Tribology and Materials
Vol. 1, No. 3, 2022, pp. 114-119
ISSN 2812-9717
https://doi.org/10.46793/tribomat.2022.011
Determination of the optimal mode of laser surface marking of
aluminium composite panels with CO2 laser
Emil YANKOV
1,
*, Roussi MINEV
1
, Nikolay TONCHEV
2
, Lyubomir LAZOV
3
1
University of Ruse "Angel Kanchev", Ruse, Bulgaria
University of Transport, Sofia, Bulgaria
3
Rezekne Academy of Technologies, Rēzekne, Latvia
*Corresponding author:
[email protected]
2
Keywords
Abstract
aluminium composite panel
CO2 laser
surface
optimisation model
laser marking
This research examines an approach for finding the optimal modes of laser
treatment with CO2 laser on advertisement boards made of aluminium composite
panels. To achieve the optimal area of the processing mode, an experimental
methodology has been developed and an experiment has been planned for finding
the limits at the given parameters of the speed and power to obtain an
optimisation model. The optimal results are obtained at speeds from 100 to 200
mm/s along the x and y operative axes, as well as the power limits from 5 to 7.5 W
to obtain a clear and well-defined image. The defined theoretical mode, obtained
because of multicriteria optimisation, is implemented in practice. It is defined as
having the relatively best quality image obtained in the shortest time.
History
Received: 27-07-2022
Revised: 15-08-2022
Accepted: 19-08-2022
1. Introduction
In recent years, composite materials combined
with various technological and physicomechanical
properties are widely used in mechanical
engineering,
construction,
production
of
information panels, signs and more. Materials that
are applied or glued to the information boards are
often used to present information. This, of course,
is associated with additional costs of materials and
technological modes. Most of them are obtained
from chemical technologies – chemical dyes. Such
are, for example, inks and paints, which are
difficult to degrade, and their extractive waste is
harmful to the environment. Therefore, in recent
years, solutions are being sought for new
technologies and processes that can replace
existing ones. In recent years, the application of
lasers in various industries is increasing, such as
mechanical engineering, energy and electronics
[1,2]. Now, it has been widely used in research in
the field of laser printing of metallic and nonmetallic materials [3-9]. This will create a strong
This work is licensed under a Creative
Commons Attribution-NonCommercial
4.0 International (CC BY-NC 4.0) license
development of laser technology in the next few
years in the field of billboards and materials,
replacing classic production technologies. Like any
new technology, it is necessary to assess
productivity and the necessary resources such as
capacity equipment for the quality of the product,
which is directly related to the economic effect of
each company or industry.
In the 90s of the previous century in
metallurgical practice [10], there has been
approved the use of the model experiment on the
specific physicochemical formulation of the target
process. In the development of a multicomponent
alloy, the optimisation problem is formulated by
determining the optimal technological mode,
ensuring the specified quality.
Regardless of the universality of the considered
methods, each specific problem requires its own
effective methods, in which case there is a need to
develop new algorithms and modification of
existing ones, which eliminates the observed
shortcomings [11-13].
Because the experimental approach does not
use information about the mechanism of ongoing
phenomena [14,15], the numerical procedure used
as a tool in this article turns out to be very
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E. Yankov et al. | Tribology and Materials 1 (2022) 114-119
universal. Each case under consideration can be
described with the same structure, but with
different coefficients. They form the mathematical
model of the examined phenomenon (process),
which can be examined from different points of
view: technological, informational, organisational,
etc. [16]. The aim of this research is to determine,
after an analysis of controlled magnitudes, a mode
corresponding to an optimal compromise solution
in a case study, similar to multi-criteria support for
decision-making by shifting restrictions [17,18].
2. Problem statement
To form a quality image, it is necessary to vary
the technological parameters of the laser system
[19-22]. For the purposes of the research, a CO2
laser with technical capabilities of a speed of
movement of 500 mm/s along the x and y axes,
and regulated laser power up to 50 W in step 0.05
W was used. This is a previous technological
procedure for the implementation of new
equipment with unidentified processes. Image
quality is determined by an experiment, most
often planned. Based on the experiment, the
technological capabilities of the CO2 laser are
determined compared to the controlled
magnitudes: speed, power and constant focus of
the spot 50.8 mm. The necessary information for
the analysis of the selected technological process is
contained in the experimentally obtained values
indicated in Table 1.
