*Corr. Author’s Address: Faculty of Mechanical Engineering, Lublin University of Technology, Poland, i.zagorski@pollub.pl 355
Strojniški vestnik - Journal of Mechanical Engineering 70(2024)7-8, 355-368 Received for review: 2023-11-28
© 2024 The Authors. CC BY 4.0 Int. Licensee: SV-JME Received revised form: 2024-05-07
DOI:10.5545/sv-jme.2023.885 Original Scientific Paper Accepted for publication: 2024-07-03
Surface Roughness Evaluation of AZ31B Magnesium Alloy After 
Rough Milling Using Tools with Different Geometries
Zagórski, I.
Ireneusz Zagórski
*
Faculty of Mechanical Engineering, Lublin University of Technology, Poland
This paper presents the experimental results of a study investigating the impact of machining parameters on 3D surface roughness after 
rough, dry milling. The following 3D roughness parameters were analysed: Sa (arithmetic mean height), Sq (root mean square height), Sz 
(maximum height), Sku (kurtosis), Ssk (skewness), Sp (maximum peak height), and Sv (maximum pit height). Roughness measurements were 
made on the end face of the specimens. Additionally, 3D surface topography maps and Abbot-Firestone material ratio curves were 
generated. Carbide end mills with variable rake and helix angles were used in the study. Experiments were conducted on AZ31B magnesium 
alloy specimens using a contact-type profilometer. The machining process was conducted using the parameters of so-called high-speed 
machining. Three variable technological parameters were analysed: cutting speed v
c
, feed per tooth f
z
, and axial depth of cut a
p
. The results 
showed that the surface roughness of the rough-milled specimens depended to a great extent on the tool geometry and applied machining 
parameters. Feed per tooth was found to have the greatest impact on surface roughness parameters. Lower values of the analysed 
surface roughness parameters (and therefore higher surface quality) were obtained (in most cases) for the tools with a 
rake angle γ of 5° and a helix angle λ
s
 of 50°. The results provided both theoretical and practical knowledge about the achievable 
surface roughness after rough milling using tools with different tool blade geometry. It was shown that rough milling is an effective and 
efficient type of machining for the AZ31B alloy. 
Keywords: rough milling, 3D surface roughness, Abbott-Firestone curve, rake angle, helix angle, magnesium alloy
Highlights
• Rough milling of magnesium alloy AZ31B is an effective and efficient type of machining. 
• Machined surface roughness depends to a large extent on the geometry of a machining tool.
• The change of selected technological parameters (in particular feed per tooth) significantly influences the surface roughness 
parameters.
• Texture and shape of machining marks are typical of rough milling (heterogeneous structure). 
• Abbott-Firestone curves have a proportional or a degressive-progressive shape.
0  INTRODUCTION
Among modern construction materials, one can 
distinguish a group of promising yet insufficiently 
studied light alloys [1], including aluminium and 
magnesium alloys. Magnesium alloys are construction 
materials characterized by low density yet quite high 
strength. Everyday devices and elements made of 
AZ91D/HP or AZ31B alloy are widely used in the 
automotive, aircraft, medical, and sports industries. 
Machinery and equipment components made of these 
alloys must meet stringent quality requirements, 
especially in terms of surface roughness [2]. Regarding 
surface roughness parameters, the best-explored 
and most widely studied is the two-dimensional 
(2D) surface roughness parameter Ra (arithmetical 
mean deviation) [3]. Nevertheless, analyses based 
on only one roughness parameter seem far from 
being exhaustive; therefore, other surface roughness 
parameters must be taken into consideration [4]. In 
addition to the widely studied 2D parameters, 3D 
surface roughness parameters can also be investigated 
in combination with surface topography maps [5] and 
[6]. 
Surface roughness is the main machinability 
indicator of its quality in rough and finish machining 
[7] and [8], as well as in other new methods and types 
of machining, including precision machining [9]. 
Studies have also been conducted on the 
machinability of different grades of magnesium alloys 
(e.g., AM60) using carbide tools with different types 
of tool coatings, e.g. made of TiN [10], where the 
surface roughness was estimated to be approx. Ra ≈ 
0.3 μm. A study conducted with TiAlN-coated end 
mills [11] investigated a substantially greater number 
of surface roughness parameters such as Rv, Rp, Rt, 
Ra, Rku, Rsk, RSm, as well as Sv, Sp, St, Sa, Ssk, and 
Sku on the lateral and the end face of the specimen. 
The machinability of AZ61 was investigated, and the 
obtained Ra parameter was in the range of 0.1 μm 
to 0.4 μm [12]. Another study [13] examined the Sa 
parameter in machining AZ61 alloy for the reversed 
and direct feed. The obtained Sa values ranged from 
approximately 0.2 μm to 0.8 μm. 

