Materials and Design 32 (2011) 414 423
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Materials and Design
journal homepage: www.elsevier.com/locate/matdes
Technical Report
Optimization of injection molding process parameters using sequential
simplex algorithm
*
Behrooz Farshi , Siavash Gheshmi, Elyar Miandoabchi
School of Mechanical Engineering, Iran University of Science & Technology, Tehran 16846, Iran
a r t i c l e i n f o a b s t r a c t
Article history:
In this study warpage and shrinkage as defects in injection molding of plastic parts have been under-
Received 21 April 2010
taken. MoldFlow software package has been used to simulate the molding experiments numerically. Plas-
Accepted 25 June 2010
tic part used is an automotive ventiduct grid. The process optimization to minimize the above defects is
Available online 30 June 2010
carried out by sequential simplex method. Process design parameters are mold temperature, melt tem-
perature, pressure switch-over, pack/holding pressure, packing time, and coolant inlet temperature.
The output parameters aside from warpage and shrinkage consist of part weight, residual stresses, cycle
time, and maximum bulk temperature. Results are correlated and interpreted with recommendations to
be considered in such processes.
Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction determination of the best set of process parameters a priori by
an optimization procedure is the best way for minimization of such
Many products in different areas such as aviation, automotive, defects [1 3].
electronic apparatus are produced using plastic injection molding. In this field some researchers have focused on finding surrogate
Having special features like capability to produce complex parts, models like support vector regression, neural network and polyno-
light weight, resistance to corrosion, ease of producing compared mial regression in lieu of expensive and time-consuming experi-
to conventional materials, are the main reasons for their popular- mentations. These surrogate models are considered as a
ity. High quality and precision can be achieved using this method mathematical approximation replacing the actual simulation anal-
for manufacturing plastic parts. The need for lighter, more aes- yses. Using response surface method and neural network model,
thetic and durable products necessitates manufacturing thinner Erzurumlu made reduction in warpage in thin shell plastic parts
parts. Since most molten plastics cannot fill the mold cavity of thin [4]. Kurtaran et al. optimized warpage for a bus ceiling lamp casing
walled parts suitably, plastic injection molding need be used which utilizing genetic algorithm and neural network model [5]. Zhou
can result in warpage [1]. Therefore, reduction and control of war- et al. used support vector regression for optimization of injection
page is of importance in enhancement of the quality. Hence, war- molding process [6]. Shen et al. optimized process parameters for
page minimization plays a key role in the product optimization. reducing maximum volumetric shrinkage difference using genetic
As the thickness decreases, the strength is also weakened. There- algorithm and neural networks [7].
fore, ultimately the problem can be solved using the right kind of These papers apparently show that surrogate models are good
material for the purpose of durability. approximations of the actual ones reducing time and computa-
Ordinarily, production shop operators can adjust only one pro- tional cost. However, these surrogate models are classified as
cess parameter at a time and this does not necessarily lead to the one-step optimization, without iterations. Therefore, the accuracy
real optimum combination of process parameters. This is particu- of the surrogate models determines how accurate the optimum
larly true when the objective function like warpage and/or volu- solution is.
metric shrinkage is an implicit function of the control variables Since it is a time-consuming work to optimize warpage and vol-
and possible interaction among them. umetric shrinkage, an efficient optimization method called
Warpage and volumetric shrinkage as major defects in such   sequential simplex optimization is used here; a zero order opti-
manufactured parts are subject to change by the shape of parts, mization method not requiring any gradient computations. In this
modifying the mold and having different sets of process parame- paper, we firstly introduce sequential simplex optimization meth-
ters. The design of mold and part are usually considered in the very od, and subsequently the working models.
start of design procedure and remain unchanged. Consequently, Huang and Tai stated that the most crucial factors that affect
warpage in injection molding of a thin shell part are packing pres-
sure, mold temperature, melt temperature and packing time [8].
* Corresponding author. Tel.: [phone]; fax: [phone].
E-mail address: [e-mail] (B. Farshi). However, since minimization of both warpage and volumetric
0261-3069/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved.
doi:10.1016/j.matdes.2010.06.043
B. Farshi et al. / Materials and Design 32 (2011) 414 423 415
shrinkage is considered in this paper, a higher number of variables
namely, mold temperature, melt temperature, pressure switch-
over, pack/holding pressure, packing time, coolant inlet tempera-
ture are considered as the variables for optimization.
Thus in this study the values of process parameters are sequen-
tially obtained by the Finite Element Analysis (FEA) software Mold-
Flow, and used in the sequential simplex algorithm for gradual
convergence to the optimum level. Many researchers have used
MoldFlow for their numerical experimentations, and have shown
that it can adequately simulate analysis of injection molding pro-
cess with a good precision and accuracy [1,2,9 12].
