D. KRAMAR, D. CICA: PREDICTIVE MODEL AND OPTIMIZATION OF PROCESSING PARAMETERS ...
597–602
PREDICTIVE MODEL AND OPTIMIZATION OF PROCESSING
PARAMETERS FOR PLASTIC INJECTION MOULDING
MODEL ZA NAPOVEDOVANJE IN OPTIMIZACIJO PROCESNIH
PARAMETROV PRI BRIZGANJU PLASTIKE
Davorin Kramar1, Djordje Cica2
1University of Ljubljana, Faculty of Mechanical Engineering, Ljubljana, Slovenia
2University of Banja Luka, Faculty of Mechanical Engineering, Banja Luka, Bosnia and Herzegovina
davorin.kramar@fs.uni-lj.si
Prejem rokopisa – received: 2016-06-25; sprejem za objavo – accepted for publication: 2017-01-16
doi:10.17222/mit.2016.129
Injection molding is one of the most widely used processes for producing engineered parts in the plastics industry. The objective
of this study is to propose a fuzzy expert system for the prediction of mechanical properties of injection-molded parts where the
fuzzy system is optimized using particle-swarm optimization. The input process parameters were the mold temperature, melt
temperature, injection velocity, packing pressure, cooling time and packing time. The predicted values were in good agreement
with the experimental ones, which indicates that the developed particle-swarm-optimization-based fuzzy expert system can be
effectively used to predict the mechanical properties of molded parts. In addition, optimization based on a particle-swarm-
optimization algorithm was carried out to obtain the optimum process parameters based on the objective to maximize the tensile
strength of the molded product.
Keywords: plastics, injection molding, particle-swarm optimization, tensile strength
Brizganje je eden izmed najpogosteje uporabljenih postopkov za izdelavo in`enirskih delov v industriji plastike. Cilj te
raziskave je predlagati enostavni ekspertni sistem za napovedovanje mehanskih lastnosti delov brizganih kosov, kjer je enostavni
sistem optimiziran z uporabo optimizacije z rojem delcev. Vhodni parametri procesa so temperature orodja, temperatura taline,
hitrost brizganja, zapiralni pritisk, ~as hlajenja in zapiralni ~as. Napovedane vrednosti se dobro ujemajo z eksperimentalnimi,
kar ka`e, da se razvit enostavni ekspertni sistem na osnovi optimizacije z rojem delcev lahko u~inkovito uporablja za napove-
dovanje mehanskih lastnosti brizganih delov. Algoritem optimizacije z rojem delcev je podal tudi optimalne procesne parametre
za doseganje ~im vi{je natezne trdnosti brizganega izdelka.
Klju~ne besede: plastika, injekcijsko brizganje, optimizacija z roji delcev, natezna trdnost
1 INTRODUCTION
Plastic injection molding is the most widely used
manufacturing process for the high-volume production
of relatively complex thermoplastic parts by injecting a
material into a mold. Within this process, a high-pressure
fluid polymer is injected to the cavity with a desired
form. In the next step, under high pressure, while cool-
ing, the fluid solidifies. However, plastic injection mold-
ing is a very complex manufacturing process due to the
strong nonlinearities and a large number of interrelated
parameters. Over the last few decades, artificial-intelli-
gence (AI) methods have become the preferred trend,
applied by most researchers for the optimization and
prediction of various parameters of the injection-molding
process.
S. Kenig et al.1 used a feed-forward artificial neural
network (ANN) with an error back-propagation algo-
rithm for the adequate control of product properties in
injection-molded plastics. W. C. Chen et al.2 developed a
self-organizing map and a back-propagation neural-net-
work model to generate a dynamic quality predictor for
the plastic-injection-molding process. C. Ozek and Y. H.
