RESEARCH PROGRESS IN MECHANICAL AND MANUFACTURING ENGINEERING VOL. 3 NO.

1 (2022) 267-277

© Universiti Tun Hussein Onn Malaysia Publisher’s Office

RPMME
Homepage: http://penerbit.uthm.edu.my/periodicals/index.php/rpmme
e-ISSN : 2773-4765

Optimisation of Surface Roughness in The Cnc

Milling Process
Muhammad Syazwan Hassan1, Azriszul Mohd Amin1*
1
Faculty of Mechanical and Manufacturing Engineering,
Universiti Tun Hussein Onn Malaysia, 86400 Parit Raja, Batu Pahat, Johor,
MALAYSIA

*Corresponding Author Designation

DOI: https://doi.org/10.30880/rpmme.2022.03.01.028
Received 15 Nov. 2021; Accepted 15 April 2022; Available online 30 July 2022

Abstract: The main aspect for machining today is to produce and achieve a better
surface quality in a short period and with a lower energy consumption. Surface
roughness is a common criterion of the quality characteristics for machining
processes. In order to increase the consistency of the surface finish, the suitable
cutting parameters should be implemented. This thesis aimed to optimise the surface
roughness in 3D cutting using CNC end milling machine. The depth of cut, the cutting
speed and the feed rate are the parameters used in optimising the surface roughness.
The best range of the cutting parameters was obtained by using Dthe esign of
Experiment (DOE) which is Response Surface Methodology (RSM) method. The
RSM method is used because it is one of the most efficient and effective techniques
to determine the best combination of parameters. The experiments were run by using
the data simulation from Mastercam X7 and all the data command were used in Nexus
410A-II 3-Axis Computer Numerical Method (CNC) machine with the MAZATROL
controller. The surface roughness of workpiece is measured using surface roughness
tester, Mitutoyo SJ-410. The analysing data are made by employing RSM and
ANOVA using Minitab 19 software. The direct effects and interaction effects were
graphically plotted which helps to study the significance of these parameters on
surface roughness.

Keywords: Surface Roughness, Response Surface Methodology, Cutting

Parameters, CNC End Milling Machine, Minitab 19 Software, Mastercam X7,
ANOVA

1. Introduction
Machining quality is measured from the surface finish and in order to improve the surface
quality, it is important to set appropriate and optimum machining parameters during machining work
[3]. Efficient machining parameters play a very important role in manufacturing process to improve
manufacturing efficiency and to cut down the cost in production [3]. There are different combinations
of parameters such as cutting speed, feed rate and depth of cut. Depending on the machining target and
tool selection, to achieve different results regarding machined surface quality and tool wear. Surface
*Corresponding author: azriszul@uthm.edu.my
2022 UTHM Publisher. All rights reserved.
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Hassan, M.S et al., Research Progress in Mechanical and Manufacturing Engineering Vol. 3 No. 1 (2022) p. 267-277

roughness has a major impact on dimensional accuracy, machine component performance, and
manufacturing costs [4]. The difference in surface roughness and tool life depending on the combination
of cutting parameters. The quality of the machined surface is evaluated by the surface roughness of the
machined part, which is the most important quality characteristic [5].
Response surface methodology (RSM) is the most effective method to analyse the result
obtained from factorial experiments. It is an effective tool for modelling and studying the manufacturing
problems which in this project is about end milling cutting parameters. RSM has been used for
roughness modelling and optimisation in CNC end milling. RSM takes on both mathematical and
statistical techniques which are useful for the modelling and analysis of problems in which a response
of interest is influenced by several variables and the objective is to optimise the response. In most of
the RSM problems, the form of the relationship between the response and the independent variables is
unknown. Thus, the first step in RSM is to find a suitable approximation for the true functional
relationship between response of interest ‘y’ and a set of controllable variables {𝑥1 , 𝑥2 … . . 𝑥𝑛 }. Usually
when the response function is not known or non-linear, a second-order model is utilised in the form of
equation (1) shown below:
𝑛 𝑛

