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Article

Modeling the Energy and Heating Efficiency of 3D Printing for Composite Materials with Dispersed Volumetric Particles

by
Teodor Grakov
1,
Valentin Mateev
2,* and
Iliana Marinova
3
1
“Georgi Nadjakov” Institute of Solid State Physics, Bulgarian Academy of Sciences, 1784 Sofia, Bulgaria
2
Department of Electrical Apparatus, Technical University of Sofia, 1000 Sofia, Bulgaria
3
Institute of Robotics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria
*
Author to whom correspondence should be addressed.
Electronics 2025, 14(4), 688; https://doi.org/10.3390/electronics14040688
Submission received: 4 January 2025 / Revised: 4 February 2025 / Accepted: 7 February 2025 / Published: 10 February 2025
(This article belongs to the Special Issue Recent Advances in 3D Printing Technologies and Applications for Electronics)
Browse Figures
Figure 1
<p>Advantages and disadvantages of FFF/FDM 3D printing using composite materials. * indicates that this can be an advantage in some cases and a disadvantage in others.</p> "> Figure 2
<p>The 3D printer extruder design assembled (<b>a</b>) and disassembled showing the main design components (<b>b</b>). Sensors and wires are not shown in the drawings.</p> "> Figure 3
<p>3D printer extruder—size of all design elements.</p> "> Figure 4
<p>Finite element mesh of the extruder assembly model, with a central cross-section through the material channel (<b>a</b>), and a close view of the meshed extruder tip (<b>b</b>).</p> "> Figure 5
<p>Infrared thermography of heated extruder (<b>a</b>); material temperature and temperature of extruder and thermal bridge are visible. Fe-PLA composite microscopy image is shown in (<b>b</b>); particles’ homogenous distribution is visible.</p> "> Figure 6
<p>Transient heating of 3D printer extruder, measured at the thermal sensor location. (<b>a</b>) represents the Fe<sub>2</sub>O<sub>3</sub> composites and (<b>b</b>) the CaO composites. The temperature variation was compared at 160 s from the beginning of the heating process. This duration was shorter than the process time constant, but it covered the temperature of material plastification in the viscose phase suitable for 3D printing.</p> "> Figure 7
<p>The temperature distribution in an extruder cross-section (<b>a</b>) and heat flux distributions (<b>b</b>–<b>d</b>). The temperature distribution is in the range between 234.58 °C and 236.98 °C, where the hotspot is located within the heater element, visualized with a circle.</p> "> Figure 8
<p>Temperature distribution of PLA filament only (<b>a</b>) and its heat flux (<b>b</b>). The viewpoint is from the heater side, indicated by the red hotspot.</p> "> Figure 9
<p>Transient heat fluxes from the heater element to the 3D printer thermal bridge. (<b>a</b>) corresponds to the Fe<sub>2</sub>O<sub>3</sub> composites and (<b>b</b>) to the CaO composites. The pure PLA filament is given as a reference in the black line.</p> "> Figure 10
<p>Transient heat fluxes from the thermal bridge to the extruder (E1). (<b>a</b>) corresponds to the Fe<sub>2</sub>O<sub>3</sub> composites and (<b>b</b>) to the CaO composites. The pure PLA filament is given as a reference in the black line.</p> "> Figure 11
<p>Transient heat fluxes from the polymer filament composite material. (<b>a</b>) corresponds to the Fe<sub>2</sub>O<sub>3</sub> composites and (<b>b</b>) to the CaO composites. The pure PLA filament is given as a reference in the black line.</p> "> Figure 12
<p>3D printer filament in the extruder for each composite. The temperature variation is due to the composite content. The viewpoint is from the left side of the extruder. The red hotspot faces the extruder heater.</p> "> Figure 13
<p>Temperature of polymer change depending on composite content at 160 s. (<b>a</b>) Heat flux of polymer change depending on composite content at 160 s (<b>b</b>).</p> "> Figure 14
<p>The 3D printer extruder’s power in the thermal bridge (<b>a</b>), extruder (<b>b</b>), and filament (<b>c</b>). Filler content in wt.% increased the power in watts.</p> ">
Versions Notes

Abstract

:
Additive manufacturing, such as the 3D printing of composite materials for electronics is rapidly evolving, enabling the production of advanced electric and magnetic composites with tailored properties. These materials require special printing conditions and advanced control to maintain the desired material properties during the 3D printing process and in the final product design. Hence, determining the heating and energy consumption and estimating the efficiency of 3D printing is essential. This work modeled the fused filament fabrication 3D printing of composite materials with a polymer carrier matrix. A 3D time-dependent thermal model of a 3D printer extruder was developed and implemented using the finite element method to study and improve the efficiency of 3D printing. As the filler content influences the operational parameters and process energy consumption of the 3D printing process, the transient heating process parameters were estimated using different composite modifier contents. Two types of modifiers were considered: Fe2O3 and CaO, both mixed in a PLA carrier material. The volumetric fill ratio of the two modifiers did not exceed 45%, as the mixing dependency of the material properties is linear in this range. The power fluxes and power efficiency were estimated. The results provide new possibilities for better control methodologies and advanced additive manufacturing for new materials in electronics. Operational control can accelerate the 3D printing process, speeding up the heating of 3D-printed composite materials and reducing the printing time and total energy consumption. Furthermore, this research provides directions for new advanced 3D printing extruder designs with better power and energy heating efficiency.

