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greater potential in the dry turning and milling of
ALSi10MG casting alloy compared with PCD and K10.
Vieira et al. [11] investigated the performance of cutting
fluids during HS face milling of steels. They reported
that semi-synthetic cutting fluid exhibited the best
cooling effects in the HS machining process, followed
by the emulsion-based mineral fluid, and the 10%concentration of synthetic fluids. The converse observa-
tion was made on the power consumption. Avila et al.
[12] investigated the effects of the HS cutting fluids on
turning hardened AISI 4340 steel using mixed alumina
(Al2O3+TiC). They found that appropriate use of
emulsion without mineral oil led to better tool life,
surface finish and chip control. Su et al. [1315] studied
the effects of the coated materials on HS milling process
using Taguchi static approach. Their results showed that
multi-layer coating construction has better performance
on the cutting tool wear than single layer at the same
thickness basis.
The research for investigating factors effects of HS
cutting process and improving its performance have
continuously received much attention worldwide. Of the
various study methodologies, Taguchi method is the
preferred approach to undertake the present study as it
has been proved to be an effective and efficient
approach. However, most past Taguchi experiments
concentrated on the optimisation of static or single
quality characteristic, indicating that only a fixed output
target instead of a wide range is developed. A new
parameter design has to be developed whenever a new
process/product is planned, leading to a waste of time
and money.Nowadays the international market in the mold and
die manufacture industry becomes increasingly compe-
titive. To meet customer requirements for short delivery,
high quality, and low cost, the high-speed CNC milling
process must have the capability of versatility, flexibility,
and robustness. Taguchi dynamic approach can be far
more powerful in developing a robust process design
with dynamic quality characteristic. Hence, the main
objective of this study is an attempt to apply Taguchi
dynamic approach to optimise the dimensional quality
of high-speed CNC milling process with dynamic quality
characteristic.
2. Equipments and materials
Feeler QM-22 CNC 3-axis milling machine with the
maximum spindle revolution 30000 rpm was used
throughout the experiments coupled with a c 6 mm
end-milling cutter. Mitutoyo MF Series toolmakers
microscope and SJ-301 surface profiler were used to
measure the dimension and surface roughness of the
machined products, respectively. Tool steels SKD61 and
SKD11 were selected as the materials with the chemical
compositions as displayed in Table 1.
3. Experimental
3.1. Engineered system and Taguchi robust design
As shown in Fig. 1, any man-made machine or
equipment is regarded by Taguchi methods as an
engineered system with a specific function, requested
by customers. The system consists mainly of four
components including control, noise, signal factors,
and output response. A control factor is a factor that
can be selected and fixed to a certain level after
parameter design. However, a noise factor is a factor
that cannot be controlled, due to either practical or
economical reasons. Noise entering a system may take
many forms, and is a true disturbance to the engineered
system. Signal factor is a factor to change the output
response which is what the system is designed toproduce. When the output response of an engineered
system can dynamically vary with the input signal to
generate a range of responses, it has the so-called
dynamic quality characteristic [17].
Engineered system starts to use energy transformation
to carry out its function when the input signal is
received. The process of energy transformation is
governed by the control factors to convert input energy
into intended output energy by using laws of physics.
The engineered system reaches its ideal function when
all of its applied energy is transformed efficiently into
creating desired output energy. However, noise factorsusually cause variability in the energy transformations
leading to unintended outputs.
In every engineered system, there exists some form of
ideal relationship between its input signal and output
response. However, correct identification of an ideal
function is not easy, and ideal function may differ from
case to case. One of the most common ways of
expressing a designs ideal function is
Y fM bM, (1)
where a linear relationship with a slope b exists between
Y (=ideal output response) and M (=input signal) as
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Table 1
The chemical compositions of tool steel [16]
Material Chemical composition (%)
C Si Mn P S Cr Mo V Cu
SKD11 1.5 0.4 0.6 0.03 0.03 12 1.0 0.35 0.25
SKD61 0.37 1.0 0.5 0.03 0.03 5.0 1.25 1.0 0.25
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shown in Fig. 2(a). However, in reality, energy
transformation of any system does not happen as
designed or intended, because there might be noise
factors disturbing the system. The reality of the system
function consists of nonlinear effects between the input
and output that can be mathematically described as
follows:
Yr fM; C1; C2; C3;. . .
