4.4.1. Optimization before the Machine Calibration

Before performing the machine calibration, the eighteen sets of injection molding trials were executed using the parameters and settings found in Tables 4 and 5. The associated characteristic lengths and their average for each set were measured are and recorded in Table 12. For example, after the first molding simulation based on Set 1 conditions, the individual characteristic lengths were −0.15, −0.25, −0.08, and −0.12 mm, respectively. Also, the average characteristic length was −0.15 mm. Based on these calculated characteristic lengths, the standard deviation Sn was 0.06 mm, which was calculated from Equation (8). Then S/N ratio (signal-to-noise ratio) was 15.82 (obtained by Equation (9)). The quality values of the remaining seventeen sets are listed in Table 12.

**Table 12.** Quality predictions based on the characteristic length for CAE-DOE before machine calibration.


Moreover, before performing the machine calibration, the response for each factor was estimated and recorded into Table 13. The responses of all factors can be plotted as shown in Figure 15. From Table 13 and Figure 15, the optimized parameter set was determined as (A2, B3, C1, D2, E1, and F3). This optimized parameter set was applied in the injection molding simulation. The result is shown as "CAE-DOE (Sim)" in Figure 16. Compared to the original design, the optimized conditions reduced the average characteristic length from −0.169 mm (original) to −0.151 mm for the numerical simulation. Obviously, using the virtual DOE method (CAE-DOE), the quality can be improved about 10.7%. Moreover, to validate the efficiency of CAE-DOE optimization before performing the machine calibration, both the original design and the optimized parameter sets were utilized to execute the injection molding experimentally, and these results are also exhibited in Figure 16. The average characteristic length of the original design for the experimental system was −0.150 mm. Using the (CAE-DOE) optimized parameter set to perform the real injection molding, the average characteristic length was reduced to −0.143 mm, as demonstrated as "CAE-DOE (Exp)" in Figure 16. Clearly, the ease of assembly improved about 5%.

about 5%.


Moreover, before performing the machine calibration, the response for each factor was estimated and recorded into Table 13. The responses of all factors can be plotted as shown in Figure 15. From Table 13 and Figure 15, the optimized parameter set was determined as (A2, B3, C1, D2, E1, and F3). This optimized parameter set was applied in the injection molding simulation. The result is shown as "CAE-DOE (Sim)" in Figure 16. Compared to the original design, the optimized conditions reduced the average characteristic length from −0.169 mm (original) to −0.151 mm for the numerical simulation. Obviously, using the virtual DOE method (CAE-DOE), the quality can be improved about 10.7%. Moreover, to validate the efficiency of CAE-DOE optimization before performing the machine calibration, both the original design and the optimized parameter sets were utilized to execute the injection molding experimentally, and these results are also exhibited in Figure 16. The average characteristic length of the original design for the experimental system was −0.150 mm. Using the (CAE-DOE) optimized parameter set to perform the real injection molding, the average characteristic length was reduced to −0.143 mm, as demonstrated as "CAE-DOE (Exp)" in Figure 16. Clearly, the ease of assembly improved

**Table 13.** Response values for various control factors before machine calibration. **Table 13.** Response values for various control factors before machine calibration.

*Polymers* **2021**, *13*, x FOR PEER REVIEW 22 of 27

Where E<sup>i</sup> <sup>1</sup>−<sup>2</sup> means the influence of the "i" factor on the S/N ratio from Level 1 to Level 2; E<sup>i</sup> <sup>2</sup>−<sup>3</sup> means the influence of the "i" factor on the S/N ratio from Level 2 to Level 3. means the influence of the "i" factor on the S/N ratio from Level 2 to Level 3.

**Figure 15.** Response plot for various control factors before machine calibration. **Figure 15.** Response plot for various control factors before machine calibration.

**Figure 16.** Average of the characteristic length quality change through DOE optimization. **Figure 16.** Average of the characteristic length quality change through DOE optimization.

4.4.2. Optimization after the Machine Calibration 4.4.2. Optimization after the Machine Calibration

After the machine was calibrated, the control factors and their levels were modified as listed in Table 14. The corresponding orthogonal array for DOE performance using CAE (i.e., CAE-DOE) is the same as that listed in Table 5. Then, eighteen sets of injection molding trials were performed. The associated characteristic lengths and their average for each set were measured and recorded into Table 15. The quality values of the eighteen After the machine was calibrated, the control factors and their levels were modified as listed in Table 14. The corresponding orthogonal array for DOE performance using CAE (i.e., CAE-DOE) is the same as that listed in Table 5. Then, eighteen sets of injection molding trials were performed. The associated characteristic lengths and their average for each set were measured and recorded into Table 15. The quality values of the eighteen