𝑦 = 𝑏0 + ∑ 𝑏𝑖 𝑥𝑖 + ∑ 𝑏𝑖𝑖 𝑥𝑖2 + Σ ∑ 𝑏𝑖𝑗 𝑥𝑖 𝑥𝑗 + 𝜀

𝑖=1 𝑖=1 𝑖<𝑗

where ε represents the noise or error observed in the response y such that the expected response is (y)
and b’s are the regression coefficients to be estimated.
2. Methodology
Determine all the influential parameters that will give big effect towards surface roughness of
the workpiece. Then, all the information will be put in the constructed design of experiment which is
RSM in Minitab 19 software. We will get sets of parameters combination and all that data will be used
to run the experiment. Simulation of milling process will be run in the Mastercam X7 software. The
simulations need to be done at first to identify the best parameters for milling and the design of the
workpiece for this experiment. After we run the simulation, the simulation data that have been created
(commands) will be use to run the experiment through CNC end milling machine. The roughed surface
of each workpiece will be measured using surface roughness tester, Mitutoyo SJ-410 to get the value
of Ra, average surface roughness. All the data obtained will be analyse to find out the best set of
parameters in minimizing the roughness of surface of workpiece. This data analysis will be performed
under RSM method.
2.1 RSM Design
In this study, Box-Behnken design had been used to determine the factors level that
simultaneously satisfy a set of desired specifications, to select the ideal combination of factors that yield
a desired response and describes the response near the optimum, to determine how a specific response
is affected by changes in the level of the factors over the specified levels of interest, and achieve a
quantitative understanding of the system behaviour over the region tested. Cutting speed, cutting feed
rate and depth of cut has been considered as the cutting parameters. 3 levels of each parameter will be
used which is 3^3 factorial design. This design of experiment which is RSM will be run using Minitab
19 software.

Table 1: Parameters setting and levels

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No Factors Levels
1 2 3
1 Cutting Speed (rpm) 960 1200 1440
2 Feed Rate (mm/min) 500 550 600
3 Depth of Cut (mm) 0.50 0.60 0.70

Table 2: Box-Behnken design

Run p. Blocks Parameters

Order type Cutting speed (rpm) Feed rate (mm/min) Depth of cut (mm)
1 2 1 1200 500 0.5
2 0 1 1200 550 0.6
3 2 1 1200 500 0.7
4 2 1 960 550 0.5
5 2 1 1200 600 0.7
6 2 1 1440 550 0.7
7 2 1 960 600 0.6
8 2 1 1440 600 0.6
9 0 1 1200 550 0.6
10 2 1 1200 600 0.5
11 2 1 960 550 0.7
12 2 1 1440 550 0.5
13 2 1 960 500 0.6
14 0 1 1200 550 0.6
15 2 1 1440 500 0.6

2.2 Experimental Details

Nexus 410A-II 3-Axis Computer Numerical Method (CNC) machine with the MAZATROL
controller is the CNC end milling machine that will be used in this project. The workpieces dimension
is 50𝑚𝑚 × 50𝑚𝑚 × 30𝑚𝑚 are suitable for the tilting table integrated into the structure. The work area
and top-value technical data on this CNC machine is created for the best access and highest precision.
Detail procedure of experimental setup are stated as below:
1. Prepare the vertical CNC milling machine system. Check and ensure the machine is ready to
perform the machining operation.
2. Preparation of 50𝑚𝑚 × 50𝑚𝑚 × 30𝑚𝑚 rectangular aluminium block in forming tool for CNC
end milling.
3. This operation is surface roughing operation and a constant dimension of flat end mill and
parameters will be used. The size of a flat end mill with a diameter of 8mm and a total length
of 65mm. Meanwhile, there are 4 constant parameters that will be used to run all 13 experiments
which are plunge rate = 250, retract rate = 500, step over = 1.5 and spindle speed = 4000rpm.
4. Sending all created code file from simulation in Mastercam X7 to the CNC end milling machine
to perform the milling operation.
5. The 15 experiments will be conducted under dry conditions with different parameters of the
milling process which are feed rate of 500mm/min, 550mm/min, 600mm/min, cutting speed of
960rpm, 1200rpm, 1440rpm and depth of cut of 0.5mm, 0.6mm, and 0.7mm.
6. The roughed surface of workpieces will be measured three times using the surface roughness
tester (Mitutoyo SJ-410) to obtain the value of average roughness surface, Ra.

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Figure 1: CNC Milling machine Figure 2: Mitutoyo (SJ-410)

Figure 3: Tested material (Aluminium)

3. Results and Discussion

The purpose of this research is to predict and optimise the cutting parameters that affect the
average surface roughness of the centreline of the milled surface. In order to evaluate the influence of
cutting parameters on the average roughness of the centreline, RSM was used. The experimental results
were transferred into Minitab 19 software. The data collection includes surface roughness as the output
response. The analysis divided into three major parts, which is RSM analysis, ANOVA analysis and
optimisation analysis.

