Thermal study of clogging during filament-based material extrusion additive manufacturing: Experimental-numerical study

One of the major drawbacks of material extrusion additive manufacturing (AM) is hot-end clogging. This study aims to answer the question, “What thermal conditions lead to clogging during filament-based material extrusion?” Answering this question requires a clear understanding of temperature distribution inside the liquefier. However, this could not be achieved only through experimental measurements. Therefore, numerical simulations were also carried out by developing a 3D finite volume model of the hot-end. The results obtained from numerical simulations show good agreement with experimental measurements. They also give us a detailed picture of the temperature gradient near the nozzle. Moreover, a series of experiments were performed to determine when clogging occurs, and some criteria for avoiding clogging were presented. These results were also compared and combined with the numerical results to investigate the thermal condition leading to clogging. As the results show, overheating the heat barrier increases the length of the filament, whose temperature is above the glass transition temperature. As this length exceeds a critical value, the filament buckles under the extruder motor force and clogging occurs .


Introduction
The global additive manufacturing (AM) market size has been growing steadily and is expected to reach USD 34.8 billion by 2024 [1]. During the AM process, the part is built layer by layer based on a computer-aided design (CAD) model. There are seven major branches of 3D printing techniques: Vat photopolymerization, material jetting, binder jetting, powder bed fusion, material extrusion, directed energy deposition, and sheet lamination [2].
Among them, material extrusion (also known as fused filament fabrication, FFF) is the most common method because its process is simple and incurs lesser manufacturing cost.
The filament-based material extrusion technique has made its way into a wide range of applications like rapid prototyping [3], art [4,5], and medical fields [6][7][8]. It is also widely used to make metamaterials that have broad potential applications [9].
Despite the wide range of applications of this technique, there are still some defects and process failures to overcome, like hot-end clogging, overflow, layer separation, and warping. Among them, hot-end clogging is one of the most significant process failures. To detect clogging, some researchers compared the printing part with the original CAD model during the printing process using various tools, such as image processing software [10], visible light 3D scanning systems [11], and augmented reality (AR) toolkit [12].
Some others presented a physics-based dynamic model of the process and identified the process errors using vibration signals gathered from vibration sensors [13,14]. The studies mentioned above have focused on detecting and monitoring clogging during the printing process. However, potential factors causing nozzle clogging must be identified to avoid this process failure. One of these factors is incorporating high loadings of nanomaterials [15] or using reinforced polymers at higher filler contents [16]. Beran et al. [16] investigated potential factors that can cause nozzle clogging for a filled polymer, such as nozzle and filler diameters, resin viscosity, and filler volume fraction.
Other factors can also lead to clogging, such as dust or burnt filament inside the liquefier, insufficient layer height, warping of the printing part [13], and inappropriate liquefier cooling. Among these factors, inappropriate liquefier cooling is one of the most common reasons for clogging since nearly half of all E3D-v6 hot-end issues are related to inadequate liquefier cooling conditions [17]. On the other hand, overcooling can lead to energy waste because more energy is needed to keep the nozzle temperature at the desired value and drive the fan at higher speeds for higher air delivery rates.
So, it seems that the liquefier's thermal behavior plays a vital role in clogging and needs to be investigated.
Jerez-Mesa et al. [18] studied the thermal behavior of the BCNozzle, designed at the BCN3D Technologies, and presented a relationship between fan air velocity and heat sink temperature. In another study [19], the thermal performance of 3 different heat sinks, including BCNozzle, were compared with each other to determine the most efficient design. Despite these limited thermal studies on hot-ends, to the knowledge of the authors, no study has addressed the thermal conditions that lead to clogging, as is the aim of this paper.
Considering growing multicolor printing applications [20][21][22], the RepRap multi-material Diamond hot-end has been selected for investigation in this study. This nozzle has also been shown to have many advantages, including efficient fabrication of gradient materials, easy calibration, and better precision [23] [24].
This study aims to give a precise and practical insight into the clogging phenomenon in filament-based material extrusion technique. Two different materials of ABS and PLA are considered in this study because of their widespread use. To investigate the thermal conditions leading to clogging, in the beginning, the temperature distribution along the heat sink has been investigated experimentally and numerically at various fan airflow velocities.
The results show considering the radiation heat transfer is vital to achieve a good agreement between numerical and experimental results, especially at low fan airflow velocities. In this paper, the effects of considering the radiation model in numerical simulations are discussed at zero and non-zero fan airflow velocities, and the minimum airflow velocity at which radiation heat transfer can be safely neglected is determined. Based on the results obtained from numerical simulations and the experiments designed and performed to detect clogging, a good insight into the clogging mechanism is achieved. The results show that in poor cooling conditions, the length of the filament inside the heat barrier, whose temperature is above the glass transition temperature, increases considerably, and under the extruder motor force, it buckles and consequently clogs the hot-end.

