Sensitivity analysis of conformal CCs for injection molds: 2D Transient Heat Transfer Analysis

Conformal Cooling Channels (CCCs) have gotten easier and more economical to manufacture in recent years. This was largely due to recent developments in additive manufacturing. The usage of CCCs in engineering applications involving injection molding provides for superior cooling performance than straight drilled channels, which have traditionally been utilized in injection molding. The fundamental reason for this is that CCCs are able to follow the molded geometry's trajectories. With the use of CCC’s, the cooling time, total injection time, thermal stresses, and warpage can all be considerably reduced. Nonetheless, the CCC design process is more dicult than that of traditional channels. The integration of computer-aided engineering (CAE) simulations is critical for achieving an effective, cost-effective design. This paper focuses the sensitivity analysis of design variables, with the intention of implementing a design optimization methodology in the future. The ultimate goal is to optimize the placement of Cooling Channels (CCs) to minimize the ejection time and maximize the uniformity of temperature distribution. It can be concluded that the parametrization done in ANSYS Parametric Design Language (APDL), as well as the selected design variables are feasible and might be useful for future optimization methodologies.


Introduction
Some research has been conducted in the eld of design and simulation of CCCs in injection molds. A few preliminary information has been obtained from the literature that provides a basis for further investigation in this project. For example, a simple relationship between four parameters for the design of CCC using additive manufacturing can be found in Mayer (Mayer S 2005). From previous literature, the use of cross-sections other than circular for channels could provide better cooling e ciency. In (Au K, Yu K, 2014), research has been performed for analyzing CCs with variable spacing for tooling applications.
In order to redesign the existing model, which was originally built with straight channels, with CCCs, the authors performed a study in which a comprehensive solution for conformal channel design was derived. Parameters such as duct diameter, pitch spacing, and wall-to-duct spacing were considered. In this work, ANSYS Mechanical APDL software was used for parameterization of cooling ducts and calculation of temperatures for 2D heat transfer problem by natural convection. The present work goals for evaluating the feasibility of the selected design variables for application in optimization routines by coupling MATALB and ANSYS Mechanical APDL.

Procedure
The optimization was done using ANSYS Mechanical APDL, in which a 2D transient thermal analysis was performed. The geometry that was object of study can be seen in section 3.1. The material properties used can be seen in section 3.2. and the conditions applied in ANSYS can be seen in section 3.2.

Geometry
The geometry of the analyzed 2D model is presented in Figure 1 To perform the optimization, 16 variables/geometric parameters were de ned in ANSYS Mechanical APDL. Eight of these variables are horizontal and eight are vertical, as shown in Table 1.  Table 2 shows the lower and upper bounds of the design variables set by ANSYS considering the de ned initial variables. Only lower and upper bounds were assigned in MATLAB, with no equality nor inequality constraints.

Materials and conditions
The materials used in the simulations were water, for the CCs, polypropylene for the injection molded part and steel P20 for the mold cavity. Of the materials shown in Table 3, only water is assumed to behave as uid, i.e. PP and steel are assumed to behave as solids. The properties of the used materials are shown in Table 3. The boundary conditions implemented in ANSYS Mechanical APDL can be seen in Table 4.

Results
Due to different scales, value IDs were used in the horizontal axis. Table 5 presents the correspondence between Value ID and values for each variable.  Fig. 4 shows the temperature amplitude.
In Fig. 2  of temperature compared to the results of the average temperature (Fig. 3), with the value of the maximum value subtracted by the minimum value close to 0.7 [°C].
In Fig. 5 For the results shown in Fig. 6 and 7, the Var ID 3, of Table 6, was considered as the reference point. Then, the Tmax (Fig. 6) and Tavg (Fig. 7) results for the other Var IDs were compared with the reference model, using Eq. 1.1 and 1.2. (1.1) For x=1,2,4 and 5.
In Fig. 6, It can be seen that the sensitivity of the maximum temperature for all variables is very low, except for VAR13. For VAR13, there is a variation of 0.269%, for the maximum temperature. For the other variables, values range from 2.19*10 −3 % to 1,75*10 −2 %.
In Fig. 7, It can be seen that the sensitivity of the maximum temperature for all variables is also very low.
The maximum value is close to 1.45*10 −1 %, for VAR10 and the minimum is 3.51*10 −2 . In Fig. 7, the values of the average temperature show lesser differences for the different variables than for the maximum temperature, shown in Fig. 6.

Conclusions
The main conclusions of this work are: