INTRODUCTION
Successful production of parts by the Metal Injection Molding (MIM) process
is closely related to the formulation of the binder for use the powders. Selection
a palm stearin as a binder system was started by Iriany (Iriany
et al., 2001) and it is believed that can be replace the conventional
binder system which mainly comprise of three to four components. Research on
palm stearin in MIM is still new and most of researchers mixing with stainless
steel powder (Iriany et al., 2001; Istikamah
et al., 2006). Characterization and rheological procedures have been
done previously to show that palm stearin binder can be successfully mixed with
titanium alloy to produce a homogeneous feedstock (Mohammad
Nor et al., 2009).
After selection of powderbinder system, mixing process and preparing the homogeneous
feedstock, the most crucial process in MIM is injecting the feedstock to produce
high quality of the green part (German and Bose, 1997).
Work by other authors (Thomas and Evans, 1988; Loh
et al., 2001) found that the defects which appeared in debinding
or sintering were not necessary due to debinding or sintering but may have their
origins in injection molding itself. Thus, during injection, controlling the
quality of green part is of great importance to ensure the reliability of the
products.
For example, defects in green part such as cracks are very difficult to detect
immediately after molding and they become apparent only after debinding and
sintering (Miura et al., 1995). Besides that,
the determination highest density of green compact plays an important role.
Molded parts may appear to be intact and free of visible defects, but the density
gradient in them may cause dimensional variation of distortion during sintering.
By verifying the molding parameters, molding defects can be overcome and green
parts quality will increase (Loh et al., 2001).
This paper reported the use of Taguchi method and grey relational analysis
to optimize the injection molding operation for feedstock of titanium alloy
and palm stearin with multiple performance characteristic of green part including
defects, strength and density. Taguchi method is a systematic application of
design and analysis for experiments. It has proved to be an effective approach
to produce high quality products at a relatively low cost. However, the original
Taguchi method has been designed to optimize a single performance characteristic.
Zu and Lin (1997) optimized the mechanical properties
of injection molded W4.9%Ni2%Fe in debinding. Ji et
al. (2001) sintered the stainless steel metal injection molding parts
using Taguchi method for final density. Jamaludin et
al. (2009) optimized the injection parameter of water atomized SS316
L powder with design of experiment method for best sintered density. Vlachos
and Chang (2009) optimized the metal powdermixing parameters for chemical
homogeneity and agglomeration. All the above methods cannot be applied to directly
solve the operation of optimization problem with multiple performance characteristics.
For injection molding process operations, defects are lowerthebetter performance
characteristic. However, strength and density of green part is a higherthebetter
performance characteristic. As a result, improvement of one performance characteristic
may lead to a degradation of another performance characteristic. In this paper,
the Grey Relational Analysis (GRA) is used to investigate the multiple performance
characteristic in the injection molding process of MIM.
Grey relational analysis (GRA): Deng (1989)
and Tsao (2009) proposed the GRA to fulfill the crucial
mathematical criteria for dealing with a poor, incomplete, and an uncertain
system in order to improve the flexibility and the ability of the Taguchi method.
Through the GRA, a Grey Relational Grade (GRG) is obtained to evaluate the characteristics
of the multiple performances. As a result, the optimization of the complicated
multiple response can be converted into the optimization of a single GRG. The
GreyTaguchi method was established for combining both the GRA and the Taguchi
method and this method has been successfully applied to optimize the multiple
responses of complicated problems in the manufacturing processes. The GRG is
obtained from the average of the Grey Relational Coefficient (GRC) of the normalized
response (Tsao, 2009; Kopac and
Krajnik, 2007). If the expected data sequence is of the form where thehigherthebetter,
then the original sequence can be normalized as:
where, x^{0}_{i} (k) is the original sequence, x^{*}_{i}
(k) is the sequence after the data preprocessing, max x^{0}_{i}
(k) the largest value of x^{0}_{i} (k) and min x^{0}_{i}
(k) implies the smallest value of x^{0}_{i} (k). The larger
normalized results correspond to a better performance and the bestnormalized
result should equal to 1 (Deng, 1989).
When the form thesmallerthebetter becomes the expected value of the data sequence, the original sequence can be normalized as:
The GRCs are calculated to express the relationship between the ideal (best) and the actual results of the experiment. The GRC ζ_{i} (k) can be expressed as:
where, Δ_{0i} is the deviation sequence of the reference sequence
(x_{o}) and the comparability sequence (x_{i}), i.e. Δ_{0i}
= x^{*}_{0} (k)–x^{*}_{i} (k),
where x_{o}(k) is the ideal result (=1) and ζ is the distinguishing
coefficient set between zero and unity; in this study, it was set to ζ
= 0.9 (Kopac and Krajnik, 2007). Δmax being the
largest value of Δ_{oi }and the Δmin as the smallest value
of Δ_{oi}. Next, GRG of ξ(x_{o },x_{i}) is
computed by averaging the GRC corresponding to each quality characteristic is
defined as:
where, n is the number of quality performance. The GRG shows the correlation between the reference sequence and the comparability sequence. The evaluated GRG fluctuates from 01 and equals to 1 if these two sequences are identically coincidental.
The GRG is ranked for each experiment. The higher the GRG, it implies that the corresponding experimental result is closer to the ideal normalized value. In other words, the larger the GRG, the better will be the characteristic of the multiple performance.
MATERIALS AND METHODS
Feedstock preparation: The particle of titanium alloy (Ti6Al4V) in spherical shape with pycnometer density 4.38 g cm^{3} was mixed with 60 wt% of PS and 40 wt% of Polyethylene (PE). The mixing process was done in a sigma blade at 150°C for 1 h. The feedstock was then injected using Battenfeld, BA 250 CDC injection molding machine. Figure 1 illustrates schematic diagram of the tensile bar cavity.

