ejemplo de taguchi en proceso de perforado
TRANSCRIPT
7/30/2019 Ejemplo de Taguchi en Proceso de Perforado
http://slidepdf.com/reader/full/ejemplo-de-taguchi-en-proceso-de-perforado 1/9
Journal of Materials Processing Technology 145 (2004) 84–92
Application of Taguchi method in the optimizationof end milling parameters
J.A. Ghani, I.A. Choudhury∗, H.H. Hassan Department of Engineering Design and Ma nufacture, Faculty of Engineering, Universiti Malaya, 50603 Kuala Lumpur, Malaysia
Received 17 April 2002; received in revised form 17 April 2002; accepted 25 June 2003
Abstract
This paperoutlines the Taguchi optimizationmethodology, whichis applied to optimize cuttingparametersin end millingwhen machining
hardened steel AISI H13 with TiN coated P10 carbide insert tool under semi-finishing and finishing conditions of high speed cutting. Themilling parameters evaluated are cutting speed, feed rate and depth of cut. An orthogonal array, signal-to-noise (S/N) ratio and Pareto
analysis of variance (ANOVA) are employed to analyze the effect of these milling parameters. The analysis of the result shows that the
optimal combination for low resultant cutting force and good surface finish are high cutting speed, low feed rate and low depth of cut.
Using Taguchi method for design of experiment (DOE), other significant effects such as the interaction among milling parameters are also
investigated. The study shows that the Taguchi method is suitable to solve the stated problem with minimum number of trials as compared
with a full factorial design.
© 2003 Elsevier B.V. All rights reserved.
Keywords: Taguchi method of DOE; High speed end milling; Hardened steel AISI H13; TiN coated carbide insert tool
1. Introduction
Robust design is an engineering methodology for obtain-ing product and process conditions, which are minimally
sensitive to the various causes of variation to produce
high-quality products with low development and manufac-
turing costs [1]. Taguchi’s parameter design is an important
tool for robust design. It offers a simple and systematic
approach to optimize design for performance, quality and
cost. Two major tools used in robust design are [1–3]:
• signal to noise ratio, which measures quality with empha-
sis on variation, and
• orthogonal arrays, which accommodate many design fac-
tors simultaneously.
When a critical quality characteristic deviates from the target
value, it causes a loss [2]. Continuously pursuing variability
reduction from the target value in critical quality character-
istics is the key to achieve high quality and reduce cost.
The successful applications of Taguchi methods by both
engineers and statisticians within British industry have lead
to the formation of UK Taguchi Club [4]. Taguchi’s ap-
proach is totally based on statistical design of experiments
[1], and this can economically satisfy the needs of problem
∗ Corresponding author.
solving and product/process design optimization [5]. By ap-
plying this technique one can significantly reduce the time
required for experimental investigation, as it is effective ininvestigating the effects of multiple factors on performance
as well as to study the influence of individual factors to de-
termine which factor has more influence, which less [1,5].
Some of the previous works that used the Taguchi method
as tool for design of experiment in various areas including
metal cutting are listed in Refs. [6–12].
This paper describes a case study on end milling parame-
ters at three levels each. The main objective is to find a com-
bination of milling parameters to achieve low cutting force
and surface roughness. Fig. 1 shows the overall set up of
the experiment, and Fig. 2 shows the geometry of two flutes
end milling cutter assembly and detailed insert dimension.