Table 1. Experimentally results and experimental plan
Experimentally obtained values for the Experimental
regulated control parameters
plan
Speed,
Power,
% (Х1) mm/s (Х2)
Time,
s (y1)
Quality,
% (y2)
Mp =
10
100
494.4
96.63
–1
–1
20
100
508.2
86.21
1
–1
30
100
514.8
74.37
–1
1
10
200
454.8
62.56
1
1
20
200
497.4
68.95
1
0
30
200
509.4
72.11
–1
0
10
300
454.8
54.05
0
1
20
300
513.6
56.34
0
–1
30
300
546.0
58.44
0
0
In the specified interval with the two variables, an
experimental plan is drawn up, as described in Table
1. As can be seen from Table 1, the variable power is
10 % (5 W), 20 % (10 W) and 30 % (15 W), and the
variable speed of operation on the x and y axes is 100
mm/s, 200 mm/s and 300 mm/s. Parameter Mp = is
the encoding of the experimental plan, with the left
vertical column corresponding to the power data in
the encoded form – 1, 0 and 1. The right column is
the speed data in the encoded form – 1, 0 and 1. For
each experimental combination of control
parameters in Figure 1 two of the controlled
quantities are defined. As a result of the conducted
experiment for y1, the reporting time for
manufacturing was chosen, and for y2 the quality of
the obtained trace was evaluated by comparative
analysis of the digital image with the obtained image
from the laser marking in %.
Figure 1. Results of test experimental modes
The experimental plan (Table 1) is embedded in
an information matrix in a way that is expected to
obtain the coefficients of the regression model.
Since we determine the structure of the model:
F (X1 ,X 2 ) = B 0 + B1 X1 + B2 X 2 +
+B3 X1X2 + B4 X12 + B5 X22 ,
(1)
the cited plan Mp occupies the second and third
columns in the information matrix F.
For the methodical purpose of obtaining the
coefficients of the regression model, an information
matrix related to Equation (1) is indicated. The
information matrix based on the experimental plan
from Table 1 has the form:
1 – 1 –1
1 1 –1
1 –1 1
1 1 1
F = 1 1 0
1 –1 0
1 0 1
1 0 –1
1 0 0
1 1 1
1 1 –1
1 1 –1
1 1 1
1 0 0 .
1 0 0
0 1 1
0 1 1
0 0 0
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E. Yankov et al. | Tribology and Materials 1 (2022) 114-119
The first column of the information matrix is
composed of ones, because the value of the free
member of the model is unknown. The remaining
columns are calculated based on the values of Х1 and
Х2 according to the selected structure. According to
the performed Мр plan for each combination of the
variables Х1 and Х2, the experimental value of the
studied quantity is determined. This is how the
vector Fst is formed. The Fst vectors are two, one is
for quality and the other is for operation time. The
values of these vectors are indicated in Table 1. Each
experimental combination of the control parameters
from Table 1 corresponds to each of the quality
indicators. The information matrix has 9 rows and
accordingly the vector of experimental values Fst
also consists of nine values. FT is a transposed
information matrix F. The coefficients of the
regression model are determined based on the
following matrix calculation:
C = (FT F)–1 FT Fst .
quality is determined based on an experiment
which determines the technological capabilities of
the equipment. In Table 2 the results from the
coefficients and the respective checks obtained for
the two examined quantities are given.
Table 2. Coefficients of the regression models for the
studied quantities
Parameter
coefficient
Quality
Operation time
B0
+ 67.9
+ 493.889
B1 X1
– 1.4
+ 27.667
B2 X2
– 14.74
– 0.5
B3 X1 X2
+ 6.625
+ 17.5
B4 X12
B5 X22
–
– 10.33
+ 3.099
+ 18.1667
R
0.9638
0.9963
Fcalc > Ftable
13.0521 > 6.3883 80.1359 > 9.0135
(2)
To conduct a planned experiment, a series of
experiments were conducted in which a specific
image was selected related to the face of the
famous Bulgarian scientist Prof. Lyubomir Kalev on
pieces of aluminium composite panel.
