Agora of Additive Manufacturing (2024) paper24001

Agora of Additive Manufacturing
journal homepage: http://additive-manufacturing.or.jp/

New 3D printer for molding continuous-fiber composites using coaxial
double nozzles
Akira Todoroki a*, Kota Hayakawa a, Masato Ueda b, Ryosuke Matsuzaki c, Keisuke Iizuka daDepartment of Mechanical Engineering, Tokyo Institute of Technology, Tokyo, Japanb

Department of Mechanical Engineering, College of Science and Technology, Nihon University, Tokyo, Japanc

Department of Mechanical and Aerospace Engineering, Faculty of Science and Technology, Tokyo University of Science, Chiba,JapandDepartment of Mechanical Engineering, Faculty of Science and Engineering, Aoyama Gakuin University, Kanagawa, Japan

ABSTRACT
Commercially available three-dimensional (3D) printers for continuous-fiber composites feature twin nozzles (one for shortfibers (or resin) and the other for continuous fibers). When designers use nonuniformly curved patterns for continuous
fibers, inevitable gaps between printing paths cause initial defects. To address this challenge, we developed 3D printerhardware with coaxially arranged nozzles for continuous and short-fiber filaments. This arrangement allows the adjustmentof the amount of the short-fiber (or resin) along the continuous-fiber path, preventing print path gaps. The short-fiber nozzle
uses a screw and pellets instead of filaments, with a hole at the center of the screw for printing continuous fibers. Aftermodifying the printing conditions, we fabricated unidirectional specimens using the proposed 3D printer and conductedtensile tests, which confirmed its effectiveness for printing continuous-fiber composites.
Keywords: Carbon fiber, 3D printing, additive manufacturing, twin-nozzle system, thermoplastics

1. Introduction
The Mark One® is a three-dimensional (3D) printer that fabricates continuous-fiber thermoplastics using the fused
filament fabrication (FFF) method. It was first unveiled in January 2014 at the SolidWorks World Design Conference inthe United States (1). In June 2014, Namiki et al. (2) attempted composite molding using an in-house 3D printer that molds
continuous-fiber-reinforced thermoplastic composite materials. Furthermore, Matsuzaki et al. (3) and Tian et al. (4)developed 3D printers that use a continuous-fiber nozzle-impregnated composite material using a modified 3D printer.
They demonstrated that composite materials comprising continuous fibers can be 3D printed using the FFF method.
Van Der Klift et al. (5) evaluated the tensile strength of continuous-fiber composites fabricated using Mark One®, whichis the first product of Markforged. The Mark One® exhibited significant variations in strength owing to problems with theinitial slicing software that determines the fiber arrangement of the 3D printer. In 2017, Markforged released Mark Two®,
which facilitated the 3D printing of continuous-fiber-reinforced composites with relatively free fiber arrangements (6). Mark
Two® allows users to select from two types of continuous-fiber arrangement methods: unidirectional and spiral or a mixtureof both. Todoroki et al. (7) reported the tensile strength of continuous-fiber composites molded using Mark Two®.
As an example of the application of 3D-printed continuous-fiber composites, Yamanaka et al. (8) demonstrated thepossibility of reducing the stress concentration around an open hole and improving the strength by bending the fibers in* Corresponding author
Email: todoroki.a.aa@m.titech.ac.jp
Received 27 March 2024; Revised 23 May 2024; Accepted 11 June 2024
Available online 26 July 2024

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various ways during fabrication. However, in commercially available Markforged 3D printers, the nozzles for short fibers(or resin) and continuous fibers are positioned differently, creating large gaps between adjacent paths with different
curvatures. Therefore, it is impossible to realize a fiber bundle arrangement in which the curvatures of adjacent fiber
bundles are different, as observed in the results obtained by Yamanaka et al. (8).
Thus, in this study, we developed a 3D printer for fabricating composite materials in which the outer nozzle for molding
short fibers and the inner nozzle for molding continuous fibers are arranged coaxially. This allows the injection amount ofshort fibers to vary depending on the location. To verify the operation of the proposed 3D printer for molding composite
materials, rectangular specimens were prepared for tensile tests, and the effectiveness of continuous-fiber reinforcement
was confirmed.
2. Basic design of proposed 3D printer2.1 Basic concepts
Fig. 1 shows a schematic representation of the printhead of the proposed 3D printer. The printer ejects short-fiberreinforced resin and long fibers coaxially to perform 3D printing. The short fibers are typically provided as pellets becauseof the low cost of pellets. Thus, a screw mechanism is used to supply the pellets. A small hole is drilled through the centerof the screw shaft, and a pipe is passed through the hole. Thereafter, the pipe is positioned coaxially with the screw as anozzle for the continuous fibers.

