Journal of Intelligent Learning Systems and Applications, 2010, 2: 28-35
doi:10.4236/jemaa.2010.21004 Published Online February 2010 (http://www.SciRP.org/journal/jilsa)
Determination of Optimal Manufacturing
Parameters for Injection Mold by Inverse
Model Basing on MANFIS
Chung-Neng Huang1, Chong-Ching Chang2
Graduate Institute of Mechatronic System Engineering, National University of Tainan, Tainan, Taiwan, China.
Received October 29th, 2009; accepted January 11th, 2010.
ABSTRACT
Since plastic products are with the features as light, anticorrosive and low cost etc., that are generally used in several
of tools or components. Consequently, the requirements on the quality and effectiveness in production are increasingly
serious. However, there are many factors affecting the yield rate of injection products such as material characteristic,
mold design, and manufacturing parameters etc. involved with injection machine and the whole manufacturing process.
Traditionally, these factors can only be designed and adjusted by many times of trial-and-error tests. It is not only
waste of time and resource, but also lack of methodology for referring. Although there are some methods as Taguchi
method or neural network etc. proposed for serving and optimizing this problem, they are still insufficient for the needs.
For the reasons, a method for determining the optimal parameters by the inverse model of manufacturing platform is
proposed in this paper. Through the integration of inverse model basing on MANFIS and Taguchi method, inversely,
the optimal manufacturing parameters can be found by using the product requirements. The effectiveness and feasibility
of this proposal is confirmed through numerical studies on a real case example.
Keywords: Optimal Manufacturing Parameter, Injection Mold, Multiple Adaptive Network Based Fuzzy Inference Sys-
tem (Manfis), Taguchi Method
1. Introduction
Recently for the surge in the prices of fuel and raw mate-
rials like steel or iron, plastic goods used in industries
and everyday life are taking the place of metal ones.
Generally, since those products combined by pieces of
parts required higher precision and smoothness, the de-
mands on quality and efficiency of production become
higher than before. In order to level up the yield rate of
made-up articles, the manufacturing process should be
improved for the required of different goods [1]. Nowa-
days, for coping with the diversifying demands of present
markets, developed countries in industry have been in-
troducing the technologies of computer-integrated manu-
facture (CIM) as CAE/CAD/CAM to get competitive ad-
vantages [2–3]. That is, for the manufacturing process of
an industrial product with completed design, first, its
prototype is designed by the original concept. Next,
through computer-aided design (CAD) tool complete the
initial design. Third, by the analysis technology of com-
puter-aided engineering (CAE) to test and modify the
design. Finally, depending on the better design, automo-
tive production can be done by computer-aided manu-
facture (CAM).
Before concurrent engineering attracting much attent-
ion, the technologies of computer-aided engineering ana-
lysis were seldom used to estimate designing faults by
manufacturers in advance. Where, mold design and man-
ufacturing process should be modified through many
times of trial-and-error tests [4–6]. It not only wastes
time and cost but also makes such experiences became
more difficult in teaching or accumulating. Besides, un-
der the situation of different product required or new
materials, the awkward problems as one more times of
teaching experience and molding can not be avoided.
Sometimes part of business chances may be losing for it.
The most helpful function of CAE is to carry out
simulation analysis of prototype design by computers [6].
By which, all possible problems and faults occurring in
manufacturing and design stages can be found in advance.
It is convenient to diagnose and modify designed before
product manufacture for reducing cost and time, and lev-

