC, polymer powders are fluidized by an upward gas flow, enabling coating of continuous fiber tows without solvents or volatile organic compounds (VOCs). However, process performance depends on the coupled behavior of (i) powder fluidization stability and (ii) tow–powder coating/retention. Fluidization is influenced by particle size, density, morphology, surface energy, gas velocity, bed geometry, air pressure and ambient humidity [22,23,24,25,26,27,28,29]. According to Geldart classification, Type A powders generally show stable fluidization, whereas fine/cohesive powders (Type C) tend to agglomerate, making stable fluidization more difficult [30,31]. Accordingly, numerous studies have investigated fluidization behavior and proposed experimental/theoretical descriptions for different powder systems [32,33,34,35,36]. On the coating side, residence time, line speed, gas temperature and flow conditions govern particle motion and fiber–powder interactions and thus affect coating uniformity and matrix adhesion [37,38,39,40].

Despite these studies, there is no integrated optimization framework that simultaneously addresses powder fluidization stability and tow kinematics during the coating process for continuous carbon fiber (CF)-reinforced poly(ether ether ketone) (PEEK) towpreg manufacturing. Many studies examine fluidization hydrodynamics and coating mechanics separately, which complicates precise control of fiber volume fraction and, consequently, the final mechanical performance. To address this gap, this study develops a lab-scale, solvent-free continuous production line for CF/PEEK towpregs and proposes a two-stage methodology. In Stage I, steady-state fluidization conditions for PEEK powder are optimized using a Taguchi L9 robust design, with bed expansion ratio ($\epsilon$) and average surface bubble diameter $(D_b)$ as response variables. In Stage II, coating performance is systematically evaluated by varying the line speed ($V_{line}$) and coating-roller position ($H_r$) under the optimized fluidization regime. The key novelty is the use of a single practical process descriptor, the coating residence time ($R_t$), derived from the coating-zone geometry to consolidate kinematic and geometric inputs for simplified process analysis and control. The main contributions of this work are as follows:

• Established a Taguchi-based operating window for stable PEEK powder fluidization using $\epsilon$ and $D_b$ as key response variables.
• Developed a coating-stage framework that links $V_{line}$ and $H_r$ to coating outcomes and tensile performance, and consolidating these inputs into a single derived descriptor, $R_t$, to facilitate practical process control.
• Experimentally validated the proposed process window and coating framework through mechanical testing and SEM-based microstructural observations.
• Propose an $R_t$-dependent coating formulation that is consistent with a potential vertical gradient in local solids holdup (powder concentration) within the fluidized bed, using $R_t$-derived coating uptake as the quantitative basis for model calibration.

2. Materials and Methods

2.1. Materials

Towpreg plies were produced by using the fluidized-bed powder coating technique. The composite material was prepared using a PEEK-based towpreg. PEEK 150PF powder (Victrex plc, Thornton-Cleveleys, UK) was used as the matrix, and T700SC-12000-60E continuous carbon fibers (Toray Industries, Inc., Tokyo, Japan) served as the reinforcement. The composite system consisted of a PEEK matrix and continuous CF reinforcement. The essential mechanical and physical properties of both constituents are presented in

Table 1. General properties of CF and PEEK.

Poly(ether ether ketone) (PEEK)			Carbon Fiber (CF)
Property	Unit	Nominal Value	Property	Unit	Nominal Value
Density	g/cm3	1.31	Density	g/cm3	1.8
Tensile Strength	MPa	100	Tensile Strength	MPa	4900
Tensile Modulus	GPa	4.1	Tensile Modulus	GPa	235
Melting Point	°C	343	Elongation	%	2.1
Average Particle Size ($D_{50}$)	µm	50	Filament Count	count	12,000

.

2.2. CFRTP Towpreg Fabrication and Fluidized-Bed System Description

The laboratory-scale continuous production line utilized in this study was developed and implemented at Mir Arastirma ve Gelistirme Inc., leveraging the company’s existing infrastructure and dedicated resources. The system (see Figure 1a) enables the production of continuous carbon fiber-reinforced thermoplastic (CFRTP) towpregs by coating carbon fibers with PEEK powder through a solvent-free fluidized-bed process. The system enabled controlled polymer deposition under continuous operation and consisted of sequential units designed to ensure stable fiber handling and uniform powder exposure. Carbon fibers were supplied from a tension-controlled creel at a constant 160 cN to maintain tow alignment and prevent undesired fluctuations. The 12 K tow then entered the spreading unit, where its width was increased to maximize surface accessibility before being directed toward the coating region. After spreading, the fibers were guided over roller 1 (Ø = 50 mm) and delivered to the entrance of the fluidized bed, where PEEK powder was fluidized by air passing through a distributor plate. Within this fluidized zone, suspended PEEK particles surrounded the tow and initiated the coating process. A coating roller ($d_r$, Ø = 12 mm) maintained the tow path inside the bed, controlled immersion geometry, and guided the coated fibers toward the outlet (see Figure 1b).

Upon exiting the fluidized bed, the coated towpregs were passed through a 100 cm long short-wave infrared (IR) heating zone to melt the deposited PEEK powder and promote its adhesion to the fiber tow. The heating system consisted of two opposing vertical arrays of quartz halogen short-wave IR lamps positioned along the heating zone, with four lamps on each side (eight lamps in total). Each lamp was rated at 1750 W and emitted radiation in the approximate wavelength range of 1.0–1.4 µm. The distance between the heater and the material surface was maintained at 56 mm. The residence time in the IR zone depended on $V_{line}$. The IR lamp power was adjusted to achieve complete melting of the deposited white powder layer, as indicated by the formation of a transparent molten coating on the tow surface. Under these conditions, the tow surface temperature was expected to exceed the melting temperature of PEEK ($T_m$ ≈ 343 °C). Once this condition was achieved, the lamp power setting was kept constant during sample collection. After IR heating, the pre-consolidated towpreg was continuously pulled at constant speed by a driven puller unit and wound onto bobbins, completing the continuous fabrication of CFRTP towpreg plies.

The geometry of the mechanically vibrated fluidized-bed system used for the fluidization and coating experiments is shown in Figure 2. The chamber had a rectangular cross-section of 22$\times$22 cm and a total fluidized-bed height of 50 cm ($H_{fb}$). A Miksan VA 4-80 DC vibration motor was installed beneath the air distributor to generate mechanical vibration, and its frequency was adjusted to examine its effect on fluidization stability. Figure 2a presents the main components of the system, including Roller 1, the coating roller, and the fluidized powder region, together with the geometric parameters required to characterize the coating process, such as fluidized powder height ($H_f$), the vertical distance between the center of the coating roller and the powder surface (coating roller position ($H_r$)), and the effective contact area ($A_e$). Figure 2b provides the geometric definition of the exposure path, where the total residence path ($X_r$) denotes the distance over which the fiber remained in contact with the fluidized powder. The initial exposure path ($X_{r1}$) is also shown, representing the region where the tow first encountered the powder before reaching Roller 1. This geometric configuration allowed for consistent determination of the process parameters and provided stable and repeatable conditions for fluidization and coating measurements.

