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Engineering, Technology & Applied Science Research Vol. 12, No. 6, 2022, 9450-9457 9450
www.etasr.com Park et al.: Development of a Prediction System for 3D Printed Part Deformation
Development of a Prediction System for 3D Printed
Part Deformation
Hong-Seok Park
School of Mechanical and Automotive Engineering
University of Ulsan
Ulsan, Republic of Korea
phosk@ulsan.ac.kr
Van-Thong Hoang
Faculty of Information Technology
University of Transport and Communications
Hanoi, Vietnam
thonghv@utc.edu.vn
Ngoc-Hien Tran
Faculty of Mechanical Engineering
University of Transport and Communications
Hanoi, Vietnam
tranhien.tkm@utc.edu.vn
Vu-Hung Bui
Faculty of Mechanical Engineering
University of Transport and Communications
Hanoi, Vietnam
bvhung.tkm@utc.edu.vn
Received: 12 August 2022 | Revised: 26 August 2022 | Accepted: 2 September 2022
Abstract-The Additive Manufacturing (AM) process is applied in
industrial applications. However, quality issues of the printed
parts, including part distortion and cracks caused by high
temperature and fast cooling, result in high residual stress. The
theoretical calculation equation shows elastic behavior which is
the linear behavior between strain and stress. However, in
practice with the additive manufacturing process, strain and
stress have nonlinear behavior. So, the prediction of the
deformation of a printed part is inaccurate. The contribution of
this research is the creation of an Inherent Strain (IS)-based part
deformation prediction method during the Selective Laser
Melting (SLM) process. To have the deformation in the design
stage, we developed software for calculating the IS value and
predicting the deformation. The difference between the
calculated results and the experimental results is still there, so,
we proposed an algorithm and developed an optimization module
for the system to minimize this difference. In the final optimal
printing process, the parameters are derived in order for the real
printing process to have the required quality of the SLM printed
part.
Keywords-selective laser melting; predicting deformation;
inherent strain; heat treatment effect zone
I. INTRODUCTION
Layer by layer manufacturing or additive manufacturing
has been used in many application fields such as aerospace,
automotive, biomedical, and energy production and
distribution. The printed parts are made from plastic or metal
powder materials [1-4]. However, the quality issues of the
printed parts, including part distortion, as well as the cracks
caused by high temperature and fast cooling, result in high
residual stress. This is a challenge that limits the industry
acceptance of AM. To overcome this challenge, a numerical
modeling method for predicting the part distortion at the design
stage plays an important role, which enables design engineers
to remove failures before carrying out printing as well as to
determine the optimal printing process parameters to minimize
part deformation. Currently, with the rapid growth of this
technology, many AM processes have been applied in
industrial applications. Selective Laser Melting (SLM) is one
of these AM processes. SLM is an AM process that directly
produces parts from metal powder. SLM is a complex thermal-
physical-chemical process of the interaction between a laser
source and metallic powders [1, 5]. The SLM mechanism is
shown in Figure 1. The SLM system includes the laser source,
the optical system, and the deposition system. The optical
system has the optical mirrors which enable the laser source to
be directed onto the powder bed surface. The thin powder layer
is distributed by the deposition system and melted by the laser
source through the optical system. The deposition system that
is the scraper or roller system enables the distribution of the
powder onto the printed area. The printed layer thickness is
determined by the distance of moving down of the build
platform. Then, another powder layer is added on the top of the
printed previous layer. This step is repeated until the entire 3D
model is completed.
For printing the metal parts, there are currently many
different AM processes using different combinations of stock
material form, material delivery, and heat source. SLM is the
most attractive method for layer by layer building of metal
parts due to advantages such as the lack of post-processing.
However, as the same with other AM processes, the distortion
and cracks of the printed parts still occur due to the residual
stress caused by the rapid heating and cooling process [6]. In
the SLM process, high temperature is required for the melting
of the metallic powders. Due to high temperature and fast
cooling, residual stress will be generated in the printed part.