Celik3 developed software to predict the quality of the
injected parts through an ANN model. H. M. Sadeghi4
studied the possibility of predicting the quality or sound-
ness of the injected parts through an ANN model and
based on computer-aided engineering software simula-
tions. C. F. Juang et al.5 developed a Takagi-Sugeno-
Kang-type recurrent fuzzy neural networks for the
control of the mold temperature. C. Karatas et al.6 deve-
loped an ANN model to determine the yield length in the
plastic molding of commercial plastics. M. Altan7
studied the optimum injection-molding conditions for the
minimum shrinkage based on Taguchi methods, ANOVA
and ANN. H. Shi et al.8 proposed an adaptive optimiza-
tion method based on an ANN model for the minimiza-
tion of the warpage of injection-molded parts. A. Krim-
penis et al.9 proposed ANN meta-models in order to
generalize from the examples connecting input-process
variables to output variables. A neural model is
employed in the fitness function of the genetic algorithm
(GA) for optimization of the injection-molding process.
C. Shen et al.10 proposed a method based on a combina-
tion of the ANN and GA for optimization of the
injection-molding process in order to improve the quality
index of the volumetric-shrinkage variation in the part.
Materiali in tehnologije / Materials and technology 51 (2017) 4, 597–602 597
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UDK 678.027.74:62:66.011 ISSN 1580-2949
Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 51(4)597(2017)
B. Ozcelik and T. Erzurumlu11 determined the most
important process parameters influencing warpage using
finite-element-analysis results based on ANOVA, while
an ANN was interfaced with an effective GA to find the
minimum warpage value. Chen et al.12 presented an
effective approach in a soft-computing paradigm for the
process-parameter optimization of the plastic-injection-
molding process. The proposed approach integrates
Taguchi’s parameter-design method, ANN, GA and
engineering-optimization concepts. Li et al.13 presented a
genetic neural fuzzy system to construct a quality-pre-
diction model for the injection process from the input
and output data. Mathivanan and Parthasarathy14 investi-
gate sink depths in injection-molded thermoplastic com-
ponents by integrating the finite-element-flow analysis
with the central composite design of experiments and
GA. Deng et al.15 proposed a hybrid of the mode-pur-
suing sampling method and the GA for the minimization
of injection-molding warpage. Park and Nguyen16 pre-
sented an injection-molding-process optimization of a
plastic car fender related to the energy consumption and
product quality. J. Cheng et al.17 proposed a multi-
objective optimization model including both mold and
process parameters as design variables in order to
achieve the optimum parameter schemes in accordance
with practical requirements of injection molding. J.
Cheng et al.18 developed a fuzzy moldability-evaluation
approach for the optimization of injection-mold schemes
based on the variable weight-profit vector. K. T. Chiang
and F. P. Chang19 and K. T. Chiang20 proposed an
approach for optimizing process parameters of an
injection-molded part with a thin shell feature based on
the orthogonal array with the grey relational analysis and
fuzzy logical analysis.
Despite the fact that there are numerous applications
of the AI in modeling the injection-molding process
reported in the literature, a review of the literature shows
that only few research works are based on the fuzzy
theory. Furthermore, previous approaches were based on
the usual approach to designing a fuzzy system by
encoding expert knowledge in a direct way using rules
with linguistic labels. However, knowledge acquisition is
not a trivial task so, in the present paper, an attempt was
made to design an optimized fuzzy expert system (FES)
using a particle-swarm-optimization algorithm for pre-
dicting the mechanical properties of the molded parts.
Furthermore, the particle-swarm-optimization (PSO)
algorithm is used in the process optimization in order to
improve the mechanical properties of the injection-
molded parts.
2 EXPERIMENTAL PART
According to the experience with polyoxymethilene
(POM) materials, the following control factors, i.e.,
injection-molding-process parameters influencing pro-
duct mechanical properties, were selected: the mold
temperature (TM), the melting temperature (Tm), the
injection velocity (vi), the packing pressure (ph), the
packing time (th), and the cooling time (tc). The levels of
process parameters are shown in Table 1, being selected
according to material-producer specifications. All the
experiments were carried out on an Engel Victory 200/50
injection-molding machine with a clamping force of 500
kN and a cylinder diameter of 18 mm. The main
characteristic of the investigated POM material is a high
melt-flow rate of 52 g/10 min.
