Design of a Novel Integrated Solid–Liquid Separation and Mixing Pin Screw for CF-PLA Particle-Based 3D Printing: Fluid Simulation and Performance Evaluation

Abstract

Particle-based 3D printing shows great potential in high-performance composite fabrication due to high raw material utilization and flexible material compatibility. However, constrained by conventional extrusion system structures, critical issues (non-uniform melt conveying, insufficient mixing efficacy, poor extrusion stability, etc.) remain. To address these, this study proposes a novel separate-type pin screw integrating solid–liquid separation (from split screws) and high-efficiency mixing (from pin screws) to improve CF/PLA composite extrusion efficiency and mixing homogeneity in particle-based 3D printing. Three-dimensional modeling, static strength/stiffness analysis, and POLYFLOW-based numerical simulation of particle melt conveying/mixing in the screw channel were conducted to analyze structural parameter effects on pressure field, shear rate, and mixing. Experiments assessed printer extrusion rate (different screws) and printed specimen mechanical properties. The simulation and experiment confirmed the optimized screw has better pressure distribution and mixing at 20 rpm, with optimal pin parameters: diameter 2 mm, height 1.6 mm, radial angle 60°, and axial spacing 10 mm. This work offers theoretical/structural support for particle-based 3D printing extrusion system optimization.

1. Introduction

As an emerging manufacturing method, additive manufacturing technology has demonstrated significant advantages in complex structure forming and personalized customization [1,2,3]. Three-dimensional printing, as the core implementation means of additive manufacturing, has been widely applied in various fields [4,5,6]. However, traditional filament-based fused deposition modeling (FDM) technology has problems such as high material cost, complex preforming process, and poor material adaptability, which limit its further development in the field of high-performance composite materials [7,8,9,10]. Particle 3D printing technology, by directly using granular raw materials for printing, not only significantly reduces raw material costs but also improves material adaptability and designability, showing promising application prospects in high-performance composite material forming [11,12,13,14]. Compared with FDM, pellet 3D printing eliminates the need for pre-manufactured filaments, thereby avoiding potential polymer property alterations caused by heating and reducing the risks of warping, creep, or clogging during material feeding [15]. Furthermore, FDM has limitations in the types of thermoplastic polymers it can utilize, and filament prices are typically more than five times higher than those of pellets [16]. From a circular economy perspective, pellet 3D printing bypasses the intermediate step of filament production, simplifying the direct recycling of plastic waste [17,18].

However, this technology still faces key technical bottlenecks in practical applications, such as unstable extrusion quality and uneven melt mixing [19,20,21]. For instance, S. Lu [22] conducted numerical simulation and optimization on the extrusion system of carbon fiber-reinforced polyetheretherketone composites. The results showed that the extrusion pressure of the screw with pins increased by 34%, and the mixing degree improved by 73%. Mechanical tests indicated that the tensile, flexural, and interlaminar shear strengths of the specimens prepared using the optimized screw were enhanced by 27%, 36%, and 63%, respectively. Michelangelli, O P [23] simulated the flow behavior of polymer pellets during single-screw extrusion using the discrete element method (DEM), focusing on analyzing the effects of friction coefficients between pellets and the screw/barrel on solid conveying efficiency, volume fraction, residence time, and velocity distribution. The study found that when the friction coefficients between pellets and the barrel/screw are similar, pellets are conveyed through collisions; if the barrel friction coefficient exceeds 2, clogging is likely to occur.

Currently, optimization research on particle extrusion systems primarily focuses on screw structural design [24,25]. The fundamental reason is that the screw extrusion system, as the core unit for particle melting, conveying, and mixing, directly influences printing efficiency and forming accuracy through its structural design and process parameters [26]. For instance, Liu B et al. [27] developed a screw-extrusion 3D printing fused deposition system. Simulation results indicated that the maximum screw deformation occurs at the tail end, with a maximum value of 0.04 mm, while fluid pressure and screw surface pressure gradually increase along the extrusion direction, with the maximum pressure (0.13 MPa) appearing near the nozzle. Fluid pressure exhibits a positive correlation with screw rotational speed and a negative correlation with screw pitch. Wang Q et al. [28] developed a twin-screw extrusion 3D printing system and analyzed the effects of screw structure and process parameters on the flow field and mixing performance. The study found that with a screw outer diameter of 20 mm and a rotational speed of 5–25 r/min, the printing efficiency was 3–4 times that of traditional filament printing, and the extrusion effect was optimal within the range of 8–15 r/min. J. Tian [29] manufactured wood flour/PHA composites using a screw extrusion process and found that compared with filament fused deposition modeling, the specimens printed by this method exhibited weaker anisotropy, and the micro-screw type, printing speed, layer thickness, and nozzle diameter all affected the workpiece performance. Silva L M D et al. [30] investigated the die swell phenomenon in the vertical twin-screw extrusion process, pointing out that the output rate and nozzle diameter had significant effects on the swell ratio, while the screw rotational speed had no significant impact. Bai Haiqing et al. [31] optimized the screw structure through POLYFLOW simulation, showing that increasing the screw lead could enhance the pressure boosting capacity but also intensify pressure and velocity fluctuations. It was recommended that the lead be 24–36 mm and the rotational speed be controlled at 8–15 r/min.

Although existing studies have optimized extrusion and mixing performance by introducing screw structures such as shear elements and pins—for example, barrier screws aim to improve melting stability, pin screws focus on enhancing mixing efficiency, and twin screws excel in mixing but have complex structures—most current research focuses on single-function improvements, and the synergistic effect of solid–liquid separation and efficient mixing has not been systematically studied. Particularly, in the pellet extrusion process of highly filled composites such as CF/PLA, there remains a lack of screw design methods that can coordinate melting, conveying, and mixing processes. To address this, this paper proposes a novel separated pin screw structure, innovatively integrating the solid–liquid separation function of separated screws with the efficient mixing function of pin screws, thereby overcoming the limitations of existing screws in multifunctional synergy. In this study, combined with the existing G5 industrial-grade pellet 3D printer on the market, the screw structure was designed and optimized. We aimed to improve the mixing effect of polylactic acid and carbon fiber materials to enhance the mechanical properties of the composite. Numerical simulation of the flow channel was carried out with the help of simulation software and verified by experiments. Finally, the influence of screw geometric parameters and process parameters on printing forming was analyzed, and the screw with optimal forming process structure parameters was obtained. This study provides new ideas and practical references for the design of multifunctional integrated screw structures in the field of screw extrusion molding.

2. Design and Static Analysis of Separated Pin Screw Structure

2.1. Working Principle of Separated Pin Screw

During the melt extrusion process, granular materials undergo three states: solid state, solid bed state, and molten state. Among these, the solid bed easily causes fluctuations in melt pressure, temperature, and output, reducing extrusion efficiency and forming accuracy [32]. To address this issue, a barrier screw can be adopted. This screw is improved based on the traditional three-section structure, with an additional thread added in the compression section to form a dual-thread structure consisting of a main thread (solid phase) and an additional thread (liquid phase) with unequal pitches [33], as shown in Figure 1. The main thread is responsible for conveying solids, while the additional thread guides the flow of the melt. Due to the larger gap between the liquid-phase thread and the barrel, the melt can cross the gap into the liquid-phase groove, while unmelted solids are blocked in the solid-phase groove for continued melting, thereby achieving solid–liquid separation. As the pitch difference gradually narrows the solid-phase region and widens the liquid-phase region accordingly, it also conforms to the variation law of the melting process.