In this paper, volumetric shrinkage is also minimized and its
corresponding warpage, cycle time, maximum bulk temperature
and part weight are obtained. I addition warpage is minimized sep-
arately, and its corresponding volumetric shrinkage, cycle time,
maximum bulk temperature and part weight are determined. Then
a comparison is made in order to find the best compromised pro-
cess parameters for highest quality commensurate with least time
as the most significant cost factor.
In this study, thin shell part which is an automotive ventiduct
Fig. 1b. Variable-size simplex procedure.
grid is selected which has also been used in the paper of Sedaghat
et al. [12].
2.2. Variable-size simplex
2. Definition of sequential simplex optimization method
Nelder and Mead made two basic modifications to the fixed-
The sequential simplex algorithm uses what is known as EVOP
size simplex of Spendley et al. [15]. These modifications let the
(EVolutionary OPeration). There are two major types of sequential
simplex expand in favorable direction and contract in unfavorable
simplex algorithm which are fixed-size simplex and variable-size
ones. Since the size of simplex is subject to change in this modified
simplex, the definition of which are given in reference [13].
method, it is called variable-size simplex. Fig. 1b shows the stages
of this procedure.
2.1. Fixed-size simplex
In fixed-size simplex, the simplex eventually rotates around the
optimum point unable to converge on it. However, in variable-size
Spendley et al. published a paper in 1962, in which they set out
simplex, the simplex continually changes its size to eventually col-
to make EVOP an automated procedure [14]. They introduced the
lapse onto the optimum point. Considering the advantages of var-
simplex geometry as a figure having one vertex more than the
iable-size simplex method it is adopted for use in this
number of variables of the optimization design space, bound by
investigation.
the lowest number of sides. The principle of this optimization
method is to successively reject the worst vertex of the simplex
as the most undesirable design point and replace it with a better
3. Finite element model of automotive ventiduct grid
one. This is done by projection of the rejected point through the
centroid of remaining vertices as is indicative of a path of progress
Geometry of the automotive ventiduct grid used in this study is
towards better points. This procedure gives a new simplex on
shown in Fig. 2a after plastic injection molding. It was designed in
which another simplex operation can be done. This procedure
CATIA without consideration of defects like warpage and volumet-
can go on till the optimum point is reached where the vertices coa-
ric shrinkage and saved as a STL file to be imported to MoldFlow.
lesce over that point. Fig. 1a shows the sequential steps involved in
Afterwards, finite elements (FE) model of the automotive ventiduct
this procedure.
grid was created by MoldFlow which is a commercial software
package using hybrid finite element/finite difference method for
solving pressure, flow, and temperature field problems [16]. The
FE model it created is shown in Fig. 2b. It has length, width and
weight of 230 mm, 180 mm and about 90 g, respectively. The auto-
motive ventiduct grid is made of high density Polyethylene. The FE
model includes 3092 fusion elements. Fig. 2c shows the FE model
with cooling channel used in the injection molding.
Sedaghat et al. [12] showed that analysis with fusion elements
in a mesh of 2801 nodes is successful in predicting the experimen-
tal results of real injection molding process by comparing values
predicted from FE model and those measured on actual automotive
ventiduct grid. In our study fusion element is chosen with different
number of nodes tested to find the number of nodes that suitably
predicts the injection molding with least analysis time. Warpage is
selected to represent the injection molding process for this pur-
pose. The analysis was carried out on a Pentium 4 PC with 3 GHz
CPU, and 1 GB of RAM. Fig. 3a shows the warpage versus the num-
ber of nodes plot indicating that the chosen 3092 nodes can virtu-
Fig. 1a. Fixed-size simplex procedure. ally be adequate for warpage computations. Fig. 3b shows the time
416 B. Farshi et al. / Materials and Design 32 (2011) 414 423
Fig. 2. (a) Automotive ventiduct grid after injection molding. (b) Finite element model of automotive ventiduct grid (3092 nodes). (c) FE model with cooling.
Fig. 3a. Warpage (mm)-number of nodes.
that takes to get the results from the PC versus the number of
4. Numerical experimentation
nodes used in the model.
It is apparent that increasing the number of nodes above 3092,
4.1. Characterization of materials
warpage shows negligible changes, while CPU time significantly in-
creases by increasing the number of nodes. Therefore, fusion ele- The material selected for experimental study in this paper was
ment with 3092 nodes is chosen in this study.
high density PolyEthylene (PE), Petrothene LS506000. This grade
B. Farshi et al. / Materials and Design 32 (2011) 414 423 417
Fig. 3b. Total time (s)-number of nodes.
