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Optimization of the Injection Molding
Parameters Using the Taguchi
Method
S. Kamaruddin, Zahid A. Khan & K. S. Wan
ABSTRACT
In this study, the Taguchi method, a powerful tool to design and process
optimization for quality, is used to determine the optimal parameters for an
injection molding process. An orthogonal array, the signal-to-noise (S/N) ratio
and the analysis of variance (ANOVA) are employed to investigate the quality
characteristics of a plastic tray which is made on an injection molding machine
from polypropylene (PP) plastic material. Through this study, not only the
optimal molding parameters for an injection molding process can be obtained,
but also the main parameters that affect the performance of the tray can be
obtained. Experimental results are provided to confirm the effectiveness of this
approach.
Keywords: Optimization; Taguchi method; Injection molding; Polypropylene
(PP); Bending strength; Shrinkage
Introduction
Plastic is known to be a versatile as well as economical material and is used in
many applications [1-4]. Plastic injection molding is the primary process for
producing plastic parts. In other words, injection molding is a technique for
converting thermoplastics as well as thermosetting materials into all types of
products [1,2]. Although the tooling is expensive, the cost per part is very low.
This technology has met the current needs of industry owing to its shorter
design cycles and improved design quality. Its area of application is wide which
includes manufacturing, military, automobile, aerospace and other industries.
Plastic injection molding uses plastic in the form of the pellets or granules
as a raw material. It is then heated until a melt is obtained. Then the melt is
injected into a mold where it is allowed to solidify to obtain the desired shape.
The mold is then opened and the part is ejected. The process parameters such as
cycle time, fill time, cooling time, injection time, injection speed, injection pressure,
holding pressure, melting temperature, mold temperature and so on need to be
79
Journal of Mechanical Engineering
optimized in order to produce finished plastic parts with good quality. Various
studies have been conducted to improve and optimize the process, so as to
obtain high quality parts produced on a wide range of commercial plastic injection
molding machines [5-7].
In this paper an attempt is made to optimize injection molding process
parameters for the production of polypropylene (PP) plastic tray. The plastic
tray is chosen in this study because it is used as a container to store goods at
many places and one example is the tool box where it is used for storing hand
tools like spanner, screw driver and many others. The effect of four process
parameters, i.e. melting temperature, injection speed, cooling time and holding
pressure, each with two levels, on the quality characteristics of the tray is
investigated. Based on the Taguchi design of experiment, experiments have been
carried out in order to determine the optimum process parameters.
In the following, the Taguchi method is introduced first. The experimental
details of using the Taguchi method to determine and analyze the optimal process
parameters are described next. The optimal process parameters with regard to
performance index such as bending strength and shrinkage are considered.
Finally, the paper concludes with a summary of this study and future work.
The Taguchi Method
The Taguchi method, indeed, is a powerful tool for the design of high quality
systems. It provides a simple, efficient and systemic approach to optimize designs
for performance, quality, and cost. Taguchi parameter design can optimize the
performance characteristics through the settings of design parameters and reduce
the sensitivity of the system performance to source variation. In the past many
researchers have used the Taguchi method for design and process optimization
[8-13]. In recent years, the rapid growth of interest in the Taguchi method had led
to numerous applications of the method in a world-wide range of industries and
nations [14]. Taguchi method uses a special design of orthogonal arrays to
study the entire parameter space with a small number of experiments only and
thus, it results in a lot of cost as well as time saving. A desired number of
experiments as suggested by the orthogonal array are performed and the
experimental results are then transformed into a signal-to-noise (S/N) ratio. Taguchi
recommends the use of S/N ratio to measure the quality characteristics deviating
from the desired values. Usually, there are three categories of quality characteristic
in the analysis of the S/N ratio, i.e. the-lower-the-better, the-higher-the-better,
and the-nominal-the-better. The S/N ratio for each level of process parameters is
computed based on the S/N analysis. Regardless of the category of the quality
characteristic stated above, a greater S/N ratio corresponds to better quality
characteristics. Therefore, the optimal level of the process parameters is the
level with the greatest S/N ratio. Furthermore, a statistical analysis of variance
80
Optimization of the Injection Molding Parameters Using the Taguchi Method
(ANOVA) is performed to see which process parameters are statistically
significant. With the S/N and ANOVA analyses, the optimal combination of the
process parameters can be predicted. Finally, a confirmation experiment is
conducted to verify the optimal process parameters obtained from the parameter
design.
Optimization of Plastic Injection Molding Process
Parameters
Selection of the Injection Molding Process Parameters and Their
Levels
Plastic injection molding process was carried out on a Battenfeld TM750/210
machine (make: Germany). Only four injection molding parameters i.e. melting
temperature, injection speed, cooling time and holding pressure were investigated
in this study.
