• Volume of Fluid, VOF.

The free liquid surface problem is quite difficult for numerical calculations. The main reason for this issue is that the boundary of a free liquid surface is a moving boundary, and the boundary changes with time. The free liquid surface must meet the free surface kinematic boundary condition (FSKBC) and the free surface dynamic boundary condition (FSDBC) [16].

The volume of fluid (VOF) [17] is a numerical calculation method that is used to establish the interface boundary conditions for a free surface or two-fluid interfaces. The VOF method is based on defining a fractional volume function that allows a single element to be full, partially filled, or to remain empty. Through the fractional volume function, three areas can be defined in the element as follows:

$$f = \begin{cases} 0, \text{ the element is empty.}\\ 1, \text{ the element is full.}\\ 0 < f < 1, \text{ there is a fluid interface in element.} \end{cases} \tag{10}$$

The fractional volume function is governed by a transport equation:

$$\frac{\partial f}{\partial t} + \stackrel{\rightarrow}{V} \cdot \nabla f = 0 \tag{11}$$

The following simple serial averages are adopted in this work to approximate the density and viscosity at the interface between fluid 1 and fluid 2.

$$
\rho\_f = f \cdot \rho\_1 + (1 - f) \cdot \rho\_2 \tag{12}
$$

$$
\eta\_f = f \cdot\_1 + (1 - f) \cdot\_2 \tag{13}
$$

#### *3.2. Simulation Process*

This study explores the gluing technology used in the iron sheet stacking process of motor cores. The resin is transferred through resin inlet to resin pool by a pump as shown in Figures 6 and 7, so the injection molding process simulation tool, Moldex3D, is used for the filling process simulation. The resin flows through the viscous flow channels and the viscous flow channels are constituted of the resin pool and the Teflon block. When the resin flows through 122 holes in a plate, hemi-spheres of resin will be formed. An iron sheet is then dipped on the emerged resin to form a thin layer of glue to bond iron layers to make a motor core.

165

182

192

sheet is then dipped on the emerged resin to form a thin layer of glue to bond iron layers 157 to make a motor core. 158 During the dipping process, the iron sheet moves with the upper die. Therefore, com- 159 pression molding process simulation is used to model the dipping process. The emerged 160 hemi-sphere shaped resin in the plate is numerically extracted as the initial condition for 161 the dipping analysis to predict whether the resin is evenly distributed on the iron sheet. 162 The stacking process is fully elucidated through the use of a mold flow analysis and 163 a dipping analysis in order to establish the simulation approach used in this study. 164

**Figure 6.** The simulation flow chart. 166 **Figure 6.** The simulation flow chart.

flow out of the system. There are 3.5 million mesh elements, for which the quality is 0.97 179 based on the skewness. 180 **Figure 7.** Mesh model used in the filling process.

**Figure 7.** Mesh model used in the filling process. 183 3.3.2. Dipping Process 184 The mesh used for the dipping process is composed of a compression surface (iron 185 sheet), a compression zone, a space above the over-flow dam (plate), and the over-flow 186 During the dipping process, the iron sheet moves with the upper die. Therefore, compression molding process simulation is used to model the dipping process. The emerged hemi-sphere shaped resin in the plate is numerically extracted as the initial condition for the dipping analysis to predict whether the resin is evenly distributed on the iron sheet.

dam, as shown in Figure 8. The compression zone part simulates the process of gluing the 187 iron sheet. In addition, since the resin on the iron sheet cannot exceed 0.002 mm, the resin 188 is compressed into a space with a thickness of 0.002 mm (the space above the over-flow 189 The stacking process is fully elucidated through the use of a mold flow analysis and a dipping analysis in order to establish the simulation approach used in this study.

#### dam) for the simulation. There is a total of 2.5 million mesh elements, for which the quality 190 *3.3. Mesh Generation*

is 0.99 based on the skewness. 191 For the purposes of the simulation, the process is divided into two parts, where the mesh is divided into two parts and constructed as a filling process and a dipping process. Rhinoceros 5 was the mesh modeling software used in this study.

#### 3.3.1. Filling Process

A solid 3D mesh model is created through geometry, as shown in Figure 7. The resin pool and the Teflon block are constructed according to the geometry provided by the Metal Industries Research and Development Center, Kaohsiung, Taiwan. The diameter of the resin inlet is 6 mm, then the resin is divided to the left and right side by three runners (Figure 3b), and finally the resin flows out through 122 holes with 1 mm diameter. The location of the holes is shown in Figure 3a. The detail dimensions of the filling model are shown in Appendix A, Figure A1. The plate is used to simulate the open space of the resin

**Figure 8.** Mesh model used in the dipping process. 193

*3.4. Process Parameters* 194 The stamping process is used for gluing the motor core. Due to the design of the 195 runner and the module, the flow of the resin is very important to the overall process. 196 Therefore, the flow is predicted through a simulation, and the experimental parameters 197 are input into the mold flow analysis software to simulate and predict the resin flow and 198 gluing results. 199

3.4.1. Filling Process 200

flow out of the system. There are 3.5 million mesh elements, for which the quality is 0.97 based on the skewness. **Figure 7.** Mesh model used in the filling process. 183

182

192

181

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#### 3.3.2. Dipping Process 3.3.2. Dipping Process 184

The mesh used for the dipping process is composed of a compression surface (iron sheet), a compression zone, a space above the over-flow dam (plate), and the over-flow dam, as shown in Figure 8. The compression zone part simulates the process of gluing the iron sheet. In addition, since the resin on the iron sheet cannot exceed 0.002 mm, the resin is compressed into a space with a thickness of 0.002 mm (the space above the over-flow dam) for the simulation. There is a total of 2.5 million mesh elements, for which the quality is 0.99 based on the skewness. The mesh used for the dipping process is composed of a compression surface (iron 185 sheet), a compression zone, a space above the over-flow dam (plate), and the over-flow 186 dam, as shown in Figure 8. The compression zone part simulates the process of gluing the 187 iron sheet. In addition, since the resin on the iron sheet cannot exceed 0.002 mm, the resin 188 is compressed into a space with a thickness of 0.002 mm (the space above the over-flow 189 dam) for the simulation. There is a total of 2.5 million mesh elements, for which the quality 190 is 0.99 based on the skewness. 191

**Figure 8.** Mesh model used in the dipping process. 193 **Figure 8.** Mesh model used in the dipping process.

#### *3.4. Process Parameters* 194 *3.4. Process Parameters*

The stamping process is used for gluing the motor core. Due to the design of the 195 runner and the module, the flow of the resin is very important to the overall process. 196 Therefore, the flow is predicted through a simulation, and the experimental parameters 197 are input into the mold flow analysis software to simulate and predict the resin flow and 198 gluing results. 199 The stamping process is used for gluing the motor core. Due to the design of the runner and the module, the flow of the resin is very important to the overall process. Therefore, the flow is predicted through a simulation, and the experimental parameters are input into the mold flow analysis software to simulate and predict the resin flow and gluing results.

#### 3.4.1. Filling Process

3.4.1. Filling Process 200 In the experiment, the resin was pushed by a pump, for which the pressure was 0.8 MPa, so the injection pressure was set at 0.8 MPa. The mold temperature and the resin temperature were both set to 45 ◦C based on the data provided by the Metal Industry Research and Development Center, which indicates that the temperature of the resin before entering the module is about 45 ◦C. The mold flow analysis mold is set at 45 ◦C because, regardless of whether it passes through the runner in the resin pool or the runner or microstructure in the Teflon block, the resin temperature is still about 45 ◦C, so the resin is flowing isothermally in the glue module. In the setting of process parameters, the initial conversion rate of plastics is very important. In this study, Moldex3D mold flow analysis software was used to calculate the initial conversion rate. The resin was taken out at room temperature (25 ◦C) for one day, and the initial conversion rate barely changed. Therefore, the initial conversion rate was set to 0%. The process parameters can be shown in Table 3. In the experiment, the volume flow rate is 0.00053 cm3/s. The volume flow rate cannot be set in the simulation analysis, so it can only be measured based on the filling time. Since the total volume of the mesh model established in this paper was 4.16 cm<sup>3</sup> , the filling time was

set to 416 s, for which the volume flow rate was 0.01 cm3/s. The reason why the volume flow rate of this study was set at 0.01 cm3/s is explained in the Results and Discussion section of this paper.

**Table 3.** The parameters of the filling process.


#### 3.4.2. Dipping Process

The parameters for the dipping process are shown in Table 4. The compression speed and compression force, which is the stamping speed and stamping force in the stamping process, respectively, were set based on the Metal Industries Research and Development Center guidelines. The thickness of the compression zone was 0.5 mm because the thickness of the compression zone only addressed the area where the iron sheet is prepared to glue the resin. The compression time was obtained by the compression gap divided by the compression speed. The resin and mold temperature settings were also set based on the data provided by the Metal Industries Research and Development Center. The initial conversion rate setting was calculated using Moldex3D software. From the filling process to the gluing stage, the resin in the module does not flow over 1 hour, so the conversion rate remained at 0%.


**Table 4.** The parameters of the dipping process.

#### *3.5. Mold Flow Analysis Software*

A commercially available CAE software Molde×3D 2020 R1 special edition for free surface simulation was used for the analysis in this study. It is a CAE software used mainly for injection molding and compression molding simulations.

#### **4. Results and Discussion**

This section discusses the influence of gravity and the flow rate on the simulation and also discusses the resin distribution during the dipping process and the distribution of the air traps, after which a comparison of the results with the experimental results are discussed.

#### *4.1. The Influence of Gravity on Simulation*

The effect of gravity in this study was very significant. Figure 9 shows the influence of gravity on the simulation. If gravity is ignored, there is a slightly unreasonable flow situation, as shown in Figure 9. When gravity is taken into account, the results are close to actual conditions. Therefore, gravity must be taken into consideration.

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**Figure 9.** The effect of gravity on simulation (**a**) considering gravity and (**b**) not considering gravity. 247 **Figure 9.** The effect of gravity on simulation (**a**) considering gravity and (**b**) not considering gravity. **Figure 9.** The effect of gravity on simulation (**a**) considering gravity and (**b**) not considering gravity. 247

#### *4.2. The Influence of Flow Rate on Simulation* 248 *4.2. The Influence of Flow Rate on Simulation 4.2. The Influence of Flow Rate on Simulation* 248

In this simulation, if the flow rate is set to be the same as the experiment in the mold 249 flow analysis, the air resistance will be too large, which will cause the resin to fail to flow 250 smoothly and cause the simulation to stop. Therefore, different fill times were set, which 251 made the flow rate respectively 0.01 (see Figure 10), 0.02, 0.03, 0.04, and 0.05 cm<sup>3</sup> /sec. The 252 simulation results of the flow rate 0.02, 0.03, 0.04, 0.05 cm<sup>3</sup> /sec are shown in Appendix B, 253 Figures B1–B4. From the simulation results of different flow rates, it can be seen that the 254 flow trend is similar at different flow rates. In this study, the flow rate closest to the ex- 255 perimental conditions was used for the simulation (0.01 cm<sup>3</sup> /sec). Experiment and simu- 256 lation results of the flow trend in the plate are shown in Table 5. 257 In this simulation, if the flow rate is set to be the same as the experiment in the mold flow analysis, the air resistance will be too large, which will cause the resin to fail to flow smoothly and cause the simulation to stop. Therefore, different fill times were set, which made the flow rate respectively 0.01 (see Figure 10), 0.02, 0.03, 0.04, and 0.05 cm3/s. The simulation results of the flow rate 0.02, 0.03, 0.04, 0.05 cm3/s are shown in Appendix B, Figures A2–A5. From the simulation results of different flow rates, it can be seen that the flow trend is similar at different flow rates. In this study, the flow rate closest to the experimental conditions was used for the simulation (0.01 cm3/s). Experiment and simulation results of the flow trend in the plate are shown in Table 5. In this simulation, if the flow rate is set to be the same as the experiment in the mold 249 flow analysis, the air resistance will be too large, which will cause the resin to fail to flow 250 smoothly and cause the simulation to stop. Therefore, different fill times were set, which 251 made the flow rate respectively 0.01 (see Figure 10), 0.02, 0.03, 0.04, and 0.05 cm<sup>3</sup> /sec. The 252 simulation results of the flow rate 0.02, 0.03, 0.04, 0.05 cm<sup>3</sup> /sec are shown in Appendix B, 253 Figures B1–B4. From the simulation results of different flow rates, it can be seen that the 254 flow trend is similar at different flow rates. In this study, the flow rate closest to the ex- 255 perimental conditions was used for the simulation (0.01 cm<sup>3</sup> /sec). Experiment and simu- 256 lation results of the flow trend in the plate are shown in Table 5. 257

A commercially available CAE software Moldex3D 2020 R1 special edition for free 234 surface simulation was used for the analysis in this study. It is a CAE software used 235 mainly for injection molding and compression molding simulations. 236

A commercially available CAE software Moldex3D 2020 R1 special edition for free 234 surface simulation was used for the analysis in this study. It is a CAE software used 235 mainly for injection molding and compression molding simulations. 236

**4. Results and Discussion** 237 This section discusses the influence of gravity and the flow rate on the simulation 238 and also discusses the resin distribution during the dipping process and the distribution 239 of the air traps, after which a comparison of the results with the experimental results are 240 discussed. 241

**4. Results and Discussion** 237 This section discusses the influence of gravity and the flow rate on the simulation 238 and also discusses the resin distribution during the dipping process and the distribution 239 of the air traps, after which a comparison of the results with the experimental results are 240 discussed. 241

*4.1. The Influence of Gravity on Simulation* 242 The effect of gravity in this study was very significant. Figure 9 shows the influence 243 of gravity on the simulation. If gravity is ignored, there is a slightly unreasonable flow 244 situation, as shown in Figure 9. When gravity is taken into account, the results are close 245

*4.1. The Influence of Gravity on Simulation* 242 The effect of gravity in this study was very significant. Figure 9 shows the influence 243 of gravity on the simulation. If gravity is ignored, there is a slightly unreasonable flow 244 situation, as shown in Figure 9. When gravity is taken into account, the results are close 245

**Figure 10.** The flow rate is 0.01 cm<sup>3</sup> /sec. (**a**) Filling 10%; (**b**) Filling 30%; (**c**) Filling 50%; (**d**) Filling 70%. 258 **Figure 10.** The flow rate is 0.01 cm3/s. (**a**) Filling 10%; (**b**) Filling 30%; (**c**) Filling 50%; (**d**) Filling 70%.

**Table 5.** Experiment and simulation results of flow trend in the plate. Since the filling process of the 259 experiment is not easy to observe, there is a large gap in the total filling time. Therefore, the time 260 difference is used to determine whether the trend is similar. 261

(Δ*t*)


3 sec 4 sec

2 sec 2 sec

Simulation (Δ*t*)

Experiment Simulation Experiment

40 sec 279 sec

43 sec 283 sec

45 sec 285 sec

**Table 5.** Experiment and simulation results of flow trend in the plate. Since the filling process of the experiment is not easy to observe, there is a large gap in the total filling time. Therefore, the time difference is used to determine whether the trend is similar.
