Proceedings of International Conference on Mechanical & Manufacturing Engineering (ICME2008), 21– 23 May 2008, Johor Bahru, Malaysia.
© Faculty of Mechanical & Manufacturing Engineering, Universiti Tun Hussein Onn Malaysia (UTHM), Malaysia.
ISBN: 97–98 –2963–59–2
Analysis of Variance on the Metal Injection molding parameters using a
bimodal particle size distribution feedstock
Khairur Rijal Jamaludin1, Norhamidi Muhamad2, Mohd Nizam Ab. Rahman2, Sri Yulis M.
Amin2, Muntadhahadi2
1
Department of Mechanical Engineering, College of Science and Technology, University of
Technology Malaysia, City Campus, 54100 Kuala Lumpur, Malaysia.
2
Precision Process Research Group, Dept. of Mechanical and Materials Engineering, Faculty of
Engineering, National University of Malaysia, 43600 Bangi, Selangor Darul Ehsan, Malaysia.
Email: khairur@citycampus.utm.my
Abstract:
The paper describes author’s work on the investigation of the molding parameter for the metal
injection molding (MIM) feedstock. Bimodal particle size distribution of SS316 L powder was
used in the investigation and the metal powder was covered with PMMA and PEG as its binder.
Taguchi’s L27 orthogonal array has been used as DOE while green defects, green density and
green strength were assumed to be the quality characteristic (response). A green defect has been
measured using parameter design for discrete data technique while the green density and green
strength were measured according to the MPIF 42 and MPIF 15 respectively. Classical analysis
of variance (ANOVA) was used to investigate the significance of each molding parameters and
finally propose the optimum molding parameter.
Keywords: Analysis of variance (ANOVA), Metal injection molding, bimodal powder
distribution, Taguchi method, Design of experiment (DOE).
1. Introduction
Metal injection molding (MIM) is
expected to be very efficient for
manufacturing small and complex metallic
components in large batch. Research on MIM
concerns three main stages: injection molding
of a feedstock, thermal or catalytic debinding,
and sintering [1]. The determination and
optimization of the process parameters have
motivated numerous research works, as it
needs deep knowledge on different processes
and accurate modeling techniques for each
stage.
Traditional approach to experimental
work is to vary one factor at a time, holding
all other factors fixed. This method does not
produce satisfactory results in a wide range of
experimental settings. Other workers [2-5],
used classical Design of Experiment (DOE)
technique to study the effects of injection
parameters on the green part quality
characteristics (response) such as density,
strength and defects.
Furthermore, for many experimental
situations in practice, more than one response
will be measured for the different
combination of values which a set of design
variables may take. When it involved several
responses, the optimum condition for one
response is not very likely equal to the
optimum condition for the other response [6].
In this paper, authors will discuss how to
find the overall optimum condition for
several responses when parameter designs
using orthogonal arrays was employed. Thus,
simultaneous optimization using analysis of
variance (ANOVA) is the best method for the
optimization of multiple characteristics
problem.
Proceedings of International Conference on Mechanical & Manufacturing Engineering (ICME2008), 21– 23 May 2008, Johor Bahru, Malaysia.
© Faculty of Mechanical & Manufacturing Engineering, Universiti Tun Hussein Onn Malaysia (UTHM), Malaysia.
ISBN: 97–98 –2963–59–2
TABLE 2 Injection parameters for three
levels Taguchi design
2. Experimental Procedure
2.1 Sample preparation
A 316L stainless steel gas atomized
powder with pynometer density of 7.93 g/cm3
has been mixed with polyethylene glycol
(PEG), polymethyl methacrylate (PMMA)
and stearic acid (SA) as a binder.
A powder metal particle size distributions
used is in a bimodal distribution consisting of
70 % of coarse powder in a weight fraction.
Particle size distribution shown in Table 1,
was measured using Mastersizer, Malvern
Instrument.