1. Introduction

Additive technologies, such as 3D printing, offer transformative possibilities for many applications in electronics and electrical engineering. Technology has become increasingly accessible for many users, particularly fused filament fabrication (FFF), also known as fused deposition modeling (FDM) 3D printing. It is applied by melting a cord filament in volumetric structures with precise coordinate control. The ability to change or mix the polymer filament material during the printing process is one of the primary advantages of FFF/FDM. Two or more material designs can be produced as such, which is significant for electronic devices. Three-dimensionally printed electronic devices [1] mostly rely on electrical conductivity [1,2,3,4,5] as a general material property. Composite materials have been implemented in various sensors [1,2,3,4,5], antennas [6], other flexible electronics [2,3,4,5,6,7], battery electrodes [8], biodevices [9], green technologies [10], sustainable materials and recycled materials [10,11,12], etc.
FFF/FDM 3D printing technology applies a melted or softened polymer material on a specific coordinate trajectory to shape the desired object. The process’s energy consumption must cover the following process steps. The filament should be heated with a special controllable extruder, and the extruder should be placed with steeper motors at a given position per the calculated 3D trajectory. The energy consumption has been significantly reduced in the last fifteen years by creating lightweight printing frames and printing heads, minimizing the weight of the printing hardware. This trend has been supported by more efficient power supplies and optimized motor propulsion. Some advanced motor control strategies synchronize the movements of three motors to reduce power consumption or provide inertial recuperation from some movements. The energy consumption of the extruder heating and providing the material supply has also been reduced during the past decade, mainly by using a reduced filament cord diameter of 3–1.75 mm, materials with low softening temperatures, more compact designs, etc. The energy consumption includes the post-processing after the filament exits the extruder: printing bed heating, mechanical and chemical cleaning, etc. Generally, comparing the energy consumption shows that the heating power is higher than the coordinate control power in the 3D printing process. Therefore, heating requires a lot of energy during operation, and further work must focus on energy consumption enhancement. FFF/FDM 3D printing is not the fastest technology available, so heat must be provided for a longer operational cycle. A longer operational duration increases the total energy consumption. Temperature-transient control can reduce the printing energy, even if the moment power is increased, by reducing the printing time for the existing 3D printing hardware.
Figure 1 highlights some of the advantages and disadvantages of FFF/FDM 3D printing technology using volumetrically dispersed composite materials.
The advantages of FFF/FDM 3D printing [1,2,3] include the following: (1) The 3D printing process is reliable and modifiable; hence, there are no special requirements for the printing domain. Some researchers have used advanced temperature control in a closed chamber or an inert gas environment for reactive materials, but this is generally unnecessary. Moreover, the risk of nanoparticle contamination is very rare. The filament can react inactively with atmospheric gases, except in humid conditions for some polymers, such as PLA. (2) The material (filament) can be changed during 3D printing; thus, multiple material objects can be printed by changing the filament for different printing layers or object parts. (3) Composites must be pre-prepared before printing. Composite filaments have sharply defined material properties and contents and are pre-prepared in a controllable environment with the desired ingredient purity. (4) Printing in parallel with two or more extruders is possible, speeding up the work and allowing working with multiple materials simultaneously. (5) The printing process can be interrupted at any time and continued after from known 3D coordinates. Thus, the filament can be replaced with a new one with different material properties. (6) A 3D-printed surface texture is porous with surface roughness, which allows the diffusion of non-solid materials after the 3D-printed object’s formation. (7) FFF/FDM works in an accessible open environment. The 3D-printed object is manipulable during the printing process for coatings, adding internal fills, re-heating, chemical treatment, etc. (8) FFF/FDM 3D printing is a sequential controllable process, where the printing parameters can be adjusted depending on the filament material properties for optimal performance [11,12,13].
The disadvantages of FFF/FDM 3D printing related to composite material [13,14,15,16] usage are as follows: (1) The production speed is relatively slow. It can take hours of printing time to produce objects by applying small portions of the material on given coordinates. (2) The energy consumption is relatively huge, deriving from the heating and long operational time. The consumption is significantly lower than in metal 3D printing via laser powder bed fusion but higher than in fast liquid resin SLA. (3) The composites must be pre-prepared before printing, which keeps the properties within predefined limits. (4) The material exhibits bad cohesion between threads in the printed object. Even visually, printing threads are not fully fused and mixed because the previously applied threads are colder than the new extruded filaments. (5) A hollow surface texture with two roughness levels is produced, which leads to the humidity absorption and material aging of the printed object. (6) Thermal deformation occurs because of cooling shrinking. (7) FFF/FDM 3D printing is a 2.5D technology because the material is extruded in only one direction. Supports are needed for full 3D printing or the control of the extrusion direction with more DoFs. (8) The produced 3D-printed layers and threads are macroscopic in scale, typically not less than 0.1 mm. Interactions on the thread surfaces can be microscopic. (9) Extruder jamming is a common issue that can be detected with modern sensors but cannot be automatically repaired. (10) As a contact method of applying material, FFF/FDM 3D printing often requires calibrating the relative position of the extruder/object/printing bed.
FFF/FDM 3D printing has significant advantages that can benefit from the properties of composite materials created or used by this technology. Even the disadvantages do not significantly differ from those of pure polymers used, and many solutions are known [12]. The application of new composite materials is a rapidly advancing trend [15,16,17]. These materials can provide electric [12,13,14,15,16,17] or magnetic properties [17,18,19,20,21,22,23,24,25,26], different from typical pure polymers used in FFF/FDM. Composites with polymer carriers and metal particles [20,21,22,23,24,25,26,27,28,29,30] as a filler allow the metal particle properties to be used at lower powers for bonding and 3D shaping. The energy consumption for PLA formation using FFF/FDM is less than 1 J/mm3 for the PLA only. If such composites can provide strong electric or magnetic properties using a micro-bonding method without completely melting, as in selective laser melting (SLM), the energy efficiency for acquiring a desired property can be increased. SLM’s energy consumption is approximately 400 J/mm3.
The material properties of FFF/FDM composites can be influenced before the 3D printing process, mainly by controlling the content concentration of the filament used; during the printing process, such as through fill patterns, material mixing, and outer physical influences [31,32,33,34,35]; and after printing via post-processing, through surface mechanical treatment, etching, chemical activation, coating application, painting, further functionalization, etc.
Notable work on the modification of material properties has covered smart materials [36,37,38,39], volumetrically controlled properties [23,24,25,26,27,28,29,30], the influence of filling patterns over the total material properties [17,21,29], and adjusting the 3D printing operational parameters, which mainly depends on the properties of the filament material used [40,41,42,43,44,45,46].
Studies on composite material properties outnumber those on the methodological improvement of 3D printing technology [40,41,42,43,44,45,46,47,48,49]. The huge quantity of new 3D printing materials requires major work to be undertaken to improve 3D printing technology, such as the adjustment of optimal process parameters [40,41,42,43,44,45,46], to achieve better results in energy and resource efficiency. Numerical modeling can fill this gap and solve the problem of the optimal control of 3D printing [40,41,42,43,44,45,46,48]. The modeling task covers three phases in the 3D FFF/FDM printing process: (1) the modeling of the material mixing and volumetric dispersion of the filament in the pre-printing stage; (2) the modeling of the composite material’s extrusion during the actual 3D printing; and (3) the modeling of the post-extrusion material’s behavior in different thermal, mechanical, chemical, electric, magnetic, and other conditions [40,41,42,43,44,45,46].
Determining the heating and energy consumption and estimating the efficiency of 3D printing is essential to realize special printing conditions and advanced control to maintain the desired material properties during the 3D printing process [47,48,49,50]. In this work, the fused filament fabrication 3D printing of composite materials with a polymer carrier matrix was modeled, and the heating and energy efficiency of the 3D printing was estimated. As the filler content influences the operational parameters and process energy consumption of the 3D printing process, a 3D time-dependent thermal model was implemented using the finite element method for the 3D printer extruder. The transient heating process parameters were estimated with different composite modifier contents. Two types of modifiers were considered: Fe2O3 and CaO, both mixed in a PLA carrier material. The volumetric fill ratio of the two modifiers did not exceed 45%, as the mixing dependency of the material properties was linear in this range. The power fluxes and power efficiency were estimated. The results provide new possibilities for better control methodologies and advanced additive manufacturing for new materials in electronics. Operational control can accelerate the 3D printing process, speeding up the heating of the 3D-printed composite materials and reducing the printing time and total energy consumption [48,49,50,51,52].
This research provides data for advanced process control using volumetrically dispersed composite materials and gives directions for the design optimization of special extruders for 3D printing with composite materials [53,54,55]. This approach could be extended and applied to 3D printing with volumetrically dispersed composite materials in different areas of advanced digitalized industry processes [55,56,57,58] and medical care automation [54].
This paper is structured as follows: After the Introduction, the 3D printer FFF/FDM extruder design under consideration is described. Next, the calculation of the composite material properties is provided. Afterward, the time-transient FEM modeling formulation is presented with the modeling implementation details. The next section provides the modeling results for each volumetrically dispersed composite and a detailed comparison of the local powers and heating efficiency. Finally, the results and conclusion are discussed.

