*Corr. Author’s Address: College of Mechanical Engineering, Hunan Institute of Science and Technology, Yueyang 414006, China, lch@hnist.edu.cn 247
Strojniški vestnik - Journal of Mechanical Engineering 70(2024)5-6, 247-258 Received for review: 2023-09-07
© 2024 The Authors. CC BY 4.0 Int. Licensee: SV-JME Received revised form: 2024-02-11
DOI:10.5545/sv-jme.2023.787 Original Scientific Paper Accepted for publication: 2024-04-03
Effect of Laser Parameters on Surface Texture  
of Polyformaldehyde and Parameter Optimization
Li, F. – Li, C. – Zhou, J. – He, J. – Wang, J. – Luo, C. – Li, S.
Fengren Li
1,2
 – Chao Li
1,2,*
 – Juan Zhou
3
 – Jiantao He
1,2
 – Jiebin Wang
1,2
 – Cong Luo
1,2
 – Si Li
1
1 
Hunan Institute of Science and Technology, College of Mechanical Engineering, China 
2 
Key Laboratory of Intelligent Manufacturing and Service Performance Optimization  
of Laser and Grinding in Mechanical Industry, China 
3 
Yueyang V ocational Technical College, College of Electromechanical Engineering, China 
This research aimed to investigate the influence of laser process parameters on the surface texture of Polyformaldehyde (POM) and to improve 
its processability and process predictability. A comparative experiment and analysis involving multiple processing parameters, including laser 
power, scanning speed, and pulse width, were conducted on POM. Statistical prediction models of laser processing POM were established 
among the laser power, scanning speed, pulse width, texture depth, surface roughness at the bottom of texture, and multi-objective 
optimization and experimental verification of process parameters were carried out based on the grey-Taguchi analysis method. Experimental 
results show that the laser power and scanning speed significantly affect the texture depth. Higher laser power and lower scanning speed are 
conducive to forming depth. The surface roughness at the bottom of the texture increases with the increase in scanning speed and shows 
a tendency to rise and then fall as the laser power increases. The surface roughness and texture depth obtained under the optimal process 
parameters(A
5
B
1
C
1
) are 1.373 μm and 466.891 μm, respectively, which were reduced by 10.08 % and increased by 3.42 % compared with 
the minimum surface roughness and maximum depth in the orthogonal experiments. The validation experiments of the prediction model show 
that it can meet the reliability requirements, and the errors of the predicted values of depth and surface roughness are 1.86 % and 7.60 %, 
respectively. The above research provides theoretical and experimental support for the precise control of surface texture prepared by laser 
processing POM.
Keywords: picosecond laser processing, parameter optimization, polyformaldehyde (POM), grey-Taguchi analysis method, prediction 
model
Highlights
• The effect of laser parameters on the surface texture features of POM was studied. 
• Established prediction models between laser parameters and texture features. 
• The optimal parameter combination is obtained based on the grey-Taguchi method.
• Laser power and scanning speed have a significant effect on texture quality.
0  INTRODUCTION
With the development of synthesis and processing 
technology for polymer materials, the use and scale 
of various polymers are growing rapidly [1] and [2]. 
As one of the most commonly used polymers today, 
POM has become a suitable substitute for traditional 
materials in many application fields (gears, seals, 
bearings, etc. [3]) due to its high stiffness, hardness, 
elastic modulus, excellent wear resistance, and low 
weight [4] to [6]. With the development of technology 
and industry, relying solely on the performance of 
the material itself has gradually failed to meet the 
requirements of surface performance. The method 
of enhancing surface performance by processing 
micro-texture on the material surface has been widely 
studied and applied [7] to [10]. Many techniques for 
fabricating surface structures have been developed, 
such as etching technologies [11], atomic layer 
deposition [12], abrasive jet processing [13], and 
micro-casting [14]. However, these methods are 
generally costly, and it is difficult to prepare micro-
nanostructures on the material surface, which do not 
meet the current low-carbon processing concept and 
high-precision processing requirements.
In recent years, lasers have proven to be a 
powerful tool for the precise processing of structures 
at the micron and nanoscale. The unique feature of 
laser processing is that it can modify materials in 
multiple length dimensions and produce complex 
micro- and nanostructures [15] to [17], resulting in 
better surface properties. Most of the existing research 
focuses on laser processing of metals [18] and [19] 
and ceramics [20] and [21], with less emphasis on 
polymers [22]. The majority of research aims to 
improve surface performance by altering texture types 
while studying the geometric quality of the texture 
itself, and the effect of laser process parameters on 
the texture quality has become a hot topic in recent 
years. Zhao et al. [23] systematically investigated the 
effect of repetition frequency on hole size morphology 
and described the relationship between repetition 