2. Taguchi method, design of experiment, and
experimental details
2.1. Taguchi method
Taguchi defines the quality of a product, in terms of the
loss imparted by the product to the society from the time
the product is shipped to the customer [13]. Some of these
losses are due to deviation of the product’s functional char-
acteristic from its desired target value, and these are called
0924-0136/$ – see front matter © 2003 Elsevier B.V. All rights reserved.
doi:10.1016/S0924-0136(03)00865-3
7/30/2019 Ejemplo de Taguchi en Proceso de Perforado
http://slidepdf.com/reader/full/ejemplo-de-taguchi-en-proceso-de-perforado 2/9
J.A. Ghani et al. / Journal of Materials Processing Technology 145 (2004) 84–92 85
Fig. 1. Schematic of the experimental set-up.
losses due to functional variation. The uncontrollable fac-
tors which cause the functional characteristics of a product
to deviate from their target values are called noise factors,
which can be classified as external factors (e.g. temperatures
and human errors), manufacturing imperfections (e.g. unit
to unit variation in product parameters) and product deteri-
oration. The overall aim of quality engineering is to make
products that are robust with respect to all noise factors.
The most important stage in the design of an experiment
lies in the selection of control factors. As many factors as
possible should be included, so that it would be possible toidentify non-significant variables at the earliest opportunity.
Taguchi creates a standard orthogonal array to accommo-
date this requirement. Depending on the number of factors,
Fig. 2. Geometries of two fluted end milling cutter and insert.
interactions and levels needed, the choice is left to the user
to select either the standard or column-merging method or
idle-column method etc.
Taguchi used the signal-to-noise (S/N) ratio as the quality
characteristic of choice [1,13]. S/N ratio is used as a measur-
able value instead of standard deviation due to the fact that
as the mean decreases, the standard deviation also decreases
and vice versa. In other words, the standard deviation cannot
be minimized first and the mean brought to the target.
Taguchi has empirically found that the two stage opti-
mization procedure involving S/N ratios indeed gives theparameter level combination, where the standard deviation
is minimum while keeping the mean on target [13]. This
implies that engineering systems behave in such a way that
7/30/2019 Ejemplo de Taguchi en Proceso de Perforado
http://slidepdf.com/reader/full/ejemplo-de-taguchi-en-proceso-de-perforado 3/9
86 J.A. Ghani et al. / Journal of Materials Processing Technology 145 (2004) 84–92
the manipulated production factors can be divided into three
categories:
1. Control factors, which affect process variability as mea-
sured by the S/N ratio.
2. Signal factors, which do not influence the S/N ratio or
process mean.
3. Factors, which do not affect the S/N ratio or processmean.
In practice, the target mean value may change during the
process development.
Two of the applications in which the concept of S/N ra-
tio is useful are the improvement of quality through vari-
ability reduction and the improvement of measurement. The
S/N ratio characteristics can be divided into three categories
when the characteristic is continuous:
nominal is the best characteristic : S/N = 10 logy
s2y
smaller the better characteristics :
S/N = −10 log1
n
y2
and
larger the better characteristics :
S/N = −10 log1
n
1
y2
where y is the average of observed data, s2y the variance of
y, n the number of observations, and y the observed data.
For each type of the characteristics, with the above S/Nratio transformation, the higher the S/N ratio the better is
the result.
2.2. Design of experiment
In this experiment with three factors at three levels each,
the fractional factorial design used is a standard L 27 (313)
orthogonal array [1]. This orthogonal array is chosen due to
its capability to check the interactions among factors. Each
row of the matrix represents one trial. However, the sequence
in which these trials are carried out is randomized. The three
levels of each factor are represented by a ‘0’ or a ‘1’ or a
‘2’ in the matrix.
The factors and levels are assigned as in Table 1 accord-
ing to semi-finishing and finishing conditions for the said
material when machining at high cutting speed.
Factors A, B, and C are arranged in columns 2, 5 and 6,
respectively, in the standard L27 (313) orthogonal array as
shown in Appendix A.