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3.1 Results
Table 3: Experiment Result

No Parameters Response
Cutting Speed, Feed Rate, Depth of Cut, Average roughness,
N(rpm) f(mm/min) d(mm) Ra (μm)
1 1200 500 0.5 0.527
2 1200 550 0.6 1.416
3 1200 500 0.7 1.009
4 960 550 0.5 0.815
5 1200 600 0.7 0.917
6 1440 550 0.7 0.725
7 960 600 0.6 1.426
8 1440 600 0.6 1.756
9 1200 550 0.6 1.416
10 1200 600 0.5 1.045
11 960 550 0.7 1.121
12 1440 550 0.5 0.746
13 960 500 0.6 0.643
14 1200 550 0.6 1.416
15 1440 500 0.6 0.940

The parameters were set to achieve best minimum average surface roughness, Ra (0.527μm)
found to be at the middle level value of cutting speed (1200rpm), minimum level of depth of cut
(0.5mm), and minimum level of feed rate (500mm/min).
3.2 RSM analysis
The second order response surface equations have been fitted using Minitab 19 software for the
response variables (Ra). The equation can be given in terms of the uncoded values of the independent
variables as the following, Regression Equation in Uncoded Units:

R a = −45.2 + 0.00691N + 0.0670f + 74.5d − 0.000002N2 − 0.000040f 2

−44.1d2 + 0.000001Nf − 0.00341Nd − 0.0305fd Eq. 1

The above model can be used to predict the surface roughness parameters of a specific design point. In
order to better understand the interaction of variables on the considered response, a three-dimensional
(3D) plot of the measured response was created based on the above model equations. Since the model
has three variables, the center level of each graph keeps one variable unchanged. The three-dimensional
(3D) graphs are produced to illustrate the relationships occurred between all experimental factors and
responses.

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Figure 4 (a) Figure 4 (b)

Figure 4 (c)

Figure 4 (a) to Figure 4 (c) give the 3D surface graphs for the roughness parameter Ra. It reveals
that Ra increases with increase in cutting speed, feed rate and depth of cut. In Figure 4 (a), when the
constant variable (hold values) is depth of cut which set at 0.6mm, it shows that average surface
roughness, Ra is at highest point when the cutting speed and feed rate are set as 1200rpm and
600mm/min, respectively. Average surface roughness, Ra increase drastically when feed rate
increasing. However, when the cutting speed increasing, Ra slightly increase and then decrease. In
Figure 4 (b), the constant variable (hold values) is feed rate which set at 550mm/min, it shows that the
average surface roughness, Ra increase and constant at high level as cutting speed increase. Next,
average surface roughness, R increase and then decrease when the depth of cut increasing. The 3D
graph shows that average surface roughness, Ra is the highest which is 1.4 when the cutting speed and
depth of cut are set as 1200rpm and 0.6mm. In Figure 4 (c), the constant variable (hold values) is cutting
speed which set at 1200rpm, it shows that the average surface roughness, Ra increase as the feed rate
increasing. Next, when the depth of cut increase, the average surface roughness, Ra is increasing and
then decrease. The graph shows that the average surface roughness, Ra are at their maximum which is
1.5 when feed rate and depth of cut are set at 600mm/min and 0.6mm.
The big change shows that feed rate is the most significant forming variable influencing the
average surface roughness Ra, which is consistent with the analysis in the ANOVA Table 5 below. In
addition to the dynamic effect on the cutting force, increasing the feed rate will also cause a large
amount of material to be cut in the same unit of time. It also leads to a corresponding increase in the
normal contact stress between the tool chip interface and the tool chip contact area. Therefore, the
cutting force is found to increase with increasing feed rate. Similarly, an increase in the depth of cut
will result in an increase in the working contact length of the tool. Subsequently, the thickness of the
chip becomes very large, resulting in an increase in the volume of the deformed aluminium and a higher
cutting force is required to cut the chips. As the cutting speed increases, the decrease in force may be

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due to the increase in the temperature of the cutting plane area, resulting in a decrease in the cutting
resistance of the material.
3.3 Response surface regression and ANOVA
Table 4: Response surface regression for Ra versus all parameters

Term Coef SE Coef T-Value P-Value VIF

Constant 1.416 0.146 9.67 0.000
N 0.0203 0.0897 0.23 0.830 1.00
f 0.2531 0.0897 2.82 0.037 1.00
d 0.0799 0.0897 0.89 0.414 1.00
N2 -0.124 0.132 -0.94 0.392 1.01
f2 -0.101 0.132 -0.77 0.479 1.01
d2 -0.441 0.132 -3.34 0.021 1.01
Nf 0.008 0.127 0.07 0.951 1.00
Nd -0.082 0.127 -0.64 0.548 1.00
fd -0.153 0.127 -1.20 0.283 1.00
R-Sq = 81.82%