Table 1 Table 3
Properties of the Petrothene LS506000. Characteristics of cooling system.
Property Unit Value, name Characteristic Unit Value, name
Family name  Polyethylenes Number of channels  3
Trade name  Petrothene LS506000 Channels diameter mm 10
Family abbreviation  HDPE Distance between the cooling system and the part mm 20
Material structure  Crystalline Distance between channel s centers mm 65
Elastic modulus MPa 911 Channels longitudinal length mm 460
Poisson s ratio  0.426 Type of channels  Longitudinal
Shear modulus MPa 319
Melt density g/cm3 0.74921
Solid density g/cm3 0.92915
Table 4
Constraints of process parameters.
offers a high stiffness with good impact strength as well as being Process parameter Unit Lower Upper
limit limit
easy to process. Its properties are shown in Table 1. Dimensional
accuracy, surface finish and serial production were requirements
Mold temperature °C20 60
Melt temperature °C 165 205
of manufacturing automotive ventiduct grid; therefore, tool steel
Pressure switch-over %Volume filled 90 99
P-20 was selected as mold material. This material keeps its proper-
Pack/holding pressure %Maximum injection 50 75
ties for a long time increasing the tool life. The surface hardness for
pressure
this material is about 32 35 RC [17]. The properties of the tool
Packing time s 10 15
steel P-20 are given in Table 2. The characteristics of cooling sys- Coolant inlet °C20 30
temperature
tem are shown also in Table 3.
4.2. Process parameters and their constraints
5. Volumetric shrinkage
Mold temperature, melt temperature, pressure switch-over,
pack/holding pressure, packing time, and coolant inlet temperature
5.1. Volumetric shrinkage optimization by sequential simplex
are considered as the variables for optimization. Their limiting con-
algorithm
straints are shown in Table 4.
Since warpage and shrinkage are considered as defects, mini-
Table 2
mizing both of them is a useful task in manufacturing processes.
Properties of the tool steel P-20.
Warpage is a term used for warping of the part in injection mold-
ing due to the non-uniform contraction of different points and vol-
Property Unit Value
umetric shrinkage is the overall contraction of the part when it is
Density g/cm3 7.8
cooled. Minimizing these two will result in better product quality.
Specific heat J/(kg °C) 460
Thermal conductivity W/(m °C) 29 Volumetric shrinkage is often compensated for by a coefficient
Young s modulus GPa 200
of contraction in practical mold designs. Excessive shrinkage may
Poisson s ratio  0.33
cause volumetric changes that can produce out of tolerance dimen-
Coefficient of thermal expansion 1/°C 1.2 10 5
sions in the final product. Consequently, one of the aims of this
418 B. Farshi et al. / Materials and Design 32 (2011) 414 423
Fig. 4a. Minimization procedure of volumetric shrinkage.
Fig. 4b. Warpage corresponding to volumetric shrinkage.
project is to minimize the shrinkage as much as possible for above shrinkage minimization trend as depicted in plots of Figs. 4c and
reason. 4d indicate that the part weight and cycle time both continually in-
Fig. 4a shows the plot of the minimization procedure used for crease towards minimum shrinkage point, while Fig. 4b shows
volumetric shrinkage of the automotive ventiduct grid using somewhat indifferent warpage response. This observation suggests
sequential simplex optimization algorithm. Figs. 4b 4e shows the that since the cycle time, part weight, and residual stress increases
corresponding warpage, part weight, cycle time, maximum bulk are undesirable a compromise must be made regarding the mini-
temperature, respectively for the volumetric shrinkage minimiza- mum volumetric shrinkage.
tion procedure. Table 5 contains the data for the optimum point
for shrinkage minimization. Following the minimization trend of
6. Warpage
generating sequential points one can also obtain a point of maxi-
mum shrinkage whose corresponding data can be significant. Ta-
6.1. Warpage optimization by sequential simplex algorithm
ble 6 contains the data related to the residual stresses
corresponding the maximum and minimum of shrinkage design
Automotive ventiduct grid is considered as a thin shell plastic
points in both the first and second directions. It is observed from
part and warpage is one of the most important defects in thin shell
the entries in Table 6 that minimum shrinkage design corresponds
parts. Consequently, minimization of warpage seems reasonable
to maximum residual stresses in both directions.
and necessary.
The residual stresses trapped in the final product can also be
Fig. 5a shows warpage minimization procedure for automotive
considered as a defect, and must be controlled. Furthermore, the
ventiduct grid using sequential simplex optimization algorithm.