> sets are also listed in Table 15. Moreover, in the presence of the machine calibration effect, based on the S/N ratio, the response for each factor was estimated, as recorded in Table

> Figure 17, after performing the machine calibration, the optimized parameter set obtained was (A2, B3, C1, D2, E2, and F3). The optimized parameter set was used in the injection molding simulation. The result is demonstrated as "CAE-DOE with calibration (Sim)" in Figure 16. Compared to the original design, the optimized conditions reduced the characteristic length significantly from −0.169 mm (original) to −0.134 mm in the numerical simulation. After the machine calibration was performed, using CAE-DOE, the assembly behavior improved about 20.7% in the simulation system. Obviously, these results are consistent with those of the simulation prediction. Moreover, the efficiency of CAE-DOE optimization after machine calibration has been validated as well. Specifically, after the machine was calibrated, the average characteristic lengths of the injected parts, based on the optimized parameter set, was reduced significantly from −0.150 mm (original) to −0.119 mm in the experimental system. In addition, the real experimental validation through the integration test was performed, as shown in Figure 18. Obviously, after the machine was calibrated, the assembly behavior improved about 20.7% in the experimental system. Overall, the driving forces to improve the ease of assembly were quite consistent for both the simulation prediction and experimental observation. Moreover, both the simulation and the experimental systems benefitted from the machine calibration effect. The contribution of machine calibration to the ease of assembly is described in Figure 16. First, from the simulation point of view, before and after machine calibration the average characteristic by CAE-DOE went from −0.151 mm to −0.134 mm. The contribution of the machine calibration effect was to enhance the ease of assembly by 11.3% in the simulation prediction. Moreover, from the experimental point of view, before and after the machine calibration the average characteristic by real injection went from −0.143 mm to −0.119 mm.

sets are also listed in Table 15. Moreover, in the presence of the machine calibration effect, based on the S/N ratio, the response for each factor was estimated, as recorded in Table 16. The responses of all factors were plotted, as shown in Figure 17. From Table 16 and Figure 17, after performing the machine calibration, the optimized parameter set obtained was (A2, B3, C1, D2, E2, and F3). The optimized parameter set was used in the injection molding simulation. The result is demonstrated as "CAE-DOE with calibration (Sim)" in Figure 16. Compared to the original design, the optimized conditions reduced the characteristic length significantly from −0.169 mm (original) to −0.134 mm in the numerical simulation. After the machine calibration was performed, using CAE-DOE, the assembly behavior improved about 20.7% in the simulation system. Obviously, these results are consistent with those of the simulation prediction. Moreover, the efficiency of CAE-DOE optimization after machine calibration has been validated as well. Specifically, after the machine was calibrated, the average characteristic lengths of the injected parts, based on the optimized parameter set, was reduced significantly from −0.150 mm (original) to −0.119 mm in the experimental system. In addition, the real experimental validation through the integration test was performed, as shown in Figure 18. Obviously, after the machine was calibrated, the assembly behavior improved about 20.7% in the experimental system. Overall, the driving forces to improve the ease of assembly were quite consistent for both the simulation prediction and experimental observation. Moreover, both the simulation and the experimental systems benefitted from the machine calibration effect. The contribution of machine calibration to the ease of assembly is described in Figure 16. First, from the simulation point of view, before and after machine calibration the average characteristic by CAE-DOE went from −0.151 mm to −0.134 mm. The contribution of the machine calibration effect was to enhance the ease of assembly by 11.3% in the simulation prediction. Moreover, from the experimental point of view, before and after the machine calibration the average characteristic by real injection went from −0.143 mm to −0.119 mm. The calibration effect enhanced the ease of assembly by 16.8% in the real injected observation.


**Table 14.** Control factors and their levels in CAE-DOE after machine calibration.

**Table 15.** Quality predictions based on the characteristic lengths for CAE-DOE after machine calibration.



**Table 15.** *Cont.*

**Table 16.** Response values for various control factors after machine calibration.


(**a**) (**b**) (**c**)

**Figure 18.** Experimental validation for the degree of assembly through the real integration test for CAE-DOE: (**a**) original

In this study, we proposed a feasible method to predict assembly behavior using the

characteristic length as the product index for two components within a family mold system, using numerical simulation and experimental observation. Several key points can be

(1) For the same operation condition settings of simulation and experimental systems, as the packing pressure is higher, the assembly behavior based on the characteristic lengths becomes poorer. The trend is consistent for both simulations and experiments, but there is some difference between the simulation and experimental results. (2) Based on the characteristic length variation (product index difference) investigation, under the same operation condition setting, the product index difference of the experimental observation was 1.65 times over that of the simulation prediction. Through the DFI investigation, the internal driving force of the experimental system was 1.59 times over that of the simulation one. This shows the internal driving force is quite matched with the product quality index. It also demonstrates that the simulation and experimental systems are not the same. Hence, the injection machine needs