Table 1: Design of experiments and comparison between experimen-
tal results and the predicted breaking force of the injection-molded
toothed rack
Process parameters Expe-riment FES PSOFES
TM
(°C)
Tm
(°C)
Vi
(mm/s)
ph
(bar)
tc
(s)
th
(s)
F
(N)
F
(N)
Error
(%)
F
(N)
Error
(%)
70 185 20 1000 6 2 64.6 62.3 3.6 64.6 0
70 195 40 1150 8 4 69.1 67.5 2.3 66.9 3.2
70 205 60 1300 10 6 72.7 72.8 0.1 72.9 0.3
85 185 20 1150 8 6 64.9 67.5 4 66.7 2.8
85 195 40 1300 10 2 71.8 72.8 1.4 71.9 0.1
85 205 60 1000 6 4 71.9 72.8 1.3 71.8 0.1
100 185 40 1000 10 4 59.6 62.3 4.5 60.5 1.5
100 195 60 1150 6 6 62.1 62.3 0.3 60.7 2.3
100 205 20 1300 8 2 77.3 76.3 1.3 77.1 0.3
70 185 60 1300 8 4 60.7 62.3 2.6 60.7 0
70 195 20 1000 10 6 66.9 67.5 0.9 66.9 0
70 205 40 1150 6 2 70.5 72.8 3.3 70.7 0.3
85 185 40 1300 6 6 59.8 62.3 4.2 60.7 1.5
85 195 60 1000 8 2 62.2 62.3 0.2 62.2 0
85 205 20 1150 10 4 70.2 72.8 3.7 69.6 0.9
100 185 60 1150 10 2 57.7 58.9 2.1 57.8 0.2
100 195 20 1300 6 4 74.2 72.8 1.9 73.8 0.5
100 205 40 1000 8 6 73.7 72.8 1.2 73.7 0
In this study, POM thermoplastic with commercial
designation Kepital F40-03 was utilized. The material is
characterized by high strength, hardness and rigidity,
thermal stability and, especially, a high melt-flow rate.
As such, this material can be used as an extremely easy-
flowing grade for the injection molding of thin-walled
precision parts. The precision of a part and mechanical
properties of a product are even more important when
parts for medical devices are produced. In this paper, the
D. KRAMAR, D. CICA: PREDICTIVE MODEL AND OPTIMIZATION OF PROCESSING PARAMETERS ...
598 Materiali in tehnologije / Materials and technology 51 (2017) 4, 597–602
MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967–2017) – 50 LET/50 YEARS
Figure 1: Plastic-toothed rack within a driving gear (left) and the
usual cause of breakage (right)
injection-molding process of a plastic toothed rack used
as the driving gear of a breast-biopsy system is investi-
gated. Beside high tolerances, dimensional stability and
low friction needed for a sufficient operation, the plastic
rack should fulfil high stiffness and tensile-strength
requirements. The rack should not break when biopsy is
executed (Figure 1).
Orthogonal array L18 was applied to run the experi-
ments (Table 1). All the experiments were repeated 10
times, and molded samples were collected. The samples
were then carefully cut to remove sprue and runner from
the final product: a toothed rack. The breaking point of
each rack was measured with a specially designed
tension test. The average value of the breaking force for
10 rack samples was then calculated. The results of
experiments are shown in Table 1.
3 PSO-BASED FUZZY EXPERT SYSTEM
Fuzzy logic is one of the most successful technolo-
gies for developing rule-based expert systems.