; Cm; N1; N2; N3;. . .
; Nn bMferrorM; C1; C2; C3; . . . ; Cm; N1; N2; N3; . . . ; Nn
YferrorM; C1; C2; C3; . . . ; Cm; N1; N2; N3; . . . ; 2Nn,
2
where Yr is the real output response, C1; C2; C3; . . . ; Cmthe control factors, N1; N2; N3; . . . ; Nn the noise factors,and ferror the difference between the ideal function
and the reality. The real function is demonstrated by
Fig. 2(b).
Orthogonal array is well known as one of the most
important tools used in Taguchi robust design because it
provides a fair comparison of any factor. This enablessufficient information to be collected by conducting only
partial series of experiments. Taguchi parameter design
strategy separates the control factors from both the
noises and the signals by using inner and outer arrays,
respectively. Noise factors coupled with signal factor are
assigned to the outer array for exposing the process to
varying noise conditions. An experiment is conducted
for all combinations between the inner and the outer
arrays. The tendencies of control factors, and how these
may affect robustness are evaluated. The best combina-
tion of control factor levels is therefore sought so that
the system becomes most insensitive to noise factors.
When such a technology is developed, it has a robust
function [17].
Taguchi robust design seeks to attain the ideal state of
an engineered system, referred to as the designs ideal
function. Proper level settings of control factors will not
only make the design robust against noise factors, but
also can adjust the output response to the desired target.Therefore, ferror stably gets close to its minimum, and
then Yr approaches to Y bM:
3.2. Proposed ideal function model for CNC milling
system
Fig. 3 is the application of Taguchis concept about an
engineering system in the high-speed CNC machining
process. The high-speed CNC milling system is essen-
tially designed to perform material removal for produ-
cing high-dimensional quality of products requested by
the customers. The input signal, reflecting the intent of
the customers, to the CNC milling system represents
the factor informing system of exactly what job to do. It
can be perceived as the programmed geometrical
dimension of product to be machined for driving
the machining function to transform the solid model
on the PC to the work piece. If there is no energy loss
due to noise factors to create symptoms of poor
function, such as tool wear, vibration, noise, lubricant
aging, etc., the geometrical shape of solid model on the
PC will be accurately duplicated on the work piece.
Hence, the ideal function of the CNC milling systemcan be defined in terms of transformability. The ideal
function Y bM is modelled as Y being the desired
product dimension, M the programmed dimension,
and b 1:
3.3. Robustness evaluation using signal/noise ratio
The signal-to-noise (S/N) ratio originated in the
communication field. Taguchi methods expanded its
function into quality engineering area including staticand dynamic characteristics. As for the dynamic-type
S/N ratio, it is written based on the ideal function of a
product or process that is related with input/output
energy transformation. For any engineered system, as
the input signal, control factors, and noise factors come
together to perform its designed function, their com-
bined impacts on the output response can be evaluated
using the dynamic-type S/Nratio to measure the quality
of energy transformation. As shown in Fig. 3, the output
response of high-speed CNC milling system consists
of the so-called useful and harmful outputs. For a
dynamic quality characteristic application, the concept
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Control Factors
Engineered
SystemsOutput Response
Noise Factors
Signal Factors
Fig. 1. An engineered system model used by Taguchi methods.
Fig. 2. (a) The systems ideal function and (b) its reality.
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of S/N ratio is [17]
Z Useful output
Harmful output
10 logLinear relationship between M and Y
Variability around the linear relationship
10 logb2
s2 , 3
where b is the slope of best-fit line between the measured
values and the inputs, and s2 the variability around the
best-fit line.
The S/N ratio measures the level of system perfor-
mance and the effects of noise factors on performance so
that it can be employed as an indicator of the
consistency of a given system. The higher this ratio,
the more the system is doing what is intended to do
regardless of noise factors and the system is more robust
against noise.