The tests showing significant regression and model coefficients were done to show goodness
of the fit for obtained model. These tests had been summarised with help of analysis of variance which
help in identifying factors which significantly affect the response variable. The determination
coefficient (R-Sq) is an important coefficient and it has found to be high at 81.82%, which means that
response model has a good fit with the actual data as shown in Table 4.
Table 5: Analysis of Variance of Ra

Source DF Adj SS Adj MS F-Value P-Value

Model 9 1.44713 0.160793 2.50 0.063
Linear 3 0.56690 0.188966 2.94 0.138
Cutting Speed 1 0.00328 0.003280 0.05 0.830
Feed Rate 1 0.51258 0.512578 7.97 0.037
Depth of Cut 1 0.05104 0.051040 0.79 0.414
Square 3 0.76021 0.253402 3.94 0.087
Cutting Speed*Cutting Speed 1 0.05654 0.056544 0.88 0.392
Feed Rate*Feed Rate 1 0.03767 0.037665 0.59 0.479
Depth of Cut*Depth of Cut 1 0.71646 0.716456 11.14 0.021
2-Way Interaction 3 0.12003 0.040010 0.62 0.631
Cutting Speed*Feed Rate 1 0.00027 0.000272 0.00 0.951
Cutting Speed*Depth of Cut 1 0.02673 0.026732 0.42 0.548
Feed Rate*Depth of Cut 1 0.09303 0.093025 1.45 0.283
Error 5 0.32164 0.064329
Lack-of-Fit 3 0.32164 0.107215 * *
Pure Error 2 0.00000 0.000000
Total 14 1.76878

Analysis of variance (ANOVA) and F-ratio tests have been carried out to check the adequacy
(suitability) of the Table 4 model. For brevity, the ANOVA table of Ra is constructed. Table 5 shows
the analysis of variance table of the second order model proposed for Ra given in the above equation.
Analysis of variance (ANOVA) is used to verify the importance and suitability of the established model.
By checking F-value and P-value, it can be seen that feed rate is the factor that has the greatest influence

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on overall surface roughness, followed by depth of cut. The coefficients in the previous equation
represent the relative influence of each factor on the response, where a positive sign represents the
ability to increase the response and vice versa. It can be seen that the P-value is less than 0.10, indicating
that the model is significant at the 90% confidence level. This means that the model is adequate or
suitable for representing the relationship between the processing response and the final CNC milling
process parameters at a 90% confidence level.
3.3 Optimisation
Checking the graph in Figure 5 below shows that the residuals generally fall in a straight line,
which means that the errors are normally distributed. Furthermore, Figure 6 below shows that there are
no obvious patterns or abnormal (unusual) structures. This means that the proposed model is sufficient
and there is no reason to suspect any violation of the assumption of independence or constant variance.
Since optimisation of machining parameters increases the utility for machining economics and product
quality, efforts have been made to estimate optimal machining conditions to produce the best surface
quality within experimental limitations. In this context, a response surface optimisation is attempted
using Minitab 19 software for centre line average surface roughness in CNC milling. The optimised
objective function is established to minimise the average surface roughness, Ra.

Figure 5: Normal probability plot

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Figure 6: Versus fits

Table 6 below shows the RSM optimisation results of the surface roughness parameters of CNC
milling. The optimisation graph in Figure 7 below shows the effect of each factor (column) on the
response. The vertical red line on the graph represents the current factor setting. The numbers displayed
at the top of the column show the current factor level settings (in red). The horizontal blue lines and the
numbers represent the responses for the current factor level. Minitab 19 calculates that centre line
average roughness are minimised when factors cutting speed are at 960rpm, depth of cut are at 0.50mm,
and feed rate at 500mm/min.
Table 6: Analysis of Variance of Ra

Cutting Feed Depth Ra Composite

Solution Speed Rate of Cut Fit Desirability
1 960 500 0.5 0.1715 1

Figure 7: Optimisation plot

4. Conclusion
The effect of cutting speed, depth of cut and feed rate on the surface roughness have been
studied and analysed by using response surface methodology technique. The parameters were measured
using the experimental design. According to the ANOVA analysis, feed rate affects the most on the
surface roughness. Besides, from the 3D graphs that were plotted, the surface roughness changes
drastically with the increasing of feed rate regardless of the change of depth of cut. Feed rate, cutting
speed and depth of cut are very crucial factors that need to be controlled and chosen carefully. The
optimisation plot has been developed by using Response Surface Methodology, RSM for prediction of
surface roughness in milling. Finally, an attempt has been made to estimate the optimum machining
conditions to produce the best possible surface quality within the experimental constraints.
Acknowledgement
The authors would like to thank the Faculty of Mechanical and Manufacturing Engineering,
Universiti Tun Hussein Onn Malaysia for its support.

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