2.3. Experimental details
The machining trials were carried out on a Cincinnati Mi-
lacron Sabre 750 VMC in dry condition, as recommended
Table 1
Factors and levels used in the experiment (axial depth of cut is kept
constant at 3 mm)
Factor Level
0 1 2
A—speed (m/min) 224 280 355
B—feed (mm per tooth) 0.1 0.16 0.25C —radial depth of cut (mm) 0.3 0.5 0.8
Table 2
The chemical composition of workmaterial in percentage by weight
C 0.37
Si 0.9
Mn 0.46
P 0.014
S 0.02
Ni 0.11
Cr 5.34
Cu 0.4
Mo 1.25
V 1
by the tool supplier for the specific workmaterial. The insert
used was flat end mill TiN coated carbide. The detail geome-
try of two flutes end milling cutter assembly and detailed in-
sert dimension are shown in Fig. 2. The cutting forces in X , Y ,
and Z directions were measured online during the milling op-
eration using Kistler dynamometer model 9275 A. The sur-
face roughness was measured using surface roughness tester
model Mpi Mahr Perthometer. Table 2 shows the chemical
composition of workmaterial in percentage by weight.
3. Experimental results and data analysis
The objective of experiment is to optimize the milling pa-
rameters to get better (i.e. low value) surface roughness and
resultant force values, the smaller the better characteristics
are used. Table 3 shows the actual data for surface rough-
ness and resultant force along with their computed S/N
ratio. Whereas Tables 4 and 5 show the mean S/N ratio for
each levels of surface roughness and resultant force, respec-
tively. These data were then plotted as shown in Figs. 3 and
4, respectively.
3.1. Conceptual S/N ratio approach
Taguchi recommends analyzing the means and S/N ratio
using conceptual approach that involves graphing the effects
and visually identifying the factors that appear to be sig-
nificant, without using ANOVA, thus making the analysis
simple [3].
The average S/N ratios for smaller the better for surface
roughness and resultant force factors and significant inter-
action are shown in Figs. 3 and 4, respectively. Study of
Fig. 3 suggests that cutting speed (factor A) and interaction
7/30/2019 Ejemplo de Taguchi en Proceso de Perforado
http://slidepdf.com/reader/full/ejemplo-de-taguchi-en-proceso-de-perforado 4/9
J.A. Ghani et al. / Journal of Materials Processing Technology 145 (2004) 84–92 87
Table 3
Experimental results for surface roughness, resultant force and their corresponding S/N ratio
Experimental
run
Factor Designation Measured parameters Calculated S/N ratio
A B C Surface roughness,
Ra (m)
Resultant
force (N)
S/N ratio for
Surface roughness
S/N ratio for
Resultant force
1 0 0 0 A0 B0C 0 0.207 469 1.368 −5.342
2 0 1 1 A0 B1C 1 0.169 1277 1.544 −6.2123 0 2 2 A0 B2C 2 0.513 2175 0.580 −6.675
4 1 0 0 A1 B0C 0 0.245 503 1.222 −5.403
5 1 1 1 A1 B1C 1 0.252 1167 1.197 −6.134
6 1 2 2 A1 B2C 2 0.27 2144 1.137 −6.662
7 2 0 0 A2 B0C 0 0.531 649 0.550 −5.624
8 2 1 1 A2 B1C 1 0.579 736 0.475 −5.734
9 2 2 2 A2 B2C 2 0.615 1831 0.422 −6.525
10 0 0 1 A0 B0C 1 0.231 1229 1.273 −6.179
11 0 1 2 A0 B1C 2 0.448 1746 0.697 −6.484
12 0 2 0 A0 B2C 0 0.418 1563 0.758 −6.388
13 1 0 1 A1 B0C 1 0.203 1125 1.385 −6.102
14 1 1 2 A1 B1C 2 0.671 1716 0.347 −6.469
15 1 2 0 A1 B2C 0 0.234 1446 1.262 −6.320
16 2 0 1 A2 B0C 1 0.263 1225 1.160 −6.176
17 2 1 2 A2 B1C 2 0.608 1334 0.432 −6.25018 2 2 0 A2 B2C 0 0.657 1208 0.365 −6.164
19 0 0 2 A0 B0C 2 1.045 1085 −0.038 −6.071
20 0 1 0 A0 B1C 0 0.756 949 0.243 −5.955
21 0 2 1 A0 B2C 1 0.872 1736 0.119 −6.479
22 1 0 2 A1 B0C 2 1.424 1203 −0.307 −6.161
23 1 1 0 A1 B1C 0 0.872 1179 0.119 −6.143