3.4. Control factors and their levels
An L18 is selected for arranging the overall experi-
mental tests. Eight dominant process conditions
of the high-speed CNC milling process are identi-
fied as the control factors, which are listed in Table 2
together with their alternative levels. It is noted
that most of the factors has three levels except factor
A, which has two. All levels are selected for proper
reasons.
3.5. Noise factors
Generally, there are a lot of noise factors associated
with the high-speed CNC milling process, such as,
material lot, machine setting variability, material hard-
ness variability, lubricant condition, tool wear, and
manufacturing variability of milling machine, etc. Due
to hard control, Taguchi methods suggested the use of
the compounding strategy to arrange them to be two
extreme conditions. For the simplification of experi-
mentation, only material hardness variability is chosen
as the noise factor. The identified two noise conditions
of N1 and N2 are displayed in Table 3. It is designed so
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Fig. 3. The schematic of an engineering system as a high-speed CNC milling system.
Table 2
Control factors and their levels
Control
factors
Level
1 2 3
A Milling type Downward
mill
Upward
mill
B Cutting speed
(m/min)
150 225 300
C Feed per tooth
(mm/tooth)
0.03 0.04 0.05
D Film material TiCN TiN TiAlN
E Tool material K10 (Co 8%) K20 (Co
10%)
K30 (Co
12%)
F Number of tooth 2 3 4
G Rake angle 41 71 101
H Helix angle 301 351 451
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because that from the standpoint of energy the softer
material is easier to be machined, and vice versa.
3.6. Test piece and signal arrangements
How to vary the signals experimentally is also one of
the most important steps in the Taguchi robust design.Since some of the research objectives are to develop
versatility and flexibility into the high-speed CNC mill-
ing process, the optimised technology development must
be applicable to a family of products and future pro-
ducts. Therefore, it is most effective to specify the signal
levels so that the range covers all usage conditions.
In view of this goal, test piece with a range of
geometrical characteristics is designed for the study. Allof the test workpieces is finish machined with a constant
depth of cut of 0.1 mm. The test piece is easier to
measure dimensions and would allow them to evaluate
multiple levels of the signal easily. Fig. 4 illustrates
the test piece we designed for the study. As shown in
Fig. 4(a), the test piece has three typical of geometrical
characteristics to be machined, including rectangular,
circle, and triangle on each of three layers with a volume
ratio of 1:2:3.
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Table 3
Noise factors arranged as two extreme conditions
Noise factors Material Hardness (HRC)
N1 (positive side extreme condition) SKD11 2123
N2 (negative side extreme condition) SKD61 1719
Fig. 4. The designed test piece for experimentations: (a) solid modeling, (b) top view with the programmed vertices, diameters, and circle center, (c)
side view.
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As illustrated in Fig. 4(b), the zero point is fixed on
the (0,0) point on the southwest corner. All locations on
the rectangular and triangles are defined by positive X
and Y coordinates relative to the fixed origin. The
diameters of three circles are defined in the same
fashion, but in relation to their fixed center point (Pi;i=2527). The programmed dimensions for positioning
the various vertices, diameters, and the common circle
center are listed in Table 4. There are a total of 51 of the
programmed dimensions used as the input signals in an
incremental way.
4. Experimental results and analysis
4.1. General effects of control factors
Fig. 5 plots the entire experimental results as the
input/output relationship that shows slight scattering
phenomena due to noise effects. Table 5 displays a
complete experimental layout, resultant data, and
performance evaluation. The linearity effects of each
experimental arrangement are evaluated by computing
their dynamic S/N ratios as shown in Table 5. The
slopes of the best-fit line for the defined ideal function
model are calculated using simple linear regression
analysis and listed in Table 5. Another importantmeaning of the combination and S/N ratio and slope
here is that it represents the input/output transform-
ability of high-speed CNC milling system under the
defined experimental conditions. That is, the larger S/N
ratio coupled with near-one slope, the higher both the
linear effects and the transformability between input and
output. Those S/N data can be further translated into
the effect each control factor has on S/N by computing
their average values as listed in Table 6. Fig. 6 is its
response graph.
