*4.1. Single Factor Test and Basic Test for Assembly Behavior*

4.1.1. Perform a Single Factor Test

As mentioned earlier, the purpose of the single test was to determine some practical operation parameters for further study of the assembly behavior. Figure 6 shows the results of the single factor test on the influence of the characteristic lengths. For each factor, there were five levels to test, as listed in Table 1. The deviation was estimated by the maximum value of the characteristic length minus the minimum value, at each location. Then, the average deviation was utilized to evaluate the sensitivity of each factor. For example, in Figure 6a, when the injection speed setting increased from 30% to 70%, the average deviation from the injection speed was about 0.023 mm. For the melt temperature effect, the average deviation was 0.065 mm, as seen in Figure 6b. Figure 6c presents data that the mold temperature does not provide significant influence, with only a 0.001 mm deviation. Moreover, when the packing pressure is increased, it provides a significant influence, with an average deviation of 0.121 mm, as shown in Figure 6d. Similarly, the average deviations for the packing time and cooling time effects were 0.046 mm and 0.058 mm, respectively, as shown in Figure 6e,f. Overall, the packing pressure effect had the most significant influence on the variation of the characteristic lengths. In addition, the variation tendency of the characteristic lengths was almost proportional to the changes of the packing pressures. Hence, the packing pressure effect was selected as the practical parameter for further study of the assembly behavior.

#### 4.1.2. Perform a Basic Test

The goal for the basic test was to understand the flow behavior and the shrinkage behavior of each location for parts A and B. It was also used to realize the correlation between the characteristic length and the assembly behavior through simulation prediction and experimental verification when the injection molding simulation was performed using the operation condition of Table 3 at a 50% packing pressure setting. In Figure 7, when the volume was filled at 37.5%, the flow behavior for both parts A and B looked similar. However, from 63% to 100% volume filled, the flow imbalance phenomenon happened as expected due to the volume difference of cavities A and B. Figure 8 shows the shrinkage behavior for parts A and B. Regarding part A, XA1 and XA3 shrunk significantly because there was no constraint. The higher packing pressure, the worse the shrinkage happened, as shown in Figure 8c. However, since XA2 and XA4 were located at the end portion with strong wall constraints, the higher packing pressure provided the expansive result. On the other hand, for part B, since XB1 and XB2 were located within a concrete plane, when the packing pressure was increased, their lengths increased slightly. At the same time, XB3 and XB4 shrunk significantly because of lack of any constraint.

1 3 3 1 3 2 1 2 2 1 1 3 3 2 2 1 2 1 2 1 1 3 3 2 2 1 3 2 2 1 1 3 2 2 1 2 3 1 3 2 2 2 2 3 1 2 1 3 2 2 3 1 2 3 2 1 2 3 1 3 2 3 1 2 2 3 2 1 3 1 2 3 2 3 3 2 1 2 3 1

As mentioned earlier, the purpose of the single test was to determine some practical operation parameters for further study of the assembly behavior. Figure 6 shows the results of the single factor test on the influence of the characteristic lengths. For each factor, there were five levels to test, as listed in Table 1. The deviation was estimated by the maximum value of the characteristic length minus the minimum value, at each location. Then, the average deviation was utilized to evaluate the sensitivity of each factor. For example, in Figure 6a, when the injection speed setting increased from 30% to 70%, the average deviation from the injection speed was about 0.023 mm. For the melt temperature effect, the average deviation was 0.065 mm, as seen in Figure 6b. Figure 6c presents data that the mold temperature does not provide significant influence, with only a 0.001 mm deviation. Moreover, when the packing pressure is increased, it provides a significant influence, with an average deviation of 0.121 mm, as shown in Figure 6d. Similarly, the average deviations for the packing time and cooling time effects were 0.046 mm and 0.058 mm, respectively, as shown in Figure 6e,f. Overall, the packing pressure effect had the most significant influence on the variation of the characteristic lengths. In addition, the variation tendency of the characteristic lengths was almost proportional to the changes of the packing pressures. Hence, the packing pressure effect was selected as the practical parameter for fur-

**4. Results and Discussion** 

4.1.1. Perform a Single Factor Test

ther study of the assembly behavior.