2. 3D Printer FFF/FDM Extruder Design

The 3D printer FFF/FDM extruder design under consideration is a part of the K8200 printer design, which is well known for its open architecture, accessibility for repayments, and easy further modifications. This design has significantly impacted many current and future improvements of the 3D FFF/FDM printing process and directed the thinking of many specialists, scientists, and enthusiasts who have used it in 3D printing attempts. Related modifications to the composite materials can be found in [27,29,30].
The design description of the 3D printer FFF/FDM extruder consists of three main elements, as shown in Figure 2: an electric heater (H), a thermal bridge (B), and the extruder body (E1) and nozzle tip (E2). Its function is to heat a cord polymer filament with a diameter of 2.75 mm to 210 °C and extrude it to a thread with a smaller diameter of 0.1–0.7 mm used for 3D printing. The filament supply velocity is controllable in the range between 0 and 5 mm/s [27].
The 3D printer extruder works as follows: The first side of the bridge (B) over the heater (H) must collect the thermal flow generated by the heater (H), equalize the flow density in the central part, and transmit it to the extruder side, which is the final third side according to the thermal flow direction. The central transmitting part must be very short with a large cross-section to reduce the heat resistance and prevent a large temperature gradient, but it must be long enough to regulate the heat flow distribution equally and heat the extruder uniformly. Moreover, the outer surface of the bridge must be minimal to reduce the heating of the surrounding air. The thermal bridge heats the extruder (E), which must concentrate the heat around the filament material, keeping a steady temperature to soften the polymer. The proper design of an optimal FFF/FDM 3D printer extruder system can be a challenging optimization problem while minimizing heat loss and maintaining 3D printing conditions.
The extruder’s internal chamber is complex in shape due to the internal channel geometry (Figure 3). It must keep the soft viscose polymer inside and provide enough heated material for smooth extrusion. The material supply must be controllable to enable the interruption of the filament supply by the motor feeder and cut the extruded thread with the extruder nozzle’s outer sharp edge if necessary [27].
The material of the extruder bridge can be used for thermal flow density redistribution. For example, an aluminum bridge can be combined with a copper or brass extruder. The thermal conductivity transition is directed toward the extruder, equalizing the flow around the material. Additionally, a second larger thermal conductivity transition occurs from the extruder to the filament, which blocks the flow. This is compensated by the very small quantity of the polymer, giving the desired heating speed.
The volumes and surfaces of the extruder design elements are presented in Table 1. The thermal conductive area along the main flow path must be maximized for lower thermal resistance. This area is a major part of the outer area of each element. The best surface coverage is on the filament; its surface is used for contact thermal conduction.
The material properties of the composite filament’s components are presented in Table 2. PLA is used as the matrix or carrier material, which is modified with Fe2O3 or CaO powder homogenously dispersed on the filament volume. Different thermal composite material properties are achieved by combining these components.

