Theoretical, Numerical and Experimental Assessment of Temperature Response in Polylactic Acid and Acrylonitrile Butadiene Styrene Used in Additive Manufacturing

Abstract

A better understanding of heat transfer through materials used for 3D-printed parts could lead to an extension and an optimization of their use. A topic of interest could be analyzing temperature variation in these materials during cooling processes. Experimental research and equipment were designed to obtain additional information on the surface temperature decrease when the opposite wall surface is exposed to a freezing temperature. Experimental tests were performed on samples made of polylactic acid (PLA) and acrylonitrile butadiene styrene (ABS). An experimental Taguchi L8 program was used, with seven independent variables at two levels of variation. The experimental data analysis with specialized software based on the least-squares method identified a mathematical model of first-degree polynomial type. The coefficients for each input factor involved provide information on the magnitude and trend of the considered output parameter when the input factors’ values change. It was found that the thickness of the 3D printing layer, the thickness of the test sample, and the 3D printing speed are the main factors that affect the temperature decrease rate.

Full text

Citation: Panaite, C.E.; Mihalache,
A.-M.; Dodun, O.; Sl˘atineanu, L.;
Popescu, A.; Hrit
,uc, A.; Nagît
,, G.
Theoretical, Numerical and
Experimental Assessment of
Temperature Response in Polylactic
Acid and Acrylonitrile Butadiene
Styrene Used in Additive
Manufacturing. Polymers 2022,14,
1714. https://doi.org/10.3390/
polym14091714
Academic Editor: Luigi Sorrentino
Received: 29 March 2022
Accepted: 20 April 2022
Published: 22 April 2022
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4.0/).
polymers
Article
Theoretical, Numerical and Experimental Assessment of
Temperature Response in Polylactic Acid and Acrylonitrile
Butadiene Styrene Used in Additive Manufacturing
Camen Ema Panaite 1, Andrei-Marius Mihalache 2, Oana Dodun 2, Laurent
,iu Slătineanu 2,
Aristotel Popescu 1, Adelina Hrit
,uc 2, * and Gheorghe Nagît
,1
1Department of Mechanical Engineering and Road Automotive Engineering, “Gheorghe Asachi” Technical
University of Ias
,i, Blvd. D. Mangeron, 43, 700050 Ias
,i, Romania;
carmen-ema.panaite@academic.tuiasi.ro (C.E.P.); aristotel.popescu@academic.tuiasi.ro (A.P.);
nagit@tcm.tuiasi.ro (G.N.)
2Department of Machine Manufacturing Technology, ”Gheorghe Asachi” Technical University of Ia¸si,
Blvd. D. Mangeron, 59A, 700050 Iasi, Romania; andrei.mihalache@tuiasi.ro (A.-M.M.);
oanadodun@tcm.tuiasi.ro (O.D.); slati@tcm.tuiasi.ro (L.S.)
*Correspondence: adelina.hrituc@student.tuiasi.ro; Tel.: +40-751640117
Abstract:
A better understanding of heat transfer through materials used for 3D-printed parts
could lead to an extension and an optimization of their use. A topic of interest could be analyzing
temperature variation in these materials during cooling processes. Experimental research and
equipment were designed to obtain additional information on the surface temperature decrease when
the opposite wall surface is exposed to a freezing temperature. Experimental tests were performed on
samples made of polylactic acid (PLA) and acrylonitrile butadiene styrene (ABS). An experimental
Taguchi L8 program was used, with seven independent variables at two levels of variation. The
experimental data analysis with specialized software based on the least-squares method identified a
mathematical model of first-degree polynomial type. The coefficients for each input factor involved
provide information on the magnitude and trend of the considered output parameter when the input
factors’ values change. It was found that the thickness of the 3D printing layer, the thickness of the
test sample, and the 3D printing speed are the main factors that affect the temperature decrease rate.
Keywords:
heat transfer; polymer materials; 3D printing; influencing factors; empirical mathematical
model; experimental Taguchi L8 program
1. Introduction
Thermal conductivity is a physical property that evaluates the ability of a material
to conduct heat. Its importance becomes significant when choosing proper materials for
different applications. For cooling or heating purposes, materials with higher thermal
conductivity are chosen, while lower thermal conductivity materials are recommended for
insulation applications.
Various methods are employed to determine the thermal conductivity of materials,
mainly based on measuring temperatures on opposite walls of a test sample of known
material and dimensions under a specified heat flux. Methods used to evaluate the thermal
conductivity of materials include the guarded hot plate method, axial flow method, cylin-
der method, flash method, hot wire method, needle probe method, and transient plane
method [1–8].
Metallic materials are good heat conductors, as temperature variation on one surface
causes a relatively rapid temperature variation on its other surfaces. On the contrary,
materials that are poor heat conductors are considered thermally insulating. This category
includes polymeric materials, usually with low thermal conductivity values.
Polymers 2022,14, 1714. https://doi.org/10.3390/polym14091714 https://www.mdpi.com/journal/polymers

