Int J Adv Manuf Technol DOI 10.1007/s00170-016-8904-x

ORIGINAL ARTICLE

Multi-objective optimization of injection molding process parameters for short cycle time and warpage reduction using conformal cooling channel Satoshi Kitayama 1 & Hiroyasu Miyakawa 2 & Masahiro Takano 2 & Shuji Aiba 3

Received: 13 February 2016 / Accepted: 9 May 2016 # Springer-Verlag London 2016

Abstract In this paper, cooling performance of conformal cooling channel in plastic injection molding (PIM) is numerically and experimentally examined. To examine the cooling performance, cycle time and warpage are considered. Melt temperature, injection time, packing pressure, packing time, cooling time, and cooling temperature are taken as the design variables. A multi-objective optimization of the process parameters is then performed. First, the process parameters of conformal cooling channel are optimized. Numerical simulation in the PIM is so intensive that a sequential approximate optimization using a radial basis function network is used to identify a pareto-frontier. It is found from the numerical result that the cooling performance of conformal cooling channel is much improved, compared to the conventional cooling channel. Based on the numerical result, the conformal cooling channel is developed by using additive manufacturing technology. The experiment is then carried out to examine the validity of the conformal cooling channel. Through numerical and experimental result, it is confirmed that the

conformal cooling channel is effective to the short cycle time and the warpage reduction. Keywords Plastic injection molding . Conformal cooling channel . Additive manufacturing . Multi-objective optimization . Sequential approximate optimization

Abbreviations PIM Plastic injection molding CAE Computer-aided engineering SAO Sequential approximate optimization NN Neural network GA Genetic algorithm ANOVA Analysis of variance RBF Radial basis function SQP Sequential quadratic programming MPS Mode-pursuing sampling EI Expected improvement DOE Design of experiment

* Satoshi Kitayama [email protected]

1 Introduction Hiroyasu Miyakawa [email protected] Masahiro Takano [email protected] Shuji Aiba [email protected] 1

Kanazawa University, Kakuma-machi, Kanazawa 920-1192, Japan

2

Industrial Research Institute of Ishikawa, 2-1, Kuratsuki, Kanazawa 920-8203, Japan

3

Sodick Co., Ltd., Ka-1-1, Miya-machi, Kaga-shi, Ishikawa 922-0595, Japan

Plastic injection molding (PIM) is one of the most widely used technologies for producing plastic products. Plastic products have several advantages such as lightweight, high-stiffness, and high productivity. In the PIM, short cycle time is much important for the high productivity. In other words, the cycle time should be minimized. In addition to this, high product quality is required in the PIM. Warpage (deformation), volume shrinkage, and weld line are major defects in the PIM, and they should be strongly avoided for the dimension accuracy and the appearance. The PIM process can be mainly classified in three phases:

Int J Adv Manuf Technol

filling, packing, and cooling phase. In the filling phase, the melt plastic is filled into the cavity with injection pressure. Next, in the packing phase, the melt plastic is packed with a high packing pressure for the desirable shape. After that, the melt plastic is cooled down for the solidification in the cooling phase. Finally, the solid plastic is ejected. To improve the cycle time and the warpage simultaneously, process parameters such as melt temperature, packing pressure, packing time, injection time, and cooling time should be optimized. To determine the optimal process parameters in the PIM, computer-aided engineering (CAE) is widely used and is recognized as one of the powerful tools available [1–3]. The numerical simulation in the PIM is so intensive that response surface approach is valid to determine the optimal process parameters. Recently, a sequential approximate optimization (SAO) that the response surface is repeatedly constructed and optimized is a popular approach to determine the optimal process parameters. Let us briefly review several representative works using the response surface and a SAO approach to determine the optimal process parameters. Shi et al. combined the neural network (NN) and the genetic algorithm (GA) for finding the optimal process parameters [4], in which the maximum shear stress was then approximated by a multilayer neural network, and the optimal process parameters (the mold temperature, the melt temperature, the injection time, and the injection pressure) were determined by the GA. Kurtaran et al. [5] and Kurtaran and Erzurumlu [6] also adopted the NN and the quadratic polynomial for the approximation of warpage and determined the optimal process parameters. Ozcelik and Erzurumlu optimized the process parameters in the PIM for warpage minimization [7], in which the critical process parameters were firstly selected by analysis of variance (ANOVA). The NN and the quadratic polynomial were then used to approximate the warpage with the selected process parameters, and the optimal process parameters were determined. The approach combining the approximation technique such as the NN, a radial basis function (RBF) network, and the Kriging and the optimization technique such as the GA and the sequential quadratic programming (SQP) is widely used for process parameter optimization in Refs. [8–12]. The above works using the response surface and the neural network belong to the set of “one-step” optimizations without iteration. Unlike the above works, in recent years, a SAO approach has gained its popularity. In the SAO, the response surface is repeatedly constructed and optimized through adding several new sampling points. A highly accurate global minimum can then be found. The general framework of SAO is well summarized in Ref. [13]. Gao and Wang applied the SAO using the Kriging to warpage reduction [14], in which the packing pressure profile was determined for the warpage reduction of a cellular phone cover. Zhang et al. applied the mode-pursuing sampling (MPS) method to the warpage reduction of scanner frame [15], in which the mold temperature, the melt temperature, and the injection time were optimized. Deng et al. also adopted the MPS method for the