3. Composite Material Properties

It is necessary to determine the material properties of a composite material, such as its thermal conductivity coefficient λ, material density ρ, and specific thermal capacity c, to model the time-dependent 3D printing process heating of the composite material in the extruder system.
The modeled composite material uses PLA as the matrix or carrier material, which is modified with Fe2O3 or CaO powder homogenously dispersed on the filament volume.
The applications of these fillers are described in [11] for CaO and in [29] for Fe2O3. These applications require homogenously dispersed fillers with micro- or nano-sized particles [11,29].
The rule of mixtures is used to calculate the thermal conductivity of a composite material. This method considers the thermal conductivities and volume fractions of the individual components of the composite material, expressed as
λ c = λ F e 2 O 3 V F e 2 O 3 V + λ P L A V P L A V
where λc is the thermal conductivity of the composite material, V F e 2 O 3 is the volume fraction of the filler material, λ F e 2 O 3 is the thermal conductivity of the filler material, VPLA is the volume fraction of the matrix material, λPLA is the thermal conductivity of the matrix material, and the volume fractions are defined by the complete material volume V.
The specific heat capacity of the composite material is calculated as a weighted average based on the mass and specific heat capacities of the individual components:
c c = c F e 2 O 3 m F e 2 O 3 m + c P L A m P L A m ,
where cc is the specific heat capacity of the composite material, m F e 2 O 3 is the mass of the filler component in the composite, m P L A is the matrix mass, m is the total composite mass, and c F e 2 O 3 and c P L A are the specific heat capacities of each component.
The rule of mixtures is also used to calculate the density of the composite material. This involves averaging the densities of the individual components based on their volume fractions:
ρ c = ρ F e 2 O 3 V F e 2 O 3 V + ρ P L A V P L A V ,
where ρc is the density of the composite material, V F e 2 O 3 is the volume fraction of the filler material, and VPLA is the volume fraction of the matrix material. The volume fraction Vi/V is the ratio of the volume of each component to the total volume of the composite. This equation weights the density of each component by its proportion of the total volume.
The calculated thermal material properties of the composites with the Fe2O3 filler are presented in Table 3. Fixed weighted values of 15, 30, and 45% wt. were used for the filler in the PLA carrier. The data show an increase in the density and specific thermal conductivity with the filler content and a decrease in the specific heat capacity.
The calculated thermal material properties of the composites with the CaO filler are presented in Table 4. Fixed weighted values of 15, 30, and 45% wt. were used for the filler in the PLA carrier. The data show an increase in the density and specific thermal conductivity with the filler content and a decrease in the specific heat capacity. The thermal conductivity change was higher than in the Fe2O3 composites, while the density and specific heat capacity variations were smaller.

4. Transient Thermal Modeling

The heating of the 3D printer extruder is modeled as a time-transient thermal field problem. It covers the heating of the extruder system’s design elements and composite filament material.
The time-dependent thermal conductivity equation is expressed as follows:
ρ ⋅ c ⋅ ∂ τ ∂ t + ρ ⋅ c ⋅ v ⋅ ∇ τ = ∇ ⋅ λ ⋅ ∇ τ + Q ,
where τ is the local temperature; v is the filament supply speed; Q is the heat source’s volumetric power density, defined by the heater’s electric power P = 32 W and its volume V = 424.11 mm3; and the used volumetric power density is 76,000 kW/m3.
The surface heat flux q is expressed with the heat conduction Fourier law:
q = − λ ⋅ ∇ τ ,
where q is the local heat flux density in W/m2, λ is the material’s thermal conductivity in W/(m·K), and ∇τ is the temperature gradient in K/m.
The extruder thermal bridge and extruder are made of copper. Copper’s thermal conductivity is λ20°C = 390 W/m·K, with a temperature correction coefficient of α = 13.5 × 10−4 1/°C, which is linearly compensated as λ(τ) = λ20°C(1 + ατ) for the temperature range of 230 °C. Copper’s density is 8300 kg/m3, and its specific heat capacity is 385 J/kgK. These values are not corrected with the temperature.
The implemented model’s details are given in this section. A three-dimensional geometric model of the 3D printer extruder was made per Figure 1 and Figure 2. A meshed finite element model of the extruder assembly model, with a central cross-section through the material channel, is presented in Figure 4a, and a close view of the meshed extruder tip is shown in Figure 4b. ANSYS 2021 software transient thermal solver was used for the modeling. The time-step value of 0.1 s for a period of 160 s was calculated using the finite element method, or 1600 local time solutions were obtained for each composite content.
The mesh statistics of the model per each design element of the extruder assembly are shown in Table 5. In total, 90% of elements were focused in bridge (B) and the extruder (E1 + E2). The filament channel (F) used almost 5% of the total number of elements.
The boundary and initial conditions for Equation (4) represent the convective power flow Ph from the outer domain surface A, defined by the convective coefficient h and the initial temperature τ0.
P h = h ⋅ A ⋅ ( τ − τ 0 )
The free air convection coefficient used in the current model is h = 10 W/m2 °C. The outer elements’ surface areas A are presented in Table 1, where the extruder bridge (B) exhibits the largest area value.
After setting all the boundary conditions, Equation (4) was calculated for each point at each time step with an interval of 0.1 s for a total period of 160 s using the finite element method via ANSYS transient thermal solver. The calculations were performed for each composite material.
The thermal energy stored in the composite polymer material is calculated as
E h = ∫ V e c c ⋅ m ⋅ τ − τ 0 d v e ,
where Eh is the total energy of the heated composite material (J) in the volume Ve, cc is the specific heat capacity of the composite material (J/kg°C), ∆τ is the temperature difference between the initial and local heated material temperatures (°C), and m is the mass of the heated material (kg).
The measured infrared thermography images of the heated extruder are presented in Figure 5a. The outgoing extruded material’s temperature and the temperature of the extruder and the thermal bridge are visible in the thermography. The measured infrared thermography results were determined for the pure PLA filament and agree with the modeled results, with an accuracy in the range of ±2 °C [27].