From the obtained results of different modes,
shown in Figure 1, it can be seen how the changed
parameters of power and speed affect the quality
image during marking. The resulting images are
captured with a digital camera. The resulting digital
images are compared to the original photo using the
Adobe Photoshop software product. It compares
the power of contrast and the power of black and
white. The difference is reported in percentages (%)
and filled in Table 1. The bounds of the planned
experiment were determined experimentally: speed
from 100 to 300 mm/s, power from 10 to 30 % at a
constant frequency of 20 kHz and a resolution of
600 dpi. The material consists of 7075 aluminium
alloy foil with a thickness of 0.25 mm on both outer
sides. The intermediate layer is made of sheet
polyethylene with a thickness of 2.5 mm. The
chemical composition of 7075 aluminium alloy
roughly includes 5.6 – 6.1 % zinc, 2.1 – 2.5 %
magnesium, 1.2 – 1.6 % copper, and less than a half
percentage of silicon, iron, manganese, titanium,
chromium and other metals.
3. Results of the research and determination
of the compromise solution
To form the image it is necessary to vary the
technological marking parameters. The image
The last two lines of Table 2 show the model
checks. The multiple correlation coefficient R for both
models is extremely high, which is proof of the
adequacy of the models. Scanning the regression
models with structure and coefficients shown in Table
2 is performed in the interval (– 1; 1) with a certain
step. In this case, a bi-dimensional space formed by
the two technological parameters of variation and the
two studied quantities is the object of research.
The values in Table 2 are obtained by performing
the matrix calculations from Equation (2). The
determined values of the tested quantity as a result
of this calculation form a corresponding array (yM)
at the respective (set) sampling. The optimisation
problem for determining yMmax and yMmin is solved
followed by the transformation of the calculated
values into a uniform percentage distribution. The
transformation is performed via the equation:
yN =
yM – yMmin
100 %.
yMmax – yMmin
(3)
When scanning the investigated quantities in the
defined area (– 1; 1) with a certain step, their
minimum and maximum value can be determined
(Equation (3)). Through these values, each
normalised value at the respective discretisation is
obtained. The value YM from Equation (3) is the
current value of the studied quantity, the one at
which the normalised value is located.
Figure 2 shows the scanned normalised values
of the two examined quantities. The intervals for
the individual colours of the very ranking direct the
decision maker to the preferred values of the
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E. Yankov et al. | Tribology and Materials 1 (2022) 114-119
examined quantity. The selected value is defined
as an even percentage distribution based on the
colour ranking. For it, the real value of the
examined quantity in the respective dimension and
the specific combination of the factors of the
technological regime can be determined. After
scanning the controlled quantities, it is possible to
create a composite image of Figure 2, built
according to the requirements of the user. In this
case, maximal quality is required in minimal time.
(a)
(a)
(b)
(b)
Figure 2. Normalised values as a percentage of:
(a) image quality and (b) operation time
This summary image of Figures 2a and 2b is
shown in Figure 3. From Figure 3, the optimal
solution can be defined as relatively good, obtained
in the shortest time. A colour map representing the
solutions in colour code was also built. The optimal
mode is obtained in the area of the yellow borders
shown in Figure 3a, where the speeds can be from
100 to 200 mm/s and laser beam power from 10 %
(5 W) to 12.5 % (7.5 W). In this area, the clearest
image is obtained by laser marking.
Figure 3. Result of: (a) optimal solution of the
planned experiment and (b) control check by a real
experiment
The planned experiment was confirmed by
conducting a series of experiments proving the
capabilities of the laser system in search of quality
and speed. The practical equation for solving the
problem is:
X1 = –1 and X 2 = –0.25,
(4)
the better solution and:
2X1 = – 0.25 and X 2 = –0.25.
(5)
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E. Yankov et al. | Tribology and Materials 1 (2022) 114-119
4. Conclusions
As a result of the performed procedure, a mode
is determined, subject to multicriteria compromise
optimisation, making it possible to obtain a
relatively high-quality image in the shortest time.
The applied methodology helped to fully assess the
regimes for the implementation of new equipment
with unidentified technological impact on
controlled factors. The proposed calculation
procedure is a tool with which it is possible to build
a complete picture of the examined process. The
approach creates a prerequisite in the examined
applications to look for models oriented to certain
savings of time, raw materials or energy.
Acknowledgement
The research and the participation in this
scientific conference were implemented with the
support of the: Research Fund at the University of
Ruse “Angel Kanchev” by contract project FMME
2020-01 for “Research of laser and layer-by-layer
technologies for obtaining prototype models” and
the Research Fund at the University of Transport
“Todor Kableshkov” by contract project No. 90-0520 for “Contribution of VTU in the analysis,
modeling and optimization of simulation and
experimental databases”.
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Emil Yankov