warpage reduction of a food tray [16], in which the mold temperature, the melt temperature, the injection time, and the packing pressure were optimized. The application of SAO can be found in Refs. [17–23], and the SAO is recognized as the effective approach for the process parameters optimization in the PIM. Table 1 shows the summary using the SAO approach in the PIM. Another technique for high product quality is to use the Taguchi method. Note that the Taguchi method can find the optimal combination of the process parameters but cannot find the optimal process parameters. Chen and Kurniawan proposed a two-stage optimization using the Taguchi method and the PSO-GA [24], in which the Taguchi method was used to select the process parameters at the first stage and the PSO-GA was used to determine the optimal process parameters at the second stage. We do not describe these approaches in detail, and some interesting applications can be found in Refs. [24–27]. Since the process parameters in PIM affect warpage as well as cycle time, it is important to determine the optimal process parameters. On the other hand, another way to improve the cycle time and the warpage is to use conformal cooling channel. Dimla et al. investigated the cooling performance of conformal cooling channel [28], in which a box-type plastic product was used. In their work, the process parameters optimization was not performed, but they suggested that the conformal cooling channel was expected to improve the cooling performance and both the cycle time and the warpage could be improved. However, we do not have any ideas about how to design the conformal cooling channel in advance. In other words, the design of conformal cooling channel strongly depends on the designer’s experiences. In addition, the re-design of cooling channel is so expensive that it is difficult to carry out the experiment. Fortunately, additive manufacturing technology is recently used and the application to molding and forming tools is reported [29]. With the additive manufacturing technology, it is attractive to develop the conformal cooling channel and to examine the cooling performance through the experiment. The objective of this paper is to examine the cooling performance of conformal cooling channel numerically and experimentally. The cycle time and the warpage of the box-type plastic product are considered as the cooling performance, and the process parameters in the PIM are optimized. In general, short cycle time will lead to a large warpage, whereas a small warpage will result from long cycle time. Therefore, trade-off between the cycle time and the warpage will be observed. To identify the trade-off (pareto-frontier), a multi-objective design optimization is formulated. The numerical simulation in the PIM is so intensive that a SAO using a radial basis function network developed by one of the authors is used to identify a pareto-frontier with a small number of simulations. Based on the numerical result, the experiment using the conformal cooling channel is carried out. Additive manufacturing technology by metal 3D printer (OPM250L, Sodick) is used to develop the conformal cooling channel. The structural optimization

Int J Adv Manuf Technol Table 1

Process parameters optimization using a sequential approximate optimization

Author(s)

Ref. no.

Year

Objective function(s)

Process parameters for optimization

Gao and Wang

14

2009

Warpage minimization

Packing profile

Zhang et al.

15

2009

Warpage minimization

Mold temperature Melt temperature Injection time Packing time

Deng et al.

16

2010

Warpage minimization

Mold temperature Melt temperature Injection time

Li et al.

17

2010

Volume shrinkage minimization

Packing profile

Shi et al.

18

2010

Warpage minimization

Xia et al.

19

2011

Warpage minimization

Mold temperature Melt temperature Injection time Packing pressure Packing time Cooling time Packing pressure Packing time Injection pressure Melt temperature Injection time Cooling time

Cheng et al.

20

2013

Maximum difference of volumetric shrinkage Total volume of runner system Sum of injection time, packing time, and cooling time

Packing time Packing pressure Cooling time

Kitayama et al. Zhao et al.