2.3. Characterization of CF/PEEK Towpreg

The produced towpreg plies were consolidated into composite panels using a hot-pressing method under identical processing conditions. Each panel consisted of six plies measuring 5.6 mm × 250 mm. The plies were first joined by ultrasonic welding and then placed in a preheated press mold. The temperature was increased from room temperature to 400 °C at a rate of 5 °C/min, followed by a 40 min dwell period under a constant pressure of 120 bar. Cooling was performed to 100 °C at the same rate while maintaining the applied pressure. This controlled thermal cycle minimized residual stresses and ensured complete consolidation between adjacent layers. Six consolidated panels were produced for each experimental condition.

Tensile properties of the consolidated towpregs were measured using a Zwick/Roell Z250 (ZwickRoell GmbH & Co. KG, Ulm, Germany) universal testing machine equipped with a ZwickRoell makroXtens II extensometer (accuracy class 0.5 according to EN ISO 9513 [41]). Tensile tests were conducted at room temperature in accordance with ASTM D3039 [42]. Five specimens were tested for each condition using a preload of 20 N and a crosshead speed of 2 mm/min. Strain was measured directly over a 50 mm gauge length using the extensometer. Young’s modulus was determined from the secant slope of the stress–strain curve between predefined reference points in the test software. After reaching 1.5% strain, the measurement was switched to crosshead displacement for the remainder of the test. Because strain was measured directly over the gauge length, the influence of machine and grip compliance on modulus determination was minimized.

$Vf$ and void content ($Vv$) of the consolidated composites were determined using a combined gravimetric–densitometric approach. First, the fiber mass fraction ($w_f$) was determined in accordance with ASTM D3171 [43] by removing the PEEK matrix via an acid digestion method. Specifically, the composite samples were immersed in 20 mL of concentrated sulfuric acid (98% ${\mathrm{H}}_2\mathrm{S}{\mathrm{O}}_4$) and heated at 160 °C for 2 h. Following this initial digestion, hydrogen peroxide was added dropwise to complete the matrix dissolution. This chemical extraction procedure was specifically employed to effectively dissolve the highly resistant PEEK matrix without degrading the carbon fibers. $Vf$ was then calculated from $w_f$ and the constituent densities using Equation (1):

$$Vf={\displaystyle \frac{\frac{w_f}{{\rho }_f}}{\left(\frac{w_f}{{\rho }_f}\right)+\frac{\left(1-w_f\right)}{{\rho }_m}}}·100$$

(1)

The void-free theoretical composite density (${\rho }_{ct}$) was subsequently calculated using Equation (2) based on the measured fiber mass fraction:

$${\rho }_{ct}={\displaystyle \frac{1}{\left(\frac{w_f}{{\rho }_f}+\frac{1-w_f}{{\rho }_m}\right)}}$$

(2)

The measured composite bulk density (${\rho }_{cr}$) was determined using the liquid displacement (immersion) method in accordance with ASTM D792-20 [44] at 23 °C using distilled water. For each experimental condition, density was measured on six specimens (n = 6). The total $Vv$ was then determined using Equation (3) by comparing ${\rho }_{cr}$ with the void-free theoretical density (${\rho }_{ct}$) following the ASTM D2734 methodology [45]:

$$Vv \left(\%\right)=\left(1-{\displaystyle \frac{{\rho }_{cr}}{{\rho }_{ct}}}\right)·100$$

(3)

where $Vf$ is the fiber volume fraction (%), $w_f$ is the fiber mass fraction, ${\rho }_f$ and ${\rho }_m$ are the densities of the carbon fibers and PEEK matrix, respectively, ${\rho }_{ct }$ is the void-free theoretical composite density (g/cm³), and ${\rho }_{cr}$ is the measured composite bulk density (g/cm³). The constituent densities used in the calculations were ${\rho }_m=1.31 \mathrm{g}/{\mathrm{c}\mathrm{m}}^3$ for PEEK and ${\rho }_f=1.80 \mathrm{g}/{\mathrm{c}\mathrm{m}}^3$ for the carbon fibers (Table 1).

2.4. Experimental Set I: Optimization of PEEK Powder Fluidization Behavior

Experimental Set I aimed to identify a suitable operating window for fluidizing PEEK powder by evaluating the effects of key process variables in the mechanically vibrated fluidized bed. A Taguchi L9 orthogonal array was employed to systematically investigate the influence of air pressure ($P$), powder weight ($W$), and vibration frequency ($f$) on two response variables, namely bed expansion ratio ($\epsilon$) and average surface bubble diameter ($D_b$). Vibration frequency was included as an auxiliary process variable to assess its potential contribution to fluidization stability and powder mobility during continuous operation. Rather than defining the optimum condition on the basis of a single response, the final Stage I operating condition was selected through a combined evaluation of fluidization efficiency, bubble stability, and practical coating applicability. The experimental factors and their levels are listed in

Table 2. Design parameters for testing PEEK powder fluidization performance (with their levels).

Factor	Unit	Level 1	Level 2	Level 3
Air Pressure ($P$)	Bar	0.06	0.10	0.20
Powder weight (W)	gram (g)	1800	5400	7200
Vibration frequency ($f$)	Hertz (Hz)	0	25	50

, and the Taguchi matrix used in the trials is presented in

Table 3. Taguchi L9 orthogonal array of Experiment Set I (PEEK powder fluidization).

Experiment No	$\mathit{P}$	$\mathit{W}$	$\mathit{f}$
1.1	1	1	1
1.2	1	2	2
1.3	1	3	3
1.4	2	1	2
1.5	2	2	3
1.6	2	3	1
1.7	3	1	3
1.8	3	2	1
1.9	3	3	2

.

To obtain accurate measurements of $\epsilon$ and $D_b$, the transparent acrylic column was equipped with measurement scales that provided a reading resolution of 0.1 cm on the side walls and top surface. $\epsilon$ was determined from the settled bed height ($H_o$) and expanded bed height ($H_f$) using Equation (4). For each experimental condition, measurements were repeated six times (n = 6), and the reported values represent the average of these repetitions. $D_b$ images were captured through the top observation window using a high-resolution digital camera and $D_b$ was determined from image analysis using ImageJ (NIH, Bethesda, MD, USA; version 1.54r). For each experimental condition, three images were analyzed; the visible $D_b$ were identified on each image and their diameters were measured, and the mean $D_b$ value was calculated as the average of the measured $D_b$ in the analyzed images. This experimental design enabled a controlled and statistically robust assessment of the individual and combined effects of $P$, $W$, and $f$ on the fluidization behavior of PEEK powder.

$$\epsilon ={\displaystyle \frac{H_f}{H_o}}$$

(4)

In these expressions, $\epsilon$ denotes the bed expansion ratio, $H_f$ represents the expanded bed height, and $H_O$ indicates the settled bed height (cm).

Representative visual results comparing two fluidization conditions corresponding to the minimum and maximum $D_b$ values are presented in Figure 3. In this figure, the $D_b$ values are outlined with red dashed circles for clarity, and the mean $D_b$ was calculated from the measured bubble diameters identified in the selected images. The same image-analysis procedure was applied to all experimental conditions. Additional representative bubble detection results are provided in Figure S1. This image-analysis procedure provided repeatable measurements, allowing for reliable evaluation of how the process parameters influenced the fluidization behavior of PEEK powder.