Determination of Optimal Manufacturing Parameters for Injection Mold by Inverse Model Basing on MANFIS 29
eling up quality. However, even though those modern
computer-aided technologies as mentioned above play an
important role in manufacture, the subject of how to de-
termine optimal manufacturing parameters for extremely
matching product required still exists [7–24]. Although
there are a lot of methods such as statistical regression
calculation, neural network model and genetic algorithm,
grey relational analysis, and fuzzy theory etc. proposed
for optimizing parameters [25–30], lacking of method-
ology and integration. For it, a concept for building the
inverse model of manufacturing platforms by multiple
adaptive network fuzzy inference system (MANFIS) is
proposed. Through data self-organized and deductive
reasoning mechanisms of MANFIS, the optimal manu-
facturing parameters corresponding to product required
can be found. In this paper, the blade of a small-scale
wind power generator is selected as a real case studying
on injection mold. Through the simulation results by
computer-aided analysis software Moldex3D, the appro-
priateness and effectiveness of the proposal can be con-
firmed.
2. Solution Design and Problem Statement
2.1 Solution Description
The main purpose of this study is to determine the opti-
mal manufacturing parameters for injection mold. Ac-
cording to the literatures mentioned above know that the
manufacturing parameters of injection mold are highly
interdependent. That is, the whole system should be con-
sidered while part of parameters is undertaken to modify.
Here, a method for finding out the optimal parameters is
proposed. Figure 1 shows the executing flow of the
method. First, since there are always a lot of manufac-
turing parameters as well as controllable factors existing,
in order to realize which ones are the key factors and
Controllable
Factors Taguchi MethodImportant Factors
Orthogonal
Arrays L 9
Random
Matrix
Simulator
Moldex3D
Inverse Model
+
-
e(k)
Controllable
Factors Taguchi MethodImportant Factors
Orthogonal
Arrays L 9
Random
Matrix
Simulator
Moldex3D
Inverse Model
+
-
e(k)
Figure 1. Flow of proposed method
reduce time and flows in computation, a less number of
important factors with more controllability can be ex-
tracted through the calculation of Taguchi method. Next,
instead of all possible experimental combinations to
simulator, the orthogonal arrays basing on those impor-
tant factors are developed. In addition, for the results
found by Taguchi method are unique, and possibly trap-
ping in local optimum, a decimal-fraction random matrix
as the numerical stirring is introduced into the orthogonal
arrays for wider-range simulation. Finally, by using the
simulated results such as warpage displacement or volu-
metric shrinkage etc. along with the corresponded or-
thogonal arrays, the proposed inverse model can be built
through MANFIS.
2.2 Real Case Selection
The real case selected for confirming the proposed
method is the manufacturing design of a blade for a
small-scale wind power generator. Since the blades are
the key part of such generators for their generation effi-
ciency and cost, the weight, smoothness, surface friction,
physical stress, and twisting angles etc. of them are re-
quired seriously in manufacture. In addition, instead of
FRP which is denounced by its environmental pollution,
the material ABS_NovodurP2GHV_1 is adopted to study.
Here, through the analysis of momentum theory and
blade element model, the geometric data of the blade is
determined as shown in Figure 2. Moreover, the hot and
cooling distributions by one-point injection and four
groups of cooling runners are shown in Figure 3.
Figure 2. Studying case designed by 3D’s flow
Figure 3. Distribution of hot runner and cooling runner

Determination of Optimal Manufacturing Parameters for Injection Mold by Inverse Model Basing on MANFIS 30
3. Numerical Studies
Since the initial controllable factors are always selected
by the product required. Through the analysis of fish
bone diagram shown in Figure 4 and the consideration of
required product strength, there are eight factors selected
such as fiber percentage of material, material temperature,
injection pressure, holding time, holding pressure, mold
temperature, cooling time, and filling time.
3.1 Selection of Important Factors by Taguchi
Method
Two major tools used in the Taguchi method are the or-
thogonal arrays and the signal-to-noise ratio. Additional
details and application of Taguchi method can be found
in the books presented by Phadke [31], Montgomery [32],
and Park [33]. In this paper, three- level orthogonal ar-
rays are used. The design parameters and the levels cho-
sen for the Taguchi experiments are listed in Table1.
Continuously, a L18 (38) orthogonal arrays with eight
columns and eighteen rows can be developed as shown in
Table 2. Each design parameter has three levels assigned
to each column of the arrays. The eighteen rows repre-
sent the eighteen experiments to be conducted.
Since the assessing indices are the warpage displace-
ments and volumetric shrinkages in three dimensions as
x, y, and z axes, respectively, through the computations
of simulator Moldex3D all indices corresponding to all
experimental combinations in L18 (38) orthogonal arrays
can be found. By substituting these indices into Equations
Figure 4. Fish bone diagram for factor analysis
Table 1. Eight controllable factors with three levels
level
factor 1 2 3
A. (%) percentage of fiber contents20 16
B. (℃) material temperature 210 225 240
C.(MPa) injection pressure 90 105 120
D. (S) holding time 2 4 6
E. (MPa) holding pressure 63 73.5 84
F. () mold te℃mperature 50 70 87
G. (S) cooling time 10 20 30
H. (S) filling time 2.3 3.65 5
1 to 3, the important factors and optimal combination for
Taguchi method can be extracted and found by assessing
the quality characteristic (in Figure 5) and signal-to-noise
ratio (in Figure 6). By above results realized that the fac-
tors with more controllability as mold temperature, mate-
rial temperature, injection pressure, and holding time are
selected as the important factors.
1
n
i
i
y
yn



(1)

