*Corr. Author’s Address: University of Technology, Mechanical Engineering Faculty, Department of Production Engineering,  
Nadbystrzycka 36, 20-618 Lublin, Poland, i.zagorski@pollub.pl 
27
Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 27-41 Received for review: 2023-04-05
© 2024 The Authors. CC BY 4.0 Int. Licensee: SV-JME Received revised form: 2023-07-03
DOI:10.5545/sv-jme.2023.596 Original Scientific Paper Accepted for publication: 2023-10-05
Roughness Parameters with Statistical Analysis and Modelling 
Using Artificial Neural Networks After Finish Milling  
of Magnesium Alloys with Different Edge Helix Angle Tools
Zagórski, I. – Kulisz, M. – Szczepaniak, A.
Ireneusz Zagórski
1,*
 – Monika Kulisz
2
 – Anna Szczepaniak
1
1 
Lublin University of Technology, Mechanical Engineering Faculty, Poland 
2 
Lublin University of Technology, Management Faculty, Poland 
The paper presents the results of a study investigating the roughness parameters Rq, Rt, Rv, and Rp of finished-milled magnesium alloys 
AZ91D and AZ31B. Carbide end mills with varying edge helix angles were used in the study. Statistical analysis was additionally performed 
for selected machining conditions. In addition, modelling of selected roughness parameters on the end face for the AZ91D alloy was carried 
out using artificial neural networks. Results have shown that the tool with λ
s
 = 20° is more suitable for the finish milling of magnesium alloys 
because its use leads to a significant reduction in surface roughness parameters with increased cutting speed. Increased feed per tooth leads 
to increased surface roughness parameters. Both radial and axial depth of cut has an insignificant effect on surface roughness parameters. 
It has been proven that finish milling is an effective finishing treatment for magnesium alloys. In addition, it was shown that artificial neural 
networks are a good tool for the prediction of selected surface roughness parameters after finishing milling of the magnesium alloy AZ91D.
Keywords: magnesium alloys, finish milling, roughness, surface quality, statistical analysis, artificial neural networks
Highlights
• Finish milling of magnesium alloys AZ31B and AZ91D is an effective kind of machining method.
• The surface roughness (Rq, Rt, Rv, and Rp) depends on the geometry of the different edge helix angles.
• The tool with λ
s
 = 20° is more suitable for the finish milling of magnesium alloys.
• The change of cutting speed vc and feed per tooth fz has a significant influence on the surface roughness parameters during 
finish milling.
• Both the radial and axial depths of cut (ae and ap) have an insignificant effect on surface roughness parameters.
• Artificial neural networks are a good tool for the prediction of selected surface roughness parameters after finishing milling of 
the magnesium alloy AZ91D.
0  INTRODUCTION
The machinability of a material is described by 
machinability indices, one of which is surface quality. 
Geometric structure is defined as the general surface 
condition, and it is the end result of the technological 
process for a given workpiece. The geometric 
structure consists of all surface texture irregularities 
that are formed due to material wear and machining. 
The evaluation of the condition of this structure 
includes considering shape deviations, waviness, and 
surface roughness. 
To compare and verify surface roughness 
requirements for constructional materials after 
machining, studies use parameters describing surface 
conditions in quantitative terms. These include 
two-dimensional (2D) and 3D surface roughness 
parameters, where 2D measurements are made on the 
profile, i.e., in the cross-section of a given workpiece, 
and 3D measurements, known as stereometric, are 
made on the surface. 
The fundamental and most widely analysed 
surface roughness parameter is Ra; however, surface 
roughness evaluation that is based on this parameter 
only is far from being exhaustive. The Ra parameter 
is widely used in industry even though it does not 
provide data about many significant roughness profile 
features. Therefore, additional parameters must 
be considered, such as Rq, Rt, Rv, and Rp. The Rq 
parameter is usually considered together with Ra, with 
the value of Rq being greater than the value of Ra (by 
approx. 25 % for random profiles). This relationship 
for random profiles can be expressed as Rq ≈ 1.25 Ra 
[1]. 
Another common parameter used for surface 
quality evaluation is the maximum height of the 
profile, Rz. Given the fact that single profile peaks 
and valleys are partly taken into account, this 
parameter should primarily be analysed for bearing 
or sliding surfaces and measurement areas [1] and 
[2]. The Rz parameter is often analysed together with 
another surface roughness parameter, Rt. These two 
parameters should also be analysed in combination 
with other parameters such as Rp (maximum profile 
peak height) and Rv (maximum profile valley depth). 
The Rt parameter (total height of profile) may affect 