*4.1. Single Factor Test and Basic Test for Assembly Behavior* 

**Figure 6.** Characteristic lengths variation due to the single factor test: (**a**) injection speed, (**b**) melt temperature, (**c**) mold temperature, (**d**) packing pressure, (**e**) packing time, (**f**) cooling time. **Figure 6.** Characteristic lengths variation due to the single factor test: (**a**) injection speed, (**b**) melt temperature, (**c**) mold temperature, (**d**) packing pressure, (**e**) packing time, (**f**) cooling time. sulting in a more difficult assembly of parts A and B. Indeed, higher packing pressure is not a solution to manage the degree of assembly in this study.

### 4.1.2. Perform a Basic Test

happened, as shown in Figure 8c. However, since XA2 and XA4 were located at the end portion with strong wall constraints, the higher packing pressure provided the expansive **Figure 7.** The flow behavior for both the simulation prediction and experimental validation. **Figure 7.** The flow behavior for both the simulation prediction and experimental validation.

same time, XB3 and XB4 shrunk significantly because of lack of any constraint.

result. On the other hand, for part B, since XB1 and XB2 were located within a concrete plane, when the packing pressure was increased, their lengths increased slightly. At the

pressure settings for simulation prediction. As the packing pressure increased, the variation of the characteristic lengths was almost linearly changed. To give better understanding, two packing pressures with lower and higher settings were selected and presented in Figure 9b. For example, at a 25% (lower) packing pressure setting, the characteristic lengths on the top plane were less than zero (X1 = −0.207 mm and X2 = −0.224 mm). Also, the characteristic lengths on the bottom plane were close to or less than zero (X3 = 0.004 mm and X4 = −0.013 mm). This means that the inner lengths of part B were less than outer lengths of part A. Theoretically, these components are not easy to assemble. When the

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

 (**c**) (**d**)

**Figure 8.** The shrinkage behavior for parts A and B: (**a**) top view, (**b**) bottom view, (**c**) individual

A basic evaluation of the assembly behavior for parts A and B is also performed experimentally. The operation conditions were the same as mentioned in the basic numerical test (see Table 3). For each packing pressure operation, six samples each of part A and part B were collected to measure the inner lengths and outer lengths, as described in Figure 5 and Equation (7). Then, the associated average characteristic lengths were obtained and plotted, as in Figure 9c. As the higher packing pressure was applied, the X1 became more positive, and the others (X2 to X4) became more negative. The basic tendency is similar to

Furthermore, since the variations of the individual lengths for parts A and B were not in the same trend, we had to define the characteristic length to measure the interaction

length variation of part A, (**d**) individual length variation of part B.

**Figure 7.** The flow behavior for both the simulation prediction and experimental validation.

packing pressure was increased to the 100% (higher) packing pressure setting, the characteristic lengths on the top plane were far less than zero (X1 = −0.175 mm and X2 = −0.255 mm). Also, the characteristic lengths on the bottom plane were less than zero (X3 = −0.061 mm and X4 = −0.083 mm). When the higher packing pressure was applied, although X1 became more positive, the others (X2 to X4) became more negative. This led the inner lengths of part B to become much smaller than outer lengths of part A, theoretically resulting in a more difficult assembly of parts A and B. Indeed, higher packing pressure is

not a solution to manage the degree of assembly in this study.

**Figure 8.** The shrinkage behavior for parts A and B: (**a**) top view, (**b**) bottom view, (**c**) individual length variation of part A, (**d**) individual length variation of part B. **Figure 8.** The shrinkage behavior for parts A and B: (**a**) top view, (**b**) bottom view, (**c**) individual length variation of part A, (**d**) individual length variation of part B.

A basic evaluation of the assembly behavior for parts A and B is also performed experimentally. The operation conditions were the same as mentioned in the basic numerical test (see Table 3). For each packing pressure operation, six samples each of part A and part B were collected to measure the inner lengths and outer lengths, as described in Figure 5 and Equation (7). Then, the associated average characteristic lengths were obtained and plotted, as in Figure 9c. As the higher packing pressure was applied, the X1 became more positive, and the others (X2 to X4) became more negative. The basic tendency is similar to Furthermore, since the variations of the individual lengths for parts A and B were not in the same trend, we had to define the characteristic length to measure the interaction among those individual lengths. In Figure 9a, there were four tests with different packing pressure settings for simulation prediction. As the packing pressure increased, the variation of the characteristic lengths was almost linearly changed. To give better understanding, two packing pressures with lower and higher settings were selected and presented in Figure 9b. For example, at a 25% (lower) packing pressure setting, the characteristic lengths on the top plane were less than zero (X<sup>1</sup> = −0.207 mm and X<sup>2</sup> = −0.224 mm). Also, the characteristic lengths on the bottom plane were close to or less than zero (X<sup>3</sup> = 0.004 mm and X<sup>4</sup> = −0.013 mm). This means that the inner lengths of part B were less than outer lengths of part A. Theoretically, these components are not easy to assemble. When the packing pressure was increased to the 100% (higher) packing pressure setting, the characteristic lengths on the top plane were far less than zero (X<sup>1</sup> = −0.175 mm and X<sup>2</sup> = −0.255 mm). Also, the characteristic lengths on the bottom plane were less than zero (X<sup>3</sup> = −0.061 mm and X<sup>4</sup> = −0.083 mm). When the higher packing pressure was applied, although X<sup>1</sup> became more positive, the others (X<sup>2</sup> to X4) became more negative. This led the inner lengths of part B to become much smaller than outer lengths of part A, theoretically resulting in a more difficult assembly of parts A and B. Indeed, higher packing pressure is not a solution to manage the degree of assembly in this study.

that of the numerical prediction. To get a better understanding, two packing pressures with lower and higher settings were selected and presented in Figure 9d. At the 25% (lower) packing pressure setting, the characteristic lengths on the top plane were less than zero (X1 = −0.035 mm and X2 = −0.24 mm). Also, the characteristic lengths on the bottom plane were also less than zero (X3 = −0.007 mm and X4 = −0.145 mm). When the packing pressure was increased to the 100% (higher) packing pressure setting, the characteristic lengths on the top plane changed. X1 becomes more positive but X2 became far less than zero (X1 = 0.042 mm and X2 = −0.267 mm). The characteristic lengths on the bottom plane were also far from zero (X3 = −0.167 mm and X4 = −0.280 mm). This means that the higher packing pressure will lead the inner lengths of part B to become much smaller than the outer lengths of part A, resulting in more difficulty in the assembly of parts A and B. Clearly, the tendency of the change of the characteristic lengths is in reasonable agreement

for both the simulation prediction and the experimental measurement.

**Figure 9.** Evaluation of the ease of assembly for parts A and B: (**a**) full range of packing pressure effect for simulation prediction, (**b**) higher and lower packing pressure effect for simulation prediction, (**c**) full range of packing pressure effect for experimental measurement, (**d**) higher and lower packing pressure effect for experimental measurement. **Figure 9.** Evaluation of the ease of assembly for parts A and B: (**a**) full range of packing pressure effect for simulation prediction, (**b**) higher and lower packing pressure effect for simulation prediction, (**c**) full range of packing pressure effect for experimental measurement, (**d**) higher and lower packing pressure effect for experimental measurement.

To realize the relationship between the characteristic lengths and the assembly behavior, a real integration test for parts A and B was performed, as shown in Figure 10. At

smooth and without difficulty. From the top view and side view, it is clearly seen that the assembly of parts A and B was completed as shown in Figure 10a. However, when the packing pressure setting was changed to 100%, the integration test for the assembly became very difficult. The integration test failed. Practically, the higher the packing pressure utilized, the more difficulty encountered in the assembly operation. The results of the integration test are consistent with the characteristic length behavior of the simulation prediction and experimental observation, as discussed previously. Obviously, this method to evaluate the assembly behavior using the characteristic lengths is feasible qualitatively so

far.

4.1.3. Correlation between Characteristic Length and Assembly Behavior

A basic evaluation of the assembly behavior for parts A and B is also performed experimentally. The operation conditions were the same as mentioned in the basic numerical test (see Table 3). For each packing pressure operation, six samples each of part A and part B were collected to measure the inner lengths and outer lengths, as described in Figure 5 and Equation (7). Then, the associated average characteristic lengths were obtained and plotted, as in Figure 9c. As the higher packing pressure was applied, the X<sup>1</sup> became more positive, and the others (X<sup>2</sup> to X4) became more negative. The basic tendency is similar to that of the numerical prediction. To get a better understanding, two packing pressures with lower and higher settings were selected and presented in Figure 9d. At the 25% (lower) packing pressure setting, the characteristic lengths on the top plane were less than zero (X<sup>1</sup> = −0.035 mm and X<sup>2</sup> = −0.24 mm). Also, the characteristic lengths on the bottom plane were also less than zero (X<sup>3</sup> = −0.007 mm and X<sup>4</sup> = −0.145 mm). When the packing pressure was increased to the 100% (higher) packing pressure setting, the characteristic lengths on the top plane changed. X<sup>1</sup> becomes more positive but X<sup>2</sup> became far less than zero (X<sup>1</sup> = 0.042 mm and X<sup>2</sup> = −0.267 mm). The characteristic lengths on the bottom plane were also far from zero (X<sup>3</sup> = −0.167 mm and X<sup>4</sup> = −0.280 mm). This means that the higher packing pressure will lead the inner lengths of part B to become much smaller than the outer lengths of part A, resulting in more difficulty in the assembly of parts A and B. Clearly, the tendency of the change of the characteristic lengths is in reasonable agreement for both the simulation prediction and the experimental measurement.

#### 4.1.3. Correlation between Characteristic Length and Assembly Behavior

To realize the relationship between the characteristic lengths and the assembly behavior, a real integration test for parts A and B was performed, as shown in Figure 10. At the 25% packing pressure setting, the integration process assemble parts A and B was smooth and without difficulty. From the top view and side view, it is clearly seen that the assembly of parts A and B was completed as shown in Figure 10a. However, when the packing pressure setting was changed to 100%, the integration test for the assembly became very difficult. The integration test failed. Practically, the higher the packing pressure utilized, the more difficulty encountered in the assembly operation. The results of the integration test are consistent with the characteristic length behavior of the simulation prediction and experimental observation, as discussed previously. Obviously, this method to evaluate the assembly behavior using the characteristic lengths is feasible qualitatively so far.

### *4.2. Discover the Reason for the Difference between Simulation and Experiment for the Assembly Behavior*

Figure 11 shows the comparison between the characteristic lengths of the simulation prediction and those of experimental measurement. When the packing pressure increased from 25% to 100%, X<sup>1</sup> increased, while the others (X<sup>2</sup> to X4) decreased for both the simulation and the experiment. However, when the comparison proceeded one-by-one from X<sup>1</sup> via X<sup>2</sup> to X4, the amounts of simulation prediction were under-predicted at the top plane for X<sup>1</sup> and X<sup>2</sup> (i.e., too much negative), and were over-predicted at bottom plane for X<sup>3</sup> and X<sup>4</sup> (i.e., too much positive). Overall, the tendency is in reasonable agreement, but the amount of characteristic length at each location was not exactly matched in both the simulation and the experiment. To discover the difference between the simulation and the experiment, the relationship between the internal driving force from the injection machine and the characteristic length difference (∆Xi) on the injected parts was investigated. Here, the characteristic length difference (∆Xi) is defined as Equation (10), as follows.

$$
\Delta \mathbf{X}\_{\mathrm{i}} = \mathrm{Xi} \text{ (at 100\%Packing)} - \mathrm{Xi} \text{ (at 25\%Packing)} \tag{10}
$$

where i is from 1 to 4.

*Polymers* **2021**, *13*, x FOR PEER REVIEW 15 of 27

**Figure 10.** Evaluation on the degree of assembly difficulty through a real integration test for different packing pressure settings on the injection parts: (**a**) 25% packing: passed, (**b**) 100% packing: failed. **Figure 10.** Evaluation on the degree of assembly difficulty through a real integration test for different packing pressure settings on the injection parts: (**a**) 25% packing: passed, (**b**) 100% packing: failed. settings. To reduce the difference between two systems, some injection machines need to be calibrated. The details will be discussed in the following section.

and the virtual machine are not the same, even they have the same operation condition

∆Xi = Xi (at 100% Packing) − Xi (at 25% Packing) (10) **Figure 11.** Comparison between simulation and experiment at 25% to 100% packing pressure set-**Figure 11.** Comparison between simulation and experiment at 25% to 100% packing pressure settings.

where i is from 1 to 4. For example, ∆X1 (the characteristic length difference of the simulation) is equal to 0.032 mm (i.e., (−0.175) − (−0.207) = 0.032 mm). Other characteristic length differences of the simulation were calculated, and are listed in Table 6. The average characteristic length differences of the simulation were further calculated and are listed in the rightmost column in Table 6. The ∆X1 of the experiment was equal to 0.077 mm (i.e., (0.042) − (−0.035) = 0.077 mm). The other characteristic length differences and their average were also calculated and are shown in Table 6. It is noted that the average of the characteristic length differences of the experiment was about 1.65 times over that of the simulation prediction (that is, 0.061/0.037 = 1.65). For the exact same operation condition settings for both simulation and experimental systems, why did the experimental system drive more dimensional variation in the final injection parts than its simulation counterpart is a very interesting question. Before we proceed to answer this question, we note that Huang et al. [33] tings. **Table 6.** Difference of the characteristic lengths between the 100% and 25% packing pressure settings for both simulation and experiment (unit: mm). **ΔX1 ΔX2 ΔX3 ΔX4 Ave ΔX**  Simulation 0.032 −0.031 −0.065 −0.084 −0.037 Experiment 0.077 −0.027 −0.160 −0.135 −0.061 *4.3. Machine Calibration Effects on Assembly Behavior*  4.3.1. Perform Machine Calibration To reduce the difference between the numerical prediction and the experimental observations, machine calibration procedures were performed based on the direction in [33]. However, the new controller was changed into the FCS injection machine and one pressure transducer was installed at gate location. Some calibration procedures needed to be modified from the the system in [33]. Specifically, the reference point to catch the injection pressure history curve was moved to the gate location; the new controller was installed, and the injection pressure history of the experiment was different. The details of the calibration procedures are as follows. Machine calibration is based on the injection pressure history curves for both the simulation and the experiment, using a circle plate system with For example, ∆X<sup>1</sup> (the characteristic length difference of the simulation) is equal to 0.032 mm (i.e., (−0.175) − (−0.207) = 0.032 mm). Other characteristic length differences of the simulation were calculated, and are listed in Table 6. The average characteristic length differences of the simulation were further calculated and are listed in the rightmost column in Table 6. The ∆X<sup>1</sup> of the experiment was equal to 0.077 mm (i.e., (0.042) − (−0.035) = 0.077 mm). The other characteristic length differences and their average were also calculated and are shown in Table 6. It is noted that the average of the characteristic length differences of the experiment was about 1.65 times over that of the simulation prediction (that is, 0.061/0.037 = 1.65). For the exact same operation condition settings for both simulation and experimental systems, why did the experimental system drive more dimensional variation in the final injection parts than its simulation counterpart is a very interesting question. Before we proceed to answer this question, we note that Huang et al. [33] mentioned that one of the reasons for the difference between numerical predictions and experimental observations in injection molding is because the real machine (experiment) and the virtual machine are not the same, even they have the same operation condition settings. To reduce the difference between two systems, some injection machines need to be calibrated. The details will be discussed in the following section.

a pressure transducer installed at the gate. The sensor location is presented in Figure 12.

Specifically, for the same operation condition settings, Figure 13a shows the injection pressure history curves for both the simulation and the experiment at the 50% injection speed setting. The experiment shows a higher injection pressure history curve than that of the simulation counterpart over the entire period, which means that the real injection machine has a higher driving force than that of the virtual simulation machine. To evaluate the driving force for the injection molding through the entire cycle, a driving force index (DFI) based on the total accumulated driving force was defined, as in Equation (11). It is also called the viscosity index [34,35]. This equation can be regarded as reflecting the accumu-

lated resistance force of melt flow during injection molding.


**Table 6.** Difference of the characteristic lengths between the 100% and 25% packing pressure settings for both simulation and experiment (unit: mm).

#### *4.3. Machine Calibration Effects on Assembly Behavior*

*Polymers* **2021**, *13*, x FOR PEER REVIEW 17 of 27

#### 4.3.1. Perform Machine Calibration

To reduce the difference between the numerical prediction and the experimental observations, machine calibration procedures were performed based on the direction in [33]. However, the new controller was changed into the FCS injection machine and one pressure transducer was installed at gate location. Some calibration procedures needed to be modified from the the system in [33]. Specifically, the reference point to catch the injection pressure history curve was moved to the gate location; the new controller was installed, and the injection pressure history of the experiment was different. The details of the calibration procedures are as follows. Machine calibration is based on the injection pressure history curves for both the simulation and the experiment, using a circle plate system with a pressure transducer installed at the gate. The sensor location is presented in Figure 12. The data of the injection pressure can be recorded from the pressure transducer at the gate, which is further used to create the pressure history curve for machine calibration. Specifically, for the same operation condition settings, Figure 13a shows the injection pressure history curves for both the simulation and the experiment at the 50% injection speed setting. The experiment shows a higher injection pressure history curve than that of the simulation counterpart over the entire period, which means that the real injection machine has a higher driving force than that of the virtual simulation machine. To evaluate the driving force for the injection molding through the entire cycle, a driving force index (DFI) based on the total accumulated driving force was defined, as in Equation (11). It is also called the viscosity index [34,35]. This equation can be regarded as reflecting the accumulated resistance force of melt flow during injection molding. DFI = 〈்ܲ௧〉 = ൫ܲ൯ ௧ ݐ݀ (11) where *i* is either simulation or experiment, 〈்ܲ௧〉 is the total accumulated driving force with (MPa·s) viscosity units, and *Pinj* is the injection pressure measured at the gate location at the time t. Through this equation, the total accumulated driving force is equal to the integration area under the injection pressure history curve for both the simulation and experiment systems. For instance, at the 50% injection speed setting, the DFI of the real experimental system, 〈்ܲ௧〉ா௫, was about 1471.6 MPa·s, and the DFI of the virtual simulation system, 〈்ܲ௧〉ௌ, was about 928.3 MPa·s, as shown in Figure 13b. Specifically, the DFI of the real experimental system was about 1.59 times over that of the virtual simulation system. This result is quite consistent with that ratio of 1.65 times for the experimental product index (characteristic lengths) difference from the simulation, as described previously. Based on this idea, the key to calibrating the machine is to determine the matched pair for both the simulation and the experimental systems that have the same DFI for the injection molding. For example, when the real injection machine keeps the 50% injection speed setting, the curve of the simulation system with the 50% injection speed setting is lower (i.e., with lower driving force). At this moment, the injection speed setting can be increased to enhance the driving force virtually. Until the injection speed setting of the simulation is increased to 110%, the injection pressure history curve is very close to that of the real injection machine with the 50% injection speed setting, as shown in Figure 13d. In this Figure, 〈்ܲ௧〉ா௫ is about 1471.6 MPa·s, and 〈்ܲ௧〉ௌ is about 1449.2 MPa·s. The DFI of the

$$\text{DFI} = \langle P\_{\text{Total}} \rangle\_{\text{i}} = \int\_{0}^{t} \left( P\_{\text{inj}} \right)\_{\text{i}} dt \tag{11}$$

where *i* is either simulation or experiment, h*PTotal*i is the total accumulated driving force with (MPa·s) viscosity units, and *Pinj* is the injection pressure measured at the gate location at the time *t*. jection speed setting is 50% in the experimental study, the counterpart in the simulation would be the 79.5 mm/s injection speed setting. Other matched pairs were evaluated, and are listed in Table 7.

**Figure 12.** The calibration system and the sensor location. **Figure 12.** The calibration system and the sensor location.

**Figure 13.** *Cont*.

**Figure 13.** Injection pressure history curves used to perform machine calibration: (**a**) original injection pressure history curves at the 50% injection speed settings for both simulation and experiment, (**b**) schematic plots for the total driving force of the real experimental and simulation systems, (**c**) comparison of the history of injection pressure between the simulation and experiment at various injection speeds from 30% to 130%, (**d**) the matched pair for both the simulation and the experiment, where the simulation 110% injection speed setting is matched with the experimental 50% injection speed setting. **Figure 13.** Injection pressure history curves used to perform machine calibration: (**a**) original injection pressure history curves at the 50% injection speed settings for both simulation and experiment, (**b**) schematic plots for the total driving force of the real experimental and simulation systems, (**c**) comparison of the history of injection pressure between the simulation and experiment at various injection speeds from 30% to 130%, (**d**) the matched pair for both the simulation and the experiment, where the simulation 110% injection speed setting is matched with the experimental 50% injection speed setting.

