s13369-023-07642-x

Arabian Journal for Science and Engineering
https://doi.org/10.1007/s13369-023-07642-x
RESEARCH ARTICLE-MECHANICAL ENGINEERING
Optimization of Cutting Parameters and Result Predictions
with Response Surface Methodology, Individual and Ensemble
Machine Learning Algorithms in End Milling of AISI 321
Deniz Demircioglu Diren1
· Neslihan Ozsoy2
· Murat Ozsoy2
· Huseyin Pehlivan2
Received: 25 July 2022 / Accepted: 18 January 2023
© King Fahd University of Petroleum & Minerals 2023
Abstract
Optimizing the parameters in the milling method is important in terms of cost, energy, and time. The forces that arise during
milling cause undesirable results, such as tool wear and energy loss. In this study, cutting parameters were optimized during
the milling of AISI 321 material. Cutting speed (60, 70, 80 m/min), feed per tooth (0.04, 0.05, 0.06 mm/tooth), and depth of
cut (0.25, 0.5, 0.75 mm) were selected as input parameters. Cutting force in the X and Y axes and the surface roughness were
selected as the output parameters. Optimum parameters (60.80 m/min for cutting speed, 0.04 mm/tooth for feed per tooth, and
0.25 mm for depth of cut) were found using response surface methodology. The effect of cutting parameters was calculated
by analysis of variance. The most influential parameters were found, depth of cut as 87.49% for cutting force on the X-axis,
86.48% on the Y -axis, and for surface roughness, the cutting speed with 36.48%. Prediction models are compared to choose
the best model. Individual (Neural network, decision tree, and k-nearest neighbor algorithms) and ensemble methods (vote)
from machine learning and response surface methodology from statistical methods were used for models. The error rates of
the models were compared according to the mean absolute percentage error performance criterion. The lowest MAPE values
were obtained with the vote method 11.163% in the X-axis force, the artificial neural network algorithm with 7.749% in the
Y -axis force, and RSM with 0.93% in the surface roughness.
Keywords Cutting force · Cutting parameters · Surface roughness · Response surface methodology · Ensemble machine
learning · Artificial neural network
Abbreviations
RSM
ANOVA
MAPE
ANN
SVR
DT
K-NN
Fx
Fy
Ra
B
Response surface methodology
Analysis of variance
Mean absolute percentage error
Artificial neural network
Support vector regression
Decision tree
K-nearest neighbor
X-axis force (N)
Y -axis force (N)
Surface roughness (μm)
Vc
fz
Ap
HB
MLP
DF
Adj SS
Adj MS
Cutting speed (m/min)
Feed per tooth (mm/tooth)
Depth of cut (mm)
Brinell hardness
Multilayer perceptron neural network
Degree of freedom
Adjusted sum of squares
Adjusted mean squares
1 Introduction
Murat Ozsoy
ozsoy@sakarya.edu.tr
1
Industrial Engineering Department, Faculty of Engineering,
Sakarya University, Sakarya, Turkey
2
Mechanical Engineering Department, Faculty of Engineering,
Sakarya University, Sakarya, Turkey
Machinability can be defined as the ease with which the
material is machined in terms of specific energy, specific
horsepower, or shear stress. In general, the larger the shear
stress or specific power values, the more difficult the material
is to machine and form, requiring greater forces and lower
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Arabian Journal for Science and Engineering
speeds [1]. One of the criteria used to evaluate machinability
is cutting force. Forces generated during milling operations
are among the critical cost items. High force values during
machining cause power and energy loss [2]. In addition, the
roughness that appears on the surfaces because of high force
values reduces the processing quality [3]. Parameters such as
cutting speed, depth of cut, spindle speed, cutting tool, cooling type, etc., affect machinability [4]. High surface quality
and low force values can be achieved by finding the optimum levels in the machining parameters; for this reason, the
response surface method is frequently used [5].
Experimental, theoretical, and modeling studies using
different values of processing parameters are summarized
below.
AISI 321 steel is stainless steel widely used in several
industries. Therefore, researchers have conducted many studies on the machinability of this material. Siddiquee et al.
studied AISI 321 austenitic stainless-steel material. They
used the Taguchi method for experiment design and found
that parameters that affect the surface roughness had been
speed, cutting fluid, feed, and hole-depth [6]. In a different
study, Vereschaka et al. [7] investigated metal cutting tools
actions on AISI 321 materials. They determined that coating
with thinner nanolayers performed better, particularly at high
speeds.