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 27-41
28 Zagórski, I. – Kulisz, M. – Szczepaniak, A.
the so-called functional properties of a given surface 
(e.g., fatigue strength, wear and tear, lubrication 
etc.) [3]. This parameter is the vertical distance 
between the maximum profile peak height and the 
maximum profile valley depth along the evaluation 
length between (it belongs to the group of so-called 
amplitude parameters). 
The Rp parameter provides information about, 
e.g., profile shape. Moreover (by analysing the Rp 
parameter), it is possible to assess the surface in terms 
of abrasion resistance. A surface with poor abrasion 
resistance is characterized by high values of Rp 
compared to Rv. Depending on the values of Rp and 
Rz and their ratio, it is possible to obtain data about 
profile shape and, thus the abrasion resistance of 
the analysed surface. If the Rp/Rz ratio considerably 
exceeds a value of 0.5, this means that the profile has 
sharp peaks and the surface is less abrasion-resistant. 
The use of the above parameters is recommended for 
evaluating sliding surfaces, bearings, and pre-coated 
surfaces, as well as for analysing close fits in terms of 
shrink behaviour [1] and [3].
Measurements and research of surface roughness 
parameters are important due to such surface features 
as friction and wear, lubrication, assembly tolerances, 
contact deformations, load capacity, contact stresses 
and other surface features related to the physical or 
functional properties of a given surface.
Previous studies on the machinability of materials 
by milling have predominantly investigated the surface 
roughness parameter Ra. A comparison of machining 
methods and evaluated roughness parameters used in 
previous studies is given in Table 1.
Table 1.  Comparison of machining methods and roughness parameters under evaluation in milling of magnesium alloys
Machining method Roughness parameters Material / Alloy grade Year Reference
milling Ra, Rq, Rz, RzDIN, Rt, Ry, RSm AZ91D/HP 2016 [4]
milling Ra Mg-SiC/B4C 2017 [5]
high-speed dry face milling Ra Mg-Ca0.8 2010 [6]
dry milling and low plasticity burnishing Ra Mg-Ca0.8 2011 [7]
milling Ra Mg-Ca0.8 2018 [8]
milling Ra Mg-Ca1.0 2017 [9]
dry end milling Ra AM60 2017 [10]
dry milling and low plasticity burnishing Mg-Ca0.8 2011 [11]
milling Ra, Rt, Rv, Rp Rku, Rsk, RSm, Sa, Sv, Sp, St, Ssk, Sku AZ91D 2019 [12]
dry face milling Ra ZE41 2018 [13]
milling Ra, Sa, RSm, Ssk, Sku AZ91D 2021 [14]
milling Ra AZ61 2017 [15]
face milling (DRY , MQL) Sa AZ61 2019 [16]
high speed milling Ra AZ91D 2016 [17]
dry milling by air pressure coolant Ra AZ31B 2010 [18]
milling Ra AZ91D 2016 [19]
precision milling Ra, Rv, Rp, Rt, Rvk, Rk, Rpk AZ91D 2023 [20]
Summing up, surface roughness analysis is 
particularly important in terms of the quality of 
finished components of machines and devices. 
Light alloys, including magnesium and aluminium 
alloys [21] and [22], occupy a special place among 
construction materials. Surface quality and roughness 
are even more important when it comes to finishing 
treatments and operations. Therefore, it seems that 
the finish milling of light alloys (aluminium and 
magnesium) is significant not only from the practical 
and implementation-related points of view but also 
due to knowledge-related reasons, as there is a lack of 
comprehensive studies devoted to this problem. 
1  METHODS
The objective of this study was to evaluate the surface 
roughness of two magnesium alloys, AZ91D and 
AZ31, after milling depending on the value of the 
technological parameters and tools with variable helix 
angle. The employed research scheme is shown in Fig. 
1. Milling was conducted on the vertical machining 
centre AVIA VMC800HS with Heidenhain iTNC 
530 control and maximum spindle speed of 24000  
[rev/min]. In the study, we used two carbide 3-edge 
end mills with a diameter of 16 mm and a variable 
helix angle λ
s 
( λ
s
 = 20°, λ
s
 = 50°). Using the ISG 2200 

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 27-41
29 Roughness Parameters with Statistical Analysis and Modelling Using ANN After Finish Milling of Magnesium Alloys with Different Edge Helix Angle Tools
shrink-fit machine from H. Diebold GmbH & CO 
(Jungingen, Germany), the end mills were mounted 
in the CELSIO HSK-A63 ϕ16 × 95 tool holder from 
SCHUNK (Lauffen am Neckar, Germany). According 
to the ISO 21940–11:2016 standard [23], the tool 
with the tool holder was balanced to G2.5 (residual 
unbalance was 0.25 g mm) with a CIMAT RT 610 
balancing machine (Bydgoszcz, Poland).
The milling process was conducted using the 
following ranges of technological parameters: 
cutting speed v
c
 = 400 m/min to 1200 m/min, feed 
per tooth f
z
 = 0.05 mm/tooth to 0.3 mm/tooth, axial 
depth of cut a
p
 = 0.1 mm to 0.5 mm, radial depth of 
cut a
e
 = 0.5 mm to 3.5 mm. The following surface 
roughness parameters were analysed: Rq, Rt, Rv, 
and Rp. Surface roughness measurements were 
made on both lateral and end faces with the use of a 
contact-type roughness tester, HOMMEL TESTER 
T1000, from ITA-K. Pollak, M. Wieczorowski 
Sp. J. (Poznań, Poland). The measurement 
parameters were as follows: total measuring 
length lt = 4.8 mm, sampling length lr = 0.8 mm, 
a) 
b) 
c) 
Fig. 1.  Research scheme: a) the test set-up, b) the measurement equipment (end mill, milling machine and 2D profilographometer),  
and c) milling visualization with the roughness measurement model with end face and lateral face on the workpiece surfaces