Fig. 1 Schematic representation of the proposed 3D printer.
To vary the mass of the short-fiber composites, the screw rotation speed was changed. This enabled us to covercontinuous fibers with short fibers by changing the injected mass depending on the fabrication location. Even when theprint path distance changed, the injected short-fiber was changed to fill the gaps.
Here, a continuous carbon fiber-reinforced polymer (CFRP) filament (Markforged, fiber volume fraction of
approximately 30 %) was used. Considering that this filament uses PA-6 resin, carbon fiber PA-6ellets (3DX Tech) wereused as short-fiber-reinforced resin pellets. The fiber volume fraction of this material was approximately 15 %.
2.2 Screw design
Fig. 2 shows a 3D model of the designed screw, and Table 1 presents the properties of the screw. The screw shape wasintended to efficiently supply resin pellets to the heating and melting sections; thus, a single screw without a compression
ratio was adopted (9)(10). In addition, considering that the size of the resin pellets was approximately 3.5 mm, the screw
groove depth was 4.5 mm, and the screw pitch was 26. A small hole (diameter = 1.4 mm; length = 175.3 mm) was madethrough the center of the screw shaft to allow the long fibers and metal pipe to pass through.

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Fig. 2 Screw design.

Table 1. Screw Properties
Screw properties
Screw length [mm]Screw diameter [mm]Screw pitch [mm]Hole diameter [mm]Channel depth [mm]Compression ratio
ChannelValues
114
15
26
1.4
4.5
1
Single2.3 Heat block design
To design the heat block, the thermal properties of the short-fiber-reinforced resin pellets were determined. A differential
scanning calorimeter (DSC-60plus, Shimadzu Corp.) was used. The experiments were performed in accordance with JIS
K7121-7123, and the melting point, heat of fusion, and specific heat of the material were determined (Table 2).
Table 2 Thermal properties of carbon fiber Nylon 6 pellets
Thermal properties [unit]
Melting point [℃]
Melting heat [J/g]Specific heat [J/kg K]

Measured results
221.6
29.5
6.48T + 968

Let us assume that the 3D printing is in a thermally steady-state. In the steady-state, an injection device, such as thescrew, exhibits a steady temperature. Thus, the amount of heat input required by the heater is the sum of the heat (Q1)required to increase the temperature of the pellets to their melting point and the heat of fusion (Q2) required to melt thepellets. In addition, because the pellets melt as the screw feeds them, the heater capacity that provides the required heat perunit time is equal to the amount of heat required to melt the resin transported by the screw per unit time. The density (r)and specific heat (Cp) can be calculated using the following equations. This is based on the temperature at the end of theheating period (Tf), temperature at the beginning of the heating period (Ts), heat of fusion of the pellets (Q), and volume ofthe pellets flowing into the screw per second (q).
#𝑄! = ∫# ! 𝑞𝜌𝐶" 𝑑𝑇.

(1)

𝑄$ = 𝑞𝜌𝑄.

(2)"

q was set to 20 mm3/s based on the filament extrusion speed of the filament manufacturing machine (FILASTRUDER).
The Cp, Q, and end-of-heating temperature were obtained from Table 2. The initial heating temperature was set to 20 °C.
The calculations yielded Q1 = 78.7 J/S and Q2 = 6.90 J/S. Some heat was lost via heat transfer through the carbon fibers of

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the pellets; thus, the safety factor of the thermal design was set to 3, and the required heat capacity of the heater was set to
250 W.
Fig. 3 shows the designed heating area. The heating area heats and melts the resin; thus, all the parts were made of metal.
The barrel and heat block, which heat and melt the resin, were made of aluminum alloy A5052, which exhibits high thermal
conductivity. The mount part, which is fixed to the plastic hopper, was made of SUS304, which exhibits low thermal
conductivity, to prevent heat transfer. Brass, frequently used in general-purpose FFF-type 3D printers, was used for thenozzle. A heat sink (diameter = 30 mm; thickness = 1.5 mm) was attached to the barrel to reduce the heat transfer to the
top of the barrel. This was because the hopper attached to the mount part was made using a resin-based 3D printer andfabricated using short carbon fiber, PA-6. In the designed heating parts shown in Fig. 3, steady-state heat transfer was
expected during the steady-state printing process. Thus, a steady-state analysis of the heating area was conducted using
Ansys Workbench 18.1. The analysis was based on the assumption that the heater temperature was 240 °C (20 °C above
the melting point of the material) and that the sides of the heat block were covered with insulating material (heat transfer
coefficient set to 0). The heat transfer coefficient of the heat sink was set to 30 W/(m2K), assuming forced air convection.