2
1
1
n
i
i
yy
Sn




(2)
2
2
10 S
Sg
Ny
lo (3)
3.2 Collection of Training Data Sets
For training the inverse model to be with more compre-
hensively deductive reasoning, all possible combinations
basing on the changes of four important factors should be
collected in general. However, it would be a cumbersome
task for experiment or computation. For the main advan-
tages of orthogonal arrays including experimental plan
simplification and feasibility of studying interaction ef-
fects among the different parameters, a L9 (34) orthogonal
arrays developing with three levels (Table 3) from above
four important factors is built as shown in Table 4.
Moreover, for more detailed numerical data, a random
matrix (Table 5) as well as a stirring is introduced into
the L9 (34) orthogonal arrays. Table 6 shows the in-
put-output training data sets through the computation of
simulator Moldex3D.
Table 2. L18 (38) orthogonal arrays
ExpA B CD E F G H
1 1 1 1 1 1 1 1 1
2 1 1 2 2 2 2 2 2
3 1 1 3 3 3 3 3 3
4 1 2 1 1 2 2 3 3
5 1 2 2 2 3 3 1 1
6 1 2 3 3 1 1 2 2
7 1 3 1 2 1 3 2 3
8 1 3 2 3 2 1 3 1
9 1 3 3 1 3 2 1 2
102 1 1 3 3 2 2 1
112 1 2 1 1 3 3 2
122 1 3 2 2 1 1 3
132 2 1 2 3 1 3 2
142 2 2 3 1 2 1 3
152 2 3 1 2 3 2 1
162 3 1 3 2 3 1 2
172 3 2 1 3 1 2 3
182 3 3 2 1 2 3 1

Determination of Optimal Manufacturing Parameters for Injection Mold by Inverse Model Basing on MANFIS 31
Figure 5. Quality characteristic (2、B1、C3、D3、E1、F1、G1、H2)
Figure 6. S/N ratio (A2、B1、C3、D3、E1、F1、G1、H2)
Table 3. Four important factors with three levels Table 5. Random matrix example
level
factor 1 2 3
B. () material temperature℃ 220 240 260
C.(MPa) injection pressure 110 120 130
D. (S) holding time 4 6 8
F. () mol℃d temperature 45 50 55
Table 4. L9 (34) orthogonal arrays
Exp B C D F
1 1 1 1 1
2 1 2 2 2
3 1 3 3 3
4 2 1 2 3
5 2 2 3 1
6 2 3 1 2
7 3 1 3 2
8 3 2 1 3
9 3 3 2 1
0.95 0.2311 0.6068 0.486
0.891 0.7621 0.4565 0.0185
0.821 0.4447 0.6154 0.7919
0.922 0.7382 0.1763 0.4057
0.935 0.9169 0.4103 0.8937
0.058 0.3529 0.8132 0.0099
0.139 0.2028 0.1987 0.6038
0.272 0.1988 0.0153 0.7468
0.445 0.9318 0.466 0.4187
3.3 Inverse Model
The proposed inverse model for finding out the optimal
manufacturing parameters corresponding to product re-
quired is built by MANFIS (in Figure 7), which is an
extension of ANFIS to produce multiple real responses
of the target system. The number of ANFIS is equal to
the number n of responses. ANFIS is a fuzzy inference

Determination of Optimal Manufacturing Parameters for Injection Mold by Inverse Model Basing on MANFIS 32
Table 6. Training data sets for MANFIS
exp B C D F X Y Z V
1 220.9 110.2 4.6 45.4 0.402 0.053 -0.1294.14
2 220.8 120.7 6.4 50.0 0.581 0.058 -0.1093.962
3 220.8 130.4 8.6 55.7 0.302 0.132 -0.0383.774
4 240.9 110.7 6.1 55.4 0.326 0.017 -0.0834.774
5 240.9 120.9 8.4 45.8 0.358 0.004 -0.1064.568
6 240.0 130.3 4.8 50.0 0.577 -0.041 -0.1374.888
7 260.1 110.2 8.1 50.6 0.305 0.028 -0.1665.32
8 260.2 120.2 4.0 55.7 0.483 -0.068 -0.2385.796
9 260.4 130.9 6.4 45.4 0.69 0.096 -0.1315.515
X：warpage displacement in x axis
Y：warpage displacement in y axis
Z：warpage displacement in z axis
V：warpage-volumetric shrinkage
Figure 7. The structure of MANFIS
Figure 8. Five-layer structure of ANFIS
system (FIS) implemented in the framework of an adap-
tive fuzzy neural network. FIS is the process of formu-
lating the mapping from a given input to an output using
fuzzy logic.
ANFIS is based on Tagaki-Sugeno FIS. ANFIS gener-
ally has two inputs, one output and its rule base contains
two fuzzy if-then rules:
Rule l: If x is A1 and y is B2 then f1 =p1 + q1+ r1.
Rule 2: If x is A2 and y is B2 then f2 =p2+ q2+ r2.
The five-layered structure of this ANFIS is depicted in
Figure 8. The detailed description about it can refer to the
studies by R. Jang et al. [34–37]. Here, by using the
training data sets in Table 6 and through thirty times of
training, the errors of the unknown constants in each
node of MANFIS have been convergent.
4. Analysis and Discussion
For a complete-trained inverse model that is charac- ter-
ized with the inverse function of the simulator Moldex3D
as well as manufacturing platform. That is, the manufac-
turing parameters can be found by the product required
inversely. Here, the correlations between two kinds of
product required and one manufacturing parameter are
shown by 3D mesh diagrams in Figure 9. In addition to
identify the reasonable areas for product required, the
limits to the four important factors in the real case are set
as following; mold temperature: over 40, material
temperature: over 210, injection pre- ssure: over
90Mpa, holding time: the smaller warpage the better.
C