**Table 7.** Matched pairs of injection speed settings for the simulation and experiment systems. **Simulation Simulation Injection Speed Setting (mm/s) Experiment Injection Speed Setting a** 90% 67.0 30% 100% 73.4 40% 110% 79.5 50% 120% 85.8 60% 130% 92.0 70% a: based on the maximum speed of the screw movement with 125 mm/s. 4.3.2. Evaluate Calibration Effect on Assembly Behavior After performing the machine calibration at various injection speed settings, the machine calibration effect on the characteristic length changes could be further examined. For example, Figure 14 presents the comparison of the characteristic lengths between the simulation and experiment at the 25% to 100% packing pressure settings before and after machine calibration at the 50% injection speed setting. Since those four different characteristic lengths have different variation behavior, the calibration effect on each characteristic length was calculated individually. The calibration rate for each characteristic length is defined as in Equation (12): Through this equation, the total accumulated driving force is equal to the integration area under the injection pressure history curve for both the simulation and experiment systems. For instance, at the 50% injection speed setting, the DFI of the real experimental system, h*PTotal*i*Exp*, was about 1471.6 MPa·s, and the DFI of the virtual simulation system, h*PTotal*i*Sim*, was about 928.3 MPa·s, as shown in Figure 13b. Specifically, the DFI of the real experimental system was about 1.59 times over that of the virtual simulation system. This result is quite consistent with that ratio of 1.65 times for the experimental product index (characteristic lengths) difference from the simulation, as described previously. Based on this idea, the key to calibrating the machine is to determine the matched pair for both the simulation and the experimental systems that have the same DFI for the injection molding. For example, when the real injection machine keeps the 50% injection speed setting, the curve of the simulation system with the 50% injection speed setting is lower (i.e., with lower driving force). At this moment, the injection speed setting can be increased to enhance the driving force virtually. Until the injection speed setting of the simulation is increased to 110%, the injection pressure history curve is very close to that of the real injection machine with the 50% injection speed setting, as shown in Figure 13d. In this Figure, <sup>h</sup>*PTotal*i*Exp* isabout 1471.6 MPa·s, and <sup>h</sup>*PTotal*i*Sim* is about 1449.2 MPa·s. The DFI of the real experimental system was about 1.02 times over that of the virtual simulation system. That is to say, the internal driving force of the 50% injection speed setting experimentally was matched by the 110% injection speed setting numerically. Specifically, when the injection speed setting is 50% in the experimental study, the counterpart in the simulation would be the 79.5 mm/s injection speed setting. Other matched pairs were evaluated, and are listed in Table 7.

where ΔL is the difference between the experimental characteristic length and that of the simulation before machine calibration, and (ΔL)cal is the difference between the experimental characteristic length and that of the simulation one after machine calibration.

For example, when the 100% packing pressure setting situation is considered, the calibration rates for each characteristic length are shown as in Table 8. The average calibration rate is about 18%. This demonstrates that the difference between simulation prediction and experimental observation was reduced by 18%. In addition, the details of the machine calibration effect for the 50% injection speed setting at various packing pressure

Calibration rate = [ΔL − (ΔL)cal]/ΔL\*100% (12)


**Table 7.** Matched pairs of injection speed settings for the simulation and experiment systems.

a : based on the maximum speed of the screw movement with 125 mm/s.