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 27-41
30 Zagórski, I. – Kulisz, M. – Szczepaniak, A.
scanning speed v
t
 = 0.5 mm/s and measuring 
range/resolution M = ±320 µm (range) / 0.04 µm 
(resolution). Every measurement was repeated five 
times per each surface.
Data from surface roughness measurements were 
subjected to statistical verification. The assumed 
level of significance was α = 0.05. There exist 
several criteria that must be taken into account when 
selecting a statistical test. In this study, output data 
were treated as independent quantitative variables. As 
shown in the scheme, results of the Shapiro-Wilk test 
for checking the normality of distribution were used 
to decide whether further tests had to performed. If 
the normal distribution was not confirmed, the non-
parametric Mann-Whitney U test was performed. 
If the zero hypothesis saying that “the distributions 
are not different from the normal distribution in 
a statistically significant way” was accepted, the 
significance of differences had to be assessed by one 
of two parametric tests: Student’s t-test or Cochran’s 
Q test. The test type was selected by assessing the 
equality of variances, which was made based on the 
results of Levene’s test and the Brown and Forsythe 
test. It should be noted that the selected test type and 
the end result depended on the p-value. All statistical 
tests were conducted using Statistica 13 [24] and [25].
Next, the modelling of selected roughness 
parameters (Rq and Rt) on the face of the magnesium 
alloy AZ91D after finishing milling was carried out 
with variable helix angle λ
s
 ( λ
s
 = 20°, λ
s
 = 50°) using 
Matlab software. The input parameters for network 
learning were machining parameters such as cutting 
speed v
c
 = 400 m/min to 1200 m/min, feed per tooth 
f
z
 = 0.05 mm/tooth to 0.3 mm/tooth and axial depth of 
cut a
p
 = 0.1 mm to 0.5 mm. At the output from network 
learning, the appropriate roughness parameter (Rq, Rt) 
was obtained for the specified tool ( λ
s
 = 20°, λ
s
 = 50°).
A shallow neural network with one hidden layer 
was used for modelling. The learning algorithm 
Levenberg-Marquardt was used. The number of 
neurons was selected experimentally in the range 
of 5 to 10. The dataset was split in a proportion of  
80 % : 20 % (for training and validation data, 
respectively) putting aside the test set due to the 
small amount of data. Network quality was assessed 
based on the value of the correlation coefficient R, 
Mean Squared Error (MSE) and root mean square 
error (RMSE). The correlation coefficient R that was 
calculated in accordance with the Eq. (1):
 Ryy
covyy
y
y






,
,
*
*
*
,

 (1)
Fig. 2.  Statistical test selection scheme [20]

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 27-41
31 Roughness Parameters with Statistical Analysis and Modelling Using ANN After Finish Milling of Magnesium Alloys with Different Edge Helix Angle Tools
where σ
y′
 is the standard deviation of values of the 
analysed roughness parameter obtained as a result of 
experimental tests, σ
y*
 standard deviation of values 
obtained as a result of the model predicting the value 
of the analysed roughness parameter. R is a real 
number in the interval between 0 and 1.
In addition, the value of the MSE, calculated 
according to Eq. (2), was taken into account: 
 MSE
n
y y
n
n
i i




1
1
2

, (2)
as well as RMSE, calculated according to the Eq. (3):
 RMSE
n
yy
n
n
i i




1
1
2

, (3)
where y
i
 is value of the analysed roughness parameter 
obtained as a result of experimental tests and y
i

 is 
values obtained as a result of the model predicting the 
value of the analysed roughness parameter.
2  EXPERIMENTAL RESULTS AND DISCUSSIONS
This section of the paper presents experimental results 
of surface roughness evaluation for two magnesium 
alloys: AZ91D and AZ31, obtained with the use of 
tools with varying helix angles ( λ
s
 = 20°, λ
s
 = 50°). 
The surface roughness of AZ31 was evaluated for the 
extreme values of the technological parameters.
Fig. 3 shows the relationship between cutting 
speed v
c
 and surface roughness parameters. It can be 
a)           b) 
c)           d) 
e)           f) 
Fig. 3.  Cutting speed versus surface roughness parameters: a) Rq of AZ91D, b) Rq of AZ31 c) Rt of AZ91D, d) Rt of AZ31,  
e) Rv, Rp of AZ91D, f) Rv, Rp of AZ31; f
z
 = 0.15 mm/tooth, lateral face: a
e
 = 2 mm, a
p
 = 8 mm, end face: a
e
 = 14 mm, a
p
 = 0.3 mm