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)7-8, 355-368
356 Zagórski, I.
The most widely used alloy in practice and 
investigated in research studies is AZ91D. In a study 
[14] on high-speed machining, the obtained Ra value 
was from about 0.06 μm to 0.13 μm. Another study 
[15] showed that the Ra parameter increased with 
v
c
 and f
z
, ranging from 0.4 μm to 1.2 μm. Other 
studies [16] and [17] investigated the optimization of 
machining parameters (v
c
, f
z
, a
p
) and the obtained Ra 
value ranged from approximately 0.07 μm to 0.21 
μm. A more comprehensive analysis and, thus, the 
results for a greater number of roughness parameters 
were reported in [11], which considered both 2D and 
3D surface roughness parameters, as well as surface 
topography maps. Although the AZ91D alloy is 
usually processed under dry machining conditions, 
studies have been conducted with the use of MQL or 
cryogenic conditions [18] and [19]. 
Another widely used albeit less popular alloy 
(probably due to its cost) is AZ31B. Components of 
this alloy grade are often produced from solid material; 
therefore, the finish allowance is quite substantial, 
posing the need for machining and machining 
process analysis [20]. For example, in a study [21], 
the variation in v
c
 and f
z
 yielded a Ra value below 0.2 
μm. The machining process was conducted by dry 
cutting with an air coolant. A study [22] compared wet 
and cryogenic machining. The obtained Ra parameter 
was lower than 1 μm, with approx. 20 % lower Ra for 
cryogenic conditions. 
Alloys with alloying elements such as zirconium, 
rare earths, zinc (e.g., ZE41) or lithium are only used 
in exceptional cases. These alloys are very expensive 
and are only used to produce aircraft components, 
if not primarily for the aerospace industry. For 
example, a study [23] investigating the milling of 
ZE41 magnesium alloy showed that Ra ranged from 
approximately 1.4 μm to 4.1 μm, and that increase in 
v
c
 and f
z 
caused the Ra parameter to increase too. A 
similar study [24] demonstrated that the Ra parameter 
value could range from approx. 0.3 μm to 0.7 μm (for 
variable f
z
 and a
p
). 
An interesting group of materials includes alloys 
containing Ca used in medical applications [25] to 
[29]. The Mg-Ca0.8 alloy was investigated, among 
others, in [25] to [27], where the obtained Ra value 
ranged from 0.2 μm to 0.8 µm. For this case, however, 
the machining process was conducted using a tool 
with a polycrystalline diamond (PCD) edge. In a study 
[28], depending on the machining strategy employed, 
the Ra values ranged from 0.9 μm to 1.4 μm (normal 
milling) and 0.09 μm to 0.8 μm (inverse milling). The 
machining of a similar alloy, Mg-Ca1.0, yielded the 
Ra parameter ranging from 0.10 μm to 0.16 μm [29]. 
In addition to using 2D and 3D parameters, 
surface quality can also be evaluated using the 
Abbott-Firestone curve [11] and parameters describing 
it. As a result, a different approach to surface quality 
and texture evaluation can be adopted, particularly in 
terms of assessing the quality of a surface machined by 
different methods [30]. Depending on the roughness 
profile shape, one can distinguish the following curve 
patterns: progressive, proportional, degressive, and 
combined (e.g., degressive-progressive, progressive-
degressive, proportional-degressive, etc.). Based on 
the curve shape and selected parameters (Rpk, Rvk, 
Rk), one can make inferences about the tribological 
resistance of a material [31]. For example, a 
progressive shape means that the surface is more 
wear-resistant (rounded peaks of the surface) [32]. 
As mentioned, previous studies investigating 
the problem of surface quality usually focus on one 
2D surface roughness parameter, i.e. Ra. However, 
this approach is far from being exhaustive due to 
the many 2D and 3D roughness parameters that can 
be used to describe machined surface roughness. 
Moreover, it seems interesting to raise the issue 
related to the roughness of the machined surface 
obtained in the milling process for both practical and 
cognitive reasons. The quality and roughness of the 
final surface obtained are very important during the 
production of various types of machine and device 
elements. The aim is to ensure that the milling process 
allows for achieving high-quality surfaces without 
the need, for example, for finish grinding. In turn, 
the Abbott-Firestone curve analysis complements 
and extends research related to the quality of the 
machined surface. This analysis may be important due 
to the maintenance characteristics of the surface. A 
progressive shape (the surface is more wear-resistant) 
is considered favourable for the A-F curves. The 
primary objective of this study is to gain insight into a 
machining process for AZ31B alloy and to determine 
the effect of machining parameters and tool geometry 
on 3D Surface roughness. In the study, 3D surface 
roughness parameters such as Sa, Sz, Sq, Sku, Ssk, Sp, 
and Sv are investigated. In addition, examples of both 
Abbott-Firestone material ratio curves and 3D surface 
topography maps are given.  
The novelty of the study lies in a comprehensive 
approach to examining the influence of tool geometry, 
in particular the rake and helix angle, on 3D roughness 
parameters in dry milling of magnesium alloys. This 
study provides new information on key aspects of the 
cutting process, offering practical tips for selecting 
the machining parameters for increased machining 
efficiency. The presented research is an extension of 

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)7-8, 355-368
357 Surface Roughness Evaluation of AZ31B Magnesium Alloy After Rough Milling Using Tools with Different Geometries
the analyses conducted so far, including the analysis 
of 2D roughness parameters and selected surface 
roughness profiles. The novelty of the research is the 
use of tools with different toll edge geometry, which 
is the result of many scientific studies conducted at 
the author’s research centre. These studies consider 
not only technical aspects such as roughness values 
and tool geometry but also process effectiveness. 
Also, taking into account the analysis of the impact 
of various technological parameters, such as cutting 
speed, feed per tooth, or axial depth of cut, on 
roughness parameters allows the identification of 
selected machining conditions, the best due to the 
quality of the machining and increasing the efficiency 
of the process.
1  METHODS AND EXPERIMENTAL
The study was performed on specimens of AZ31B 
alloy. This grade of material is suitable for forming 
processes. The main application of the AZ31B alloy is 
the aviation industry; this alloy can also be used in the 
automotive and electronics industries. In the aviation 
industry, the AZ31B alloy is manufactured, for 
example, cockpit and door panels, aircraft hubs and 
levers, brackets and gearbox housings. Experiments 
Fig. 1.  Research schematic: a) measuring equipment (e.g. end mill, milling machine and profilometer), and  
b) milling visualization with a 3D roughness measurement model for the end face on the workpiece

