Sensitivity Analysis of Conformal Cooling Channels for Injection Molds: Two-Dimensional Transient Heat Transfer Analysis ^†

Abstract

In recent years, conformal cooling channels (CCCs) have become simpler and less costly to produce. This was largely the product of recent developments in additive manufacturing. In injection molding engineering applications, CCCs provide superior cooling performance compared to the usual usage of straight-drilled channels. This is because CCCs can be conformed for more uniform cooling of the molded part. Using CCCs decreases cooling time, total injection time, thermal stresses, and warpage by a significant amount. Despite this, CCC design is more difficult than conventional channel design. The production of a cost-effective and efficient design is dependent upon CAE simulations. This inquiry focuses on the sensitivity analysis of design features in preparation for the adoption of a design optimization approach in the future. The goal is to optimize the position of cooling channels (CCs) so as to decrease ejection time and promote temperature distribution uniformity. The ANSYS Parametric Design Language (APDL) parametrization and the given design variables are useable and may be used in future optimization attempts.

1. Introduction

Injection molding, compression molding, blow molding, and hot stamping are significant industrial production techniques used to manufacture the majority of plastic items used today. Molds are required for these procedures, in which CCCs play a significant role in increasing cooling performance. Initially, cooling channels were developed for injection molding [1,2,3] in order to reduce warpage and residual stresses in injection-molded parts with variable thickness, large dimensions, and/or complex shapes, as well as flat parts with partial thick volume [4], complex large automotive parts [5,6,7], and (local) thin-walled parts [8,9]. CCCs have also demonstrated promise for manufacturing high-precision items with strict dimensional tolerances, such as screw caps [10], contact lenses [11], and large diameter aspherical plastic lenses [12]. In terms of cooling performance, CCCs surpass the typical (straight-drilled) channels used in injection molding. The primary reason for this is that CCCs can follow the trajectories of the molded geometry, whereas conventional channels made using conventional machining methods cannot. CCCs can enhance several parameters, including cooling time, total injection time, uniform temperature distribution, thermal stress, and distortion thickness. However, the manufacturing process for CCCs is more complex than for conventional channels. Even though in some processes, the channels in injection molds are used for heating rather than cooling of the cavity, the use of conformal channels is recommended to promote more uniform and efficient heating. Despite the fact that transfer molding uses conformal heating channels instead of CCCs, the design and layout of conformal heating channels (as well as the physics of the process) are similar to CCCs in injection molds [13].

A mold of similar geometry and in similar analysis was studied in [14,15,16,17]. Two review articles on a closely related topic have also been published [18,19]. This study uses the ANSYS Mechanical APDL 2025 R2 software to parameterize the cooling ducts and compute the temperatures for the 3D heat transfer issue utilizing design variables for use in optimization techniques. This research aims to assess the applicability of the indicated design factors in optimization approaches.

2. Procedure

Using ANSYS Mechanical APDL, a 2D transient thermal analysis was conducted for optimization purposes. This investigation’s subject matter, geometry, is provided in Section 2.1. In Section 2.2, the employed material parameters and ANSYS conditions are described in detail.

2.1. Geometry and Methodology

The geometry of the analyzed 2D model is presented in Figure 1.

The components shown in Figure 1 (left) are explained in

Table 1. Components of the geometry used in the simulations [14,15,16,17].

Component ID	Quantity	Description
1–-8	8	Channels
9	1	Part
10	1	Mold

below:

The sensitivity analysis was performed using ANSYS Mechanical APDL to conduct 3D transient thermal tests. APDL (ANSYS Parametric Design Language) was used to program the outputs. For the optimization, 16 variables/geometric parameters were constructed in ANSYS Mechanical APDL. According to

Table 2. Information regarding variables and components.

Component	Designation	Component ID	Direction, as in Figure 1
CCs	VAR1	1	Horizontal
	VAR2	2
	VAR3	3
	VAR4	4
	VAR5	5
	VAR6	6
	VAR7	7
	VAR8	8
	VAR9	1	Vertical
	VAR10	2
	VAR11	3
	VAR12	4
	VAR13	5
	VAR14	6
	VAR15	7
	VAR16	8
Part	-	9	-
Mold	-	10	-

, eight of these variables are horizontal and the remaining eight are vertical.