B. Farshi et al. / Materials and Design 32 (2011) 414 423 419
Fig. 4c. Part weight corresponding to volumetric shrinkage.
Fig. 4d. Cycle time corresponding to volumetric shrinkage.
Figs. 5b 5e shows the corresponding volumetric shrinkage, part warpage design corresponds to maximum residual stresses in both
weight, cycle time, maximum bulk temperature, respectively of directions.
the procedure.
Table 7 contains the data for optimum point for warpage mini- 7. Discussion and results
mization. Following the minimization trend of generating sequen-
tial points one can also obtain a point of maximum warpage whose The followings are the results obtained in this study:
corresponding data can be significant. Table 8 contains the data re-
lated to the residual stresses corresponding the maximum and When minimizing volumetric shrinkage, corresponding war-
minimum of warpage design points in both the first and second page was fluctuating slightly about the warpage corresponding
directions. It is observed from the entries in Table 8 that minimum to the minimized volumetric shrinkage, 2.382 mm. Correspond-
420 B. Farshi et al. / Materials and Design 32 (2011) 414 423
Fig. 4e. Maximum bulk temperature corresponding to volumetric shrinkage.
part weight during the minimization procedure of volumetric
Table 5
shrinkage was about 90.28. This shows that part weight is of
Minimized volumetric shrinkage data.
no importance in determining the best process parameters
Name Unit Value
because the total difference between the lowest and highest
Minimum volumetric shrinkage  2.3077
part weight is about 2.5 g or about 3%.
Corresponding warpage mm 2.382
When minimizing volumetric shrinkage, it followed a trend of
Corresponding part weight g 92.9012
sharp increase in cycle time. Therefore, it is not recommended
Corresponding cycle time s 105.8
Corresponding maximum bulk °C 32.471 to use its corresponding process parameters when time is of
temperature
concern as in a mass production process.
Corresponding mold temperature °C 30.9827646
A decreasing trend was observed in maximum bulk tempera-
Corresponding melt temperature °C 165.3093513
ture when minimizing volumetric shrinkage.
Corresponding pressure switch- % Volume filled 98.72913442
As shown in Table 6, residual stresses were increased when
over
Corresponding pack/holding % Maximum injection 72.81917651
volumetric shrinkage was minimized. However, if the resid-
pressure pressure
ual stresses increase is of concern then a compromise
Corresponding packing time s 11.77099053
regarding the use of corresponding process parameters must
Corresponding coolant inlet °C 26.44657231
be made.
temperature
When minimizing warpage, corresponding volumetric shrink-
age fluctuated about minimum warpage s corresponding
shrinkage of 5.8076%. This value is relatively close to the mini-
mized volumetric shrinkage i.e., 2.3077%. Comparing this value
Table 6
to the worst volumetric shrinkage in optimization procedure
Results regarding max. and min. volumetric shrinkage.
which is about 11%; it can be concluded that using the mini-
Name Unit Value
mum warpage parameters results in reasonable minimum
Maximum volumetric shrinkage s maximum residual stress in MPa 64.05
shrinkage also in most cases.
1st direction
As shown in Table 8, residual stresses increased about 10%
Maximum volumetric shrinkage s maximum residual stress in MPa 56.47
when warpage was minimized. However, in most cases such
2nd direction
an increase is not considered alarming.
Minimum volumetric shrinkage s maximum residual stress in MPa 77.82
1st direction
Part weight was increasing as the warpage was being mini-
Minimum volumetric shrinkage s maximum residual stress in MPa 57.03
mized. Part weight corresponding to minimum warpage
2nd direction
reached 92.1248 g which is only 3% higher than the lowest
value of 90.28 during the process. This shows that part weight
is of no importance in determining the best process parameters
whether it is shrinkage or warpage minimization.
ing warpage was almost constant around 2.382 mm which is
When minimizing warpage, a decreasing trend of cycle time
close to minimized warpage, 2.086 mm. Therefore, using the
was seen. The corresponding cycle time of minimized warpage
corresponding process parameters of minimized volumetric
was about six times less than that of minimized volumetric
shrinkage is reasonable when minimum volumetric shrinkage
shrinkage. Consequently, it is reasonable to use the correspond-
and minimum warpage are both of concern and time is not
ing process parameters of minimized warpage, with some com-
important because few parts are needed.
promise on the shrinkage when time is the most important
Part weight was increasing as the volumetric shrinkage was
factor.
going towards the minimum point. When volumetric shrinkage
Maximum bulk temperature was almost constant in the proce-
was minimized, the part weight reached 92.9012 g. The lowest
dure of minimizing warpage.
B. Farshi et al. / Materials and Design 32 (2011) 414 423 421
Fig. 5a. Minimization procedure of warpage.
