## 2 Materials and Methods
\[\frac{\mathrm{d}\alpha}{\mathrm{d}t}=(\mathrm{k_{1}}+\mathrm{k_{2}}\alpha^{ \mathrm{m}})(1-\alpha)^{\mathrm{n}} \tag{2}\]  
\[\mathrm{k_{i}}=\mathrm{k_{0}}\mathrm{e^{-E_{\mathrm{ii}}/RT}} \tag{3}\]  
In the formula above, \(\mathrm{d}\alpha/\mathrm{d}t\) is the isothermal curing rate, \(\mathrm{k_{1}}\) is the reaction rate constant primary epoxy-amine reaction rate, \(\mathrm{k_{2}}\) is the reaction rate constant secondary epoxy-amine reaction rate, \(\mathrm{k_{0}}\) is the exponential front factor, \(\alpha\) is the conversion rate, m, n is the order of reaction, R is the gas constant, and \(\mathrm{E_{a}}\) is the activation energy. For the rheometer measurement results, Cross Castro-Macosko Model Equation (4) [35; 36], a reactive viscosity model frequently used in epoxy resins that explains the occurrence of chemical reactions and changes in viscosity, was used. Equation (4) shows that viscosity depends only on temperature and curing and does not depend on shear rate. Therefore, it was converted into a reactive visibility variable through the improved Equation (5) [37; 38; 39] of the Castro-Macosko model, which has a dependence on shear rate, and applied to the Moldflow process [40; 41; 42]. In the equation below, n is viscosity, T is temperature, \(\alpha_{\mathrm{g}}\) is curing at gelation point, \(\alpha\) is curing, \(\mathrm{C_{1}}\), \(\mathrm{C_{2}}\) is experimental constant, \(\tau^{*}\) is critical shear stress, and \(\gamma\) is shear rate. \[\mathrm{n}(\alpha,\,\mathrm{T},\,\gamma)=\,\mathrm{n_{0}}(\mathrm{T})\!\left( \frac{\alpha_{\mathrm{g}}}{\alpha_{\mathrm{g}}-\alpha}\right)^{\mathrm{C_{1} }+\mathrm{C_{2}}\alpha}\mathrm{where\,n_{0}}(\mathrm{T})=\mathrm{Bexp}\!\left( \frac{\mathrm{T_{b}}}{\mathrm{T}}\right) \tag{4}\]  
\[\mathrm{n}(\alpha,\,\mathrm{T},\,\gamma)=\frac{\mathrm{n_{0}}(\mathrm{T})}{1 +\left(\frac{\mathrm{n_{0}}(\mathrm{T})\gamma}{\tau^{*}}\right)^{1-\mathrm{n} }}\!\left(\frac{\alpha_{\mathrm{g}}}{\alpha_{\mathrm{g}}-\alpha}\right)^{ \mathrm{C_{1}}+\mathrm{C_{2}}\alpha} \tag{5}\]  
In this paper, Moldflow software (Autodesk, San Rafael, CA, USA) was used to simulate the APG process of an insulating spacer for GIS. Figure 1 shows a 3D modeled spacer for GIS and a 3D mesh image. Because changes in heater temperature do not affect the mold shape, we only showed one figure although we have 4 different conditions. As a component of the GIS spacer, there are 16 inserts in the outer shell and 3 inserts in the center. The spacer drawings were modified by creating a mesh in dual domain type, and then converted it to a solid 3D type mesh. About 5.6 million meshes were used for 3D modeling, and about 4.4 million meshes were used for the spacer mold. A contact surface mesh between the insert and the spacer was integrated to prevent a calculation error caused by mesh. In addition, a total of 16 heaters were arranged with 8 heaters each on the front and rear sides for heating the mold. The heater size was designated as 16 mm in the same size as the actual mold, and the inlet size was designated as 20 mm. The designed heater was simulated by tying each heater together as shown in Figure 2 to derive optimal curing conditions by dividing each heater into subdivisions in consideration of heater position and mold thickness. The thermal characteristics of the mold were simulated by applying tool steel P-1 material. Table 1 shows the thermal characteristics of the mold used in the Moldflow simulation. In the case of inserting parts into spacers, aluminum attributes of the set value of the Moldflow program were given, and the initial temperature of each insert was set to 140 \({}^{\circ}\)C. In the simulation, the temperature of the resin was set to 63 \({}^{\circ}\)C provided by the manufacturer, and the injection time was set to 350 s. Each heater temperature condition of the mold is shown in Tables 2 and 3.