21 22

2014

Warpage minimization Volume shrinkage Sink marks

Pressure profile in filling and packing phase Injection time Melt temperature Packing pressure Packing time Cooling temperature Cooling time

dimension, from which it is found that the product has the protrusion with the height of 8 mm in the box. The overview of the cooling channel is shown in Fig. 2, in which Fig. 2a shows the conformal cooling channel and Fig. 2b the conventional cooling channel. In the same figure, the blue arrow denotes the inlet of the coolant, and the red one the outlet of the coolant. Figure 3 shows an enlarged view of the conformal cooling channel enclosed by the black circle in Fig. 2a.

43

Gate

8 z

2 Overview of numerical simulation model

x

Product

y

(a) 3D view

This section describes an overview of the numerical simulation model. Figure 1 shows the box-type plastic product with the

z

x

z

x

29.7

y

2°

28.0

z

y

y

2.5

1.6°

5 1

25

6

29.7

(topology optimization) is an important approach to determine the conformal cooling channel, but in this paper, the conformal cooling channel is determined by the designer’s experiences. Therefore, the structural optimization is not performed. The rest of this paper is organized as follows. The overview of numerical simulation model is described in Section 2, in which the conventional and the conformal cooling channels are shown. A multi-objective design optimization is explained in Section 3. The SAO procedure using RBF network to identify a pareto-frontier is briefly described in Section 4. Through the numerical simulation, the cooling performance between the conventional and the conformal cooling channel is discussed in Section 5, in which the experiment using additive manufacturing technology by metal 3D printer is also carried out. Moldex3D (R13) is used for the numerical simulation in the PIM.

29.7 x

Unit [mm]

(b) Dimension

Fig. 1 Overview of plastic product with dimension. a 3D view. b Dimension

Int J Adv Manuf Technol Fig. 2 Overview of cooling channel. a Conformal cooling channel. b Conventional cooling channel

Coolant (Inlet)

Coolant (Inlet)

Coolant (Outlet) z y Hose

x Coolant (Outlet)

(a) Conformal cooling channel

Figure 4 shows the dimension of the cooling channel and the molding die, in which it can be noted that the cooling channel with the diameter of 8 mm is used in the conventional cooling channel (Fig. 4b), whereas the cooling channel with the diameter of 5.4 mm is used in a part of cooling channel in the conformal cooling channel. The polyacetal resin is used, and its material property is listed in Table 2. In the numerical simulation, the mold temperature is set to 90 °C.

Hose

x

(b) Conventional cooling channel

3.2 Design variables The process parameters in PIM strongly affect the cycle time as well as the warpage. In this paper, the melt temperature (Tmelt), the injection time (tinj), the packing pressure (P), the packing time (tp), the cooling time (tc), and the cooling temperature (Tc) are taken as the design variables. The lower and upper bounds of the design variables are set as follows: 0:1 ≤ t in j ≤ 1:0½s   180 ≤ T melt ≤ 210 ÅC

3 Multi-objective optimization for cycle time and warpage

z y

50≤ P ≤ 100½MPa   40≤ T c ≤ 90 ÅC


1:0 ≤ t p ≤ 15½s : 1:0 ≤ t c ≤ 40½s

ð2Þ

3.1 Multi-objective design optimization

3.3 Objective functions

In general, a multi-objective design optimization is formulated as follows [30]:

The cycle time and the warpage are considered as the objective functions. The first objective function f1(x), which is the cycle time, is given as the explicit form of the design variables as follows:


ð f 1 ðxÞ; f 2 ðxÞ; ⋯; f K ðxÞÞ→min ; x∈X

ð1Þ

where fi(x) is theith objective function to be minimized and K represents the number of objective functions. x = (x1, x2, …, xn)T denotes the design variables with n dimensions and X feasible region.

f 1 ðxÞ ¼ t in j þ t p þ t c →min:

ð3Þ

Next, let us consider the second objective function f2(x). Figure 5 shows the warpage, and the maximum deformation denoted by the arrow is taken as the warpage. This can be obtained through the numerical simulation.