Melting temperature can be defined as the temperature of the cylinder of the
machine which determines the temperature of the material that will be injected
into the mold. On the other hand, injection speed is the speed of advance of the
screw which is driven by a motor coupled with it. Cooling time can be defined as
the time needed for the circulated water around the mold to cool and solidify the
plastic part. Finally, holding pressure is the pressure used for regulating and
closing the mold.
The selected injection molding process parameters along with their levels
are given in Table 1. The process parameters, shown in Table 1 were selected
because they are the most critical and significant parameters and the quality of
the products produced by injection molding process mainly depend upon properly
selecting the level of these four parameters. The levels of the process parameters
shown in Table 1 were selected in light of the data available in the literature [4].
Each parameter had two levels as being the most significant levels [4] and
interaction between the parameters was not considered in the present study.
Table 1: Injection Molding Process Parameters and Their Levels
Symbol
Process parameters
Unit
A
B
C
D
Melting temperature
Injection speed
Cooling time
Holding pressure
o
81
C
rpm
sec.
psi
Level 1
200
203
10
110
Level 2
230
261
20
120
Journal of Mechanical Engineering
Selection of Orthogonal Array
In order to select an appropriate orthogonal array for the experiments, the total
degrees of freedom need to be computed. The degrees of freedom are defined as
the number of comparisons between process parameters that need to be made to
determine which level is better and specifically how much better it is. For example,
a two-level process parameter counts for one degree of freedom. The degrees of
freedom associated with the interaction between two process parameters are
given by the product of the degrees of freedom for the two process parameters.
In the present study, the interaction between the process parameters is neglected.
Therefore, there are four degrees of freedom owing to there being four process
parameters in the injection molding process.
Once the required degrees of freedom are known, the next step is to select
an appropriate orthogonal array to serve the specific purpose. Basically, the
degrees of freedom for the orthogonal array should be greater than or at least
equal to those for the process parameters. In this study, an L8 orthogonal array
with seven columns and eight rows was used. This array has seven degrees of
freedom and it can handle two-level design parameters. Each process parameter
is assigned to a column, eight process-parameter combinations being available.
Therefore, only eight experiments are required to study the entire parameter
space using the L8 orthogonal array. The experimental layout for the four process
parameters using the L8 orthogonal array is shown in Table 2. Since the L8
orthogonal array has seven columns, the first four columns of the array are
assigned to the selected process parameters and the last three columns are left
empty for the error of experiments: orthogonality is not lost by letting the columns
of the array remain empty. Each row of Table 2 represents an experiment with
different combination of parameters and their levels.
Table 2: Experimental Layout Using L8 Orthogonal Array
Experiment
Number
1
2
3
4
5
6
7
8
A
Melting
Temperature
1
1
1
1
2
2
2
2
Process Parameter Level
B
C
D
Injection
Cooling Holding
Speed
Time
Pressure
1
1
1
1
1
2
2
2
1
2
2
2
1
2
1
1
2
2
2
1
1
2
1
2
82
Error
Error Error
Optimization of the Injection Molding Parameters Using the Taguchi Method
Preparation of the Test Specimen for Bending Test
According to the experimental plan shown in Table 2, eight plastic trays were
produced on the Battenfeld TM 750/210 injection molding machine. Figure 1
shows the isometric view of the tray. Subsequently, eight test specimens were
prepared from the eight trays for performing the bending test. The size of each
test specimen was 4.8 cm x 1.8 cm x 0.3 as shown in Figure 2. The test specimens
were cut away manually from the base of the plastic trays. After the cutting
process, the rough edges of the specimens were scrapped and polished for
better surface finish. Then, the test specimens were washed with water and
cleaned by using a piece of cloth.
Figure 1: Isometric View of the PP Plastic Tray
Figure 2: Isometric View of the Test Specimen
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Journal of Mechanical Engineering
Bending Test for the Specimen
After preparing eight test specimens as discussed in section 3.3, bending tests
were performed using a bending test apparatus to investigate bending deflection
under the application of a constant load. The schematic view of the bending test
is shown in Figure 3. The test specimens, prepared from the eight trays, were
chosen in a random manner for bending test which is one of the requirements of
the Taguchi method. One end of the specimen was fixed in the jig and the other
end was kept free. Thus, the specimen behaved as a cantilever. The pointer of
the dial indicator (having least count of ± 0.05 mm) was allowed to touch the free
end of the specimen and the indicator was set at zero. A constant load of 500 gm
was applied to the free end which caused bending of the specimen. The amount
of bending deflection was recorded from the dial indicator. The procedure was
repeated three times for each specimen to obtain three different values of bending
deflections and then average bending deflection was computed. It should be
noted that the higher bending deflection corresponds to the higher bending
strength and vice versa. Finally, the results obtained from this test were used for
further analysis.