Table 6 suggests that the best levels for each control
factors are A1; B1; C3; D3; E2; F3; G1; and H1 due to
their maximum S/N ratios. The maxmin value is
equal to the range of S/N ratio variance due to the
change in the level setting. The larger the range,
the more powerful impact the control factor has on
the dimensional precision. The ranking in Table 6
demonstrates that factor A (milling type), factor B
(cutting speed), and factor F (number of tooth) have
relatively strong impacts on the dimensional precision,
while C, D, E, G, and H have relatively weak impacts.
Factors A, B, and F should be strictly controlled for
high-dimensional precision during the high-speed CNC
milling process.
Factor B (cutting speed) has been found to be the
most important factor governing process robustness
(dimensional quality) because of the maximum changein S/Nratios. It is due to cutting speed directly affecting
tool wear. This is why the lowest speed level B1 results
in the best dimensional quality. Factor A (milling type)
is identified as the second due to its significant influence
in vibration. A1 is downward milling type, causing
smaller vibration. Factor F (number of tooth) is the
third. F3 is the best level setting due to smaller cutting
force.
The slope of the best-fit line in the study technically
denotes the overcutting or undercutting effects of
the machined products. When the slope is greater
than 1, the machined product has the undercuttingeffects, the larger the more serious, and vice versa.
It is noted in Table 5 that all of the arranged
experimental conditions in L18 array led to under-
cutting effects. Table 7 shows the average effects
each control factors have on slope and Fig. 7 is its
response graph. The same observation about under-
cutting effects is made for all of the control factors.
The ranking in Table 7 displays that control factors A,
B, and F have stronger cutting effects on the dimen-
sional accuracy of machined products. Of the control
factors, factor A is the most important due to its largest
impact.
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Table 4
Input signals, and their corresponding positions and programmed dimensions
Input signal M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 M12 M13 M14Position P1X P1Y P6Y P7X P19Y P2X P8X P2Y P5Y P20Y P3X P9X P3Y P6Y
Programmed dimension (mm) 2.4 2.4 2.4 2.4 2.4 5.55 5.55 6.4 6.4 6.4 9.06 9.06 12.4 12.4
Input signal M15 M16 M17 M18 M19 M20 M21 M22 M23 M24 M25 M26 M27 M28
Position P19Y P24 P13Y P14Y P15Y P25Y P26Y P27Y P23 P6X P12X P5X P11X P23Programmed dimension (mm) 12.4 19.2258 24.9 24.9 24.9 24.9 24.9 24.9 27.1894 29.04 29.04 32.55 32.55 33.3
Input signal M29 M30 M31 M32 M33 M34 M35 M36 M37 M38 M39 M40 M41 M42
Position P4X P10X P9Y P12Y P18Y P8Y P11Y P17Y P7Y P10Y P16Y P25X P26X P27XProgrammed dimension (mm) 35.7 35.7 37.4 37.4 37.4 43.4 43.4 43.4 47.4 47.4 47.4 58.425 58.425 58.425
Input signal M43 M44 M45 M46 M47 M48 M49 M50 M51
Position P13X P14X P15X P21X P21X P17X P20X P18X P19XProg rammed dimensi on ( mm) 81. 15 84. 3 87. 81 1 07 .79 10 7. 79 1 11 .3 1 11 .3 114 .4 5 11 4.4 5
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4.2. Analysis of variance (ANOVA)
The analysis of variance (ANOVA) on the experi-
mental results is performed to evaluate the source of
variation during the high-speed CNC milling process.
From the analysis, it is easy to identify which factors are
the most important in terms of quality characteristic.
Consequently, those important factors have to be
carefully monitored during the process for a consistently
high-quality product.
Table 8 shows the ANOVA that is done on
the S/N ratios. It is therefore easy to see that
factors A, B, and F are the most important in terms
of dimensional quality. These three factors account
for about 65 percent of the experimental variance.