BarrelFig. 3 Schematic representation of heating area.
Fig. 4 shows the results of the steady-state analysis. In the designed heating region, the temperature of the feed zone
gradually increased from top to bottom. Furthermore, because the heat zone reached a temperature range of 227–240 °C(exceeding the melting point of PA-6 (220 °C)), we determined that the PA-6 heated through the feed zone can be melted
in the heat zone. The temperature of the mount part was 87 °C, and the continuous use temperature of the structural material(PA-6) of the hopper was in the range of 80–150 °C. The load on this part was only the weight of the hopper and the weightof the pellets; thus, we conclude that continuous use is entirely possible even in the designed heating region.

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Fig. 4 Finite element method analysis results of heated parts.
2.4 Motor and gear settings
The proposed 3D printer uses a coaxial double nozzle mechanism. Thus, a pipe for the continuous-fiber passes throughthe coaxial hole of the screw, and the space above the screw is used as the feed space for the fiber. Therefore, the motorthat rotates the screw is positioned away from the screw shaft, and the resin is heated and melted as the screw rotates,
thereby increasing its viscosity. It has been reported that viscosity increases when reinforcing fibers are combined with thebase resin; thus, a high torque is required to rotate the screw (11).
Therefore, a worm gear was used. Considering that the worm gear comprised two parts, a worm and worm wheel, there
was no need to place the motor on the screw axis. Furthermore, compared with other gears, the worm gear is more likely
to achieve a large reduction ratio and can generate high torque, rendering it suitable for the proposed 3D printer. Equation(3) was used to calculate the output after deceleration.
𝑇$ = 𝑇! 𝑖𝜂% .

(3)

T1 is the motor torque, T2 is the output torque, i is the reduction ratio, and hR is the transmission efficiency of the worm
gear when driven from the worm side (12). Generally, the transmission efficiency is within the range of 0.3–0.9 and is 0.5
or less in the low-speed range (13). Here, it was set to 0.4 as a design guideline.
The T1 required to calculate T2 was calculated with two types of output torque (0.4 and 1.19 Nm), using the Nema 17
stepping motor (frequently used in general-purpose 3D printers) and the Nema 23 stepping motor (higher output torque).
The reduction ratio was calculated by varying the reduction ratio of commercially available worm gears in the range of 10–
60. The target output torque was set to a motor torque of 15.6 Nm, which is the setting used in the commercially available
filament molding machine, FILASTRUDER (14). As a high-output torque was required, the Nema23 motor was determined
appropriate for obtaining a motor torque of 15.6 Nm. The target value could be achieved by setting the reduction ratio to
40 or above. Here, a worm gear with a reduction ratio of 40 was used.
2.5 PrintheadFig. 5 shows an image of the designed printhead. Fig. 6 shows the external dimensions and cross-section of the printhead.

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Fig. 5 Designed printhead.

Fig. 6 Dimensions and cross-sectional view of printhead.
Considering the ease of installation and control of the printhead of the proposed 3D printer, we selected the Velleman
K8200 3D printer as the body. Fig. 7 shows the complete 3D printer.

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Fig. 7 Appearance of proposed 3D printer.
The 3D printer requires control of the X, Y, and Z axes, rotation control of the screw in the extruder section, andtemperature control of the heating area. The difference between this printer and a general-purpose FFF 3D printer is thehigh motor current in the extruder section and the heater capacity. Thus, we adopted the Megatronics v3.3 control board(RepRap) (hereinafter referred to as Megatronics), which features an easy-to-replace motor driver. Considering that
Megatronics can use an external driver for motor control that requires a higher current than usual, it was possible to use theTB6600 (SainSmart) motor driver, which can control the Nema 23 used in the extruder section. In addition, because theoutput of Megatronics was insufficient, we adopted the MTCD (MISUMI) temperature controller to control the temperatureof the heater. This controller can use a 100 V-driven heater; this allowed us to use the high-output heater required for the
3D printer.
Using the proposed 3D printer, we printed continuous carbon fiber/PA-6 and short carbon fiber/PA-6 to optimize theprinthead temperature, molding speed, and tip position of the inner pipe of the coaxial double nozzle. A nozzle with adiameter of 2.4 mm was used, considering that the pipe would pass through the inside. After trial-and-error experiments, a
printhead temperature of 240 °C and molding speed of 100 mm/min were determined as conditions that minimized theoccurrence of voids between paths and deviations in the continuous fibers. The screw rotation speed was 3.5 min−1.
The position of the pipe for the continuous-fiber in the screw could be set independently of the screw tip. This pipe wasused to protect the continuous-fiber and adjust the position at which it was injected. If the continuous-fiber were supplied
without a pipe, it would rub against the edge of the rotating screw. The primary purpose of using the pipe was to prevent
this damage. The secondary purpose was to adjust the position of the pipe tip such that the continuous-fiber was embeddedin the center of the path of the thermoplastic resin injected by the screw. Without the pipe, the continuous-fiber would bendin the direction of the path from the screw hole and be positioned above the path of the injected thermoplastic resin. The
pipe was installed to adjust the position of the continuous-fiber (see Appendix).
Three types of pipe position adjustments were experimentally examined: Types A, B, and C, in which the pipe tip wasplaced 1 mm in the nozzle tip, 0.2 mm beyond the nozzle tip, and 0.5 mm beyond the nozzle tip, respectively. However,
because the material was not uniformly extruded if the screw extrusion amount was small, the distance between the nozzle
and bed (layer pitch) was set to 0.6 mm. The Type B state was set to less than half the layer pitch, whereas the Type C state