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)7-8, 355-368
358 Zagórski, I.
were conducted under dry, rough milling conditions. 
Variable technological parameters of milling and 
different tool geometry were used. The experiments 
were conducted using carbide end mills (the number 
of blades z = 3) with variable rake angle ( γ
 
= 5°, γ
 
= 
30°) and helix angle ( λ
s 
= 20°, λ
s 
= 50°). Milling was 
conducted as a high-speed machining process. The 
tools had a diameter of 16 mm. Milling was conducted 
on the vertical machining centre A VIA VMC800HS. 
The employed research structure is shown in Fig. 1. 
The end mills with variable geometry were 
mounted in heat-shrinking tool holders. The holder-
tool system was balanced at G2.5 with a balancing 
machine CIMAT RT 610 in compliance with the ISO 
21940–11:2016 standard [33].
The following technological parameters of 
milling were applied, as shown in Table 1.
Table 1.  Milling technological parameters
End mill v
c
 [m/min] f
z
 [mm/tooth] a
p
 [µm] a
e
 [mm]
γ = 5°  
γ = 30°
λ
s
 = 20° 
λ
s
 = 50°
400
0.15 6.0
14
1200
800
0.05
6.0
0.30
800 0.15
0.5
6.0
The following 3D roughness parameters were 
analysed: Sa, Sq, Sz, Sku, Ssk, Sp, and Sv. Additionally, 
selected 3D surface topography maps and Abbot-
Firestone curves were generated. All surface 
roughness measurements were made on the end face 
of the specimen using a contact-type profilometer, 
Hommel Etamic T8000 RC120-400. The 3D 
roughness parameters were measured in the direction 
perpendicular to the machining marks. The scanning 
area was 4.8 mm × 4.8 mm with 100 scanning steps.
2  RESULTS AND DISCUSSION
This section presents the experimental results of 3D 
surface roughness evaluation for AZ31B magnesium 
alloy. The results are described in two separate 
subsections, depending on the tool blade geometry. 
The effects of variable rake angle γ (Subsection 
2.1) and variable helix angle λ
s
 (Subsection 2.2) 
are discussed separately. Moreover, the impact of 
variations in the technological parameters of milling, 
i.e., v
c
, f
z
, a
p
, is analysed. In addition to that, selected 
3D surface topography maps (Subsection 2.3) of the 
machined surface roughness and Abbott-Firestone (A-
F) curves (Subsection 2.4) are presented.
2.1  Various Rake Angle γ Versus Roughness Parameters
Fig. 2 shows the results of 3D surface roughness 
parameters for variable cutting speeds and different 
rake angles. 
It can be observed that the type of tool, and 
particularly its rake angle, has a considerably 
significant effect on surface roughness. Smaller values 
of the 3D surface roughness parameters Sa, Sq, Sz, Sv, 
and Sp were obtained when the tool with a smaller 
rake angle ( γ of 5°) was used. This observation is 
quite interesting because references often recommend 
that light alloys, including magnesium alloys, should 
be machined using tools with the sharpest possible 
blade geometry. The term “tools with the sharpest 
possible blade geometry” should mean the values of 
the rake angle, clearance angle, and helix angle should 
be as large as possible. Common recommendations 
regarding the values angles of the end mill are rake 
angle in the range of 15° to 25°, clearance angle in 
the range of 12° to 20°, and helix angle in the range of 
30° to 40°. For this case, however, the use of the tool 
with a smaller rake angle made it possible to obtain a 
surface of higher quality and, thus, with lower values 
of the analysed 3D surface roughness parameters.
An analysis of the Ssk parameter reveals that for 
lower cutting speeds this parameter takes negative 
values, which may indicate a higher frequency of deep 
valleys (defined as a plateau and considered optimal). 
The symmetric distribution of the profile is reflected 
by zero skewness (this value is similar to that obtained 
with v
c
 1200 and γ 30°). Moreover, the Rsk/Ssk 
parameter can be used to, e.g., enhance lubrication 
and support technological process analysis because 
surfaces with positive skewness show good adhesion 
resistance. As for Sku, lower values of kurtosis were 
obtained with higher cutting speed and sharper tool 
geometry. It is generally assumed that high values of 
Rku indicate the presence of sharp peaks and grooves 
(above 3), while the values below 3 indicate that the 
peaks and grooves are rounded. A study [32] showed 
that without lubrication, the surfaces with positive Rsk 
and high Rku should result in a lower static friction 
coefficient compared to the surfaces with Rsk = 0 and 
Rku = 3. 
Fig. 3 shows the results of 3D surface roughness 
parameters for variable feed per tooth and different 
rake angles. 
The parameters Sa, Sq, Sp, and Sv depend on 
variations in feed per tooth and rake angle. An increase 
in feed per tooth considerably impacts the analysed 
surface roughness parameters. The use of higher rake 
angle results in increased values of Sa, Sq, Sp, and Sv, 

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)7-8, 355-368
359 Surface Roughness Evaluation of AZ31B Magnesium Alloy After Rough Milling Using Tools with Different Geometries
Fig. 2.  Cutting speed and rake angle versus 3D surface roughness 
parameters: a) Sa, Sq, b) Sp, Sv, c) Sz, d) Ssk, e) Sku 
Fig. 3.  Feed per tooth and rake angle versus 3D surface 
roughness parameters: a) Sa, Sq, b) Sp, Sv, c) Sz, d) Ssk, e) Sku

