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Cooling of an Injection Mold
Introduction
Cooling is an important process in the production of injection molded plastics. First of all, the cooling time may well represent more than half of the production cycle time. Second, a homogeneous cooling process is desired to avoid defects in the manufactured parts. If plastic materials in the injection molding die are cooled down uniformly and slowly, residual stresses can be avoided, and thereby the risk of warps and cracks in the end product can be minimized.
As a consequence, the positioning and properties of the cooling channels become important aspects when designing the mold.
The simulation of heat transfer in molds of relatively complex geometries requires a 3D representation. Simulation of 3D flow and heat transfer inside the cooling channels are computationally expensive. An efficient short-cut alternative is to model the flow and heat transfer in the cooling channels with 1D pipe flow equations, and still model the surrounding mold and product in 3D.
This example shows how you can use the Nonisothermal Pipe Flow interface together with the Heat Transfer in Solids interface to model a mold cooling process. The equations describing the cooling channels are fully coupled to the heat transfer equations of the mold and the polyurethane part using Pipe Wall Heat Transfer multiphysics coupling.
Figure 1: The steering wheel of a car, made from polyurethane.
Model Definition
Model Geometry and Process conditions
The polyurethane material used for a steering wheel is produced by several different molds. The part considered in this model is the top half of the wheel grip, shown in gray in Figure 2.
Figure 2: Polyurethane parts for a steering wheel. The top half of the grip is modeled in this example.
The mold consists of a 50-by-50-by-15 cm steel block. Two cooling channels, 1 cm in diameter, are machined into the block as illustrated in Figure 3.
Figure 3: Mold block and cooling channels.
The after injection of the polyurethane, the average temperature of the mold a the plastic material is 473 K. Water at room temperature is used as cooling fluid and flows through the channels at a rate of 10 liters/min. The model simulates a 10 min cooling process.
For numerical stability reasons, the model is set up with an initial water temperature of 473 K, which is ramped down to 288 K during the first few seconds.
Results and Discussion
The mold and polyurethane part, initially at 473 K, are cooled for 10 minutes by water at room temperature. Figures below show sample results when flow rate of the cooling water is 10 liters/minute and the surface roughness of the channels is 46 μm. After two minutes of cooling, the hottest and coldest parts of the polyurethane part differ by approximately 40 K (Figure 4).
Figure 4: Temperature distribution in the polyurethane part and the cooling channels after 2 minutes of cooling.
Figure 5 shows the temperature distribution in the steel mold after 2 minutes. The temperature footprint of the cooling channels is clearly visible.
Figure 5: Temperature distribution in the steel mold block after 2 minutes of cooling.
After 10 minutes of cooling, the temperature in the mold block is more uniform, with a temperature at the center of approximately 333 K (Figure 6). Still, the faces with cooling channel inlets and outlets are more than 20 K hotter.
Figure 6: Temperature distribution in the steel mold block after 10 minutes of cooling.
To evaluate the influence of factors affecting the cooling time, use Material and Parametric sweeps. Figure 7 shows the average temperature of the polyurethane part as function of the cooling time for the several flow rates of the cooling water, the surface roughness of the cooling channels, and the mold materials.
Figure 7: Average temperature of the polyurethane part as function of time and cooling conditions.
Application Library path: Pipe_Flow_Module/Heat_Transfer/mold_cooling
Modeling Instructions
From the File menu, choose New.
New
In the New window, click  Model Wizard.
Model Wizard
1
In the Model Wizard window, click  3D.
2
In the Select Physics tree, select Fluid Flow>Nonisothermal Flow>Nonisothermal Pipe Flow (nipfl).
3
Click Add.
4
In the Select Physics tree, select Heat Transfer>Heat Transfer in Solids (ht).
5
Click Add.
6
Click  Study.
7
In the Select Study tree, select General Studies>Time Dependent.
8
Global Definitions
Parameters 1
1
In the Model Builder window, under Global Definitions click Parameters 1.