TABLE 1 Particle size distributions in µm
Coarse
Fine
D10
D50
D90
SW
9.563
5.780
19.606
11.225
40.058
19.840
4.159
4.873
Prior injection, the compositions were
mixed in a sigma blade mixer for 95 minutes
at 70 oC. MPIF 50 standard tensile bars were
injection molded using Battenfeld BA 250
CDC injection molding machine.
2.2 Design of experiment (DOE)
Taguchi’s orthogonal arrays were used in
engineering analysis and they consist of the
ranges of MIM process parameters based on
three-level design of experiments as shown in
Table 2.
Beside those parameters, interactions
between three important parameters such as
injection pressure, injection temperature and
powder loading were involved in the
investigation. As the overall degree of
freedom for the single parameters and
interactions being 24, Taguchi orthogonal
array L27 is the most suitable for the DOE.
Physical defects of the green part, green
strength and green density were the quality
characteristics which to be investigated by the
authors. Score for the green defects is as
shown in Table 3 while the green strength
and green density were measured according
to the MPIF Standard 15 and MPIF Standard
42 respectively.
A
0
350
Level
1
450
2
550
B
130
140
150
C
64
64.5
65
D
45
48
51
E
700
900
1100
F
10
15
20
Parameters
Injection
Pressure (bar)
Injection
Temperature
(oC)
Powder Loading
(% volume)
Mold
Temperature
(oC)
Holding
Pressure (bar)
Injection Speed
(ccm/s)
TABLE 3 Rating for defects
Weld lines
Incomplete filling
Binder separation
Binder burnt out
Green broken during mold opening
Slumps
Deflection
Chipping at gate
Flashing
Green broken during ejection
1
3
0.5
0.5
3
3
3
2
0.5
3
3. Results and Discussion
Taguchi technique utilizes the signal
noise ratio (SN) approach to measure the
quality characteristic deviating from the
desired value. It is also used the SN ratio
approach instead of the average value to
convert the experimental results into a value
for the evaluation characteristic in the
optimum parameter analysis [7]. The SN ratio
is quoted in decibel is as shown in equation
(1).
SN = -10 log (MSD)
(1)
where MSD is the mean-square deviation for
the quality characteristic. The smallest-thebetter quality characteristic was employed for
the green defects and, the largest-the-better
was for the green strength and density. The
MSD for the smallest-the-better is as shown
Proceedings of International Conference on Mechanical & Manufacturing Engineering (ICME2008), 21– 23 May 2008, Johor Bahru, Malaysia.
© Faculty of Mechanical & Manufacturing Engineering, Universiti Tun Hussein Onn Malaysia (UTHM), Malaysia.
ISBN: 97–98 –2963–59–2
in equation (2) and for the largest-the-better
as in equation (3).
 N 2
 Yi 


 i =1

∑
MSD =
1
N
MSD =
1  N 1
∑
N  i =1 Yi 2
(2)




(3)
where Yi in equation (2) is the amount of
score for the defects obtained from Table 3
and, N is the total number of shots for each
trial. However, the Yi in equation (3) is the
green strength and green density respectively.
Table 4 tabulated the SN ratio for each
response calculated with equation (1).
TABLE 4 SN ratios for defects, green
strength and density
Run
SN for
defects
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
-12.78
-12.79
-11.38
-9.16
-9.98
-11.38
-2.67
-12.16
-14.15
-15.15
-15.23
-9.47
-6.48
-12.27
-12.00
-11.09
-13.04
-12.03
-8.66
-7.28
-12.52
-14.18
-10.99
-15.94
-12.39
-12.38
-15.34
SN for
green
strength
20.47
19.83
17.97
20.55
19.63
20.84
19.35
19.72
18.91
19.15
20.16
20.63
19.78
20.72
19.88
20.82
19.91
17.18
19.02
21.16
18.47
19.98
20.16
17.47
19.50
17.88
20.81
SN for
green
density
14.45
14.46
14.54
14.58
14.52
14.82
14.41
14.60
14.48
14.25
14.50
14.84
14.40
14.58
14.47
14.58
14.54
14.39
14.19
14.69
14.16
14.52
14.53
14.20
14.41
14.30
14.68
The ANOVA table for defects is as
shown in Table 5. The optimum condition for
defects is A0 B2 C0 D2 F1 and, A0 B2 is the
interaction of A×B. From Table 5, we judge
that A, B and E are not significant because its
significant level is greater than 10%. It shows
that A×B and F is significant at the 1% level,
as well as factors C, A×C; and B×C, D is
significant at the 2.5% and 5% level
respectively.