2.5. Experiment Set II: Optimization and Modeling of the Coating Process

Experiment Set II was designed to investigate the influence of the coating process parameters, namely $V_{line}$ and $H_r$, on the coating/impregnation outcome and the mechanical performance of the resulting towpregs under the previously optimized fluidization conditions. In this set, the relationship between $Vf$ and ${\sigma }_c$ was also quantified to clarify how variations in fiber loading affected the overall tensile response of the CFRTP towpregs. First, $V_{line}$ was varied at six levels between 1.0 and 3.0 m/min while keeping $H_r$ constant at 0.5 cm (Runs 2.1–2.6). To examine the combined influence of increased roller submergence, additional trials were conducted at $H_r=3.0 \mathrm{c}\mathrm{m}$ using selected $V_{line}$ levels (Runs 2.7–2.9). Finally, the isolated effect of $H_r$ was evaluated by varying $H_r$ from 5.5 to 10.5 cm at a fixed $V_{line}$ of 1.5 m/min (Runs 2.10–2.12). In total, twelve experimental runs were performed under identical fluidization conditions, as summarized in

Table 4. Experimental design and coating parameters for Experiment Set II.

Exp. No.	${\mathit{V}}_{\mathit{l}\mathit{i}\mathit{n}\mathit{e}}$ (m/min)	${\mathit{H}}_{\mathit{r}}$ (cm)
2.1	1.0	0.5
2.2	1.2	0.5
2.3	1.5	0.5
2.4	2.0	0.5
2.5	2.5	0.5
2.6	3.0	0.5
2.7	1.0	3.0
2.8	1.5	3.0
2.9	2.0	3.0
2.10	1.5	5.5
2.11	1.5	8.0
2.12	1.5	10.5

. In order to ensure reproducibility of the coating performance results, each processing condition was repeated three times, and the reported values represent the average of the repeated measurements.

To provide a theoretical reference for the ideal composite response, the rule of mixtures was applied by assuming perfect interfacial bonding and complete load transfer between the fiber and the matrix. The ideal tensile strength of the composite (${\sigma }_{ic}$) was calculated using the rule-of-mixtures expression given in Equation (5) [46]. The corresponding tensile-strength efficiency (${\eta }_t$), which represents the percentage of the ideal performance achieved under the actual processing conditions, was calculated using Equation (6) based on the experimentally measured ${\sigma }_c$ and $Vf$ values obtained from the twelve runs in Experiment Set II.

$${\sigma }_{ic}={\sigma }_f·Vf+{\sigma }_m·\left(1-Vf\right)$$

(5)

$${\eta }_t \left(\%\right)={\displaystyle \frac{{\sigma }_c}{{\sigma }_{ic}}}·100$$

(6)

where ${\eta }_t$ denotes the tensile-strength efficiency, ${\sigma }_{ic}$ and ${\sigma }_c$ denote the theoretical and experimental composite tensile strengths, respectively, ${\sigma }_f$ and ${\sigma }_m$ are the tensile strengths of the fiber and the matrix (as given in Table 1), and $Vf$ is the fiber volume fraction.

To enable a more concise and unified evaluation of the coating process, the two independently controlled operational variables, namely $V_{line}$ and $H_r$, were combined into a single time-based derived parameter. In this context, $R_t$ was defined as the characteristic time during which the fiber bundle is exposed to the fluidized powder environment within the effective contact region. The residence distance ($X_r$) used to calculate $R_t$ was derived from the geometric configuration shown in Figure 2b using similarity relations. In developing the model, the fluidized powder surface was assumed to be planar, and a 180° wrap/contact around the coating roller was assumed. In addition, the spread width of the fiber bundle was considered constant throughout production, while the effects of fiber thickness and surface roughness were neglected in the geometric representation. Under these assumptions, $X_r$ and the corresponding $R_t$ are given by Equations (7) and (8), respectively.

$$X_r=H_r+{\displaystyle \frac{\pi ·d_r}{2}}+X{r}_1=(H_r)+({\displaystyle \frac{\pi ·d_r}{2}})+(\sqrt{\left({\left({\displaystyle \frac{16.20·H_r}{H_r+17.60}}\right)}^2+{H_r}^2\right)})$$

(7)

$$R_t\left(s\right)={\displaystyle \frac{X_r}{V_{line}}}· {\displaystyle \frac{\left(60 \mathrm{s}\right)}{\left(100 \mathrm{c}\mathrm{m}\right)}}$$

(8)

where $X_r$ denotes the residence distance (cm), $d_r$ is the diameter of the coating roller (cm), $R_t$ represents the residence time (s), $V_{line}$ is the line speed (m/min), and $H_r$ denotes coating roller position (vertical distance between the center of the coating roller and the powder surface).

3. Results and Discussion

3.1. Optimization of Fluidization Behavior and Morphological Characterization of PEEK Powder

The fluidization performance of PEEK powder was evaluated using the Taguchi L9 design described in Section 2.4. The influences of $P$, $f$, and $W$ on $\epsilon$ and $D_b$ were examined to identify a suitable Stage I fluidization window for subsequent coating trials. The experimental matrix and corresponding response values are given in

Table 5. Taguchi L9 design and fluidization results for PEEK powder (Set I).

Ex. No	Air Pressure ($\mathit{P}$, bar)	Vibration Frequency ($\mathit{f}$, Hz)	Powder Weight ($\mathit{W}$, g)	Settled Bed Height (${\mathit{H}}_{\mathit{o}}$, cm)	Expanded Bed Height (${\mathit{H}}_{\mathit{f}}$, cm)	Bed Expansion Ratio ($\mathsf{\epsilon }$)	Average Surface Bubble Diameter (${\mathit{D}}_{\mathit{b}}$, mm)
1.1	0.06	0	1800	6.25	10.0	1.60	7.32
1.2	0.06	25	5400	18.75	31.1	1.66	6.96
1.3	0.06	50	7200	25.00	44.0	1.76	6.82
1.4	0.10	0	5400	18.75	33.4	1.78	21.48
1.5	0.10	25	7200	25.00	46.3	1.85	41.18
1.6	0.10	50	1800	6.50	11.0	1.76	5.98
1.7	0.20	0	7200	25.00	48.0	1.92	55.08
1.8	0.20	25	1800	6.25	11.5	1.84	9.27
1.9	0.20	50	5400	18.75	35.5	1.90	32.75

, while the signal-to-noise (S/N) ratios and ANOVA results used to quantify the significance of each parameter are presented in Figure 4a,b and

Table 6. ANOVA and S/N ratio results from the Taguchi L9 analysis for PEEK powder fluidization (Set I).

Model Summary of Bed Expansion Ratio ($\mathsf{\epsilon }$)				Model Summary of Average Surface Bubble Diameter (${\mathit{D}}_{\mathit{b}}$, mm)
R-sq		0.99		R-sq		0.98
Analysis of Variance of $\epsilon$				Analysis of Variance of $D_b$
Source	DF	Contribution (%)	p-Value	Source	DF	Contribution (%)	p-Value
$P$	2	83.41	0.01	$P$	2	52.73	0.071
$f$	2	1.34	0.01	$f$	2	3.01	0.571
$W$	2	15.22	0.001	$W$	2	40.21	0.091
Error	2	0.03	-	Error	2	4.05	-
Total	8	100	-	Total	8	100	-

.