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)5-6, 247-258
248 Li, F. – Li, C. – Zhou, J. – He, J. – Wang, J. – Luo, C. – Li, S.
frequency and micropore size (such as diameter and 
depth) during picosecond laser ablation of metallic 
materials. Deepu et al. [24] investigated the effect of 
laser fluence, pulse overlap and pulse repetition rate 
on hole diameter, depth, and other factors. It was 
found that the best hole geometry could be obtained 
with a fluence of 0.44 J/cm, 10 kHz repetition rate and 
85 % pulse overlap.
At present, the lack of research on process 
parameters is the key reason for the inability to 
consistently obtain surface textures with excellent 
structure and significant functionality. The interaction 
and coupling between various process parameters also 
make it difficult to establish a feasible and complete 
theoretical model. Therefore, to achieve precise 
control of laser processing and obtain better quality 
texture, it is crucial to establish a predictive model 
between process parameters and texture geometric 
features, as well as to optimize the process parameters. 
Some scholars have studied the relationship between 
the geometric characteristics of material surface 
texture and laser process parameters using various 
analytical methods. Lian et al. [25] established a 
predictive model for the relationship between laser 
process parameters and the width of the clad layer, 
surface roughness, and dilution rate. They analysed 
the impact of process parameters on various response 
variables, and experimental results showed that the 
predictive model had good accuracy. Cui et al. [26] 
established regression prediction models between 
process parameters and coating width, coating height, 
coating depth, aspect ratio and dilution rate. The 
average error between the predicted values of each 
regression prediction model and the experimentally 
measured values is less than 10 %.
To improve the surface performance of POM 
materials, it is necessary to achieve precise control 
of the surface texture of POM. In this paper, the 
elliptical texture is processed on the surface of POM 
by picosecond laser, and the influence of process 
parameters (laser power, scanning speed, pulse 
width) on the texture characteristics (depth, surface 
roughness) is investigated, and the relationship 
between process parameters and texture characteristic 
morphology is determined. The effect of process 
parameters on texture characteristics and the 
interaction between the process parameters were 
analysed using the grey-Taguchi method, and the 
optimal combination of process parameters was 
obtained for the elliptical texture. Also, a prediction 
model of the geometric characteristics of the surface 
texture of POM was established, which provides 
an experimental and theoretical basis for further 
optimization of ultrafast laser processing of POM 
materials.
1  EXPERIMENTAL
1.1  Materials and Equipment
The experiment sample is M90-type POM 
(YUNTIANHUA CO., Ltd., Yunnan, China) with 
the specification of 25 mm × 25 mm × 10 mm 
(length×width×thickness). The samples were 
ultrasonically cleaned in anhydrous ethanol before 
and after laser processing, then naturally dried and 
placed on a two-dimensional moving table, which 
was computer-controlled for precise movement along 
x and y directions. The laser processing system used 
in this experiment is shown in Fig. 1a, where the 
laser is an infrared ultrashort pulse picosecond laser 
developed and produced by LinitiaLase, and the 
main technical parameters of the laser are shown in 
Table 1. The 3D measuring laser microscope (LEXT 
a)          b) 
Fig. 1.  Experimental instruments; a) laser processing system, and b) 3D laser scanning microscope