Polymers 2022,14, 1714 2 of 15
The last decades have highlighted an expansion of polymeric material usage in many
areas (automotive or other means of transportation [
9
–
11
], household items [
10
,
12
–
14
],
industrial equipment [
15
,
16
], medicine [
17
–
19
], etc.). Moreover, there is a clear trend toward
expanding the fabrication of polymer parts through 3D printing processes. As 3Dprinting
equipment patents expired more than two decades ago, many companies got involved in
the industrial manufacturing of 3D printers.
3D printing is part of the broader category of additive manufacturing processes,
i.e., parts are obtained gradually by successive addition of new layers of a material. 3D
printing processes developed further when software advancements made part dimensional
characterization possible with adequate accuracy, which is crucial for successive layer
deposition.
One of the 3D printing processes is based on melting a polymer wire and gradual
molten material deposition, with the part being generated from successive layers. The
shape of each layer is generated by complex relative movement between the nozzle with
the molten material and the printer base plate. This is called the fused filament fabrication
method.
The analysis of some practical aspects of this manufacturing method revealed sev-
eral input factors that influence the material properties of the final product. Therefore,
researchers performed more in-depth investigations on fused filament additive manufac-
turing processes regarding input factors that influence different physical and mechanical
properties of the 3D-printed part, such as thermal conductivity.
There is a special interest in using polymeric materials for thermal insulation of
residential, commercial, or industrial buildings to reduce the effects of excessive cold or
heat. Such materials’ low heat transfer conductive capacity may represent a significant
argument for using polymers as thermal insulating materials [
8
,
9
,
15
,
16
,
20
–
26
]. However,
the material properties of a part manufactured by 3D printing can be influenced by thermal
interactions during the 3D printing process between the process components (filaments,
printing support, environment) [20].
Elkholy and Kempers evaluated the thermal properties of polymers test samples
manufactured by 3D printing [
27
]. The test sample is placed between two blocks, one for
cooling and one for heating, and the blocks’ temperatures are determined. Elkholy et al.
developed research that aimed to highlight the anisotropic behavior of some samples made
by fused filament fabrication [28].
In a review paper on expanded polystyrene in building construction, Ramli Sulong
et al. also highlighted this material’s good thermal insulation capacity [21].
Extensive research completed by a doctoral thesis that addresses issues related to the
thermal insulation capacity of 3D-printed materials was conducted by M. Harris [
22
]. Exper-
imental research was performed on samples of polylactic acid and blends of high-density
polyethylene and polypropylene with different thermoplastics (acrylonitrile butadiene
styrene and polylactic acid).
Do˘gan and Tan [
23
] theoretically investigated (using a model based on finite elements
and ANSYS software) and performed experimental research on the thermal behavior of
some expanded polystyrene blocks.
An evaluation of the thermal insulation capability of some polystyrene foam structures
containing rice hulls was made by Flores [
29
]. The author estimated that the density of a
material could significantly influence the thermal insulation value. Polystyrene is currently
used as a thermally insulating material where appropriate conditions are available and
there are no health risks.
Eom et al. conducted experimental research to highlight the behavior of the thermal
insulation capacity of structures made of 3D-printed thermoplastic polyurethane [
24
]. They
found that increasing the air gap is more effective than increasing the pore size.
Grabowska and Kasperski addressed the issue of structure optimization for 3D-printed
polypropylene multilayer films, with closures of different shapes and sizes [
25
]. The
authors found that the best thermal insulation corresponds to single-layer quadrangle and

Polymers 2022,14, 1714 3 of 15
hexagonal closures, with a structural density of 180 kg/m
3
. The thermal conductivity was
0.0591 W/(m·K).
T. de Rubeis addressed the issue of manufacturing 3D-printed blocks used as thermal
insulation materials for buildings [
26
]. The author used a specially designed hot box to
assess the thermal insulation capability to ensure known, repeatable, and steady thermal
experimental conditions. The infrared thermography technique and heat flow meter
method were also used to characterize the thermal insulation of the 3D-printed blocks.
Other published research assessed the ability of polymeric materials as a heat transfer
medium or issues involving the thermal conductivity of polymers [30,31].
Given the fairly widespread use of polystyrene as thermal insulation for buildings,
researchers have been concerned with better characterizing the behavior of this material
from the point of view of thermal conductivity [21,29,32–35].
The research presented in this paper aimed to highlight the influence of some fac-
tors regarding test sample thickness or the influence of manufacturing conditions on a
temperature decrease for test samples of polylactic acid (PLA) and acrylonitrile butadiene
styrene (ABS), respectively. It also identified empirical mathematical models that would
provide information on the temperature decrease rate for changing values of several factors
defining test sample thickness and the conditions of the 3D printing process.
2. Materials and Methods
Assumptions Regarding Heat Transfer in Plastic Parts Made by Additive Manufacturing
The quality of thermally insulating materials of 3D-printed parts can effectively refer
to the decrease in heat transfer rate for different materials.
The test arrangement shown in Figure 1was considered. A flexible-wall package
containing a low-temperature liquid solution (gel coolant) was used. The package flexibility
enables contact over a large area between the coolant and the test sample surface of the
3D-printed material.
Polymers 2022, 14, x FOR PEER REVIEW 3 of 15
Grabowska and Kasperski addressed the issue of structure optimization for 3D-
printed polypropylene multilayer films, with closures of different shapes and sizes [25].
The authors found that the best thermal insulation corresponds to single-layer quadrangle
and hexagonal closures, with a structural density of 180 kg/m3. The thermal conductivity
was 0.0591 W/(m∙K).
T. de Rubeis addressed the issue of manufacturing 3D-printed blocks used as thermal
insulation materials for buildings [26]. The author used a specially designed hot box to
assess the thermal insulation capability to ensure known, repeatable, and steady thermal
experimental conditions. The infrared thermography technique and heat flow meter
method were also used to characterize the thermal insulation of the 3D-printed blocks.
Other published research assessed the ability of polymeric materials as a heat transfer
medium or issues involving the thermal conductivity of polymers [30,31].
Given the fairly widespread use of polystyrene as thermal insulation for buildings,
researchers have been concerned with better characterizing the behavior of this material
from the point of view of thermal conductivity [21,29,32–35].
The research presented in this paper aimed to highlight the influence of some factors
regarding test sample thickness or the influence of manufacturing conditions on a
temperature decrease for test samples of polylactic acid (PLA) and acrylonitrile butadiene
styrene (ABS), respectively. It also identified empirical mathematical models that would
provide information on the temperature decrease rate for changing values of several
factors defining test sample thickness and the conditions of the 3D printing process.
2. Materials and Methods
Assumptions Regarding Heat Transfer in Plastic Parts Made by Additive Manufacturing
The quality of thermally insulating materials of 3D-printed parts can effectively refer
to the decrease in heat transfer rate for different materials.
The test arrangement shown in Figure 1 was considered. A flexible-wall package
containing a low-temperature liquid solution (gel coolant) was used. The package
flexibility enables contact over a large area between the coolant and the test sample surface
of the 3D-printed material.
Figure 1. Clamping of the flexible-wall package with gel coolant on the test sample side.
This research aimed to develop diagrams of temperature variation on the free surface
of the 3D-printed test samples manufactured with different adjustments to the printer’s
working parameters. Measurements were performed on the test sample’s free flat surface
opposite the cooled surface. The flexible-wall package ensured that the gel coolant was
Figure 1. Clamping of the flexible-wall package with gel coolant on the test sample side.
This research aimed to develop diagrams of temperature variation on the free surface
of the 3D-printed test samples manufactured with different adjustments to the printer’s
working parameters. Measurements were performed on the test sample’s free flat surface
opposite the cooled surface. The flexible-wall package ensured that the gel coolant was
initially at
−
15
◦
C. It is expected that the temperature of the free flat surface will gradually
decrease due to heat transfer through the test sample material. The rate of this process
depends on the material thermal properties, especially its thermal conductivity.