Experimental set-up
According to Fig. 1 bridges, and small details to provide a suitable base for the next layer [25].
Incorrect use of this terminal for heat sink cooling fan is one of the common causes of clogging in the actual printing process [17].  Percentage values of 15%, 20%, 30%, 40%, 50%, and 60% of board input voltage were applied using Repetier manual control tab to produce different voltages and airflow rates. The board input voltage was 12 . It should be noted that higher voltage percentages were avoided since further increasing the airflow velocity had little effect on the temperature distribution along the heat sink. This is mostly due to the dominance of forced convection that will be discussed later.
The experimental procedure to study the temperature distribution along the heat sink was as follows: • At the beginning of each test, the fan was turned on at the desired percentage of the input voltage.
• The ambient temperature was approximately 27°, and the nozzle was heated to 210° for the PLA, and 260° for the ABS.
• The heat sink was left for at least 30 minutes to reach a stable thermal condition.
• Under stable conditions, temperature values obtained from the thermistors were recorded.
Experiments repeated at least four times for all voltages and nozzle temperatures. Finally, the average of the results was calculated and reported.
A cube with dimensions of 15mm×15mm×20mm was printed to investigate the impact of heat sink cooling conditions on the clogging phenomenon during the printing process. The process parameters are shown in Table 1. The clogging test steps were as follows: • The ambient temperature was approximately 27°. The first five layers were printed at maximum fan speed to ensure that other potential factors such as the presence of burnt filament and dust did not cause clogging.
• After the first five layers, the fan voltage was adjusted to the desired value for that test.
• The printing process was monitored precisely. There were three different scenarios: (1) Complete clogging, (2) no complete clogging but with some problems, and (3) the printing process without any problem. If clogging was identified, the operation was stopped, and the hot-end was cleaned for the next experiment.
These experiments were also repeated four times for all fan voltages.

Numerical simulation
As shown in Fig Where is the fluid density and ⃗ is the fluid velocity.
Where is the fluid pressure, is the fluid dynamic viscosity, is the unit tensor, and ⃗ is the gravitational force.
Where is the thermal capacity, is the thermal conductivity, and is the temperature. Note that, as the Brinkman number is quite small, energy transfer through viscous dissipation was neglected.
The k-ε turbulence model was used to capture any turbulence in the airflow field. This model yields good accuracy in the absence of large adverse pressure gradients [27] while it uses just two additional transport equations, one for the turbulent kinetic energy (k) (Eq. 4) and one for the dissipation rate of turbulent kinetic energy (ε) (Eq. 5). Therefore, computational costs are not drastically affected. Also and are the generation of turbulent kinetic energy due to mean velocity gradients and buoyancy, respectively, and represents turbulent viscosity.
In this study, the Discrete Ordinate (DO) model was used to model the radiation effects. As a beam of radiation travels through a medium, it may lose energy because of medium absorption, gain energy from medium emissions, or its energy may be increased or decreased by medium scattering. The differential form of radiative transfer equation (RTE) for a beam in the direction ⃗ and position ⃗ can be written as: Where ⃗ is the position vector, ⃗ is the direction vector, ⃗ ′ is the scattering directional vector, is the path length, is the absorption coefficient, is the reflective index, is the scattering coefficient, is the phase function, ′ is the solid angle, and is the radiation intensity. is the Stefan-Boltzmann constant and equal to 5.67 × 10 −8 2 4 ⁄ .
DO transforms RTE into a set of simultaneous partial differential equations.
In the DO model, the equation of RTE (Eq. 6) is solved for a set of discrete directions that covers total angular space 4π sr. So that each octant of angular space was discretized to 4 polar angles ( ) and 4 azimuthal angles ( ∅ ), which means 8 × 4 × 4 solid angles. All solid angles were divided into 3 × 3 pixels. All surfaces were assumed to be opaque, diffuse, and gray.