5. Results

The results for the transient heating of the 3D printer extruder are presented in Figure 6.
The results of the transient heating of the 3D printer extruder agree with the measured results presented in [27]. The initial heating of the extruder took approximately 200 s. Afterward, the temperature was measured with the controller, switching the heater every 5 to 10 s to keep the temperature in the defined operational range.
The results of the transient heating of the 3D printer extruder measured at the thermal sensor location are presented in Figure 6. Figure 6a represents the Fe2O3 composites and Figure 6b the CaO composites. The temperature variation was compared at 160 s from the beginning of the heating process. This duration was shorter than the process time constant, but it covered the temperature of material plastification in the viscose phase suitable for 3D printing.
The thermal transient process is expressed as an exponential function:
τ ( t ) = τ s ( 1 − e − t T )
where τs is the steady-state temperature, and T is the process time constant.
The thermal transient process time constant is expressed using the calculated or measured datasets τ(t) of each composite material as
T = t l n 1 − τ τ s
The transient process time constant is a parameter of the whole thermal transient process. It represents the heating speed in time of the whole 3D printing head with the composite material inside.
The following minimization expression was used to fit the modeled data for each composite material with the unknown transient process time constant:
min ∆ τ → 0 ⁡ ∑ t τ t m − τ ( t )
where τ(t)m represents the FEM-modeled results, and τ(t) represents the results calculated using (8).
The minimization error was cumulative and less than 140 °C, where the dataset derived from 1600 temperature values, or exhibited a cumulative fitting difference of less than 0.09 °C per single-value interval, which is a much higher accuracy than the achieved measurement accuracy of 2 °C [27].
The time constants for all composites are presented in Table 6.
The field pictures of the temperature distribution in an extruder cross-section are presented in Figure 7a and the heat flux distribution in (b). The temperature distribution is in the range between 234.58 °C and 236.98 °C, where the hotspot is located within the heater element, visualized with a circle. The field pictures of the temperature distribution in the PLA filament cross-section are presented in Figure 8a and the heat flux distribution in Figure 8b. The viewpoint is from the heater side direction, indicated by the red hotspot in the center of Figure 8a.
The thermal time constants for all composites are presented in Table 6. The thermal time constant was influenced by the composite content. This was especially evident for Fe2O3, where it jumped from 894.7 s to 1165 s, defining a longer heating duration for the 35% wt. filled composite. The applied interval of 160 s was shorter than the standard process time, but it was equal to the process control duration and sufficient for the change in the physical state of the filament.
The time constant is a parameter of the whole thermal transient process. It represents the heating speed of the whole 3D printing head with the composite material inside. A change in the relatively small quantity of the model, such as the filament, can influence the complete heating process dynamics.
The next set of figures (Figure 9, Figure 10 and Figure 11) show the transient heat flux across the main thermal conduction path. The three pairs correspond to (1) the heater element to the 3D printer thermal bridge (Figure 9); (2) the thermal bridge to the extruder (Figure 10); and (3) the extruder to the polymer filament composite material (Figure 11). The (a) sets correspond to the Fe2O3 composites, and the (b) sets correspond to the CaO composites. The pure PLA filament is given as a reference in all graphical sets. The results show a decrease in the heat flux of 72 > 44 > 32 kW/m2, where the largest drop was from the bridge to the extruder. This can be explained by the huge outer area of the thermal bridge and the convective outflow. The filament gained a significant portion of the heat flux for all composites.
Figure 12 shows the 3D printer filament in the extruder for each composite. The temperature field is uniform, but small variations are observable. The temperature variation is due to the composite content differences. The observer’s viewpoint is from the left side of the extruder. The red hotspot faces the extruder heater. An approximately 1 °C difference in the filament exists because of the proximity of the filament right side to the thermal bridge.
The calculation of the total power incoming in each extruder element for the CaO composites is presented in Table 7. The power was calculated via the heat power flow and the area along the main thermal conduction path for each element. The starting heater power was 32 W. After the extruder, in the filament, approximately 7 W or 25 W was lost to the outer environment. The calculation of the total power incoming in each extruder element for the Fe2O3 composites is presented in Table 8. The power values are similar to those of the CaO composites.
Considering the obtained results, lowering the material’s specific heat capacity leads to faster heating because less energy is required to raise the material’s temperature. However, the temperature differences between the material’s heated and unheated parts can be larger, especially at low thermal conductivity. At high thermal capacity, the material reacts more slowly by accumulating more energy, resulting in a more even distribution of heat in sufficient time.
High thermal conductivity reduces the temperature gradient in the material, accelerating the transfer of heat from the heated to unheated parts. This reduces local heating but increases the overall efficiency of heat transfer. Low thermal conductivity limits heat distribution, creating a high temperature gradient near the heating zone. This case is common in polymers and polymer composites.
A material’s density plays an important role in thermal inertia and energy balance, as it is directly related to the material’s ability to accumulate heat. Hence, at higher densities, the material requires more energy to achieve the same temperature rise in the 3D printing process.
The materials with 15% Fe2O3 and 45% Cao in PLA seem best suited for energy-efficient applications, based on Table 7 and Table 9, respectively. The balance between moderate thermal conductivity, specific capacitance, and density makes it optimal for applications requiring fast, uniform, and energy-efficient heating.
The heating efficiency ηe is calculated as a ratio of the produced heater power Pheater and that accumulated in the filament Pfilament using Equation (11) and the datasets in Table 7 and Table 8:
η e = P f i l a m e n t P h e a t e r
The temperature of the polymer change depending on the composite content at 160 s is presented in Figure 13a. The heat flux change of the polymer depending on the composite content at 160 s is presented in Figure 13b.
The heating efficiency results in % for each composite are presented in Table 9 and Table 10.
The efficiency results show the efficiency of the extruder was approximately 22%. This is not a high value and can open a discussion on extruder design optimization. Meanwhile, this also means that the energy efficiency of 3D printing can be increased. The filament content influences the thermal heating process and total efficiency.