Pekşen and Kalyon studied the optimization of cutting
parameters during the machining of AISI 430 material on a
lathe. During the study, optimization was conducted using
the surface roughness results [8]. In another study, Ross
et al. studied the performance of coated carbide tools with
cryogenic cooling in machining titanium alloy material with
high strength and corrosion resistance. They investigated the
optimum cutting parameters [9]. Li et al. studied a milling
simulation work about surface quality and compared experimental results. They investigated the effects of parameters
for AISI H13 steel [10]. Zhang et al. investigated optimum
parameters in milling 300 M steel under different lubrication
types. They advised cryogenic minimum quantity lubrication
for low surface roughness and cutting force [11]. Choudhury
et al. conducted experimental research on the end milling
of bamboo composites via the Taguchi method. Spindle
speed, feed, depth of cut, and milling cutter were chosen as
cutting parameters. According to optimization analysis, the
depth of cut had the maximum effect on the force, and the
milling cutter was the dominant parameter on temperature
[12]. Effects of fiber orientations and direction of machining on cutting forces and surface roughness in the milling of
ceramic matrixed carbon fiber reinforced composites were
investigated by Zhang et al. [13]. They reported that the
machining parameters had essential importance. Çakıroğlu
investigated the cutting force, and surface roughness of the
Inconel 718 superalloy in the turning process in different
environmental conditions. He used the Taguchi method to
123
design experiments and then optimized the results by GreyTaguchi Relational analysis [14]. Karabulut et al. studied the
effects of machining variables on the milling force and tool
wear during milling of Al7075 and the open cell SiC foam
metal matrix composite using the Taguchi and the Response
Surface Method. They found that cutting depth was the dominant parameter [15]. In another study, Badiger et al. produced
Al and Ti multilayer coatings on WC tool insert with the
chemical composition of TiN/AlN and examined the machinability of MDN431 alloyed steel. They developed quadratic
mathematical models using regression analysis and artificial
neural network [16].
In addition to previous studies, machine learning techniques for parameter optimization and estimating the results
of experiments have recently become popular. Some of the
studies are summarized below.
Abbas et al. worked on the algorithm using an artificial
neural network (ANN) with the Edgeworth-Pareto method
to optimize the cutting parameter in CNC face milling operations. They aimed to reduce production costs and increase
accuracy by optimizing surface roughness and minimum
unit volume material removal rates [17]. Jurkovic et al. [18]
compared several machine learning methods for predicting
cutting parameters in turning operation. Machine learning
methods used for prediction are support vector regression
(SVR), polynomial regression, and the ANN. As a result,
the SVR performed better than the ANN for cutting force
and surface roughness estimation. In another study [19],
CO2 hydrogenation optimization was performed using the
ANN and the RSM. As a result, it is stated that the ANN
provides satisfactory results in a noisy non-linear process.
In the study by Daniel et al. [20] machining parameters of
hybrid composites in Al5059/SiC/MoS2 milling were estimated. Taguchi S/N ratio analysis, ANN, and Gray relational
analysis were performed. The ANN proved to be the most
successful. Another study focused on predicting tool wear
during the rotation of the Inconel 718. According to the
average absolute percentage error (MAPE) results, the ANN
was the most successful method [21]. Pimenov et al. used
artificial intelligence methods to estimate the surface roughness, considering the main drive power and tool wear. They
ensured the most efficient use of the cutting tool by estimating maximum tool wear, machining time, and cutting power
to create a certain surface roughness [22]. Balasubramanian
et al. analyzed the change of cutting forces applied to the tool
according to the cutting parameters for end milling operation
using a deep neural network. CutPro simulation software
automatically changed and simulated the parameters. As a
result, it was stated that the neural network formed by choosing the optimum parameters was found with an error of less
than one percent of the estimation rates [23]. Correa et al.
aimed to predict surface roughness in high-speed milling
with bayesian networks. These network methods are used
Arabian Journal for Science and Engineering
for estimation. As a result, Bayesian networks were strong
and successful, with 81.2% [24]. The study by Gupta aimed
to predict tool power, surface roughness, and tool wear in
turning operations. Artificial neural networks, support vector regression, and response surface methodology were used
for the prediction model. The three methods were compared
using data from twenty-seven experiments. As a result, it
has been concluded that the artificial neural network and the
support vector regression methods are good compared to the
response surface methodology [25]. In the machining of AISI
1045 steel, parameters such as the feed per tooth, the cutting
speed, the flank wear, the machined length, the sliding distance, the processing time were chosen by Pimenov et al.
[26]. They improved the surface roughness and reduced the
cutting power, thus reducing the machining cost and time by
determining the optimum cutting conditions. Besides, they
conducted a multilayer regression analysis. In the study of
Natarajan et al. [27] the surface roughness of brass C26000
material was estimated. A prediction back propagation ANN
model is designed. The designed model was compared with
the experimental data, and it was concluded that there was no
significant difference, and that ANN was found to be dependable.
As mentioned in the literature survey above, there is
limited numerical, analytical, or experimental research investigating the effect of cutting force and surface roughness
for AISI 321 material on the milling process. Many studies investigating the cutting parameters during the milling of
AISI 321 were found in current literature review However,
none of the previous studies has not done extensive research
on the optimization and prediction of both force and surface roughness. On the other hand, the ensemble application
of DT, K-NN and ANN algorithms, which have not been
used before, has been seen as successful for the results. It is
thought that it will be useful to apply it for future state prediction in similar experiments. Therefore, this article aims
to fill this gap, examine the force, and surface roughness
during milling of AISI 321. One of the primary purposes of
this study is to optimize the cutting parameters in a milling
operation, and the other is the prediction of the experimental
results. This exploratory study investigated how axial forces
and surface quality affect the milling process and optimized
cutting parameters by response surface methodology. While
estimating the experimental results, a new perspective was
presented by looking for an answer to the question, "Do the
ensemble machine learning methods increase the prediction
accuracy of machine learning methods?" which is the main
hypothesis of the study.
The paper is organized as follows: the materials and the
methods used in the study are presented in Sect. 2. The results
and discussions are given in Sect. 3. Prediction of the results
of experiments with machine learning are given in Sect. 4.
Finally, the study is concluded in Sect. 5.
Fig. 1 The architectural structure of the study
2 Material and Methods
The stages of the study consist of the following five steps.