3-2 Boundary conditions
As previously mentioned, only one-third of the geometry was modeled in the simulation. Fig. 6 shows the adopted boundary conditions. The gauge pressure at the pressure outlet boundaries (Fig. 6a) was considered to be zero, as it was sufficiently far from the main flow stream.
The static temperature at these boundaries was equalized with the ambient temperature 27°. The internal emissivity for all of these boundaries was assumed to be 1.
The no-pressure-drop periodic boundaries (Fig. 6b) used in this study implies that velocity components repeat themselves as follows: ( , , ) = ( , + , ) The same applies to the temperature.
The fan airflow was modeled by velocity inlet boundary condition (Fig. 6c).
As the nozzle temperature is continuously controlled at the desired temperature by the thermistor within the feedback loop, the constant temperature of 210° for PLA and 260° for ABS was considered for the Diamond nozzle domain.
In conjugate boundaries, equality of the temperature and heat flux for corresponding cells on the boundaries were provided.

Mesh study
A mesh convergence study was performed to ensure that obtained results are independent of mesh discretization. 4 different mesh sizes were tested and brought in Table 2. Mesh 2, shown in Fig. 7, was used throughout the study as it provided a good compromise between accuracy and computational costs. Increased mesh resolution produced negligible changes in the temperature values (the variable of interest), while in lower resolution (Mesh 3), slight inaccuracies were observed.

4-1-1 Heat sink thermal analysis at zero airflow velocity
Although the amount of voltage applied to the fan was known in each of the experiments, the value of the fan airflow velocity resulting from the applied voltage was not known except when the fan was off and the fan airflow velocity was zero. Therefore, the zero-velocity condition is of high importance to evaluate the numerical simulation. However, it seems this condition has not been considered earlier with the justification that turning off the fan is not recommended in the actual printing process [18].
The study of the zero-airflow condition illustrates the significance of considering radiation heat transfer. Four different nozzle temperatures of 100°, 125°, 150°, and 200° were considered for investigating the zeroairflow velocity condition to validate our numerical simulation. However, it is expected that at higher fan airflow velocities, this error will be reduced (this will be discussed below).

4-1-2 Heat sink thermal analysis at non-zero airflow velocities
For the experimental investigation of non-zero velocity conditions, different airflow rates were created by applying different voltages to the cooling fan.
Then, by comparing the experimental results of heat sink temperature distribution with numerical results, the cooling airflow velocity was obtained for each of the applied voltages according to Table 3.   respectively). Aside from good agreement observed between numerical and experimental results, Fig. 9 demonstrates that by increasing the fan airflow velocity, we reach a point that further increase in air velocity does not cause much change in the heat sink temperature distribution. This is the main reason why further voltage percentages were not studied. and the heat sink temperature is high compared to the surrounding temperature. Therefore, the convection and radiation heat transfer rates are comparable. According to Fig. 10(b), increasing the airflow velocity to 0.571 / and enhancing forced convection heat transfer causes a significant reduction in the heat sink temperature and its difference with the surrounding temperature. So, the effect of radiation heat transfer is expected to be negligible at higher airflow velocities. In order to determine precisely when the radiation heat transfer can be ignored, the effect of considering radiation heat transfer in numerical simulations at different fan airflow velocities was investigated for both PLA and ABS printing processes. As Fig. 11 shows, for air velocities of 0.2 / and greater, radiation heat transfer can be safely neglected with no considerable effect on the heat sink temperature distribution. Fig. 11 The effect of radiative heat transfer simulation on the heat sink temperature distribution at four different airflow velocities for ABS and PLA printing processes

4-1-3 Correlation of fan air velocity and heatsink temperature
As presented in Table 3, based on the numerical simulations that proved to have a very good agreement with the experimental results, fan air velocities were determined. In order to present a correlation to predict the heat sink temperature based on the fan airflow velocity, thermistor 4, shown in Fig. 4, was selected as it was easier to measure in practical conditions.
Correlations (9) and (10) In which, is the fan airflow velocity in m/s.  fig. 12 can be used to intraplate the fan airflow velocity with acceptable accuracy when the nozzle temperature is in the range of 210℃ to 260℃. Moreover, the result obtained in Fig. 9 is again evident here that increasing the fan airflow velocity will not always decrease the heat sink temperature significantly, and for fan velocities greater than 0.45m/s, it only increases energy consumption.