Polymers 2022,14, 1714 4 of 15
There are heat gains towards the gel-coolant package during measurements from the
test sample and from the environment. All components shown in Figure 1were enclosed in
a wooden box (low thermal conductivity) and insulated with polystyrene foam to minimize
the latter ones. To ease the process of changing the test samples and cooling packages, the
box was provided with two doors with holes in the central areas; these doors were also
used to perform periodic temperature measurements using IR thermometers (Figure 2).
Polymers 2022, 14, x FOR PEER REVIEW 4 of 15
initially at −15 °C. It is expected that the temperature of the free flat surface will gradually
decrease due to heat transfer through the test sample material. The rate of this process
depends on the material thermal properties, especially its thermal conductivity.
There are heat gains towards the gel-coolant package during measurements from the
test sample and from the environment. All components shown in Figure 1 were enclosed
in a wooden box (low thermal conductivity) and insulated with polystyrene foam to
minimize the latter ones. To ease the process of changing the test samples and cooling
packages, the box was provided with two doors with holes in the central areas; these doors
were also used to perform periodic temperature measurements using IR thermometers
(Figure 2).
Figure 2. Schematic representation of the experimental arrangement.
The test materials were PLA and ABS. They are two polymeric materials frequently
used in 3D printing processes.
The PLA filament used in this experimental research was brown and was delivered
by Fillamentum Manufacturing Czech s.r.o. (Hulín, Czech Republic). The filament of the
second material (white ABS) was produced by the manufacturer of the 3D printing
equipment (Ultimaker, Utrecht, Netherlands). The use of ABS filament made by the
manufacturer of the 3D printing equipment was preferred, considering that this is a safer
solution and verified by the manufacturer. It was estimated that more rigorous
requirements would accomplish ABS test sample manufacturing by printing.
Observation. The glass transition temperature is when the material changes from a
brittle, hard state to a soft rubbery state. The Differential Scanning Calorimetry (DSC)
evaluates the heat flow and compares the amount of heat supplied to the test sample with
a similarly heated “reference” to establish the transition points. The Dynamic Mechanical
Analysis (DMA) evaluates a material’s response to an applied oscillating stress and the
influence of temperature and frequency on that response [36].
ABS white is a mixture of acrylonitrile-co-butadiene-co-styrene, polyethylene
terephthalate, and polycarbonate. The manufacturers indicated the characteristics of the
two materials. Thus, PLA is an industrial composter containing more than 98% polylactide
resin. Similar information and compositions on the two filament materials (ABS and PLA)
are also provided by other manufacturers of materials used in 3D printing. Some physical
properties of the two materials analyzed in this research are presented in Table 1.
Figure 2. Schematic representation of the experimental arrangement.
The test materials were PLA and ABS. They are two polymeric materials frequently
used in 3D printing processes.
The PLA filament used in this experimental research was brown and was delivered
by Fillamentum Manufacturing Czech s.r.o. (Hulín, Czech Republic). The filament of
the second material (white ABS) was produced by the manufacturer of the 3D printing
equipment (Ultimaker, Utrecht, Netherlands). The use of ABS filament made by the
manufacturer of the 3D printing equipment was preferred, considering that this is a safer
solution and verified by the manufacturer. It was estimated that more rigorous requirements
would accomplish ABS test sample manufacturing by printing.
Observation. The glass transition temperature is when the material changes from
a brittle, hard state to a soft rubbery state. The Differential Scanning Calorimetry (DSC)
evaluates the heat flow and compares the amount of heat supplied to the test sample with
a similarly heated “reference” to establish the transition points. The Dynamic Mechanical
Analysis (DMA) evaluates a material’s response to an applied oscillating stress and the
influence of temperature and frequency on that response [36].
ABS white is a mixture of acrylonitrile-co-butadiene-co-styrene, polyethylene tereph-
thalate, and polycarbonate. The manufacturers indicated the characteristics of the two
materials. Thus, PLA is an industrial composter containing more than 98% polylactide
resin. Similar information and compositions on the two filament materials (ABS and PLA)
are also provided by other manufacturers of materials used in 3D printing. Some physical
properties of the two materials analyzed in this research are presented in Table 1.