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was set to between half the layer pitch and the layer pitch. The Type B position, which experimentally produced the fewest
voids, was selected (see Appendix). Table 3 lists the selected molding conditions. It should be noted that a fiber-cutting
device was not installed on the proposed 3D printer.
Table 3 Three-dimensional printing conditions used in this study

3D printing conditions [unit]

Value

Nozzle temperature [℃]240

Print speed [mm/min]

100

Distance between print paths [mm]2.4

3. Verification of effectiveness through strength testing
Using the proposed 3D printer, test specimens containing a mixture of continuous and short fibers were prepared. In
addition, 0° tensile tests, in which a tensile load was applied in the direction of the continuous fibers, and 90° tensile tests,
in which a tensile load was applied perpendicular to the fiber direction, were performed.
3.1 Preparation of test specimens
The proposed 3D printer was not equipped with a function for cutting continuous fibers. Thus, when preparing the plateshaped test specimen, the fibers were continuously molded to avoid cutting, and the curved portions of the fiber bundles
were removed after molding. For example, Fig. 8 shows a schematic diagram of the print path of a 0° layer tensile test
specimen. A unidirectional continuous-fiber path was created by bending the continuous fibers at their ends on the print
bed. When moving to the upper layer, the nozzle was raised at the end of the specimen and a unidirectional continuousfiber path was started without cutting the fibers. Through this method, the continuous fibers were connected in the stacking
direction at the ends. Thus, the ends were cut to conduct tensile tests.

Fig. 8 Example of a print path for the fabrication of unidirectional composite specimens.
The test specimen was 120 mm long × 16.8 mm wide × 2.4 mm thick, with a print path distance of 2.4 mm and a layer
pitch of 0.6 mm, with four layers laminated. Under these fabrication conditions, the volume fraction of continuous fibers,
when using continuous-fiber filaments, was approximately 3 %. After 3D printing, both ends of the test specimen were cut
by 5 mm to eliminate the influence of the ends, and the test specimens were only fabricated in the 0° direction. Three test
specimens were fabricated using only short-fiber-reinforced resin, and three were formed using long fibers. The tests wereconducted by bonding 1.5-mm-thick glass fiber-reinforced polymer (GFRP) tabs to the 25-mm sections at both ends of thetest specimens. Uniaxial strain gauges were attached to both sides of the center of the test specimen to measure the strain
in the tensile direction.
Fig. 9 shows the 90° test specimen, which was 120 mm long × 15 mm wide × 1.8 mm thick, with a print path distanceof 2.4 mm and a layer pitch of 0.6 mm. The specimen was fabricated through three layers of lamination. To eliminate the

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influence of the folded fiber bundle, the ends were cut at 5-mm intervals after 3D printing to prepare the test specimens.
Similar to the 0° test specimens, three test specimens were fabricated using only short-fiber-reinforced resin, and threewere prepared using long fibers. GFRP tabs (thickness = 1.5 mm) were attached to both ends of the fabricated test
specimens, 25 mm from each end, and the test was performed. Uniaxial strain gauges were attached to both sides of thecenter of the test specimen to measure the strain in the tensile direction.

Fig. 9 Print path of 90° specimen.
The test specimens prepared using the aforementioned procedures were subjected to tensile tests using a universal tester(AUTOGRAPH AG-I 100kN, Shimadzu Corp.) at a test speed of 1 mm/min. To avoid the effects of moisture absorption,
the specimens were stored in a desiccator at a humidity level of 10 % or less for more than 72 h after preparation prior to
the tests.
3.2 Tensile tests
Fig. 10 shows the stress–strain curves obtained from the tensile tests. Figs. 10 (a) and 10 (b) show the stress–strain
relationship of the specimens with and without (only short fibers) continuous fibers in the 0° direction, respectively. Figs.
10 (c) and 10 (d) show the results of the specimens with and without (only short fibers) continuous fibers in the 90° direction,
respectively.

Strain(a) 0° specimen with continuous carbon fibers.

10-2

Strain10-2(b) 0° specimen without continuous carbon fibers (short-fiber
composites)

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10-2

Strain(c) 90° specimen with continuous carbon fibers.

10-2

Strain(d) 90° specimen without continuous carbon fibers(short-fiber composites).