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)5-6, 247-258
249 Effect of Laser Parameters on Surface Texture of Polyformaldehyde and Parameter Optimization 
OLS5000, Olympus) shown in Fig. 1b enables fast 
and efficient accurate sub-micron 3D measurements 
and surface roughness measurements. It was used to 
observe the texture morphology and measure texture 
depth and surface roughness.
Table 1.  Main technical parameters of ultraviolet nanosecond laser
Parameter Value
Central wavelength [nm] 1028±5
Maximum output power [W] 30
Maximum pulse energy [μJ] 200
Laser frequency [kHz] 1 to 200
Pulse width [μs] 0.05 to 50
Beam divergence [urad] <20
Beam quality [-] M2<1.2
1.2  Experimental Design
1.2.1  Univariate Experiments
To study the effect of laser parameters on the geometry 
of the POM ellipse (long axis 1.5 mm × short axis 1 
mm) texture, the controlled variable method was used 
to explore the effect of laser power, scanning speed 
and pulse width on the depth of texture and surface 
roughness. Table 2 displays the specific experimental 
parameters used, while Table 3 outlines the laser 
parameters that were not discussed in this study.
During the laser processing, the POM workpiece 
is placed on a high-precision motion platform, and 
the pulse laser with high repetition frequency and 
high energy density is applied to the surface of the 
workpiece using different laser processing parameters 
[26], which is radiated on the surface of the specimen 
according to the set scanning path and causes it to 
melt and vaporize [27], thus processing the elliptical 
texture with a certain depth. The ultrasonic cleaning 
device was used to clean the processed samples. After 
natural air drying, the elliptical texture was observed 
and calculated with a 3D measuring laser microscope 
on the surface of the POM. To ensure the accuracy 
of the surface roughness measurement on the bottom 
surface of the texture, the overall measurement of the 
centre area of the elliptical texture bottom surface was 
performed using a 20× magnification, as shown in 
a)  
b) 
Fig. 2.  Measurement of a) surface roughness and b) depth

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)5-6, 247-258
250 Li, F. – Li, C. – Zhou, J. – He, J. – Wang, J. – Luo, C. – Li, S.
Fig. 2a. The depth is measured as shown in Fig. 2b. 
Both values are taken as the average value after three 
repeated measurements.
Table 2.  Laser processing experimental parameters
Laser power  
[W]
Scanning speed 
[mm·s
–1
]
Pulse width  
[μs]
19.5, 21, 22.5, 24, 
25.5, 27, 28.5, 30
600 12
24
450, 500, 550, 600, 
650, 700, 750, 800
12
24 600 4, 12, 20, 28, 36, 44
24 600 12
Table 3.  Values of laser parameters not discussed
Frequency 
[kHz]
Current 
strength [A]
Number of 
scans [-]
Laser line 
spacing [mm]
Ring spacing 
[mm]
60 1 10 0.005 0.5
1.2.2  Orthogonal Experimental Design
The Taguchi method is a local optimization algorithm 
based on an orthogonal experiment and signal-to-
noise ratio (S/N) designed by Genichi Taguchi [28]. 
Orthogonal table design experiments can reasonably 
reduce the number of experiments and blindness. 
Statistical analysis of the experimental results with 
the S/N as a measure of quality characteristics can 
lead to the best combination of reliable and stable 
process parameters, achieving a combination of high 
efficiency and low cost. This article takes the depth of 
texture and surface roughness as the response targets, 
and the three process parameters of laser power, 
scanning speed, and pulse width are the influencing 
factors. The levels of the three process parameters are 
shown in Table 4. Based on the Taguchi experiment 
principle, the L
25
 (5
3
) orthogonal experiment table 
with five levels and three factors is designed as shown 
in Table 5, where A, B, and C represent laser power, 
scanning speed, and pulse width, respectively. After 
the corresponding data were measured experimentally, 
the influencing factors of each response target were 
explored independently, and then the multi-mass target 
optimization problem was transformed into a single-
objective optimization problem using grey correlation 
analysis to obtain the degree of influence [29], trend, 
and the best process parameter combination of the 
three process parameters on the response target. The 
optimal process parameters were also used for laser 
processing to verify the effectiveness of process 
parameter optimization, and the accuracy of the model 
was verified by substituting it into the established 
prediction model for the solution. The measured data 
from the orthogonal experiments are shown in Table 
6.
Table 4.  Factors and their levels
Level
Factor
A 
Laser power 
[W]
B 
Scanning speed 
[mm·s
–1
]
C 
Pulse width 
[μs]
1 18 400 4
2 21 500 12
3 24 600 20
4 27 700 28
5 30 800 36
Table 5.   L
25
 (5
3
) Taguchi orthogonal experimental design
No A B C No A B C
1 18 400 4 14 24 700 4
2 18 500 12 15 24 800 12
3 18 600 20 16 27 400 28
4 18 700 28 17 27 500 36
5 18 800 36 18 27 600 4
6 21 400 12 19 27 700 12
7 21 500 20 20 27 800 20
8 21 600 28 21 30 400 36
9 21 700 36 22 30 500 4
10 21 800 4 23 30 600 12
11 24 400 20 24 30 700 20
12 24 500 28 25 30 800 28
13 24 600 36
Table 6.  Results of orthogonal experiment
No
Depth 
[μm]
Surface 
roughness 
[μm]
No
Depth 
[μm]
Surface 
roughness 
[μm]
1 197.142 1.558 14 227.206 3.268
2 171.335 1.527 15 204.575 4.099
3 148.198 1.883 16 394.915 2.429
4 134.415 2.190 17 338.945 2.259
5 118.957 2.559 18 299.383 2.504
6 289.134 1.947 19 267.142 3.812
7 251.768 2.149 20 241.586 4.371
8 216.943 2.618 21 451.443 3.289
9 190.783 3.273 22 394.611 1.942
10 166.790 3.701 23 340.797 3.151
11 354.549 2.237 24 300.774 4.819
12 296.081 2.098 25 267.183 5.598
13 260.960 2.601

