Int J Adv Manuf Technol DOI 10.1007/s00170-015-7862-z

ORIGINAL ARTICLE

Integration optimization of molding and service for injection-molded product Wenjuan Liu 1 & Xinyu Wang 1 & Zheng Li 1 & Junfeng Gu 1 & Shilun ruan 1 & Changyu Shen 1 & Xicheng Wang 1

Received: 24 April 2015 / Accepted: 13 September 2015 # Springer-Verlag London 2015

Abstract Different settings of process parameters in injection molding can directly influence the internal residual stress of injection parts, while to a certain degree, the internal residual stress field will, in turn, affect the performance of parts during assembly and service process. Therefore, for most parts which will be subjected to external loads as part of a system, it has practical significance to improve their performance through integration optimization of molding and service. In this paper, the service of a molded part is divided into three stages: molding, assembly, and service, and an integration model is built for optimizing its service performance, considering all these three stages. A sequential optimization algorithm based on kriging surrogate model and expected improvement sampling criteria is used to perform the optimization analysis on polycarbonate material parts. Results show that the integration optimization strategy proposed in this paper can decrease the maximum service stress effectively. Furthermore, the nonassembly and non-load carrying parts are also considered and the stresses are optimized. Comparison among these three situations shows that integration optimization is essential when service performance is considered for the molded parts.

Keywords Service stress optimization . Injection molding . Process parameters . Kriging surrogate model . Expected improvement method

* Junfeng Gu [email protected] 1

State Key Laboratory of Structural Analysis for Industrial Equipment, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology, Dalian 116024, China

1 Introduction Polymer material, such as plastic, is characterized by high specific intensity, light quality, corrosion resistance, good electrical insulation, etc. These excellent properties qualify a plastic material for its wide use in our daily life. However, there exist many kinds of molding defects, like air traps, weld line, warpage, and residual stress, which are caused by the problem of product design, unreasonable design of mold, or inadequate choice of process parameters. In all of these defects, the residual stress has a huge influence on the subsequent use of the injection-molded products, such as assembly and withstanding load. Many researches focusing on the optimization approach development to eliminate the molding defects have emerged in the recent 20 years [1–6]. Dang [7] reviewed and concluded the advantages, disadvantages, and scope of application of many optimization approaches used in the injection molding optimization problem, and briefly introduced the response surface model, kriging surrogate model, artificial neural network, and genetic algorithm (GA). Most of these previous researches aimed at decreasing the warpage of the product. For instance, Lee and Kim [8] used direct optimization method to perform the warpage optimization by optimizing the wall thickness and process parameters, and the results showed that the objective value was reduced by more than 70 %. Kurtaran and Erzurumlu [9] used the analysis of variance (ANOVA) method to analyze multiple design variables based on the statistics experimental design method, and then chose melt temperature, mold temperature, and packing pressure as the optimization process parameters. Finally, the warpage was reduced by combining response surface model and GA. In contrast to Kurtaran and Erzurumlu,

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Fig. 1 The sketches for the molding process, assembly process, and service process

Ozcelik and Erzurumlu [10] optimized warpage of the injection-molded parts by combining the artificial neural network (ANN) and GA. Zhou and Turng [11] used an adaptive surrogate model based on the Gaussian process and hybrid GA to optimize the deformation of the plastic product efficiently. Shen et al. [12] employed the ANN and GA to reduce the difference between maximum and minimum volume shrinkage. Gao and Wang [13] used kriging surrogate model to design the warpage optimization of injection-molded parts with respect to melt temperature, mold temperature, packing pressure, etc. In this study, the author found that the filling time has the greatest influence on the warpage. Kitayama et al. [14] employed the radial basis function to evaluate the warpage of product to perform the process optimization. Besides, there are some literatures which aim at the sink defect [15, 16]. These researches are helpful to understand the relations between molding and defects, and, hereby, to guide the process technology for improving the product quality. However, the service performance of the injected product is more concerned by users in practical application. Xu et al. [17] combined the anti-impact behavior of the plastic parts with the injection molding process and used the ANN method and particle swarm optimization (PSO) to optimize the maximum von Mises stress within the injection parts against impact. However, there is still lack of integration studies about the influence of the injection molding process parameters on the stress of the injected product in the practical usage. The internal stress during molding is composed of the flow-induced part during filling and packing [18, 19] and the thermal-induced part during cooling [20, 21]. When the Table 1 Material properties of Lexan 151 PC

Melt density (g/cm3) Solid density (g/cm3) Poisson ratio Transition temperature (°C) Elastic module (MPa)