The large residual stress results in part distortion which is a
negative effect of the product performance. Part distortion
caused by the tensile residual stress not only reduces the part
Corresponding author: Vu-Hung Bui, Ngoc-Hien Tran
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www.etasr.com Park et al.: Development of a Prediction System for 3D Printed Part Deformation
geometrical accuracy, but also affects the functional
performance of the printed parts. To acquire good printed part
quality, key factors such as powder properties, printing process
parameters, and SLM machine characteristics must be
considered.
Fig. 1. Mechanism of the selective laser melting process.
Currently, the method for keeping the quality of the printed
part is trial-and-error testing. This method depends on the
user’s experience and requires larger manufacturing costs,
while producing waste and scrap [7]. Therefore, it is necessary
for predicting the part’s quality at the design stage which
enables to remove failures before carrying out the real printing.
Many researchers have used the inherent strain method for
predicting part deformation in welding processes. However,
some proposals for modifying the conventional IS method have
been applied to apply this method to AM processes such as the
SLM process, [8, 9]. Authors in [9] proposed the extraction of
the IS value from micro-scale thermo-mechanical analysis.
This IS value was applied to the part-scale model to have the
part deformation. However, it is challenging to predict the
residual deformation in the part-scale model [10]. To overcome
this challenge, a multi-scale modeling approach is proposed in
[11, 12]. Currently, some commercial tools based on the IS
method enable the prediction of deformation. However, the
algorithms to calculate the IS value and how to apply this value
to the part-scale model are not publicly available [13].
This paper presents a new method for predicting the
deformation of the 3D printed part using the ISs. For carrying
out this research, a method for calculating the IS value is
proposed. These IS values are used for calculating the
deformation. Both simulation and experiments were
implemented for comparing the IS values and deformations.
II. MODEL FOR DETERMINING THE IS VALUE
A. Theoretical Model
The term of IS was firstly introduced in 1975 for analyzing
the welding process. It is a general name for the expression of
non-elastic strains which include the thermal strain �������� ,
phase transfer strain � ��
� , plastic strain � ��
��� , and creep
strain ����� [7]. During the SLM process with the heating and
cooling cycles, the total strain is the sum of the elastic strain ����
��� and IS � ∗, as shown below:
������ = ����
��� + � ∗ (1)
The inherent strain is calculated as:
�∗ = �������� + � ��
��� + � ��
� + ����� (2)
Strain and stress are unknown variables. We can determine
the value of one of these variables by experiments. The
remaining variable is determined by the equation showing the
relationship between strain and stress. The commercial tools
enable engineers to estimate the IS value. However, the
algorithms for calculating the IS value are not published.
During the printing process, the material begins at the melting
temperature via the heating stage and is changed to a lower
temperature via the cooling stage at a high rate. The material
of the printed part will receive a compressive force due to the
thermal change. Thus, the three-dimensional ISs are
compressive strains, and the equations can be defined as [14]:
��∗ = − ���� ; ��∗ = −
��
�� ; ��∗ = −
��
�� (3)
in which Fx, Fy, and Fz are the zone areas where Wx, Wy, and
Wz respectively are distributed. The total volume Wx of ��∗, the
total volume Wy of ��∗ , and the total volume Wz of ��∗ in unit
length are calculated as follows:
Wx = ξ ∙ qv ; Wy = Wz = K ∙ qv (4)
in which qv is the linear energy density (J/mm) [15]:
�� = ���� "#$%&�' (5)
ξ and K (mm/J) are longitudinal and transverse inherent strain
coefficients, respectively. Figure 2 shows the components of
the inherent strain εx, εy , and εz with these parameters.
Fig. 2. Inherent strain components.
The inherent strains in the x, y, and z directions for the first
layer are calculated as follows:
��(�)� = − * ∙ ,-�� ; ��(�)� = −
. ∙ ,-
�� ; ��(�)� = −
. ∙ ,-
�� (6)
Figure 3 shows the calculation of the IS for n layers. After
printing the first layer, the IS value is ��(� . If we add the
second layer via the SLM process mechanism, the first layer is
re-melted with the new heat treatment effect zone, so the
remaining IS value for the first layer is:
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�/0 = ��(� − 1� ��(� (7)
When the second layer is added, its IS value is:
�2 = �/0 + ��(� = 2��(� − 1� ��(� (8)
If a third layer is added, the remaining IS value in the
second layer is:
�20 = �2 − 1� ��(� = 2��(� − 21� ��(� (9)
and the IS value in the third layer is calculated as:
�4 = �20 + ��(� = 3��(� − 21� ��(� (10)
Repeating this SLM process for n layers, we can calculate
the IS value for the n
th
layer as follows:
�( = �()/0 + ��(� = 6��(� − (()/)1� ��(� (11)
For whole part, in x, y, and z directions, we have the IS
value as follows:
⎩⎪
⎨
⎪⎧�� (( �����) = 6��(�)� −
(()/)1
� ��(�)�
�� (( �����) = 6��(�)� − (()/)1� ��(�)�
�� (( �����) = 6��(�)� − (()/)1� ��(�)=
(12)
Fig. 3. Method for calculating inherent strain for whole part.
B. Simulation and Experiments
1) Simulation Results
The mathematical model of the heat transfer, which we
used to determine the temperature distribution during the SLM
process, is [16]:
>? @A@� + >?u ∇D = ∇(E∇D) + FG (13)
where T is the temperature, ρ, С, and k are density, thermal
capacity, and thermal conductivity factor respectively, u is the
printing speed. QG is the power distribution given by the
moving Goldak’s double-ellipsoid heat source model as shown
in Figure 4 [17], this heat source model from the welding
process, however, it is also suitable for research on the SLM
process. QG is the total of the absorbed laser in front and rear
of the Goldak heat source model [18]. We used this heat
transfer model and printing process parameters (as shown in
Table I) for simulation using Comsol
TM
. We also run tests with
the same material (316L steel), however, with differences in
the printing process parameters (300W laser power, 1300mm/s
laser velocity, and 0.045mm layer thickness). In this case, the
inherent strain in Z direction is -0.153 [19].
Fig. 4. Goldak heat source in the finite element model of the AM process.
The temperature distribution during the SLM process is
shown in Figure 5. The Heat Treatment Effect Zone (HTEZ)
surfaces are shown in Figures 6-8. The HTEZ surface in the
ZX plane as shown in Figure 6 is calculated as follows:
H� = (I + J) ∙ K − J ∙ L (14)
with d = 0.112mm, c = 0.0522mm, e = 0.5255mm, and
x = 2.429mm, we have Fx = 0.3035mm
2
.
The HTEZ surface in the XY plane as shown in Figure 7 is
calculated as follows:
H� = 2(I + J) ∙ (M + N) − 2M ∙ J − O ∙ 6 (15)
with a = 0.089mm, b = 0.137 mm, e = 0.5255 mm, f = 0.258,
n = 3.166, and x = 2.429 mm, we have Fy = 0.425 mm
2
.
The HTEZ surface in the ZY plane as shown in Figure 8 is
calculated as:
H� = 2[(M + N) ∙ K − M ∙ L] (16)
with a = 0.089mm, b = 0.137mm, d =0.112mm, and
c = 0.0522mm, we have FZ = 0.0413 mm
2
.
Fig. 5. Goldak heat source in the finite element model of the AM process.
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TABLE I. PRINTING PROCESS PARAMETERS [18]
Name Description Value
x0 Path center X-Coordinate 0mm
y0 Path center Y-Coordinate 0mm
Qheat source Laser power 250W
p
Length of the y-semi-axis of
ellipsoid (mm)
0.173mm
c
Length of the z-semi-axis of
ellipsoid (mm)
0.230mm
af
Length of the x -semi-axis of
front ellipsoids (mm)
0.173mm
ar
Length of the x -semi-axis of rear
ellipsoids (mm)
0.347mm
u Laser velocity 1100mm/s
C Thermal capacity 500×10
-3
J/(g.K)
λ Thermal conductivity factor 19.4×10
-3
W/(mm.K)
Ta Ambient temperature 293K
h Layer thickness 0.05mm
ha Hatch distance 0.07mm
Fig. 6. HTEZ surface in in the ZX plane.
Fig. 7. HTEZ surface in in the XY plane.
Fig. 8. HTEZ surface in in the ZY plane.
The inherent strains in the x, y, and z directions for the first
layer are calculated by applying (6) with ξ =1.57×10
-3
mm
3
/J,
K =0.58×10
-3
mm
3
/J [14], and qv = 0.2273J/mm for 316L
stainless steel, Fx = 0.3035mm
2
, Fy = 0.425mm
2
, and
FZ= 0.0413mm
2
, we have: ��(�)� = −0.00118, ��(�)� = −0.00031 and ��(�)� = −0.003. In comparison with
the reported IS value for the first layer in the welding process,
which also considers the influence of the temperature
distribution to the IS value, the calculated IS value is
acceptable. In the z direction, where the highest temperature is
1500
0
C (or 1773
0
K) the inherent strain value is 0.0017 [20].
Thus, the IS value for the whole part after 60 printed layers
(with layer thickness of 0.05mm and printed part height of
3mm) is calculated as follows: Assuming that the depth (d) that
affects the inherent strain distribution equals to (1/3) of the
layer thickness (h), we have the following IS values using (12):
�� (R���� ���) = −0.04742, �� (R���� ���) = −0.0125, �� (R���� ���) =−0.1286.
2) Experimental Results
Experiments on printing a cantilever beam were carried out
on an SLM machine at the Laboratory of Production
Engineering, Ulsan University, Republic of Korea (Figure 9).
The geometrical model of the cantilever beam and the printing
direction (0, 45°, and 90°) are shown in Figure 10. Specimens
were printed on the MetalSys 250.
Fig. 9. Experiments on the SLM machine.
The highest deformation of the cantilever beam at the
position in the z direction with 0° printing direction after
cutting the part from the base plate by the Electrical Discharge
Machining (EDM) machine is 1.45mm as shown in Figure 9
and Table II. The IS is calculated as follows:
� = − � )�S�S = −
/4.UV)/2.V
/2.V = −0.116 (17)
where lo is the part length before cutting by EDM and lt is the
part length after cutting by EDM. Considering the z direction,
with the part height before and after cutting being 12.5mm and
13.95mm, we have εz = −0.116, and the deformation in the z
direction is 1.45mm. The IS value in the z direction predicted
by simulation is −0.1286. The difference between simulation
and experiment is considered acceptable.
TABLE II. GEOMETRY MEASUREMENT AFTER CUTTING
Geometry
measurement
Distortion (mm)
1 2 3 4 5 Average
Scan pattern (0
o
) 13.93 13.94 13.96 14.02 13.90 13.95
Scan pattern (90
o
) 13.24 13.19 13.21 13.19 13.12 13.19
Scan pattern (45
o
) 13.50 13.48 13.50 13.51 13.43 13.484
With the proposed method, the IS value in the z direction is
εz = −0.1286. From this IS value, with a total part height of
H = 12.5mm, the deformation (δ) of the printed part in the Z
direction is 1.608mm, which is calculated by:
δ = |εz(whole part)|∙H (18)
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Fig. 10. Specimens printed by SLM.
III. ARCHITECTURE OF FUNCTIONALITY MODULES
A. Module for Calculating the HTEZ Surfaces
To develop the proposed system, we drive out the
architecture of functionality modules. Figure 11 shows the
architecture of the module for calculating HTEZ surfaces. With
the input parameters such as 3D model of part, layer thickness
(h), hatch distance (ha), scanning speed (u), and laser power
(Q), the databases of the system are updated which are printing
parameter database and part dimension database. In the printing
parameter database u, Q and the heat source (Goldak model)
with parameters such as c, b, af, ar, are used for calculating the
absorbed laser. Other databases are also built which are the
material properties (thermal capacity, thermal expansion, and
thermal conductivity factor), and the coefficient for printing
(lattice parameter, laser interaction time). The thermal capacity
(C) in material properties database and the absorbed laser are
used for calculating the temperature distribution through the
heat transfer equation. From the temperature distribution and
the material properties and coefficient for printing databases,
we have the HTEZ parameters (x, e, c, d, a, b, f, n). Then, we
calculate the HTEZ surfaces (Fx, Fy, Fz).