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)5-6, 247-258
251 Effect of Laser Parameters on Surface Texture of Polyformaldehyde and Parameter Optimization 
2  RESULTS AND DISCUSSION
2.1 Texture Morphology Analysis
2.1.1 Influence of Laser Power on Texture
To investigate the effect of laser power on the 
geometry of the texture, the surface of the POM 
sample was irradiated with lasers at power levels 
within the range of 19.5 W to 30 W under constant 
scanning speeds of 600 mm/s and pulse widths of 12 
μs. The variation of the relevant parameters is shown 
in Fig. 3. With the gradual increase in laser power, 
the depth of elliptical texture shows an increasing 
trend, increasing from 160.709 μm to 302.197 μm. 
The increase in laser power means that the energy of 
individual laser pulses gradually increases, the energy 
density acting on the surface of POM increases, 
and when the laser energy density is higher than the 
ablation threshold of POM, the absorption of laser 
energy by POM produces ionization. The process 
of ionization becomes significant with increasing 
laser power, resulting in an increase in the volume 
of material removed and a greater depth of texture. 
Laser radiation to the site, with the increase in depth, 
began to move away from the original focal surface, 
and the laser energy to reach the bottom of the texture 
gradually decreased. Coupled with the gradual 
increase in the depth of the texture, the formation of 
molten spatter takes longer to fly out of the texture, as 
well as the laser processing process generated by the 
plasma on the laser shielding effect. As a result, the 
depth of the texture will increase with the laser power 
and tend to level off.
Meanwhile, it can be seen from Fig. 3 that the 
surface roughness of the elliptical texture bottom 
increases with the increase in laser power, but when 
the power reaches 24 W, the surface roughness 
reaches the maximum and continues to increase the 
power afterwards, the surface roughness starts to 
decrease instead. As shown in Fig. 4, the structure of 
the bottom surface of the texture structure is relatively 
regular when the laser power is small (19.5 W to 24 
W), and most of the bottom surface is formed by the 
uniform cooling of the melt that fails to vaporize in 
time. However, as the laser power gradually increases, 
the melt vaporized on each laser path increases, and 
the melt that did not vaporize at this time could not 
effectively lap to form a good surface, thus making 
the overall surface roughness gradually increase. Also, 
when the laser power is higher (25.5 W to 30 W), the 
macrostructure of the texture bottom surface is poorer, 
but its overall surface roughness starts to decrease 
compared to the power of 24 W. This phenomenon 
is caused as follows: the melt vaporized on the 
laser sweeping path is more than the non-vaporized 
melt, and the non-vaporized melt becomes a single 
individual after cooling, thus forming a structure of 
multiple crystalline particles on a smooth surface on 
the bottom surface, at which time the overall surface 
roughness of the bottom surface will gradually 
decrease as the smooth surface area increases and the 
number and volume of crystalline particles decrease.
Fig. 3.  The changes in texture depth and surface roughness  
under different laser power
Fig. 4.  Texture bottom morphology under different laser power
2.1.2  Influence of Scanning Speed on Texture
To further investigate the influence of laser scanning 
speed on texture, in a fixed other parameter situation, 
different laser scanning speeds (ranging from 450 
mm/s to 800 mm/s with an increment of 50 mm/s) 
were employed for texture processing. The variations 
in texture-related parameters are shown in Fig. 5. 
From Fig. 5, it can be seen that the depth decreases 
with the increase in scanning speed, with a relatively 
stable depth variation within the range of 600 mm/s 
to 650 mm/s. The scanning speed affects the action 
time of the laser and the material surface. With the 
increase of the scanning speed, the laser irradiation 
time per unit area becomes shorter, and the number 
of times radiated by the pulsed laser becomes 