2
In the Settings window for Parameters, locate the Parameters section.
3
Step 1 (step1)
Create a smooth step function to decrease the coolant temperature at the beginning of the process.
1
In the Home toolbar, click  Functions and choose Global>Step.
2
In the Settings window for Step, locate the Parameters section.
3
In the Location text field, type 2.5.
4
In the From text field, type 1.
5
In the To text field, type 0.
6
Click to expand the Smoothing section. In the Size of transition zone text field, type 5.
Optionally, you can inspect the shape of the step function:
7
Variables 1
1
In the Home toolbar, click  Variables and choose Global Variables.
2
In the Settings window for Variables, locate the Variables section.
3
Geometry 1
Import 1 (imp1)
First, import the steering wheel part from a CAD design file.
1
In the Home toolbar, click  Import.
2
In the Settings window for Import, locate the Import section.
3
Click  Browse.
4
5
Click  Import.
6
Locate the Selections of Resulting Entities section. Find the Cumulative selection subsection. Click New.
7
In the New Cumulative Selection dialog box, type Wheel in the Name text field.
8
Second, draw the mold and cooling channels. To simplify this step, insert a prepared geometry sequence from file. After insertion you can study each geometry step in the sequence.
9
Click the  Zoom Extents button in the Graphics toolbar.
10
In the Geometry toolbar, click Insert Sequence and choose Insert Sequence.
11
12
In the Geometry toolbar, click  Build All.
13
Click the  Zoom Extents button in the Graphics toolbar.
14
Click the  Transparency button in the Graphics toolbar.
Work Plane 1 (wp1)
Create the selections to simplify the model specification.
1
In the Model Builder window, click Work Plane 1 (wp1).
2
In the Settings window for Work Plane, locate the Selections of Resulting Entities section.
3
Find the Cumulative selection subsection. Click New.
4
In the New Cumulative Selection dialog box, type Cooling channels in the Name text field.
5
Materials
The next step is to specify material properties for the model. First, select water from the built-in materials database.
Add Material
1
In the Home toolbar, click  Add Material to open the Add Material window.
2
Go to the Add Material window.
3
In the tree, select Built-in>Water, liquid.
4
Click Add to Component in the window toolbar.
Materials
Water, liquid (mat1)
1
In the Settings window for Material, locate the Geometric Entity Selection section.
2
From the Geometric entity level list, choose Edge.
3
From the Selection list, choose Cooling channels.
Material Switch 1 (sw1)
Define the mold materials to switch between during a solver sweep.
1
In the Materials toolbar, click  More Materials and choose Local>Material Switch.
2
Add Material
1
Go to the Add Material window.
2
In the tree, select Built-in>Aluminum.
3
Right-click and choose Add to Material Switch 1 (sw1).
4
In the tree, select Built-in>Steel AISI 4340.
5
Right-click and choose Add to Material Switch 1 (sw1).
6
In the Materials toolbar, click  Add Material to close the Add Material window.
Materials
Polyurethane
Next, create a material with the properties of polyurethane.
1
In the Model Builder window, under Component 1 (comp1) right-click Materials and choose Blank Material.
2
In the Settings window for Material, type Polyurethane in the Label text field.
3
Locate the Geometric Entity Selection section. From the Selection list, choose Wheel.
4
Locate the Material Contents section. In the table, enter the following settings:
Nonisothermal Pipe Flow (nipfl)
1
In the Model Builder window, under Component 1 (comp1) click Nonisothermal Pipe Flow (nipfl).
2
In the Settings window for Nonisothermal Pipe Flow, locate the Edge Selection section.
3
From the Selection list, choose Cooling channels.
Pipe Properties 1
1
In the Model Builder window, under Component 1 (comp1)>Nonisothermal Pipe Flow (nipfl) click Pipe Properties 1.
2
In the Settings window for Pipe Properties, locate the Pipe Shape section.
3
4
In the di text field, type 1[cm].
5
Locate the Flow Resistance section. From the Surface roughness list, choose User defined.