Horizontal
Stand
Dial
Indicator
Test
Specimen
Clamp
Vertical
Stand
Jig for
holding test
specimen
Pointer
Magnetic
Base
Figure 3: Schematic Diagram of the Bending Test
84
Optimization of the Injection Molding Parameters Using the Taguchi Method
Shrinkage Test for the Plastic Tray
The purpose of doing shrinkage test was to observe the shrinkage behaviour
of the plastic tray when it is used in extreme temperature conditions where it is
exposed to change in temperature gradient. In order to perform this test the
dimension of all eight trays was measured with the help of vernier dial caliper
(least count = ± 0.002 cm; make: Mitotoyo, Japan) and then they were heated to
a temperature of 130oC in an oven for 30 minutes. After that the specimen was
taken out of the oven and cooled for 5 minutes at room temperature under
normal conditions and then the dimension was measured. The difference in the
dimension i.e. the difference in the length of the specimen before heating and
after heating indicated the amount of shrinkage occurred in the tray due to
change in temperature. The results obtained from this test were used for further
analysis.
Results and Discussion
η1
m
m
In the following section, results of the bending and shrinkage tests are studied
using the S/N ratio and ANOVA analyses. Based on the results of these analyses,
optimal parameters of injection molding process for bending deflection and
shrinkage are obtained and verified.
1
∑T 2
i =1 i
Analysis of the S/N Ratio
In the Taguchi method, the term “signal” represents the desirable value (mean)
for the output characteristic and the term “noise” represents the undesirable
value (S.D.) for the output characteristic. Therefore, the S/N ratio is the ratio of
the mean to the S.D. Taguchi uses the S/N ratio to measure the quality
characteristic deviating from the desired value. The S/N ratioη is defined as [8]:
= −10 log (M.S.D.)
(1)
where M.S.D. is the mean-square deviation for the output characteristic.
As mentioned earlier, there are three categories of quality characteristics,
i.e. the-lower-the-better, the-higher-the-better, and the-nominal-the better. To
obtain optimal performance of the tray, the-higher-the-better quality characteristic
for bending strength must be taken. The mean-square deviation (M.S.D.) for
the-higher-the-better quality characteristic can be expressed as [8]:
M.S.D. =
(2)
85
Journal of Mechanical Engineering
where m is the number of tests and Ti is the value of bending deflection for the
i th test.
Table 3 shows the experimental results for the bending deflection and the
corresponding S/N ratio using Eqs. (1) and (2). Since the experimental design is
orthogonal, it is then possible to separate out the effect of each cutting parameter
at different levels. For example, the mean S/N ratio for the melting temperature at
levels 1 and 2 can be calculated by averaging the S/N ratio for the experiments 1
– 4, and 5 – 8, respectively. The mean S/N ratio for each level of the other process
parameters can be computed in the similar manner. The mean S/N ratio for each
level of the process parameters is summarized and called the S/N response table
for bending strength (Table 4). In addition, the total mean S/N ratio for the nine
experiments is also calculated and listed below Table 4.
Table 3: Experimental Results for Bending Deflection and S/N Ratio
Experiment Melting
Injection Cooling Holding Average bending S/N ratio
number temperature speed
time
pressure
deflection
(dB)
(oC)
(rpm)
(sec.)
(psi)
(mm)
1
2
3
4
5
6
7
8
200
200
200
200
230
230
230
230
203
203
261
261
203
203
261
261
10
10
20
20
20
20
10
10
110
120
110
120
110
120
110
120
1.90
2.02
2.19
2.10
2.31
1.76
1.80
1.93
5.58
6.11
6.81
6.44
7.27
4.91
5.11
5.71
Table 4: S/N Response Table for Bending Deflection
Symbol
A
B
C
D
Process parameter
Mean S/N ratio (dB)
Level 1
Level 2
Max-min
Melting temperature
Injection speed
Cooling time
Holding pressure
6.24
5.97
5.63
6.19
The total mean S/N ratio = 5.99 (dB)
86
5.75
6.02
6.36
5.79
0.49
0.05
0.73
0.40
Optimization of the Injection Molding Parameters Using the Taguchi Method
Figure 4 shows the S/N response graph for the output characteristic (bending
deflection). As shown in Eqs. (1) and (2), the greater the S/N ratio, the smaller is
the variance of the output characteristic around the desired (the-higher-thebetter) value. However, the relative importance amongst the process parameters
for bending deflection still needs to be known so that optimal combinations of
the process parameter levels can be determined more accurately. This will be
discussed in the next section using the analysis of variance.