Polymers 2022,14, 1714 5 of 15
Table 1. Some physical properties of the materials of test samples made by 3D printing [37,38].
Physical Property Material
PLA ABS
Thermal conductivity
[W/(m·K)] 0.13 0.173
Density [kg/m3]1240 1040
Glass transition [◦C] 57 by DSC
63 by DMA
105 by DSC
108 by DMA
Heat deflection temperature
[◦C] 49 96
Coefficient of thermal
expansion [m/m·K] 41 ×10−672 ×10−6
Heat capacity [J/kg·K] 1800 1670
Theoretically, a model of heat transfer following the first law of thermodynamics [
39
]
yields the equation:
dEΩ
dt =Pstr +Qexch , (1)
A mathematical model such as Equation (1) can be used to detect possible thermal
degradation of polymeric material when chemical changes occur due to exposure to higher
temperatures in the absence of oxygen, where E
Ω
is the internal energy, tis the time, P
str
is the stress power, and Q
exch
is the exchanged heat rate. This theoretical relationship
considers the stress power factor when the power is converted into heat by dissipation [
39
].
3. Results
3.1. Finite Element Modeling of Thermal Conductivity Variation
The finite element analysis models the temperature variation within the test sample
for a certain time after the flexible-wall package with gel coolant was placed on the sample
side surface. Using the ANSYS R19.2 software, the graphical representation in Figure 3
provides an image of temperature distribution in a PLA test sample.
Polymers 2022, 14, x FOR PEER REVIEW 5 of 15
Table 1. Some physical properties of the materials of test samples made by 3D printing [37,38].
Physical Property Material
PLA ABS
Thermal conductivity [W/(m·K)] 0.13 0.173
Density [kg/m
3
] 1240 1040
Glass transition [°C] 57 by DSC
63 by DMA
105 by DSC
108 by DMA
Heat deflection temperature [°C] 49 96
Coefficient of thermal expansion [m/m∙K] 41 × 10
−6
72 × 10
−6
Heat capacity [J/kg∙K] 1800 1670
Theoretically, a model of heat transfer following the first law of thermodynamics [39]
yields the equation:
𝑑𝐸
𝑑𝑡 =𝑃
 +𝑄
, (1)
A mathematical model such as Equation (1) can be used to detect possible thermal
degradation of polymeric material when chemical changes occur due to exposure to
higher temperatures in the absence of oxygen, where E
Ω
is the internal energy, t is the
time, P
str
is the stress power, and Q
exch
is the exchanged heat rate. This theoretical
relationship considers the stress power factor when the power is converted into heat by
dissipation [39].
3. Results
3.1. Finite Element Modeling of Thermal Conductivity Variation
The finite element analysis models the temperature variation within the test sample
for a certain time after the flexible-wall package with gel coolant was placed on the sample
side surface. Using the ANSYS R19.2 software, the graphical representation in Figure 3
provides an image of temperature distribution in a PLA test sample.
Figure 3. Result of finite element modeling of the temperature variation in the sample test plate
(modeling using ANSYS, PLA specimen thickness: 3 mm).
Test samples of various thicknesses were subjected to a gel coolant at a temperature
of about −15 °C on one of the large side flat surfaces. The experimental research intended
to analyze the temperature variation in time during the cooling process, especially in the
center of the surface opposite the one being cooled. Numerical modeling used the finite
element method with the working conditions mentioned in Table 2. Thermal
Figure 3.
Result of finite element modeling of the temperature variation in the sample test plate
(modeling using ANSYS, PLA specimen thickness: 3 mm).
Test samples of various thicknesses were subjected to a gel coolant at a temperature of
about
−
15
◦
C on one of the large side flat surfaces. The experimental research intended
to analyze the temperature variation in time during the cooling process, especially in the

Polymers 2022,14, 1714 6 of 15
center of the surface opposite the one being cooled. Numerical modeling used the finite
element method with the working conditions mentioned in Table 2. Thermal conductivities
values of 0.13 W/(m·K) for PLA and 0.173 W/(m·K) for ABS were considered.
Figure 3shows the temperature distribution of the investigated area after 180 s from
the start of the cooling process. The test sample temperature reaches
−
5
◦
C in the center and
has higher values towards the edges of the test sample. The smaller values of temperature
decrease at the edges and corners of the test sample may be explained by the larger influence
of the clamping subsystem and the heat gain effect from the outside.
Eventually, the corners will reach the same temperature as the center area, provided
the test sample’s cooling process is long enough. In the case of the ABS material, with a
thickness of 3 mm, the temperature difference between the corners and the center area of
the test sample is about 1.5
◦
C. In contrast, for the case of PLA material, the difference is
2.5
◦
C. The numerical model developed using the finite element method shows that the
ABS polymeric material cools faster and is more uniform than the PLA material.
Similar behavior is observed for thinner samples of 1 mm, but the samples cooled
faster than the 3 mm thick ones.
Graphical representations obtained using the finite element method agree with the
results obtained from thermal imaging infrared camera (Figure 4). The temperature distri-
bution images from the IR camera provided visual information on temperature variation
during the cooling process. The ST 660 Series infrared thermometer performed more accu-
rate temperature measurements at a particular location on the sample surface. Knowing
the temperature distribution within the part used for the FEM analysis is important when
the parts are subjected to mechanical stress in an environment with large temperature
variations.
Polymers 2022, 14, x FOR PEER REVIEW 7 of 15
(a) (b)
Figure 4. Images of the free surface of the test sample obtained using thermal imaging cameras: (a)
image obtained using the thermal imaging camera AMG8833, after 180 s from the start of the cooling
process for the test sample no. 3; (b) image obtained using the infrared camera FLIR T630 SC after
120 s from the start of the cooling process for the test sample no. 8.
3.2. Experimental Conditions
The main objective of the experimental research was to study the behavior of some
3D-printed test samples of two different polymers subjected to a temperature decrease.
Another objective was to model the influence exerted by some factors that characterize
the 3D printing process on the temperature decrease rate when one of the test sample
surfaces was subjected to a forced decrease in temperature.
An Ultimaker 2 printer was used as 3D printing equipment to manufacture the eight
test samples (Figure 5).
Figure 5. Image while printing a test sample (experiment no. 8).
The possibility of using an experimental test program was considered [40,41]. A
Taguchi L8 program with seven independent variables at two levels of experimentation
was preferred, which accepts a monotonous variation of the values of the output
parameters of the investigated process, i.e., without the presence of minimums or
maximums. The statement may be valid for not-too-large intervals of the input factor
values in the investigated process. However, processing the results of the experimental
tests by the least-squares method may also lead to the identification of mathematical
models for the variation of an output parameter, which is more complex than the
mathematical model corresponding to a polynomial of first-degree.
Two levels of variation were adopted for each of the variables considered. In columns
2–8 of Table 2, the coded values of the input factor values were taken into account as
independent variables (at the fraction numerator), and the actual values of those factors
(at the fraction denominator) were entered as fractions.
Figure 4.
Images of the free surface of the test sample obtained using thermal imaging cameras:
(
a
) image obtained using the thermal imaging camera AMG8833, after 180 s from the start of the
cooling process for the test sample no. 3; (
b
) image obtained using the infrared camera FLIR T630 SC
after 120 s from the start of the cooling process for the test sample no. 8.