24 1 2 1 A1 B2C 1 0.888 1944 0.103 −6.577
25 2 0 2 A2 B0C 2 1.392 1761 −0.287 −6.492
26 2 1 0 A2 B1C 0 1.024 1270 −0.021 −6.208
27 2 2 1 A2 B2C 1 1.202 1826 −0.160 −6.523
between feed rate and depth of cut (interaction B × C) are
more significant. Feed rate (factor B) and depth of cut (fac-
tor C ) are insignificant. The highest cutting speed ( A2) ap-
pears to be the best choice to get low value of surface finish,
and thus making the process robust to the cutting speed in
particular. The feed rate (factor B) and depth of cut (factor
C ) are insignificant on the average S/N response. Since the
interaction B×C is significant, Park [1] has recommended
to use the two ways B × C table to select their levels as
calculated and tabulated in Appendix B(a). From the two
ways B × C table, the optimum combination for factor B
and factor C to get the best result is B0C 1 as explained in
[1]. Therefore, the optimal combination to get low value of
surface roughness is A2 B0C 1 within the tested range.
Table 4
Response table for average S/N ratio for surface roughness factors and
significant interaction
Symbol Cutting
parameter
Mean S/N ratio
Level 0 Level 1 Level 2 Maximum−
minimum
A Cutting speed 0.727 0.718 3.144 2.426
B Feed rate 0.703 0.559 0.605 0.144
C Depth of cut 0.652 0.788 0.331 0.457
B × C Interaction
B × C
0.944 0.853 −0.025 0.969
Study of Fig. 4 suggests that feed rate (factor B) and depth
of cut (factor C ) are more significant, followed by the inter-
action between feed rate and depth of cut (interaction B×C)
on average S/N response for cutting force. Cutting speed
(factor A) is insignificant as the slope gradient is very small.
The same procedure as in the surface roughness response is
used to find the best combination for interaction B × C as
calculated in Appendix B(b).
From the two ways B × C table, it is found that B0C 0is the best combination to lower the cutting force during
machining within the range of experiment. Since cutting
speed (factor A) is insignificant, it could be set at the highest
cutting speed to obtain high rate of metal removal or at the
lowest cutting speed to prolong the tool life depending on
Table 5
Response table for average S/N ratio for resultant force factors and
significant interaction
Symbol Cutting
parameter
Mean S/N ratio
Level 0 Level 1 Level 2 Maximum−
minimum
A Cutting speed −6.198 −6.219 −6.188 −0.0301
B Feed rate −5.950 −6.176 −6.475 −0.525
C Depth of cut −5.949 −6.235 −6.421 −0.472
B × C Interaction
B × C
−6.035 −6.281 −6.29 −0.255
7/30/2019 Ejemplo de Taguchi en Proceso de Perforado
http://slidepdf.com/reader/full/ejemplo-de-taguchi-en-proceso-de-perforado 5/9
88 J.A. Ghani et al. / Journal of Materials Processing Technology 145 (2004) 84–92
Fig. 3. The smaller the better S/N graph for surface roughness.
application. However, analysis of Tables 6 and 7 suggests
choosing the highest cutting speed ( A2).
3.2. Pareto ANOVA: an alternative analysis
One of the methods to analyze data for process optimiza-
tion is the use of Pareto ANOVA [1]. Pareto ANOVA is a
simplified ANOVA method which uses Pareto principles. It
is a quick and easy method to analyze results of parameter
design. It does not require an ANOVA table and therefore
does not use F -tests.
Following are the Pareto ANOVA table for surface rough-
ness and resultant force analysis, respectively.
The Pareto ANOVA technique of analysis has been per-formed, which requires least knowledge about ANOVA
method and suitable for engineers and industrial practi-
tioners.