6. Discussion

The relationship between a material’s thermal properties and the 3D printing energy efficiency plays a critical role in 3D printing, as this process relies on precise dynamic temperature control to achieve printing quality and optimal energy utilization. The main aspects of the relationship between the material’s thermal properties and the requirements of 3D printing are as follows: (1) Precise temperature control is required in the 3D printing process. The material must undergo three main temperature stages, including heating to the operating temperature (usually in the extruder); printing and cooling for curing; and a smooth transition between these stages to avoid defects, such as shrinkage, deformation, or cracking. In this case, moderate thermal conductivity ensures that the material heats evenly and cools predictably without large temperature gradients that can lead to internal stresses. A moderately low specific heat capacity allows the material to reach the operating temperature faster, which speeds up the printing process. A moderate density ensures that the material accumulates enough heat for stable heating without consuming excess energy. (2) Thermal defects must be avoided during layer deposition, such as low adhesion between layers. This is problematic if the material does not retain enough heat to ensure good contact between layers. An energy-efficient material helps by balancing between thermal conductivity and density, which reduces the cooling difference between the layers. A slight reduction in the specific heat capacity will provide fast but stable cooling of the printed composite material. (3) Energy savings are required in large prints. Energy-efficient technology and materials provide reduced heating and cooling times, less energy loss during long print cycles, and optimal heat distribution in large volumes, which is important for large or dense 3D prints.
The 3D printer extruder’s power is represented in Figure 14. In all elements—the thermal bridge, the extruder, and the filament—the power increased with the filler content. Therefore, the filler content in wt.% increased the power in watts and the total 3D printing efficiency. The filament influenced the total temperature distribution and fluxes in the complete 3D printer extruder system.
The time constant is a parameter of the whole thermal transient process that represents the heating speed of the whole 3D printing head with the composite material inside. A change in a relatively small quantity of the model, such as the filament, can influence the complete heating process dynamics. The calculated results show changes in the heating speed (time constant) up to 10%.
The efficiency results show that the heating efficiency of the extruder was approximately 22%. This is not a high value and can open a discussion on extruder design optimization. Meanwhile, this also means that the 3D printing energy efficiency can be increased. The filament content influences the thermal heating process and total efficiency.
A general comparison of the energy consumption shows that the heating power is higher than the coordinate control power in the 3D printing process, so heating requires significant energy during operation; thus, further research activities must focus on energy consumption enhancement. This can be carried out with optimal process control, including controlling very accurate temperature distributions and time durations. This will require more sensors for optimal process control and faster controllers with multiple control objectives. AI can obtain fast and multichannel data processing and significantly reduce the printing time, increasing both productivity and energy efficiency.
The design optimization of the extruder can focus on bridge removal or its complete reshaping. The heater incorporated directly into the extruder can be more energy-efficient than a thermal bridge design. The outer heater surface is problematic as it loses heat flux to the outer environment. A good solution to this problem is an internally situated heater, which is almost completely covered by the melted material flow. This will provide almost perfect usage of the heater’s electric power while allowing the use of larger quantities of material, increasing the total size of the extruder. Another option is to use the filament’s electrical conductivity to heat the material directly. Electrically conductive filaments enable this.

7. Conclusions

Volumetrically dispersed composite materials require special printing conditions and advanced process control to maintain the desired material properties during the 3D printing process and in the final product design. Transient heating process parameters are estimated with different composite modifier contents. Thus, this research provides a deeper insight into the mechanism of composite material melting in extruders and can be used in the creation of non-standard composite material mixtures. Two types of modifiers were considered: Fe2O3 and CaO, both mixed in a PLA carrier material. The volumetric fill ratio of the two modifiers did not exceed 45%, as the mixing dependency of the material properties is linear in this range. The power fluxes and power efficiency were estimated. The efficiency results show the process efficiency of the extruder was approximately 22%. The variation in the final efficiency with the composite material content was ±2%. The transient results showed changes in the heating speed (process time constant) up to 10%. The results separately estimated the 3D printing process efficiency coming from the extruder device design and the material heating efficiency that varied depending on the filament properties only. The extruder control parameters must be carefully adjusted with the filament material properties to achieve an optimal 3D printing process performance.
The filler content influenced the operational parameters and process energy consumption of the 3D printing process. The results provide new possibilities for better control methodologies and the advanced additive manufacturing of new materials for electronics. In some cases, control can accelerate the 3D printing process, speeding up the heating of 3D-printed composite materials and reducing the printing time and total energy consumption. The material’s optimal thermal properties are key to achieving quality prints and energy efficiency in 3D printing. Materials with moderate thermal conductivity, low specific heat capacity, and moderate density offer the best balance between performance and cost. This makes them suitable for both small parts and large industrial projects.