#### 4.3.2. Evaluate Calibration Effect on Assembly Behavior *Polymers* **2021**, *13*, x FOR PEER REVIEW 20 of 27

After performing the machine calibration at various injection speed settings, the machine calibration effect on the characteristic length changes could be further examined. For example, Figure 14 presents the comparison of the characteristic lengths between the simulation and experiment at the 25% to 100% packing pressure settings before and after machine calibration at the 50% injection speed setting. Since those four different characteristic lengths have different variation behavior, the calibration effect on each characteristic length was calculated individually. The calibration rate for each characteristic length is defined as in Equation (12): lengths improved about 10%. Moreover, after the machine calibration was completed, the relationship between the characteristic lengths and the assembly behavior was further measured using the integration test described in Figure 10. The result of the integration test is shown in Table 10. Specifically, when it was at the 25% packing pressure setting, although all Xi were smaller than zero, the real components A and B could be integrated together smoothly. Similarly, all components passed the integration test from the 25% to the 75% packing pressure settings. At the 100% packing pressure setting, the integration

$$\text{Calibration rate} = \left[\Delta \text{L} - \left(\Delta \text{L}\right) \text{cal}\right] / \Delta \text{L} \* 100\% \tag{12}$$

where ∆L is the difference between the experimental characteristic length and that of the simulation before machine calibration, and (∆L)cal is the difference between the experimental characteristic length and that of the simulation one after machine calibration. assure the good assembly of parts A and B can be obtained when one characteristic length is not smaller than −0.243 mm numerically, as listed in Table 11. Based on these results, using numerical simulation to predict the ease of assembly has been verified as a feasible and quantitative method.

**Figure 14.** At the 50% injection speed setting, the comparison of the characteristic length deviation between simulation and experiment at the 25% to 100% packing pressure settings before and after machine calibration. **Figure 14.** At the 50% injection speed setting, the comparison of the characteristic length deviation between simulation and experiment at the 25% to 100% packing pressure settings before and after machine calibration.

**Table 8.** Measurements of the calibration effect for the 50% injection speed setting at the 100% packing pressure setting.  **Before Calibration After Calibration Calibration Character. Length Sim Exp ΔL (Sim)cal (Exp)cal (ΔL)cal Rate (%)**  X1 −0.175 0.042 0.217 −0.170 0.042 0.212 2 X2 −0.255 −0.267 −0.012 −0.260 −0.267 −0.007 42 X3 −0.080 −0.167 −0.087 −0.096 −0.167 −0.071 18 X4 −0.103 −0.280 −0.177 −0.119 −0.280 −0.161 9 Average calibration rate 18 For example, when the 100% packing pressure setting situation is considered, the calibration rates for each characteristic length are shown as in Table 8. The average calibration rate is about 18%. This demonstrates that the difference between simulation prediction and experimental observation was reduced by 18%. In addition, the details of the machine calibration effect for the 50% injection speed setting at various packing pressure settings are listed in Table 9. It is noted that the calibration effect on the characteristic lengths improved about 10%. Moreover, after the machine calibration was completed, the relationship between the characteristic lengths and the assembly behavior was further measured using the integration test described in Figure 10. The result of the integration

**Table 9.** Measurement of the calibration effect for the 50% injection speed setting at various packing

 **Machine Calibration Rate (%) Packing Pressure Setting (%) X1 X2 X3 X4 Average** 

> 25 0 0 9 0 2 50 1 0 11 8 5 75 2 42 14 8 17 100 2 42 18 9 18

> > Total average calibration rate 10

pressure settings.

test is shown in Table 10. Specifically, when it was at the 25% packing pressure setting, although all X<sup>i</sup> were smaller than zero, the real components A and B could be integrated together smoothly. Similarly, all components passed the integration test from the 25% to the 75% packing pressure settings. At the 100% packing pressure setting, the integration test failed. At this moment, it could be found that as long as one characteristic length is smaller than −0.25 mm, it would fail the integration test. Similarly, the virtual criteria to assure the good assembly of parts A and B can be obtained when one characteristic length is not smaller than −0.243 mm numerically, as listed in Table 11. Based on these results, using numerical simulation to predict the ease of assembly has been verified as a feasible and quantitative method.

**Table 8.** Measurements of the calibration effect for the 50% injection speed setting at the 100% packing pressure setting.


**Table 9.** Measurement of the calibration effect for the 50% injection speed setting at various packing pressure settings.


**Table 10.** Quantification of the degree of assembly through the integration test for the 50% injection speed system, experimentally.


**Table 11.** Quantification the degree of assembly for the 50% injection speed setting in the simulation system.


### *4.4. Optimize the Assembly Behavior Using CAE-DOE*