These are:
1. Experimentation: In this study, experiments were conducted for milling AISI material.
2. Determination of effects of parameters and the optimum
parameter levels: The effects of the parameters on the
results were determined by ANOVA and the optimum
levels were found by the RSM.
3. Development and training of models: RSM, ANN, DT,
K-NN, and ensemble machine learning methods were
used to detect the experimental results. The dataset is
divided into 80% training and 20% testing.
4. Evaluation of the results: The method with the most successful prediction level was decided by MAPE between
the measured and predicted values of experiments.
The architectural structure of the study is shown below in
Fig. 1. First, a solid model of the part used in the experimental
study was created. Then, using the solid model, the G-codes
created for performing the experiments on the CNC milling
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Arabian Journal for Science and Engineering
Fig. 2 Technical representation
and CAM model of the
workpiece
Table 1 The chemical content of the workpiece [28]
Element
Cr
Ni
C
Mn
P
S
Si
Ti
N
%
17–19
9–12
0.08
2
0.045
0.03
0.75
0.5–0.7
0.1
machine. Experiments were carried out according to the input
parameters shown in Table 5. F x and F y forces generated during machining have been obtained, and surface roughness
was measured. After this step, the study was divided into
two parts. The effects of parameters on outputs were investigated in the first part using the ANOVA method. Then, RSM
was used to find the optimum parameter and level values. In
the second part, to train machine learning methods, experiments were divided into two datasets as training and testing.
Initially, machine learning methods were applied independently. Then, ensemble methods were used to improve the
prediction performance. RSM, individual machine learning
algorithms, and ensemble machine learning algorithms were
compared to check whether the targeted prediction success
rates were achieved. Appropriate prediction methods were
selected for the parameters.
Table 2 Mechanical properties for the workpiece [28]
2.1 Work Piece Material
Choosing suitable cutting tool material and geometry is vital
for achieving low surface roughness and low axial forces.
Therefore, during the experiments, an aluminum titanium
nitride coated cutting tool with a diameter of 10 mm, 40°
helix angle, 0.5 mm corner radius, 4-flute, 22 mm cutting
depth, 70 mm long, which is suitable for end milling, was
used. The geometry of the cutting tool is given in Fig. 3, and
the cutting tool properties are presented in Table 3.
Three different parameters, such as cutting speed, depth of
cut, and feed per tooth, were chosen at three levels. Selected
parameters and levels are specified in Table 4.
The workpiece material was AISI 321 with approximately
150 × 50 × 8 mm3 . The technical representation and CAM
model of the workpiece are given in Fig. 2. AISI321 stainless
steel is like 304 quality stainless material in terms of its structure. It has excellent resistance to corrosion with a maximum
of 0.7% titanium additive. Welding capability is extremely
high, but machinability is low. It is widely used in the food
and machinery industries, especially in parts operating at
high temperatures (Aircraft exhaust manifolds, blowers, heat
exchangers, et al.). Milling is widely used in the manufacture of parts from this material. Since the machinability of
this material is low, it is cost-effective to examine tool wear
and optimize cutting parameters during milling.
Table 1 shows the chemical, and Table 2 shows the
mechanical properties of the AISI 321 material.
123
Yield
strength
Ultimate tensile
strength
Elongation
Hardness
205 MPa
515 MPa
40%
217 HB
Fig. 3 Cutting tool geometry
2.2 Sample Preparation and Cutting Parameters
2.3 Force and Surface Roughness Measurement
All experimental studies were performed in Hartford brand
four axes CNC vertical machining center. The G codes used
in the end milling process were created using the 2d trajectory
Arabian Journal for Science and Engineering
Table 3 Cutting tool properties
Brand
Kyocera
Description
4QFRM100-220-10-R05-VE
Tool material
Solid carbide
Workpiece material
Stainless steel/Cast iron/Steel
Diameter (D)
10 mm
Number of flutes
4
Cutting length (Lc)
22 mm
Total length (L)
70 mm
Corner radius (r)
0.5 mm
Helix angle (Ha)
40°
Coating
AlTiN
Table 4 Parameters and levels
Fig. 4 Schematic diagram of the test setup
Cutting speed (m/min)
Symbol
Levels
Cutting speed (m/min)
Vc
60
70
Depth of cut (mm)
Ap
0.25
0.5
Feed per tooth (mm/tooth)
fz
0.04
0.05
milling strategy in the PTC Creo Parametric software. There
are twenty-seven experiments in the study. Each sample contains nine experiments. A total of three samples were used
for twenty-seven experiments. Each experiment was repeated
three times. After three repetitions, the mathematical average of the maximum forces obtained in the X and Y axes was
taken. The X axis is parallel to the machining direction, and
the Y axis is perpendicular. The coordinate system used in
the study can be seen in Fig. 2.
The workpiece used in the experiments was fixed to the
3-component Kistler 9257B dynamometer with two screws.
It has a maximum capacity of five KN measurement range
on each axis. Kistler 5010 charge amplifier, data acquisition
interface DT9837B and Spinscope software were used for
data acquisition of cutting force during end milling operations. The schematic view of the experimental setup can be
seen in Fig. 4. The forces in the X and Y axes were examined
during this study. One thousand samples per second were
collected during cutting force measurement. Each experiment was repeated three times. After repeated experiments,
the data were exported to Microsoft Excel software. A data
set was created for each experiment by averaging the data of
three measurements. Maximum values for F x and F y were
determined from the generated datasets.