The Taguchi L9 analysis revealed clear trends in the influence of process parameters on $\epsilon$ and $D_b$. The “larger-the-better” criterion was used for $\epsilon$, since higher $\epsilon$ improves fluidization efficiency, reduces local powder density, and supports a greater fiber fraction during coating. Under this criterion, the effect of $f$ on the S/N ratio was minimal, whereas increases in $P$ and $W$ led to substantial improvements in fluidization performance, as shown in Figure 4a. Based on $\epsilon$ alone, the condition associated with the highest bed expansion was $P=0.20 \mathrm{b}\mathrm{a}\mathrm{r}$, $W=7200 \mathrm{g}$, and $f=50 \mathrm{H}\mathrm{z} (\mathrm{E}\mathrm{x}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t} 1.7)$. ANOVA results (Table 6) confirmed that $P$ was the dominant factor, accounting for 83.4% of the total variance (p < 0.05), followed by $W$ (15.2%). Although $f$ also had a statistically significant effect on $\epsilon$ (p = 0.01), its contribution remained limited (1.3%), indicating that its effect was secondary in practical terms. The high coefficient of determination ($R^2=0.99$) demonstrated excellent agreement between the predictive model and experimental measurements.

The “smaller-the-better” criterion was applied to $D_b$ because large bubbles generate strong internal turbulence, which leads to unstable fluidization and non-uniform powder deposition. As shown in Figure 4b, $D_b$ decreased with increasing $f$ and with reductions in both $P$ and $W$. Across the experimental domain, $D_b$ exhibited a wide response range (6.82–55.08 mm), highlighting the strong sensitivity of bubble behavior to operating conditions. Based on $D_b$ alone, the lowest average bubble diameter was obtained at $P=0.06$ bar, $W=7200$ g, and $f=50$ Hz (Experiment 1.6).

The ANOVA results (Table 6) indicated that $P$ (52.7%) and $W$ (40.2%) were the primary contributors to $D_b$, while $f$ accounted for only a minor portion of the variation (3.0%). Unlike the statistically significant but practically limited effect of $f$ on $\epsilon$, the influence of vibration frequency on $D_b$ remained statistically non-significant (p = 0.571), indicating that $f$ did not play a decisive role in controlling bubble diameter within the investigated range. Although the obtained p-values for $P$ (p = 0.071) and $W$ (p = 0.091) slightly exceeded the conventional 0.05 threshold for statistical significance, these results should be interpreted in the context of the inherently dynamic and stochastic nature of bubble formation in fluidized beds. In such systems, bubbles are not static structures; rather, they continuously undergo processes of formation, growth, coalescence, and fragmentation. This dynamic behavior inherently leads to natural temporal variability in the measured bubble diameters. Previous imaging and signal analysis studies have shown that bubbles of varying sizes pass through the same observation plane over time, and that the bubble size distribution continuously evolves under the competing mechanisms of coalescence and fragmentation [47,48,49]. Furthermore, since bubbles are three-dimensional structures but are typically evaluated using two-dimensional imaging techniques, this methodological limitation also contributes to variability in the measured diameters [47]. Despite the slightly elevated p-values, the high coefficient of determination ($R^2=0.98$), the low residual error (4.05%), and the substantial contribution ratios (52.7% and 40.2%) indicated that $P$ and $W$ were the main physical contributors to bubble behavior within the investigated parameter range.

Increasing $P$ from 0.06 to 0.20 bar caused a substantial rise in gas density, which in turn increased the drag force acting on the particles. As a direct result of this stronger drag, the bed expanded by approximately 20% (from 1.60 to 1.92), indicating improved fluidization. At the same time, the higher gas density and volumetric flow rate intensified bubble coalescence, which led to a nearly eightfold increase in $D_b$. These pressure-dependent effects are consistent with trends reported for Geldart Group A materials by Chitester et al. [50] and Sidorenko and Rhodes [51]. The PEEK powder used in this study, with an average particle size of about 50 µm, also belongs to Group A, and therefore exhibits behavior similar to that observed in previous studies. Verma et al. [52] likewise showed that elevated pressure strengthens gas–solid interactions, thereby promoting rapid bubble growth. Consequently, although higher pressure improved fluidization quality by enhancing $\epsilon$, it simultaneously generated excessively large bubbles, ultimately reducing coating uniformity at the upper pressure range.

Increasing the vibration frequency ($f$) had a limited but positive effect on fluidization stability by improving gas distribution and reducing channeling within the bed. According to the Taguchi L9 analysis, the statistical contribution of $f$ to $\epsilon$ was limited to 1.31% (p = 0.01), indicating that its effect was statistically significant but practically minor within the experimental window. The applied vibration likely increased particle mobility and promoted a more uniform gas flow, contributing to smoother bed expansion and more consistent fluidization behavior. In addition, $D_b$ decreased by approximately 3% with increasing $f$, suggesting that vibration may have helped suppress bubble coalescence and stabilize gas–solid interactions. Similar stabilizing trends in $\epsilon$ and $D_b$ have been reported by Zhao et al. [53] and Guo et al. [54].

Although the statistical contribution of $f$ was limited within the selected conditions, vibration was retained in the system as a supportive stabilization measure rather than as a primary performance-driving variable. Its effect on the main response variables remained small; however, it helped reduce cohesive powder effects and channel formation, thereby promoting more uniform gas–solid interactions and more repeatable fluidization behavior during continuous operation. Because these benefits were achieved with relatively low additional energy input and minimal mechanical complexity, the use of vibration was considered a practical and cost-effective way to support process stability.

The influence of powder weight ($W$) on fluidization performance was much more pronounced than that of $f$. Increasing $W$ intensified gas–solid interactions within the denser bed, which improved fluidization behavior and increased $\epsilon$ by approximately 10%. A similar enhancement in $\epsilon$ was reported by Musademba and Prabhansu [55], where doubling the static bed height from 60 mm to 120 mm resulted in a 16% increase in $\epsilon$. However, higher powder loading simultaneously promoted stronger bubble coalescence, producing a substantial increase in $D_b$. In the present study, $D_b$ increased by about 65%, indicating a deterioration in fluidization uniformity at elevated $W$ levels. This observation is consistent with the ≈66% rise reported by Shi et al. [56], where larger static bed heights intensified bubble coalescence within deeper and denser fluidized regions.

The regression models developed for both $\epsilon$ and $D_b$ showed excellent agreement with the experimental measurements, with coefficients of determination exceeding 0.95. This confirmed that the selected process variables, namely $P$, $W$, and $f$, could be used to adequately control the fluidization behavior of PEEK powder. However, the parameter levels associated with maximum $\epsilon$ did not coincide with those yielding minimum $D_b$, indicating a clear trade-off between fluidization efficiency and bubble stability. Therefore, the final Stage I operating conditions were not selected on the basis of $\epsilon$ or $D_b$ alone. Instead, $\epsilon$, $D_b$, and coating requirements were considered together to identify the most suitable operating window for the subsequent coating experiments. On this basis, $P=0.06 \mathrm{b}\mathrm{a}\mathrm{r}$, $W=7200 \mathrm{g}$, and $f=50 \mathrm{H}\mathrm{z}$ (Experiment 1.3) were selected as the most suitable Stage I operating conditions for the subsequent coating experiments. Under these conditions, a balanced combination of bed expansion and bubble stability was obtained, with $\epsilon =1.76$ and $D_b$ = 6.82 mm. In addition, the high $W$ ensured sufficient active powder availability for continuous coating, while the high $f$ provided a limited but beneficial contribution to fluidization stability by reducing the cohesive behavior of the PEEK powder.