The use of S/N ratio for selecting the best levels com-
bination for surface roughness suggests that cutting speed
(factor A) and interaction B × C have strong effect on the
Fig. 4. The smaller the better S/N graph for resultant force.
surface roughness. From the result obtained, the best com-
bination to get low value of surface roughness is at level‘2’ of cutting speed, level ‘0’ of feed rate, and level ‘1’ of
depth of cut. Since the role of depth of cut is minimum in
obtaining good surface finish, it is indicated that in order to
achieve good surface finish, always use high cutting speed
and low feed rate.
On the other hand, the use of S/N ratio for selecting the
best levels combination for resultant force suggests that feed
(factor B), depth of cut (factor C ) and interaction B × C
have strong effect on the resultant force, whereas the effect
of cutting speed can be ignored. From the result, the best
combination to get low value of resultant cutting force is at
level ‘0’ of feed rate, level ‘0’ of depth of cut and level ‘2’ of cutting speed. Since the effect of cutting speed is negligible
in this case, it is suggested to cut at low feed rate and depth
of cut so that the force produced during the cutting process
is kept at minimum value. By increasing the cutting speed,
both the resultant cutting force and surface roughness values
are kept at minimum.
7/30/2019 Ejemplo de Taguchi en Proceso de Perforado
http://slidepdf.com/reader/full/ejemplo-de-taguchi-en-proceso-de-perforado 6/9
J.A. Ghani et al. / Journal of Materials Processing Technology 145 (2004) 84–92 89
Table 6
Pareto ANOVA analysis for surface roughness
Factor and interaction
B × C A B C B × C A × B A × C A × B A × C
Sum at factor level
0 8.495 6.544 6.325 5.865 4.678 5.991 5.020 4.893 5.621
1 7.678 6.464 5.034 7.096 4.968 5.412 6.105 6.409 5.0072 −0.229 28.296 5.443 2.983 6.298 4.542 4.818 4.642 5.316
Sum of squares of difference (S ) 139.292 949.771 2.613 26.742 4.481 3.192 2.874 5.485 0.566
Contribution ratio (%) 12.272 83.679 0.230 2.356 0.395 0.281 0.253 0.483 0.050
Pareto diagram
83.679
12.272
2.356 0. 395 0. 48 3 0.281 0.253 0.23 0.05
A B × C C B × C A × B A × B B A × C A × C
Cumulative contribution 83.679 95.951 98.702 98.702 99.185 99.466 99.719 99.949 100
Check on significant interaction BC two-way table (Appendix B(a))
Optimum combination of
significant factor level
A2 B0C 1
Remarks The significant factors and interactions are chosen from the left-hand side in the above
Pareto diagram which cumulatively contribute about 90%
Estimate of error variance 0.026
Table 7
Pareto ANOVA analysis for resultant force
Factor and interaction
B × C A B C B × C A × B A × C A × B A × C
Sum at factor
0 −54.313 −55.785 −53.551 −53.548 −55.153 −55.344 −55.410 −55.551 −55.766
1 −56.534 −55.972 −55.589 −56.117 −55.676 −55.529 −56.004 −56.503 −56.159
2 −56.608 −55.696 −58.276 −57.789 −56.626 −56.580 −56.040 −55.400 −55.529
Sum of squares of difference (S ) 10.201 0.119 33.701 27.390 3.345 2.667 0.752 2.149 0.607
Contribution ratio (%) 12.605 0.147 41.642 33.844 4.13268 3.29564 0.929 2.655 0.749
Pareto diagram
41.642
33.844
12.605
4.133 3.296 2.6550.929 0.749 0.147
B C B × C B × C A × B A × B A × C A × C A
Cumulative contribution 41.642 75.486 88.091 92.224 95.519 98.174 99.103 99.852 100.000
Check on significant BC two-way table (Appendix B(b))
Optimum combination of
significant factor
B0C 0 A2
Remarks The significant factors and interactions are chosen from the left-hand side in the above
Pareto diagram which cumulatively contribute about 90%
Estimate of error variance 0.0198
7/30/2019 Ejemplo de Taguchi en Proceso de Perforado
http://slidepdf.com/reader/full/ejemplo-de-taguchi-en-proceso-de-perforado 7/9
90 J.A. Ghani et al. / Journal of Materials Processing Technology 145 (2004) 84–92
4. Discussion
In the above case study two techniques of data analysis
have been used. Both techniques draw similar conclusions.