On the other hand, the-lower-the-better quality characteristic for shrinkage
should be taken for obtaining optimal performance of the tray. The M.S.D. for
the-lower-the-better quality characteristic can be expressed as [8]:
M.S.D.=
1
m
m
∑ S i2
(3)
i =1
where S i is the value of shrinkage for the i th test.
Figure 4: S/N Graph for Bending Deflection
Table 5 shows the experimental results for the shrinkage and the corresponding
S/N ratio using Eqs. (1) and (3). The S/N response table and S/N response graph
for shrinkage are shown in Table 6 and Figure 5. Regardless of the the-lower-the
better or the-higher-the-better quality characteristic, the greater S/N response
corresponds to the smaller variance of the output characteristic around the
desired value (Eqs. (1) – (3)).
87
Journal of Mechanical Engineering
Table 5: Experimental Results for Shrinkage and S/N Ratio
Experiment Melting
Injection
number temperature speed
(rpm)
(oC)
1
2
3
4
5
6
7
8
200
200
200
200
230
230
230
230
203
203
261
261
203
203
261
261
Cooling
time
(sec.)
Holding
pressure
(psi)
10
10
20
20
20
20
10
10
110
120
110
120
110
120
110
120
Shrinkage S/N ratio
(cm)
(dB)
0.102
0.070
0.112
0.084
0.092
0.056
0.068
0.060
19.83
23.10
19.02
21.51
20.72
25.04
23.35
24.44
Table 6: S/N Response Table for Shrinkage
Symbol
A
B
C
D
Process parameter
Melting temperature
Injection speed
Cooling time
Holding pressure
Mean S/N ratio (dB)
Level 1
Level 2
Max-min
20.87
23.39
2.52
22.17
22.08
0.09
22.68
21.57
1.11
20.73
23.52
2.79
The total mean S/N ratio = 22.13 (dB)
Figure 5: S/N Graph for Shrinkage
88
Optimization of the Injection Molding Parameters Using the Taguchi Method
Analysis of Variance
The purpose of the analysis of variance (ANOVA) is to investigate which design
parameters significantly affect the quality characteristic. This is accomplished
by separating the total variability of the S/N ratios, which is measured by the
sum of squared deviations from the total mean S/N ratio, into contributions by
each of the design parameters and the error. First, the total sum of squared
deviations SST from the mean S/N ratio η m is calculated as [8]:
SST =
n
∑ (ηi − η m )2
i =1
(4)
where n is number of experiments in the orthogonal array, η i is the mean S/N
ratio for the i th experiment.
The total sum of squared deviations SST is decomposed into two sources:
the sum of squared deviations SSd due to each process parameter and the sum of
squared error SSe. The percentage contribution p by each of the process
parameter in the total sum of squared deviations SST is a ratio of the sum of
squared deviations SSd due to each process parameter to the total sum of squared
deviations SST.
Statistically, there is a tool called F test to see which process parameters
have significant effect on the quality characteristic. For performing the F test,
the mean of squared deviations SSm due to each process parameter needs to be
calculated. The mean of squared deviations SSm is equal to the sum of squared
deviations SSd divided by the number of degrees of freedom associated with the
process parameter. Then, the F value for each process parameter is simply the
ratio of the mean of squared deviations SSm to the mean of squared error SSe.
Usually, when F > 4, it means that the change of the process parameter has
significant effect on the quality characteristic.
Table 7 shows the results of ANOVA for the bending deflection. It can be
found that the change of process parameters in the range given in Table 1 has an
insignificant effect on the bending deflection since for all process parameters F
value is less than 4. However, based on the S/N analysis, the optimal injection
molding process parameters for bending strength are A1B2C2D1 i.e. the melting
temperature at level 1, the injection speed at level 2, the cooling time at level 2,
and the holding pressure at level 1. Table 8 shows the results of ANOVA for
shrinkage. Melting temperature and the holding pressure are the significant
process parameters for affecting the shrinkage behaviour of the tray. However,
the contribution order of the process parameters for shrinkage is holding pressure
(46.44%), then melting temperature (37.89%), then cooling time (7.30%), and
then injection speed (0.04%). The optimal process parameters for shrinkage are
A2B1C1D2 i.e. the melting temperature at level 2, the injection speed at level 1, the
cooling time at level 1, and the holding pressure at level 2.