Also, HOMMEL Tester T 500 Mobile semi-automatic
device was used for surface roughness measurement. Measurements were made from three regions, the beginning,
middle and end of the machined surface, and the average
was taken.
2.4 Machine Learning and Statistical Methods
Machine learning and statistical methods were used to
develop prediction models. Among the statistical methods,
RSM was preferred. Machine learning methods were applied
in two stages. First, the three basic machine learning methods
are discussed separately. These methods are ANN, DT, and
K-NN. Then, these four algorithms are combined to increase
the prediction accuracy. Vote ensemble method, one of the
ensemble machine learning methods, was used for merging. Analysis of variance was used to determine the effects
of parameters on the results. For parameter dependent outcome estimation, RSM-based regression was performed. In
addition, optimization based on the desirability function was
made via RSM. Error rates of prediction models compared to
MAPE values. The methods are described in detail in Sects. 3
and 4.
3 Results and Discussions
3.1 Experimental Plan and Results
The experimental plan and results are given in Table 5.
The experiments were planned according to the 33 factorial
design. So, 27 experiments were conducted. Axial forces the
F x and the F y were measured while the experiments were taking place. Maximum force values were used in the analyses.
The average surface roughness measurements were made on
test specimens after the experiments.
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Arabian Journal for Science and Engineering
Table 5 Experimental plan and results
Exp. No
Input parameters
Vc (m/min)
Fz (mm/tooth)
Calculated values
Ap (mm)
n (rpm)
Vf (mm/min)
Results
Time (s)
F x (N)
F y (N)
Roughness (Ra)
1
60
0.04
0.25
1910
306
10.78
24
42
0.42
2
60
0.04
0.5
1910
306
10.78
85
112
0.47
3
60
0.04
0.75
1910
306
10.78
117
165
0.53
4
60
0.05
0.25
1910
382
8.64
55
70
0.44
5
60
0.05
0.5
1910
382
8.64
115
148
0.52
6
60
0.05
0.75
1910
382
8.64
143
205
0.58
7
60
0.06
0.25
1910
458
7.21
70
90
0.55
8
60
0.06
0.5
1910
458
7.21
124
177
0.61
9
60
0.06
0.75
1910
458
7.21
155
235
0.68
10
70
0.04
0.25
2228
356
9.27
32
45
0.48
11
70
0.04
0.5
2228
356
9.27
87
111
0.55
12
70
0.04
0.75
2228
356
9.27
139
176
0.65
13
70
0.05
0.25
2228
445
7.42
38
54
0.53
14
70
0.05
0.5
2228
445
7.42
100
129
0.58
15
70
0.05
0.75
2228
445
7.42
150
194
0.7
16
70
0.06
0.25
2228
534
6.18
38
59
0.6
17
70
0.06
0.5
2228
534
6.18
97
132
0.62
18
70
0.06
0.75
2228
534
6.18
160
205
0.64
19
80
0.04
0.25
2546
407
8.11
35
43
0.59
20
80
0.04
0.5
2546
407
8.11
77
88
0.62
21
80
0.04
0.75
2546
407
8.11
117
140
0.67
22
80
0.05
0.25
2546
509
6.48
35
47
0.63
23
80
0.05
0.5
2546
509
6.48
84
100
0.66
24
80
0.05
0.75
2546
509
6.48
114
163
0.71
25
80
0.06
0.25
2546
611
5.40
38
46
0.62
26
80
0.06
0.5
2546
611
5.40
80
120
0.68
27
80
0.06
0.75
2546
611
5.40
137
187
0.72
3.2 ANOVA Results
The ANOVA table is used to express numerically the effect of
the parameters with various statistical values. Quality characteristics vary by changing quality parameters. The sum
of the squares of the quality attributes is calculated as the
difference between the mean value and the results of each
experiment. Each design parameter affects this total. The
result remaining from the total of these effects indicates the
error. By dividing the sum of squares of the parameters by
the sum of squares, the contribution of that parameter as
a percentage is found. The mean squares are calculated by
dividing the sum of squares for each design parameter and
error by the degrees of freedom. As the F value of the parameter increases, its effect on the result also increases. If the P
value is below 0.05, the parameter is significant [29]. With
the help of ANOVA, the effects of cutting speed, feed per
123
tooth, and depth of cut on cutting force and surface roughness were found. Table 6 shows the ANOVA results for the
cutting force in the X-direction. In the variance analysis performed in this study, the confidence interval was 95%, and
the significance level was 5%. The effects of parameters
in ANOVA were calculated by comparing the F-Value of
each parameter. The contribution of each factor to the total
variation is shown in the last column of the tables. Table
6 shows the ANOVA results for the F x . The contribution
rates of the parameters on cutting force in the X-direction
were 3.617% for Vc, 4.129% for fz, and 87.495% for Ap,
respectively. From these results, the effective parameter on
the cutting force in the X direction was the depth of cut with
87.495%.
Table 7 shows the analysis of variance results for the F y .