Clogging detection and prevention
In order to use the hot-end reliably and efficiently, it is important to determine the minimum airflow velocity needed to prevent clogging. As described in section 2, a series of experiments were performed to investigate the clogging problem. The experiments led to one of the following three conditions: 1. Complete clogging: in such cases, the heat barrier was completely blocked, as shown in Fig. 13(a). In this condition, unclogging the hot-end was only possible by stopping the printing process and cleaning the nozzle and heat barrier. The process had to be re-started from the beginning. The "" mark indicates this condition in Tables 4 and 5. 2. No complete clogging, but with some problems: in this case, the filament could not be fed because a part of the filament inside the heat barrier was swelled due to high temperature and stuck to the inside wall of the heat barrier ( Fig. 13(b)). Unlike the complete clogging condition, there was no need to stop the entire printing process. Instead, the process had to be paused to pull out the filament and cut off the swollen part. The "" mark represents this condition in Tables 4 and 5. 3. The printing process without any problem: The "✓" mark indicates this condition in Tables 4 and 5.  Table 4 shows, for the PLA printing process, the complete clogging occurred when the fan air velocity was 0.112 / . Table 4 also shows that the second scenario mentioned above occurred in two experiments at 0.289 / . So, the airflow velocity of 0.445 / is considered the lowest possible airflow velocity that can be used reliably in this study. At this fan airflow velocity, according to correlation (10), the temperature at thermistor 4 is about 40° that can be considered as a criterion under practical conditions. As can be seen in Table 5, in the ABS printing process, the clogging only happened when the fan airflow velocity was decreased to 0.048 / .
Therefore, to avoid clogging, the airflow velocity of 0.112 / seems sufficient. In this case, according to correlation (9), the temperature at thermistor 4 is about 69° that can be used as a criterion under practical conditions. It should be noted that under this condition, as shown in Fig. 9, the temperature distribution along the heat sink is in the range of 69° to 73° that is higher than the of PLA. Therefore, if the Diamond hot-end cooler shield is made of PLA or other materials with similar , higher airflow velocities should be considered to prevent thermal damages.

4-3 Clogging mechanism
In material extrusion additive manufacturing, the pressure required to extrude the molten material is provided by the solid filament above it. In fact, the unmelted filament acts as a piston and pushes the molten filament through the nozzle. But based on the results of this research, insufficient hotend cooling condition and heat barrier overheating cause the temperature of a significant length of the filament within the heat barrier to rise above the filament glass transition temperature ( ). Therefore, under the stepper motor's driving force, it cannot play its role and, instead, it deforms. Fig. 14 shows the part of the filament pulled out of the heat barrier after the clogging occurred, and it well illustrates the condition described.
In which, is filament cross-section area. The pressure drop in a tube with length and radius is given by [29,30]: In which is the viscosity at nozzle temperature which is approximately 100 . for PLA [31] and 350 . for ABS [32] assuming that the shear rate in the nozzle is about 575 −1 [33] and is the flow rate and can be roughly calculated as follow: In which is layer height, is layer width, and is print velocity. This pressure is applied through the solid part to the melted material. On the other hand, the critical buckling load for elastic columns is given by [34]: In which, is the elastic modulus of the material, is the second moment of area, is the column effective length which in the case of both ends pinned, the value would be = ℓ. The critical length can be calculated from Eq. 11 and Eq. 14: In which is the filament radius.
It should be noted that Eq. 15 can only give a rough approximation of the critical length ( ) mainly because it assumes the behavior of the material to be quite elastic. Also, the module values for both PLA and ABS were considered constant at the average temperature of that region and obtained from the literature [35,36].
However, the calculated still shows a relatively good match with the experimental and numerical simulation results. Fig. 16 illustrates the length ℓ resulted from numerical simulations at different fan airflow velocities for the ABS printing process. As the figure shows, by decreasing the fan airflow velocity to around 0.048 / , the length ℓ increases so that it exceeds the critical length calculated from Eq. 15, and eventually, it buckles and clogs the hot-end. This is entirely in agreement with the experimental results presented in Table (5).