The traditional screw, the optimized barrier screw, and the barrier pin screw are shown in Figure 2. The structural parameters and three-zone configuration of the traditional screw are illustrated in Figure 2a. In this study, a two-step optimization was performed on the traditional screw, resulting in the designs shown in Figure 2b,c.

The main body of the designed separated pin screw structure remains a revolving body, and the additional thread can be precisely formed through a CNC turning-milling compound machining center. The pin array can be realized by five-axis linkage CNC milling or electrical discharge machining (EDM) technology, both of which are mature manufacturing processes with good engineering manufacturability. The key interface dimensions of the screw (length, shaft diameter, flange connection dimensions, etc.) are strictly referenced to the mature G5 industrial-grade pellet 3D printer available on the market to ensure that it can be used as a replacement part and integrated into existing industrial printing platforms.

2.2. Separate-Type Pin Screw Design

The barrier screw utilizes the property of solid–liquid phase separation to isolate the incompletely molten solid phase in the solid bed within the solid-phase channel, while the molten phase from the solid bed enters the liquid-phase channel. Therefore, the width of the solid-phase screw channel should be determined in conjunction with the width of the solid bed [9]. The meanings of all parameters in the formulas are shown in

Table 1. Explanation of Formula Symbols and Meanings.

k: Parameters determined by cutting tools	${\mathrm{e}}_1$: Width of main thread ridge (mm)	$\mathsf{\Phi }$: Thread lead angle (°)	${\mathrm{e}}_2$: Width of the separating flight
$\phi$: Liquid volume fraction in the solid bed	$\mathrm{Q}$: Quantity of output	$\beta$: Yield influence coefficient	D: Screw diameter (mm)
$n$: Screw rotational speed (r/min)	$l$: Pitch of the screw (mm)	$\varphi$: Helix angle of the screw (°)	$D$: Outer diameter of the screw (mm)
${\sigma }_y$: Yield limit (Pa)	$n_y$: Safety factor	$\tau$: Shear stress generated by the torque	C: Ratio of the screw cooling water bore diameter to the root diameter
$J$: Moment of inertia (kg·m2)	$W$: Angular acceleration (rad/s2)	$m$: Combined mass of the screw and material (kg)	V: Worn volume (mm3)
$F_n$: Normal load (N)	L: Sliding distance (m)	H: Material Vickers hardness (MPa)	$\rho$: Density (Kg/m3)
$\mathrm{t}$: Time (s)	$u$: Velocity vector components in the x directions (m/s)	$v$: velocity vector components in the y directions (m/s)	$w$: Velocity vector components in the z directions (m/s)
$p$: Static pressure (Pa)	$\rho$: Density (Kg/m3)	$F_x$: Volume force of the microelement in the x direction (N)	$F_y$: Volume force of the microelement in the y direction (N)
$F_z$: Volume force of the microelement in the z direction (N)	$\eta \left(\dot{\gamma }\right)$: The relationship between the melt viscosity and temperature of composite materials	$H\left(T\right)$: The relationship between the shear rate and temperature of composite materials	${\eta }_0$: Zero-shear viscosity

.

2.2.1. Calculation of Optimal Screw Pitch for Separation Screw

To achieve high separation efficiency of the screw, the width ratio of the liquid-phase groove to the solid-phase groove in the separation section should be equal to the volume ratio of the liquid-phase groove to the solid-phase groove. This screw utilizes the different pitches of the main screw and the separation screw to separate the liquid-phase groove and the solid-phase groove within the screw groove of the main screw. The difference in their pitches determines the ratio of the solid phase to the liquid phase in the solid bed of the composite material, thereby ensuring better separation efficiency. The width of the solid-phase groove can be determined by the length of the separation section and the number of thread lifts of the main thread. Here, let the number of thread lifts of the main thread be N, and the width of the last solid-phase groove is

$${\mathrm{X}}_1^{\prime }=\mathrm{N}{\mathrm{l}}_1-\left(\mathrm{N}-1\right){\mathrm{l}}_2-{\displaystyle \frac{2{\mathrm{e}}_1+2\mathrm{k}}{\cos \mathsf{\varphi }}}$$

(1)

In the formula, $\mathrm{k}$ is the parameter determined by the tool [34]; $e_1$ is the main thread land width (mm); $\phi$ is the thread lead angle (°).

The width of the liquid-phase groove can be determined from the width of the solid-phase groove obtained from Equation (1).

$$X_2^{\prime }=l_1-X_1^{\prime }-e_1-e_2=\left(N-1\right)\left(l_2-l_1\right)+{\displaystyle \frac{2e_1+2k}{\cos \varphi }}-e_1-e_2$$

(2)

In the formula: $e_2$ is the width of the separating flight (mm).

In the separation section, the width ratio of the liquid-phase screw channel to the solid-phase screw channel at the end is equal to the volume ratio φ of the liquid phase to the solid phase in the solid bed of the composite material, thus satisfying

$$\mathsf{\phi }={\displaystyle \frac{{\mathrm{X}}_2^{\prime }}{{\mathrm{X}}_1^{\prime }{+\mathrm{X}}_2^{\prime }}}$$

(3)

In the formula, $\phi$ is the liquid volume fraction of the liquid phase in the solid bed.

From (1)–(3), the formula for the separated helical screw is derived:

$${\mathrm{l}}_2={\displaystyle \frac{\left(\mathrm{N}-1\right){\mathrm{l}}_1+\phi \left({\mathrm{l}}_1-{\mathrm{e}}_1-{\mathrm{e}}_2\right)-\mathrm{A}+{\mathrm{e}}_1+{\mathrm{e}}_2}{\left(\mathrm{N}-1\right)}}$$

(4)

In the formula, $A={\displaystyle \frac{2e_1+2k}{\cos \phi }}$.

From Equation (4), it can be observed that the pitch of the separation screw primarily depends on the pitch of the main screw and the volume fraction of the liquid phase in the solid bed. Therefore, once the pitch of the main thread, the flight width of the main screw, and that of the separation screw are determined, the pitch of the separation screw can be calculated according to the liquid volume fraction in the solid bed to meet different application requirements.

2.2.2. Separation Screw Main Screw Design

According to China’s national standards for extruder screws, the diameters of extruder screws are specified as 20, 30, 45, 65, 90, 120, and 150 mm. The screw diameter is correlated with the extruder’s output. In this study, considering the application of a micro-screw extruder, a screw diameter of 20 mm was selected. The relevant formula is as follows:

$$\mathrm{Q}=\beta {\mathrm{D}}^{3}n$$

(5)

In the formula, $Q$ represents the quantity of output, β is the yield influence coefficient with a typical value range of 0.032 to 0.075, D denotes the screw diameter (mm), and n stands for the screw rotational speed (r/min).

The formula for the shear speed of the screw and groove is

$$\gamma ={\displaystyle \frac{\pi Dn}{H}}$$

(6)

The compression ratio refers to the ratio of the volume of the first screw channel to the volume of the last screw channel in the screw, reflecting the degree of compression of materials by the screw. It is determined by factors such as the state, viscosity, density, and thermal sensitivity of the materials. For separable screws, the compression ratio is generally set in the range of 1.8–2.3.

The volume of the first screw channel in the feeding section is denoted as

$$V_1=\pi \left(D-H_1\right)H_1\left(l_1-e_1\right)$$

(7)

It can be calculated that $V_1= 3.62 {\mathrm{c}\mathrm{m}}^3$.