3.2. Experimental Set II: Optimization of Fluidized-Bed Coating Process Performance

Consolidated composite specimens produced in Experimental Set II were evaluated to characterize their mechanical, physical, and microstructural properties under various coating conditions. Mechanical performance was determined from the ${\mathsf{\sigma }}_c$ and elastic modulus ($E$). The corresponding ${\mathsf{\sigma }}_c$ and $E$ values for the specimens are shown in Figure 5. Consolidation quality, fiber packing, and the extent of interfacial impregnation were assessed through $Vf$ and $Vv$. These critical physical parameters were determined by comparing the experimentally measured composite bulk density (${\rho }_{cr}$) with the void-free theoretical density (${\rho }_{ct}$). Tensile-strength efficiency (${\eta }_t$) was also determined to quantify the effectiveness of stress transfer between the fibers and the PEEK matrix.

The results are presented in

Table 7. Tensile strength, density, and fiber volume fraction of towpreg composites (Set II).

Exp. No.	${\mathit{V}}_{\mathit{l}\mathit{i}\mathit{n}\mathit{e}}$ (m/min)	${\mathit{H}}_{\mathit{r}}$ (cm)	${\mathit{R}}_{\mathit{t}}$ (s)	${\mathsf{\sigma }}_{\mathit{c}}$ (MPa)	$\mathit{E}$ (GPa)	${\mathsf{\rho }}_{\mathit{c}\mathit{t}}$ (g/cm3)	${\mathsf{\rho }}_{\mathit{c}\mathit{r}}$ (g/cm3)	$\mathit{V}\mathit{v}$ (%)	$\mathit{V}\mathit{f}$ (%)	${\mathsf{\eta }}_{\mathit{t}}$ (%)
2.1	1.0	0.5	0.82	1380.6 ± 28.1	85.5 ± 3.0	1.573 ± 0.008	1.509 ± 0.011	4.10 ± 0.85	53.73 ± 1.63	51.5 ± 1.8
2.2	1.2	0.5	0.68	1530.8 ± 30.2	106.0 ± 3.5	1.597 ± 0.009	1.528 ± 0.006	4.32 ± 0.66	56.24 ± 1.84	54.7 ± 2.0
2.3	1.5	0.5	0.54	1800.5 ± 43.1	108.0 ± 3.3	1.612 ± 0.004	1.536 ± 0.009	4.71 ± 0.61	61.57 ± 0.82	58.9 ± 1.6
2.4	2.0	0.5	0.41	1581.2 ± 35.3	87.0 ± 3.5	1.631 ± 0.009	1.551 ± 0.006	4.89 ± 0.64	65.57 ± 1.84	48.7 ± 1.7
2.5	2.5	0.5	0.33	1426.6 ± 37.2	82.0 ± 3.8	1.647 ± 0.010	1.566 ± 0.008	4.92 ± 0.75	68.72 ± 2.04	42.0 ± 1.6
2.6	3.0	0.5	0.27	1268.8 ± 34.5	76.4 ± 4.1	1.654 ± 0.010	1.571 ± 0.007	5.02 ± 0.71	70.16 ± 2.02	36.6 ± 1.4
2.7	1.0	3.0	4.20	1103.8 ± 28.8	64.2 ± 2.9	1.521 ± 0.006	1.458 ± 0.013	4.12 ± 0.93	43.16 ± 1.22	50.8 ± 1.9
2.8	1.5	3.0	2.80	1231.7 ± 32.1	76.4 ± 2.7	1.543 ± 0.008	1.474 ± 0.012	4.50 ± 0.92	47.58 ± 1.63	51.7 ± 2.2
2.9	2.0	3.0	2.10	1118.9 ± 34.2	84.0 ± 2.7	1.563 ± 0.010	1.491 ± 0.011	4.63 ± 0.93	51.65 ± 2.03	43.4 ± 2.1
2.10	1.5	5.5	4.96	1080.6 ± 27.0	66.0 ± 2.3	1.514 ± 0.006	1.452 ± 0.009	4.07 ± 0.71	35.85 ± 1.35	59.3 ± 1.9
2.11	1.5	8.0	7.06	963.1 ± 20.7	47.9 ± 2.1	1.449 ± 0.004	1.387 ± 0.008	4.25 ± 0.61	28.36 ± 0.71	65.9 ± 2.3
2.12	1.5	10.5	9.12	838.7 ± 19.3	45.2 ± 2.7	1.428 ± 0.009	1.371 ± 0.007	4.02 ± 0.78	24.12 ± 1.84	66.7 ± 4.5

, which compares ${\mathsf{\sigma }}_c$, $E$, ${\rho }_{ct}$, ${\rho }_{cr}$, $Vf$, $Vv$, and ${\eta }_t$ for different combinations of $V_{line}$, $H_r$, and $R_t$. In this dataset, $R_t$ represents the effective duration of fiber exposure within the fluidized bed and is directly governed by $V_{line}$ and $H_r$. SEM imaging was performed on selected specimens to examine surface morphology and coating uniformity, providing complementary insight into the relationships among $R_t$, $Vf$, and $Vv$, and the resulting mechanical performance of the powder-coated composite. The original unprocessed SEM micrographs corresponding to Figure 6 are provided in Figure S2 to ensure transparency of the image-processing procedure.

Experimental Set II, consisting of twelve individual coating trials, was analyzed using multiple regression to determine the effects of $V_{line}$ and $H_r$ on ${\mathsf{\sigma }}_c$ and $Vf$ of the towpreg composites. To examine whether interaction effects between the process parameters contributed meaningfully to the coating response, extended second-order regression models including quadratic and interaction terms were initially constructed, and the corresponding statistical results are presented in the Supplementary Materials (Table S1). The interaction term ($V_{line}·H_r$) showed a very limited contribution for both responses, remaining low for ${\mathsf{\sigma }}_c$ (1.47%) and negligible for $Vf$ (0.01%) while also being statistically insignificant in both cases (p = 0.343 for ${\mathsf{\sigma }}_c$ and p = 0.915 for $Vf$). These findings indicate that inclusion of the interaction term ($V_{line}·H_r$) did not provide sufficient additional explanatory improvement within the investigated design space to warrant its retention in the final empirical models.

Therefore, the regression structure was simplified by excluding the interaction term while retaining the main and quadratic terms that contributed to model adequacy and interpretability. The final empirical models are given in Equations (9) and (10), where Equation (9) corresponds to ${\mathsf{\sigma }}_c$ and Equation (10) corresponds to $Vf$, and the associated ANOVA results are presented in

Table 8. Regression and ANOVA results for coating process (Experiment II).