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 27-41
32 Zagórski, I. – Kulisz, M. – Szczepaniak, A.
observed that the milling process for AZ91D alloy 
conducted with the cutting speed v
c
 ranging from 600 
m/min to 1200 m/min results in a clear decrease in the 
values of Rq and Rt with increasing the cutting speed. 
The surface roughness parameters only increased on 
the lateral face after milling with the λ
s
 = 50° tool 
and increasing the cutting speed value from v
c
 = 800 
m/min to 1000 m/min. It should be stressed that 
the surface roughness parameters are lower on the 
lateral face. The lowest values of these parameters 
were obtained with λ
s
 = 50° at v
c
 = 1200 m/min 
(Rq = 0.29 μm, Rt = 2.02 μm). The lowest values of 
the parameters were obtained with λ
s
 = 50° on the end 
face for the milling process conducted with v
c
 = 600 
m/min (Rq = 5.54 μm, Rt = 18.04 μm). The values of 
Rv and Rp on the lateral face are similar for all tested 
cutting speeds and range from 0.89 μm to 3.44 μm. 
On the end face the parameters Rv and Rp clearly 
decreased with increasing the cutting speed and their 
values range 3.29 μm to 9.61 μm.
An increase in cutting speed leads to decreased 
values of the surface roughness parameters Rq, Rt, 
Rv and Rp for both AZ91D and AZ31. The greatest 
differences between these surface parameters can be 
observed on the end face for the λ
s
 = 50° tool. The 
parameter Rq value decreased by 3.14 μm and that of 
Rt by 13.87 μm. Regarding the parameters Rv and Rp, 
increasing the cutting speed from 400 m/min to 1200 
m/min had the greatest impact on these parameter 
a)           b) 
c)           d) 
e)           f) 
Fig. 4.  Feed per tooth f
z
 versus surface roughness parameters: a) Rq of AZ91D, b) Rq of AZ31, c) Rt of AZ91D, d) Rt of AZ31,  
e) Rv, Rp of AZ91D, f) Rv, Rp of AZ31; v
c
 = 800 m/min, lateral face: a
e
 = 2 mm, a
p
 = 8 mm, end face: a
e
 = 14 mm, a
p
 = 0.3 mm