2.2. Materials and Conditions

In the simulations, water was used for the CCs, polypropylene (PP) for the injection-molded component, and steel P20 for the mold cavity. The water in the cooling channels should maintain a temperature of 40 degrees Celsius.

Table 3. Properties of water, PP, and P20 steel used in the simulations.

Material	Water in Liquid State	PP, with 10% Mineral	P20 Steel
Application	Cooling channels (inside)	Injected part	Mold
Density [(kg/m3)]	998.2	1050	7861
Specific heat [J/(kg · °C]	4182	1800, considered constant	502.48
Thermal conductivity [W/(m · K)]	0.6	0.2, considered constant	41.5

details the characteristics of the materials used. Among the materials indicated in Table 3, only water is predicted to behave as a fluid, whereas PP and steel are expected to behave as solids.

The boundary conditions imposed by ANSYS Mechanical APDL are displayed in

Table 4. Thermal conditions applied [14,16].

Condition	Component ID (Figure 1)	Value °C	Application
Initial Temperature, varies with time	9	210	Part, 1 area
	1–8	40	Cooling channels, 8 areas
Temperature, constant	10	40	Mold, 1 area
	10	23	Boundary, 4 lines

.

3. Results

Due to varying scales, the horizontal axis made use of value IDs. The value of each point, in millimeters, for all 16 variables, is displayed in

Table 5. Value of each point, in millimeters, for all 16 variables.

Var ID	1	2	3	4	5
Var1	5	7.5	10	12.5	15
Var2	5	7.5	10	12.5	15
Var3	5	7.5	10	12.5	15
Var4	5	7.5	10	12.5	15
Var5	2.5	3.75	5	6.25	7.5
Var6	5	7.5	10	12.5	15
Var7	5	7.5	10	12.5	15
Var8	5	7.5	10	12.5	15
Var9	7.5	10	12.5	15	17.5
Var10	5	7.5	10	12.5	15
Var11	7.5	8.75	10	11.25	12.5
Var12	5	7.5	10	12.5	15
Var13	1	2	3	4	5
Var14	2	4	6	8	10
Var15	2	4	6	8	10
Var16	2	4	6	8	10

.

Figure 2 indicates the maximum (left) and average temperatures (right). The temperature readings for each value ID and variable are comparable in Figure 2, with the exception of Var10 for Value ID 5. The highest temperature varied from a little below 45.68 degrees Celsius to close to 45.71 degrees Celsius. In accordance with Figure 2, the average temperature ranged from about 42.5 °C for Var10 and value ID 1 to roughly 43.2 °C for Var10 and Var3, value ID 2 and 4, respectively.

For the results depicted in Figure 3 and Figure 4, the Var ID 3 from Table 5 served as the point of reference. The Tmax, Figure 2 (left) and Tavg, Figure 2 (right) findings for the remaining Var IDs were compared to the reference model using Equations (1) and (2).

$$vaTM[\%]=Maximum\left({\displaystyle \frac{T{M}_x-T{M}_{ref}}{T{M}_{ref}}}\right)\times 100$$

(1)

$$vaTA[\%]=Maximum\left({\displaystyle \frac{T{A}_x-T{A}_{ref}}{T{A}_{ref}}}\right)\times 100$$

(2)

For x = 1, 2, 4, and 5.

In Figure 3, the maximum temperature’s sensitivity to all variables, with the exception of VAR13, is extremely low. There is a maximum temperature variation of 0.269 percent for VAR13. For the other variables, values vary between 2.19 × 10⁻³ and 1.75 × 10⁻² percent.

In Figure 4, the maximum temperature’s sensitivity to all factors is similarly quite low. The greatest value for VAR10 is close to 1.45 × 10⁻¹ percent, while the minimum value is 3.51 × 10⁻². In Figure 4, the discrepancies between the values of the average temperature for the various factors are smaller than for the highest temperature in Figure 3.

4. Conclusions

This study allowed several important conclusions to be drawn. The selected design variables are applicable to the investigated situation, since the temperature values change when the variable values are altered. The parameterization conducted on the ANSYS input file was shown to be useful for determining the effect of design factors on the analyzed case’s temperatures. In the future, the findings of the sensitivity analysis can be used to determine the variable weights in optimization procedures/methodologies.