Fig. 10 Stress–strain curves of tensile test specimens.

Table 4 Mechanical properties of 0° orientation specimen

Tensile strength [MPa](Standard deviation)
Elastic modulus [GPa](Standard deviation)

0° orientation specimen
with continuous fibers

0° orientation specimen
without continuous fibers

121.4(6.14)
5.74(0.49)

54.9(2.18)
2.95(0.04)

Table 5 Mechanical properties of 90° direction specimen

Tensile strength [MPa](Standard deviation)
Elastic modulus [GPa](Standard deviation)

90° orientation specimen
with continuous fibers

90° orientation specimen
without continuous fibers

5.22(0.81)
1.31(0.27)

4.35(0.31)
1.12(0.06)

Tables 4 and 5 present the average values and standard deviations of the mechanical properties of the 0° and 90°
specimens, respectively. Fig. 11 shows the appearance of each specimen after fracturing.

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(b) 0° specimen without continuous carbon fibers (short-fiber
composites).

(b) (c) 90° specimen with continuous carbon fibers. (d) 90° specimen without continuous carbon fibers (short-fiber
composites).

Fig. 11 Specimens after tensile tests.

For the 0° direction (fiber orientation) of the composite containing continuous fibers, the slope of the stress–strain
relationship differed for each specimen, resulting in a variation in the elastic modulus. However, the stress–strain
relationship was only slightly nonlinear in the high-stress region. The elastic modulus and strength in the 0° direction are
subsequently discussed.
In the extrusion direction of the short carbon fiber PA-6 without continuous fibers (Fig. 10 (b)), a nonlinear stress–strain
relationship was observed. The elastic modulus and tensile strength were 2.95 GPa and 54.9 MPa, respectively (Table 4).
In the 90° direction (Table 5), the elastic modulus was 1.12. The compressive strength of the fiber was 4.35 GPa, which
was practically one-third of the original strength. The tensile strength was 4.35 MPa, which was less than one-tenth of theoriginal strength. As reported by Koga et al. (15), this was caused by the anisotropy that occurs when short fibers are alignedin the ejection direction from the nozzle (print path direction) during 3D printing.
The elastic modulus with continuous fibers in the 0° direction was 5.74, and the tensile strength was 122 MPa. The
continuous-fiber was used as a continuous-fiber filament with a fiber volume fraction of approximately 30 %. The
continuous-fiber-reinforced PA-6 filament occupied 10 % of the volume of one print path. The measured tensile strengthof the Markforged continuous-fiber-reinforced PA-6 filament in the 0º direction was 701 MPa, and the elastic modulus was
60. Considering that the elastic modulus was 1 GPa, it was calculated using the rule of mixtures (8), with the following
equation, assuming that the volume fraction of the continuous-fiber filaments is VCF = 10 %:𝐸& = 𝐸'( 𝑉') + (1 − 𝑉') )𝐸*( = 60 × 0.1 + 0.9 × 2.95 = 8.7 GPa.
The strength was calculated using the following equation:(4)

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𝜎& = 𝜎'( 𝑉') + (1 − 𝑉') )𝜎*( = 701 × 0.1 + 0.9 × 54.9 = 120 MPa.

(5)Comparing the results calculated using the mixture rule with the measured values, the tensile strength was practicallyconsistent with the measured value (121 MPa). This showed that the continuous fibers were effective and that fiber breakage
during molding did not occur to a problematic degree. The measured elastic modulus (5.74 GPa) was slightly smaller thanthe calculated value (8.7 GPa). Owing to the variation in the stress–strain relationship, it was determined that the strain
gauge did not correctly measure the average tensile strain because of the influence of the warping of the test piece, surface
unevenness, and the volume fraction of the continuous fibers being only 3%. In addition, the mixture rule of Equation (4)does not consider the effects of voids; however, a mixture rule (16) that considers voids exists. Here, we were unable toobserve the detailed distribution of voids in the test piece; therefore, we will include a detailed observation of the void
distribution in the future.
Furthermore, as shown in Figs. 11(a) and (b), vertical cracks occurred on the fracture surface in the print path direction.
This implied that the fusion between the print paths was insufficient; thus, further optimization of the molding conditions
is necessary.
The 0° test piece containing continuous fibers was subjected to X-ray computed tomography (CT, Comscan Techno,
ScanXmate-L080HT, 1 pixel per 50 µm) (Fig. 12). The vertical direction in the image is the fiber direction of 0°, and black
shadows of voids can be observed along the fiber orientation. Fig. 13 shows the results of the X-ray CT observations of
only the short carbon fiber composite. Voids were observed between the print paths, indicating that the fusion between theprint paths was insufficient.

Fig. 12 X-ray CT observation result of 0° specimen with continuous carbon fibers.