Polymers 2022,14, 1714 7 of 15
Table 2. Experimental conditions and results for a factorial experimental plan L8(27−4= 8 experimental tests).
Experiment
No.
Input Factors (Coded Value/Real Value) Output
Parameter
1
Test Sample
Material,
m(PLA/ABS)
2
Test Sample
Thickness, h,
mm
3
Printing
Speed, s,
mm/s
4
Cooling, c,
%
5
Infill, i,
%
6
Deposited
Layer
Thickness, l,
mm
7
Time, t,
min
Real Value,
∆θ, after 120 s
According to the
Polynomial of
First-Order
Empirical Model
According to the
Power Type
Empirical Model
Column No. 1 2 3 4 5 6 7 8 9 10 11
1 1/PLA 1/1 1/45 1/0 1/22 1/0.06 1/0 36 35.98 38.5
2 1/PLA 1/1 1/45 2/100 2/18 2/0.15 2/120 31 30.97 31.3
3 1/PLA 2/3 2/55 1/0 1/22 2/0.15 2/120 22 21.97 22.5
4 1/PLA 2/3 2/55 2/100 2/18 1/0.06 1/0 25 24.99 24.4
5 2/ABS 1/1 2/55 1/0 2/18 1/0.06 2/120 38 37.97 38.8
6 2/ABS 1/1 2/55 2/100 1/22 2/0.15 1/0 25 24.98 24.3
7 2/ABS 2/3 1/45 1/0 2/18 2/0.15 1/0 11 10.99 10.8
8 2/ABS 2/3 1/45 2/100 1/22 1/0.06 2/120 24 23.97 24.2

Polymers 2022,14, 1714 8 of 15
3.2. Experimental Conditions
The main objective of the experimental research was to study the behavior of some
3D-printed test samples of two different polymers subjected to a temperature decrease.
Another objective was to model the influence exerted by some factors that characterize the
3D printing process on the temperature decrease rate when one of the test sample surfaces
was subjected to a forced decrease in temperature.
An Ultimaker 2 printer was used as 3D printing equipment to manufacture the eight
test samples (Figure 5).
Polymers 2022, 14, x FOR PEER REVIEW 7 of 15
(a) (b)
Figure 4. Images of the free surface of the test sample obtained using thermal imaging cameras: (a)
image obtained using the thermal imaging camera AMG8833, after 180 s from the start of the cooling
process for the test sample no. 3; (b) image obtained using the infrared camera FLIR T630 SC after
120 s from the start of the cooling process for the test sample no. 8.
3.2. Experimental Conditions
The main objective of the experimental research was to study the behavior of some
3D-printed test samples of two different polymers subjected to a temperature decrease.
Another objective was to model the influence exerted by some factors that characterize
the 3D printing process on the temperature decrease rate when one of the test sample
surfaces was subjected to a forced decrease in temperature.
An Ultimaker 2 printer was used as 3D printing equipment to manufacture the eight
test samples (Figure 5).
Figure 5. Image while printing a test sample (experiment no. 8).
The possibility of using an experimental test program was considered [40,41]. A
Taguchi L8 program with seven independent variables at two levels of experimentation
was preferred, which accepts a monotonous variation of the values of the output
parameters of the investigated process, i.e., without the presence of minimums or
maximums. The statement may be valid for not-too-large intervals of the input factor
values in the investigated process. However, processing the results of the experimental
tests by the least-squares method may also lead to the identification of mathematical
models for the variation of an output parameter, which is more complex than the
mathematical model corresponding to a polynomial of first-degree.
Two levels of variation were adopted for each of the variables considered. In columns
2–8 of Table 2, the coded values of the input factor values were taken into account as
independent variables (at the fraction numerator), and the actual values of those factors
(at the fraction denominator) were entered as fractions.
Figure 5. Image while printing a test sample (experiment no. 8).
The possibility of using an experimental test program was considered [
40
,
41
]. A
Taguchi L8 program with seven independent variables at two levels of experimentation
was preferred, which accepts a monotonous variation of the values of the output param-
eters of the investigated process, i.e., without the presence of minimums or maximums.
The statement may be valid for not-too-large intervals of the input factor values in the
investigated process. However, processing the results of the experimental tests by the
least-squares method may also lead to the identification of mathematical models for the
variation of an output parameter, which is more complex than the mathematical model
corresponding to a polynomial of first-degree.
Two levels of variation were adopted for each of the variables considered. In columns
2–8 of Table 2, the coded values of the input factor values were taken into account as
independent variables (at the fraction numerator), and the actual values of those factors (at
the fraction denominator) were entered as fractions.
The seven independent variables were as follows:
1.
The nature of the test sample material. Test samples of polylactic acid (PLA) and
acrylonitrile butyl styrene (ABS) with dimensions of 100 mm
×
100 mm
×
(1 or 3) mm
were printed, respectively. In Table 2, the values defining the experimental conditions
and the values of an output parameter were entered. The PLA material and the ABS
material were assigned symbols 1 and symbol 2, respectively. The symbol mwas used
for the material identified as an independent variable;
2.
The test sample thickness h. The two levels of this factor correspond to a thickness of
1 mm and 3 mm, respectively;
3.
Printing speed s. The values of this input factor were 45 mm/s and 55 mm/s, respec-
tively. It was considered that the printing speed could affect the arrangement of the
molten polymer when the layers of the future test sample were generated, and thus,
the thermal conductivity of the deposited material could be affected;
4.
The cooling conditions provided by the 3D printer, symbolized by the letter cand
expressed as a percentage, using the symbol 1 for lack of cooling and 2 for the
maximum use of the cooling subsystem of the 3D printer;
5.
Level iof the infill, for which the values used were 22% (level 1) and 18% (level 2),
respectively;