4 Sequential approximate optimization using radial basis function network 4.1 Sequential approximate optimization for a multi-objective optimization

z y

y

x z (a) Outside of product

x

(b) Inside of product

Fig. 3 Enlarged view of conformal cooling channel. a Outside of product. b Inside of product

The numerical simulation of the PIM is so numerically intensive that a SAO approach is valid. In this paper, two objective functions are defined for the cycle time and the warpage, and the aim is then to identify the pareto-frontier. The general procedure to identify a pareto-frontier using SAO is summarized as follows:

Int J Adv Manuf Technol

200

8 x

y

38 110

z

z y

129

100

60

56.4

28

153

200

28

100 15 10 22 28 25 10 19

Fig. 4 Dimension of cooling channel and molding die. a Conformal cooling channel. b Conventional cooling channel

Unit [mm] x

(a) Conformal cooling channel

200

100

29

8

x y

60

z y

z

129

25 100

110

(Step 1) Initial sampling points are determined by using the Latin hypercube design (LHD). (Step 2) Numerical simulation is carried out at the sampling points, and objective functions are numerically evaluated. (Step 3) Objective functions are approximated by the RBF network. Here, the approximated objective functions are denoted as ~f i ðxÞ (i = 1, 2, ⋯, K). Table 2

25 22 28

28

153

200

28

Unit [mm] x

(b) Conventional cooling channel

(Step 4) We find a pareto-optimal solution of response surface with the weighted lp norm method formulated as follows: 9 X  p 1=p K = ~ α i f i ð xÞ →min ; i¼1 ; x∈X

ð4Þ

Material property of polyacetal resin

Melt density [g/cm3] Solid density [g/cm3] Eject temperature [°C] Maximum shear stress [MPa] Thermal conductivity [W/(m °C)] Elastic module [GPa] Poisson ratio Specific heat [J/(kg °C)] Material characteristics Recommended mold temperature [°C] Recommended melt temperature [°C]

1.19 1.4 135 56 0.336 2.8 0.38 2503 Crystalline 60–120 180–210

Cavity Fig. 5 Illustrative example of warpage (×20)

Product

Int J Adv Manuf Technol Fig. 6 Flow of sequential approximate optimization for multi-objective optimization

Generation of m initial sampling points with the LHD Calculation of the width with m sampling points.

Calculation of the responses of all functions. Construction of the response surfaces. Pareto-optimal solution by the weighted lp norm. The number of sampling points is updated. m:= m + 1 count = 1

Density function Calculation of the width with m sampling points Construction of D(x) from m sampling points. Addition of the point such as D(x) min m := m + 1 count = count+1

Y

count < int(n/2)

N

Y

Terminal criterion

N End

where αi (i = 1, 2, ⋯, K) represents the weight of the ith objective function. p is the parameter and is set to 4 in this paper. In order to obtain a set of pareto-optimal solutions, various weights are assigned. The optimal solution of Eq. (4) is taken as the new sampling point for updating the response surface. As the result, the local accuracy is improved. (Step 5) To find the unexplored region, the density function described in Section 4.3 is used [31]. The density function is constructed and minimized. The optimal solution of the density function is added as a new sampling point. This step is repeated till a terminal criterion is satisfied. This step is introduced for uniform distribution of

Extrapolation

Interpolation

D(x) 1

Extrapolation

Figure 6 shows the flow of the SAO for a multiobjective optimization problem. In this paper, the RBF network is adopted throughout the SAO procedure, and we will briefly describe it in the following section. In addition, the density function to find an unexplored region is also described.

Density function D(x) Warpage [mm]

0.6 0.4 A

B

Conventional cooling channel Conformal cooling channel

0.5 46%

0.4

Point B

0.3 0.2 0.1

53%

Point A

0.0

x Fig. 7 Illustrative example of density function in one dimension

Point C

0.6

0.8

0.2

the sampling points. As the result, global approximation can be achieved. (Step 6) If terminal criterion is satisfied, the SAO algorithm will be terminated. Otherwise, it will return to step 2. The average error between the response surface and the numerical simulation at the pareto-optimal solutions obtained in step 4 is taken as the terminal criterion. The SAO algorithm will be terminated when the average error is within 5 %.