6
In the Surface roughness text field, type e.
Initial Values 1
1
In the Model Builder window, click Initial Values 1.
2
In the Settings window for Initial Values, locate the Initial Values section.
3
In the u text field, type 0.1.
4
In the T text field, type T_init_mold.
Temperature 1
1
In the Model Builder window, click Temperature 1.
2
In the Settings window for Temperature, locate the Temperature section.
3
In the Tin text field, type T_inlet.
Inlet 1
1
In the Physics toolbar, click  Points and choose Inlet.
2
3
In the Settings window for Inlet, locate the Inlet Specification section.
4
From the Specification list, choose Volumetric flow rate.
5
In the qv,0 text field, type Qw.
Heat Outflow 1
1
In the Physics toolbar, click  Points and choose Heat Outflow.
2
Wall Heat Transfer 1
1
In the Physics toolbar, click  Edges and choose Wall Heat Transfer.
2
In the Settings window for Wall Heat Transfer, locate the Edge Selection section.
3
From the Selection list, choose Cooling channels.
Internal Film Resistance 1
In the Physics toolbar, click  Attributes and choose Internal Film Resistance.
Heat Transfer in Solids (ht)
Initial Values 1
1
In the Model Builder window, under Component 1 (comp1)>Heat Transfer in Solids (ht) click Initial Values 1.
2
In the Settings window for Initial Values, locate the Initial Values section.
3
In the T2 text field, type T_init_mold.
Heat Flux 1
1
In the Physics toolbar, click  Boundaries and choose Heat Flux.
2
In the Settings window for Heat Flux, locate the Boundary Selection section.
3
From the Selection list, choose All boundaries.
4
Locate the Heat Flux section. From the Flux type list, choose Convective heat flux.
5
In the h text field, type 2.
Multiphysics
Pipe Wall Heat Transfer 1 (pwhtc1)
In the Physics toolbar, click  Multiphysics Couplings and choose Edge>Pipe Wall Heat Transfer.
Mesh 1
Edge 1
1
In the Mesh toolbar, click  Boundary and choose Edge.
2
In the Settings window for Edge, locate the Edge Selection section.
3
From the Selection list, choose Cooling channels.
Size 1
1
Right-click Edge 1 and choose Size.
2
In the Settings window for Size, locate the Element Size section.
3
From the Predefined list, choose Extra fine.
Free Tetrahedral 1
1
In the Mesh toolbar, click  Free Tetrahedral.
Even with a maximum element size of 0.003 m, the mesh contains some collapsed elements, resulting in solver errors. Trial and error gives that lowering the curvature factor somewhat will create a mesh with good quality.
Size
1
In the Model Builder window, click Size.
2
In the Settings window for Size, locate the Element Size section.
3
Click the Custom button.
4
Locate the Element Size Parameters section. In the Minimum element size text field, type 0.003.
5
In the Curvature factor text field, type 0.55.
6
In the Model Builder window, right-click Mesh 1 and choose Build All.
Study 1
Step 1: Time Dependent
1
In the Model Builder window, under Study 1 click Step 1: Time Dependent.
2
In the Settings window for Time Dependent, locate the Study Settings section.
3
In the Output times text field, type range(0,2,28) range(30,30,600).
Definitions
To evaluate the average temperature of the polyurethane part for different conditions and mold materials (Figure 7), perform parametric and material sweeps. To avoid accumulating a lot of data while solving, keep only last solution and save the average wheel temperature in a table. For this purpose, add a global probe to the model.
Domain Probe 1 (dom1)
1
In the Definitions toolbar, click  Probes and choose Domain Probe.
2
In the Settings window for Domain Probe, locate the Source Selection section.
3
From the Selection list, choose Wheel.
4
Click Replace Expression in the upper-right corner of the Expression section. From the menu, choose Component 1 (comp1)>Heat Transfer in Solids>Temperature>T2 - Temperature - K.
5
Locate the Expression section.
6
Select the Description check box. In the associated text field, type Average wheel temperature.