Fig. 13 X-ray CT observation result of 0° specimen without continuous carbon fibers.
To measure the void ratio, a cross-sectional observation was performed on the 0º test specimen containing continuous
fibers. The test specimen in this study was a composite of continuous and short carbon fibers; thus, the combustion method

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was not employed, and the void ratio was measured from the cross-sectional image. Fig. 14 shows a cross-sectional imageof the 0° test specimen containing continuous fibers. Black areas were observed between the print paths and voids.

Voids

Fig. 14 Cross-sectional observation of 0° specimen with continuous carbon fibers.
A void fraction of 6.8% was measured using the ImageJ image processing software on the observation results. Van Der
Klift et al. stated that the void fraction was approximately 7% based on cross-sectional observations of a Mark One
continuous-fiber test piece (5). Thus, the void fraction did not improve, and it was considered that this affected the error
between the measured and calculated elastic moduli. However, the void fraction could be improved by adjusting themolding conditions, which is a future challenge.
4. Conclusions
The purpose of this study was to develop a 3D printer for molding composite materials that can change the ratio ofcontinuous-fiber to thermoplastic resin or short-fiber-reinforced thermoplastic resin during printing. A nozzle for molding
short-fiber or resin and a nozzle for molding continuous-fiber were arranged coaxially. The injection amount of the shortfiber or resin was dependent on the location. The results are summarized as follows:(1)

We developed a 3D printer with a continuous-fiber nozzle at the center of the screw that injects thermoplastic resinor short-fiber-reinforced thermoplastic resin. The amount of thermoplastic resin between the print paths can bevaried, and the operability of the printer was validated.

(2)

Owing to the inner continuous-fiber pipe of the coaxial double nozzle, protruding from the outer nozzle by 0.2 mm,
it was possible to mold the fibers in a print path in which they are encased in thermoplastic resin.

(3)

The molded tensile test specimens practically exhibited the same strength as the theoretical strength in the 0° tensile
test, and the effects of fiber breakage that occurred during printing were observed to be minimal.

(4)

The molded continuous-fiber-reinforced thermoplastic resin had a void ratio of 6.8 %; thus, the molding conditions
require optimization.

Acknowledgments
Some of the experiments reported in this paper were supported by AGC Ltd. We would like to express our gratitude to
all of those involved.
Appendix
As mentioned in Section 2.5, three adjustments to the pipe position were experimentally investigated. They include
Types A–C, in which the pipe tip was placed 1 mm in the nozzle tip, protruded 0.2 mm from the nozzle tip, and protruded
0.5 mm from the nozzle tip, respectively. Fig. A1 shows the schematic representation of the pipe positions.

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Fig. A1 Schematic representation of pipe position used for the nozzle for continuous-fiber filaments.
The solidified resin was fused to the bed or lower layer during lamination; thus, continuous fibers were fixed to the bedat that point. When the nozzle moved to the right (Fig. A1), the continuous fibers in the pipe were pulled by the nozzle
because they were fixed on the left side, where the resin had solidified. Furthermore, the thermoplastic resin in the nozzle
and near the outlet was molten. Thus, in the Type A state, the continuous fibers contacted the edge of the nozzle, and thefiber bundle ended at the top of the print path; therefore, the fiber bundle was not wrapped in the resin layer (short-fiber
CFRP, abbreviated herein as sCFRP). This result was practically the same even when the heights of the pipe and nozzle
were the same. Based on the above, Types B and C, were considered, and Type A was used for comparison. Fig. A2 shows
the cross-sectional images of the printing path.

(a) Type A.

(b) Type B.

(c) Type C.

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Fig. A2 Cross-sectional observations of the print path of Types A–C.
As shown in Fig. A2(a), in Type A, the continuous-fiber was fixed at the top end of the print path, and the sCFRP could
not encase the continuous-fiber. In addition, the continuous-fiber filament was lifted from the printed thermoplastic resin,
and a large void was formed on the underside of the continuous-fiber filament. In Type B (Fig. A2(b)), the continuous-fiber
bundle successfully encased the sCFRP. Although voids still existed, they were relatively small. In Type C, the grooves
created by the pipe remained. These grooves could become large voids during lamination.
We considered this phenomenon using a simple model. Fig. A3 shows the coordinate system for Type C, in which agroove is created in the print path by extending a pipe from the nozzle. The nozzle moved in the positive x-axis direction.
A printing path with a groove created by the pipe was printed to the left of the nozzle.