Fig.16
The length of the filament, which is at a temperature higher than glass transition temperature, ℓ, at different fan airflow velocities during ABS printing process A similar analysis can be applied to the PLA printing process. Fig. 17 shows the length ℓ resulted from numerical simulations at different fan airflow velocities for the PLA printing process. Similarly, when the length ℓ exceeds the critical length ( ), the clogging happens, which is in agreement with the experimental results presented in Table (4). Interestingly, Fig. 17 suggests that the second scenario that happened in airflow speed of 0.289 / in the PLA printing process can be explained by the closeness of the length ℓ and . Fig.17 The length of the filament, which is at a temperature higher than glass transition temperature, ℓ, at different fan airflow velocities during PLA printing process The analogous thermal behavior of two different thermoplastics of PLA and ABS in terms of clogging suggests that when the length ℓ exceeds the critical length ( ), the filament buckles in this region. This is the main reason for clogging in filament-based material extrusion printing process of thermoplastics. Our rough estimate of the critical length ( ) in both ABS and PLA printing processes matches very well with the experimental observations and numerical results, although more research can be done in this area to determine more precise value of .
Moreover, since the geometry of the heat sink and the heat barrier in the Diamond hot-end are similar to those in E3D hot-ends, the same analysis about clogging occurrence can be applied to them. Also, the practical criteria of 40° and 69° presented for 4 to prevent clogging in the printing process of PLA and ABS, respectively, still gives a good approximation for E3D hotends. However, the input airflow velocities corresponding to those temperatures may differ.

Conclusion
Thermal performance and the potential conditions leading to clogging inside a hot-end were studied experimentally and numerically. A core x-y filamentbased material extrusion 3D printer constructed by authors was equipped with a RepRap multi-material Diamond hot-end. The heat sink temperature was measured in a wide range of airflow rates at the nozzle temperatures of 210℃ and 260℃ (for PLA and ABS, respectively). Also, to find a criterion for predicting the clogging occurrence, a series of experiments were performed by printing a cube of 15 × 15 × 20 dimensions and under different airflow velocities for both PLA and ABS printing processes.
Moreover, a 3D finite volume model of the Diamond hot-end was developed to analyze the hot-end thermal behavior during the printing process. The numerical simulation results were in good agreement with experimental data in the whole air velocity range, including the zero-velocity condition, which was the only pre-known velocity condition in the experiments, so it was highly important in evaluating the numerical simulation. The derived conclusions of this study can be summarized as follows: • Numerical simulation of the Diamond hot-end agreed well with experimental results. The study of the effects of radiation heat transfer showed that for air velocities of 0.2 / and greater, radiation heat transfer could be safely neglected as it had no considerable effect on the heat sink temperature distribution. But in lower cooling airflow velocities, this heat transfer mechanism cannot be ignored.
• Mathematical correlations for predicting the heat sink temperature were presented. For both PLA and ABS printing processes, the temperature at a certain point in the upper part of the sink (location of thermistor 4, as a convenient place for practical measurements) was presented in terms of cooling airflow velocity.
• In both PLA and ABS printing processes, as the airflow velocity increases, the heat sink temperature decreases steadily. But for velocities more than 0.45 / , while the power demand increases, no significant change in the sink temperature was observed.
• To avoid clogging in the Diamond hot-end, the maximum heat sink temperature in its upper part (thermistor 4) should be less than 40° for PLA (equivalent to the fan airflow velocity of 0.445 / or more) and less than 69° for ABS printing process (equivalent to the fan airflow velocity of 0.112 / or more). Due to geometrical similarities, these temperature criteria can also be considered as a good approximation for other similar hot-ends like E3d hot-ends.
• Experimental and numerical studies on both PLA and ABS printing processes revealed that the clogging problem depends on the length of the filament, whose temperature is higher than the glass transition temperature. When this length exceeds the critical length, the filament buckles, and clogging occurs. This conclusion may be generalized to other thermoplastics, while more investigations are needed to confirm it.

Funding
The authors declare they have no financial interests.