Multiple Performance Optimization for the Best Metal Injection Molding Green Compact
M.N. Ab. Rahman,
N.H. M. Nor,
This study presents and demonstrates the effectiveness of optimizing multiple quality characteristics of the injection molding of the MIM green compacts via Taguchi method-based Grey analysis. The modified algorithm adopted here was successfully used for both detraining the optimum setting of the process parameters and for combining multiple quality characteristics into one integrated numerical value called Grey relational grade. The significant molding parameters were identified as (1) Injection Pressure (2) Injection Temperature (3) Powder Loading (4) Mold Temperature (5) Holding Pressure and (6) Injection Speed. In addition, the multiple quality characteristics required are: (1) less defects (2) strong and (3) denser compact. The result concluded that the powder loading (C) is very significant for the combination of the quality characteristics.
Received: October 22, 2010;
Accepted: November 01, 2010;
Published: April 18, 2011
Manufacturing a defect free Metal Injection Molding (MIM) compact with superior
final density that is very close to the theoretical density is desirable. Besides
that, the strength of the green compact is also desirable because stronger green
compact is easy to be handled for the next processes. Many optimization of the
MIM process parameter has been published by many authors (Omar,
1999; Ismail et al., 2005; Barriere
et al., 2002; Chuankrerkkul et al., 2008)
without using any of the statistical based Design of Experiment (DOE) methodology,
ends with unsatisfactory results in a wide range of experimental settings. However,
authors of literatures (Berginc et al., 2006;
Jamaludin et al., 2007) use the Taguchi method
as a DOE to optimize the green part quality. The Taguchi method has been extensively
adopted in manufacturing to solve some confusing problems and to improve product/process
design optimization with a single quality performance (Tsao,
2009; Park, 1996). In order to improve the flexibility
and ability of the Taguchi method, Deng (1989) proposed
a grey relational analysis to fulfill the crucial mathematical criteria for
dealing with a poor, incomplete and uncertain system (Tsao,
2009). Grey relational analysis can effectively be recommended as a method
for optimizing the complicated inter-relationships among multiple responses
(Tsao, 2009; Kopac and Krajnik,
2007). Through the Grey relational analysis, a Grey Relational Grade (GRG)
is obtained to evaluate the multiple performance characteristics. As a result,
optimization of the complicated multiple response can be converted into the
optimization of a single Grey Relational Grade (GRG). The Grey-Taguchi method
was established for combining both Grey relational analysis and the Taguchi
method. The Grey-Taguchi method was successfully applied to optimize the multiple
responses of complicated problems in manufacturing processes. In this study,
the Grey-Taguchi method was used to optimize the injection molding process parameter.
The multiple response included defect free, strong and dense green compact.
This is by the fact that the optimum injection molding process parameter is
crucial for making sure the final compact manufactured by this advanced manufacturing
process is tremendous.
MATERIALS AND METHODS
A 316L stainless steel gas atomized powder with pycnometer density of 7.93 g cm-3 has been mixed with Polyethylene Glycol (PEG), Polymethyl Methacrylate (PMMA) and Stearic Acid (SA) as a binder. The binder composition is 73% PEG + 25% PMMA + 2% SA based on the weight fraction. A powder metal particle size distributions used is in a bimodal distribution consisting of 70% of coarse powder in a weight fraction.
RESULTS AND DISCUSSION
The Design Of Experiment (DOE) includes six controllable injection parameters
at three level and coded values are tabulated in Table 1.
The experimental frame is a region determined by the lower and upper limits
of parameters settings that are of major interest. The range of the injection
pressure (A) and injection temperature (B) is limited by the rheological result
of the feedstock as presented in the previous publications (Jamaludin
et al., 2008; Jamaludin et al., 2010).
The powder loading (C) was selected based on the critical powder loading (Ismail
et al., 2005)of the metal powder used in this study while other parameters
were based on the preliminary experiment done prior to the optimization using
As shown in Table 2 the Taguchi orthogonal array of L27
(3)13 has been employed to explore the process interrelations within
the experimental setting. The orthogonal array has 13 columns and 27 rows; each
injection molding parameter was assigned to a column, according to standard
linear graph (Park, 1996; Jamaludin
et al., 2009a). The mean of the quality performance (response) of
the experiment parameter is as shown on the right hand side of the Table
2, green appearance, flexure strength and density of the injection molded
green compacts are to be optimized in this study.
|| Injection parameters and their levels
Further, they are linear normalized according to the type of response. In the
context of Taguchi method, the green compact surface appearance is the lower-the-better
performance response whilst on the other hand the green compact density and
strength is the higher-the-better performance. The Grey Relational Grade (GRG)
shown in Table 2 was 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 the-higher-the-better, then the original
sequence can be normalized as:
where, xi° is the original sequence, x* (k) the sequence
after the data preprocessing, max xi° (k) the largest value of xi° (k)
and min xi° (k) implies the smallest value of xi° (k) for the i th experimental
run. Note that the complete experiments result is not presented in this study,
however the max xi° (k) and min xi° (k) was obtained from the data replication
of each experiment run, i based on the Taguchis orthogonal array. The
larger normalized results correspond to better performance and the best normalized
result should be equal to 1 (Deng, 1989).