The cutting speed has found to be the most significant effect
to produce low value of average surface roughness ( Ra). The
explanation for the influence of cutting speed on surfacefinish is still not available. This could be explained in terms
of the velocity of chips that is faster at high cutting speed
than at low cutting speed. This leads to a shorter time for
the chips to be in contact with the newly formed surface
of workpiece and the tendency for the chips to wrap back
to the new face form is little as compared to low speed.
The condition of seizure and sublayer plastic flow occurred
at high speed and the term flow-zone is used to describe
secondary deformation in this range [16]. The time taken for
the chips at this flow-zone for high speed cutting is short as
compared to lower speed, as the velocity of chip is faster.
Further more, the chip formation process is influenced by
the shear length (ls) in the shear zone. The shear length (ls) isgiven as ls = t/Sin φ, where t is undeformed chip thickness,
and φ is the shear angle [17]. Philip [18] f ound the shear
angle (φ) is large at high cutting speeds, therefore the shear
length (ls) is small, as shown in Fig. 5. Consequently, the
chip will break away with less material deformation at the
immediate tool tip, which in turn preserved the machined
surface properties.
The surface roughness produced in milling operation de-
pends on feed rate [14], and the tool angular position de-
pends on the depth of cut and radius of the cutter [15].
Martelotti [14] describes the chip thickness model as fol-
lows: t = sSin b, where s and b represent feed per toothand tool angular position, respectively. Whereas the height
of the tooth mark is given by the following:
h =s2
8[R+ (sxN /π)]
Fig. 5. Shear length and shear angle in chip formation process.
where h is the height of tooth mark above point of lowest
level, mm; s the feed per tooth, mm; R the radius of cutter,
mm; N the number of teeth in cutter.
The height of tooth mark can be reduced by increasing
the radius of the cutter and by decreasing the feed per tooth
until the tooth mark becomes scarcely distinguishable, par-
ticularly at the lower feed rates.The use of S/N ratio for selecting the best levels of com-
bination for surface roughness ( Ra) value suggests the use of
low value of feed rate in order to obtain good finish. Smaller
angle of tool angular position is obtained at lower depth of
cut [15]. Therefore, it is preferable to set the depth of cut
to a low value. Therefore, one can say that the set values
for level ‘0’ and ‘1’ are both suitable to obtain good quality
of surface finish. From the result, the interaction of factor B
and factor C is more important than the effect of the individ-
ual factors. In other words, in order to get the best result it
requires experience to combine these two factors to achieve
a suitable combination of feed rate and depth of cut.
The S/N ratio suggests that cutting force depends on feedrate and depth of cut. Both the feed rate and depth of cut are
found to be at level ‘0’ for the best combination to obtain
low value of cutting force. The combination of feed rate and
depth of cut determines the undeformed chip section and
hence the amount of energy required to remove a specified
volume of material. The required force to form the chips is
dependent on the shear yield strength of the work material
under cutting conditions and on the area of the chip section
and the shear zone. The feed per tooth and the depth of
cut determine this area. The low value of cutting force is
desired to cut an unsupported beam or thin sections as well
as to preserve material properties against residual stress andchange in micro hardness at the subsurface.
5. Conclusions
From the analysis of result in end milling using conceptual
S/N ratio approach and Pareto ANOVA, the following can
be concluded from the present study:
1. Taguchi’s robust design method is suitable to analyze the
metal cutting problem as described in this paper.
