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Prediction of Dimensional Error in Down-Facing Surfaces for Laser Powder Bed Fusion Parts


Abstract and Figures

The growing rise of popularity of Additive Manufacturing technologies and its increased adoption for manufacturing has created a requirement for its fast development and maturity. However, it still lags far behind conventional manufacturing in terms of predictability, quality and robustness. Statistical modelling has proven to be an excellent tool to develop process knowledge and to optimize different processes efficiently and effectively. This paper establishes a methodology to predict dimensional errors in hard to print down-facing surfaces. Using the process parameters – laser power, scan speed, scan spacing, scan pattern and layer thickness, a predictive process model is developed. An ANOVA analysis concluded the laser power to be the most significant process parameter, followed by layer thickness and scan speed. This paper also discusses some of the interaction effects between parameters. Some thoughts on the next steps to be taken for validation of the model are discussed.
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Prediction of Dimensional Error in Down-Facing Surfaces for Laser
Powder Bed Fusion Parts
Amal Charles1*, Ahmed Elkaseer1, 2, Lore Thijs3, Veit Hagenmeyer1, Steffen Scholz1, 4
1 Institute for Automation and Applied Informatics, Karlsruhe Institute of Technology, Karlsruhe, Germany
2 Faculty of Engineering, Port Said University, Port Said, Egypt
3 Direct Metal Printing Engineering, 3D Systems, Leuven, Belgium
4Karlsruhe Nano Micro Facility, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany
Corresponding author. Tel.: +49 721 608-25851, E-mail address:
The growing rise of popularity of Additive Manufacturing technologies and its increased adoption for manufacturing
has created a requirement for its fast development and maturity. However, it still lags far behind conventional
manufacturing in terms of predictability, quality and robustness. Statistical modelling has proven to be an excellent
tool to develop process knowledge and to optimize different processes efficiently and effectively. This paper
establishes a methodology to predict dimensional errors in hard to print down-facing surfaces. Using the process
parameters laser power, scan speed, scan spacing, scan pattern and layer thickness, a predictive process model
is developed. An ANOVA analysis concluded the laser power to be the most significant process parameter, followed
by layer thickness and scan speed. This paper also discusses some of the interaction effects between parameters.
Some thoughts on the next steps to be taken for validation of the model are discussed.
Keywords: Additive Manufacturing, Process modelling, Laser Powder Bed Fusion, ANOVA
1. Introduction
Additive Manufacturing (AM), colloquially known
as 3D printing is a rapidly evolving group of
manufacturing and fabrication techniques that are
currently revolutionising design and production
practises across industries. They have displayed their
potential to disrupt and affect globally established
process chains. Their main advantages include almost
unlimited design freedom, shortening of lead times, as
well as reduction in material usage [1]. This combined
with the ability to print on demand, allows AM to fit in
well with today’s industrial trends of digital
manufacturing and mass customisation [2]. Therefore,
this combination of factors and modern trends has
allowed AM to arrive as a modern solution for current
and future demands.
Laser-based powder bed fusion (L-PBF) is one of
the AM techniques that is gaining an increased market
acceptance and penetration, particularly in a wide
range of industrial applications that include
automotive, aerospace, medical/dental and robotics
[1]. This is primarily due to all the advantages
mentioned above, as well as the availability of
printable super-alloys such as Ti-6Al-4V, which
possess high strength-to-weight ratios and corrosion
resistances. Which makes them prime candidates for
applications where low-density and excellent corrosion
resistant materials are required, such as the
aerospace industry [3].
However, the L-PBF process still faces some
technological challenges that need addressing in order
to improve the robustness and repeatability of parts
produced. In particular, when compared to other
conventional manufacturing technologies, AM and L-
PBF in particular lags behind when it comes to being
able to predict different quality marks of the parts
produced, such as dimensional accuracy and surface
Therefore, a significant portion of current AM
research is focussed on investigating these different
aspects of precision, namely the repeatability,
predictability and robustness of the process. Various
approaches have been employed for this purpose,
including investigating design for precision AM using
topology optimisation, developing design guidelines
for AM, thermal modelling of the L-PBF process as well
as statistical process optimisation studies [4, 5]. These
methods are also complemented by studies on
improving methods for finishing of parts [6] as well as
for metrology [7].
This current work concentrates on understanding
the effects of process parameters on the dimensional
accuracy of printed parts, particularly on the
dimensional accuracy of down-facing surfaces. Down-
facing or down-skin surfaces are present on parts that
contain overhanging features that are not printed over
solid bulk material, but on lose powder, see Fig. 1. It is
especially difficult to print these surfaces as they
normally show large dimensional errors and require
support structures, thereby necessitate extra process
steps for support removal and finishing.
The main cause for these dimensional deviations
is dross formation [8] that is the result of melting of
excess material. This excess melting is caused by the
overheating of unmelted lose powder resulting in the
formation of large dimensional deviations from the
CAD design. The degree of the dross formation is
dependent on the process parameters and the effect
of dross formation on the dimensional deviation and
surface topography can vary. Therefore, the aim of this
paper is to present results of a statistical analysis of
45° down-facing surfaces. Using regression modelling,
a predictive process model was developed for L-PBF
parts using various scanning strategies, layer
thickness and down-facing process parameters.
2. Methodology
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2.1. Experimental design
Since the paper focusses on investigating down-
facing surfaces. A simple design with a 45° inclined
down-facing surface was used as the test piece. The
45° down-facing surface is usually the limit when it
comes to printing without support structures. However,
it is also not recommended as often, major
dimensional errors happen even at 45° surfaces.
Therefore, achieving minimal errors at this angle would
depict an improvement over the state of the art. The
different process parameters and their levels chosen
to investigate the effect on the dimensional accuracy
are listed in Table 1:
Table 1: Process parameters and levels
Laser Power (W)
50, 90, 150, 210, 250
Scan Speed (mm/s)
200, 465, 850, 1235, 1500
Scan Spacing (µm)
50, 60, 75, 90, 100
Scan Pattern
Strips, Rectangular cells,
Hexagonal cells
Layer Thickness (µm)
60, 90
An inscribed central composite experimental
design was used and the Design of Experiments (DoE)
is shown in Table 2.
The parameters presented in Table 2 were used
to print the samples for each of the various scan
patterns and layer thickness, resulting in six unique
tables and a total of 144 test pieces for analysis. Trials
15 to 24 represent parts printed with same parameters,
while the test pieces were arranged in the build
platform following no particular order in order to
improve the randomization
Table 2: DoE for experimental trials
Power (W)
15 - 24
The process parameters were only varied within
the down-facing area of the part; see Fig. 1, while the
rest of the part was printed with the same printing
parameters for all test pieces as seen in the image.
2.2. Test Piece design
The test piece was designed to a 10 mm by 20
mm down-facing surface area as seen in Fig 1 and
was printed on a 3D Systems ProX® DMP 320 using
a TiAl6V4 metal powder. All parts were pre-processed
using the 3DXpert software for assigning of the
process parameters and printing strategies.
Fig. 1 Depiction of dross formation on the down-facing surfaces of a part produced by Laser-based powder bed fusion
2.3. Measurements
Using an optical microscope, images were made
of the side view of all test pieces. An image processing
technique was developed and employed to measure
the thickness of the overhanging surface. The image
processing technique first works by gray scaling the
image and applying a threshold in order to detect the
edges of the test piece. The program then scans
image both vertically and horizontally and extrapolates
a straight line though the detected edge points. As the
scale of the image is known, it is then possible to
calculate the distance between the two straight lines,
which gives the thickness of the overhanging surfaces
of the parts. The measured thickness was then
compared to the CAD design to determine the error in
the printed part and the percentage of this error. Both
sides of the part were measured to detect any
differences in thickness within the same part. As see
on Figure 2, the dotted lines depict the detected edge
of the part, which are used to measure the thickness.
The obtained measurements were validated by
comparing with Vernier Calliper measurements
3. Results
3.1 Predictive process modelling
Data processing and statistical modelling were
done using MATLAB (R2019a). A linear regression
model with interaction effects was used to describe the
relationship between the different process parameters
with the dimensional error percentage. This model was
used to generate the interaction plots as seen in the
figure 5. The interaction effects depicted below show
the estimated effects on the response from changing
each variable value while averaging out the effects of
the other process parameters. From the interaction
effects it is clear that:
1. Increasing the scan speed tends to decrease the
dimensional error at all laser powers, to various
2. Increasing laser powers at any scan spacing
increases the dimensional error
3. While increasing the scan speed at any scan
spacing decreases dimensional error
This predictive process model was then used to
generate the predictive slice plots as shown in Figure
6. The prediction slice plot shows the main effect of
each process parameter and displays the estimated
dimensional error percentage. The prediction slice plot
can be used to determine the predicted dimensional
Fig. 2. Printed part that undergoes image processing,
green lines indicate the detected edges that will be used
for measurement
Fig. 3. Plots depicting the interaction effects of laser power, scan speed and scan spacing
error in a part at various process parameters as well
as scanning strategies and layer thickness. The plot
was tested against the initial experimental results and
its predictions were found to be a maximum of 5%
away from measured value. In the case of the Figure
4, the model predicts an error percentage of 4.8%
while the actual measured error percentage for this
parameter combination was 2.02%.
ANOVA analysis was also conducted in order to
get a deeper understanding of the significance of the
process parameters on the dimensional accuracy as it
also considers the interaction effects. The results
indicate that the laser power (P-Value = 0.00088723)
is the most significant process parameter followed by
the layer thickness (P-Value = 0.0032135) and scan
speed (P-Value = 0.0048101). The next highest
significance is given to the interaction effect of laser
power and scan speed (P-Value = 0.30819). These
were the four most significant effects.
4. Conclusions
This paper has presented the first results of
predictive modelling of dimensional error in L-PBF
parts. An image processing technique was developed
to measure the thickness of printed samples. The
process parameters under investigation are the laser
power, scan speed, scan spacing, scan strategy and
the layer thickness. A statistical study was conducted
and using linear regression a model was developed.
The interaction effects of the process parameters were
plotted and clear trends can be seen in their effects on
the dimensional error and are summarized in section
3.1. The model was then used to generate predictive
slice plots which were tested with the original dataset.
The predictions showed a maximum error of 5% on the
original dataset, which is promising. This early
predictive model can be used to suggest process
parameters combinations that will contribute towards
the least error in the printed part. However, the
prediction slice plot needs to be validated by
performing further prints. Therefore, validation of the
model is to be done in the next step.
The ANOVA analysis also depicted the laser
power to be the most significant process parameters
on the dimensional error, which concurs with previous
research work and results. In terms of significance,
laser power is followed by layer thickness, scan speed
and the interaction effect of laser power and scan
speed. Therefore, in further studies the effect of
combined factors such as linear energy density or
volumetric energy density will be taken into account.
This study establishes a starting point, further
validation of the model and further data collection is
required in order to improve prediction. This is the
focus of current and future work.
5. Acknowledgements
This work was done in the H2020-MSCA-
ITN-2016 project PAM2, Precision Additive Metal
Manufacturing, which is funded by The EU Framework
Programme for Research and InnovationGrant
Agreement No. 721383.
6. References
[1] M. Attaran, The rise of 3-D printing: The advantages of
additive manufacturing over traditional manufacturing,
Business Horizons.
[2] B. Berman, 3-D printing: The new industrial revolution,
Business Horizons 55(2) (2012) 155-162.
[3] H. Shipley, D. McDonnell, M. Culleton, R. Coull, R. Lupoi,
G. O'Donnell, D. Trimble, Optimisation of process parameters
to address fundamental challenges during selective laser
melting of Ti-6Al-4V: A review, International Journal of
Machine Tools and Manufacture 128 (2018) 1-20.
[4] M. Bayat, S. Mohanty, J.H. Hattel, Multiphysics modelling
of lack-of-fusion voids formation and evolution in IN718 made
by multi-track/multi-layer L-PBF, International Journal of Heat
and Mass Transfer 139 (2019) 95-114.
[5] A. Charles, A. Elkaseer, L. Thijs, V. Hagenmeyer, S.
Scholz, Effect of Process Parameters on the Generated
Surface Roughness of Down-Facing Surfaces in Selective
Laser Melting, Applied Sciences 9(6) (2019) 1256.
[6] J. dos Santos Solheid, H. Jürgen Seifert, W. Pfleging,
Laser surface modification and polishing of additive
manufactured metallic parts, Procedia CIRP 74 (2018)
[7] M. Baier, F. Zanini, E. Savio, S. Carmignato, A new
conversion approach between different characterization
methods to measure the spot size of micro computed
tomography systems, 2018.
[8] D. Wang, S. Mai, D. Xiao, Y. Yang, Surface quality of the
curved overhanging structure manufactured from 316-L
stainless steel by SLM, The International Journal of
Advanced Manufacturing Technology 86(1) (2016) 781-792.
Fig. 4. Prediction slice plots created using the developed predictive process model
... A number of researchers have employed different analytical and statistical approaches to build predictive process models for various fields within Additive Manufacturing [25,26]. Tapia et al. developed a Gaussian process regression formula for the prediction of porosity in L-PBF processes and discussed the difficulty in modeling the L-PBF processes due to the low process repeatability [27]. ...
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