The observation agrees well with those reflected in
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Table 5
Experimental layout, resultant data, and performance evaluation
NO Control factors M1 (2.4mm) M2 (2.4mm) M50 (114.45mm) M51 (114.45mm) Performance evaluation
A B C D E F G H N 1 N2 N1 N2 N1 N2 N1 N2 S/N (db) Slope (b)
1 1 1 1 1 1 1 1 1 2.3392 2.3474 2.3547 2.3565 114.5024 114.4947 114.4930 114.4514 26.3816 1.000001
2 1 1 2 2 2 2 2 2 2.3426 2.3960 2.3956 2.3908 114.4463 114.5182 114.4510 114.4645 30.0520 1.000051
3 1 1 3 3 3 3 3 3 2.4030 2.3968 2.3848 2.4046 114.5107 114.4803 114.5012 114.4508 31.5543 1.000270
4 1 2 1 1 2 2 3 3 2.2512 2.3144 2.2703 2.3849 114.5619 114.5108 114.5201 114.4604 21.4463 1.000260
5 1 2 2 2 3 3 1 1 2.3269 2.3904 2.3280 2.3733 114.5227 114.4910 114.5659 114.4735 26.1627 1.000324
6 1 2 3 3 1 1 2 2 2.2854 2.3493 2.3074 2.3755 114.6139 114.6169 114.6715 114.6003 21.1510 1.000929
7 1 3 1 2 1 3 2 3 2.1593 2.3501 2.2139 2.3792 114.6374 114.4911 114.6078 114.4749 19.6770 1.000283
8 1 3 2 3 2 1 3 1 2.3809 2.3657 2.3372 2.3376 114.5573 114.4899 114.5087 114.4664 24.1879 1.000105
9 1 3 3 1 3 2 1 2 2.3296 2.3652 2.3396 2.3929 114.5438 114.4695 114.5461 114.4281 23.6981 1.000300
10 2 1 1 3 3 2 2 1 2.3458 2.3863 2.3265 2.3925 114.5476 114.4933 114.5326 114.4704 24.0331 1.000273
11 2 1 2 1 1 3 3 2 2.3134 2.3033 2.3096 2.3656 114.5829 114.4428 114.6165 114.5200 20.7488 1.000213
12 2 1 3 2 2 1 1 3 2.3379 2.3653 2.3447 2.3524 114.6115 114.5321 114.6151 114.5331 22.4899 1.000859
13 2 2 1 2 3 1 3 2 2.1212 2.3235 2.0641 2.3146 114.8699 114.5506 114.8776 114.5712 14.0266 1.001444
14 2 2 2 3 1 2 1 3 2.3485 2.3645 2.3459 2.3810 114.5181 114.4941 114.5665 114.4937 21.7157 1.000340
15 2 2 3 1 2 3 2 1 2.3382 2.3878 2.3158 2.3966 114.5993 114.4978 114.6720 114.4842 24.3425 1.000624
16 2 3 1 3 2 3 1 2 2.3256 2.3925 2.3223 2.3645 114.5560 114.5319 114.5801 114.5310 25.4485 1.000453
17 2 3 2 1 3 1 2 3 2.0989 2.2817 2.1220 2.3633 114.7854 114.5193 114.7802 114.4915 13.8235 1.001144
18 2 3 3 2 1 2 3 1 2.1808 2.3856 2.1357 2.2879 114.8085 114.5074 114.7783 114.5056 16.4607 1.001239
Table 6
S/N ratio response table
Level A B C D E F G H
1 24.9234 25.8766 21.8355 21.7401 21.0225 20.3434 24.3161 23.5947
2 20.3433 21.4741 22.7818 21.4781 24.6612 22.9010 22.1798 22.5208
3 20.5493 23.2828 24.6817 22.2164 24.6556 21.4041 21.7845
Maxmin 4.5802 5.3274 1.4472 3.2036 3.6387 4.3122 2.9120 1.8103Ranking 2 1 8 5 4 3 6 7
0
10
20
30
40
50
60
70
80
90
100
110
120
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120
Programmed dimension(mm)
Product
dimension(mm)
Fig. 5. The complete results plotted as the input/output relationship.