Regression Equation for ${\mathsf{\sigma }}_{\mathit{c}}$				Regression Equation for $\mathit{V}\mathit{f}$
${\mathsf{\sigma }}_c=578+1306·V_{line}-109.9·H_r-361{V_{line}}^2+2.27{H_r}^2$ (9)				$Vf=51.15+7.34·V_{line}-3.8·H_r$ (10)
R-sq		0.92		R-sq		0.98
R-sq (adj)		0.88
S		116.399		S		2.53
Analysis of Variance (${\mathsf{\sigma }}_c$)				Analysis of Variance ($Vf$)
Source	DF	Contribution (%)	p-Value	Source	DF	Contribution (%)	p-Value
Regression	4	92.02	0.002	Regression	2	98.19	0.02
$V_{line}$	1	0.18	0.03	$V_{line}$	1	26.21	0.01
$H_r$	1	78.59	0.042	$H_r$	1	71.98	0.01
${V_{line}}^2$	1	12.86	0.02	${V_{line}}^2$	$-$	$-$	$-$
${H_r}^2$	1	0.39	0.606	${H_r}^2$	$-$	$-$	$-$
Error	7	7.98	-	Error	9	1.81	$-$
Total	11	100.00	-	Total	11	100.00	$-$

. The reduced models showed good agreement with the experimental data ($R^2=0.92$ for ${\mathsf{\sigma }}_c$ and $R^2=0.98$ for $Vf$), indicating that the coating behavior within the investigated operating window could be adequately interpreted using the retained regression terms. Accordingly, all subsequent interpretations of process behavior were based on the reduced regression models, in which, the interaction term was excluded and the remaining terms were retained according to their contribution to model adequacy and interpretability.

ANOVA results (Table 8) confirmed that both factors were statistically significant (p < 0.05). For ${\mathsf{\sigma }}_c$, $H_r$ was the dominant contributor, explaining 78.59% of the total variance, whereas the linear effect of $V_{line}$ was minimal (0.18%, p = 0.03). In contrast, the quadratic term of $V_{line}$ (12.86%, p = 0.02) was significant, revealing a nonlinear relationship between $V_{line}$ and ${\mathsf{\sigma }}_c$ that produced an optimum region rather than a proportional trend. The quadratic term of $H_r$ (0.39%, p = 0.606) was not significant, indicating that ${\mathsf{\sigma }}_c$ varied linearly with immersion depth within the studied range. For the $Vf$ model, $V_{line}$ contributed positively (26.21%), whereas $H_r$ had a negative influence (71.98%). These trends were consistent with the Pareto charts in Figure 7a,b, confirming that both parameters exerted substantial and independent effects on coating performance and the resulting mechanical response.

$V_{line}$ had a pronounced influence on coating behavior and, consequently, on the mechanical performance of the CF/PEEK towpregs. As shown in Figure 8a, ${\sigma }_c$ increased with $V_{line}$ up to an optimum value, whereas $Vf$ continued to rise across the entire investigated range. At the lowest $V_{line} ($1.0 m/min, $R_t=0.82 \mathrm{s}$), the extended $R_t$ in the fluidized bed led to excessive PEEK deposition, producing a thick polymer-rich coating and a reduced fiber fraction ($Vf=53.7\mathrm{\%}$; ${\sigma }_c=1380.6 \mathrm{M}\mathrm{P}\mathrm{a}$). Because the extended exposure allowed the polymer to fully encapsulate the fiber bundle, the measured bulk density (${\rho }_{cr}$) approached the theoretical limit (${\rho }_{ct}$), resulting in a minimal $Vv$. However, the excessive matrix volume limited the specific load-bearing capacity of the composite. Increasing $V_{line}$ to 1.5 m/min ($R_t=0.54 \mathrm{s}$) improved coating uniformity and fiber impregnation, resulting in a denser and more homogeneous fiber distribution without drastically increasing internal voids. SEM observations (Figure 6a) supported this transition, showing smoother and more continuous coating layers with improved fiber wetting and interfacial contact. These microstructural features coincided with the highest ${\mathsf{\sigma }}_c$ (1800.5 MPa) and $Vf$ (61.5%) values, consistent with the nonlinear relationship between $V_{line}$ and mechanical response identified in the regression model. A similar upward trend in $Vf$ and ${\mathsf{\sigma }}_c$ at moderate $V_{line}$ values was reported by Celik et al. [57], reinforcing the observed improvement up to the optimum region.

When $V_{line}$ was increased to 3.0 m/min ($R_t=0.27 \mathrm{s}$), the significantly shortened exposure time reduced matrix infiltration and produced very dense fiber packing, which resulted in incomplete impregnation and discontinuous coating layers. The corresponding SEM image (Figure 6b) showed pronounced voids and partially exposed fibers, indicating that insufficient wetting at higher speeds weakened interfacial bonding. Under these conditions, the combination of a high fiber volume fraction ($Vf=70.2\mathrm{\%}$) and limited exposure time restricted both the available space and duration for polymer penetration between adjacent filaments, leading to poor resin flow and an increased number of unimpregnated regions. These microstructural deficiencies disrupted fiber–matrix continuity and lowered the efficiency of stress transfer, directly contributing to the reduction in tensile performance. Overall, the morphological observations demonstrate that, although they result in higher tighten fiber packing, excessively elevated speeds restrict coating contact time, hinder impregnation, and diminish the mechanical efficiency of CF/PEEK composites. This behavior is also related to the limited melt mobility of PEEK, which restricts polymer penetration between densely packed filaments and reduces effective stress transfer across the fiber–matrix interface.

In contrast to the behavior observed for $V_{line}$, $H_r$ exerted a consistently negative influence on both ${\mathsf{\sigma }}_c$ and $Vf$, as shown in Figure 8b. ANOVA results confirmed that $H_r$ was the dominant factor, explaining 78.59% of the variance in ${\mathsf{\sigma }}_c$ and 71.98% of the variance in $Vf$. Increasing $H_r$ placed the fibers deeper within the fluidized bed, thereby extending $R_t$ and promoting excessive polymer deposition. This led to a marked decline in tensile performance together with a substantial reduction in $Vf$. This trend is further supported by the fracture surface analysis shown in Figure 6 for different $H_r$ conditions. In particular, Figure 6a,c represent specimens produced at the same $V_{line}$ (1.5 m/min) but at different $H_r$ values, namely $H_r$ $=0.5 \mathrm{c}\mathrm{m}$ and $H_r$ $=10.5 \mathrm{c}\mathrm{m}$, respectively. This direct comparison shows that increasing $H_r$ led to greater matrix accumulation around the fibers and the formation of thicker polymer-rich regions. Consistent with this observation, $Vf$ decreased from 61.57% in Figure 6a to 24.12% in Figure 6c, while ${\mathsf{\sigma }}_c$ dropped from 1800.5 MPa to 838.7 MPa. The SEM micrograph in Figure 6c clearly shows dense polymer agglomeration surrounding the fibers, confirming that excessive immersion depth promoted overcoating and reduced the effective load-bearing contribution of the fiber phase. A comparable trend was reported by Barletta and Tagliaferri [58], who showed that extended coating duration increased film thickness from 25 μm to 45 μm, indicating that prolonged exposure enhances powder deposition and matrix buildup, in agreement with the behavior observed in the present study.

One of the primary objectives of this study was to determine the coating conditions that maximized the tensile performance of CF/PEEK towpregs while preserving a relatively low-density structure. The multiple regression analysis provided a reliable predictive framework, demonstrating that $V_{line}$ and $H_r$ were strongly correlated with the mechanical response. The model indicated an optimum $V_{line}$ of approximately 1.82 m/min at $H_r=0.5 \mathrm{c}\mathrm{m}$, corresponding to a predicted tensile strength of 1682 MPa. Experimentally, the highest tensile strength value of 1800.5 MPa was obtained at $V_{line}=1.5 \mathrm{m}/\mathrm{m}\mathrm{i}\mathrm{n}$ and $H_r=0.5 \mathrm{c}\mathrm{m}$, showing close agreement with the predicted optimum. The deviation of approximately 6.5% was considered acceptable, indicating that the regression model adequately captured the dominant process behavior within the investigated operating window.