In the last solid-phase screw channel of the metering section, the mass is (1 − φ)m, and thus, the volume of the solid screw channel can be derived as

$$V_2={\displaystyle \frac{\left(1-\phi \right)m}{{\rho }_{\mathrm{S}\mathrm{o}\mathrm{l}\mathrm{i}\mathrm{d} \mathrm{p}\mathrm{h}\mathrm{a}\mathrm{s}\mathrm{e}}^{\prime }}}$$

(8)

Currently, studies have systematically examined the effects of fiber content (10–50%) and annealing on the mechanical properties of components. The results showed that annealed components with a fiber content of 20 wt% exhibited a maximum tensile strength of 135.8 MPa, which was a 94% increase compared to pure PEEK [35]. Therefore, the mass fraction of carbon fiber-reinforced polylactic acid composite was set to 20% herein [36]. For the convenience of calculation, the density of the solid phase was taken as the density of carbon fiber, ${\rho }_{Carbon fiber}^{\prime }=1.75 \mathrm{g}/{\mathrm{c}\mathrm{m}}^3$.

The compression ratio ε is

$$\epsilon ={\displaystyle \frac{V_1}{V_2}}={\displaystyle \frac{\pi \left(D-H_1\right)H_1\left(l_1-e_1\right)}{\frac{\left(1-\phi \right)m}{{\rho }_{Solid phase}^{\prime }}}}$$

(9)

The pitch, helix angle, and screw diameter of the main thread satisfy the following equation:

$$\mathrm{l}=\mathsf{\pi }\mathrm{D}\tan \mathsf{\varphi }$$

(10)

In the formula, $l$ is the pitch of the screw (mm), $\varphi$ is the helix angle of the screw (°), and $D$ is the outer diameter of the screw (mm).

The screw lead angle affects production efficiency, and the empirical solid conveying theory shows that the solid conveying efficiency is highest when the thread lead angle is between 17° and 20°. Here, we take $l_1=D=20 \mathrm{m}\mathrm{m}$. According to Formula (10), the lead angle of the main thread of the screw is ${\varphi }_1=17.65°$. The optimized structural parameters of the split-type screw are shown in

Table 2. The optimized structural parameters of the split-type screw.

Parameters	Numerical Value	Parameters	Numerical Value
Aspect ratio L/D	20	Lead $s$	12.5 mm
Barrel diameter $D_b$	16.2 mm	Feed section $L_1$	36 mm
Outer diameter of the screw $D_e$	16 mm	Metering section $L_3$	36 mm
The width of the spiral rib $e$	1.6 mm	Total screw length L	144 mm
Screw–barrel clearance $\delta$	0.1 mm	Feed section channel depth $H_1$	4 mm
Pitch angle of the screw $\theta$	14°	Metering section channel depth $H_3$	2 mm

.

2.2.3. Strength Calculation of Separation Screw

The separation screw is positioned vertically relative to the horizontal plane. The screw is primarily subjected to material pressure, the torque required to overcome material resistance, and its own gravity. Here, since the material pressure is equal in magnitude and opposite in direction radially on the screw, radial pressure is not considered; only the effect of axial pressure on the screw is taken into account. The strength of the screw mainly involves the combined strength calculation of pressure, torsion, and bending at the root diameter of the screw.

The selection of screw material directly affects its thermal conductivity and extrusion performance. Based on the actual working conditions, the material must be a high-strength material with wear resistance, high temperature resistance, and corrosion resistance. Therefore, the screw is made of high-grade nitrided steel 38CrMoAlA, and its actual physical parameters are shown in

Table 3. Physical property parameters of 38CrMoAlA.

Property	Numerical Value	Unit
Density	7850	$\mathrm{K}\mathrm{g}/{\mathrm{m}}^3$
Young’s modulus	200–210	GPa
Poisson’s ratio	0.3	-
Yield strength	833.6	MPa
Allowable stress	557	MPa
Tensile strength	980	MPa
Safety factor	2.5~3	-

.

To calculate the strength of the separation screw, the allowable pressure is as follows:

$$\left[\sigma \right]={\displaystyle \frac{{\sigma }_y}{n_y}}$$

(11)

In the formula, ${\sigma }_y$ represents the yield limit (Pa), and $n_y$ is the safety factor, which typically ranges from 2.5 to 3. Therefore, a safety factor of ny = 3 is adopted in this study.

The axial force-induced compressive stress in the screw is

$${\sigma }_c={\displaystyle \frac{1.2P_{max}{D}^2}{d^2}}$$

(12)

The shear stress $\tau$ generated by the torque is

$$\tau ={\displaystyle \frac{N_{max}\eta }{\frac{\pi }{16}{n}_{max}{d}^3\left(1-C^4\right)}}$$

(13)

In the formula, C represents the ratio of the screw cooling water bore diameter to the root diameter, which is taken as 0 in this study.

The torque generated by the screw to overcome the material resistance can be expressed as

$$T=J\cdot W={\displaystyle \frac{m}{4}}\left({\displaystyle \frac{D}{4}}+{\displaystyle \frac{L}{3}}\right)W$$

(14)

In the formula, $J$ represents the moment of inertia ($\mathrm{k}\mathrm{g}·{\mathrm{m}}^2$), $W$ denotes the angular acceleration ($\mathrm{r}\mathrm{a}\mathrm{d}/{\mathrm{s}}^2$), and $m$ is the combined mass of the screw and material ($\mathrm{k}\mathrm{g}$).

According to the third strength theory formula in material mechanics,

$${\sigma }_r=\sqrt{({\sigma }_c+{\sigma }_b{)}^2+4{\tau }^2}$$

(15)

The calculated radial stress ${\sigma }_r$ is far below the allowable stress, indicating that the combined stress generated in the screw during the extrusion process remains within the material’s strength limit. Therefore, the dimensional design of the proposed separable screw is reasonable.

The wear of the screw is mainly caused by the abrasive wear of carbon fibers. For quantitative evaluation, the Archard wear model [37] is used for theoretical calculation, and its formula is as follows:

$$V=K{\displaystyle \frac{F_{n}L}{H}}$$

(16)

In the formula, V is the wear volume (mm³); K is the wear coefficient (taking the wear coefficient K ≈ 1.0 × 10⁻⁶ mm³/(N·m) of CF/PLA composite against nitrided steel); F is the normal load (N); L is the sliding distance (m); and H is the Vickers hardness of the material (MPa).

2.3. Static Analysis of Screw Structure

The strength and rigidity of the screw directly affect the quality of extrusion printing and mixing effect. Therefore, in this study, ANSYS Workbench 2022R1 software was used to analyze the strength, rigidity, stress concentration, and shear deformation of conventional screws, separated screws, and separated pin screws to verify whether their performance meets the theoretical calculation and service requirements and to provide a basis for subsequent fluid simulation. The material 38GrMoAlA was selected for the simulation analysis.

In the establishment of the finite element model, to balance computational efficiency and accuracy, the following rationalized assumptions are introduced in this study: (1) the screw material is treated as an isotropic linear elastic body, neglecting potential material nonlinearity and residual stress; (2) minor detailed features such as small fillets at the thread roots are ignored to avoid stress singularity and reduce mesh generation difficulty; (3) in terms of load application, the complex distributed load of the melt on the screw is simplified to a concentrated torque and axial force acting on the head. These simplifications are based on classical mechanics theory and engineering practice. Although they may lead to underestimation of local stress concentration factors, they are reasonable and efficient for evaluating the overall strength, rigidity, and deformation trends of the screw and can provide reliable qualitative comparisons and trend judgments for subsequent optimization design.

2.3.1. Mesh Generation and Boundary Condition Setup

In this study, idealized assumptions and simplifications are applied based on the operational conditions of the screw to facilitate structural analysis and computation. Taking the conventional screw as an example, the finite element model and mesh generation of the extrusion screw are illustrated in Figure 3, with the number of elements and nodes summarized in

Table 4. The number of elements and nodes in mesh generation.