Polymers 2022,14, 1714 9 of 15
6.
The thickness lof the layer deposited during 3D printing is 0.06 mm and 0.15 mm, re-
spectively. The values of the input factors that define the working conditions used for
the 3D printing process were established by taking into account the recommendations
for such a manufacturing process;
7.
The size tof the time interval at which the temperature measurement was performed.
In Figure 6, the eight test samples (four of PLA and four of ABS) used in the experiment
can be observed, with the corresponding data listed in Table 2. After a flexible-wall
package containing the gel coolant was placed in contact with one test sample surface, the
temperature was measured on the opposite surface at 60 s intervals using an ST 660 Series
infrared thermometer.
Polymers 2022, 14, x FOR PEER REVIEW 8 of 15
The seven independent variables were as follows:
1. The nature of the test sample material. Test samples of polylactic acid (PLA) and
acrylonitrile butyl styrene (ABS) with dimensions of 100 mm × 100 mm × (1 or 3) mm
were printed, respectively. In Table 2, the values defining the experimental
conditions and the values of an output parameter were entered. The PLA material
and the ABS material were assigned symbols 1 and symbol 2, respectively. The
symbol m was used for the material identified as an independent variable;
2. The test sample thickness h. The two levels of this factor correspond to a thickness of
1 mm and 3 mm, respectively;
3. Printing speed s. The values of this input factor were 45 mm/s and 55 mm/s,
respectively. It was considered that the printing speed could affect the arrangement
of the molten polymer when the layers of the future test sample were generated, and
thus, the thermal conductivity of the deposited material could be affected;
4. The cooling conditions provided by the 3D printer, symbolized by the letter c and
expressed as a percentage, using the symbol 1 for lack of cooling and 2 for the
maximum use of the cooling subsystem of the 3D printer;
5. Level i of the infill, for which the values used were 22% (level 1) and 18% (level 2),
respectively;
6. The thickness l of the layer deposited during 3D printing is 0.06 mm and 0.15 mm,
respectively. The values of the input factors that define the working conditions used
for the 3D printing process were established by taking into account the
recommendations for such a manufacturing process;
7. The size t of the time interval at which the temperature measurement was performed.
In Figure 6, the eight test samples (four of PLA and four of ABS) used in the
experiment can be observed, with the corresponding data listed in Table 2. After a flexible-
wall package containing the gel coolant was placed in contact with one test sample
surface, the temperature was measured on the opposite surface at 60 s intervals using an
ST 660 Series infrared thermometer.
Figure 6. Test samples obtained by 3D printing of ABS (white) and PLA (brown) used to evaluate
the temperature decrease in a certain time interval.
The IR thermometer can measure temperatures between −50 °C and 999 °C.
According to the manufacturer’s specifications, the thermometer has a repeatability of ± 1
°C and a resolution of 1 °C.
To verify the accuracy of the IR thermometer, test measurements were performed to
determine the temperature at the bottom of an aluminum container with a 30 mm thick
layer of boiling distilled water. The temperature indicated by the infrared thermometer
from a distance of 250 mm was 99 °C. The experimental results were consistent with the
device characteristics provided by the manufacturer, even if possible influences of the
presence of water, the variation of the water layer thickness due to the boiling, and the
thermal behavior of the aluminum container’s bottom wall are taken into account.
Figure 6.
Test samples obtained by 3D printing of ABS (white) and PLA (brown) used to evaluate the
temperature decrease in a certain time interval.
The IR thermometer can measure temperatures between
−
50
◦
C and 999
◦
C. According
to the manufacturer’s specifications, the thermometer has a repeatability of
±
1
◦
C and a
resolution of 1 ◦C.
To verify the accuracy of the IR thermometer, test measurements were performed to
determine the temperature at the bottom of an aluminum container with a 30 mm thick
layer of boiling distilled water. The temperature indicated by the infrared thermometer
from a distance of 250 mm was 99
◦
C. The experimental results were consistent with the
device characteristics provided by the manufacturer, even if possible influences of the
presence of water, the variation of the water layer thickness due to the boiling, and the
thermal behavior of the aluminum container’s bottom wall are taken into account.
First measurements of temperature variation were taken (as shown in the schematic
representations in Figures 1and 2) to establish the magnitude of the time interval required
to determine the empirical mathematical model. As the parameter of interest was the
ability of the test sample material to sense the temperature decrease, measurements were
performed until, after the initial decrease, the temperature remained somewhat constant for
a short time and then began to rise. The results of the measurements are listed in Table 3.
A graphical representation of the temperature decrease measured on the free surface
of the test sample can be seen in Figure 7. The analysis of the data in Table 3and Figure 7
defined the initial 120 s as the optimum time interval that could provide useful information
on the thermal conductivity of the test sample material by a certain temperature decrease
∆θ.
The graph in Figure 7shows that for the time interval between 0 and 120 s, the
temperature of the test sample free surface decreased continuously, even reaching the
approximately constant temperature period before starting to grow again. For each test
sample made of the two materials (PLA and ABS) and each experiment, the values
∆θ
of
the temperature decrease were entered for 0–120 s in column 9 of Table 2.