The contribution rates of the parameters on cutting force in
the Y direction were 5.905% for Vc, 6.672% for fz, and
Arabian Journal for Science and Engineering
Table 6 ANOVA results for F x
Table 7 ANOVA results for F y
Source
DF
Adj SS
Vc
2
1734.3
fz
2
1980.1
Ap
2
41,949.4
Vc × fz
4
1074.1
Adj MS
867.1
990
20,974.7
F-value
47.49
P-value
Contribution%
0
3.617
54.22
0
4.129
1148.72
0
87.495
2.24
268.5
14.71
0.001
12.2
0.002
1.857
0.144
0.353
Vc × Ap
4
890.8
222.7
fz × Ap
4
169.7
42.4
Error
8
146.1
18.3
Total
26
47,944.5
Source
DF
Adj SS
Vc
2
5357.9
2678.9
fz
2
6054.3
3027.1
Ap
2
76,656.5
38,328.3
Vc × fz
4
1403.7
350.9
Vc × Ap
4
540.8
135.2
7.16
fz × Ap
4
564.4
141.1
7.48
0.008
0.622
Error
8
Total
26
151
90,728.5
84.489% for Ap, respectively. From these results, the effective parameter on the cutting force in the Y direction was the
depth of cut with 86.489%.
Table 8 shows the analysis of variance results for Ra. The
contribution rates of the parameters on surface roughness
were 38.485% for Vc, 17.417% for fz, and 33.244% for Ap,
respectively. From these results, the most influential parameter on the surface roughness was the cutting speed with
38.485%. Since there is not much difference between the
levels of fz parameter, its effect is less compared to other
parameters.
3.3 Effects of Parameters
Contour plots can show relationships with the parameters in
two dimensions. The F x , F y , and Ra variations obtained from
experiments are given in Figs. 5, 6, and 7.
The plot gives the values of the Z variable for the combinations of the X and Y variables. The X and Y values are
located along the X and Y axes, while the contour lines and
stripes represent the Z value. In the contour drawings, it is
seen that the values from dark red to light red tend to increase,
and the values from light blue to dark blue reach the highest
values.
2.32
0.304
100
Adj MS
18.9
F-value
P-value
Contribution%
141.96
0
5.905
160.42
0
6.672
2031.13
0
84.489
0
1.547
0.009
0.596
18.6
0.166
100
Figure 5 shows the contour plots of F x . Force distribution
according to fz and Vc in 5a, force distribution according to
Ap–fz in 5b, and force distribution according to Ap–Vc in
5c are given. Figure 6 shows the contour plots of F y . Force
distribution according to fz and Vc in 6a, force distribution
according to Ap–fz in 6b, and force distribution according to
Ap–Vc in 6c are given. As the Ap and fz levels increased, the
force values increased. It is seen that the increase in Vc also
tends to increase the force. A maximum value of around 160
N is seen for F x . For F y , a maximum value of around 190 N
is observed. Figure 7 shows the contour plots of Ra. Surface
roughness distribution according to fz and Vc in 7a, force
distribution according to Ap–fz in 7b, and force distribution
according to Ap–Vc in 7c are given. It is seen that the surface
roughness is higher at the maximum levels of all parameters.
Values of about 0.7 and above were found.
From contour plots (Figs. 5a, 6a) cutting speed and
feed per tooth had minor effects on cutting forces results.
As the depth of cut increases (Figs. 5b, c and 6b, c), the
cutting forces in the X and Y axes also increase in direct
proportion. Higher depth of cut values generates more force.
This increases the roughness due to a greater deformation of
the chip being pushed more violently against the machined
surface. As a result, the surface quality decreases [30].
These results overlap with the ANOVA results. It is observed
(Fig. 7a–c) that the surface roughness value increased with
increasing parameter levels.
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Arabian Journal for Science and Engineering
Table 8 ANOVA results for Ra
Source
Vc
DF
2
Adj SS
Adj MS
F-Value
P-Value
Contribution%
0.067222
0.033611
51.93
0
38.485
fz
2
0.030422
0.015211
23.5
0
17.417
Ap
2
0.058067
0.029033
44.86
0
33.244
Vcxfz
4
0.010356
0.002589
4
0.045
5.928
VcxAp
4
0.001911
0.000478
0.74
0.592
1.094
fzxAp
4
0.001511
0.000378
0.58
0.684
Error
8
0.005178
0.000647
Total
26
0.174667
Fig. 5 Effect of parameters on F x a F x versus fz, Vc b F x versus Ap, fz c F x versus Ap, Vc (calculated with Minitab software)
Fig. 6 Effect of parameters on F y a F y versus fz, Vc b F y versus Ap, fz c F y versus Ap, Vc (calculated with Minitab software)
Fig. 7 Effect of parameters on Ra a Ra versus fz, Vc b Ra versus Ap, fz c Ra versus Ap, Vc (calculated with Minitab software)
123
0.865
2.964
100
Arabian Journal for Science and Engineering
3.4 Probability Analysis
Figure 8 shows normal probability plots of residual values and prediction values for surface roughness and force.
Deviation from a straight line represents a departure from
normality. Looking at the figure, half of the data is on the
right and the other half on the left. It is seen that the data
follow a straight line, and the proposed model is compatible
[31].