Study 1
1
In the Model Builder window, click Study 1.
2
In the Settings window for Study, locate the Study Settings section.
3
Clear the Generate default plots check box.
Parametric Sweep
1
In the Study toolbar, click  Parametric Sweep.
2
In the Settings window for Parametric Sweep, locate the Study Settings section.
3
From the Sweep type list, choose All combinations.
4
5
6
7
Locate the Output While Solving section. Select the Accumulated probe table check box.
8
Locate the Study Settings section. Find the Memory settings for jobs subsection. From the Keep solutions list, choose Only last.
Material Sweep
1
In the Study toolbar, click  Material Sweep.
2
In the Settings window for Material Sweep, locate the Study Settings section.
3
Solution 1 (sol1)
1
In the Study toolbar, click  Show Default Solver.
2
In the Model Builder window, expand the Solution 1 (sol1) node.
Since the problem involves only heat conduction, you can solved it more efficiently by relaxing nonlinear setting.
3
In the Model Builder window, expand the Study 1>Solver Configurations>Solution 1 (sol1)>Time-Dependent Solver 1 node, then click Fully Coupled 1.
4
In the Settings window for Fully Coupled, click to expand the Method and Termination section.
5
In the Damping factor text field, type 1.
6
From the Jacobian update list, choose Minimal.
7
In the Study toolbar, click  Compute.
Results
In the Home toolbar, click  Add Predefined Plot.
Add Predefined Plot
1
Go to the Add Predefined Plot window.
2
In the tree, select Study 1/Solution 1 (sol1)>Heat Transfer in Solids>Temperature (ht).
3
Click Add Plot in the window toolbar.
Results
Wheel and Cooling Channels Temperature
1
In the Settings window for 3D Plot Group, type Wheel and Cooling Channels Temperature in the Label text field.
2
Locate the Data section. From the Dataset list, choose Study 1/Parametric Solutions 1 (sol2).
3
From the Time (s) list, choose 120.
Selection 1
1
In the Model Builder window, expand the Wheel and Cooling Channels Temperature node.
2
Right-click Surface and choose Selection.
3
In the Settings window for Selection, locate the Selection section.
4
From the Selection list, choose Wheel.
5
In the Wheel and Cooling Channels Temperature toolbar, click  Plot.
6
Click the  Transparency button in the Graphics toolbar.
7
In the Wheel and Cooling Channels Temperature toolbar, click  Plot.
Wheel and Cooling Channels Temperature
In the Model Builder window, under Results click Wheel and Cooling Channels Temperature.
Line 1
1
In the Wheel and Cooling Channels Temperature toolbar, click  Line.
2
In the Settings window for Line, locate the Coloring and Style section.
3
From the Line type list, choose Tube.
4
In the Tube radius expression text field, type 0.5*nipfl.dh.
5
Clear the Rounded end caps check box.
6
Click to expand the Inherit Style section. Locate the Coloring and Style section. From the Scale list, choose Logarithmic.
7
Locate the Inherit Style section. From the Plot list, choose Surface.
8
Clear the Color and data range check box.
9
In the Wheel and Cooling Channels Temperature toolbar, click  Plot.
10
Locate the Coloring and Style section.
11
Select the Radius scale factor check box. In the associated text field, type 1.
12
In the Wheel and Cooling Channels Temperature toolbar, click  Plot.
Mold Temperature
1
In the Model Builder window, right-click Results and choose Add Predefined Plot>Study 1/Parametric Solutions 1 (sol2)>Heat Transfer in Solids>Temperature (ht).
2
In the Settings window for 3D Plot Group, type Mold Temperature in the Label text field.
3
Locate the Data section. From the Time (s) list, choose 120.
4
In the Mold Temperature toolbar, click  Plot.
5
Click to expand the Title section. From the Title type list, choose Manual.
6
In the Title text area, type Temperature (K).
7
In the Mold Temperature toolbar, click  Plot.