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 27-41
33 Roughness Parameters with Statistical Analysis and Modelling Using ANN After Finish Milling of Magnesium Alloys with Different Edge Helix Angle Tools
values on the end face for the λ
s
 = 50° tool, the value 
of Rv decreased by 6.57 µm and that of Rp by 7.3 µm.
Comparing, for example, the machinability of 
both magnesium alloys for the highest cutting speed 
value, it can be seen that for the Rq parameter, a lower 
value roughness was obtained on the end face for the 
AZ31B alloy (Rq = 1.45 μm), while for the AZ91D 
alloy (Rq = 1.67 μm). 
Fig. 4 shows the relationship between feed per 
tooth f
z
 and surface roughness parameters. Regardless 
of the tool used, increased feed per tooth has no 
significant effect on the surface roughness parameters 
on the lateral face of magnesium alloy AZ91D, and 
the values of these parameters range as follows: Rq 
0.32 µm to 0.72 µm, Rt 1.95 µm to 4.28 µm, Rv 0.96 
µm to 1.94 µm, Rp 0.99 µm to 2.45 µm. However, the 
roughness parameters show a sudden increase on the 
end face with increasing the feed per tooth value from 
f
z
 = 0.05 mm/tooth to f
z
 = 0.1 mm/tooth. In the range 
f
z 
 = 0.1 mm/tooth to –0.3 mm/tooth, the feed per tooth 
increases. The highest values of the surface roughness 
parameters were observed for f
z
 = 0.3 mm/tooth. The 
highest values of Rq = 3.5 μm and Rt = 15.91 μm are 
obtained on the end face for λ
s
 = 50° at f
z
 = 0.3 mm/
tooth. Moreover, for the feed per tooth range f
z
 = 0.1 
mm/tooth to 0.25 mm/tooth ( λ
s
 = 50, end face), the 
values of Rp are higher than those of Rv, which means 
that the surface has poor abrasion resistance [1].
Regarding magnesium alloy AZ31, increased 
feed per tooth results in a slight increase in the 
values of Rq and Rt. The values of Rq and Rt range: 
Rq 0.17 μm to 0.65 μm and Rt 1.25 μm to 3.77 μm. 
For λ
s
 = 20°, the values of the parameters Rq and Rt 
are higher on the end face, both at v
c
 = 400 m/min 
(Rq = 1.08 μm, Rt = 5.18 μm) and at v
c
 = 1200 m/
min (Rq = 1.99 μm, Rt = 8.96 μm). Increasing the feed 
per tooth value from 0.05 mm/tooth to 0.3 mm/tooth 
also causes an increase in the values of Rv and Rp. 
The highest values are obtained on the end face with 
the λ
s
 = 20° tool, both at f
z
 = 0.05 mm/tooth (Rv = 2.41 
μm, Rp = 2.76 μm) and at f
z
 = 0.3 mm/tooth (Rv = 3.58 
μm, Rp = 5.21 μm).
Comparing both magnesium alloys on the 
example of the results for the Rq parameter, it can be 
seen that at f
z
 = 0.3 mm/tooth (similarly to the cutting 
speed analysis) a lower value of the Rq parameter 
was recorded on the end face for the AZ31B alloy 
(Rq = 1.99 μm), than for AZ91D alloy (Rq = 2.17 μm).
Fig. 5 illustrates the relationship between axial 
depth of cut and surface roughness parameters. For 
alloy AZ91D, no significant changes in the parameters 
Rq, Rt, Rv, Rp are observed in the entire tested 
axial depth of cut range. The values of the surface 
roughness parameters are similar and range as follows: 
for λ
s
 = 20°: Rq (1.8 μm to 2.13 μm), Rt (8.43 μm to 
10.99 μm), Rv (3.97 μm to 4.66 μm), Rp (4.47 μm to 
6.53 μm), and for λ
s
 = 50°: Rq (1.69 μm to 3.36 μm), 
Rt (8.56 μm to 12.9 μm) Rv (3.96 μm to 5.57 μm), 
Rp (4.71 μm to 7.33 μm). However, it should be noted 
that the differences between the values of the above 
parameters depending on the tool can particularly 
be observed for a
p
 = 0.2 mm to 0.5 mm. The results 
demonstrate that the above axial depth of cut range 
leads to higher values of Rp compared to Rv.
The increased axial depth of cut has no significant 
effect on the surface roughness parameters of both 
AZ91D and AZ31. It is noteworthy that the roughness 
parameters obtained with the λ
s
 = 50° tool are smaller 
than the values of these parameters obtained after 
milling with the λ
s
 = 20° tool (AZ31). 
An inverse relationship can be observed by 
analysing the change in the axial depth of cut on 
the end face, the value of the Rq parameter in the 
conditions when a
p
 = 0.5 mm, for the AZ31B alloy 
is higher (Rq = 1.99 μm), than for the AZ91D alloy 
(Rq = 1.81 μm).
Fig. 6 shows the relationship between the radial 
depth of cut a
e
 and surface roughness parameters. The 
results demonstrate that the radial depth of cut has no 
significant effect on the roughness parameters Rq, Rt, 
Rv, Rp of both AZ91D ( λ
s
 = 20°) and AZ31 ( λ
s
 = 20° 
and λ
s
 = 50°). The obtained values are similar and 
range as follows: Rq (0.53 μm to 0.73 μm), Rt (2.4 
μm to 4.24 μm), Rv (1.08 μm to 2.07 μm), Rp (1.53 
μm to 2.17 μm). In contrast, for the tool with λ
s
 = 50° 
one can observe a sharp increase in the values of Rq 
(by 2.56 μm) and Rt (by 13.39 μm), Rv (by 6.59 μm), 
Rp (by 6.8 μm) when the radial depth of cut value is 
changed from a
e
 = 1.5 mm to 2.5 mm.
Similarly, analysing the radial depth of cut on 
the end face, it can be seen that for a
e
 = 3.5 mm, the 
machining results are better (lower value of the Rq 
parameter) for the AZ91D alloy (Rq = 0.56 μm), while 
for the AZ31B alloy (Rq = 0.70 μm). 
Thus, comparing the results obtained using 
carbide cutters for roughing and the analysis of the 
surface of the end face of the workpiece AZ91HP/D 
[4] and [12], the following conclusions can be drawn:
• when employing a carbide cutter coated with 
titanium aluminium nitride (TiAlN), higher 
values of the parameters Rq, Rp, and Rv were 
recorded, specifically: 
1. for the variable parameter v
c
, the parameters Rv 
and Rp range between 6.8 μm to 8.32 μm, while 
the parameter Rt spans from 14.24 μm to 17.72 
μm; 

