 Open Access
 Total Downloads : 29
 Authors : Van – Nguyen Le , He Thong – Bui
 Paper ID : IJERTV8IS100030
 Volume & Issue : Volume 08, Issue 10 (October 2019)
 Published (First Online): 10102019
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
The Effect of Cutting Parameters on Surface Roughness of C45 Carbon Steel by Experimental Design Method
Van – Nguyen Le
Department of Industrial Education,
The university of Technology and Education, The university of Da Nang, Viet Nam.
He Thong – Bui
Department of Mechanical Engineering,
The university of Technology and Education, The university of Da Nang, Vietnam.
Abstract In this study, the author use the experimental design method to determine the relation between cutting parameters and surface roughness in lathe processing. The machine lathe model T620 with ceramic cutting tool is used to cutting C45 carbon steel samples which is widely using for machining process. The requirement for qualified worker is medium. The cutting parameters: cutting velocity (v), feed rate(s) are change while the cutting depth is 0.5mm. The surface roughness of specimens are measured by handle surface roughness machine Mitutoyo SJ310 model. By using Box Hunter experimental design method, the equation of regression is determined. Thanks to this equation, the optimum cutting parameters is find out.
Keywords Surface roughness; cutting parameters; carbon steel C45; optimum parameters; Box Hunter experimental design.

INTRODUCTION
Cutting parameters: cutting velocity (v), feed rate (s) and the cutting depth (t) are important factors of cutting process [1], [2]. Cutting parameters effect on productive, costly and surface quality. The productivity is high with rough cutting
regression equation that show the relationship between surface roughness and cutting parameters. The advantage of this method is that the number of experiments is smaller than the traditional method, and the results are highly reliable.

THEORY
Experimental design method was proposed in 1935 by statistician Ronal Fisher and continued to be researched and developed by George Edward Pelham Box and Genichi Taguchi. This method relies on regression modeling and graphical analysis to optimize experimental models using algorithms. The goal is to find out relationship between the set of input parameters and the value of output parameters.
In this study, a secondorder Box – Hunter design rotation method [7], [8] was used. Due to the rotation properties, the accuracy of the regression equation is equal in all points of the element of design space, at an equal distance from the planning center. The combination between the evenness and rotation mean that the variance is constant in a certain region from the planning center. The accuracy increases, when the value of cutting parameter near to the planning center. Therefore, we must adjust the input values close to planning center.
mode but surface quality is low. In contrast, finishing cutting mode bring out high surface roughness and low productivity [3], [4]. Therefore, determination of optimal cutting parameters is important mission of cutting process [5]. The simple method is using technology handbook [6], to find out the optimum parameters corresponding with material and requirement of surface quality. This method is simple but productivity is low. Because the technology handbooks [9]
1,+1
1,1
0,0
+1,+1
+1,1
were built by statistical methods, conducting test cutting on a series of samples and summarize into tables. Methods of analysis and experimental design [7], [8] were born based on the use of algorithms to process data, so the results are highly accurate and reliable with a small number of experiments. In
Fig. 1. Structure diagram with a uniform rotation center, with k =2
The regression equation has the form:
y b b .x b .x .x b .x (1)
y b b .x b .x .x b .x (1)
k k k
2
0 i i ij i j ij i
this study, the author used 13 samples of solid round
i1
i, j 1;
i j
i1