Screw Type	Number of Elements	Number of Nodes
Traditional screw	36,339	65,293
Separable screw	339,652	485,887
Separable pin screw	342,684	492,059

.

The overall mesh quality is typically quantified on a scale from 0 to 1, where a value closer to 1 indicates superior mesh generation. The comprehensive quality evaluation of the screw mesh is illustrated in Figure 4.

In the boundary condition setup, minor influencing factors are neglected for simplification. According to Equations (11)–(14), the inertial load caused by the screw’s self-weight (9.8066 m/s²) is applied on the screw’s axial cross-section, directed toward the screw head. During rotation, the screw is subjected to torque from the molten material at the nozzle. To simplify modeling, a constant torque is directly applied to the screw head to simulate the maximum torque load experienced during material extrusion. The calculated value of this torque is determined to be 32.5 N·m. Additionally, the screw head experiences an axial reaction force from the molten material during extrusion; this force is calculated to be 248 N. To simulate the mechanical constraints accurately, cylindrical surface constraints are applied to the cylindrical portion of the screw, fixing the axial and radial directions while allowing free rotation in the tangential direction. This constraint setup ensures the screw remains stable without lateral displacement during simulation while still being able to rotate freely.

2.3.2. Finite Element Result Analysis

The finite element analysis results of different types of screws are shown in Figure 5, Figure 6, Figure 7 and Figure 8.

The traditional stress distribution cloud diagram of the screw is shown in Figure 5. It can be observed from the figure that the maximum equivalent stress of the screw is 524.03 MPa, and the minimum equivalent stress is 4.74 × 10⁻⁵ MPa. Both values satisfy the yield strength limit, indicating that all stress indicators of the screw meet the strength requirements. The maximum equivalent stress is located at the starting position of the thread at the end of the screw, which, in actual working conditions, corresponds to the thread in the feeding section being the dangerous cross-section, consistent with practical scenarios. Therefore, the screw can be safely used under normal operating conditions. The deformation cloud diagram of the screw under load is shown in Figure 6. It can be observed from the figure that the maximum deformation of the screw is 0.286 mm, occurring at the thread on the top end. This phenomenon is attributed to the gradual increase in material pressure along the conveying direction, which arises from the compressive effect of the material barrel and the resistance of the internal flow channel during the extrusion and transmission process of the material. These simulation results are consistent with the actual working conditions, confirming the reliability of the screw design under operational loads.

For the sake of computational convenience, the bottom corner portions of the separated screw and separated pin screw are neglected herein. The equivalent stress diagrams and load deformation nephograms of the separated screw and separated pin screw are shown in Figure 7 and Figure 8. According to the simulation results, the maximum equivalent stresses of the separated screw and separated pin screw are 233.93 MPa and 233.69 MPa, respectively, which are much lower than the yield limit of the 38GrMoAlA material of the screw, meeting the safety factor range. The maximum deformation amounts are 0.195 mm and 0.194 mm, respectively, which are within the deformable range of the screw. Moreover, the equivalent stress and deformation of the optimized screw are lower than those of the traditional screw. These results indicate that the optimized screw structure design is more reasonable and meets the process strength requirements.

Based on the finite element simulation results, the wear behavior of the separated pin screw was theoretically evaluated using the Archard wear model (Equation (16)). Finite element analysis revealed that the stress concentration areas on the surface of the pin screw are mainly distributed at the top of the screw flight and the contact area between the pin and the melt (Figure 7b), and these high-stress regions also correspond to potential high-wear locations. Nitrided 38CrMoAlA was used as the screw material, with a surface Vickers hardness of HV1100. The stress data obtained from the simulation were substituted into the Archard formula for calculation. Under the working conditions of a screw speed of 20 rpm and continuous operation for 1000 h, the theoretical wear depth at the pin root and the edge of the main thread was approximately 1.31 μm, which is within an acceptable range. Although wear is inevitable, the wear process can be effectively delayed by optimizing the material (such as surface nitriding treatment) and structural design (such as using fillet transitions to reduce stress concentration), thereby ensuring the service life of the screw under long-term high-shear and high-filling conditions.

3. Numerical Simulation Analysis of the Melt Flow Field of Screw Particles

The molten flow problem of composite materials typically involves solving partial differential equations, but due to the complex geometry and nonlinear characteristics of the fluid domain, it is difficult to obtain analytical solutions. Computer numerical simulation can effectively reduce experimental costs and deeply reveal fluid behaviors. As a finite element-based CFD software(ANSYS Workbench 2022R1), POLYFLOW is specialized for simulating the flow and heat transfer of viscoelastic fluids (such as polymer materials) during extrusion, stretching, and mixing processes and is particularly widely used in polymer processing simulations. Therefore, this paper selects POLYFLOW to conduct fluid analysis of carbon fiber-reinforced polylactic acid composites [38].

3.1. Mathematical Model of Flow Field Control Equation

During the extrusion molding of thermoplastic melts, it is necessary to solve the flow field based on the continuity equation, momentum equation, and constitutive equation. The expressions of the continuity equation, momentum equation, and constitutive equation for the mathematical model of compressible fluids are as follows:

3.1.1. Continuity Equation

The continuity equation states that the rate of mass increase per unit volume is equal to the net mass increment per unit volume over the same time interval, and its mathematical model expression is given as follows [39]:

$${\displaystyle \frac{\partial \rho }{\partial t}}+{\displaystyle \frac{\partial \left(\rho u\right)}{\partial x}}+{\displaystyle \frac{\partial \left(\rho v\right)}{\partial y}}+{\displaystyle \frac{\partial \left(\rho w\right)}{\partial z}}=0$$

(17)

In the formula, $\rho$ represents density ($\mathrm{K}\mathrm{g}/{\mathrm{m}}^3$); t represents time ($\mathrm{s}$); $u, v, w$ represent the velocity vector components in the $x, y, z$ directions ($\mathrm{m}/\mathrm{s}$), respectively.

3.1.2. Momentum Equation

The momentum equation represents the relationship between the change in momentum during fluid motion and the external forces acting on the fluid. Screw extrusion printing follows the law of conservation of momentum, which is related to the velocity and mass of the fluid within a unit volume. The mathematical model expression is as follows [40]:

$$\left\{\begin{array}{c}\rho \left({\displaystyle \frac{\partial u}{\partial t}}+u{\displaystyle \frac{\partial u}{\partial x}}+v{\displaystyle \frac{\partial u}{\partial y}}+w{\displaystyle \frac{\partial u}{\partial z}}\right)=-{\displaystyle \frac{\partial p}{\partial x}}+\eta \left({\displaystyle \frac{{\partial }^{2}u}{\partial x^2}}+{\displaystyle \frac{{\partial }^{2}u}{\partial y^2}}+{\displaystyle \frac{{\partial }^{2}u}{\partial z^2}}\right)+\rho F_x\\ \rho \left({\displaystyle \frac{\partial v}{\partial t}}+u{\displaystyle \frac{\partial v}{\partial x}}+v{\displaystyle \frac{\partial v}{\partial y}}+w{\displaystyle \frac{\partial v}{\partial z}}\right)=-{\displaystyle \frac{\partial p}{\partial y}}+\eta \left({\displaystyle \frac{{\partial }^{2}v}{\partial x^2}}+{\displaystyle \frac{{\partial }^{2}v}{\partial y^2}}+{\displaystyle \frac{{\partial }^{2}v}{\partial z^2}}\right)+\rho F_y\\ \rho \left({\displaystyle \frac{\partial w}{\partial t}}+u{\displaystyle \frac{\partial w}{\partial x}}+v{\displaystyle \frac{\partial w}{\partial y}}+w{\displaystyle \frac{\partial w}{\partial z}}\right)=-{\displaystyle \frac{\partial p}{\partial z}}+\eta \left({\displaystyle \frac{{\partial }^{2}w}{\partial x^2}}+{\displaystyle \frac{{\partial }^{2}w}{\partial y^2}}+{\displaystyle \frac{{\partial }^{2}w}{\partial z^2}}\right)+\rho F_z\end{array}\right.$$

(18)

In the formula, $u, v, w$ are the velocity components of the velocity vector in the x, y, z directions, respectively; p is the static pressure ($\mathrm{P}\mathrm{a}$); $\rho$ is the density ($\mathrm{K}\mathrm{g}/{\mathrm{m}}^3$); $F_x, F_y,{ F}_z$ are the body forces per unit volume ($\mathrm{N}$) acting on the fluid element.