According to the inventor of fuzzy logic L. A. Zadeh21,
fuzzy logic attempts to formalize two human abilities: to
reason in the presence of imperfect information and to
carry out different mental and physical tasks without any
numerical measurements or computations. A fuzzy
inference system (FIS) combines the fuzzy set theory,
fuzzy rules and fuzzy reasoning. According to 22, a FIS is
composed of three parts: a rule base, which contains the
collection of fuzzy rules, a database (or dictionary)
which specifies the membership functions (MFs) used in
the fuzzy rules, and a reasoning mechanism, which infers
the output based on the rule base, database and the given
input.
In this study, the authors designed the rule base and
database of the FES, based on their knowledge of the
injection-molding process. In this FES, the input varia-
bles are: the mold temperature, the melt temperature, the
injection velocity, the packing pressure, the cooling time
and the packing time, while the output variable is the
breaking force. The input variables have three MFs
labeled as low, medium and high, while the output
variable, that is, the breaking force, has five MFs labeled
as very fine, fine, medium, coarse and very coarse. In
order to describe the fuzzy sets for the input and output
variables, a triangular shape of the MFs is employed. In
this study, a Mamdani-type fuzzy inference system is
used, due to its relatively simple structure and intuitive
nature of the rule base, for correlating the injection-
molding parameters with the breaking force. However,
this usual approach for the FES design is characterized
by disadvantages such as dependence of the system
performance on the knowledge of the human expert,
adequate fuzzy rules, MFs and their boundaries. In order
to overcome these shortcomings, a significant amount of
research was carried out on automatic tuning of a FES
using bio-inspired algorithms, such as PSO.
Particle-swarm optimization was first introduced by
J. Kennedy and R. Eberhart23 who defined a swarm as a
population of interactive elements or agents, able to
optimize some global objective through a collaborative
search in space. PSO is a population-based method
where the population is referred to as a swarm. The
swarm consists of a number of individuals called the
particles, which are initialized with random solutions.
These particles fly in a d-dimensional space through
many iterations to search a better solution for the
problem. Every particle in the swarm is represented by a
specific position, initialized by the initial position and by
velocity, where each particle moves in the space accord-
ing to a specific velocity. Furthermore, each particle
holds the information about the best position, the one
associated with the best fitness value the particle has
achieved so far, and the global best position, the one
associated with the best fitness value found among all of
the particles. In this way, the trajectory of each particle is
influenced by the trajectories of the neighborhood
particles as well as the flight experience of the particle
itself. During the iteration time, each particle updates
this information and adjusts its own trajectory in order to
move towards its best position and global best position.
The PSO method has many advantages, such are its
effectiveness, robustness, simplicity and extreme ease of
implementation without the need for cumbersome deri-
vative calculations. The focus of this study is to employ a
PSO for optimizing an already existing fuzzy-rule-based
system. The main idea is the adaptation of the parame-
ters of the input and output MFs by the PSO according to
a fitness function that specifies the design criteria in a
quantitative manner. In this paper, the triangular shape of
MFs is employed to describe the fuzzy sets for the input
and output variables, so the optimization of MF distri-
butions is reduced to the changes of the base widths.
Furthermore, fuzzy rule weights are also optimized by
the PSO.
A parametric study was carried out to find the
optimum values of PSO parameters in order to achieve a
good result. The fitness value of a PSO solution is
estimated based on the mean absolute percentage error of
each training-data sample. The error of each set of the
training data is the deviation of the result (the breaking
force) of the PSO-based FES from that of the desired
one. The optimum values of the PSO parameters for
cognitive acceleration, social acceleration, number of
generations and population size were 0.3, 1.3, 880 and
370, respectively. Figure 2 shows the optimized MF
distributions of the input-output MFs obtained after
fine-tuning using the PSO.
To verify the performances of the proposed FES, the
results of these systems were compared with that ob-
tained using the experimental tests as shown in Table 1.