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)5-6, 247-258
252 Li, F. – Li, C. – Zhou, J. – He, J. – Wang, J. – Luo, C. – Li, S.
less, the energy absorbed by the material surface 
decreases, and the material removal rate decreases, 
resulting in a decrease in the depth of the elliptical 
texture. Additionally, Fig. 5 indicates that the surface 
roughness of the bottom surface of the elliptical 
texture increases with increasing scanning speed, and 
the increase is gradually increasing. Combined with 
Fig. 6, it is found that the molten structure formed 
by laser ablation of POM gradually decreases with 
increasing scanning speed, and although the decrease 
of melt-like structure is beneficial to the macroscopic 
morphology, it has a negative effect on the surface 
roughness. As a common polymer, the crystallization 
properties of POM materials are positively correlated 
with heat treatment time and temperature in a specific 
temperature range [30]. As the scanning speed 
increases, the time for the texture to be radiated by the 
laser becomes shorter, the conduction and diffusion 
processes of energy on the material are shortened, the 
heat treatment time is shorter, and the crystallinity of 
the bottom surface of the texture is poor, which leads 
to the rise of its overall surface roughness.
Fig. 5.  The changes in texture depth and surface roughness  
under different scanning speeds
Fig. 6.  Texture bottom morphology under different scanning speed
2.1.3 Influence of Pulse Width on Texture
Pulse width is an important parameter in laser 
processing, which represents the duration of laser 
pulse energy output. Under the condition of unchanged 
pulse energy, increasing the pulse width will extend 
the period during which each laser pulse acts on the 
material surface, consequently elevating the total heat 
absorbed by the material and expanding the thermally 
affected zone of the processing site. As can be seen 
from Fig. 7, the depth of the elliptical texture becomes 
more significant with increasing pulse width, and the 
depth of the texture increases from 215.591 μm to 
224.512 μm when the pulse width increases from 4 μs 
to 44 μs, but the overall change is not significant. A 
comparison with Figs. 3 and 5 shows that the effect of 
pulse width on depth is much less than that of power 
and scanning speed. Fig. 7 also shows that the surface 
roughness of the texture’s bottom surface fluctuates 
between 2.65 μm and 2.95 μm with the variation of 
pulse width, which is relatively small compared with 
the influences of power and scanning speed. 
Fig. 7.  The changes of texture depth and surface roughness  
under different pulse width
Fig. 8.  Texture bottom morphology under different pulse width
During the process from a pulse width of 4 μs 
to 44 μs, the overall surface roughness exhibits a 
continuous decreasing trend. The rate of decrease is 
faster when the pulse width increases from 4 μs to 20 
μs, while it becomes more moderate when the pulse 
width increases from 20 μs to 44 μs. From Fig. 8, it can 

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)5-6, 247-258
253 Effect of Laser Parameters on Surface Texture of Polyformaldehyde and Parameter Optimization 
be observed that the morphology of the texture bottom 
surface does not undergo significant changes with 
increasing pulse width. Typically, larger pulse widths 
imply an extended duration of individual laser pulses 
and longer conduction times for laser energy inside 
the material, resulting in increased amounts of melt 
and corresponding changes in surface morphology. 
However, for a material like POM, variations in pulse 
width at the microsecond level have less effect on the 
melting process.
2.2  Model Building and Parameter Optimization
2.2.1  Model Building
Based on the data results obtained from the orthogonal 
experiment, the quadratic regression polynomials 
between laser power p, scanning speed v, pulse 
width w, depth D, and surface roughness Ra were 
constructed by Minitab. The obtained expressions are 
shown in Eqs. (1) and (2). According to the variance 
analysis results of depth shown in Table 7, the model 
coefficient P of the depth prediction model is much 
less than 0.05, indicating the high significance of 
the model at a 95 % confidence level. The multiple 
coefficients of determination R
2
 value is 0.9957, and 
the adjusted R
2
 value is 0.9945, both of which are 
close to 1, indicating the reliable predictive power of 
the model. Fig. 9a shows the residual normal plot of 
the depth regression model, from which it can be seen 
that the data points are evenly distributed around the 
fitted line with no abnormal data points, indicating 
a good fit for the regression model. In addition, 
the effect of pulse width on depth is not significant 
enough to exceed the 95 % confidence level, and 
variance analysis has automatically eliminated it. 
Similarly, as shown in Table 8 and Fig. 9b, the model 
coefficient P is less than 0.001, the P values of linear, 
square, and interaction terms are all less than 0.05, 
the multivariate coefficient R
2
 is 0.9319, the adjusted 
R
2
 is 0.9091, and the distribution of data points in the 
residual normal plot is reasonable, indicating that the 
prediction model has high overall reliability and fit.
2.2.2  Parameter Optimization
The Taguchi method evaluates the results of 
orthogonal experiments using the S/N ratio, which 
typically can be classified into three categories based 
on the research objectives: larger-the-better (LTB), 
smaller-the-better (STB), and nominal-the-best (NTB) 
[31]. In this study, the depth and surface roughness 
of the elliptical texture are chosen as the response 
variables. The objective was to achieve a large depth 
while maintaining a low surface roughness at a certain 
number of processing cycles. Therefore, the LTB 
criterion was used for the depth target, while the 
STB criterion was applied for the surface roughness 
target in calculating the S/N, and the magnitude of the 
influence of each process parameter on the target was 
sought using the range analysis. The specific results 
and data are shown in Tables 9 to 11, and the S/N ratio 
calculation formula is shown in Eq. (3).
 