C

Moreover, for the convenience in observation, the
reasonable intervals of each product required are summa-
rized in Table 7.
In order to confirm the reliability and preciseness of
inverse model, two groups of numerical comparisons are
made as shown in Table 8. Here, by comparing with the
inputs of inverse model with the outputs of simulator
which are corresponding to the outputs of inverse model,
the differences between them are tolerably small. This
appropriate performance of inverse model also can be
observed in Figure 10.
Table 7. Reasonable intervals for product requirements
factor
Product
required
B C D F
X(㎜) 0.302~0.65 0.302~0.65 0.302~0.40.302~0.5
Y(㎜) -0.05~0.05-0.025~0.075 -0.05~0.05-0.05~0.1
Z(㎜) -0.15~0.008 -0.175~0.008 -0.1~0.008 -0.15~0.008
V(％) 4 4 4 4
Table 8. Reliability performance of inverse model
Inverse Model Simulator Moldex3D
Input Output Output
group X Y Z V B C D F X Y Z V
1 0.302 0.09 0.008 4 220 126 7.26 43.4 0.5040.012 -0.102 3.851
2 0.302 0.09 -0.07 4 215 108 6.28 57.9 0.3460.016 -0.028 3.738

Determination of Optimal Manufacturing Parameters for Injection Mold by Inverse Model Basing on MANFIS 33
a. warpage-x-displacement and wa
r
page
y
-
displacement to material temperature.
b
. warpage-z-displacement and wa
r
page-volu-
metric-shrinkage to material temperature.
c. warpage-x-displacement and wa
r
page-
y-displacement to injection pressure.
d. warpage-z-displacement and wa
r
page-
volumetric-shrinkage to injection pressure.
e. warpage-x-displacement and wa
r
page-
y-displacement to pressure holding time.
f. warpage-z-displacement and wa
r
page-
volumetric-shrinkage to pressure holding time.
g. warpage-x-displacement and wa
r
page-
y-displacement to mold temperature.
h. warpage-z-displacement and wa
r
page-
volumetric-shrinkage to mold temperature.
Figure 9. Correlations between two product requirements and one manufacturing parameter in 3D mesh diagrams

Determination of Optimal Manufacturing Parameters for Injection Mold by Inverse Model Basing on MANFIS 34
Table 9. Optimized comparisons between Taguchi method
and proposed method 5. Conclusions
factor
method B C D F
Taguchi method 220℃ 130Mpa 8s 55℃
Proposal 215℃℃ 108Mpa 6.28s 57.9℃
requirement
method X Y Z V
Taguchi method 0.46mm 0.09mm 0.008mm3.79%
Proposal 0.346 0.016 -0.028 3.74%
For solving the optimal problem in manufacturing design
of injection mold, the method basing on the concept of
inverse model is proposed in this paper. Through the me-
thod, the optimal manufacturing parameters can be found
by using the product required inversely. In addition, the
effectiveness and appropriateness of the proposal are
confirmed by the numerical studies on the real case. Yet
the studied results show that the proposed method not
only can improve the insufficiencies of Taguchi method
but also offers a more précising and concise approach for
the optimization of manufacturing design.
6. Acknowledgments
The authors would like to thank Prof. F.B. Hsiao, who is
with the Department of Aeronautics and Astronautics at
National Cheng Kung University, for his providing valu-
able real data for this study.
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