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Table 6 and Fig. 6. Additionally, error contributing
about 3.4% to total variance indicates that experi-
mentation is fairly successful and reliable. It is also
found that ANOVA has almost the same function as
Table 6 except for the provision of more detailed
information.
4.3. High-speed CNC milling process optimisation
The goal for study is to seek a robust process design
for which the high-speed CNC milling process can
always produce a variety of products with high-
dimensional quality. To meet this goal, Taguchi
proposed a two-step optimisation strategy in obtaining
the best process conditions. The two-step optimisation
strategy reduces the variations in the product dimension
in the first step and then adjusts the slope of the bestfitting line to the desired level. The optimisation is:
Step 1: reduce dimensional variability. To produce the
strongest linear relation between signal factor (M=pro-
grammed dimension) and output response (Y=product
dimension), it is necessary to reduce dimensional
variability. As such, the optimal levels for each control
factors are those levels that maximise S/Nratios leading
to a robust machining performance, i.e. high-dimen-
sional precision. The selected levels are A1; B1; C3; D3;E2; F3; G1; and H1:
Step 2: adjust slope to the desired level. According to
the dynamic formula Y bM; it appears to select the
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26.6333
A1 A2 B1 B2 B3 C1 C2 C3 D1 D2 D3 E1 E2 E3 F1 F2 F3 G1 G2 G3 H1 H2 H3
Controlfactors and their levels
S/Nratio(db)
22.6333
18.6333
Fig. 6. S/N ratio response graph.
Table 7
Slope response table
Level A B C D E F G H
1 1.000280 1.000278 1.000452 1.000424 1.000501 1.000747 1.000379 1.000428
2 1.000732 1.000653 1.000363 1.000700 1.000392 1.000410 1.000551 1.000565
3 1.000587 1.000703 1.000395 1.000626 1.000361 1.000588 1.000526
Max-min 0.000452 0.000376 0.000341 0.000305 0.000234 0.000386 0.000209 0.000137Ranking 1 3 4 5 6 2 7 8
1.000206
1.000506
1.000806
A1 A2 B1 B2 B3 C1 C2 C3 D1 D2 D3 E1 E2 E3 F1 F2 F3 G1 G2 G3 H1 H2 H3
Control factors and their levels
Slope
Fig. 7. Slope response graph.
Table 8
Analysis of variance
Control factors S F V r (%)
A 94.4012 1 94.4012 24.5815
B 97.2363 2 48.6181 25.3198
C 6.4818 2 3.2409 1.6878
D 37.9696 2 18.9848 9.8871
E 41.2854 2 20.6427 10.7505
F 56.4299 2 28.2149 14.6940
G 27.2900 2 13.6450 7.1062
H 9.9452 2 4.9726 2.5897
Error 12.9939 2 6.4970 3.3835
Total 384.0333 100
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slope (b) closer to 1 for higher machining accuracy.
However, it must be noted that the adjustment of the
slope is best not to affect the process robustness. Based
on this principle, since all other control factors working
at the optimal level have already achieved both highest
S/N ratios and smallest slopes, the slope for control
factor C (feed per tooth) is the best choice foradjustment. It is therefore predicted that the change
from C3 to C2 leads to a highest machining accuracy
without significantly affecting process robustness. Thus,
the predicted optimal combination is selected as A1; B1;C2; D3; E2; F3; G1; and H1:
4.4. Optimal performance forecasting
Taguchi methods require a confirmation run to check
for both the validity of experimentation and, also the
reproducibility of the experimental results. It is im-
portant to predict the performance under the optimal
conditions before running the confirmation. The pre-
dictions of S/N ratio and slope for the optimal
conditions can be calculated by means of the additively
law as follows:
For the optimal conditions: A1; B1; C2; D3; E2; F3; G1;H1
Zopt A1 B1 C2 D3 E2 F3 G1 H1 7TZ
24:9234 25:8766 23:2828 24:6817 24:6612
24:6556 24:3161 23:5947 7 22:6333
37:5588 db,
bopt A1 B1 C2 D3 E2 F3 G1 H1 7Tb
1:000280 1:000278 1:000363 1:000395
1:000392 1:000361 1:000379 1:000428
7 1:000506
0:999334.