Fig. 1: 
Dimension (mm) of Tensile bar cavity with thickness of 3.17
mm 
Design of Experiment (DOE): In this paper, six injection molding process parameters were investigated i.e., injection pressure, injection temperature, powder loading, mold temperature, holding temperature and injection rate. Other significant effects such as the interaction between three parameters of injection pressure, injection temperature, powder loading were also investigated. The selection injection molding parameters along with their levels are given in Table 1. After injection molding process, three quality objectives of the green part are chosen including the defects, strength and density. Typically, lowest value of defects whilst on the other hand the highest value of strength and density are desirable. Amount of score for defects obtained from Table 2.
RESULTS AND DISCUSSION
Best experimental run: The experiment results for the defects, strength and density are listed in Table 3. The GRG for each experiment of the L_{27} orthogonal array was listed by applying Eq. 3 and 4.
In this study, a linear data preprocessing method for the green defects is thesmallerthebetter and is expressed as Eq. 2 whilst on the other hand green strength and density is thehigherthe better and is expressed as Eq. 1. According to performed experiment design, it is clearly observed that the injection molding parameters setting of the experiment no. 14 has the highest GRG. Thus, the fourteenth experiment gives the best multiperformance characteristics among the 27 experiments.
Most influence factor: Using the same method, calculations were performed
for each factor level and response table was generated, as shown in Table
4. Since the GRG represented the level of correlation between the reference
and the comparability sequences, the larger GRG means the comparability sequence
exhibits a stronger correlation with the reference sequence. Therefore, the
comparability sequence has a larger value of GRG for the green defects, strength
and density.