3.1.3. Constitutive Equation

During the screw extrusion process, the material undergoes a transition from a solid to a viscous state. The viscosity model of the composite material plays a crucial role in simulating the extrusion process. To reduce computational complexity, the study only considers the effects of temperature and shear rate on viscosity, as described by Equation (19). The changes in the viscosity of the composite material are described using the Cross and WLF models, with equations given by (19) and (20). The WLF viscosity model is typically applicable only above the glass transition temperature (143 °C). In this study, the barrel temperature at the beginning of the compression section is approximately 160 °C. Therefore, to reduce computational time and facilitate intuitive analysis, the simulation of the extrusion screw begins at the compression section [41].

$$\eta =\eta \left(\dot{\gamma }\right)\times H\left(T\right)$$

(19)

In the formula, $\eta (\stackrel{·}{\gamma } )$ and $H\left(T\right)$ represent the relationships between the melt viscosity, shear rate, and temperature of the composite material, respectively.

The Cross model is represented by Equation (20).

$$\eta \left(\dot{\gamma }\right)={\displaystyle \frac{{\eta }_0}{1+{\left(\lambda \dot{\gamma }\right)}^{1-n}}}$$

(20)

In the formula, ${\eta }_0$ represents zero-shear viscosity; $\lambda$ is the natural time (the reciprocal of the shear rate at which the fluid transitions from Newtonian to power-law behavior);$n$ is the non-Newtonian index.

The temperature dependence of melt viscosity is described by the WLF model, as shown in Equation (21).

$$\mathrm{Ln}\left(H\left(T\right)\right)={\displaystyle \frac{c_1\left(T_r-T_a\right)}{c_2+T_r-T_a}}-{\displaystyle \frac{c_1\left(T-T_a\right)}{c_2+T-T_a}}$$

(21)

In the formula, $c_1$ and $c_2$ are WLF constants, and $T_r$ and $T_a$ are reference temperatures.

The index for evaluating mixing performance is still calculated using POLYFLOW software (ANSYS Workbench 2022R1). To simplify the calculation, only the mixing in the metering section is considered here, and the mixing degree calculation equation is shown in Formula (22) in the table below. In this section, only the flow model is considered to evaluate the mixing effect without involving the heat transfer model. Aimed at isolating the purely mechanical effects of flow and mixing, this approach neglects the influence of temperature inhomogeneity on local viscosity but significantly reduces computational complexity, making it suitable for preliminary screening and mechanistic analysis. The Carreau–Yasuda law is used to fit the viscosity model of 20% CF/PLA material, which is expressed by the following Equation (23):

$$M_d={\displaystyle \frac{{\delta }_i-{\delta }_o}{{\delta }_i}}$$

(22)

In the formula, ${\delta }_i$ is the distribution index at the inlet, and ${\delta }_o$ is the distribution index at the outlet.

$$\eta \left(\dot{\gamma }\right)={\eta }_{\mathrm{\infty }}+\left({\eta }_0-{\eta }_{\mathrm{\infty }}\right){\left[1+{\left(\lambda \dot{\gamma }\right)}^a\right]}^{{\displaystyle \frac{n-1}{a}}}$$

(23)

In the formula, ${\eta }_0$ denotes the zero-shear viscosity, ${\eta }_{\infty }$ represents the infinite-shear viscosity, $\lambda$ is the natural time (the reciprocal of the shear rate at which the fluid transitions from Newtonian to power-law behavior), $a$ stands for the transition index from the Newtonian plateau to the power-law region, and $n$ is the power-law index.

The rheological parameters of the 20% CF/PLA composite fitted under the Carreau–Yasuda law are presented in

Table 5. The rheological parameters of the 20% CF/PLA composite material.

${\mathit{\eta }}_0$/(Pa·s)	${\mathit{\eta }}_{\mathbf{\infty }}$/(Pa·s)	$\mathit{\lambda }$/s	$\mathit{a}$	$\mathit{n}$
$7.54\times {10}^4$	$0.81{\times 10}^{-3}$	0.0124	0.39	0.50

.

3.2. The Setting of Boundary Conditions

Detailed material parameters and boundary conditions are provided in

Table 6. 20% CF/PLA Material Parameter Table.

Component	Materials	Density (kg/m3)	Specific Heat Capacity (J/(kg·°C))	Thermal Conductivity (W/m·K)
Composite materials	20%CF/PLA	1300	1400	0.5
Screw	38CrMoAlA	7850	460	50

and

Table 7. The basic structural parameters and boundary conditions table of the calculation model.

Boundary Conditions	Fluid Boundary Conditions	Thermal Boundary Condition
Inlet	${\mathrm{F}}_{\mathrm{n}}={\mathrm{F}}_{\mathrm{s}}=$ 0	453.15 K
Outlet	${\mathrm{F}}_{\mathrm{n}}={\mathrm{F}}_{\mathrm{s}}=$ 0	Outflow
Inner wall	ω = 1.047, 1.5708, 2.094 rad/s	Insulated
Outer wall	${\mathrm{V}}_{\mathrm{n}}={\mathrm{V}}_{\mathrm{s}}=$ 0	453.15 K
Screw	$\mathrm{n}=$ 10, 15, 20 rpm	-

. To reduce computational complexity, the physical parameters were simplified, assuming that the specific heat capacity and thermal conductivity of the composite melt are independent of temperature.

The boundary conditions for the fluid simulation in this study are set as follows: the normal and tangential forces at the inlet of the fluid domain are set to zero to ensure a free-flow state of the fluid at the inlet, while a certain normal pressure is applied at the outlet of the fluid domain; for the inner holes on both sides, boundary conditions with zero normal velocity and tangential force are specified to prevent fluid flow through these boundaries; the outer wall of the fluid domain is set with both normal and tangential velocities equal to zero to ensure no slip at the wall. The flow field characteristics formed under the screw rotational speeds of 10 rpm, 15 rpm, and 20 rpm are analyzed, and the results are discussed.

In the table, the inner wall refers to the region where the melt contacts the root of the screw; the outer wall indicates the area where the melt contacts the inner wall of the barrel. $F_n$ and $F_s$ represent the normal force and tangential force, respectively; $V_n$ and $V_s$ denote the normal velocity and tangential velocity, respectively. The symbol n denotes the rotational speed of the extrusion screw.