For the initial conditions: A1; B1; C1; D1; E1; F1; G1; H1
Zinitial A1 B1 C1 D1 E1 F1 G1 H1 7TZ
24:9234 25:8766 21:8355 21:7401 21:0225
20:3434 24:3161 23:5947 7 22:6333
25:2190 db,
binitial A1 B1 C1 D1 E1 F1 G1 H1 7Tb
1:000280 1:000278 1:000452 1:000424
1:000501 1:000747 1:000379 1:000428
7 1:000506
0:999946,
where TZ and Tb represented the average effects of the
overall control factors.
As a result, 12.3398 db db gain in S/N ratio is
predicted.
4.5. Confirmation run
Fig. 8 is plotted from confirmation results for the
optimal conditions. Table 9 is the comparison of the
prediction and the confirmation between the initial and
the optimal conditions. It is noted that the confirmed
S/N ratio 37.2933 db for the optimal conditions is still
the best when compared to the entire results in Table 5.
The actual gain is 10.9117 db that is very close to the
predicted 12.3398 db. This indicates the best combina-
tion of the control factors level setting is robust enough
against noise effects and results in high reproducibility.
Accordingly, as demonstrated in Fig. 8, there is a very
strong linear relationship between the input pro-
grammed dimension and the product dimension.
Furthermore, the % variability range improved can be
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y = 1.000101 x
0
10
20
30
40
50
60
70
80
90
100
110
120
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120
Programmed dimension (mm)
Productdimension(m
m)
Fig. 8. Plot of the confirmation results as input/output relationship.
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calculated by the equation
% variabilityrange improved 1
2
gain=6
% variability rangeinitial. 4
So the gain of 10.9117 db is equivalent to reducing thevariation range by 10.5(10.9117/6)=71.6508 which in-
dicates that the process robustness has improved 3.53
times.
It is also noted in Fig. 8 that using simple regression
analysis of the confirmation run data generates the best-
fit line equation Y=1.000101X. This is in practice the
best functional relationship between input signal and
output response of the high-speed CNC milling system
under the optimal conditions. It can be estimated
through the equation Y=1.000101M that the under-
cutting of the machined product dimension is
1:000101 M M=M 100% 0:0101%.
If there is still a need to adjust the product dimension for
suitable dimensional allowance for meeting post-proces-
sing and customer requirements, the input programmed
dimension can be modified through the following
mathematical relationship:
adjusted 1
1:000101Yfinal, (5)
where Madjusted is the adjusted input programmeddimension, and Yfinal is the desired final product
dimension.
4.6. Cutter flank wear and work piece surface roughness
analysis
Table 10 shows the cutter flank wear and the work
piece surface roughness analysis comparison between
the raw experimental runs and the confirmation trial.
Flank wear values are the average of the data mea-
sured on each tooth of the milling cutter. Roughness
values are the average of 18 data measured on thesurface of the machined product. It is clear that
the average flank wear values are among the range
of 132.43411887.0565mm for N1 condition and of
60.9085375.2826mm for N2 condition. The average
surface roughness values are found among the range of
0.25330.4833mm for N1 and of 0.18330.3617mm for
N2 condition. The results indicate that for both the
cutter flank wear and the work piece surface roughness,
N2 is appreciably better than N1 because of their lower
values plus with narrower ranges. This is due to that
material used in N1 is harder, causing more cutting tool
wear and then worse surface quality.