2. Conceptual S/N ratio and Pareto ANOVA approaches for
data analysis draw similar conclusion.
3. In end milling, use of high cutting speed (355 m/min),
low feed rate (0.1 mm per tooth) and low depth of cut
(0.5 mm) are recommended to obtain better surface finish
for the specific test range.
4. Low feed rate (0.1 mm per tooth) and low depth of cut
(0.3 mm) lead to smaller value of resultant cutting force
the specific test range.
5. Generally, the use of high cutting speed, low feed rate
and low depth of cut leads to better surface finish and
low cutting force.
7/30/2019 Ejemplo de Taguchi en Proceso de Perforado
http://slidepdf.com/reader/full/ejemplo-de-taguchi-en-proceso-de-perforado 8/9
J.A. Ghani et al. / Journal of Materials Processing Technology 145 (2004) 84–92 91
Appendix A
L27 (313) standard orthogonal array table with factors A, B, and C arranged in columns 2, 5 and 6, respectively. The interactions
among factors are indicated as in columns 1, 7, 8, 9, 11 and 12
Experimental run 1 2 3 4 5 6 7 8 9 10 11 12 13
1 0 0 0 0 0 0 0 0 0 0 0 0 02 0 0 0 0 1 1 1 1 1 1 1 1 1
3 0 0 0 0 2 2 2 2 2 2 2 2 2
4 0 1 1 1 0 0 0 1 1 1 2 2 2
5 0 1 1 1 1 1 1 2 2 2 0 0 0
6 0 1 1 1 2 2 2 0 0 0 1 1 1
7 0 2 2 2 0 0 0 2 2 2 1 1 1
8 0 2 2 2 1 1 1 0 0 0 2 2 2
9 0 2 2 2 2 2 2 1 1 1 0 0 0
10 1 0 1 2 0 1 2 0 1 2 0 1 2
11 1 0 1 2 1 2 0 1 2 1 1 2 0
12 1 0 1 2 2 0 1 2 0 0 2 0 1
13 1 1 2 0 0 1 2 1 2 0 2 0 114 1 1 2 0 1 2 0 2 0 1 0 1 2
15 1 1 2 0 2 0 1 0 1 2 1 2 0
16 1 2 0 1 0 1 2 2 0 1 1 2 0
17 1 2 0 1 1 2 0 0 1 2 2 0 1
18 1 2 0 1 2 0 1 1 2 0 0 1 2
19 2 0 2 0 0 2 1 0 2 1 0 2 1
20 2 0 2 0 1 0 2 1 0 2 1 0 2
21 2 0 2 0 2 1 0 2 1 0 2 1 0
22 2 1 0 1 0 2 1 1 0 2 2 1 0
23 2 1 0 1 1 0 2 2 1 0 0 2 1
24 2 1 0 1 2 1 0 0 2 1 1 0 2
25 2 2 1 2 0 2 1 2 1 0 1 0 2
26 2 2 1 2 1 0 2 0 2 1 2 1 0
27 2 2 1 2 2 1 0 1 0 2 0 2 1
B × C A B C B × C A × B A × C A × B A× C
Appendix B
(a) The calculated BC two-way table for surface roughness. From the BC two-way table, B0C 1 is found to be an optimal
condition.
B0 B1 B2 Total
C 0 1.368 + 1.222 + 0.550 = 3.14 0.243 + 0.119 − 0.021 = 0.341 0.758 + 1.262 + 0.365 = 2.385 5.866
C 1 1.273 + 1.385 + 1.160 = 3.818 1.544 + 1.197 + 0.475 = 3.216 0.119 + 0.103 − 0.160 = 0.206 7.24C 2 −0.038 − 0.287 − 0.307 = −0.632 0.432 + 0.347 + 0.697 = 1.476 0.580 + 1.137 + 0.422 = 2.139 2.983
Total 6.326 5.033 4.73 16.089
(b) The calculated BC two way table for resultant force. From the BC two-way table, B0C 0 is found to be an optimal condition.