Fig. 5b. Volumetric shrinkage corresponding to warpage.
It can be concluded that warpage minimization in the process of a sensitivity analysis with respect to the process parameters has
injection molding with compromise to control shrinkage can result been performed. The results indicate that the three most important
in shorter cycle time and less residual stresses and can be best for parameters are pressure switch-over, mold temperature and cool-
economical production process. At the optimum point for warpage ant inlet temperature with values of 7%, 5% and 3% respectively.
422 B. Farshi et al. / Materials and Design 32 (2011) 414 423
Fig. 5c. Part weight corresponding to warpage.
Fig. 5d. Cycle time corresponding to warpage.
The other parameters showed lower sensitivities. This seems to be tive ventiduct grid has been developed. It is based on sequential
in contrast with the results of [1,8] indicating packing pressure and simplex method which takes into consideration six process
[2] indicating packing time as the most important factors. How- parameters. Unlike many similar attempts, side effects on other
ever, results of [11] seem to be in agreement with those obtained factors not directly included in the procedure are also investi-
in this study. gated. Consequently, it was observed that some factors such
Furthermore, it was shown that the sequential simplex optimiza- as cycle time showed drastic increase in case of volumetric
tion method [13] is an effective and useful procedure for online opti- shrinkage as compared to warpage minimization. Therefore, a
mization of such process problems as was also recommended in [3]. compromise recommendation can be offered for a near opti-
mum shrinkage in combination with optimum warpage
involving low cycle time and low residual stresses simulta-
8. Conclusions
neously. It was shown that the sequential simplex optimization
procedure is a viable and efficient method for injection molding
In this study an optimization procedure for minimum war-
problems.
page and volumetric shrinkage of injection molding of automo-
B. Farshi et al. / Materials and Design 32 (2011) 414 423 423
Fig. 5e. Maximum bulk temperature corresponding to warpage.
Table 7 [2] Gao Y, Wang X. Surrogate-based process optimization for reducing warpage in
injection molding. J Mater Process Technol 2009;209:1302 9.
Minimized warpage data.
[3] Kamoun A, Jaziri M, Chaabouni M. The use of the simplex method and its
Name Unit Value
derivatives to the on-line optimization of the parameters of an injection
moulding process. Chemometr Intell Lab Syst 2009;96:117 22.
Minimum warpage mm 2.086
[4] Kurtaran H, Erzurumlu T. Effective warpage optimization of thin shell plastic
Corresponding volumetric  5.8076
parts using response surface methodology and genetic algorithm. Int J Adv
shrinkage
Manuf Technol 2006;27:468 72.
Corresponding part weight g 92.1248
[5] Kurtaran H, Ozcelik B, Erzurumlu T. Warpage optimization of a bus ceiling
Corresponding cycle time s 20.7
lamp base using neural network model and genetic algorithm. J Mater Process
Corresponding maximum bulk °C 112.38
Technol 2005;169:314 9.
temperature
[6] Zhou J, Turng LS, Kramschuster A. Single and multi-objective optimization for
Corresponding mold temperature °C 46.6902761 injection molding using numerical simulation with surrogate models and
genetic algorithm. Int Polym Process 2006;21:50 520.
Corresponding melt temperature °C 180.5392475
[7] Shen CY, Wang LX, Zheng QX. Process optimization of injection molding by the
Corresponding pressure switch- % Volume filled 98.35565248
combining ANN/HGA method. Polym Mater: Sci Eng 2005;21:23 7.
over
[8] Huang MC, Tai CC. The effective factors in the warpage problem of an injection-
Corresponding pack/holding % Maximum injection 73.9989183
molded part with a thin shell feature. J Mater Process Technol 2001;110:1 9.
pressure pressure
[9] Zhil tsova TV, Oliveira MSA, Ferreira JAF. Relative influence of injection
Corresponding packing time s 13.11980438
molding processing conditions on HDPE acetabular cups dimensional
Corresponding coolant inlet °C 28.28933632
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Table 8
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Name Unit Value
[12] Sedaghat O, Ghafoori Ahangar R, Ayatollahi MR. Investigation of injection
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Maximum warpage s maximum residual stress in 1st MPa 60.58
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direction
Science and Technology, Tehran, Iran; 2007.
Maximum warpage s maximum residual stress in 2nd MPa 53.57
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direction
Optimization. Boca Raton, Florida, United States: CRC Press; 1991.
Minimum warpage s maximum residual stress in 1st direction MPa 66.46
[14] Spendley W, Hext GR, Himsworth FR. Sequential application of simplex
Minimum warpage s maximum residual stress in 2nd MPa 58.74
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