The distribution of the measured and calculated results
was checked. The probability graph confirmed the values
given in Table 5 in Fig. 8. The probability plot of the F x is
given in Fig. 8a, that of the F y in 8b, and that of the Ra in
7c. Graphs are drawn at 95% confidence intervals. As seen
in the graphs, the test results are quite close to the central
axis. Therefore, these data can be used for optimization and
experimental research.
i=1
βi X i +
k
i=1
− 69454 f zx f z − 111, 3x Apx Ap − 92.5V cx f z
R = 94.13
2
(2)
F y = − 988 + 16.92x V c + 17525x f z + 307x Ap
− 0.0725x V cx V c − 62983x f zx f z − 157.4x V cx f z
− 2.33x V cx Ap + 22.57x f zx Ap
R 2 = 96.96
(3)
Ra = − 0.974 + 0.01783x V c + 20.53x f z
+ 0.237x Ap − 0.235x f z
R = 82.36
RSM can optimize multiple parameters simultaneously. It
also determines the linear, square and interaction effect of the
parameters. Estimation of a quality characteristic with high
reliability is achieved by multiple regression. RSM model
consisting of at least three factors should be designed for
each control parameter. The relationship between the control parameter and the quality characteristic is obtained by
RSM [31]. This study used experimental data to improve the
mathematical models using RSM in milling by MINITAB 19.
The relationship between input parameters in RSM problems
and their responses is usually expressed through a quadratic
polynomial equation given below Eq. (1).
k
F x = − 510 + 3.75x V c + 14375x f z + 308.3x Ap
2
3.5 Regression by RSM
Y = β0 +
to Eq. 1, and a stepwise method was used. Equations (2),
(3) and (4) indicate regression equations for F x , F y and Ra,
respectively.
βii X i2 +
k k
βi j X i X j + ε
i=1 j=1
(1)
Equation 1 is a coded model for second-order polynomial
equation. In this equation, Y is the corresponding response,
X i and X j are process parameters, β 0 is a constant, β ii and
β ij are the first and the second-degree coded input parameters
and parameters interactions of linear, quadratic and second
order terms. k is the number of independent parameters, and
the ε is the error term. k is 3 in this work. β i is the regression
coefficient, and β 0 is the average response in an experimental
design. The term regression coefficient of β ij represents the
interaction between the process parameters X i and X j .
Mathematical models were derived between responses
and milling parameters using experimental results according
(4)
The models were checked by employing the coefficient of
determination R2 . The value of R2 is always desired bigger.
All the R2 values are over 80% in this work, which shows
the high correlation between the experimental results and
predicted values.
3.6 Optimization by RSM
The desirability function method, one of the most popular
techniques, was used to find optimum levels of parameters.
With this method, a desirability value di is calculated for
each response, which measures how close the optimum value
of the factors is to the desired value. These values are then
used to generate composite desirability for the response variable. d i ranges from 0 to 1 for any given response. In this
study, it is desired to have minimum force and surface roughness values [32]. The measured quality characteristics of the
predicted response are transformed to a dimensionless desirability value (d i ) by this function. The d i value increases
when the desirability of the sharp response rises. This study
aimed to reduce force in milling and have minimum surface
roughness, so the more minor (the better-quality characteristic) was chosen. The equation is given in Eq. (5).
w
1 U − yi
di =
0 U −T
yi < T
T ≤ yi ≤ U
yi > U
(5)
Here T is the target value of the ith response yi , T is the
acceptable lower limit, U is the allowable upper limit for
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Arabian Journal for Science and Engineering
Fig. 8 a Probability plot of F x b Probability plot of F y c Probability plot of Ra (calculated with Minitab software)
4 Prediction of the Results of Experiments
with Machine Learning
4.1 Development of Prediction Models
The study used artificial neural networks, decision trees,
k-nearest neighbor algorithms from basic individual algorithms, and vote methods from ensemble algorithms to
develop prediction models. It is aimed to predict new experimental results. The parameters of the algorithms were
determined heuristic through experience, trial, and error.
Rapidminer Studio Version 9.8 program was used to determine the success of the models.
4.2 Artificial Neural Network
Fig. 9 Response optimization plot for parameters (calculated with
Minitab software)
Artificial neural networks are an essential classification tool
that includes parallel computing programs that work like the
human brain. Based on the precedent examples and their relationships, the computer systems that make learning decisions
are peculiar to humans. Artificial neural networks consist of
artificial neurons whose function is presented in Eq. (6) [34].
y= f
this response [33]. The optimum levels were obtained from
the analysis, results shown in Fig. 9 by using Minitab 19
software. Figure 9 shows optimum cutting conditions and
optimized response parameters. The high and low represent
the boundary conditions for the parameters. Optimum values
are in red. Where y indicates the optimum value obtained, d
indicates desirability for each input. It is aimed to minimize
surface roughness and force values with optimized parameter
levels. The desirability value was obtained at 0.968. According to research, optimum levels are 60.80 m/min for cutting
speed, 0.040 mm/tooth for feed per tooth, and 0.250 mm
for depth of cut. The optimized values are 0.419 for the Ra,
49.183 for the F y , and 31.524 for the F x .
123
d
wi xi
(6)
i
Here d is the total number of inputs, w is the weights, and x
is the inputs.
Multilayer perceptron neural network (MLP), the most
used artificial neural network model, consists of three layers:
input, hidden, and output. Layers are connected by process
elements that enable information transmission. The number
of process elements in the input and output layer is determined according to the problem. The number of elements in
the hidden layer is defined by trial and error to achieve the
best performance. The weights that show the importance of
the information are chosen randomly at the beginning [35].
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similarity between two samples is needed to find the location of the nearest neighbors. These can be expressed as the
Euclidean, Manhattan, and Minkowski Distance [38, 39].
4.5 Ensemble Machine Learning
Fig. 10 Artificial neural network architecture [35]
In the study, feed-forward back propagation MLP is used.