TABLE 5 ANOVA table for defects
Source of
variation
Degree
of
freedom
Sum of
Squares
(2)
A
(10.74)
(2)
B
(0.61)
4
A×B
58.23
2
C
26.56
4
A×C
44.58
4
B×C
33.09
2
D
17.33
(2)
E
(1.31)
2
F
32.63
8
error
14.44
26
Total:
226.87
**
indicates 1 % significant
*
indicates 2.5 % significant
†
indicates 5 % significant
Variance
pooled
pooled
14.56
13.28
11.15
8.27
8.67
Pooled
16.32
1.81
F
8.04**
7.34*
6.16*
4.57†
4.79†
9.02**
TABLE 6 ANOVA Table for green strength
Source
Degree
Sum of
of
of
Squares
variation freedom
(2)
(0.8585)
A
(2)
(1.3601)
B
(4)
(1.8732)
A×B
2
3.3975
C
(4)
(0.5206)
A×C
(4)
(1.957)
B×C
2
15.5046
D
(2)
(1.9)
E
2
2.6891
F
20
8.7154
error
26
30.3066
Total:
**
indicates 1 % significant
†
indicates 5 % significant
‡
indicates 10 % significant
Variance
polled
polled
polled
1.6988
Polled
Polled
7.7523
Polled
1.3445
0.43577
F
3.9†
17.79**
3.09‡
Moreover, Table 6 shows the ANOVA
table for the green strength. Only C, D and F
were significant for the green strength while
the optimum condition being C1 D0 F1 and, the
remaining were pooled because its significant
level is greater than 10%. From Table 6, D is
Proceedings of International Conference on Mechanical & Manufacturing Engineering (ICME2008), 21– 23 May 2008, Johor Bahru, Malaysia.
© Faculty of Mechanical & Manufacturing Engineering, Universiti Tun Hussein Onn Malaysia (UTHM), Malaysia.
ISBN: 97–98 –2963–59–2
significant at 1% while C and F are
significant at 5% and 10% respectively.
On the other hand, only A and D were
significant for the green density (Table 7),
and the optimum condition is A0 D0. D and A
is significant at 1% and 10% respectively.
TABLE 7 ANOVA Table for green density
Source
Degree
Sum of
of
of
Squares
variation freedom
2
0.08460
A
(2)
(0.01579)
B
(4)
(0.05257)
A×B
(2)
(0.05739)
C
(4)
(0.05822)
A×C
(4)
(0.06435)
B×C
2
0.33120
D
(2)
(0.03794)
E
(2)
(0.04843)
F
22
0.34639
error
26
0.76219
Total:
**
indicates 1 % significant
‡
indicates 10 % significant
Variance
F
0.0423
pooled
pooled
pooled
pooled
pooled
0.1656
pooled
pooled
0.01575
2.69‡
10.51**
The summary table shown in Appendix 1
shows the mean of SN ratios of significant
factors. Appendix 1 shows factor A is only
significant for the green density of only 10%
significant compared to A×B for the green
defects of 1% significant. In addition, factor
C0 for the green defects (2.5% significant) is
more significant than the green strength of
5% significant. While, factor D0 for the green
density and green strength is 1% significant
compared to the D2 for the green defects of
only 5% significant. Factor F1 for the green
defects is more significant than for the green
strength.
Since A×B for the green defects is 1%
significant, thus A2B0 is the optimum. Note
that lower the percentage of significant
indicates
higher
confidence
interval.
However, factor B and E are the nonsignificant factors that does not contribute for
the overall optimum condition. Furthermore,
B×C is 5% significant but it is less
meaningful in appearance compared to factor
A×B of 1% significant and factor C of 2.5%
significant.