(3) After the injection machine was calibrated, the criteria for good assembly based on the integration test could be constructed. Specifically, the individual characteristic lengths should be not smaller than −0.250 mm in the real system (or not smaller than

(4) To handle complex injection molding processing, the CAE-DOE optimization method was verified with high efficiency in ease of assembly improvement. Moreover, after finishing the machine calibration, the improvement of the CAE-DOE optimization method could approach 20%. In addition, the driving forces to improve the assembly behavior were quite consistent for both the simulation prediction and the

−0.243 mm in the virtual simulation system). The consistency was good.

**Figure 17.** Response plot for various control factors after machine calibration. **Figure 17.** Response plot for various control factors after machine calibration.

design, (**b**) optimization before machine calibration, (**c**) optimization before machine calibration.

**5. Conclusions** 

obtained, as follows:

to be calibrated.

**Figure 17.** Response plot for various control factors after machine calibration.

**Figure 18.** Experimental validation for the degree of assembly through the real integration test for CAE-DOE: (**a**) original design, (**b**) optimization before machine calibration, (**c**) optimization before machine calibration. **5. Conclusions Figure 18.** Experimental validation for the degree of assembly through the real integration test for CAE-DOE: (**a**) original design, (**b**) optimization before machine calibration, (**c**) optimization before machine calibration.

#### **5. Conclusions**

characteristic length as the product index for two components within a family mold system, using numerical simulation and experimental observation. Several key points can be obtained, as follows: (1) For the same operation condition settings of simulation and experimental systems, In this study, we proposed a feasible method to predict assembly behavior using the characteristic length as the product index for two components within a family mold system, using numerical simulation and experimental observation. Several key points can be obtained, as follows:

In this study, we proposed a feasible method to predict assembly behavior using the


**Author Contributions:** Conceptualization, C.-T.H. and T.-W.L.; methodology, C.-T.H. and T.-W.L.; software, T.-W.L.; validation, C.-T.H. and T.-W.L.; formal analysis, C.-T.H. and T.-W.L.; investigation, C.-T.H. and T.-W.L.; resources, W.-R.J. and S.-C.C.; data curation, T.-W.L.; writing—original draft preparation, C.-T.H.; writing—review and editing, C.-T.H.; visualization, C.-T.H., W.-R.J. and S.-C.C.; supervision, W.-R.J. and S.-C.C.; project administration, C.-T.H., W.-R.J. and S.-C.C.; funding acquisition, W.-R.J. and S.-C.C. All authors have read and agreed to the published version of the manuscript.

**Funding:** The authors would like to thank Ministry of Science and Technology of Taiwan. (Project number: MOST 109-2218-E-033-001-) for partly financially supporting for this research.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study are available on request from the corresponding author.

**Conflicts of Interest:** The authors declare no conflict of interest.

### **References**


**Chil-Chyuan Kuo 1,2,\*, Jing-Yan Xu <sup>1</sup> , Yi-Jun Zhu <sup>1</sup> and Chong-Hao Lee <sup>1</sup>**


**Abstract:** Metal additive manufacturing techniques are frequently applied to the manufacturing of injection molds with a conformal cooling channel (CCC) in order to shorten the cooling time in the injection molding process. Reducing the cooling time in the cooling stage is essential to reducing the energy consumption in mass production. However, the distinct disadvantages include higher manufacturing costs and longer processing time in the fabrication of injection mold with CCC. Rapid tooling technology (RTT) is a widely utilized technology to shorten mold development time in the mold industry. In principle, the cooling time of injection molded products is affected by both injection mold material and coolant medium. However, little work has been carried out to investigate the effects of different mold materials and coolant media on the cooling performance of epoxy-based injection molds quantitatively. In this study, the effects of four different coolant media on the cooling performance of ten sets of injection molds fabricated with different mixtures were investigated experimentally. It was found that cooling water with ultrafine bubble is the best cooling medium based on the cooling efficiency of the injection molded parts (since the cooling efficiency is increased further by about 12.4% compared to the conventional cooling water). Mold material has a greater influence on the cooling efficiency than the cooling medium, since cooling time range of different mold materials is 99 s while the cooling time range for different cooling media is 92 s. Based on the total production cost of injection mold and cooling efficiency, the epoxy resin filled with 41 vol.% aluminum powder is the optimal formula for making an injection mold since saving in the total production cost about 24% is obtained compared to injection mold made with commercially available materials.

**Keywords:** conformal cooling channel; rapid tooling technology; mold material; cooling medium