1.0656 1.1915 0.417 144 2280

Shear module (MPa)

804.5

product is ejected out of the cavity, some stress will be relaxed while the rest will be kept in parts and the product will achieve the new stress equilibrium. This relaxation process leads to warpage, shrinkage, or other molding defects and leaves residual stress in the product after ejection. The residual stress cannot be neglected since it can weaken the mechanical behavior of the parts and induce serious failure in the practical usage. When the plastic product is assembled, the residual stress may also redistribute. Especially, when the product is subjected to load, like pressure on the surface of the product, the actual service performance will be affected by the residual stress, the assembly, and the loading conditions. The main goal of this paper is to build an integration optimization model between process parameter and service performance of parts. This optimization issue integrates three processes including molding, assembly, and service, and therefore, it is called the molding-service optimization. The sketches for these three processes of parts are shown in Fig. 1. The rest of this paper is organized as follows. Section 2 demonstrates the basic implementations about this stress optimization issues. In order to optimize the stress in a thin-walled shell, the kriging surrogate model and expected improvement (EI) function as described in Section 3 are employed. Section 4 describes the results obtained and the discussion. Finally, Section 5 gives the concluding remarks.

2 Molding-service optimization issues of a plastic shell-shaped window Lots of plastic parts will be subjected to load after assembly, like pressure, friction, impact, etc. The working load usually results in great change of the internal stress. The service performance in the working condition not only affects the lifespan of the plastic product but also relates to the personal and property security. In this section, we will elaborate the implementations of the molding-service optimization issue on a thin-walled shell which is under internal pressure with the side boundary assembled. It is assumed that the plastic shell is the window of a hydraulic tank, and the shell is subjected to a uniform pressure on the inner surface (as shown in Fig. 1). The value of the pressure is 5 atm (about 0.5 MPa).

Int J Adv Manuf Technol Fig. 2 The finite element model of the thin-walled shell for injection molding analysis

2.1 The finite element model and material properties of the thin-walled shell The product used in this study is a plastic shell-shaped component. The length of this shell is 250 mm. The chord length and arch height are 308 and 87 mm, respectively, and the thickness is 3 mm. The finite element model has 3875 nodes and 7753 triangular elements. This window is molded by polycarbonate produced by SABIC Innovative Plastics US Company. The main material properties are shown in Table 1. The mold system is shown in Fig. 2. 2.2 The influence of warpage and residual stress on service performance of parts Many plastic products need to be assembled onto other structures and subjected to load after ejection (see the illustration in Fig. 1). It is noteworthy that the warpage, shrinkage deformation, and residual stress cannot be neglected since they can

affect not only the distribution but also the values of the assembly and service stress. For verifying the important effects of these two defects on assembly stress, four edges of the thinwalled plastic shell are assembled as shown in Fig. 1 and the stress nephograms are given in Fig. 3. In case A, the residual stress during assembly is not considered, so the assembly stress mainly derives from the warpage and shrinkage deformation due to unreasonable molding process conditions. Case B has the same assembly condition with case A but takes the residual stress after ejection into account. Through the comparison of cases A and B, we can easily find that the residual stress after ejection will greatly influence the assembly stress as well. Another analysis which aims at verifying the important effects of these two defects on service stress is performed, and the stress nephograms are given in Fig. 4. The thin-walled shell has the same assembly condition as in Fig. 3. After the assembly process, a uniform pressure, which is 5 atm, is applied on the inner surface (as shown in Fig. 1). Figure 4 shows the comparison of service stress nephograms between loadbearing assemblies, one of which considers the residual stress

Fig. 3 a, b Different stress nephograms in the shell. Case A does not consider the residual stress during assembly. Case B takes the residual stress into account during assembly

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Fig. 4 a, b Different stress nephograms in the shell. Case A does not consider the residual stress during service. Case B takes the residual stress into account during service

and the other does not, and similar results can be obtained with Fig. 3. According to the analyses above, warpage and residual stress have an obvious influence on the service stress and usually weaken the performance of injection-molded parts. Therefore, this paper takes the residual stress after ejection of parts as the initial stress condition and uses the warpage and shrinkage deformation as the assembly conditions in the molding-service optimization.

them to the objective location with the opposite of warpage value. c. Pressure of 5 atm is applied on the inner surface of the shell. Subsequently, the structure analysis under this condition is performed using the ANSYS software. The maximum Mises stress derived from the service analysis in the ANSYS software is obtained and regarded as the objective function of the molding-service stress optimization problem.