0

5

10

15

20

25

Cycle time [s] Fig. 8 Comparison of pareto-frontier between the conventional and the conformal cooling channel

Int J Adv Manuf Technol Numerical data at points A, B, and C

Table 3

Injection time [s]

Point A (conformal cooling 0.72 channel) Point B (conventional 0.23 cooling channel) Point C (conventional 0.24 cooling channel)

Packing pressure Packing [MPa] time [s]

Melt temperature [°C]

Cooling temperature [°C]

91.47

5.47

198.46

57.16

9.72

53.83

6.67

The RBF network is a three-layer feed-forward network. The output of the network ŷ(x), which corresponds to the response surface, is given by Xm

w h ðxÞ; j¼1 j j

ð5Þ

where m denotes the number of sampling points, hj(x) is the jth basis function, and wj denotes the weight of the jth basis function. The following Gaussian kernel is generally used as the basis function: h j ðxÞ ¼ exp −

x−x j

T

x−x j

:

ð6Þ

In Eq. (6), xj represents the jth sampling point, and rj is the width of the jth basis function. The response yj is calculated at the sampling point xj. The learning of RBF network is usually accomplished by solving E¼

Xm  j¼1

Warpage [mm]

53.23

2.84

7.90

0.22

203.53

64.41

10.91

20.86

0.24

205.29

58.48

2.00

8.90

0.54

ð8Þ

where H, Λ, and y are given as follows: 2 3 h1 ðx1 Þ h2 ðx1 Þ ⋯ hm ðx1 Þ 6 h1 ð x 2 Þ h 2 ð x 2 Þ ⋯ h m ð x 2 Þ 7 7 H ¼6 4 ⋮ ⋮ ⋱ ⋮ 5 h1 ðxm Þ h2 ðxm Þ ⋯ hm ðxm Þ 3 2 λ1 0 ⋯ 0 6 0 λ2 ⋯ 0 7 7 Λ¼6 4⋮ ⋮ ⋱ ⋮ 5 0 0 0 λm y ¼ ðy1 ; y2 ; ⋯; ym ÞT

!

r2j

Cycle time [s]



−1 w ¼ H T H þ Λ H T y;

4.2 Radial basis function network

^yðxÞ ¼

Cooling time [s]

 2 X m y j −^y x j þ λ w2 →min; j¼1 j j

ð7Þ

where the second term is introduced for the purpose of the regularization. It is recommended that λj in Eq. (7) is sufficient small value (e.g., λj = 1.0 × 10−2) [32]. Thus, the learning of RBF network is equivalent to finding the weight vector w. The necessary condition of Eq. (7) results in the following equation.

ð9Þ

ð10Þ ð11Þ

It is clear from Eq. (8) that the learning of RBF network is equivalent to the matrix inversion (HTH + Λ)−1. The new sampling points are added through the SAO process. The following simple estimate is adopted to determine the width in Eq. (6) [31]: d j;max ffiffiffiffiffiffiffiffiffi r j ¼ pffiffiffip n n m−1

j ¼ 1; 2; ⋯; m ;

ð12Þ

where n denotes the number of design variables, m the number of sampling points, and dj,max the maximum distance between the jth sampling point and another one in the sampling points.

Warpage 10-1[mm] 4.000

2.133

0.000

x

Point A

z

y

x

Point B

z

y

x

Point C

Fig. 9 Warpage at points A, B, and C in Fig. 8 (×20)

z

y

: Outlet : Inlet

：Coolant (Inlet) ：Coolant (Outlet)

Fig. 10 Molding die of conformal cooling channel

Int J Adv Manuf Technol

Equation (12) is successfully applied to the least-square support vector machine [33].

Core Molding die

4.3 Density function using radial basis function network In the SAO, it is important to find out the unexplored region for global approximation. The Kriging can achieve this objective with the expected improvement (EI) function. In order to find out the unexplored region with the RBF network, we have developed a function called the density function [31]. The procedure to construct the density function is summarized as follows: (D-step 1) The following vector yD is prepared at the sampling points.

yD ¼ ð1; 1; ⋯; 1ÞTm1

ð13Þ

(D-step 2) The weight vector wD of the density function D(x) is calculated as follows:

j¼1

wDj h j ðxÞ→min

ð15Þ

(D-step 4) The point minimizing D(x) is taken as the new sampling point. Figure 7 shows an illustrative example in one dimension. The black dots denote the sampling points. It is found from Fig. 7 that local minima are generated around the unexplored region. The RBF network is basically the interpolation between sampling points: therefore, points A and B in Fig. 7 are the lower and upper bounds, respectively, of the design variables of the density function. As shown in Fig. 6, the parameter count is introduced. This parameter controls the number of sampling points that can be obtained by the density function. If the parameter

Cavity Fig. 11 Cavity and core for box-type plastic product

count is less than int(n/2), this parameter is increased as count = count + 1, where int() represents the rounding-off. This implies that the density function is repeatedly constructed and optimized in order to achieve uniform distribution of the sampling points.