Outer nozzle

Printed path grooved by the pipe

Moving direction

z
o

y
x

Pipe of the internal nozzle

Fig. A3 Schematic representation of the printing process when the pipe makes a groove on the printed path.
Fig. A4 shows a schematic diagram of the nozzle movement, viewed from above. The double circles represent the coaxial
double nozzle. When viewed from above the bed (above the z-axis in Fig. A3), the nozzle moved to the right in a straightline from A1 to A2 (Fig. A4). The inner diameter of the outer nozzle of the double nozzle is d0, and the outer diameter ofthe inner pipe nozzle is di. The solid double circles in Fig. A4 represent the position of the double nozzle at time t0 (central
position, a0).
t1 (t1 > t0), when the nozzle moved a distance L = (do + di)/2 to the left, is indicated by a dashed double circle in Fig. A4(central position, a3). For simplicity, we only considered the A1–A2 line. The molten resin was injected into the right endof the inner pipe of the double nozzle (a1, Fig. A4) at time t0 (a0). As the inner pipe nozzle moved to the right, a groove wascreated with a depth equal to the amount of pipe protrusion (dh) from the tip of the outer nozzle. The width of the groove
was the pipe diameter (di). Fig. A5 shows the schematic representation of a grooved printed path.

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𝑑" + 𝑑$2

Outer nozzle: doInner nozzle: diyNozzle moving direction

A2

A1

o

a0

a1 a2

a3

x

Fig. A4 Modeling of nozzle movement.
As shown in Fig. A5, the sCFRP (or thermoplastic resin) injected from the outer nozzle indicated by the broken line in Fig.
A4 between a1 and a2 was scraped off to a depth of dh by the pipe. The pipe protruded by the dh from the tip of the outer
nozzle.

Heat blockz
Protruding lengthof the pipedhOuter nozzle
Inner nozzle pipeoInjected sCFRP or ThermoplasticyContinuous fibers injectedfrom the inner nozzle

Fig. A5 Schematic representation of a grooved printed path.
The continuous fibers ejected from the pipe of the inner nozzle fused with the surrounding sCFRP at a position lower thanthe dh (Fig. A5). Thus, the depth of the groove created by the pipe was equal to the dh regardless of the continuous fibers.
If the resin flow was not considered, this groove was backfilled by the ejection of sCFRP from the outer nozzle as thenozzle moved to the right (ejection of sCFRP between a1 and a2 on the A1–A2 line in Fig. A4). In an analysis of the 3D
printing of sCFRP by Imaeda et al. using a particle method (17), the ejected sCFRP in the part that did not come into contact
with the nozzle edge was solidified immediately. The groove created by the pipe did not remelt unless molten sCFRP was
supplied from the outer nozzle when the pipe moved, and the movement of the resin due to melting was considered minimal.
For simplicity, the unit area injected from the outer nozzle and the injection volume per unit time was uniform anddesignated as W [mm/s], and the nozzle movement speed was V [mm/s] (generally, W = V). As shown in Fig. A4, on theA1–A2 line, a groove was created by the pipe movement when the right end of the pipe reached position a1, and the outer
nozzle at position a1 completed the backfilling of the groove when the left end of the pipe reached position a2. Consideringthat the nozzle movement distance was L = (d0 + di)/2, the time Δt for the nozzle center position to move from a0 to a3 wasgiven by Δt = L/V. However, the time until the left end of the pipe passed position a1 was used for the pipe to create the

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Agora of Additive Manufacturing (2024) paper24001

groove; thus, this movement time was not used to backfill the groove (Fig. A6). As the pipe passed from position a1 to theposition indicated by the dashed line in Fig. A6, it was not used to backfill the groove. At this time, the center of the nozzle
was shifted to the right of a0 by twice the radius of the pipe (i.e., the pipe diameter). Thus, it is necessary to subtract thetime it takes for the nozzle to move the pipe diameter from the nozzle travel distance L, and the actual backfilling time was

ΔtT = (L − di)/V = (do − di )/(2V).

y

A2

A1

o

x
a1+ 𝑑"

a1

Fig. A6 Starting point of backfilling.
The volume of sCFRP injected per unit area in time ΔtT was ΔtTW. Thus, the height of the sCFRP injected per unit area
into the groove made by the pipe was ΔtTW. If this exceeds the depth of the groove created by the pipe, the groove will
be filled. As shown in Fig. A6, the depth of the groove created by the pipe was dh. Thus, the following equation was
obtained as the pipe installation condition:ΔtTW > dh.

(A1)

In the experiment, the injection speed W = V = 100 mm/min (1.67 mm/s); thus, Equation (A1) became(do − di)/2 > dh.

(A2)

The inner diameter of the outer nozzle was 2.5 mm, and the outer diameter of the pipe was 1.2 mm. By substituting these
into Equation (A2), the following condition was obtained:
0.65 mm > dh.

(A3)

In Type B (Fig. A1), dh = 0.2 mm, which fully satisfies Equation (A3). In Type C, dh = 0.5 mm, which satisfies Equation(A3); however, the groove was not filled.
This was believed to be because when the dh is deep, the pipe undergoes bending elastic deformation due to the resistanceof the sCFRP being pushed aside (Fig. A7). The resistance pushing against the sCFRP caused the pipe to bend to the left,
opposite the direction of the nozzle movement (to the right). This bending deformation was denoted as db. The backfilling
start time was delayed by the amount of db. However, because the nozzle movement speed did not change, the backfillingend time did not change; thus, the time available for backfilling was reduced.