Temperature (pwhtc1)
1
Right-click Results and choose Add Predefined Plot>Study 1/Parametric Solutions 1 (sol2)>Pipe Wall Heat Transfer 1>Temperature (pwhtc1).
2
In the Settings window for 3D Plot Group, click to expand the Title section.
3
From the Title type list, choose Manual.
4
In the Title text area, type Temperature (K).
Surface 1
1
Right-click Temperature (pwhtc1) and choose Surface.
2
In the Settings window for Surface, locate the Expression section.
3
In the Expression text field, type 1.
4
Locate the Coloring and Style section. From the Coloring list, choose Uniform.
5
From the Color list, choose Gray.
Selection 1
1
Right-click Surface 1 and choose Selection.
2
In the Settings window for Selection, locate the Selection section.
3
From the Selection list, choose Wheel.
4
In the Temperature (pwhtc1) toolbar, click  Plot.
Surface 2
1
In the Model Builder window, right-click Temperature (pwhtc1) and choose Surface.
2
In the Settings window for Surface, locate the Expression section.
3
In the Expression text field, type T2.
4
Click to expand the Inherit Style section. From the Plot list, choose Slice 1.
Selection 1
1
Right-click Surface 2 and choose Selection.
2
3
In the Temperature (pwhtc1) toolbar, click  Plot.
Evaluate the average temperature of the polyurethane part for different conditions and mold materials(Figure 7).
Accumulated Probe Table 1
1
In the Model Builder window, expand the Results>Tables node, then click Accumulated Probe Table 1.
2
In the Settings window for Table, locate the Data section.
3
From the Presentation format list, choose Filled.
4
Click  Update.
Accumulated Probe Table 1.1
1
Right-click Accumulated Probe Table 1 and choose Duplicate.
2
In the Settings window for Table, locate the Data section.
3
Find the Filled table structure subsection. From the Parameter value list, choose 2: matsw.comp1.sw1=1, Qw=10.
Accumulated Probe Table 1.2
1
Right-click Accumulated Probe Table 1 and choose Duplicate.
2
In the Settings window for Table, locate the Data section.
3
Find the Filled table structure subsection. From the Parameter value list, choose 3: matsw.comp1.sw1=2, Qw=20.
Accumulated Probe Table 1.3
1
Right-click Accumulated Probe Table 1 and choose Duplicate.
2
In the Settings window for Table, locate the Data section.
3
Find the Filled table structure subsection. From the Parameter value list, choose 4: matsw.comp1.sw1=2, Qw=10.
Probe Table Graph 1
1
In the Model Builder window, expand the Results>Probe Plot Group 1 node, then click Probe Table Graph 1.
2
In the Settings window for Table Graph, locate the Data section.
3
From the Table list, choose Accumulated Probe Table 1.
4
From the Plot columns list, choose All excluding x-axis.
5
Click to expand the Legends section. From the Legends list, choose Manual.
6
7
In the Probe Plot Group 1 toolbar, click  Plot.
Probe Table Graph 1.1
1
Right-click Probe Table Graph 1 and choose Duplicate.
2
In the Settings window for Table Graph, locate the Data section.
3
From the Table list, choose Accumulated Probe Table 1.1.
4
Locate the Legends section. In the table, enter the following settings:
Probe Table Graph 1.2
1
Right-click Probe Table Graph 1 and choose Duplicate.
2
In the Settings window for Table Graph, locate the Data section.
3
From the Table list, choose Accumulated Probe Table 1.2.
4
Locate the Legends section. In the table, enter the following settings:
Probe Table Graph 1.2.1
1
Right-click Probe Table Graph 1.2 and choose Duplicate.
2
In the Settings window for Table Graph, locate the Data section.
3
From the Table list, choose Accumulated Probe Table 1.3.
4
Locate the Legends section. In the table, enter the following settings:
Average wheel temperature
1
In the Model Builder window, under Results click Probe Plot Group 1.
2
In the Settings window for 1D Plot Group, type Average wheel temperature in the Label text field.