Author Contributions

Conceptualization, T.G., V.M. and I.M.; methodology, T.G., V.M. and I.M.; software, T.G., V.M. and I.M.; validation, T.G., V.M. and I.M.; formal analysis, T.G., V.M. and I.M.; investigation, T.G., V.M. and I.M.; data curation, T.G., V.M. and I.M.; writing—original draft preparation, T.G., V.M. and I.M.; writing—review and editing, T.G., V.M. and I.M.; visualization, T.G. and V.M.; supervision, I.M.; project administration, I.M.; funding acquisition, I.M. All authors have read and agreed to the published version of the manuscript.

Funding

This work is supported by the National Science Fund of the Ministry of Education and Science of the Republic of Bulgaria under contract KP-06-N47/2.

Data Availability Statement

The datasets are available from the corresponding authors on reasonable request.

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1. Advantages and disadvantages of FFF/FDM 3D printing using composite materials. * indicates that this can be an advantage in some cases and a disadvantage in others.
Figure 1. Advantages and disadvantages of FFF/FDM 3D printing using composite materials. * indicates that this can be an advantage in some cases and a disadvantage in others.
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Figure 2. The 3D printer extruder design assembled (a) and disassembled showing the main design components (b). Sensors and wires are not shown in the drawings.
Figure 2. The 3D printer extruder design assembled (a) and disassembled showing the main design components (b). Sensors and wires are not shown in the drawings.
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Figure 3. 3D printer extruder—size of all design elements.
Figure 3. 3D printer extruder—size of all design elements.
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Figure 4. Finite element mesh of the extruder assembly model, with a central cross-section through the material channel (a), and a close view of the meshed extruder tip (b).
Figure 4. Finite element mesh of the extruder assembly model, with a central cross-section through the material channel (a), and a close view of the meshed extruder tip (b).
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Figure 5. Infrared thermography of heated extruder (a); material temperature and temperature of extruder and thermal bridge are visible. Fe-PLA composite microscopy image is shown in (b); particles’ homogenous distribution is visible.
Figure 5. Infrared thermography of heated extruder (a); material temperature and temperature of extruder and thermal bridge are visible. Fe-PLA composite microscopy image is shown in (b); particles’ homogenous distribution is visible.
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Figure 6. Transient heating of 3D printer extruder, measured at the thermal sensor location. (a) represents the Fe2O3 composites and (b) the CaO composites. The temperature variation was compared at 160 s from the beginning of the heating process. This duration was shorter than the process time constant, but it covered the temperature of material plastification in the viscose phase suitable for 3D printing.
Figure 6. Transient heating of 3D printer extruder, measured at the thermal sensor location. (a) represents the Fe2O3 composites and (b) the CaO composites. The temperature variation was compared at 160 s from the beginning of the heating process. This duration was shorter than the process time constant, but it covered the temperature of material plastification in the viscose phase suitable for 3D printing.
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Figure 7. The temperature distribution in an extruder cross-section (a) and heat flux distributions (b–d). The temperature distribution is in the range between 234.58 °C and 236.98 °C, where the hotspot is located within the heater element, visualized with a circle.
Figure 7. The temperature distribution in an extruder cross-section (a) and heat flux distributions (b–d). The temperature distribution is in the range between 234.58 °C and 236.98 °C, where the hotspot is located within the heater element, visualized with a circle.
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Figure 8. Temperature distribution of PLA filament only (a) and its heat flux (b). The viewpoint is from the heater side, indicated by the red hotspot.
Figure 8. Temperature distribution of PLA filament only (a) and its heat flux (b). The viewpoint is from the heater side, indicated by the red hotspot.
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Figure 9. Transient heat fluxes from the heater element to the 3D printer thermal bridge. (a) corresponds to the Fe2O3 composites and (b) to the CaO composites. The pure PLA filament is given as a reference in the black line.
Figure 9. Transient heat fluxes from the heater element to the 3D printer thermal bridge. (a) corresponds to the Fe2O3 composites and (b) to the CaO composites. The pure PLA filament is given as a reference in the black line.
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Figure 10. Transient heat fluxes from the thermal bridge to the extruder (E1). (a) corresponds to the Fe2O3 composites and (b) to the CaO composites. The pure PLA filament is given as a reference in the black line.
Figure 10. Transient heat fluxes from the thermal bridge to the extruder (E1). (a) corresponds to the Fe2O3 composites and (b) to the CaO composites. The pure PLA filament is given as a reference in the black line.
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Figure 11. Transient heat fluxes from the polymer filament composite material. (a) corresponds to the Fe2O3 composites and (b) to the CaO composites. The pure PLA filament is given as a reference in the black line.