Dp vp
vp v
  

341 75 06 20 311 0 4673
0 000381 0 02036
2
2
.. ..
.. , (1)
 
Ra pvw
vp s
 
 
87 40 0067 0 0247 0 0884
0 000015 0 000572 00 0
2
.. ..
...0 0119vw. (2)
Table 7.  Variance analysis table of depth
Source
Degree of 
freedom
Adj SS Adj MS F P
Model 5 179199 35839.7 873.28 <0.001
Laser  
power (A)
1 5713 5713.3 139.21 <0.001
Scanning 
speed (B)
1 355 355.0 8.65 0.008
AA 1 1238 1238.3 30.17 <0.001
BB 1 1018 1017.8 24.80 <0.001
AB 1 3732 3732.3 90.94 <0.001
Pure Error 19 780 41.0
Total 24 179978
R
2
 = 99.57 % R
2
(adj) = 99.45 %
Table 8.  Variance analysis table of surface roughness
Source
Degree of 
freedom
Adj SS Adj MS F P
Model 6 24.4912 4.08186 41.03 <0.001
Laser  
power (A)
1 0.8477 0.84766 8.52 0.009
Scanning 
speed (B)
1 2.1672 2.16720 21.78 <0.001
Pulse  
width (C)
1 0.9156 0.91561 9.20 0.007
BB 1 1.6432 1.64322 16.52 0.001
AB 1 2.1639 2.16388 21.75 <0.001
BC 1 0.6701 0.67012 6.74 0.018
Pure Error 18 1.7909 0.09950
Total 24 26.2821
R
2
 = 93.19 % R
2
(adj) = 90.91 %
The degree of influence of each parameter on the 
texture depth at different levels can be seen in Tables 
9 and 11. Due to the LTB characteristic of depth, when 
the combination of laser power (A), scanning speed 
(B), and pulse width (C) is set to A
5
B
1
C
3
 (laser power 

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)5-6, 247-258
254 Li, F. – Li, C. – Zhou, J. – He, J. – Wang, J. – Luo, C. – Li, S.
correlation values obtained by the three steps are 
shown in Table 12.
 SN
n y
LTB
n
yS TB
i
n
i
i
n
i
/
log
log






















10
11
10
1
1
2
1
2
 



, (3)
where () is the value of the response quantity,  is the 
number of experiments.
 Xk
yk yk
yk yk
LTB
yk yk
y
i
ii
ii
ii
 
  
  
  
min
maxm in
max
max
i ii
ky k
STB
  







min
, (4)
where X
i
(k) is the normalized value of the k
th
 response 
quantity for the i
th
 experiment; y
i
(k) is the value of the 
SNR for the i
th
 experiment of the k
th
 response quantity; 
max y
i
(k) and min y
i
(k) represent the maximum and 
minimum values of the k
th
 response volume in the 25 
sets of experiments, respectively.
GRCk
xx kx xk
xx kx xk
i
ii ii ii
ii ii i
 
   
  
minm ax
max
00
00

  
, (5)
where GRC
i
(k) is the value of the grey correlation 
coefficient of the i
th
 experiment of the k
th
 response; 
x
i
(k) is the normalized value of the k
th
 response 
quantity for the i
th
 experiment; x
i
0
 is the ideal value 
for the experiment, which is set to 1 in this study; ξ is 
the distinguishing coefficient which is defined in the 
range of 0 ≤ ξ ≤ 1, ξ was taken as 0.5 in this study.
 GRC
n
GRCk
i
k
n
i
 