3.2.1. $Vf$–${\sigma }_c$–${\eta }_t$ Association in Thermoplastic Composites

The coating quality and mechanical performance of the CF/PEEK composites were evaluated using the results of Experimental Set II (Table 7), with particular focus on the relationship among $Vf$, ${\sigma }_c$, $Vv$, and ${\eta }_t$. Both $Vf$ and ${\sigma }_c$ increased with increasing $V_{line}$ and reached their highest values in Exp. 2.3, where $Vf=61.57\%$ and ${\sigma }_c=1800.5 \mathrm{M}\mathrm{P}\mathrm{a}$ were obtained. This condition was considered to provide the most favorable balance between fiber reinforcement and matrix continuity, thereby enabling more effective stress transfer within the composite structure. At fiber contents above this level, the mechanical performance decreased, although $Vf$ continued to increase. When $Vf$ reached 70.16% (Exp. 2.6), ${\sigma }_c$ and ${\mathsf{\eta }}_t$ decreased to 1268.8 MPa and 36.6%, respectively. This behavior indicated that further fiber packing did not improve reinforcement efficiency; instead, excessive fiber crowding reduced the matrix availability required for effective impregnation and interfacial bonding. The void data supported this interpretation, showing that $Vv$ increased from 4.10% to 5.02%, which indicated that the highly viscous PEEK melt could not fully displace entrapped air within the fiber bundle. These results showed that increasing fiber fraction alone did not guarantee improved tensile performance once impregnation became restricted by matrix flow and pore retention.

The optimum fiber volume fraction identified in this study was consistent with thermoplastic composite systems reported in the literature, where tensile strength reached a maximum within an intermediate fiber-content range rather than at the highest attainable $Vf$. Previous studies reported optimum $Vf$ values of approximately 69% for CF/PPS, 64% for GF/PPS, and 56% for GF/HDPE systems, while powder-coated carbon fiber systems similarly showed peak performance near 60% $Vf$ [57,59]. These observations indicated that composite performance depended not only on fiber content, but also on maintaining sufficient matrix continuity to enable effective stress transfer between adjacent filaments. Accordingly, the optimum mechanical condition in the present CF/PEEK system was not identified as the point of maximum $Vf$ or maximum ${\mathsf{\eta }}_t$, but as the condition at which fiber content, matrix continuity, and impregnation quality were most effectively balanced.

Although ${\mathsf{\eta }}_t$ theoretically reaches 100% when the intrinsic tensile strength of the fibers is fully utilized under ideal load-transfer conditions, the experimental results showed that the maximum ${\mathsf{\eta }}_t$ remained well below this limit. The highest ${\mathsf{\eta }}_t$ value (66.7%) was obtained at the lowest $Vf$ level (24.12%), where ${\sigma }_c$ was relatively low (838.7 MPa). Since ${\mathsf{\eta }}_t$ is normalized by $Vf$, lower fiber contents yielded higher apparent efficiency because of improved wetting and reduced fiber–fiber interaction, even though the overall load-bearing capacity remained limited. The highest ${\sigma }_c$ value (1800.5 MPa) was obtained at $Vf=61.57\%$, corresponding to ${\mathsf{\eta }}_t=58.9\%$.

In the ideal rule-of-mixtures framework, ${\eta }_t=100\%$ corresponds to full utilization of the intrinsic fiber tensile strength under perfect stress transfer, complete impregnation, and ideal fiber alignment. In real thermoplastic composite systems, however, such conditions are rarely achieved because the tensile response is influenced by process-dependent factors such as incomplete wetting, residual porosity, imperfect fiber alignment, and interfacial limitations. For this reason, deviations from the ideal rule-of-mixtures response have often been interpreted in the literature using empirical efficiency terms or modified formulations that account for processing-induced limitations [60,61]. In the present study, ${\mathsf{\eta }}_t$ was therefore discussed not as a direct correction factor, but as an empirical indicator of how far the actual composite response remained from the ideal theoretical load-transfer condition within the investigated processing window. On this basis, the deviation was interpreted through the combined influence of microstructural and processing-related factors.

The difference between the theoretical and experimental ${\mathsf{\eta }}_t$ was attributed to the combined influence of several microstructural and processing-related constraints. First, incomplete impregnation within the fiber bundle limited the effective transfer of stress from the matrix to the fibers, particularly at elevated $Vf$ levels where matrix availability became insufficient. Second, the measured void content ($Vv=4.02–5.02\%$) and the SEM observations in Figure 6 indicated the presence of entrapped air and local discontinuities in matrix continuity, both of which reduced the effective interfacial contact area. Third, imperfect fiber alignment within the towpreg structure reduced axial load transfer, especially at higher $Vf$ values where increased fiber–fiber interactions promoted local waviness and stress concentration. The high melt viscosity of PEEK was another factor that limited impregnation efficiency by restricting polymer flow during consolidation and hindering complete penetration of the matrix into densely packed fiber bundles.

In this context, higher processing temperatures can reduce the melt viscosity of PEEK, thereby facilitating matrix flow and improving penetration into the fiber bundle. Such an effect can enhance wetting, reduce entrapped porosity, and improve interfacial continuity, provided that the thermal exposure remains within a controlled processing window. Similar behavior was reported for CF/PEEK composites processed under high-viscosity conditions, where limited impregnation reduced stress transfer and tensile efficiency [62,63,64]. Previous studies also showed that optimized consolidation pressure, controlled thermal history, and vacuum-assisted densification improved interfacial bonding and reduced porosity in thermoplastic composites [65,66]. Taken together, these results showed that the observed ${\mathsf{\eta }}_t$ response was governed by the combined effects of impregnation quality, residual porosity, fiber alignment, and viscosity-controlled matrix flow.

3.2.2. Effect of Residence Time on Fiber Volume Fraction

Expressing the results from all twelve experiments in Set II as a function of Rt revealed a clear inverse relationship between $R_t$ and $Vf$. $Vf$ increased at short $R_t$ values and decreased progressively as $R_t$ became longer. This trend was most evident at the extremes, ranging from a maximum $Vf$ of 70.16% at $R_t$ $= 0.27 \mathrm{s}$ to 24.12% at $R_t= 9.12 \mathrm{s}$. This behavior is consistent with the findings of Barletta and Tagliaferri [51], who reported that shorter particle–fiber interaction times generally result in reduced polymer deposition and therefore higher $Vf$ values in fluidized-bed coating systems. A polynomial fit of the full dataset yielded R² = 0.92 (Figure 9a), indicating that the $R_t$-based formulation successfully captures the overall coating response.

However, the $R_t$–$Vf$ relationship did not follow a purely linear trend but instead exhibited a pronounced polynomial form. While $R_t$ governs the duration of particle–fiber interaction, the observed curvature indicates that additional physical factors influence the coating process. To examine this behavior more clearly, a controlled subset of five experiments was analysed separately, where $V_{line}$ was kept constant at 1.5 m/min and only Hr was varied (0.5–10.5 cm). This subset produced $R_t$ values between 0.54 and 9.12 s and corresponding $Vf$ values between 61.57% and 24.12%, resulting in an almost perfect quadratic fit (R² = 0.99, Figure 9b). The improved fit confirms that $R_t$ remains a governing parameter for polymer deposition, but also indicates that $R_t$ alone does not fully explain the non-linear response observed in the full dataset.