Polymers 2022,14, 1714 10 of 15
Table 3.
The time variation of the free surface temperature after bringing the opposite test sample
surface in contact with the gel coolant package.
Exp.
No.
Time, t, s
0 60 120 180 240 300 360 420 480 540 600 660
1 23 −8−13 −15 −16 −17 −15 −13
2 23 −5−8−12 −12 −9−5−5
3 23 4 1 0 −3−3−8−7−6−5
4 23 5 −2−5−6−7−8−9−9−8−8−8
5 23 −15 −15 −14 −11 −11 −11 −11
6 23 5 −2−4−5−5−5−3−2
7 23 17 12 8 5 3 2 0 −1 0 1
8 23 3 −1−6−8−6−5−8
Polymers 2022, 14, x FOR PEER REVIEW 9 of 15
First measurements of temperature variation were taken (as shown in the schematic
representations in Figures 1 and 2) to establish the magnitude of the time interval required
to determine the empirical mathematical model. As the parameter of interest was the
ability of the test sample material to sense the temperature decrease, measurements were
performed until, after the initial decrease, the temperature remained somewhat constant
for a short time and then began to rise. The results of the measurements are listed in Table
3.
Table 3. The time variation of the free surface temperature after bringing the opposite test sample
surface in contact with the gel coolant package.
Exp.
No.
Time, t, s
0 60 120 180 240 300 360 420 480 540 600 660
1 23 −8 −13 −15 −16 −17 −15 −13
2 23 −5 −8 −12 −12 −9 −5 −5
3 23 4 1 0 −3 −3 −8 −7 −6 −5
4 23 5 −2 −5 −6 −7 −8 −9 −9 −8 −8 −8
5 23 −15 −15 −14 −11 −11 −11 −11
6 23 5 −2 −4 −5 −5 −5 −3 −2
7 23 17 12 8 5 3 2 0 −1 0 1
8 23 3 −1 −6 −8 −6 −5 −8
A graphical representation of the temperature decrease measured on the free surface
of the test sample can be seen in Figure 7. The analysis of the data in Table 3 and Figure 7
defined the initial 120 s as the optimum time interval that could provide useful
information on the thermal conductivity of the test sample material by a certain
temperature decrease Δθ.
Figure 7. Graphical representation of the temperature decrease on the surface of the test sample
opposite to that affected by a cooling process, for all 8 experimental tests, according to the values
entered in Table 3.
The graph in Figure 7 shows that for the time interval between 0 and 120 s, the
temperature of the test sample free surface decreased continuously, even reaching the
approximately constant temperature period before starting to grow again. For each test
sample made of the two materials (PLA and ABS) and each experiment, the values Δθ of
the temperature decrease were entered for 0–120 s in column 9 of Table 2.
4. Discussion
The values of the input factors taken into account and the values Δθ of the
temperature decrease were introduced in a specialized software designed to identify an
empirical mathematical model according to the results of the experimental tests [42]. This
program is based on the least-squares method. It allows the selection of the most
Figure 7.
Graphical representation of the temperature decrease on the surface of the test sample
opposite to that affected by a cooling process, for all 8 experimental tests, according to the values
entered in Table 3.
4. Discussion
The values of the input factors taken into account and the values
∆θ
of the temperature
decrease were introduced in a specialized software designed to identify an empirical
mathematical model according to the results of the experimental tests [
42
]. This program is
based on the least-squares method. It allows the selection of the most appropriate empirical
mathematical model from five such possible models (first-degree polynomial, second-
degree polynomial, power type function, logarithmic function, and hyperbolic function).
The selection of the most appropriate program is based on the value of the so-called Gauss
criterion.
The value of the Gauss criterion is calculated as a sum of the squares of the ordinate
differences corresponding to the experimental results and those determined using the
empirical mathematical model considered for the same values of the input factors. The
lower the value of Gauss’s criterion, the better the empirical mathematical model considered
agrees with the experimental results.
It was found that, among the five versions of empirical mathematical models, the most
appropriate concerning the experimental results is the first-degree polynomial type, which
has the form:
∆θ=39.916 −3.999m−5.999h+0.200s−0.00499c+0.124i−94.444l+0.0374t, (2)
where the value of Gauss’s criterion is SG= 2.379693 ×10−9.
Note that this first-degree polynomial provides direct information about the magni-
tude and direction of the variation of the output parameter (
∆θ
) to the variation of each
input factor value by analyzing the values of the coefficients attached to each of the input
factors considered. A similar property is presented by the mathematical model of the

Polymers 2022,14, 1714 11 of 15
power-type function. Power-type empirical mathematical models have often been pre-
ferred (for example, to highlight the influence of cutting conditions on tool life, surface
roughness, cutting force component sizes, etc.). For this reason, it was considered useful
to take into account, for the analyzed situation, an empirical mathematical model of the
power function type, which has the form:
∆θ=0.214m−0.336h−0.457s0.691 c0.00415i0.512 l−0.411t0.016, (3)
where the value of the Gauss’s criterion is S
G
= 2.430406
·×
10
−7
, a value higher than that
when using the mathematical model of the first-degree polynomial type, identified by the
software used as the most suitable for the experimental results.
The last two columns (10 and 11) in Table 2list the values calculated for those two
empirical mathematical models. Thus, the extent to which the values determined by using
the two types of empirical mathematical models (first-degree polynomial and power-type
function) approach the values determined by experimental research may be observed.
Analysis of the differences between the real values of the temperature decrease
∆θ
and
the values determined using the first-degree polynomial empirical mathematical model
shows that these errors are between the limits of 0.19
◦
C (for experiment no. 7) and 2.53
◦
C
(for experiment no. 1). One may observe the relatively low differences between the values
obtained experimentally and those determined using the proposed empirical mathematical
models, highlighting the empirical models’ adequacy to the experimental results.
Using the mathematical model based on Equation (2), the graphical representations
from Figures 8–10 were elaborated.
Polymers 2022, 14, x FOR PEER REVIEW 11 of 15
Figure 8. Influence of test sample thickness h and printing speed s on the temperature decrease Δθ
(m = 1 (PLA), c = 100%, i = 18%, l = 0.06 mm, t = 120 s; the differences between the real values and
those implied by the proposed empirical mathematical model are between the limits of 0.19 °C (for
experiment no. 7) and 2.53 °C (for experiment no. 1)).
Figure 9. Influence of infill i and layer thickness l on temperature decrease Δθ (m = 1 (PLA), h = 1
mm, s = 45 mm/s, c = 100%, t = 120 s; the differences between the real values and those implied by
the proposed empirical mathematical model are between the limits of 0.19 °C (for experiment no. 7)
and 2.53 °C (for experiment no. 1)).
Figure 8.
Influence of test sample thickness hand printing speed son the temperature decrease
∆θ
(m= 1 (PLA), c= 100%, i= 18%, l= 0.06 mm, t= 120 s; the differences between the real values and
those implied by the proposed empirical mathematical model are between the limits of 0.19
◦
C (for
experiment no. 7) and 2.53 ◦C (for experiment no. 1)).