2.3 Molding-service stress optimization issue In the following molding-service stress optimization problem of the plastic shell, it is divided into three stages: molding, assembly, and service. The detail of the integration method is listed as follows: a. Use the Moldflow software to perform the injection molding analysis with given process parameters and obtain the warpage value and internal residual stress value (σres). The negative warpage value and the residual stress are regarded as the assembly displacement load and the initial stress, respectively. b. Import the warped structure into the ANSYS software and apply the residual stress load and then force the nodes on the warped edges, which need to be assembled, to move Table 2

Range of the process parameters Process parameters

Upper Lower

3 The basic knowledge of surrogate model-based optimization method 3.1 Kriging surrogate model Kriging surrogate model is a semi-parametric interpolation technology based on statistical theory. It is a welldeveloped Gaussian process model at present and can efficiently solve the engineering problems of which the variable number is less than 50 [22–24]. In the literatures about the molding defect optimization, a kriging model is used to construct the relationship of objective function and process parameters [25, 26].A kriging surrogate model is composed of a polynomial part and a random error part [27, 28], expressed as Eq. (1), if given the sample set S={x1, x2…, xn} and the response vector Y={y1, y2…, yn} for the single objective optimization problem

A/°C

B/°C

C/%

D/s

E/s

yðxÞ ¼ f T ðxÞβ þ zðxÞ

250 293

87 121

20 100

1 10

0.5 6

where β is the regression coefficient, f(x) is the polynomial vector with respect to x, and z(x) is the normally distributed error term with mean zero and variance σz2,

ð1Þ

Int J Adv Manuf Technol Fig. 5 The optimization flow chart

which provides the local approximate simulation discrepancy. The statistic characteristics are illustrated as follows: E ½zðxÞ ¼ 0

ð2Þ

Var½zðxÞ ¼ σz 2 
 
 Cov zðxi Þ; z x j ¼ σz 2 Ri j θ; xi ; x j

ð3Þ ð4Þ

where xi and xj are any two points in sample, respectively. R(θ, xi, xj) is the relevant function with parameter θ and represents the spatial correlation between the sample points. The predicted value and the predicted variance of the ordinary kriging (OK) are demonstrated by Eqs. (5) and (6), respectively.   l T R−1 Y l T R−1 Y yðxnew Þ ¼ T −1 þ rT ðxnew ÞR−1 Y−l T −1 ð5Þ l R l l R l Table 3

Service stress optimization result Process parameters

Before optimization After optimization

Objective

A/°C

B/°C

C/%

D/s

E/s

σ/MPa

278.02 277.11

95.41 121

96.36 86.8

5.05 9.90

5.19 43.49 6 37.31

" s ðxnew Þ ¼ σz 2

2




1−l T R−1 r 1−r R r þ l T R−1 l T

−1

2 # ð6Þ

where l is the vector in which the element is 1. R represents the correlation matrix of spatial points. r=[R(x1, xnew), R(x2, xnew)…, R(xn, xnew)] stands for the spatial correlation between the new point (xnew) and the sample points. 3.2 Expected improvement method Expected improvement-based optimization method is regarded as the efficient global optimization method by many researchers [28]. In the EI-based optimization method, improvement function (IF; I(x)) is defined as I ðxÞ ¼ max½0; Ymin −yðxÞ

ð7Þ

where Ymin is the minimum value in current response vector Y, and y(x) is the kriging model with Gaussian statistics characteristic. Therefore, I(x) follows the Gaussian distribution as well. EI is the expectation of I(x) and reads as E ½I ðxÞ ¼ sðxÞ½uΦðuÞ þ ϕðuÞ

ð8Þ

where u ¼ ½Ymin −yðxÞ =s ðxÞ. Φ and ϕ are the standard

Int J Adv Manuf Technol

Fig. 6 Molding-service stress nephograms before optimization (a) and after optimization (b)

normal probability distribution function and standard normal probability density function, respectively. The maximum value of E[I(x)] (MEI) indicates a significant mathematical meaning for the current kriging model that points out either the most uncertain location globally or a better response locally. According to mathematical sense of the maximum E[I(x)], the original minimization formula can be changed into the maximization about E[I(x)]. If we reconstruct the kriging model by infilling the design point associated to the MEI into the current sample set and recall this procedure in order to minimize the MEI, the kriging model will become more and more precise. Finally, the optimum value of the original optimization will be searched. The procedure is known as the surrogate-based sequence optimization process. Find x Max : E ½I ðxÞ S:T: : g ðxÞ≤ 0