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 27-41
34 Zagórski, I. – Kulisz, M. – Szczepaniak, A.
approximately 3 μm, with the Rt parameter 
spanning from 10 μm to 15 μm, 
3. concerning the variable parameter a
p
, the Rq 
parameter consistently approximates 3 μm, while 
the value of Rt does not exceed approximately 15 
μm.
Therefore, these values are much higher than 
those observed in the present experiment. This is 
due to the larger cross-sections of the cutting layer 
obtained during roughing. However, as the literature 
lacks a broader analysis of surface roughness 
parameters, especially after finishing machining while 
roughing mainly analyses the basic surface roughness 
parameters (usually mainly Ra), it seems advisable to 
extend the state of knowledge in this area.
2. considering the variable parameter f
z
, the 
parameters Rv and Rp lie within the spectrum 
of 1.94 μm to 15.84 μm, with the parameter Rt 
standing at 4 μm to 31.04 μm; 
3. for the variable parameter a
p
, the values of Rv and 
Rp present remarkable similarity, recorded within 
the interval of 5.26 μm to 7.78 μm, and for Rt the 
values range from 12.02 μm to 24.82 μm;
• in instances of machining with cutters of diverse 
blade geometry (different rake angles γ), the 
parameters Rq and Rt were investigated: 
1. for the variable parameter v
c
, the parameter Rq 
did not surpass 4 μm, with Rt recorded within the 
range of 10 μm to 15 μm, 
2. in relation to the variable parameter f
z
, the Rq 
parameter ascends to a maximum value of 
a)             b) 
c)             d) 
e)             f) 
Fig. 5.  Axial depth of cut ap versus surface roughness parameters: a) Rq of AZ91D, b) Rq of AZ31 c) Rt of AZ91D, d) Rt of AZ31,  
e) Rv, Rp of AZ91D f) Rv, Rp of AZ31; v
c
 = 800 m/min, f
z
 = 0.15 mm/tooth, a
e
 = 14 mm

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35 Roughness Parameters with Statistical Analysis and Modelling Using ANN After Finish Milling of Magnesium Alloys with Different Edge Helix Angle Tools
3  STATISTICAL ANALYSIS
The experiments were followed by statistical analysis. 
Significance tests were performed to determine if the 
following technological parameters: cutting speed v
c
, 
feed per tooth f
z
, axial depth of cut a
p
 and radial depth 
of cut a
e
 affected the mean values of surface roughness 
parameters. The statistical analysis made it possible to 
determine whether the differences were statistically 
significant for the assumed level of confidence. 
Hypotheses were tested taking account of the 
extreme values of the technological parameters, i.e., 
cutting speed v
c
 = 400 m/min, and 1200 m/min, feed 
per tooth f
z
 = 0.05 mm/tooth, and, 0.3 mm/tooth, axial 
depth of cut a
p
 = 0.1 mm, and 0.5 mm, radial depth of 
cut a
e
 = 0.5 mm, and 3.5 mm. In this paper, we report 
the final test results, i.e. the median and mean values 
from the tests. 
Fig. 7 shows an example of results obtained by 
the Student’s t-test for the zero hypothesis of normal 
distribution and the equality of variance hypothesis.
Tables 2 and 3 give the results of the Mann-
Whitney U test, Student’s t-test, and Cochran’s Q 
test. The results make it possible to statistically assess 
the significance of differences between the mean and 
median values obtained for the compared groups.  
The statistical analysis results demonstrate that, 
irrespective of the magnesium alloy grade, for the 
tool with λ
s
 = 20° increased cutting speed has, in most 
cases, the greatest impact on the mean and median 
values of the surface roughness parameters. 
Feed per tooth also has a significant impact on 
the surface roughness parameters for the tool with 
a)             b) 
c)             d) 
e)             f) 
Fig. 6.  Radial depth of cut ae versus surface roughness parameters: a) Rq of AZ91D, b) Rq of AZ31, c) Rt of AZ91D, d) Rt of AZ31,  
e) Rv, Rp of AZ91D, f) Rv, Rp of AZ31; v
c
 = 800 m/min, f
z
 = 0.15 mm/tooth, a
p
 = 8 mm

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 27-41
36 Zagórski, I. – Kulisz, M. – Szczepaniak, A.
Fig. 7.  Student’s t-test results
Table 2.  Results of Mann-Whitney U test, Student’s t-test, 
Cochran’s Q test for the roughness parameters of magnesium alloy 
AZ91D after milling
λ
s
 = 20° λ
s
 = 50°
Lateral face End face Lateral face End face 
p-value p-value p-value p-value
v
c
 [m/min] 400 vs. 1200
Rq 0.0008 0.01354 0.09172 0.00124
Rt 0.00794* 0.00384 0.18904 0.00794*
Rv 0.15079* 0.06089 0.22089 0.00794*
Rp 0.01587* 0.00009 0.21357 0.00794*
f
s
 [mm/tooth] 0.05 vs. 0.3
Rq 0.22222* 0.00466 0.03175* 0.00004
Rt 1* 0.00902 0.06349* 0.00028
Rv 0.84127* 0.0007 0.06349* 0.00794*
Rp 0.78555 0.03114 0.03175* 0.00422
a
e
 [mm]  
0.5 vs. 3.5
 a
e
 [mm]  
0.1 vs. 0.5
a
e
 [mm]  
0.5 vs. 3.5
a
e
 [mm]  
0.1 vs. 0.5
Rq 0.17048 0.95209 0.00149 0.0001
Rt 0.35526 0.69048* 0.00103 0.00536
Rv 0.43513 0.40148 0.00282 0.150794*
Rp 0.27617 0.97658 0.01587* 0.03102
* Mann-Whitney U test for checking the equality of the medians
Table 3.  Results of Mann-Whitney U test, Student’s t-test, 
Cochran’s Q test for the roughness parameters of magnesium alloy 
AZ31 after milling
λ
s
 = 20° λ
s
 = 50°
Lateral face End face Lateral face End face 
p-value p-value p-value p-value
v
c
 [m/min] 400 vs. 1200
Rq 0.00794* 0.00093 0.00362 0.00088
Rt 0.000004 0.00287 0.159 0.00443
Rv 0.00018 0.00126 0.35012 0.00435
Rp 0.00003 0.02907 0.19048* 0.00507
f
s
 [mm/tooth] 0.05 vs. 0.3
Rq 0.00813 0.00022 0.01372 0.13088
Rt 0.01587* 0.00953 0.07128 0.51158
Rv 0.05556* 0.00052 0.15926 0.966295
Rp 0.00794* 0.054187 0.02645 0.278767
a
e
 [mm]  
0.5 vs. 3.5
 a
e
 [mm]  
0.1 vs. 0.5
a
e
 [mm]  
0.5 vs. 3.5
a
e
 [mm]  
0.1 vs. 0.5
Rq 0.3862 0.77097 0.76164 0.06349*
Rt 0.84127* 0.42063* 0.61483 0.12539
Rv 0.38109 0.55077 0.94354 0.195110
Rp 0.12928 0.92479 0.42396 0.087671
* Mann-Whitney U test for checking the equality of the medians