The neural network consists of three inputs, one hidden layer
containing three neurons, and one output, as seen in Fig. 10.
Artificial neural network models are set up separately for
each cutting parameter (F x , F y , Ra). The inputs consist of
experimental parameters. The parameters used for the neural
network are shown in Table 10. It was used as a sigmoid,
popular in studies as an activation function [36].
4.3 Decision Tree
The Decision Tree algorithm has a tree structure consisting
of root, intermediate, and leaf nodes. The model is easy to
understand and interpret. It can work with continuous and
categorical data, even with missing or missing data. Because
of these features, it is one of the most widely used algorithms.
Some criteria are used to determine which variable the root
node will be. These are information gain, gini index, and gain
ratio. The choice of this criterion affects the success of the
algorithm. The working steps of the algorithm start from the
root node, then continue by dividing up to the intermediate,
and then the leaf node [37].
4.4 K-Nearest Neighbor
The nearest neighbor algorithm classifies unlabeled samples
by assigning them to the class of k most similar labeled
samples. The user determines the k number here. Since the
decision is made by voting, the odd number k should be preferred. The number k should be greater than one, but it should
be considered that a vast number will reduce the method’s
effectiveness. Apart from this, a formula that measures the
It is thought that using ensemble methods by combining
them instead of using machine learning algorithms alone will
increase prediction accuracy [40]. The prediction ability of
ensemble methods is often stronger than using basic algorithms individually. Ensemble algorithms are divided into
dependent and independent according to how they are connected. According to the algorithm type, it is classified as
homogeneous and heterogeneous [41]. Four ensemble algorithms are bagging, boosting, stacking, and voting. Bagging
is independent and homogeneous, boosting is dependent and
homogeneous, stacking is dependent and heterogeneous, and
voting is independent and heterogeneous. In this study, three
heterogeneous machine learning algorithms were used in parallel, so the voting method was used.
5 Comparisons of the Results
In the study, five models were established for each result
(F x , F y , Ra) using RSM, neural network, DT, K-NN, and
Vote (neural network + DT + K − NN) methods. It is
aimed to estimate the result values to be obtained according to the cutting parameters in the models. The parameters
of the algorithms used in the models were determined heuristically, working performances of the models were compared.
Performances are evaluated according to the MAPE value is
presented in Eq. (7).
n
100 Yi − Ŷ MAPE :
Yi n
(7)
i=1
Here, Y i is the measurement value, Ŷ is the predictive value. If
the MAPE value of the models is below 10%, they are considered as ’very good’, between 10 and 20% as ’good’, between
20 and 50% as ’acceptable’, and above 50% as ’wrong’ [42].
The predicted results were compared with the experimental results on the five selected samples. According to these
comparisons, the most suitable method was selected for the
experimental set used in the study.
In all model’s, the learning rate is 0.01, momentum 0.9,
and sigmoid function were used in the neural network, mixed
measure and mixed Euclidian were used in K-NN, and since
the target value of the data set is not nominal, the DT criterion
is chosen as at least square. Apart from these values, the
selected parameter for the individual values is shown in Table
9. Null values are used for parameters other than these.
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Arabian Journal for Science and Engineering
Table 9 Parameter of individual machine learning algorithms
Neural Network
DT
K-NN
Parameters
Fx
Neural.Net_Cycle
200
Maximal Depth
10
k
11
Fy
750
30
9
Ra
200
10
3
Results
Algorithms
In the study, individual algorithms were combined with
the voting method from the ensemble machine learning
algorithms. Moreover, in ensemble algorithms, the same
parameters are used when the algorithms are used individually. To measure F x , F y and Ra values, the regression models
derived from Vc, fz and Ap was estimated with RSM, individual and ensemble machine learning algorithms. Measured
values of experiments and prediction values of models are
shown in Table 10.
According to Table 10, MAPE values of the models, which
express the error rate, are shown in Fig. 11. Low error rates
are desirable for the success of the model. When the MAPE
values are examined; it is evaluated as ’good’ for the F x and
’very good’ for the F y and the Ra according to the Fig. 11.
The lowest error for the F x result was obtained when the
vote method was used with a MAPE value of 11.163%. The
second method with an error rate is the RSM method with
12.834%. In the model established with the DT algorithm,
the MAPE value is 17.298%. Furthermore, an error rate of
18.195% was seen in the model set with ANN. The highest error occurred when the K-NN algorithm was used with
30.568%.