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)7-8, 355-368
360 Zagórski, I.
this increase being approx. by 4 to 5 times. It can be 
observed that a further increase in feed per tooth and 
rake angle also has an impact on the other analysed 3D 
surface roughness parameters. For Sz, this increase is 
substantial (approx. by 4 to 5 times) due to a higher 
cut layer section. The Sz values are higher for the tool 
with a higher rake angle (sharper geometry). 
An analysis of the parameters Ssk and Sku reveals 
two trends. The Ssk parameter takes negative values 
(a higher frequency of valleys and hence of a surface 
defined as a plateau, considered optimal). However, 
for the milling process conducted with f
z
 0.05 and γ 
30°, the skewness is about zero, and the profile has a 
symmetric distribution. The Sku parameter takes only 
positive values. Similarly to the case with variable v
c
, 
lower kurtosis values were obtained for a tool with 
sharper geometry ( γ 30°).
Fig. 4 shows the results of 3D surface roughness 
parameters for variable axial depth of cut and different 
rake angles. 
An opposite trend can be observed when the 
milling process is conducted with a variable axial 
depth of cut. Specifically, the 3D surface roughness 
parameters (Sa, Sq, Sp, Sv, Sz) are lower (for higher 
a
p
), particularly for the tool with a rake angle of 30°. 
An increase in the rake angle results in an increase 
in the values of these parameters. This situation is 
analogous to that observed for variable cutting speed 
and feed per tooth. 
An analysis of the relationship between variations 
in axial depth of cut and rake angle and the Ssk and 
Sku parameters demonstrates that all obtained values 
are positive (even though for γ 5° and a
p
 6.0 mm, 
the Ssk value is close to zero, amounting to 0.02; a 
symmetric distribution of the profile is reflected by 
zero skewness). The positive skewness value may 
indicate a higher frequency of sharp peaks. The 
positive high values of kurtosis indicate the presence 
of sharp peaks and grooves (above 3). For a
p
 equal 
to 0.5 mm, the results obtained with both tools are 
similar, while for ap of 6.0 mm, the Sku value is lower 
for the γ 30° tool.
2.2  Various Helix Angle λs Versus Roughness Parameters
Fig. 5 shows the results of 3D surface roughness 
parameters for variable cutting speeds and different 
helix angles. 
Considering the tools with various helix angles, 
the analysed 3D surface roughness parameters (Sa, 
Sq, Sp, Sv, Sz) are higher for a helix angle of 20°. An 
increase in cutting speed leads to an increase in the 
surface roughness parameters Sa and Sq. The trend for 
Fig. 4.   Axial depth of cut and rake angle versus 3D surface 
roughness parameters: a) Sa, Sq, b) Sp, Sv, c) Sz, d) Ssk, e) Sku

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)7-8, 355-368
361 Surface Roughness Evaluation of AZ31B Magnesium Alloy After Rough Milling Using Tools with Different Geometries
the parameters Sa and Sv is similar to that observed 
for Sa and Sq; however, when the milling process is 
conducted with a helix angle of 20°, an opposite trend 
is observed for the Sp parameter. 
It can be observed that for the tool with a helix 
angle of 20°, the Ssk parameter is positive, and its 
value increases with an increase in cutting speed, 
whereas for the tool with a helix angle of 50° the Ssk 
parameter takes a negative value which decreases with 
an increase in cutting speed. The Sku parameter takes 
only positive values. The kurtosis values below 3 
indicate that the peaks and grooves are rounded.
Fig. 6 shows the results of 3D surface roughness 
parameters for variable feed per tooth and different 
helix angles. 
An analysis of the effect of feed per tooth on the 
parameters Sa, Sq, Sp, and Sv reveals that the surface 
roughness parameters increase with feed per tooth. 
An increase in helix angle causes a decrease in Sa 
when the feed per tooth is 0.05 mm/tooth. An opposite 
situation can be observed when the feed per tooth 
is equal to 0.30 mm/tooth. The value of Sv and Sp 
decreases with increasing helix angle; however, when 
the feed per tooth is 0.30 mm/tooth, an opposite trend 
can be observed as the Sv parameter value increases.
As for Sz, this surface roughness parameter 
increases with an increase in feed per tooth. 
The skewness parameter takes positive values 
when the feed per tooth is equal to 0.05 mm/tooth. 
The skewness value is close to zero when the feed 
per tooth is 0.30 mm/tooth, and the helix angle is 20°. 
The Ssk parameter value is negative when the feed per 
tooth is 0.30 mm/tooth and the helix angle is 50°. A 
consistent trend can be observed for kurtosis, where 
an increase in helix angle causes an increase in Sku. 
The use of a higher feed per tooth causes an increase 
in Sku for a helix angle of 20° and a decrease in Sku 
when the helix angle is equal to 50°.
Fig. 7 shows the results of 3D surface roughness 
parameters for variable axial depth of cut and different 
helix angles. 
With the axial depth of the cut varying, two 
opposite trends can be observed. For the end mill 
with a helix angle of 20°, the use of a higher a
p
 causes 
an increase in Sa and Sq. The same situation can be 
observed for λ
s
 20° and Sv. A different observation 
can be made when the helix angle is equal to 50°. 
Both Sa, Sq and Sv, Sp decrease with increasing axial 
depth of cut. A similar situation can be observed 
for a helix angle of 20° and the Sp parameter. For a 
lower axial depth of cut, the Sz value is higher when 
the milling process is conducted using the tools with 
Fig. 5.  Cutting speed and helix angle versus 3D surface roughness 
parameters: a) Sa, Sq, b) Sp, Sv, c) Sz, d) Ssk, e) Sku

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)7-8, 355-368
362 Zagórski, I.
Fig. 6.  Feed per tooth and helix angle versus 3D surface 
roughness parameters: a) Sa, Sq, b) Sp, Sv, c) Sz, d) Ssk, e) Sku
Fig. 7.  Axial depth of cut and helix angle versus 3D surface 
roughness parameters:  a) Sa, Sq, b) Sp, Sv, c) Sz, d) Ssk, e) Sku