The difference in boundary condition settings here compared to those in Table 7 lies in the absence of thermal boundary conditions. The core objective is to isolate and reveal the pure mechanical effects of screw geometry on mixing behavior, avoiding the interference of complex coupling introduced by the temperature field in the analysis of key mechanisms. Although thermal boundary conditions are neglected, the dependence of viscosity on shear rate is considered through the Carreau–Yasuda constitutive model, which is sufficient to capture the core characteristics of polymer melt flow under high shear. Herein, only the analysis at a screw rotational speed of 20 rpm is considered to investigate the differences in mixing performance between the separated pin screw and the conventional screw, with the boundary conditions presented in

Table 8. The boundary conditions of the calculation model for basic structural parameters.

Boundary Conditions	Flow Conditions	Mixed Conditions
Inlet	${\mathrm{F}}_{\mathrm{n}}={\mathrm{F}}_{\mathrm{s}}=$ 0	Inflow
Outlet	${\mathrm{F}}_{\mathrm{n}}={\mathrm{F}}_{\mathrm{s}}=$ 0	Outflow
Inner wall	${\mathrm{V}}_{\mathrm{n}}=$$0, {\mathrm{F}}_{\mathrm{s}}=$ 0	Non-penetrable
Outer wall	${\mathrm{V}}_{\mathrm{n}}={\mathrm{V}}_{\mathrm{s}}=$ 0	Non-penetrable
Screw	$\mathrm{n}$ = 20 rpm	$\mathrm{n}$ = 20 rpm

.

3.3. Analysis of Different Screw Pressure Fields

During the process of screw extrusion, a certain pressure is generated inside the barrel, and an appropriate pressure difference is beneficial for the uniform extrusion and forming of the material. To compare the effect of screw speed on the fluid pressure field, the screw speeds were set at 10 rpm, 15 rpm, and 20 rpm, respectively. Simulations were conducted to analyze the pressure fields formed at these different screw speeds. The pressure field distributions for the three different screw speeds are shown in Figure 9, Figure 10, and Figure 11, respectively.

As shown in Figure 9, in the flow channel pressure of the traditional screw, the pressure of the material in the gap between the screw flight and the barrel is lower than that in the screw groove. The different extrusion degrees experienced by the material also help to improve the extrusion efficiency. However, the pressure in the screw groove is greater than that at the screw flight, indicating that the traditional screw structure hinders the extrusion of the internal flow channel during the extrusion process, which does not meet the requirements for improving extrusion quality.

As shown in Figure 10, the maximum pressure of the barrier screw is mainly concentrated in the flight area, which differs from the pressure distribution of the conventional screw. The concentration of pressure in the flight area helps to exert a squeezing effect on the flow channel within the screw groove, facilitating the improvement of extrusion efficiency.

As shown in Figure 11, with the increase of rotational speed, the pressure in the barrier-type pin screw gradually rises along the axial direction and reaches the maximum at the bottom of the metering section. The pressure at the flight is generally higher than that in the screw groove area, while the pressure distribution in the compression section is relatively uniform. According to the screw structure and fluid mechanics principles, the metering section has the shallowest screw groove, the smallest flow channel cross-sectional area, and the largest flow resistance, thus becoming the main pressure accumulation zone. Meanwhile, the pin structure enhances local shearing and flow disturbance, further increasing the resistance and forming a high-pressure region. In addition, the increase in rotational speed leads to an increase in material flow rate and shear rate, exacerbating the pressure concentration in the metering section. This pressure distribution meets the requirements of the actual extrusion process and is the result of the combined action of the screw structure and fluid characteristics.

3.4. Analysis of Different Screw Shear Rates

The indicator for measuring the magnitude of inter-polymer interactions is determined based on the shear rate. Shear rate has a significant impact on regulating material viscosity, improving mixing homogeneity, and optimizing interlayer bonding strength. By adjusting viscosity, mixing effectiveness, and interlayer bonding strength, shear rate influences the quality of molded products. Shear rate plays a crucial role in achieving the stability and strength performance of high-performance composites. As the screw speed changes, the shear distribution cloud maps for different screws are shown in Figure 12, Figure 13 and Figure 14.

From Figure 14, it can be observed that there are prominent bright spots in the flow field of the screw metering section, which are located around the pin regions. This indicates that the shear rate in these areas is higher than that in the surrounding flow fields. The high shear rate facilitates the adequate shearing and plasticizing of the internal flow channel composite melt, enhancing the mixing effect between different materials. This suggests that the designed pin structure has achieved the desired shearing and plasticizing effect. Moreover, as the screw speed increases, the shear rate gradually rises, with the maximum shear rate increasing from $2.35\times {10 }^3{\mathrm{s}}^{-1}$ to $2.68\times {10 }^3{\mathrm{s}}^{-1}$ and reaching a peak of $3\times {10 }^3{\mathrm{s}}^{-1}$. This trend aligns with the actual operating conditions, meeting the requirements for high shear and strong plasticization.

3.5. Analysis of Different Screw Viscosity Fields

The viscosity of the melt within the screw extruder’s internal flow channel determines the mixing efficiency inside the melt and the mechanical properties of the composite polymer material. The distribution of viscosity is inversely related to the distribution of shear rate because the shear force generated by the shear rate causes shear thinning in the high-molecular-weight polymer fluid, thereby reducing the internal viscosity of the fluid. Therefore, viscosity can serve as an indicator to evaluate the mixing efficiency within the flow channel. In this study, simulations were conducted at three different screw speeds: 10 rpm, 15 rpm, and 20 rpm, to analyze the resulting viscosity fields. The viscosity distributions for these three screw speeds are shown in Figure 15, Figure 16, and Figure 17, respectively.

As can be seen in Figure 15 and Figure 16, the barrier screw exhibits a more uniform viscosity distribution compared to the conventional screw, which can effectively avoid viscosity aggregation. The viscosity tends to decrease with the increase of screw rotational speed.

As shown in Figure 17b, the viscosity within the pin zone is significantly lower than that in the surrounding flow channel, and a gradual increase in viscosity, along with viscosity accumulation, occurs between two adjacent pins along the extrusion direction. Compared with the maximum viscosity of $3.5\times {10}^4 \mathrm{P}\mathrm{a}·\mathrm{s}$ in the flow channel, the viscosity within the pin region is approximately $3.5\times {10}^3 \mathrm{P}\mathrm{a}·\mathrm{s}$, indicating that the pin structure induces a reduction in viscosity within the flow field. This phenomenon suggests that the pin design enhances the mixing efficiency within the channel, thereby promoting a more uniform and thorough dispersion of the composite material. In contrast, the conventional screw does not exhibit abrupt changes or accumulation of viscosity, implying that the average viscosity of the pin-type screw is relatively lower under the same processing conditions. High-viscosity fluids generally exhibit poorer flowability within the channel; therefore, the reduction in viscosity achieved by the optimized pin structure aligns with the desired outcome for the mixing extrusion of carbon fiber and polylactic acid (PLA) composites. These findings demonstrate that the pin-structure screw significantly improves the mixing performance and homogeneity of the resulting composite material.

4. Experimental Verification

The experiment primarily involved testing the extrusion rate of a printer with different screw configurations and evaluating the mechanical properties of printed specimens made from various materials. The extrusion conveying performance of the printer screws was assessed by measuring the extrusion flow rate of a pellet 3D printer under different screw models. Printed test specimens consisted of two material types: pure PLA and 20% carbon fiber-reinforced PLA (20% CF/PLA) composites, fabricated using three distinct screw designs. Specifically, there were six tensile specimens and six compressive specimens, whose mechanical properties were determined by testing their tensile and compressive strengths. The printed specimens were categorized into tensile specimens with dimensions of 100 mm × 20 mm × 4 mm and bending specimens sized at 100 mm × 10 mm × 4 mm, as illustrated in Figure 18. Both tensile and bending tests were conducted using a universal testing machine, with the experimental setup depicted in Figure 19.