(Tmelt, A), mold temperature (Tmold, B), packing pressure fraction (Ppacking, C), packing time (tpacking, D), and filling time (tfilling, E). The ranges of these variables are listed in Table 2. The optimization model reads as Eq. (10). Find x Max : maxσMises ðxÞ S:T: : x ≤ x ≤ x

ð10Þ

where x is design variables, σMises(x) is the maximum Mises stress in the shell, and x and x are the upper and lower limits of variables. With the knowledge of Section 3.2, the optimization model is changed to Find x Max : E ½I ðxÞ

ð11Þ

S:T: : x ≤ x ≤ x

ð9Þ The convergence criteria are the combination of Eqs. (12) and (13).

3.3 The stress optimization model

E ½I ðxÞ ≤ε1

ð12Þ

For the optimization issue in this paper, the maximum Mises stress inside the plastic shell is set as the optimization objective. The design variables are melt temperature

jσk −σ⌢ k j≤ ε2

ð13Þ

Table 4

Residual stress optimization result Process parameters

Before optimization After optimization

Objective

A/°C

B/°C

C/%

D/s

E/s

σ/MPa

289.66 293

97.54 121

24.38 20

9.57 1

3.89 0.5

11.98 5.58

where ε1 and ε2 are the given convergence accuracy, k stands for the number of iterations of optimization solution, σk represents the true value of the stress from numerical simulation for the current iteration, and σk is the predicted response values from the kriging model. The stress optimization process is demonstrated as follows: a. Select sample S as the initial sample. We use orthogonal Latin hypercube sampling methods to achieve evenly distributed initial sample [29, 30].

Int J Adv Manuf Technol

Fig. 7 Residual stress nephograms before optimization (a) and after optimization (b)

b. Obtain response value Y of initial sample. The warped structure is imported into the ANSYS software, and then, an assembly analysis in consideration of residual stress is performed using the ANSYS software. Finally, the pressure of 5 atm pressing on the inner surface of the structure is applied and the objective value is the maximum Mises stress after this structural analysis in the ANSYS software. c. Use initial sample S and corresponding response value Y to establish the kriging surrogate model and the corresponding expectation function E[I(x)]. d. Use a sequence quadratic programming (SQP) method to search the maximum value of E[I(x)] of the current surrogate model. Find the corresponding space point (xnew) and calculate the actual objective value (y(xnew)) with respect to xnew. e. Determine whether the convergence criteria are satisfied. If not, xnew and y(xnew) need to be put into current sample set S and corresponding response set Y to modify the kriging model. f. Repeat steps c to e until the convergence criteria of the optimization process are satisfied. The optimization flow chart is shown in Fig. 5.

Table 5

Assembly stress optimization result Process parameters A/°C

B/°C

C/%

Objective D/s

E/s

σ/MPa

Before optimization 269.33 109.15 88.28 9.59 1.86 31.07 After optimization 289.15 102 94.77 8.16 3.75 27.10

4 Results and discussion The maximum Mises stress in the molding-service stress optimization issue is optimized to 37.31 MPa, while the best case in the initial design set is 43.49 MPa, which is reduced by 14.20 % numerically. The optimized result is listed in Table 3. The Mises stress nephograms are shown in Fig. 6. Compared with the process parameters of the best case in the initial design set, the optimized process parameters have a higher mold temperature, a higher packing time, and a higher filling time while the packing pressure fraction is 86.8 %, about 10 % lower than initial design. Before and after optimization, the melt temperature shows a slightly change and the maximum Mises stress distribution is changed from the injecting gate to the fixed assembly edges. In order to make a comprehensive analysis of the moldingservice optimization procedure, the stresses of the thin-walled shell under two other different conditions are considered and optimized. One condition is that the shell does not need to be assembled onto other structures after ejection and has no load on it, and another is that it is assembled but is non-load carrying. For the first condition, the residual stress after ejection of this shell is the main concern and it is called the residual stress optimization issue. The second condition aims at optimizing the maximum Mises stress in the consideration of the side assembly condition but without load, so it is called the assembly stress optimization issue. The result of the residual stress optimization issue is listed in Table 4. In the initial sample set of the residual stress optimization issue, the residual Mises stress of the best sample is 11.98 MPa. After optimization, the objective is reduced to 5.58 MPa. It is reduced by 53.45 % numerically. The residual stress nephograms of these two cases are shown in Fig. 7.