5 Numerical and experimental result

ð14Þ

(D-step 3) The density function D(x) is minimized. Xm

Fig. 12 Overview of experiment

5.1 Numerical result



−1 w D ¼ H T H þ Λ H T yD

D ð xÞ ¼

Plastic product

Core

Fifteen initial sampling points are generated by the LHD, and the pareto-frontier between the cycle time and the warpage is identified with the SAO using the RBF network. The pareto-frontier is shown in Fig. 8, where the black circles denote the optimal solutions of the conformal cooling channel and the black triangles the ones of the conventional cooling channel. It is clear from Fig. 8 that the pareto-frontier of the conformal cooling channel is much improved, compared to the conventional cooling channel. With the conformal cooling channel, the improvement of 53 % can be achieved in the cycle time and the improvement of 46 % can be achieved in the warpage. Here, we select three points in Fig. 8 denoted by points A, B, and C, and at which the warpage and the cycle time are approximately same. The numerical data are listed in Table 3. First, let us compare the points B and C in the conventional cooling channel. It is found from Table 3 that the high packing pressure, the long packing time, the low melt temperature, the high cooling temperature, and the long cooling time are effective to the warpage reduction. However, the long cycle time is required to reduce the warpage, and it is clear from Fig. 8 that the trade-off between the warpage and the cycle time is observed. This result implies that the cooling channel should be redesigned for more effective reduction of both the warpage and the cycle time. Then, let us compare the points A and C, at which the cycle time is approximately same with the

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Numerical results of conventional cooling channel Numerical results of conformal cooling channel Experimental results of conventional cooling channel Experimental results of conformal cooling channel

0.6

Warpage [mm]

0.5 0.4 0.3 0.2

0.1 0.0 0

5

10

15

20

25

Cycle time [s] Fig. 13 Comparison of pareto-frontier between numerical simulation and experiment

different cooling channel. It is found from Table 3 that the warpage reduction with the high packing pressure and the short packing time can be achieved with the conformal cooling channel. Next, let us compare points A and B, at which the warpage is approximately same with the different cooling channel. It is clear from Fig. 8 and Table 3 that the cycle time is much improved with the conformal cooling channel. In addition, the warpage reduction can be achieved with the high packing pressure, the short packing time, the low cooling temperature, and the short cooling time. It is clear from the above discussion that the conformal cooling channel is effective to the short cycle time and the warpage reduction. The warpage at points A, B, and C is shown in Fig. 9, from which it is found that the warpage reduction can be achieved with the conformal cooling channel.

5.2 Experimental result The effectiveness of conformal cooling channel is experimentally examined. The molding die is developed by metal 3D printer (OPM250L, Sodick) and is shown in Fig. 10 with the numerical simulation model. The cavity and the core for the box-type plastic product developed by the metal 3D printer are shown in Fig. 11. The PIM machine (GL30-LP, Sodick) is used in the PIM experiment. The overview of the experiment is shown in Fig. 12. The experiment is carried out at all points of pareto-frontier, and the result is shown in Fig. 13, in which the white circles denote the experimental results with the conformal cooling channel and the white triangles the ones with the conventional cooling channel. It is confirmed from the experimental result that the cooling performance using the conformal cooling channel is improved, compared to the conventional cooling channel.

6 Conclusion In this paper, the cooling performance of conformal cooling channel is numerically and experimentally examined. As the cooling performance, the cycle time and the warpage is considered, and the process parameters in the PIM are optimized. Therefore, a multi-objective design optimization is performed. The SAO using the RBF network is used to identify the pareto-frontier between the cycle time and the warpage. It is clarified from the numerical result that the conformal cooling channel improves the cooling performance, compared to the conventional cooling channel. The metal 3D printer (OPM250L, Sodick) is also used to develop the conformal cooling channel, and the experiment is carried out. It is confirmed from the experimental result that the conformal cooling channel shows good cooling performance. In this paper, the conformal cooling channel is determined by the designer’s experiences, and the process parameters in the PIM are optimized using the SAO. The structural optimization (topology optimization) is also an important approach to determine the conformal cooling channel, and the following two-step optimization will be useful. At the first stage, the conformal cooling channel is determined by using the topology optimization. At the second stage, the process parameters of the conformal cooling channel are optimized.

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