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 27-41
37 Roughness Parameters with Statistical Analysis and Modelling Using ANN After Finish Milling of Magnesium Alloys with Different Edge Helix Angle Tools
λ
s
 = 20°. The only exception are the results obtained 
for the lateral end of AZ91D, as they show that 
changing the feed per tooth value from 0.05 mm/
tooth to 0.3 mm/tooth does not result in statistically 
significant differences between the values of the 
surface roughness parameters. The opposite can be 
observed for the tool with λ
s
 = 50°, where the p-values 
are either smaller than the assumed confidence level 
or verge on the statistically significant limit. 
For alloy AZ91D, the differences in the mean and 
median values of the surface roughness parameters 
are affected by the radial and axial depth of cut, and 
depend on the tool.
For alloy AZ31, irrespective of the tool used, 
the radial and axial depth of cut has no effect on the 
mean and median values of the surface roughness 
parameters Rq, Rt, Rv, Rp (on the statistical level).
4  MODELLING OF ARTIFICIAL NEURAL NETWORKS
Artificial neural networks were trained for the 
magnesium alloy AZ91D in order to build four models 
showing the relationship between the technological 
parameters (cutting speed v
c
, feed per tooth f
z
 and axial 
depth of cut a
p
) and the predicted roughness on the 
face surface of the Rq and Rt parameters, respectively, 
after machining with the tool with variable helix angle 
(λ
s
 = 20°, λ
s
 = 50°). Approximately 100 networks were 
trained for each model.
The quality of the obtained models was assessed 
on the correlation coefficient R, value of MSE and 
RMSE. Table 4 presents four different models obtained 
from an artificial neuron network (ANN.)
The best modelling results for the Rq and Rt 
parameters after machining with a tool with a helix 
Table 4.  Network parameters
Model No. Roughness parameter Helix angle λ
s
MSE RMSE R training data set R validation data set R all data set
1 Rq
20
0.0022 0.0467 0.99999 0.99029 0.99563
2 Rt 0.1058 0.3252 0.99999 0.9989 0.99358
3 Rv
50
0.0193 0.1391 0.99999 0.96648 0.99263
4 Rp 0.3424 0.5851 0.99999 0.95309 0.98741
a)            b) 
c)            d) 
Fig. 8.  ANN best training performance for a) parameter Rq, λ
s
 = 20°, b) parameter Rt, λ
s
 = 20°,  
c) parameter Rq, λ
s
 = 50°, d) parameter Rt, λ
s
 = 50°

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 27-41
38 Zagórski, I. – Kulisz, M. – Szczepaniak, A.
angle λ
s
 = 20° were obtained for the network with 10 
neurons in the hidden layer. The network for the Rq 
parameter was obtained in five iterations, and for the 
Rt parameter in ten iterations. In the case of the tool 
with the helix angle λ
s
 = 50°, for the Rq parameter, 
it was also a network with 10 neurons (obtained in 
6 iterations), and for the Rt parameter a network 
with eight neurons in the hidden layer (obtained in 
5 iterations). The best validation performance was 
obtained respectively for iteration 5 (for Rq parameter 
when machined with helix angle λ
s
 = 20°), which is 
shown in Fig. 8a, for iteration 6 (for Rt parameter 
when machined with helix angle λ
s
 = 20°); Fig. 8b, 
for iteration 10 (for the Rq parameter when machining 
with a helix angle λ
s
 = 50°); Fig. 8c and for iteration 
5 (for the Rt parameter when machining with a helix 
angle λ
s
 = 50°); Fig. 8d.
ANN regression statistics for individual sets and 
the total set was presented in Fig. 9. Respectively 
for parameter Rq when machining with tool with 
helix angle λ
s
 = 20°; Fig. 9a, for parameter Rt when 
machining with tool with helix angle λ
s
 = 20°; Fig. 9b, 
for parameter Rq when machining with tool with helix 
angle λ
s
 = 50°; Fig. 9c and for parameter Rt when 
machining with tool with helix angle λ
s
 = 50°; Fig. 9d. 
Taking into account the quality of the presented 
models measured by the level of MSE, RMSE and the 
R value (R in each case is a value greater than 0.95), 
a)         b) 
c)          d) 
Fig. 9.  ANN regression statistics for individual sets and the total set: a) parameter Rq, λ
s
 = 20°, b) parameter Rt, λ
s
 = 20°,  
c) parameter Rq, λ
s
 = 50°, c) parameter Rt, λ
s
 = 50°