cylinders with diameter of Ã˜50mm and grade of C45 steel, the model is machined on a machine lathe T620, with different cutting modes for every time. This means that sample is installed once, then turning each time with change of cutting mode. Surface roughness is determined by
While: k number of elements xi, xj are elements
System of standard regression equations:
i ts
i ts
B G1.(XT .Y ); S 2 (b ) mii .S2
(2)
Mitutoyo SJ310 roughness meter. The experimental design method Box – Hunter [8] is used to process data and define
With: mii rank term ii of the matrix G1, with G=XT.X
Solve equations, coefficients and variances defined:
n k n
b a y
a . x2 .y
(3)
0 1 j j 1
n
2
i1
j 1
ij j
bi a3. xij .y j i 1 k
j 1
n
n
biu a4 . xij . xuj y j u 1;i, u 1 k
j 1
n k n k
n k n k
b a . x2 .y a . x2 .y a . y
Figure 4. Surface roughness meter
B. Experimental parameters
ii 5
j 1
ij j
6
i1
j 1
ij j
7 i
i1
Samples were machined on machine lathe T620, lathe
S 2 a .S 2
(4)
machine is popularly equipped in mechanical processing
b0 1 ts
b 3 ts
b 3 ts
S 2 a .S 2
i
b 4 ts
b 4 ts
S 2 a .S 2
iu
S 2 a a .S 2 a .S 2
facilities, ceramic cutting tool. The parameters of the cutting parameters includes 3 elements: v, s, t. The task is to find the optimal values of them. However, the experimental design with 3 elements is often difficult to implement, so the cutting depth t is fixed at 0.5mm. The variable of Box Hunter
experimental design method reduce to two, includes cutting
bii
5 6 ts
7 ts
With k = 2, look up the table with the coefficients a
TABLE I. FACTOR a
k
a1
a2
a3
a4
a5
a6
a7
2
0.2
0.1
0.125
0.25
0.125
0.0185
0.1438

EXPERIMENT
A. Model of experiment
The sample was used in this study is hot rolled cylindrical solid round, diameter Ã˜50mm, steel grade C45.
Figure 2. Sample of experiment
Ceramicpiece turning tools are used because of the advantages of processing highhardness materials, or materials after heat treatment without cool water, highgloss surfaces, easy to replace cutting tools during machining.
Type
Chamfering angle
Radius of knife (mm)
Thickness T(mm)
A(mm)
SNGN120708T02025
0.2×150
0.8
4.76
12.7
Type
Chamfering angle
Radius of knife (mm)
Thickness T(mm)
A(mm)
SNGN120708T02025
0.2×150
0.8
4.76
12.7
Figure 3. Ceramic piece turning tool TABLE II. PARAMETERS OF CUTTING TOOL
velocity (v) and feed rate (s), with values given in table 3:
TABLE III. EXPERIMENTAL CUTTING PARAMETERS
td>
60100
Factor
t (mm)
v (m/min)
s (mm/revolution)
Value
0.5
0.0240.06
The cutting velocity is selected in the range of 60 – 100 m/min, this is a large cutting velocity zone and surpassing built up edge (BUE) area [5] so it is easy to achieve surface gloss. The feed rate is chosen at a relatively small area from
0.023 to 0.06 mm/revolution to increase surface gloss.
In order to carry out experimental design method, the real variables v, s, t must be converted into virtual variables x0, x1, x2.
TABLE IV. REPLACE THE REAL INTO VIRTUAL VARIABLE
Factor
t (mm)
v (m/min)
s (mm/revolution)
Value
0.5
60100
0.0230.06
virtual variable
x0
x1
x2
Virtual variables have only values 1, 0 and +1. Therefore, the conversion value between real and virtual variables is shown in the following table:
TABLE V. VALUE OF VIRTUAL VARIABLE
Real variable
Virtual variables
Variable range
Level
+
Upper level (+1)
Base level (0)
Lower level (1)
Level
–
X1 (mpm)
108
100
80
60
52
20
X2
(mm/revolution)
0.067
0.06
0.042
0.02
0.013
0.018
For the experimental design method of rotation Box – Hunter with 2 elements, we need to perform 13 experiments, the number of experiments at the center is m = 5.
Surface roughness was measured by Mitutoyo SJ310
k 2 1
roughness meter, measuring tip radius 2Âµm.
Lever arm: 24 24 22 2 1.414 [8] (5)
After performing experiments, determining surface roughness, we have an experimental matrix that rotates evenly:
No.
x0
x1
x2
x1x2
x12
2
x2
y
1
+
–
–
+
+
+
2.52
2
+
+
–
–
+
+
2.47
3
+
+
+
+
+
+
2.93
4
+
–
+
–
+
+
3.16
5
+
1.414
0
0
2
0
2.62
6
+
+1.414
0
0
2
0
2.51
7
+
0
1.414
0
0
2
2.65
8
+
0
+1.414
0
0
2
2.76
9
+
0
0
0
0
0
2.27
10
+
0
0
0
0
0
2.53
11
+
0
0
0
0
0
2.26
12
+
0
0
0
0
0
2.33
13
+
0
0
0
0
0
2.35
No.