By considering factors with higher
confidence interval have closer significance
to the overall optimum condition, the
simultaneous optimal parameter for this
injection process is A2B0 C0 D0 F1.
4. Conclusions
a. Simultaneous optimum condition for
the MIM using bimodal particle size
distribution feedstock was found by
analysis of variance.
b. Each
response
has
different
significant factors and different
optimal levels.
c. Interaction of A×B is more significant
than other interactions, i.e. A×C and
B×C.
d. Factor E and B (without interaction) is
the non-significant factors that do not
contribute for the overall optimum
condition.
Acknowledgement
Thanks you to the Universiti Kebangsaan
Malaysia for the research grant, UKM-KK02-FRGS0013-2006 and the Universiti
Teknologi Malaysia for the PhD scholarship.
References
[1] German R.M dan A. Bose, Injection
Molding of Metals and Ceramics, MPIF,
New Jersey 1997.
[2] T. Barriere, B. Liu and J.C. Gelin,
Journal
of
Materials
Processing
Technology, 143-144, pp. 636-644, 2003.
[3] Mohd Afian Omar, Injection molding of
316L stainless steel and NiCrSiB alloy
powders using a PEG/PMMA binder,
Ph.D Thesis. University of Sheffield,
1999.
[4] Muhammad Hussain Ismail, Kesan
pembebanan serbuk logam terhadap
fenomena pemprosesan dalam pengacuan
suntikan logam, Tesis Sarjana Sains.
Universiti Kebangsaan Malaysia, 2002.
[5] Murtadhahadi, Parameter penyuntikan
bagi proses pengacuan suntikan logam
Proceedings of International Conference on Mechanical & Manufacturing Engineering (ICME2008), 21– 23 May 2008, Johor Bahru, Malaysia.
© Faculty of Mechanical & Manufacturing Engineering, Universiti Tun Hussein Onn Malaysia (UTHM), Malaysia.
ISBN: 97–98 –2963–59–2
[7] H. Oktem, T. Erzurumlu, and I. Uzman,
bagi bahan suapan daripada SS 316L
PEG, PMMA dan Asid Stearik, Tesis
Materials and Design, 28, pp. 1271-1278,
Sarjana Sains. Universiti Kebangsaan
2007.
Malaysia, 2006.
[6] Park, S.H, Robust Design and Analysis
for Quality Engineering, Chapman &
Hall, London 1996.
APPENDIX 1
OVERALL SUMMARY TABLE FOR OPTIMAL CONDITIONS
FACTOR
LEVEL
DEFECTS
A×
×B **, A×
×C*,
B×
×C†, C*, D†,
F**
A
B
C
D
E
F
A×
×B
A×
×C
B×
×C
**
0
1
2
0
1
2
0
1
2
0
1
2
0
1
2
0
1
2
A0 B0
A0 B1
A0 B2
A1 B0
A1 B1
A1 B2
A2 B0
A2 B1
A2 B2
A0 C0
A0 C1
A0 C2
A1 C0
A1 C1
A1 C2
A2 C0
A2 C1
A2 C2
B0 C0
B0 C1
B0 C2
B1 C0
B1 C1
B1 C2
B2 C0
B2 C1
B2 C2
indicates 1 % significant
indicates 2.5 % significant
†
indicates 5 % significant
‡
indicates 10 % significant
*
GREEN
DENSITY
A‡, D**
GREEN
STRENGTH
C†, D**, F‡
OVERALL
OPTIMUM
19.85
19.91
19.13
20.57
19.59
18.72
√
14.54
14.50
14.41
-10.29
-11.79
-12.69
-11.77
-12.47
-10.53
-12.70
-10.09
-11.98
-12.32
-10.1753
-9.66
-13.28
-10.25
-12.05
-9.49
-13.71
-13.37
-8.20
-11.64
-12.31
-10.91
-13.51
-11.17
-11.75
-10.22
-14.60
-12.20
-11.77
-11.12
-9.94
-11.08
-13.11
-8.72
-12.53
-13.84
14.64
14.43
14.38
19.58
20.04
19.27
√
√
√