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Table 9
The comparison between the prediction and the confirmation
Level combination Prediction Confirmation
S/N (db) Slope (b) S/N (db) Slope (b)
Initial A1B1C1D1E1F1G1H1 25.2190 0.999946 26.3816 1.000001
Optimum A1B1C2D3E2F3G1H1 37.5588 0.999334 37.2933 1.000101
Gain 12.3398 10.9117
Table 10
Cutter flank wear and work piece surface roughness results
NO Control factors Average flank wear (mm) Average roughness: Ra (mm)
A B C D E F G H N 1 N2 N1 N2
1 1 1 1 1 1 1 1 1 323.8422 215.8492 0.2533 0.1844
2 1 1 2 2 2 2 2 2 417.3984 140.2617 0.4028 0.1911
3 1 1 3 3 3 3 3 3 136.6434 133.7832 0.3983 0.3617
4 1 2 1 1 2 2 3 3 275.0565 194.1669 0.2556 0.1833
5 1 2 2 2 3 3 1 1 477.6723 158.6058 0.3600 0.2461
6 1 2 3 3 1 1 2 2 729.1758 60.9085 0.2856 0.2361
7 1 3 1 2 1 3 2 3 945.8786 177.0516 0.3867 0.3189
8 1 3 2 3 2 1 3 1 537.9706 86.3831 0.2756 0.2811
9 1 3 3 1 3 2 1 2 1283.2963 167.0189 0.4394 0.3344
10 2 1 1 3 3 2 2 1 132.4341 97.5158 0.3178 0.2767
11 2 1 2 1 1 3 3 2 323.2417 154.5529 0.2694 0.2733
12 2 1 3 2 2 1 1 3 725.3799 273.2197 0.3778 0.2739
13 2 2 1 2 3 1 3 2 1470.6875 375.2826 0.4833 0.2250
14 2 2 2 3 1 2 1 3 229.2672 338.1873 0.3289 0.3039
15 2 2 3 1 2 3 2 1 202.1113 67.3019 0.3667 0.3106
16 2 3 1 3 2 3 1 2 620.2814 119.4116 0.3428 0.3261
17 2 3 2 1 3 1 2 3 747.5027 117.9605 0.3806 0.2378
18 2 3 3 2 1 2 3 1 1887.0565 124.0422 0.3472 0.3578
Confirmed 1 1 2 3 2 3 1 1 180.6815 79.9970 0.3111 0.2244
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It is noted in Figs. 9(a), (c), (e), and (g) that the
optimal conditions results in better form shape at the
corners of the machined products. It is also observed in
Figs. 9(b), (d), (f), and (h) that flank wear has been
significantly improved at the optimal conditions which
has 180.6815mm for N1 condition, and 79.9970 mm for
N2 condition. Compared to the entire results in the L18
array, they are better than most of the data. Similar
observation is made on the surface roughness analysis.
It seems to point out that the optimised processparameters developed in terms of dimension vs. dimen-
sion also works in both the reduction in tool wear and
the improvement in surface roughness.
4.7. Conclusion remarks
The study using Taguchi dynamic experiment coupled
with the ideal function model of programmed dimension
vs. product dimension has been very successful in
developing a robust, versatile, high-dimensional quality
of high-speed CNC milling technology. Based on the
experimental results, conclusions can be drawn as
follows:
1. The optimised control factors are: A1 (milling type),
B1 (cutting speed), C2 (feed per tooth), D3 (film
material), E2 (tool material), F3 (number of tooth),
G1 (rake angle), and H1 (helix angle).
2. The most important factors identified by S=N andANOVA analysis affecting the process robustness are
in a decreasing manner: factor B (cutting speed),factor A (milling type), and F (number of tooth).
They account for about 65% of total variance.
3. Actual gain 10.9117 db is very close to the predicted
12.3398 db. It shows very good reproducibility and
confirms the success of the experiment.
4. Dimensional variability after process optimization
has been significantly improved to be 28.3492% of
the initial conditions, leading to 3.55903 times
improvement in the process robustness.
5. The optimal function between input signal and
output response can be linearly described as
Y=1.000101M.
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Fig. 9. OM photographs of the form shape of the machined products and the flank wear of the cutting tools. (a), (b), (c), and (d) are for the initialconditions and (e), (f), (g), (h) for the optimal conditions.
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