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db

y

o

A2

A1
x
a1

a1+ 𝑑" +db

Fig. A7 Retardation of starting point of backfilling because of bending of pipe.
The cross-section in Fig. A2 shows continuous fibers just below the pipe groove, and it is clear that they had not been
backfilled at all. This was presumably because the pipe was in contact with the left end of the nozzle (Fig. A7). As shownin Fig. 9, the pipe was fixed to the top of the motor mount; thus, the pipe length was approximately 220 mm. When astainless steel pipe (outer and inner diameters of 1.2 and 0.8 mm, respectively) was used, the second moment of area was
0.081681 mm4, and the load that causes a displacement of 0.6 mm at the tip of a cantilever beam with a length of 220 mm
was only approximately 0.27 g. In addition, this was confirmed by the cross-sectional observation image shown in Fig. A2.
It was expected that the pipe would move left and right because of the use of the screw. Thus, fundamental improvements
are required to prevent the pipe from moving left and right; this will be addressed in the future.
We estimated the viscous resistance (F) when a pipe moves through molten sCFRP. Considering that the flow was very
slow, and the resin was in contact with the pipe, which had reached its melting point, the surrounding resin was considered
to be a molten viscous fluid. If we consider the pipe as a cylinder and use the Stokes approximation for a slow-moving
viscous fluid around the cylinder (18), the F acting on the cylinder is given by the following equation:
F = 8pµU /{1+2log(La/a)}.

(A4)Here, µ is the viscosity coefficient, U is the fluid velocity, La is an arbitrary length, and a is the radius of the cylinder.
Although the Stokes approximation around a cylinder is not accurate (18), it is simple. As an approximation, let La = a.
Multiplied by the pipe extension length (depth of groove made by pipe) dh as the length that receives the load, the following
equation was obtained:
F = 2.67pµUdh.

(A5)

The viscosity coefficient of PA-6 was approximately 2000 Poise near its melting point (19). However, because PA-6 contains
10% fiber by volume and was thought to rapidly solidify when it leaves the pipe (17), it was estimated to have an averagevalue of 3000 Poise. The flow velocity, U, considering the speed of movement through the pipe, was calculated to be 0.2
g, which was close to 0.27 g. In reality, it was estimated that the reaction force Ff, caused by the continuous fibers being
sheared at the end of the pipe, acted in the direction in which the pipe bent.
The deformation of the pipe due to viscous resistance acted in a direction that reduced the left side of Equation (A2);therefore, if we define this deformation as d1, the equation was modified as follows:

A. Todoroki et al.

Agora of Additive Manufacturing (2024) paper24001(do − di)/2 – d1 > dh.

(A6)

However, for the bending of a cantilever beam, if F is the load at the tip, Lb is the length, and EI is the bending rigidity,
the following equation was obtained:

d = FLb3/(3EI).

(A7)

Substituting Equation (A5) into F in Equation (A7) and then into Equation (A6), the following equation was obtained:(do − di)/2-2.76pµULb3dh/(3EI) > dh.

(A8)

We used a viscosity coefficient of 3000 Poise in Equation (A8) and calculated, as mentioned earlier, that the condition
was satisfied even when dh = 0.5 mm. As previously mentioned, the Ff caused by the continuous-fiber being sheared at theend of the pipe bent the pipe. By inserting Equations (A7) into (A8), the following equation was obtained:(do − di)/2 − 2.76pµULb3dh /(3EI) − Ff Lb3 /(3EI) > dh.

(A9)

In the viscosity coefficient model used in a study (16), when the rate dependency was ignored, the viscosity coefficient
was approximately 1960 Poise near the melting point of PA-6. The viscosity coefficient may reach approximately 3000
Poise because of the presence of short fibers and solidification.
The exact effects of viscosity and continuous-fiber shearing are unknown; thus, it is convenient to divide the left side ofEquation (A9) by a safety factor, S. Transforming Equation (A9) yielded the following:(do − di)/2 > {2.76pµULb3/(3EI) + 1} dh + Ff Lb3/(3EI)(A10)

Here, if Ff can be measured, Equation (A10) can be calculated. If the external force that causes a 0.6-mm displacementin the pipe is 0.27 g and the difference between the viscous force of 3000 Poise is 0.07 g, then Equation (A10) is no longer
satisfied at dh = 0.5 mm. The measurement of Ff will be investigated in the future.
Appendix data
Hole screw STL data <screw.stl here>

Printing process video https://youtube.com/shorts/4NwIi-WuFd0
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