4.1. Orthogonal Experimental Design and Range Analysis of Pin Structure

In the extrusion process of composites, poor mixing efficiency also exists during the mixing of the molten state. Therefore, to improve the mixing efficiency of composites, a pin structure was applied here, and orthogonal experiments were used to consider the influence of pin parameters on mixing efficiency. According to the description in Section 2.1, a cylindrical pin structure was adopted here, and the design range of pin structure parameters is shown in

Table 9. Structural parameters of extrusion screw pin.

Classification	Diameter of the Pin (d/mm)	Pin Height (h/mm)	Pin Spacing (e/mm)	Axial Angle of the Pin (θ/°)
1	1.5	1.4	6	60
2	2	1.6	8	45
3	2.5	1.8	10	36

.

Nine groups of pins with different structures were designed using the orthogonal experimental method, as shown in

Table 10. Orthogonal experimental design for the extrusion screw pin structure.

Group Number	Diameter of the Pin (d/mm)	Pin Height (h/mm)	Pin Spacing (e/mm)	Axial Angle of the Pin (θ/°)
1	1.5	1.4	6	60
2	1.5	1.6	8	45
3	1.5	1.8	10	36
4	2	1.4	8	36
5	2	1.6	10	60
6	2	1.8	6	45
7	2.5	1.4	10	45
8	2.5	1.6	6	36
9	2.5	1.8	8	60

.

Nine groups of pin structures with different parameter combinations designed by orthogonal experimental design were analyzed in groups. The mixing performance of the pin structures with nine different process parameter combinations can be calculated using the mixing degree Formula (22). As shown in

Table 11. The degree of integration of the pin structure under different combinations of process parameters.

Group Number	Degree of Mixture
1	0.601
2	0.824
3	0.613
4	0.817
5	0.912
6	0.841
7	0.657
8	0.749
9	0.489

, the 5th group exhibits the optimal mixing degree with a value of 0.912, indicating that the parameter combination of the 5th group achieves the best mixing effect.

Due to the limitations and random errors inherent in solely examining the nine groups of experiments in the orthogonal test, the average mixing degree of pin structural parameters for different combinations in the orthogonal array was calculated to evaluate the influence intensity of each pin structural parameter on the mixing effect. The average mixing degrees of different structural parameters are presented in

Table 12. The average mixture degree of various pin structure parameters.

Parameters	Evaluation Indicators	The Average Values Under Different Combination Levels of the Three Parameters			Range
		Level 1	Level 2	Level 3
Diameter of the pin d	Degree of mixture	0.679	0.857	0.632	0.225
Pin height h		0.692	0.828	0.648	0.180
Pin spacing e		0.730	0.710	0.727	0.020
Axial angle of the pin θ		0.726	0.774	0.667	0.107

.

In the table, “Level 1”, “Level 2”, and “Level 3” represent the three different levels set for each parameter (such as pin diameter d, height h, etc.) in Table 9. The values under each level are the average values of the corresponding mixing degrees from all nine groups of experiments when the parameter is set to that level. The influence of each parameter on mixing performance can be determined from the range values of the average mixing degree for each pin parameter, with the order of influence intensity from strongest to weakest being pin diameter > pin height > pin radial angle > pin axial spacing. The average mixing degrees of different pin structural parameters are plotted in a bar chart, as shown in Figure 20. As indicated in the figure, the maximum average mixing degree for individual parameters is achieved when the pin diameter is 2 mm, the pin height is 1.6 mm, the pin radial angle is 45°, and the pin axial spacing is 6 mm. To achieve optimal mixing performance, the pin structural parameters with the highest average mixing degrees were selected for optimal combination, and the mixing degree was calculated for comparative analysis of mixing performance with the 5th group combination from the orthogonal experiment.

After calculation, the mixing degree of the parameter combination with the optimal average mixing degree was determined to be 0.926, which is higher than that of the optimal 5th orthogonal mixing degree combination, as shown in Figure 21.

Although the design of the pin structure improves the mixing effect between polymers, it also hinders the fluid flow process, thereby reducing the extrusion pressure effect. Considering this influence, this section conducts a comparative calculation of the extrusion pressure for the pin structures of the optimal average mixing degree combination and the optimal orthogonal mixing degree combination to evaluate which structural combination achieves better extrusion mixing performance with less impact on extrusion pressure. The calculated pressure difference of the optimal pin structure is 19.64 KPa, while that of the orthogonal combination pin structure is 21.84 KPa, as shown in Figure 22. To achieve the optimal mixing effect and extrusion pressure, the pin structure from the orthogonal experiment combination is selected as the optimal process parameter, specifically a pin diameter of 2 mm, pin height of 1.6 mm, pin radial angle of 60°, and pin axial spacing of 10 mm.

4.2. Extrusion Flow Rate Test

To investigate the quality of the extruded melt, this study examined the mass flow rate and flow stability of the extruded melt under different screw types and rotational speeds. The test measured the extrusion volume flow rate at the nozzle outlet within one minute, conducted at rotational speeds of 5 rpm, 10 rpm, 15 rpm, 20 rpm, and 25 rpm. As shown in Figure 23, In the low-speed region (<15 rpm), the separated pin screw outperformed the conventional screw in both throughput and mixing degree due to its excellent solid conveying and melting efficiency. However, as the rotational speed increased to 20 rpm, the additional flow resistance introduced by the pin structure became the dominant factor, resulting in the throughput of neat PLA extrusion even slightly lower than that of the separated screw. This phenomenon precisely confirms the trade-off effect between throughput and mixing: higher shear and more complex flow fields (caused by the pins) significantly enhance the mixing effect (as shown in Table 10 and Table 11, with the mixing degree reaching up to 0.912) but inevitably increase the flow resistance, thereby restricting the maximum throughput. Nevertheless, this structure still exhibits superior melt mixing uniformity, so the reduced flow rate does not contradict its advantages in mixing performance. In conclusion, both the barrier-type screw and the barrier-type pin screw outperform the conventional screw in terms of extrusion rate, which validates the correctness of the previous numerical simulation of the screw. The optimized barrier-type pin screw and barrier-type screw demonstrate superior extrusion quality for composite materials compared to the conventional screw.

Orthogonal experiments and range analysis (see Table 11) indicate that pin diameter (d) and height (h) are the most significant parameters affecting the mixing effect and also the key geometric factors influencing flow resistance. Through optimization, an optimal parameter combination (d = 2 mm, h = 1.6 mm, axial spacing = 10 mm, and radial angle = 60°) was found. This combination achieves the best balance between mixing degree (0.912) and extrusion pressure (pressure difference of 21.84 KPa, see Figure 22). This means that under this configuration, the screw achieves a significant leap in mixing performance at the cost of acceptable throughput loss, resulting in the optimal comprehensive performance. Based on the above analysis, the screw design can be flexibly adjusted according to printing requirements in practical applications: if high mixing quality is pursued, the number or height of pins can be appropriately increased; if high printing speed is desired, the pin structure can be reduced to lower flow resistance.

4.3. Mechanical Property Testing

To visually investigate the influence of different screws on extrusion quality, the mechanical properties of workpieces formed by different screws were evaluated, with the tensile and flexural properties of the workpieces serving as direct indicators for assessing their mechanical performance. Figure 24a,b present bar charts showing the variations in tensile strength and elastic modulus of samples printed using different extrusion screws and materials.