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)7-8, 355-368
363 Surface Roughness Evaluation of AZ31B Magnesium Alloy After Rough Milling Using Tools with Different Geometries
a helix angle of 50°. For a
p
 equal to 6.0 mm, the Sz 
values are similar. 
It can be observed that, in most cases, the Ssk 
parameter takes negative values (the higher frequency 
of deep valleys is defined as a plateau and is 
considered optimal). However, for the milling process 
conducted with a helix angle of 20° and a
p
 of 0.5 mm, 
this parameter takes a positive value. Moreover, the 
symmetric distribution of the profile is reflected by 
zero skewness (the value is similar to that observed 
for a
p
 0.5 and λ 50°). The Sku parameter takes only 
positive values. These values decrease with increasing 
the axial depth of cut (for a helix angle of 20°) and 
remain on a similar level for a helix angle of 50°.
2.3 Surface Topography Maps
For illustrative purposes and better insight, Fig. 8 
presents examples of 3D surface topography maps 
obtained from the rough milling process for AZ31B 
magnesium alloy conducted with a cutting speed 
of 400 m/min, using all analysed cutting tools (with 
various rake and helix angles). 
     
     
Fig. 8.  Surface topography maps: a) γ 5°, b) γ 30°, and c) λ
s
 20°, d) λ
s
 50° (v
c
 400 m/min)
An analysis of the isometric images demonstrates 
that all 3D surfaces have a typical, heterogeneous 
structure. There are high peaks and deep valleys, and 
the machining marks are characteristic of the applied 
machining method. The surfaces machined with the 
use of all tools do not differ from each other to any 
significant extent; however, a greater ratio of valleys 
can be observed on the surface obtained with the end 
mill described by a rake angle γ
 
of 30°. It can be seen 
that an increase in the rake angle causes an increase in 
the height of the peaks and the depth of the valley on 
the machined surface. Surfaces obtained from milling 
using tools with variable helix angles have a similar 
heterogeneous structure and texture. Similarly to the 
case of various rake angles, relatively high peaks and 
deep valleys can be observed on the specimen surface.
2.4 Abbott-Firestone Curves 
This section presents all obtained Abbott-Firestone 
curves. The curves were shown for the rake angles of 
5° (Fig. 9) and 30° (Fig. 10) and for the helix angles 
of 20° (Fig. 11) and 50° (Fig. 12). These curves were 

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)7-8, 355-368
364 Zagórski, I.
obtained for the milling process conducted with 
variable cutting speed, feed per tooth and axial depth 
of cut. 
From the point of view of surface maintenance, 
the material ratio curves provide important 
information. The Abbott-Firestone curve can assume 
different shapes, the most favourable in terms of 
functional properties of the surface being the curves 
with a progressive or a progressive-degressive shape. 
Based on the shape of a material ratio curve, one can 
     ˝ 
      
Fig. 9.  Abbott-Firestone curves obtained from milling a tool with a rake angle γ 5°:  
a) v
c
 400 m/min, b) v
c
 1200 m/min, c) f
z
 0.05 mm/tooth, d) f
z
 0.30 mm/tooth, e) a
p
 0.5 mm, and f) a
p
 6.0 mm
      
      
Fig. 10.  Abbott-Firestone curves obtained from milling a tool with a rake angle γ 30°:  
a) v
c
 400 m/min, b) v
c
 1200 m/min, c) f
z
 0.05 mm/tooth, d) f
z
 0.30 mm/tooth, e) a
p
 0.5 mm, and f) a
p
 6.0 mm

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)7-8, 355-368
365 Surface Roughness Evaluation of AZ31B Magnesium Alloy After Rough Milling Using Tools with Different Geometries
draw inferences about, for example, the tribological 
wear resistance of a given surface. A progressive 
shape curve indicates that the analysed surface has 
rounded peaks and is more resistant to wear than the 
surface described by a degressive shape curve [30].
Fig. 9 shows the Abbott-Firestone curves for 
the tool with a rake angle of 5°. The curves have a 
degressive-progressive shape (mixed). A curve with 
the most uniform distribution of material share is 
obtained in the milling process conducted with a 
      
      
Fig. 11.  Abbott-Firestone curves obtained from milling a tool with a helix angle λ 20°:  
a) v
c
 400 m/min, b) v
c
 1200 m/min, c) f
z
 0.05 mm/tooth, d) f
z
 0.30 mm/tooth, e) a
p
 0.5 mm, and f) ap 6.0 mm
      
      
Fig. 12.  Abbott-Firestone curves obtained from milling a tool with a helix angle λ 50°:  
a) v
c
 400 m/min, b) v
c
 1200 m/min, c) f
z
 0.05 mm/tooth, d) f
z
 0.30 mm/tooth, e) a
p
 0.5 mm, and f) a
p
 6.0 mm

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)7-8, 355-368
366 Zagórski, I.
cutting speed v
c
 1200 m/min and a feed per tooth f
z
 