1
1
, (6)
where GRC
i
 is the grey correlation value of the 
i
th
 experiment; GRC
i
(k) is the value of the grey 
of 30 W, scanning speed of 400 mm/s, pulse width 
of 20 μs), this combination represents the optimal 
process parameter combination for controlling texture 
depth. Additionally, based on the extreme difference, 
the impact of each parameter on depth can be ranked 
in descending order as follows: laser power > 
scanning speed > pulse width. Similarly, the optimal 
combination of process parameters for controlling 
the surface roughness of the texture bottom surface 
is A
1
B
2
C
1
 (laser power of 18 W, scanning speed of 
500 mm/s, pulse width of 4 μs). The impact of each 
parameter on surface roughness can be ranked in 
descending order as follows: scanning speed > laser 
power > pulse width.
Although the optimal parameters of the two 
responses are obtained respectively, the optimal 
parameters of one response quantity could not take 
into account the other response quantity due to the 
different influence of each process parameter on 
both. To obtain the best combination of process 
parameters with two response quantities, the grey 
correlation method is used. The grey correlation 
method is a method to determine the significance 
of the relationship between factors in the order of 
grey correlation. The combination of grey relational 
analysis theory with the Taguchi method provides 
an effective solution for complex multi-response 
problems. By transforming multiple laser process 
parameter optimization problems into optimizing 
a single grey relational degree problem, the optimal 
combination of parameters can be obtained to 
achieve minimal surface roughness and maximum 
depth. The grey correlation analysis requires a series 
of calculations on the signal-to-noise data: S/N 
normalization, calculation of the grey correlation 
coefficient for each response quantity, and calculation 
of the grey correlation. The formulas used in the three 
steps are shown in Eqs. (4) to  (6), and the final grey 
Fig. 9.  Normal probability plot of residuals for a) depth data and b) surface roughness data

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)5-6, 247-258
255 Effect of Laser Parameters on Surface Texture of Polyformaldehyde and Parameter Optimization 
correlation coefficient of the i
th
 experiment of the 
k
th
 response quantity; n is the number of response 
quantities and is 2 in this study.
Table 9.  SNR of response targets
No. Depth
Surface 
roughness
No. Depth
Surface 
roughness
1 45.896 -3.851 14 47.128 -10.286
2 44.677 -3.677 15 46.217 -12.254
3 43.417 -5.497 16 51.930 -7.709
4 42.569 -6.809 17 50.603 -6.482
5 41.508 -8.161 18 49.525 -7.973
6 49.222 -5.787 19 48.535 -11.623
7 48.020 -6.645 20 47.661 -12.812
8 46.727 -8.359 21 53.092 -10.341
9 45.611 -10.299 22 51.923 -5.765
10 44.443 -11.366 23 50.650 -9.969
11 50.994 -6.993 24 49.565 -13.976
12 49.428 -6.436 25 48.536 -14.961
13 48.331 -8.303
Table 10.  The SNR mean and range of depth
Factor level A B C
Mean 1 43.613 50.227 47.783
Mean 2 46.805 48.930 47.860
Mean 3 48.420 47.730 47.931
Mean 4 49.651 46.682 47.838
Mean 5 50.753 45.673 47.829
Range 7.140 4.554 0.148
Table 11.  The SNR mean and range of surface roughness
Factor level A B C
Mean 1 -5.599 -6.936 -7.848
Mean 2 -8.491 -5.801 -8.662
Mean 3 -8.854 -8.020 -9.185
Mean 4 -9.320 -10.599 -8.855
Mean 5 -11.002 -11.911 -8.717
Range 5.403 6.110 1.337
Table 12.  Grey relational analysis data
No. GRC No. GRC No. GRC
1 0.708 10 0.412 19 0.487
2 0.704 11 0.682 20 0.449
3 0.565 12 0.642 21 0.729
4 0.499 13 0.549 22 0.781
5 0.445 14 0.477 23 0.588
6 0.664 15 0.427 24 0.488
7 0.594 16 0.708 25 0.447
8 0.511 17 0.684
9 0.448 18 0.593
According to grey relational analysis theory, the 
degree of correlation between factors and the system 
depends on the value of the correlation degree. The 
larger the correlation deegree value of a process 
parameter, the greater its response in optimizing the 
objective function. Fig. 10 shows the main effect plot 
of the grey correlation of each process parameter, and 
it can be seen that the optimal process parameter is 
A
5
B
1
C
1
, i.e., the laser power is 30 W, the scanning 
speed is 400 mm/s, and the pulse width is 4 μs.
2.2.3 Validation Analysis
Since the optimal combination of process parameters 
(A
5
B
1
C
1
) was not included in the orthogonal 
experiment, a new set of machining experiments was 
conducted using the optimal parameter combination. 
Table 13 presents the optimized process parameters 
and the relevant parameters of the elliptical texture. 
Combining grey correlation theory with the data from 
the orthogonal experiment, the minimum surface 
roughness and maximum depth were selected as 
references. The surface roughness obtained from the 
optimized parameters was 1.373 μm, which decreased 
by 10.08 % compared to the minimum surface 
roughness obtained from the orthogonal experiment 
(1.527 μm); the depth obtained from the optimized 
parameters was 466.891 μm, which increased by 3.42 
% compared to the maximum depth obtained from 
the orthogonal experiment (451.443 μm). The results 
demonstrate that the effect of the optimized parameters 
is consistent with the previous expectations, as it 
enables the simultaneous attainment of low surface 
roughness and a greater depth. It can also be seen 
from Fig. 11 that compared to the two texture 
substrates obtained through separate optimization 
using the Taguchi method, the substrate prepared after 
further optimization using the grey correlation method 
exhibits a greater abundance of molten-like structures.
Fig. 10.  Main effects plot for the SNR analysis of GRC