Polymers 2022,14, 1714 12 of 15
Polymers 2022, 14, x FOR PEER REVIEW 11 of 15
Figure 8. Influence of test sample thickness h and printing speed s on the temperature decrease Δθ
(m = 1 (PLA), c = 100%, i = 18%, l = 0.06 mm, t = 120 s; the differences between the real values and
those implied by the proposed empirical mathematical model are between the limits of 0.19 °C (for
experiment no. 7) and 2.53 °C (for experiment no. 1)).
Figure 9. Influence of infill i and layer thickness l on temperature decrease Δθ (m = 1 (PLA), h = 1
mm, s = 45 mm/s, c = 100%, t = 120 s; the differences between the real values and those implied by
the proposed empirical mathematical model are between the limits of 0.19 °C (for experiment no. 7)
and 2.53 °C (for experiment no. 1)).
Figure 9.
Influence of infill iand layer thickness l on temperature decrease
∆θ
(m= 1 (PLA), h= 1
mm, s= 45 mm/s, c= 100%, t= 120 s; the differences between the real values and those implied by
the proposed empirical mathematical model are between the limits of 0.19
◦
C (for experiment no. 7)
and 2.53 ◦C (for experiment no. 1)).
Polymers 2022, 14, x FOR PEER REVIEW 12 of 15
Figure 10. The influence exerted by time t on the temperature decrease Δθ for the two mate-rials
considered (h = 1 mm, s = 45 mm/s, c = 100%, i = 18%, l = 0.06 mm; the differences between the real
values and those implied by the proposed empirical mathematical model are between the limits of
0.19 °C (for experiment no. 7) and 2.53 °C (for experiment no. 1)).
Thus, an increase in the values of printing speed s, infill i, deposited layer thickness
l, and time t increases the temperature Δθ because the values of coefficients attached to
the respective input factors in the first-degree polynomials are positive. At the same time,
an increase in the test sample thickness h and the characteristic related to cooling
conditions c lead to a reduction in the temperature decrease Δθ, which is highlighted by
the negative values of the coefficients associated with the factors concerned in Equation
(2). One cannot obtain qualitative information based on the value of factor m, as this factor
is used only to differentiate the results obtained for the two test samples materials (PLA
and ABS).
Among all six factors considered and whose values can be modified, the strongest
influence is exerted by the deposited layer thickness l and by the test sample thickness h,
which corresponds, in this order, to the highest absolute values of the coefficients attached
in the first-degree polynomial empirical mathematical model (2). It was also expected that
an increase in the test sample thickness h would reduce the temperature decrease Δθ for
the same time interval due to the larger distance traveled by the heat flow. A minimal
influence is exerted by the factor c, which considers the cooling conditions. This is
emphasized by the low value of the coefficient attached to this factor in Equation (2) and
thus has virtually no influence on the output parameter taken into account.
The diagram in Figure 10 depicts the evolution of the temperature decrease Δθ as a
function of time t for the two materials, according to the empirical mathematical model
constituted by Equation (2). As expected, the increase in time t results in an increase in
temperature decrease Δθ, but values recorded for the ABS material are lower than those
in the case of the PLA material, which shows a lower thermal conductivity of the latter
material.
5. Conclusions
The thermal conductivity of materials for parts made by 3D printing is important
when used for the thermal insulation of some spaces affected by temperature variations.
The research highlighted the transmission of temperature through various 3D-printed
Figure 10.
The influence exerted by time ton the temperature decrease
∆θ
for the two mate-rials
considered (h= 1 mm, s= 45 mm/s, c= 100%, i= 18%, l= 0.06 mm; the differences between the real
values and those implied by the proposed empirical mathematical model are between the limits of
0.19 ◦C (for experiment no. 7) and 2.53 ◦C (for experiment no. 1)).
Thus, an increase in the values of printing speed s, infill i, deposited layer thickness l,
and time tincreases the temperature
∆θ
because the values of coefficients attached to the
respective input factors in the first-degree polynomials are positive. At the same time, an
increase in the test sample thickness hand the characteristic related to cooling conditions c
lead to a reduction in the temperature decrease
∆θ
, which is highlighted by the negative

Polymers 2022,14, 1714 13 of 15
values of the coefficients associated with the factors concerned in Equation (2). One cannot
obtain qualitative information based on the value of factor m, as this factor is used only to
differentiate the results obtained for the two test samples materials (PLA and ABS).
Among all six factors considered and whose values can be modified, the strongest
influence is exerted by the deposited layer thickness land by the test sample thickness h,
which corresponds, in this order, to the highest absolute values of the coefficients attached
in the first-degree polynomial empirical mathematical model (2). It was also expected that
an increase in the test sample thickness hwould reduce the temperature decrease
∆θ
for the
same time interval due to the larger distance traveled by the heat flow. A minimal influence
is exerted by the factor c, which considers the cooling conditions. This is emphasized by
the low value of the coefficient attached to this factor in Equation (2) and thus has virtually
no influence on the output parameter taken into account.
The diagram in Figure 10 depicts the evolution of the temperature decrease
∆θ
as a
function of time tfor the two materials, according to the empirical mathematical model
constituted by Equation (2). As expected, the increase in time tresults in an increase in
temperature decrease
∆θ
, but values recorded for the ABS material are lower than those
in the case of the PLA material, which shows a lower thermal conductivity of the latter
material.
5. Conclusions
The thermal conductivity of materials for parts made by 3D printing is important
when used for the thermal insulation of some spaces affected by temperature variations.
The research highlighted the transmission of temperature through various 3D-printed
plates of polylactic acid (PLA) and acrylonitrile butadiene styrene (ABS), respectively. On
one surface of the test sample, a flexible-wall package with a gel coolant at
−
15
◦
C was
placed. The influence of the thickness of the test samples and the values of some input
factors in the 3D printing process on the decrease of the temperature on the opposite surface
were taken into account. Equipment to ensure conditions for fixing the test sample inside
a box of insulating material, placing a flexible-wall package, and temperature measuring
possibilities was designed and fabricated. Following the recommendations for a Taguchi
type L8 factorial experiment, experimental tests were performed with 2
7−4
= 8 experimental
tests. The experiments involved using seven input factors at two levels of variation. By
mathematical processing of the experimental results, using specialized software based on
the least-squares method, an empirical mathematical model of the first-degree polynomial
type was identified. The values of the coefficients attached to each of the input factors in this
first-degree polynomial provide information on the variation direction, and the magnitude
of the temperature decrease when the values of the input factors change within certain
limits. The analysis of the empirical mathematical model and graphic representations
highlighted that the ABS material ensures better thermal insulation conditions than the
PLA material. Among the input factors in the 3D printing process, the strongest influence
is exerted by the deposited layer thickness, test sample thickness, and printing speed. The
cooling conditions during the 3D printing process have a lesser influence on the decrease
in temperature over time.
In the future, it is intended to expand the theoretical and experimental research on
thermal conductivity and other materials used in parts manufacturing by 3D printing.
Author Contributions:
Conceptualization, C.E.P. and L.S.; methodology, O.D. and A.P.; software,
A.-M.M.; validation, A.H. and L.S.; formal analysis, G.N.; investigation, A.P.; resources, O.D.; writing—
original draft preparation, L.S.; writing—review and editing, C.E.P., A.P. and O.D.; visualization,
G.N.; supervision, C.E.P. All authors have read and agreed to the published version of the manuscript.
Funding: This research received no external funding.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.

Polymers 2022,14, 1714 14 of 15
Data Availability Statement: Not applicable.
Conflicts of Interest: The authors declare no conflict of interest.
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