x0
x1
x2
x1x2
x12
2
x2
y
1
+
–
–
+
+
+
2.52
2
+
+
–
–
+
+
2.47
3
+
+
+
+
+
+
2.93
4
+
–
+
–
+
+
3.16
5
+
1.414
0
0
2
0
2.62
6
+
+1.414
0
0
2
0
2.51
7
+
0
1.414
0
0
2
2.65
8
+
0
+1.414
0
0
2
2.76
9
+
0
0
0
0
0
2.27
10
+
0
0
0
0
0
2.53
11
+
0
0
0
0
0
2.26
12
+
0
0
0
0
0
2.33
13
+
0
0
0
0
0
2.35
TABLE VI. MATRIX OF EXPERIMENTAL DESIGN WITH 2 ELEMENTS
Recalculating the coefficients bi:
Because the experimental design method is not
orthogonal, when value of bi is excluded, we have to
recalculate the significant coefficients according to the least square method:
G.B XT .Y
Replacing the meaningful coefficients bi into the equation above, the unmeaningful coefficient is considered as zero. We obtain the system of equations.:
13.b0 8.b11 8.b22 33.26
7.9988b2
1.1555
(7)
8.b0 12.b11 4.b22 21.24
8.b0 4.b11 12.b22 21.8
Solve the system of equations (7) we have: b0 = 2.348; b2
= 0.144459; b11 = 0.136; b22 = 0.206.
The temporary regression equation has the form:
2.65
No.
t(mm)
n(rpm)
s (mm/revolution)
Ra (Âµm)
1
0.5
60
0.036
2.52
2
0.5
100
0.036
2.47
3
0.5
60
0.05
2.93
4
0.5
100
0.05
3.16
5
0.5
60
0.043
2.62
6
0.5
100
0.043
2.51
7
0.5
85
0.023
8
0.5
85
0.058
2.76
9
0.5
85
0.043
2.27
10
0.5
85
0.043
2.53
11
0.5
85
0.043
2.26
12
0.5
85
0.043
2.33
13
0.5
85
0.043
2.35
No.
t(mm)
n(rpm)
s (mm/revolution)
Ra (Âµm)
1
0.5
60
0.036
2.52
2
0.5
100
0.036
2.47
3
0.5
60
0.05
2.93
4
0.5
100
0.05
3.16
5
0.5
60
0.043
2.62
6
0.5
100
0.043
2.51
7
0.5
85
0.023
2.65
8
0.5
85
0.058
2.76
9
0.5
85
0.043
2.27
10
0.5
85
0.043
2.53
11
0.5
85
0.043
2.26
12
0.5
85
0.043
2.33
13
0.5
85
0.043
2.35
TABLE VII. EXPERIMENTAL PARAMETERS
R 2.348 0.144459.x 0.136.x2 0.206.x2
a 2 1 2
Check equation compatibility: fdu = nh(m1) = 134(51)=5
F(fts;fdu;) = F(4;5;0.05)=6.2561
m 2
S
S
2
ts (0)
y0 y0
a
a
vÃ
vÃ
i1
m 1
^
y X .B
(8)

RESULT AND DISCUSSION
The regression equation has the form:
TABLE IX. CHECKING COMPATIBILITY OF EQUATION
R b b .x b .x b .x .x b .x2 b .x2
(6)
a 0 1 1 2 2 12 1 2 11 1 22 2
With: b0 = 2.384, b1 = 0.0419, b2 =0.1445, b12 = 0.02,
b11=0.136, b22 =0.206
Check meaning of coefficients bi: Coefficient bi meaning when:
New B
yi
y
y y 2
i
2.348
2.52
2.5455
0.00065
0
2.47
2.5455
0.0057
0.144459
2.93
2.8345
0.00912
0
3.16
2.8345
0.10595
0.136
2.62
2.6200
0
0.206
2.51
2.6200
0.0121
2.65
2.5557
0.008892
2.76
2.9643
0.041738
2.27
2.3480
0.006084
2.53
2.3480
0.033124
2.26
2.3480
0.007744
2.33
2.3480
0.000324
2.35
2.3480
4E06
New B
yi
y
y y 2
i
2.348
2.52
2.5455
0.00065
0
2.47
2.5455
0.0057
0.144459
2.93
2.8345
0.00912
0
3.16
2.8345
0.10595
0.136
2.62
2.6200
0
0.206
2.51
2.6200
0.0121
2.65
2.5557
0.008892
2.76
2.9643
0.041738
2.27
2.3480
0.006084
2.53
2.3480
0.033124
2.26
2.3480
0.007744
2.33
2.3480
0.000324
2.35
2.3480
4E06
Spt y y
n 0 2
i1 i i
0.231432
m 2 S y0 y0 tn u1 u u
0.04728
fdu = nh(m1)
5
S 2 Spt Stn du f
du
0.03683
S2 Stn ts m 1
0.01182
S 2
Ft du
S 2
ts
3.115939
Spt y y
n 0 2
i1 i i
0.231432
m 2 S y0 y0 tn u1 u u