Fig. 2: 
Response graph of GRG 
Table 1: 
Injection molding parameters for three levels taguchi design 

Table 2: 
Rating for defects 

Based on this premise, this study selects the level that provides the largest
average response.
Figure 2 shows the response graph of the GRG of each injection parameter at a different level respectively. It is clearly shown that the optimum combination of the injection molding parameter to fulfill the requirement of the quality of the green part is A1 B1 C1 D2 E0 F0. This means that the injection pressure at 450 bar; injection temperature, 140°C; powder loading, 65 vol.%; mold temperature, 50°C; holding pressure, 500 bar and the injection rate at 10 ccm/s are the optimum level.
The influence of each injection molding parameter can be more clearly presented
by means of the GRG graph. When the last column of Table 4
was compared, it is observed that the difference between the maximum and minimum
value of the GRG for factor B is bigger among other factors. This indicates
that the injection temperature has stronger effect on the multiperformance
characteristics of green part followed by injection pressure, powder loading,
mold temperature injection rate and holding pressure.
Table 3: 
Taguchis L27 (313) Orthogonal Array (OA) demonstrate the
quality characteristic 

Table 4: 
Response table for GRG 

If the number of injection molding parameters increases, the importance of
the controllable factors on the multiperformance characteristics will be determined
by ordering max–min grade relational values.
Additionally, Table 5 gives the results of the analysis of variance (ANOVA) for the multi performance characteristic using the calculated value from GRG. According to ANOVA, the factor B, the injection temperature with 26.37% of contribution is the most significant controlled parameters for the injection molding process, the injection pressure with 15.33% contribution, the powder loading with 12.14%, and the mold temperature with 3.20% of contribution. The contribution of holding pressure and injection rate are very small. However, the interaction between the injection pressure and powder loading (factor AXC) shows a contribution of 18.43% followed by interaction between injection pressure and injection temperature (factor AXB) with contribution of 17.64% and the interaction between injection temperature and powder loading (factor BXC) with contribution of 4.08% which are in fact, the most important factors that cannot be neglected.
Furthermore, since all factors have a confident level greater than 90% thus all factors were used to calculate the optimum performance of GRG. This is shown in Table 6 where the optimum performance is at 0.7878 compared to the current grand average performance of 0.6809 (Table 3).
The confident interval is calculated with Eq. 5 (Roy,
2001):
where, F_{α}(f_{1},f_{2}) is the variance ratio for DOF of f_{1} and f_{2} at level of significance α. The confidence level is (1α), f_{1} is the DOF of mean (usually equal to 1) and f_{2} is the DOF of the error. Variance for error terms is V_{e} and number of equivalent replication is given as ratio of number of trials (1+DOF of all factors used in the estimate). The confident interval will indicate the maximum and minimum levels of the optimum performance and it is shown as the expected result as optimum performance in Table 6.
Table 5: 
ANOVA results 

Table 6: 
Estimation of performance as the optimum design 

Table 7: 
Confirmation test 

Confirmation experiments were conducted by running another ten replications at combined setting of A1, B1, C1, D2, E0 and F0. Table 7 shows the results and it was found that the average green strength obtained from the confirmation experiment fell within the prediction 90% confident interval.
CONCLUSION
Effect and optimization of process parameters in injection molding of Ti4V6Al
powder and binders of palm stearin and polyethylene to produce the quality of
green part were successfully investigated through Taguchi Method and GRA. The
optimum injection parameter were found to be A1, B1, C1, D2, E0 and F0 corresponding
to 450 bar of injection pressure, 140°C of injection temperature, 65% vol.of
powder loading, 50°C of mold temperature, 500 bar of holding pressure, and
10ccm/s of the injection rate. Through ANOVA, the injection temperature is the
most significant factor with 26.37% of contribution. The Interaction of factors
between injection pressure and powder loading has shown a contribution rate
of 18.43%, which must not be neglected to produce the green part with high quality.
ACKNOWLEDGMENTS
The authors would like to thank Universiti Teknologi MARA for the research grant, 600IRDC/ST/FRGS 5/3/1300 and Ministry of Higher Education, Malaysia and Universiti Kebangsaan Malaysia for the PhD scholarship.