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)5-6, 247-258
256 Li, F. – Li, C. – Zhou, J. – He, J. – Wang, J. – Luo, C. – Li, S.
Additionally, these molten structures are 
distributed in a wider and more uniform manner, 
which is also the reason for the further reduction 
in surface roughness. By substituting the optimal 
combination of process parameters into Eqs. (1) 
and (2), the predicted values for depth and surface 
roughness are obtained as 475.570 μm and 1.486 μm, 
respectively, and the errors between these predicted 
values and the actual measured values are 1.86 % and 
7.60 %. This shows that the predictive model exhibits 
high accuracy and reliability, meeting the objectives 
of predicting and optimizing process parameters, 
and it has a positive effect on the accurate control 
of the texture morphology and quality as well as the 
improvement of the efficiency of ablation.
Table 13.  Optimized parameters and response
Laser  
power 
[W]
Scanning 
speed 
[mm·s
–1
]
Pulse  
width
[μs]
Depth  
[μm]
Surface 
roughness
30 400 4 466.891 1.373
3  CONCLUSION
This paper investigates the impact of laser process 
parameters on the surface texture characteristics 
of POM. The predictive model was established to 
correlate three laser parameters (laser power, scanning 
speed, and pulse width) with texture depth and surface 
roughness at the bottom of the texture. The grey-
Taguchi method was employed for multi-objective 
optimization and experimental verification of the 
process parameters. The results indicate that with the 
increase of laser power and the decrease of scanning 
speed, the depth of the weave gradually increases, 
but its increase decreases with the further change of 
these two influencing factors. The surface roughness 
at the bottom of the texture decreases with increasing 
pulse width and exhibits a trend of initially increasing 
and then decreasing with increasing scanning speed, 
with a maximum value observed at a power of 24 
W. The variation of pulse width has no significant 
effect on either the depth or surface roughness. 
Multi-objective optimization using the grey-Taguchi 
method resulted in obtaining the optimal combination 
of laser parameters as A
5
B
1
C
1
 (laser power is 30 W, 
the scanning speed is 400 mm/s and pulse width is 4 
μs). Compared with the corresponding data obtained 
from the orthogonal experiments, the texture depth 
increased by 3.42 %, and the surface roughness of 
the bottom surface decreased by 10.08 % under 
the optimal parameter combination, achieving a 
significant optimization of surface roughness while 
obtaining a larger depth. Experimental validation of 
the established prediction model using the optimal 
parameter combination showed that the predicted 
values of depth and surface roughness had errors of 
1.86 % and 7.60 %, respectively, compared to the 
experimental measurements, and the model was 
accurate enough to achieve accurate prediction of the 
surface texture properties of POM.
4  ACKNOWLEDGEMENTS
Financial support for this work was provided by 
the National Natural Science Foundation of China 
Youth Project (Grant no. 51905170) and the Natural 
Science Foundation of Hunan Province (Grant no. 
2020JJ4334).
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