For the author-defined Mamdani FES, Pearson’s linear-
correlation coefficient was 0.9644, and the mean abso-
lute percentage error was 2.2 %, while the maximum
D. KRAMAR, D. CICA: PREDICTIVE MODEL AND OPTIMIZATION OF PROCESSING PARAMETERS ...
Materiali in tehnologije / Materials and technology 51 (2017) 4, 597–602 599
MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967–2017) – 50 LET/50 YEARS
absolute percentage error was 4.2 %. Pearson’s linear-
correlation coefficient of the PSO-based FES was
0.9899. The mean absolute percentage error and the
maximum absolute percentage error of the PSO-based
FES were 0.8 % and 3.2 %, respectively. Figure 3 shows
a comparison of the predictions of the breaking force of
the injection-molded toothed rack obtained using the
fuzzy-rule-based expert system and the PSO-based fuzzy
expert systems in terms of % error. It is obvious that
there is a very good agreement between the estimated
and experimental values of the breaking force for both
models. On this basis, it can be concluded that the
fuzzy-logic technique is a good alternative for predicting
the breaking force of the injection-molded part within
the range of the input parameters under consideration.
However, in almost all the cases, the prediction results
using a fuzzy system optimized with a PSO algorithm
are more accurate than the conventional fuzzy-rule-based
expert system.
4 INJECTION-PROCESS-PARAMETER
OPTIMIZATION USING A PSO ALGORITHM
In addition to modeling, optimization of process
parameters is one of the most important elements of
injection molding. The selection of optimum process
parameters enables the control of the manufacturing
process to achieve better quality products at a low cost
and high productivity levels. Therefore, the second goal
of our research was to determine the process conditions
to improve the mechanical performance of the part using
the PSO technique as the optimization tool.
Prior to the optimization process, it is necessary to
establish the relationships between the process parame-
ters and objective functions. For this purpose, in this
paper, a systematic methodology based on the response-
surface methodology was applied. A response-surface
model correlating the breaking force and the considered
injection-molding parameters was developed using an
ANOVA24 of the experimental results in the form of a
reduced quadratic model. The determination of the
significant model degree and parameter effects was
based on the F and P values (Table 2). Model F-value is
a test for comparing the model variance with the residual
(error) variance. If the variances are close to the same,
the ratio will be close to one and it is less likely that any
of the factors have a significant effect on the response.
Model F-value is calculated using the model mean
square divided by the residual mean square.
The model F-value of 15.88 implies the model is
significant. There is only a 0.02 % chance that a "model
F-value" this large could occur due to noise. P-values
smaller than 0.05 indicate model terms that are signi-
ficant. In our case, parameters Tm and vi, and products
TM·vi, and ph·tc are significant model terms. However, for
statistical reasons, models contain subsets of all the
possible effects that preserve the hierarchy. A model is
hierarchal if the presence of quadratic terms and
interactions requires the inclusion of all the linear terms
contained within those of the higher order, even if they
do not appear to be significant on their own. The
signal-to-noise ratio of 14.28 and R-squared coefficient
of 0.93 indicate that the model can be used for the
breaking-force prediction. The following mathematical
relationship is obtained with Equation (1):
F T T
v i
= − + ⋅ + ⋅ +
+ ⋅ −
759 2212 0 40865 85927
061292 0 069
. . .
. .
M m
4246 10 2512
0 00910714 0 00876190
⋅ − ⋅ −
− ⋅ + ⋅
p t
T v p ti
h c
M h
.
. . c
m
−
− ⋅0 0209018 2. T
(1)