B0 B1 B2 Total
C 0 −5.342 − 5.403 − 5.624 = −16.369 −5.955 − 6.143 − 6.208 = −18.306 −6.388 − 6.320 − 6.164 = −18.872 −53.547
C 1 −6.179 − 6.102 − 6.176 = −18.457 −6.212 − 6.134 − 5.734 = −18.08 −6.479 − 6.577 − 6.523 = −19.579 −56.116
C 2 −6.071 − 6.161 − 6.492 = −18.724 −6.484 − 6.469 − 6.250 = −19.203 −6.675 − 6.662 − 6.525 = −19.862 −57.789
Total −53.55 −55.589 −58.313 −167.452
7/30/2019 Ejemplo de Taguchi en Proceso de Perforado
http://slidepdf.com/reader/full/ejemplo-de-taguchi-en-proceso-de-perforado 9/9
92 J.A. Ghani et al. / Journal of Materials Processing Technology 145 (2004) 84–92
References
[1] S.H. Park, Robust Design and Analysis for Quality Engineering,
Chapman & Hall, London, 1996.
[2] R. Unal, E.B. Dean, Taguchi approach to design optimization for
quality and cost: an overview, in: Proceedings of the International
Society of Parametric Analyst 13th Annual, May 21–24, 1991.
[3] M.S. Phadke, Quality Engineering Using Robust Design, Prentice-Hall, Englewood Cliffs, NJ, 1989.
[4] T. Bendell, Taguchi methods, in: Proceedings of the 1988 European
Conference on Taguchi Method, Elsevier, Amsterdam, 13–14 July,
1988.
[5] V.K. Roy, Nutek, Inc. http://www.vkroy.com/up-doe.html .
[6] W.H. Yang, Y.S. Tarng, Design optimisation of cutting parameters for
turning operations based on the Taguchi method, J. Mater. Process.
Technol. 84 (1998) 122–129.
[7] T.R. Lin, Experimental design and performance analysis of tin-coated
carbide tool in face milling stainless steel, J. Mater. Process. Technol.
5654 (2002) 1–7.
[8] K.L. Tsui, Modeling and analysis of dynamic robust design experi-
ments, IEE Trans. 31 (1999) 113–1122.
[9] C. Zhang, H.P. Wang, Robust design of assembly and machining
tolerance allocations, IEE Trans. 30 (1998) 17–29.
[10] C.T. Si, L.I. Tong, Multi response robust design by principal com-
ponent analysis, Total Qual. Manage. 8 (1997) 409–416.
[11] J. Kopac, M. Bahor, M. Sokovic, Optimal machining parameters for
achieving the desired surface roughness in fine turning of cold pre-
formed steel workpieces, Int. J. Mach. Tool Manuf. 42 (2002)
707–796.
[12] P.G. Benardos, G.C. Vosniakos, Prediction of surface roughness
in cnc face milling using neural networks and Taguchi’s design
of experiments, Robot. Comput. Integr. Manuf. 18 (2002) 343–
351.
[13] M.S. Phadke, Quality Engineering Using Design of Experiments,
Quality Control, Robust Design, and the Taguchi Method, Wadsworth
& Books, California, 1988.
[14] M.E. Martellotti, An analysis of the milling process, Trans. ASME
(1941) 677–695.
[15] C.H. Borneman, Chip thickness in milling, Am. Mach. Ref. Book
Sheet 82 (1938) 189–190.
[16] E.M. Trent, Metal Cutting, 3rd ed., Butterworths, Heinemann,
1991.
[17] H.Z. Li, X.P. Li, Milling force prediction using a dynamic shear
length model, Int. J. Mach. Tools Manuf. 42 (2002) 277–286.
[18] P.K. Philip, Built-up edge phenomena in machining steel with car-
bide, Int. J. Mach. Tool Des. Res. 11 (1971) 121–132.