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Fig. 8 Assembly stress nephograms before optimization (a) and after optimization (b)

The optimized molding parameters get the bound values in the residual stress optimization issue. Actually, it is profitable to increase the melt temperature and mold temperature for reducing the thickness of frozen layer during filling the cavity. Longer filling time will result in higher shear stress in the frozen layer which can cause larger deformation after ejection. Thus, the optimized filling time of this stress optimization is reasonable. Packing pressure and packing time are usually very important molding parameters in practice. In order to avoid the unacceptable volumetric shrinkage, it is essential to sustain the proper packing pressure for a proper duration of packing time. However, since the objective of this issue is the residual stress, the lower packing parameters can weaken the flow-induced stress during packing. Therefore, it is understandable that both the optimized values of packing pressure and packing time get the bound values. In the assembly stress optimization issue, the optimized assembly stress is 27.10 MPa. Compared with the best sample

in the initial designs, the optimized result is reduced by 12.78 % from 31.07 MPa. Table 5 shows the list of this result. The Mises stress nephograms of these cases are shown in Fig. 8. Unlike molding-service optimization and residual stress optimization, the variation of these process parameters before and after optimization has no specific rules to follow. In assembly optimization issue, the melt temperature is increased by about 20° compared with the best sample; the packing pressure fraction and the filling time are both higher after optimization, while the packing time is decreased and the mold temperature has a slight change. In addition, it is notable that the minimum Mises stress is also reduced in the assembly stress optimization issue, as shown in Fig. 8. However, this phenomenon does not happen in the molding-service stress optimization issue. For demonstrating the necessity of the integration optimization strategy, another two experiments are performed. For the first experiment which is named as case 1, the assembly process with fixed boundary condition is executed on the

Fig. 9 Stress nephograms of the assembly and service process of case 1. a Assembly stress contours. b Service stress contours

Int J Adv Manuf Technol Fig. 10 The stress nephogram of the shell of case 2, in which a load of 5 atm was applied on the optimum solution of the assembly stress optimization

optimized result of the residual stress optimization issue and then an additional pressure which is the same with the molding-service optimization issue is applied on the thin shell. The Mises stress nephograms of these two processes of case 1 are shown in Fig. 9. For the second one, pressure of 5 atm is applied on the optimum solution of the assembly stress optimization and is named as case 2 and the stress results of which are compared with the optimal results in the molding-service optimization issue. The Mises stress nephogram of case 2 is shown in Fig. 10. Figure 9a gives the assembly stress nephogram of case 1, and Fig. 8b gives the assembly stress nephogram of the assembly stress optimization issue. The residual stress after injection of case 1 is the optimal solution of the residual stress optimization, and the maximum Mises stress is 5.58 MPa. The maximum residual stress after injection of the assembly stress optimization issue is 31.28 MPa, which is much higher than the maximum residual stress of case 1. However, the final assembly stress shown in Fig. 9a is much higher than Fig. 8b. According to the above comparison, we can reach the conclusion that optimal residual stress does not result in optimal assembly stress, although the assembly stress is greatly influenced by the residual stress which is formed during the molding process. For case 2, the maximum and minimum Mises stresses in Fig. 10 are both higher than those in Fig. 6b, which indicates that the load applied on the assembled part will cause the stress to be distributed, and optimal assembly stress will not lead to optimal service stress. The above analyses show that it is not sufficient to simply consider the molding quality of the injection-molded parts when we are more concerned about the serving performance of the parts, and it is necessary to optimize the molding process

parameters with an integration method as proposed in this work.

5 Conclusion Stress in plastic product is an important performance index in many structural plastic components. This paper has integrated the molding, assembly, and service process and proposed an integration optimization strategy of molding and service. The kriging surrogate model and the EI method are employed to construct the stress optimization model. A thinwalled shell is used as a representative part to evaluate the proposed optimization method, and its service stress is significantly decreased. For thoroughly analyzing the moldingservice optimization, residual stress optimization and assembly stress optimization are also performed. Through the comparative analysis of the optimization results, we can see that for a service-oriented molding research of injection-molded parts, it is necessary to adopt an integration strategy, which shall simultaneously consider the influence of assembly and loading conditions. This proposed strategy has high common serviceability and can be applied to analyze parts under various service conditions, which will guide the molding of the injection-molded parts with complex service conditions.

Acknowledgments The authors gratefully acknowledge the financial support for this work from the National Natural Science Funds of China (Nos. 11202049 and 11432003), the National Basic Research Program of China (No. 2012CB025905), the 111 Project (B14013), and the Fundamental Research Funds for the Central Universities (DUT15ZD112).

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