D. KRAMAR, D. CICA: PREDICTIVE MODEL AND OPTIMIZATION OF PROCESSING PARAMETERS ...
600 Materiali in tehnologije / Materials and technology 51 (2017) 4, 597–602
MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967–2017) – 50 LET/50 YEARS
Figure 2: Optimized membership-function distributions for melt
temperature, injection velocity, cooling time and breaking force of the
PSO fuzzy expert system
Table 2: ANOVA of the experimental results from Table 1
Source Model TM Tm vi ph tc TM·vi ph·tc Tm2
F-value 15.88 1.06 37.60 24.81 0.015 0.33 6.48 8.25 3.49
P-value 0.0002 0.3307 0.0002 0.0008 0.9038 0.5774 0.0314 0.0184 0.0944
Figure 3: Error profile of the predicted breaking-force values obtained
using the author-defined FES and PSO-based FES
The mechanical properties of injection-molded parts
are influenced by many process variables, and five
key-process parameters were selected as the design
variables of the mathematical model: the mold tempera-
ture, melt temperature, injection velocity, packing
pressure and cooling time. The mathematical model of
the injection-molding optimization problem can be
formulated as follows:
Find X = [TM, Tm, vi, ph, tc]
Maximize F(X)
Subject to: 70 = TM = 100, 185 = Tm = 205, 20 = vi = 60,
1000 = ph = 1300, 6 = tc = 10.
The optimum values of the injection-molding-process
parameters were efficiently obtained with the PSO algo-
rithm. In the PSO optimization process, the commonly
used PSO operation parameters were adopted; namely,
the population size, the generation size, the cognitive
acceleration and the social attraction were set as 340,
1240, 0.5 and 1.25, respectively. The optimized results
are listed in Table 3. Compared with the recommended
process parameters, the optimized process parameters
have higher values of the breaking force. The increasing
percentage is approximately 19 % of the average value
of the breaking force (67.2 N).
Table 3: Optimized parameters of the injection-molding process
Optimized parameters Predictedvalue
TM
(°C)
Tm
(°C)
vi
(mm/s)
ph
(bar)
tc
(s)
F
(N)
100 205 20 1000 6 80.4
4.1 Verification of the optimization results
A confirmation test is needed to verify the results of
optimization. A set of 10 experimental repetitions with
the optimum process-parameter settings were conducted.
The results are shown in Table 4. The mean value of 10
repetitions is approximately 80 N, which is in good
agreement with the predicted value.
Table 4: Results of the confirmation test
Repetition 1 2 3 4 5 6 7 8 9 10 Mean
Breaking
force (N) 79 78 79 79 84 81 79 79 81 79 79.8
5 CONCLUSIONS
The present work aims at estimating the mechanical
properties of injection-molded parts using two fuzzy
expert systems as the tools for the prediction. First, the
authors designed a conventional fuzzy expert system,
based on their knowledge of the injection-molding
process and the predicted results for the breaking forces
achieved via this system were compared to the experi-
mental values. The results obtained indicated that the
proposed fuzzy expert system has a prediction accuracy
of 97.8 %. However, the performances of the author-
defined fuzzy expert system are highly dependent on the
expert knowledge, adequate fuzzy rules, membership
functions and their boundaries. In order to overcome
these problems and significantly improve the perfor-
mance of the fuzzy expert system, a particle-swarm-
optimization algorithm was interfaced with the fuzzy
system. The results of the developed particle-swarm-
optimization-based fuzzy expert system were compared,
in terms of accuracy prediction, with the real expe-
rimental data and it was shown that the hybridization
between fuzzy systems and particle-swarm optimization
provides a more accurate result compared to an author-
defined fuzzy expert system. The accuracy of 99.2 %
indicates that the particle-swarm-optimization-based
fuzzy expert system can be used effectively to predict the
mechanical properties for an injection-molding process.
The second objective of this work was to find the
optimum process parameters to improve the mechanical
properties of injection-molded parts using a particle-
swarm-optimization algorithm as the optimization
technique. In the first stage, the response-surface
methodology was deployed to establish the relationship
between the process parameters and the performance of
the objective functions. In the second stage, the
particle-swarm-optimization algorithm was interfaced
with this nonlinear model of the injection-molding sys-
tem to find the optimum values of the process para-
meters. The same design variables as for the fuzzy expert
system were considered, while the optimum values of
these process parameters were obtained for the maximi-
zation of the breaking force subject to some constraints.
The research results indicate that the proposed
optimization method can effectively help manufacturers
to determine the optimum injection-molding-process
parameters and, thereby, significantly improve the
mechanical performance of injection-molded parts.
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