Fig. 11. Architecture of the module for calculating HTEZ surfaces.
B. Module for Calculating the IS for One Layer
Figure 12 shows the architecture of the module for
calculating the IS value for one layer. With the input
parameters including the printing process parameters, and the
HTEZ surfaces, the system allows to calculate the melting
energy, the laser power, and the linear energy density. Then,
the linear energy density (qv) and the layer thickness are used
for calculating the longitudinal, transverse IS coefficients (ξ,
K). From the qv, ξ, and K, we calculate the IS value for one
layer using (6).
Fig. 12. Architecture of the module for calculating IS for one layer.
C. Module for Calculating the IS for the Whole Part
Figure 13 shows the architecture of the module for
calculating the IS value for whole part. With the input
parameters including the IS value for one layer, part dimension,
and printing parameters, the layer number and the HTEZ depth
are calculated. Then, these data are used for calculating the IS
value for the whole part using (12).
Fig. 13. Architecture of the module for calculating the IS for the whole
part.
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D. Module for Optimizing the Difference Between the
Simulations and the Experiments
Figure 14 shows the architecture of the module for
optimizing the difference between the simulations and the
experiments. From the simulation and experimental results, the
system enables to calculate the new IS value in case the
difference between them in the printed part deformation is
more than 0.01.
Fig. 14. Architecture of the module for optimizing the difference between
the simulation and experiment.
IV. IMPLEMENTATION OF THE SYSTEM
Fig. 15. Architecture of the system for calculating inherent strain.
To acquire the deformation in the design stage, we
developed software for calculating the IS and for predicting the
printed part deformation. The developed system includes 4
modules: a module for calculating the HTEZ surfaces, a
module for calculating the IS for one layer, a module for
calculating the IS of whole part, and a module for optimizing
the difference between the simulations and the experiments.
For programming the proposed system, we used C++
language in Visual Studio 2019 environment. The system
architecture is shown in Figure 15 which describes the
information flow among the modules. Figure 16 shows the
interface module which shows the integration of modules for
one complete system. With the input data including printing
process parameters (such as volumetric energy density, layer
thickness, hatch distance, scanning speed, and efficiency) and
the HTEZ surfaces, the developed system allows to calculate
the IS value for one layer as shown in Figure 17. The
volumetric energy density value is 40J/mm
3
[21]. From the
calculated IS values for one layer and part information (such as
length, width, and part height), the developed system enables to
calculate the IS value of the whole part in x, y, z directions as
shown in Figure 18.
Fig. 16. Screenshot of the system interface with four modules.
V. CONCLUSION
The contribution of this research is the creation of an inherent
strain-based part deformation prediction method during the
Selective Laser Melting (SLM) process. To determine the
Inherent Strain (IS) value, a micro-scale model for analyzing the
temperature distribution was created. The IS value for one layer
is calculated from the temperature gradient. For calculating the
IS value for the whole part, the HTEZ is used. Then, the IS value
is used to determine the part deformation. The proposed
methodology has been developed and evaluated using 316L
stainless steel cantilever beams, and both simulated and
experimental results were obtained. To acquire the deformation
in the design stage, we developed the IS-based deformation
prediction software. The functionality of the developed system
was tested successfully.
Future research can be conducted with the consideration of
other factors affecting the printed part quality in order to
minimize part deformation. In addition, other printing processes
also should be added to the developed system.
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Fig. 17. Screenshot of the module for calculating inherent strain for one layer.
Fig. 18. Screenshot of the module for calculating IS of whole part.
Engineering, Technology & Applied Science Research Vol. 12, No. 6, 2022, 9450-9457 9457
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ACKNOWLEDGMENT
This research is funded by the University of Transport and
Communications (UTC) under grant number T2022-CK-12,
supported by the University of Ulsan.
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