A spatially non-uniform particle concentration within the fluidized bed provides a plausible explanation for the observed deviation from linear behavior. Fibers positioned deeper in the bed are exposed to regions of higher particle concentration, which increases the frequency of particle–fiber interactions and promotes greater polymer deposition, leading to lower $Vf$ values. In contrast, fibers located closer to the upper region of the bed encounter fewer particles and therefore experience reduced coating intensity, resulting in higher $Vf$ values. This interpretation is consistent with the microstructural differences observed in Figure 6 and agrees with the height-dependent behavior reported by Oshitani et al. [67].

Accordingly, the polynomial $R_t$–$Vf$ relationship is attributed not only to particle exposure time, but also to vertical variations in local powder concentration within the fluidized bed. These results indicate that $R_t$ provides a physically meaningful parameter for describing coating behavior while the non-linear response reflects the combined influence of exposure duration and spatial variations in particle distribution.

4. Conclusions

A continuous CF/PEEK towpreg coating line based on solvent-free fluidized-bed powder coating was established, and the key process variables affecting towpreg quality and process control were systematically evaluated and simplified through a two-stage experimental approach: Stage I optimized PEEK powder fluidization, while Stage II quantified the effects of $V_{line}$ and $H_r$ on $Vf$ and ${\mathsf{\sigma }}_c$, and introduced $R_t$ as a single practical descriptor of the coating conditions. The main conclusions are summarized as follows:

• Optimization of fluidization performance: The fluidization behavior of PEEK powders was successfully optimized by adjusting $P$, $W, \mathrm{a}\mathrm{n}\mathrm{d} f$. ANOVA results showed that $P$ and $W$ dominated bed hydrodynamics, accounting for 83.4% and 15.2% of the variation in $\epsilon$, and 52.7% and 40.2% of the variation in $D_b$, respectively, while the influence of $f$ remained limited. The regression models developed for $\epsilon$ and $D_b$ showed excellent predictive performance ($R^2=0.99$ and $R^2=0.98$). Based on the combined evaluation of $\epsilon$, $D_b$, and coating applicability, the selected Stage I operating conditions were $P = 0.06 \mathrm{b}\mathrm{a}\mathrm{r}$, $W = 7200 \mathrm{g}$, and $f = 50 \mathrm{H}\mathrm{z}$. These conditions provided a stable and sufficiently homogeneous fluidization regime suitable for continuous, solvent-free powder coating.
• Optimization of coating performance: The coating response, evaluated through ${\mathsf{\sigma }}_c$ and $Vf$, was governed primarily by $H_r$ and $V_{line}$. $H_r$ accounted for the majority of the variation in ${\mathsf{\sigma }}_c$ (78.6%) and $Vf$ (73.8%), while $V_{line}$ contributed more modestly through combined linear and nonlinear effects. The regression models showed strong predictive capabilities ($R^2=0.92$ for ${\mathsf{\sigma }}_c$ and $R^2=0.98$ for $Vf$) and identified an optimal coating window at $V_{line} \approx 1.5–1.8 \mathrm{m}/\mathrm{m}\mathrm{i}\mathrm{n}$ and $H_r=0.5 \mathrm{c}\mathrm{m}$. This condition yielded the highest mechanical performance (${\mathsf{\sigma }}_c=1800.5 \mathrm{M}\mathrm{P}\mathrm{a}$, $Vf\approx 61.6\mathrm{\%}$), demonstrating that moderate $V_{line}$ and shallow $H_r$ promote uniform powder deposition, efficient fiber impregnation, and improved tensile behavior in CF/PEEK towpregs. Furthermore, it was revealed that deviations from this optimum processing window led to severe mechanical degradation driven by distinct microstructural defects: excessive $V_{line}$ hindered resin impregnation and caused air entrapment (increasing $V_v$ up to 5.02%), while excessive roller depths resulted in polymer overcoating that severely diluted the load-bearing fiber phase.
• Residence time–Fiber volume fraction relationship: Using $R_t$ as a single parameter provided a simple and physically meaningful descriptor of the coating process and retained strong predictive accuracy for the overall dataset ($R^2 = 0.92$). However, the $R_t-Vf$ relationship did not exhibit a purely linear trend, indicating that $R_t$ alone does not fully describe the coating response. The combined evaluation of the full dataset, the controlled $H_r$ subset, and the corresponding microstructural observations supports the interpretation that this non-linearity is associated with height-dependent variations in local powder concentration within the fluidized bed. Accordingly, the observed polynomial $R_t-Vf$ behavior should be interpreted as reflecting the combined influence of particle exposure time and spatial variations in powder distribution, rather than being attributed solely to $R_t$ itself. In this respect, $R_t$ remains a robust and practically useful descriptor of coating behavior, while the non-linear response provides indirect evidence of a height-dependent powder-density effect within the bed.
• From an economic perspective, the solvent-free fluidized-bed coating process offers practical advantages compared to conventional impregnation methods. The dry powder approach eliminates the need for solvents and drying stages, thereby reducing material handling requirements and process complexity. In addition, the continuous-coating configuration enables efficient material utilization with minimal waste. The relatively simple equipment design and moderate energy requirement further support the cost-effectiveness of the process. These characteristics indicate that the proposed method provides an economically attractive alternative for the continuous production of CF/PEEK towpregs.

Overall, this integrated optimization framework provides a robust and physically grounded methodology for parameter selection and process control in the solvent-free continuous manufacturing of high-performance thermoplastic composites. Furthermore, the proposed approach is based on physically meaningful parameters, particularly $R_t$, which is derived from geometric and kinematic relationships rather than equipment-specific characteristics. This formulation allows the methodology to be adapted to different system sizes and configurations. By decoupling process control from equipment-specific dimensions and anchoring it to universal physical parameters such as $R_t$, the proposed framework provides a transferable basis for scaling the process from laboratory conditions toward high-throughput industrial production environments.

5. Future Work

Future work may focus on the following aspects to further improve the understanding and optimization of the fluidized-bed coating process for CF/PEEK towpregs:

Three-dimensional, time-resolved investigation of bubble dynamics within the fluidized bed, including bubble nucleation, growth, coalescence, breakup, and surface eruption, in order to better understand how transient gas–solid flow behavior influences local powder concentration, $R_t$, and coating uniformity.

• Direct experimental characterization of the vertical powder concentration distribution within the fluidized bed, enabling improved understanding of the relationship between $H_r$, $R_t$, and coating behavior.
• Investigation of the influence of powder material properties, including particle size distribution, particle shape, surface morphology, and flowability, on coating uniformity and process stability for different thermoplastic powder systems.
• Evaluation of different thermoplastic matrices beyond PEEK, in order to assess the applicability of the proposed residence-time-based framework to materials with varying melt viscosity, surface energy, and adhesion behavior.
• Assessment of consolidation conditions, including temperature, pressure, and vacuum-assisted consolidation strategies, to reduce void content and improve polymer infiltration and interfacial bonding quality.
• Scale-up studies addressing industrial processing conditions, including larger fluidized-bed geometries, different bed aspect ratios, and continuous production environments, in order to evaluate the transferability of the proposed $R_t$-based optimization approach to manufacturing-scale systems.