0.30 mm/tooth. It can, therefore, be concluded that the 
A-F curves have the desirable characteristics (owing 
to the rounded peaks and thus higher resistance to 
wear and friction) only in the so-called lower part of 
the material share curve.
Fig. 10 shows the Abbott-Firestone curves for 
the tool with a rake angle of 30°. The curves have 
approximately either a proportional or a degressive-
progressive shape. Fig. 11 shows the Abbott-Firestone 
curves for the tool with a helix angle of 20°. In 
simple terms, the A-F curves have approximately 
a degressive-progressive shape. Fig. 12 shows the 
Abbott-Firestone curves for the tool with a helix 
angle of 50°. In simple terms, the A-F curves have 
approximately either a proportional or a degressive-
progressive shape.
3  DISCUSSION
The results of this study investigating the rough 
milling of AZ31B magnesium alloy can be compared 
to some extent to the results reported in [34], which 
studied the roughness of AZ91D/HP alloy after rough 
milling using the end mill with various rake angles, 
and in [7] and [8], which described preliminary 
research on finish milling of AZ91D/HP and AZ31B 
magnesium alloys using the end mill with various 
helix angles. 
A comparison of the results obtained from 
rough milling of magnesium alloys revealed that 
[34] an increase in cutting speed caused a decrease in 
roughness parameters while an increase in feed per 
tooth caused an increase in roughness parameters (Ra, 
Rz, RSm) on the lateral face of the workpiece. Similar 
relationships were also observed for roughness 
parameters (Ra, Rq, RzDIN, Rt, Ry, RSm) on the end 
face of the specimen. Lower roughness parameters 
were observed for the tool with a rake angle γ of 
5°. For all tested technological parameters, the Ra 
parameter value was below 1.0 µm on the lateral face 
and approx. 1.5 µm on the end face of the specimen. 
A direct comparison of parameters, e.g. Ra and Sa, is 
quite troublesome; however, in the case of analysis, 
among others, for the Ra parameter, a similar tendency 
can be observed as for the Sa parameter. Smaller 
values of Sa were obtained when the tool with a 
smaller rake angle was used. This is due to the mutual 
relationship of these parameters; the Ra parameter 
was measured on the so-called sampling length (total 
measuring length lt = 4.8 mm, sampling length lr = 
0.8 mm), while the Sa parameter was created from 
multiple repetitions of the measurement for the entire 
observed surface (scanning area 4.8 mm × 4.8 mm 
with 100 scanning steps).
Considerably lower values of the surface 
roughness parameters were reported in [7] and [8]. 
This resulted from the finish milling process being 
conducted under different conditions, i.e., with 
significantly smaller undeformed chip thickness or 
cross-section. It was found that to increase the stability 
of machining and to obtain a high surface finish, a 
more suitable tool for finishing milling was that with a 
helix angle of 20°. Like in the rough milling process, 
an increase in cutting speed led to a decreased surface 
roughness, while roughness parameters (Ra, Rz, RSm, 
Rku, Rsk) increased with feed per tooth. For variable 
v
c
 and f
z
, the Ra parameter value was below approx. 
1.0 µm on the lateral face and approx. 3.0 µm to 
5.5 µm on the end face of the specimen, depending 
on the type of tool. A statistical analysis of Ra and 
Rz confirmed the inequality of the mean and median 
values for varying v
c
. The statistical analysis results 
also showed that for all cases, the variations in f
z
 had 
an impact on the Ra parameter. Similar relationships 
were observed for other surface roughness parameters, 
i.e., Rq, Rt, Rv and Rp. 
A comparison of the Abbott-Firestone curves 
demonstrates that for most studied cases of machining, 
e.g., in [9], the curves have a degressive-progressive 
shape. 
This research on rough milling of AZ31B focuses 
on 3D surface roughness parameters. For example, 
the Sa parameter value for the tool with γ 5° is below 
1.0 µm for variable cutting speed, which indicates the 
high quality of the machined surface. The machining 
marks on the surface are characteristic of the milling 
process, with sharp peaks or deep valleys (typical 
heterogeneous structures). Although, for most cases, 
the Abbott-Firestone curves have a degressive-
progressive shape that is typical of machining 
processes, some of these curves are distorted, taking 
on a proportional shape. 
4  CONCLUSIONS
The results of this study lead to the following 
conclusions: 
• 3D roughness parameters largely depend on the 
machining tool,
• better machining results and, hence lower surface 
roughness values were obtained when the milling 
process was conducted using the tools with a rake 
angle of 5° and a helix angle of 50°,
• regarding the tool with γ 5° and the Sa parameter, 
it was observed that with variables v
c
 and a
p,
 the 