89
Journal of Mechanical Engineering
Table 7: Results of the Analysis of Variance for Bending Deflection
Symbol Process
parameters
A
B
C
D
Error
Melting temperature
Injection speed
Cooling time
Holding pressure
Total
Degrees Sum of
freedom squares
1
1
1
1
3
0.471
0.0054
1.066
0.320
2.853
7
4.715
Mean square
0.471
0.0054
1.066
0.320
0.951
F
Contribution
(%)
0.495
0.0057
1.120
0.336
10.00
0.12
22.60
6.80
60.48
100.00
Table 8: Results of the Analysis of Variance for Shrinkage
Symbol Process
parameters
A
B
C
D
Error
Melting temperature
Injection speed
Cooling time
Holding pressure
Total
Degrees of Sum of
freedom squares
1
1
1
1
3
12.72
0.015
2.451
15.59
2.794
7
33.57
Mean square
square
F
Contribution
(%)
12.72
0.015
2.451
15.59
0.931
13.66
0.016
2.633
16.75
37.89
0.04
7.30
46.44
8.33
100.00
Confirmation Tests
Once the optimal combination of process parameters and their levels was obtained,
the final step was to verify the estimated result against experimental value. It
may be noted that if the optimal combination of parameters and their levels
coincidently match with one of the experiments in the orthogonal array, then no
confirmation test is required. Estimated value of the output characteristics
(bending deflection and shrinkage) at optimum condition is calculated by adding
the average performance to the contribution of each parameter at the optimum
level using the following equations [15]:
(5)
(6)
where m is the average performance, T is the grand total of output characteristic
for each experiment, n is the total number of experiments and mAopt is the average
90
Optimization of the Injection Molding Parameters Using the Taguchi Method
value of the output characteristic for parameter A at its optimum level, mBopt is the
average value of the output characteristic for parameter B at its optimum level,
mCopt is the average value of the output characteristic for parameter C at its
optimum level, and mDopt is the average value of the output characteristic for
parameter D at its optimum level.
Confirmation test is required in the present study only for shrinkage because
the optimum combination of parameters and their levels i.e. A2 B1 C1 D2 does not
correspond to any experiment of the orthogonal array.
One plastic tray at the optimal combination of parameters and their levels A2
B1 C1 D2 was produced on the same injection molding machine and from the same
material and the shrinkage test was performed in the same way as discussed in
section 3.4. The value of shrinkage obtained from the experiment was then
compared with the estimated value as shown in Table 9. It can be seen from this
table that the difference between experimental result and the estimated result is
very small. This indicates that the experimental value of shrinkage is very close
to the estimated value. This verifies that the experimental result is strongly
correlated with the estimated result.
Table 9: Results of the Confirmation Experiment for Shrinkage
Optimal process parameters
Estimation
Experiment
Difference
Level
Total shrinkage (cm)
S/N ratio (dB)
A 2 B 1C 1 D 2
0.054
25.35
A 2B 1 C 1D 2
0.062
24.15
–
0.008
1.20
Conclusions
This paper has presented an application of the Taguchi method for optimizing
the process parameters of an injection molding process that is used to produce
a polypropylene plastic tray. As shown in this study, the Taguchi method provides
a systematic and efficient methodology for the optimization of the process
parameters with far less effect than would be required for most optimization
techniques. On the basis of the results obtained from the present study the
following can be concluded:
•
The combination of parameters and their levels for optimum bending
deflection and therefore, for optimum bending strength of PP plastic tray
under the constant load is A1B2C2D1 (i.e. melting temperature-200°C, injection
speed- 261 rpm, cooling time – 20 sec., and holding pressure – 110 psi).
91
Journal of Mechanical Engineering
•
•
•
The contribution of melting temperature, injection speed, cooling time, and
holding pressure to the quality characteristic (bending strength) is 10.00%,
0.12%, 22.60%, and 6.80% respectively.
The combination of parameters and their levels for optimum shrinkage of PP
plastic tray is A2B1C1D2 (i.e. melting temperature-230°C, injection speed- 203
rpm, cooling time – 10 sec., and holding pressure – 120 psi).
The contribution of melting temperature, injection speed, cooling time, and
holding pressure to the quality characteristic (shrinkage) is 37.89%, 0.04%,
7.30%, and 46.44% respectively.
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Optimization of the Injection Molding Parameters Using the Taguchi Method
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S. KAMARUDDIN & K. S. WAN, School of Mechanical Engineering, Universiti
Sains Malaysia, 14300 Nibong Tebal, Pulau Pinang, Malaysia.
ZAHID A. KHAN, Department of Mechanical Engineering, Faculty of Engineering
and Technology, Jamia Millia Islamia, New Delhi – 110 025, India
93