Elsevier

Materials & Design

Volume 32, Issue 1, January 2011, Pages 414-423
Materials & Design

Technical Report
Optimization of injection molding process parameters using sequential simplex algorithm

https://doi.org/10.1016/j.matdes.2010.06.043Get rights and content

Abstract

In this study warpage and shrinkage as defects in injection molding of plastic parts have been undertaken. MoldFlow software package has been used to simulate the molding experiments numerically. Plastic part used is an automotive ventiduct grid. The process optimization to minimize the above defects is carried out by sequential simplex method. Process design parameters are mold temperature, melt temperature, 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.

Introduction

Many products in different areas such as aviation, automotive, electronic apparatus are produced using plastic injection molding. Having special features like capability to produce complex parts, light weight, resistance to corrosion, ease of producing compared to conventional materials, are the main reasons for their popularity. High quality and precision can be achieved using this method for manufacturing plastic parts. The need for lighter, more aesthetic and durable products necessitates manufacturing thinner parts. Since most molten plastics cannot fill the mold cavity of thin walled parts suitably, plastic injection molding need be used which can result in warpage [1]. Therefore, reduction and control of warpage is of importance in enhancement of the quality. Hence, warpage minimization plays a key role in the product optimization. As the thickness decreases, the strength is also weakened. Therefore, ultimately the problem can be solved using the right kind of material for the purpose of durability.

Ordinarily, production shop operators can adjust only one process parameter at a time and this does not necessarily lead to the real optimum combination of process parameters. This is particularly true when the objective function like warpage and/or volumetric shrinkage is an implicit function of the control variables and possible interaction among them.

Warpage and volumetric shrinkage as major defects in such manufactured parts are subject to change by the shape of parts, modifying the mold and having different sets of process parameters. The design of mold and part are usually considered in the very start of design procedure and remain unchanged. Consequently, determination of the best set of process parameters a priori by an optimization procedure is the best way for minimization of such defects [1], [2], [3].

In this field some researchers have focused on finding surrogate models like support vector regression, neural network and polynomial regression in lieu of expensive and time-consuming experimentations. These surrogate models are considered as a mathematical approximation replacing the actual simulation analyses. Using response surface method and neural network model, Erzurumlu made reduction in warpage in thin shell plastic parts [4]. Kurtaran et al. optimized warpage for a bus ceiling lamp casing utilizing genetic algorithm and neural network model [5]. Zhou et al. used support vector regression for optimization of injection molding process [6]. Shen et al. optimized process parameters for reducing maximum volumetric shrinkage difference using genetic algorithm and neural networks [7].

These papers apparently show that surrogate models are good approximations of the actual ones reducing time and computational cost. However, these surrogate models are classified as one-step optimization, without iterations. Therefore, the accuracy of the surrogate models determines how accurate the optimum solution is.

Since it is a time-consuming work to optimize warpage and volumetric shrinkage, an efficient optimization method called “sequential simplex” optimization is used here; a zero order optimization method not requiring any gradient computations. In this paper, we firstly introduce sequential simplex optimization method, and subsequently the working models.

Huang and Tai stated that the most crucial factors that affect warpage in injection molding of a thin shell part are packing pressure, mold temperature, melt temperature and packing time [8]. However, since minimization of both warpage and volumetric 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 temperature are considered as the variables for optimization.

Thus in this study the values of process parameters are sequentially obtained by the Finite Element Analysis (FEA) software MoldFlow, 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 process with a good precision and accuracy [1], [2], [9], [10], [11], [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 separately, 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 process 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 grid is selected which has also been used in the paper of Sedaghat et al. [12].

Section snippets

Definition of sequential simplex optimization method

The sequential simplex algorithm uses what is known as EVOP (EVolutionary OPeration). There are two major types of sequential simplex algorithm which are fixed-size simplex and variable-size simplex, the definition of which are given in reference [13].

Finite element model of automotive ventiduct grid

Geometry of the automotive ventiduct grid used in this study is shown in Fig. 2a after plastic injection molding. It was designed in CATIA without consideration of defects like warpage and volumetric shrinkage and saved as a STL file to be imported to MoldFlow. Afterwards, finite elements (FE) model of the automotive ventiduct 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

Characterization of materials

The material selected for experimental study in this paper was high density PolyEthylene (PE), Petrothene LS506000. This grade offers a high stiffness with good impact strength as well as being easy to process. Its properties are shown in Table 1. Dimensional accuracy, surface finish and serial production were requirements of manufacturing automotive ventiduct grid; therefore, tool steel P-20 was selected as mold material. This material keeps its properties for a long time increasing the tool

Volumetric shrinkage optimization by sequential simplex algorithm

Since warpage and shrinkage are considered as defects, minimizing both of them is a useful task in manufacturing processes. Warpage is a term used for warping of the part in injection molding due to the non-uniform contraction of different points and volumetric shrinkage is the overall contraction of the part when it is cooled. Minimizing these two will result in better product quality.

Volumetric shrinkage is often compensated for by a coefficient of contraction in practical mold designs.

Warpage optimization by sequential simplex algorithm

Automotive ventiduct grid is considered as a thin shell plastic part and warpage is one of the most important defects in thin shell parts. Consequently, minimization of warpage seems reasonable and necessary.

Fig. 5a shows warpage minimization procedure for automotive ventiduct grid using sequential simplex optimization algorithm. Fig. 5b, Fig. 5c, Fig. 5d, Fig. 5e shows the corresponding volumetric shrinkage, part weight, cycle time, maximum bulk temperature, respectively of the procedure.

Table

Discussion and results

The followings are the results obtained in this study:

  • When minimizing volumetric shrinkage, corresponding warpage was fluctuating slightly about the warpage corresponding to the minimized volumetric shrinkage, 2.382 mm. Corresponding warpage was almost constant around 2.382 mm which is close to minimized warpage, 2.086 mm. Therefore, using the corresponding process parameters of minimized volumetric shrinkage is reasonable when minimum volumetric shrinkage and minimum warpage are both of concern

Conclusions

In this study an optimization procedure for minimum warpage and volumetric shrinkage of injection molding of automotive ventiduct grid has been developed. It is based on sequential simplex method which takes into consideration six process parameters. Unlike many similar attempts, side effects on other factors not directly included in the procedure are also investigated. Consequently, it was observed that some factors such as cycle time showed drastic increase in case of volumetric shrinkage as

References (17)

There are more references available in the full text version of this article.

Cited by (0)

View full text