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)7-8, 355-368
367 Surface Roughness Evaluation of AZ31B Magnesium Alloy After Rough Milling Using Tools with Different Geometries
Sa value was below 1.0 µm while with variable f
z
, 
it was below 2.0 µm,
• for the tool with λ
s
 50°, the Sa value was below 
4.0 µm for variable v
c
, below 1.0 µm for f
z
 0.05 
mm/tooth, below 8.0 µm for f
z
 0.30 mm/tooth, 
and below 6.0 µm for variable a
p
,
• the Sku parameter takes only positive values 
which are predominantly below 3, which may 
prove that the peaks and grooves are rounded,
• an increase in cutting speed did not lead to 
any significant increase in surface roughness 
parameters for different rake angles; however, 
such an increase was observed for different helix 
angles,
• an increase in feed per tooth led to an increase 
in surface roughness parameters for the analysed 
tools, 
• an increase in axial depth of cut did not cause 
any consistent trend in the change in surface 
roughness,
• the obtained 3D surface roughness maps show 
machining marks that are characteristic of rough 
milling, reflecting a typical heterogeneous 
structure with sharp peaks or deep valleys,
• the Abbott-Firestone curves are the easiest 
to interpret for the tool with γ 5° due to their 
degressive-progressive shape; the other curves 
have a distorted shape and hence are more 
difficult to interpret; nevertheless, their shape can 
approximately be described as proportional or 
degressive-progressive.
To provide more insight and further contribution 
to the development of mechanical engineering, 
future research should focus on investigating the 
parameters Rvk, Rpk, and Rk on Abbott-Firestone 
curves. Although the present study concludes, to 
some extent, the body of research on rough milling of 
magnesium alloys, studies can still be made on finish 
and precision milling as the two processes have not 
yet been thoroughly investigated. The present study 
was only conducted for the end face of the specimen. 
Further studies can be conducted for the lateral face 
of the specimen, particularly using tools with variable 
helix angles. In addition, studies can be conducted on 
rough, finish and precision milling of ultra-light alloys 
(both magnesium and aluminium alloys) containing 
lithium.
5  ACKNOWLEDGEMENTS
The project/research was financed with FD-20/IM-
5/138.
6  REFERENCES
[1] Kuczmaszewski, J., Pieśko, P., Zawada-Michałowska, M. 
(2016.) Surface roughness of thin-walled components 
made of aluminium alloy EN AW-2024 following 
different milling strategies. Advances in Science and 
Technology Research Journal, vol. 10, no. 30, p. 150-158, 
DOI:10.12913/22998624/62515.
[2] Pradeep Kumar, M., Venkatesan, R., Manimurugan, M. 
(2022). Optimization of process parameters in turning of 
magnesium AZ91D alloy for better surface finish using genetic 
algorithm. Acta Innovations, vol. 43, p. 54-62, DOI:10.32933/
ActaInnovations.43.5.
[3] Muralidharan, S., Karthikeyan, N., Kumar, A.B., Aatthisugan, I. 
(2017). A study on machinability characteristic in end milling 
of magnesium composite. International Journal of Mechanical 
Engineering and Technology, vol. 8, no. 6, p. 455-462.
[4] Ciecieląg, K. (2022). Study on the machinability of glass, 
carbon and aramid fiber reinforced plastics in drilling and 
secondary drilling operations. Advances in Science and 
Technology Research Journal, vol. 16, no. 2, p. 57-66. 
DOI:10.12913/22998624/146079.
[5] Matuszak, J. (2022). Comparative Analysis of the Effect 
of Machining with Wire and Ceramic Brushes on Selected 
Properties of the Surface Layer of EN AW-7075 Aluminium 
Alloy. Advances in Science and Technology Research Journal, 
vol. 16, no. 2, p. 50-56, DOI:10.12913/22998624/146211.
[6] Grzesik, W. (2015). Effect of the machine parts surface 
topography features on the machine service. Mechanik, vol. 
8-9, p. 587-593, DOI:10.17814/mechanik.2015.8-9.493. (in 
Polish)
[7] Zagórski, I., Szczepaniak, A., Kulisz, M., Korpysa, J. (2022). 
Influence of the tool cutting edge helix angle on the surface 
roughness after finishing milling of magnesium alloys. 
Materials, vol. 15, no. 9, 3184, DOI:10.3390/ma15093184.
[8] Zagórski, I., Kulisz, M., Szczepaniak, A. (2024). Roughness 
parameters with statistical analysis and modelling using 
artificial neural networks after finish milling of magnesium 
alloys with different edge helix angle tools. Strojniški vestnik - 
Journal of Mechanical Engineering, vol. 70, no. 1-2, p. 27-41, 
DOI:10.5545/sv-jme.2023.596.
[9] Korpysa, J., Kuczmaszewski, J., Zagórski, I. (2023). Surface 
quality of AZ91D magnesium alloy after precision milling 
with coated tools. Strojniški vestnik - Journal of Mechanical 
Engineering, vol. 69, no. 11-12, p. 497-508, DOI:10.5545/sv-
jme.2023.651.
[10] Sathyamoorthy, V., Deepan, S., Sathya Prasanth, S.P., Prabhu, 
L. (2017). Optimization of machining parameters for surface 
roughness in end milling of magnesium AM60 alloy. Indian 
Journal of Science and Technology, vol. 10, no. 32, p. 1-7, 
DOI:10.17485/ijst/2017/v10i32/104651.
[11] Zagórski, I., Korpysa, J. (2019). Surface quality in milling 
of AZ91D magnesium alloy. Advances in Science and 
Technology Research Journal, vol. 13, no. 2, p. 119-129, 
DOI:10.12913/22998624/108547.
[12] Alharti, N.H., Bingol, S., Abbas, A.T., Ragab, A.E., El-Danaf, 
E.A., Alharbi, H.F. (2017). Optimizing cutting conditions and 
prediction of surface roughness in face milling of AZ61 using 