0.04728
fdu = nh(m1)
5
S 2 Spt Stn du f
du
0.03683
S2 Stn ts m 1
0.01182
S 2
Ft du
S 2
ts
3.115939
TABLE X. DETERMINATION VALUE OF Ft
t t f ;1
i ts
With: fts = m1 = 51 = 4
Look up the Student distribution rule table with significance level = 0.05, we have: t(4;0.05)=2.776.
tij
bij S
ij
TABLE VIII. VALUE OF ti
t0
t1
t2
t11
t12
t22
48.29
1.09
3.75
0.3679
3.298
4.9966
The system of coefficients b1, and b12 disqualified because of the condition t t f ; is not satisfied.
We have Ft = 3.115939 < F(fts;fdu;) = F(4;10;0.05)=6.2561.
Therefore, the regression equation is compatible.
i ts
So the regression equation for the encoded variable takes the form:
a 2 1 2
a 2 1 2
R 2.348 0.144459x 0.136×2 0.206×2 (9)
Convert the equation to a real variable:
Fig. 6 shows the optimum cutting parameters area of the
machine when machining on lathe T620, with a thin ceramic cutting tool, carbon steel sample C45. Value of surface
x V 80
1 20
; x S 0.042 . Replace to the equation (9)
2 0.018
roughness (Ra) of the test sample will be the smallest when 0.025<s<0.047 mm/revolution and 65 <v <95 m/min.
R 2.348 0.144459x 0.136×2 0.206×2
a 2 1 2
S 0.042 V 80 2
S 0.042 2

CONCLUSION
2.348 0.144459
0.018
0.136
20 0.206
0.018
By using the experimental design method of the Box –
2 2
2 2
a 5.30848 45.3819074S 0.0544V 0.00034V 635.802S
(10)
The graph in Fig. 5 shows the relationship between surface roughness (Ra) and cutting parameterss (v, s), when we machine samples on lathe T620, with the cutting depth t = 0.5mm. It is easy to see that the surface roughness Ra decreases as feed rate (s) decreases, but there is a sign of increase again when s <0.025 mm/revolution [6].
Figure 5. Graph of correlation between surface roughness and cutting mode
Because, when the feed rate decreases, the surface roughness decreases. However, if the feed rate is too small, the nose radius affects the roughness, causing the surface roughness to increase [9]. Surface roughness decreases as the cutting velocity increases from 60 m/min to 85 m/min. Beside, surface roughness increases when the cutting velocity is greater than 85m/min.
Figure 6. The graph determines the optimal cutting parameters
Hunter 02 elements, this study has determined the relationship between surface roughness (Ra) and cutting parameters, namely cutting velocity (v) and feed rate (s) with machining conditions: machine lathe T620, C45 carbon steel samples, ceramic piece cutting tool. With the regression equation achieved, it is easy to choose the optimal parameters for the cutting process, serving the task design as well as automating the production process. The experimental design method allows us to accurately determine the regression equation with the number of experiments performed much less than the traditional method, which in turn changes the cutting parameters v, s, t to find out regression equation.
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