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 27-41
39 Roughness Parameters with Statistical Analysis and Modelling Using ANN After Finish Milling of Magnesium Alloys with Different Edge Helix Angle Tools
a)           b) 
Fig. 10.  Simulation results of the Rq surface roughness parameter after machining with tool with helix angle λ
s
 = 20°  
a) for the v
c
 and f
z
, and b) for the v
c
 and a
p
a)           b) 
Fig. 11. Simulation results of the Rt surface roughness parameter after machining with tool with helix angle λ
s
 = 20°  
a) for the v
c
 and f
z
, and b) for the v
c
 and a
p
a)          b) 
Fig. 12. Simulation results of the Rq surface roughness parameter after machining with tool with helix angle λ
s
 = 50°  
a) for the v
c
 and f
z
, and b) for the v
c
 and a
p

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 27-41
40 Zagórski, I. – Kulisz, M. – Szczepaniak, A.
it can be concluded that the presented ANN models 
show an acceptable level of error and can be used to 
predict approximate values of roughness parameters.
The simulation results of the appropriate 
roughness parameters Rq / Rt of the AZ91D alloy for 
the appropriate tool with helix angle λ
s
 = 20°, and 
50°, for the assumed range of cutting speed v
c
, feed 
per tooth f
z
 and axial depth of cut a
p
 parameters are 
shown in Figs. 10 to 13. The simulation results for 
each model are presented in two graphs, depending on 
cutting speed v
c
 and feed per tooth f
z
 or cutting speed 
v
c
 and axial depth of cut a
p
. 
5  CONCLUSIONS
The experimental and statistical analysis results of the 
study leads to the following conclusions:
• for the λ
s
 = 20° tool increased cutting speed leads 
to a considerable decrease in surface roughness 
parameters, whereas for the tool with λ
s
 = 50° 
increased cutting speed has no significant effect 
on lateral face surface roughness parameters;
• increased feed per tooth leads to increased 
surface roughness, which was particularly visible 
when the feed per tooth f
z
 = 0.05 mm/tooth was 
changed to f
z
 = 0.1 mm/tooth for AZ91D alloy;
• irrespective of the magnesium alloy grade, for 
the tool with λ
s
 = 20° both axial and radial depth 
of cut has an insignificant effect on surface 
roughness parameters;
• the statistical analysis results show that for the 
tool with λ
s
 = 20° increased cutting speed has, in 
most cases, the greatest effect on the mean and 
median values of the roughness parameters for 
both AZ91D and AZ31;
• the statistical analysis results for the tool with 
λ
s
 = 50° show that the roughness parameters of 
magnesium alloy AZ91D are most affected by 
varying feed per tooth as well as axial and radial 
depth of cut;
• as a result of modelling the Rq and Rt parameters 
after machining with a variable helix angle λ
s
 tool 
( λ
s
 = 20°, λ
s
 = 50°), the best models were obtained 
primarily for the network with 10 neurons in the 
hidden layer, only in the case of the Rt parameter 
with helix angle λ
s
 = 50° the best model had 8 
neurons in the hidden layer;
• networks obtained as a result of modelling 
surface roughness parameters show a satisfactory 
predictive ability, as evidenced by the obtained 
regression values R: Rq
( λs=20°)
 = 0.99563, 
Rt
(λs=20°)
 = 0.99358, Rq
( λs=50°)
 = 0.99263 and 
Rt
(λs=50°)
 = 0.98741;
• as a result of the conducted modelling of neural 
networks, it can be concluded that they are an 
effective tool that can be used to predict surface 
roughness parameters.
6  ACKNOWLEDGEMENTS
The project/research was financed with FD-20/IM-
5/138 and FD-20/IM-5/061.
a)           b) 
Fig. 13.  Simulation results of the Rt surface roughness parameter after machining with tool with helix angle λ
s
 = 50°  
a) for the v
c
 and f
z
, and b) for the v
c
 and a
p

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 27-41
41 Roughness Parameters with Statistical Analysis and Modelling Using ANN After Finish Milling of Magnesium Alloys with Different Edge Helix Angle Tools
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