As shown in Figure 24a,b, in the tensile performance test, the influence of the conventional screw and the separated screw on the tensile properties of neat PLA and composite materials is relatively small. In contrast, the optimized separated pin screw exhibits more excellent mechanical properties. The composite material sample prepared by it achieves a tensile strength of 75.3 MPa and an elastic modulus of 115.1 MPa. Meanwhile, the elastic modulus of the composite material printed by this screw gradually increases with the different structures of the conventional screw, separated screw, and separated pin screw, reaching a maximum of 7.8 GPa, while the performance difference of neat PLA under different screws is still not significant. In conclusion, in the tensile sample test, the samples printed by the separated pin screw show better printing quality in terms of tensile strength and elastic modulus.

The flexural strength measurements of samples extruded by different screws are shown in Figure 25a,b.

As shown in Figure 25a, the flexural strength of specimens prepared by the three types of screws increases sequentially, with the separated pin screw performing the best. The flexural strength of its neat PLA and CF/PLA composite specimens reaches 120 MPa and 186 MPa, respectively. It can be seen from Figure 25b that in terms of flexural modulus, the flexural modulus of neat PLA gradually increases with the change of screw structure. For CF/PLA composites, the modulus difference between the conventional screw and the separated screw is small, while the separated pin screw has the highest flexural modulus, reaching up to 3.14 GPa (neat PLA) and 9.98 GPa (CF/PLA), respectively. The results indicate that the specimens produced by the separated pin screw are superior to those by other screws in both flexural strength and flexural modulus, demonstrating that the composite materials achieve more sufficient mixing effect in the inner flow channel and thus better mechanical properties.

4.4. Summary of This Section

(1)

In this study, a wear-resistant screw structure was designed to address the high hardness and high strength characteristics of carbon fiber (CF), and this design is also applicable to other common reinforcing fibers. Although these fibers differ from CF in terms of density, aspect ratio, and surface properties, the screw enables stable conveying of the solid phase through a solid–liquid separation mechanism and effectively disperses fibers using the high shear field generated by pins to prevent agglomeration. Thus, it can be used in composite systems such as GF/PLA and GF/PA. For short fibers or nanofillers (e.g., carbon nanotubes), the strong convective mixing effect induced by the pins will also play an important role.

(2)

Although PLA is a thermosensitive bio-based polymer, the Cross/WLF and Carreau–Yasuda constitutive models employed in this study are equally applicable to the nonlinear viscous behavior of engineering plastics such as ABS, PA, and PEEK. Therefore, the flow field simulation method established herein can be extended to these materials. However, it is necessary to adjust the solid–liquid separation point (i.e., the φ value in Equation (3)) according to the specific melting characteristics of the polymer and achieve this by optimizing the geometric parameters of the separation section threads.

(3)

By systematically reviewing representative screw design schemes in recent studies, this research analyzes them alongside the integrated design proposed in this work using a tabular comparison format. The comparison focuses on key factors such as the core functions, characteristics, and limitations of each design, and the results are presented in

Table 13. Comparison of Different Screw Performance.

Screw Type	Core Function	Characteristics	Limitations
Traditional three-section small screw	Basic conveying, compression, and melting	Simple structure and convenient manufacturing.	Poor mixing effect, large pressure fluctuation, and unsuitability for high-filled composites
General-purpose screw	Basic plasticization and conveying, suitable for general extrusion processing	Simple structure, low compression ratio, and high output	At high rotational speeds, the melt is uneven, prone to cold slug and temperature instability, and cannot handle high-filled or high-viscosity materials.
Barrier screw	The barrier structure separates the melt from unmelted solids to ensure complete plasticization	A secondary thread is introduced in the compression section to form a melt channel and a solid channel, resulting in high melt quality and good temperature uniformity	The barrier structure increases the surface area, leading to excessive shear heat and energy consumption at high rotational speeds, thus requiring additional cooling
Fractal screw	Multi-channel design improves melt uniformity and energy efficiency	The channels in the feeding section, transition section, and metering section are different, and adiabatic decompression is used to control temperature and improve melt consistency	Poor design of the transition section leads to large pressure fluctuations, poor melt consistency, complex structure, and high manufacturing cost
Double screw	Independent adjustment of screw speed allows flexible control of shear intensity and residence time, resulting in wide material applicability	The screw is composed of multiple elements, which can be flexibly configured according to material characteristics	Difficult to manufacture and assemble, insufficient torque at high rotational speeds, limited maximum rotational speed, and small printing volume
Separating-pin screw	Integration of solid–liquid separation and efficient mixing.	It balances pressure stability and mixing uniformity with a reliable structure, achieving high performance at low rotational speeds	Its manufacturing is slightly more complex than that of traditional screws

[25,33,42,43].

5. Conclusions

In this study, focusing on the novel separated pin screw structure, the effects of screw structural parameters on pressure distribution, shear rate, and mixing performance were systematically evaluated through static analysis, fluid simulation, and experimental verification. Compared with existing screw designs, this structure exhibits significant advantages in the synergistic effect of solid–liquid separation and mixing. The results show the following:

(1)

With the increase of screw rotational speed, the pressure field and viscosity field of the conventional screw flow field gradually decrease, while the shear rate field increases. The separated screw outperforms the conventional screw in all aspects, and the separated pin screw exhibits better mixing performance than the separated screw, which is more conducive to improving screw extrusion quality and mixing efficiency.

(2)

At a rotational speed of 20 rpm, the screw with pin structure exhibits a lower viscosity, which is beneficial to the mixing of polymer melts. The optimal pin structure parameters are determined as follows: pin diameter of 2 mm, screw height of 1.6 mm, screw radial angle of 60°, and pin axial spacing of 10 mm.

(3)

The extrusion quality of both the separated screw and the separated pin screw is higher than that of the conventional screw. The samples printed with the separated pin screw show the best performance in tensile strength and flexural strength tests compared with those printed with other types of screws.

(4)

This screw design provides an effective solution to the difficulty in stable and efficient extrusion of high-filled composite granular materials during 3D printing. It allows the direct use of low-cost raw granules or recycled materials, significantly reducing material costs (by an estimated over 50%), and supports flexible material switching and customized formulations. The technology is suitable for the rapid manufacturing of high-end fields such as aerospace lightweight components, automotive functional parts, and medical personalized aids. Meanwhile, it offers a new approach for the green and high-value recycling of waste composites, aligning with the strategic direction of circular manufacturing.

The following is a prospect for future research work:

The main work of this study focuses on the optimized design of the barrier pin screw, conducting simulation analysis and numerical modeling of the designed structure. This research provides certain theoretical guidance and reference value for the screw design of extrusion-based 3D printers. However, the current research is primarily based on simulation and numerical analysis. Due to time constraints and experimental conditions, the experimental validation remains insufficient. Therefore, there is still room for further in-depth investigation. Potential areas for future research include the following:

(1)

In this study, a conventional barrier screw thread profile was employed in the design of the barrier screw. However, various types and forms of screw thread profiles exist, and their influence on the melting and extrusion process requires further in-depth investigation.

(2)

The pin design and distribution in this study were based on a uniform circumferential arrangement with equal pin height. A broader range of pin configurations has not yet been explored. To better understand the influence of pin arrangement on mixing efficiency and extrusion quality, future studies should investigate different pin distributions and identify the optimal configuration.

(3)

The current research primarily focuses on the melt flow behavior of a single material. Future work could be extended to multi-material co-extrusion systems, aiming to explore interfacial behavior and mixing characteristics between different materials. Additionally, artificial intelligence algorithms—such as genetic algorithms and neural networks—could be introduced for the optimization of screw structural parameters, thereby enhancing both design efficiency and performance.