The lowest error for the F y ’s result was obtained with
7.749% when using ann. In the model established with the
Vote method, it is seen that the MAPE value is the second
with 10.586%. In the model based with RSM, there was an
error of 19.41% and a DT with an error rate of 26.056%. The
Table 10 Measured values of experiments and prediction values of models
Method
RMS
ANN
DT
K-NN
Vote
Cutting parameters
Result in F x
Measured
Result in F y
Result in Ra
Vc
fz
Ap
Prediction
Measured
Prediction
Measured
Prediction
80
0.05
0.5
80
0.05
0.75
84
91.44
100
97.52
0.66
0.65
114
133.73
163
155.88
0.71
0.71
80
0.06
0.25
38
28.58
46
24.85
0.62
0.61
80
0.06
0.5
80
84.79
120
88.85
0.68
0.67
80
0.06
0.75
137
127.08
187
152.86
0.72
0.73
80
0.05
0.5
84
106.3
100
106.3
0.66
0.67
80
0.05
0.75
114
168.18
163
168.18
0.71
0.69
80
0.06
0.25
38
55.39
46
55.39
0.62
0.66
80
0.06
0.5
80
125.5
120
125.5
0.68
0.69
80
0.06
0.75
137
194.98
187
194.98
0.72
0.7
80
0.05
0.5
84
98.5
100
130.5
0.66
0.61
80
0.05
0.75
114
146.5
163
199.5
0.71
0.67
80
0.06
0.25
38
37
46
74.5
0.62
0.61
80
0.06
0.5
80
98.5
120
130.5
0.68
0.61
80
0.06
0.75
137
157.5
187
199.5
0.72
0.67
80
0.05
0.5
84
81.55
100
101.84
0.66
0.64
80
0.05
0.75
114
92.6
163
121.58
0.71
0.65
80
0.06
0.25
38
73.69
46
81.58
0.62
0.61
80
0.06
0.5
80
83.87
120
103.45
0.68
0.65
80
0.06
0.75
137
92.6
187
123.7
0.72
0.65
80
0.05
0.5
84
83.71
100
107.41
0.66
0.64
80
0.05
0.75
114
118.57
163
157.47
0.71
0.67
80
0.06
0.25
38
50.43
46
57.86
0.62
0.63
80
0.06
0.5
80
86.6
120
113.86
0.68
0.65
80
0.06
0.75
137
126.02
187
166
0.72
0.68
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Arabian Journal for Science and Engineering
Fig. 11 Comparison of MAPE of models
highest error occurred when the K-NN algorithm was used
with 30.568%.
When the result of the Ra is examined, it is seen that the
RSM has the lowest error rate, that is, the most successful
algorithm. The algorithm with the highest error rate was the
DT algorithm with 6.38%.
6 Conclusions
This paper optimized the cutting parameters on cutting forces
and surface roughness in trajectory milling of the AISI 321
material in wet conditions. Optimal cutting parameters were
determined by the RSM method and the desirability function.
In addition, a new perspective was presented by estimating
the experimental results with ensemble methods.
There are three output results in the study: F x , F y , and Ra.
The aim of the study is to predict the experimental results in
the most accurate way. Both machine learning and statistical methods were used for prediction. The statistically based
method is the RSM. In machine learning methods, first, three
basic machine learning methods were discussed individually.
These methods are ANN, DT, and K-NN. Then, aiming to
increase the prediction accuracy, these four algorithms were
combined with the vote ensemble method. The easiest way
to combine different algorithms is by voting. Therefore, it is
preferred. In addition, the aggregation method was used in
the vote method. Since the target value of the experimental
set is continuously variable, the models are regression based.
Performance evaluations of models vary according to the
analysis method used in the model. Since regression-based
models were developed in the study, their performance was
evaluated according to the error value. Models were compared according to their MAPE values, as it is the most
frequently used measurement value when examining error
values. The lowest MAPE values for the models provide the
most successful accuracy rates. The results from this study
are summarized below.
When the results are examined, it can be said that the
prediction accuracies of the models show that a different
algorithm is successful for each experimental result. If the F x
is to be estimated, the prediction model should be developed
with the vote ensemble method. The error rate was obtained
as 11.163%. If the F y is to be estimated, the prediction model
should be developed with the ANN algorithm. The error rate
was 7.749%. If the Ra is to be predicted, the estimation model
should be developed with the RSM method. The error rate
was 0.930%. When the MAPE values are examined; it is
evaluated as ’good’ for the F x and ’very good’ for the F y and
the Ra. The main hypothesis of the study is: “The ensemble
machine learning methods are machine learning methods that
increase their prediction accuracy". The results of the vote
ensemble method show that it is validated for the F x output.
Performing the experiments requires long time and high
cost. The number of experiments needed can be significantly
reduced as future situations will be predicted by the developed prediction models.
The ensemble application of DT, K-NN, and ANN algorithms, which have not been used before, has been seen as
successful for the F x result. It is thought that it will be useful
to apply it for future state prediction in similar experiments.
ANOVA results showed that while the effective parameter on the cutting forces both in X and Y direction was the
depth of cut, the cutting speed had been the most dominant
parameter on the surface roughness. The contribution rates
of the parameters on cutting force in the X-direction were
3.617% for the Vc, 4.129% for the fz, and 87.495% for Ap,
respectively. From these results, the effective parameter on
the cutting force in the X direction was the depth of cut with
87.495%. The contribution rates of the parameters on cutting
force in the Y direction were 5.905% for the Vc, 6.672% for
the fz, and 84.489% for Ap, respectively. From these results,
the effective parameter on the cutting force in the Y direction
was the depth of cut with 86.489%. The contribution rates
of the parameters on surface roughness were 38.485% for
the Vc, 17.417% for the fz, and 33.244% for the Ap, respectively. From these results, the most influential parameter on
the surface roughness was the cutting speed with 38.485%.
As a result of response surface optimization and desirability function method, optimum milling levels of parameters
are 60.80 m/min for the cutting speed, 0.040 mm/tooth for
the feed per tooth, and 0.250 mm for the depth of cut.
The effects of parameters on the force and the surface
roughness were supported by contour plots.
Experimental results confirmed by the probability graphs.
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Arabian Journal for Science and Engineering
Different machine learning algorithms and parameter optimization methods will be used in future studies.
Declarations
Conflict of Interest On behalf of all authors, the corresponding author
states that there is no conflict of interest.
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