When the form the-smaller-the-better becomes the expected value of the data sequence, the original sequence can be normalized as:
The Grey relational coefficients are calculated to express the relationship between the ideal (best) and the actual experimental results. The Grey relational coefficient, ζi (k) can be expressed as:
where, Δoi is the deviation sequence of the reference sequence
(xo) and the comparability sequence (xi), i.e., Δoi
= || xo (k)-xi (k)||, where xB (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). Δ max is the largest value of Δoi
and the Δ min is the smallest value of Δoi. Next, the Grey
relational grade ζ(xo, xi) is computed by averaging
the Grey relational coefficient corresponding to each quality characteristic
is defined as:
where n is the number of quality performance.
|| The design of experiment
|| Response table for grey relational grade
The Grey Relational Grade (GRG) shows the correlation between the reference
sequence and the comparability sequence. The evaluated GRG fluctuates from 0
to 1 and equals 1 if these two sequences are identically coincident. The GRG
is ranked for each experiment. The higher GRG implies that the corresponding
experimental result is closer to the ideal normalized value. In the other words,
the larger the GRG, the better will be the multiple performance characteristic.
Owing to the fact that experiment 14 has the highest GRG (0.920098), it has
the best multiple performance characteristics among all experiments. The injection
parameters are: (1) Injection Pressure, 450 bar; (2) Injection Temperature,
140°C; (3) Powder Loading, 64.5% Vol; (4) Mold Temperature, 45°C; (5)
Holding Pressure, 900 bar; and (6) Injection Speed, 10 cm s-1.
Table 3 shows the response table and graph of the GRG of
each injection parameters at different level respectively. The response of the
GRG shown in Table 3 indicates the powder loading, C is the
most critical parameter for the best multiple performance characteristic, followed
by the holding pressure (E), injection pressure (A), while the least important
is the injection temperature (B). Although the injection pressure (A) and injection
temperature (B) are not ranked as the first but they are still important to
displace the melt into the mold cavity. Poor green compact appearance and density
are predominantly resulted from the extreme injection pressure (A) and injection
temperature (B). The influence of the extreme injection pressure (A) and injection
temperature (B) has been discussed thoroughly from the rheological perspective
of the feedstock by literatures (Jamaludin et al.,
2008; Jamaludin et al., 2010; Mohamad
Nor et al., 2009).
The combination of the A0 B0 C1 D2 E0 F2 is the optimal combination of the
injection parameter for the best multiple performance characteristics and the
optimal parameter is as shown in Table 4. The Taguchi method
can not only provide the solid suggestion in recommending the dominant parameter
for single quality characteristics, but also offer an effective algorithm for
clarifying the specific cross interaction between parameters.
||The cross interaction between factors: Injection Pressure
(A) Vs. Injection Temperature (B) and Powder Loading (C)
|| Process performance at optimal parameter levels
Consequently, the evaluated data can also be rearranged to indicate cross interaction
between factors. Figure 1 illustrates the cross interaction
between the injection pressure (A) versus injection temperature (B) and powder
loading (C). As clearly shown in the figure, the factors had cross interaction
between each other. The highest point indicates the optimum performance (A1xB1
and A1xC1). The cross interaction between the two parameters thus might mislead
the regular Taguchi method recommendation and make it necessary to reconsider
from a fresh perspective of optimizing the injection molding parameter. To further
optimize the injection pressure, injection temperature and the powder loading,
the highest Grey grade is to be considered and thus the new optimum injection
molding parameter is A1B1 C1 D2 E0 F2.
A confirmation experiment is the last step for the Grey-Taguchi method to verify
the improvement of the multiple performance characteristics at the optimal levels
of selected injection molding parameters. The optimum combinations for the injection
molding parameters combination were set and ten trials were conducted in the
confirmation experiment and the result lies in the range of the optimum GRG.
The optimum combination will be used for injection molded the green compact
for the next process, debinding and sintering (Jamaludin
et al., 2009b).
Optimization of multiple MIM green compact quality performance using Taguchi method based Grey relational analysis was studied in this study. The calculation of the Grey relational grade helped to quantify the integrated quality performance required for the MIM green compacts. Accordingly, the optimum combination of the injection molding parameter to fulfill the requirement of the green part quality is A1B1 C1 D2 E0 F2 and the powder loading (C) is the most important parameter that needs to pay more attention during the injection molding process.
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