Figure 11. Transient heat fluxes from the polymer filament composite material. (a) corresponds to the Fe2O3 composites and (b) to the CaO composites. The pure PLA filament is given as a reference in the black line.
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Figure 12. 3D printer filament in the extruder for each composite. The temperature variation is due to the composite content. The viewpoint is from the left side of the extruder. The red hotspot faces the extruder heater.
Figure 12. 3D printer filament in the extruder for each composite. The temperature variation is due to the composite content. The viewpoint is from the left side of the extruder. The red hotspot faces the extruder heater.
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Figure 13. Temperature of polymer change depending on composite content at 160 s. (a) Heat flux of polymer change depending on composite content at 160 s (b).
Figure 13. Temperature of polymer change depending on composite content at 160 s. (a) Heat flux of polymer change depending on composite content at 160 s (b).
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Figure 14. The 3D printer extruder’s power in the thermal bridge (a), extruder (b), and filament (c). Filler content in wt.% increased the power in watts.
Figure 14. The 3D printer extruder’s power in the thermal bridge (a), extruder (b), and filament (c). Filler content in wt.% increased the power in watts.
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Table 1. Extruder design elements’ volumes and surfaces.
Table 1. Extruder design elements’ volumes and surfaces.
Design ElementOuter Element Area
mm2		Thermal Conductive Area Along Main Flow Path
mm2		Outer Convective Surface
mm2		Element Volume
mm3
Heater (H)339.26282.7356.53424.11
Bridge (B)1708.10327.491380.612443.10
Extruder (E)948.47327.49620.981033.50
Filament (F)227.39220.297.10162.64
Table 2. Thermal material properties of composite filament’s components.
Table 2. Thermal material properties of composite filament’s components.
Material PropertyPLAFe2O3CaO
Density (ρ) kg/m3124052403340
Thermal conductivity (λ) W/mK0.170.5819.5
Heat capacity (c)
J/kgK		1800653679
Table 3. Calculated thermal material properties of composites with Fe2O3 filler.
Table 3. Calculated thermal material properties of composites with Fe2O3 filler.
Fe2O3 in PLADensity
kg/m3		Thermal Conductivity
W/mK		Heat Capacity
J/kgK
0% Fe2O312400.171800
15% Fe2O318400.23151188
30% Fe2O320400.2521061
45% Fe2O324400.293910
Table 4. Calculated thermal material properties of composites with CaO filler.
Table 4. Calculated thermal material properties of composites with CaO filler.
CaO in PLADensity
kg/m3		Thermal Conductivity
W/mK		Heat Capacity
J/kgK
0% CaO12400.171800
15% CaO15553.06951438
30% CaO16604.0361199
45% CaO18705.9691028
Table 5. Model mesh statistics per each design element of the extruder heater assembly.
Table 5. Model mesh statistics per each design element of the extruder heater assembly.
ElementsNodes
Heater (H)14116405
Bridge (B)29,22643,777
Extruder (E1 + E2)14,19022,322
Filament channel (F)20323520
Total:46,85976,024
Table 6. Thermal time constants for all composite materials.
Table 6. Thermal time constants for all composite materials.
Composite Filler Content 15% wt.30% wt.45% wt.
CaOT = 707.2 sT = 727.8 sT = 704.9 s
Fe2O3T = 894.7 sT = 1042 sT = 1165 s
Table 7. The total power incoming in each extruder element for the CaO composites.
Table 7. The total power incoming in each extruder element for the CaO composites.
CaO in PLAHeater (H)
W		Bridge (B)
W		Extruder (E1)
W		Filament (F)
W
0% CaO32.0020.35314.2227.064
15% CaO32.0020.29914.1106.953
30% CaO32.0020.31014.1236.948
45% CaO32.0020.32014.1496.939
Table 8. The total power incoming in each extruder element for the Fe2O3 composites.
Table 8. The total power incoming in each extruder element for the Fe2O3 composites.
Fe2O3 in PLAHeater (H)
W		Bridge (B)
W		Extruder (E1)
W		Filament (F)
W
0% Fe2O332.0020.35314.2227.064
15% Fe2O332.0020.30514.1297.002
30% Fe2O332.0020.31514.1497.013
45% Fe2O332.0020.33514.1887.038
Table 9. Extruder efficiency table for CaO composites.
Table 9. Extruder efficiency table for CaO composites.
CaO in PLAHeater (H)
%		Bridge (B)
%		Extruder (E1)
%		Filament (F)
%
0% CaO100.0063.6044.4422.08
15% CaO100.0063.4344.0921.73
30% CaO100.0063.4644.1321.71
45% CaO100.0063.5144.2221.68
Table 10. Extruder efficiency table for Fe2O3 composites.
Table 10. Extruder efficiency table for Fe2O3 composites.
Fe2O3 in PLAHeater (H)
%		Bridge (B)
%		Extruder (E1)
%		Filament (F)
%
0% Fe2O3100.0063.6044.4422.08
15% Fe2O3100.0063.4544.1521.88
30% Fe2O3100.0063.4844.2121.92
45% Fe2O3100.0063.5544.3421.99
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Grakov, T.; Mateev, V.; Marinova, I. Modeling the Energy and Heating Efficiency of 3D Printing for Composite Materials with Dispersed Volumetric Particles. Electronics 2025, 14, 688. https://doi.org/10.3390/electronics14040688

AMA Style

Grakov T, Mateev V, Marinova I. Modeling the Energy and Heating Efficiency of 3D Printing for Composite Materials with Dispersed Volumetric Particles. Electronics. 2025; 14(4):688. https://doi.org/10.3390/electronics14040688

Chicago/Turabian Style

Grakov, Teodor, Valentin Mateev, and Iliana Marinova. 2025. "Modeling the Energy and Heating Efficiency of 3D Printing for Composite Materials with Dispersed Volumetric Particles" Electronics 14, no. 4: 688. https://doi.org/10.3390/electronics14040688

APA Style

Grakov, T., Mateev, V., & Marinova, I. (2025). Modeling the Energy and Heating Efficiency of 3D Printing for Composite Materials with Dispersed Volumetric Particles. Electronics, 14(4), 688. https://doi.org/10.3390/electronics14040688

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