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)7-8, 355-368
368 Zagórski, I.
regression analysis and artificial neural network. Advances 
in Materials Science and Engineering, vol. 2017, no. 1, 
7560468, DOI:10.1155/2017/7560468.
[13] Chirita, B., Grigoras, C., Tampu, C., Herghelegiu, E. (2019). 
Analysis of cutting forces and surface quality during face 
milling of a magnesium alloy. IOP Conference Series: 
Materials Science and Engineering, vol. 591, 012006, 
DOI:10.1088/1757-899X/591/1/012006.
[14] Ruslan, M.S., Othman, K., Ghani, J.A., Kassim, M.S., Haron, 
C.H. (2016). Surface roughness of magnesium alloy AZ91D in 
high speed milling. Jurnal Teknologi, vol. 78, no. 6-9, p. 115-
119, DOI:10.11113/jt.v78.9158.
[15] Shi, K., Zhang, D., Ren, J., Yao, C., Huang, X. (2016). Effect of 
cutting parameters on machinability characteristics in milling 
of magnesium alloy with carbide tool. Advances in Mechanical 
Engineering, vol. 8, no. 1, DOI:10.1177/1687814016628392.
[16] Marakini, V., Pai, S., Bhat, U., Singh, D., Achar, B. (2022). 
High speed machining for enhancing the AZ91 magnesium 
alloy surface characteristics: Influence and optimisation of 
machining parameters. Defence Science Journal, vol. 72, no. 
1, p. 105-113, DOI:10.14429/dsj.72.17049.
[17] Marakini, V., Pai, S., Bhat, A., Bangera, S. (2022). Surface 
integrity optimization in high speed milling of AZ91 magnesium 
alloy using TOPSIS considering vibration signals. Materials 
Today: Proceedings, vol. 52, p. 802-809, DOI:10.1016/j.
matpr.2021.10.154.
[18] Jouini, N., Ruslan, M.S.M., Ghani, J.A., Haron, C.H.C. (2023). 
Sustainable high-speed milling of magnesium alloy AZ91D in 
dry and cryogenic conditions. Sustainability, vol. 15, no. 4, 
3760, DOI:10.3390/su15043760.
[19] Kanan, M., Zahoor, S., Habib, M.S., Ehsan, S., Rehman, M., 
Shahzaib, M., Khan, S.A., Ali, H., Abusaq, Z., Hamdan, A. 
(2023). Analysis of carbon footprints and surface quality in 
green cutting environments for the milling of AZ31 magnesium 
alloy. Sustainability, vol. 15, no. 7, 6301, DOI:10.3390/
su15076301.
[20] Gobivel, K., Vijay Sekar, K.S. (2022). Influence of cutting 
parameters on end milling of magnesium alloy AZ31B. 
Materials Today: Proceedings, vol. 62, p. 933-937, 
DOI:10.1016/j.matpr.2022.04.075.
[21] Kim, J.D., Lee, K.B. (2010). Surface Roughness Evaluation 
in dry-cutting of magnesium alloy by air pressure coolant. 
Engineering, vol. 2, no. 10, p. 788-792, DOI:10.4236/
eng.2010.210101.
[22] Chhetri, S., Tariq, M., Mohapatra, S., Sumi, V., Zhimomi, 
A., Davis, R., Singh, A. (2020). Surface characteristics 
enhancement of biocompatible Mg alloy AZ31B by cryogenic 
milling. IOP Conference Series: Materials Science and 
Engineering, vol. 1004, 012011, DOI:10.1088/1757-
899X/1004/1/012011.
[23] Sivam, S.P., Bhat, M.D., Natarajan, S., Chauhan, N. (2018). 
Analysis of residual stresses, thermal stresses, cutting 
forces and other output responses of face milling operation 
on ZE41 magnesium alloy. International Journal of Modern 
Manufacturing Technologies, vol. 10, no. 1, p. 92-101.
[24] Kumar, R., Katyal, P., Kumar, K. (2023). Effect of end milling 
process parameters and corrosion behaviour of ZE41A 
magnesium alloy using Taguchi based GRA. Biointerface 
Research in Applied Chemistry, vol. 13, no. 3, 214, 
DOI:10.33263/briac133.214.
[25] Guo, Y.B., Salahshoor, M. (2010). Process mechanics and 
surface integrity by high-speed dry milling of biodegradable 
magnesium-calcium implant alloys. CIRP Annals - 
Manufacturing Technology, vol. 59, no. 1, p. 151-154, 
DOI:10.1016/j.cirp.2010.03.051.
[26] Salahshoor, M., Guo, Y.B. (2011). Surface integrity of 
magnesium-calcium implants processed by synergistic dry 
cutting-finish burnishing. Procedia Engineering, vol. 19, p. 
288-293, DOI:10.1016/j.proeng.2011.11.114.
[27] Salahshoor, M., Guo, Y.B. (2011). Cutting mechanics in high 
speed dry machining of biomedical magnesium-calcium alloy 
using internal state variable plasticity model. International 
Journal of Machine Tools & Manufacture, vol. 51, no. 7-8, p. 
579-590, DOI:10.1016/j.ijmachtools.2011.04.004.
[28] Qiao, Y., Wang, S., Guo, P., Yang, X., Wang, Y. (2018). 
Experimental research on surface roughness of milling medical 
magnesium alloy. IOP Conference Series: Materials Science 
and Engineering, vol. 397, 012114, DOI:10.1088/1757-
899X/397/1/012114.
[29] Desai, S., Malvade, N., Pawade, R., Warhatkar, H. (2017). 
Effect of high speed dry machining on surface integrity 
and biodegradability of Mg-Ca1.0 biodegradable alloy. 
Materials Today: Proceedings, vol. 4, no. 6, p. 6817-6727, 
DOI:10.1016/j.matpr.2017.06.447.
[30] Skoczylas, A., Kłonica, M. (2023). Selected properties of the 
surface layer of C45 steel samples after slide burnishing. 
Materials, vol. 16, no. 19, 6513, DOI:10.3390/ma16196513.
[31] Pawlus, P., Reizer, R., Wieczorowski, M. (2021). Functional 
importance of surface texture parameters. Materials, vol. 14, 
no. 18, 5326, DOI:10.3390/ma14185326.
[32] Sedlaček, M., Gregorčič, P., Podgornik, B. (2017). Use of the 
roughness parameters Ssk and Sku to control friction - a 
method for designing surface texturing. Tribology Transactions, 
vol. 60, no. 2, p. 260-266, DOI:10.1080/10402004.2016.1159
358.
[33] ISO 21940-11:2016. Mechanical Vibration-Rotor Balancing-
Part 11: Procedures and Tolerances for Rotors with Rigid 
Behavior. International Organization for Standardization. 
Geneva
[34] Gziut, O., Kuczmaszewski, J., Zagórski, I. (2015). Surface 
quality assessment following high performance cutting of 
AZ91HP magnesium alloy. Management and Production 
Engineering Review, vol. 6, no. 1, p. 4-9, DOI:10.1515/mper-
2015-0001.