The model shown in Figure 6.3 is a one-eighth symmetry model of a disk which will be shrink fit onto a hub.
Figure 6.3: Cold Model Geometry
1. First model the disk in the heated-up configuration using the equations to adjust the dimensions. Note that at this point the interference can be a perfect zero or can be chosen to include a "gap" between the parts. A gap should only be included if the contact (gap) elements will be created manually.
2. Define a stress free reference temperature for the disk (outer part) so that the assigned default nodal temperature will cause the disk to contract.
3. The stress free reference temperature of the hub (inner part) and the default nodal temperature should be the same. Therefore, the hub will not move due to thermal effects.
Controlling Equations:
dT = Tref – Tdefault = [Radial Interference / (Ri + Radial Interference)] / α Ro' = Ro / (1-α *dT)
Ri' = Ri / (1-α *dT) t' = t / (1-α *dT) where:
Tref is the stress free reference temperature
Tdefault is the default temperature assigned to the parts (basis of FEA solution) α is the coefficient of expansion of the disk
Ri, Ro and t are the cold dimensions of the disk Ri', Ro' and t' are the hot dimensions of the disk
The inner part is drawn with the cold dimensions because it will experience no thermal expansion.
The outer part is drawn with the hot dimensions. Then the thermal expansion will contract the outer part and create the interference.
Given:
α = 6.5e-6 Ri = 2.997"
Ro = 10.000"
t = 2.000"
Radial Interference = 0.003" (= 0.006" Diametral Interference) Tdefault = 0 °F
Hot Disk Geometry: Case 1 Case 2
Tref (°F) 153.85 °F 153.85 °F
Ro' (inch) 10.010" 10.010"
t' (inch) 2.002" 2.002"
Ri' (inch) 3.000" 3.000"
Model Setup: Case 1 Case 2
Elements Brick Brick
E (psi) 30e6 psi 30e6 psi
ν 0.3 0.3
alpha (1/F°) 10e-6 10e-6
Tref (°F) 153.85 °F for outer ring 153.85 °F for outer ring Tref (°F) 0 °F for inner ring 0 °F for inner ring
Tdefault (°F) 0 °F 0 °F
Load case turn on thermal effect turn on thermal effect
Friction Bonded surfaces 0.3
Figure 6.4: Heated Model Geometry
For this example, we will use the CAD solid model file Shrink.stp located in the "Chapter 6 Example Model\Input File" directory in the class directory or in the copy of the solutions folders on your computer.
Case 1
"Start: All Programs:
Autodesk: Autodesk Algor Simulation 2012: Autodesk Simulation 2012"
Press the Windows "Start" button and access the "All Programs" pull-out menu. Select the "Autodesk" folder and then the "Autodesk Algor Simulation 2012" pull-out menu. Choose the "Autodesk Simulation 2012 software"
command.
"Open" Click on the "Open" icon at the left side of the dialog.
"STEP (*.stp, *.ste, *.step)" Select the " STEP (*.stp, *.ste, *.step)" option in the CAD Files section of the "Files of type:" drop-down box.
"Shrink.stp" Select the file "Shrink.stp" in the "Chapter 6 Example Model\Input File" directory.
"Open" Press the "Open" button.
"Use STEP file units"
"OK"
Choose the option to "Use STEP file units" if it is not already selected and click the "OK" button. The original STEP file length unit is inches.
"Linear: Static Stress with Linear Material Models"
"OK"
A dialog will appear asking you to choose the analysis type for the model. From the pull-out menu, choose "Linear:
Static Stress with Linear Material Models" and press the
"OK" button.
Mouse
"Part…"
Right-click on the "CAD Mesh Options" heading under Part 2 in the tree view and select the "Part…" command.
Mouse
"40%"
Move the "Mesh size" slider to the right to decrease the size to "40%" for this part only.
"OK" Press the "OK" button.
"Mesh: Mesh: Generate 3D Mesh"
Select the "Mesh" tab. Click on the "Generate 3D Mesh"
button in the "Mesh" panel.
"Selection: Shape: Point" Select the "Selection" tab. Make sure the "Point" button is selected in the "Shape" panel.
"Selection: Select: Surfaces" Also make sure the "Surfaces" button is selected in the
"Select" panel.
Mouse
Click and drag using the middle mouse button to rotate the model viewpoint so that all three symmetry planes can be clearly seen and selected.
Mouse Referring to Figure 6.5, click on one of the surfaces that is to have X symmetry.
<Ctrl> Mouse Holding down the <Ctrl> key, click on the other surface that has X symmetry.
"Setup: Constraints: General Constraint"
Select the "Setup" tab. Click on the "General Constraint" button in the "Constraints" panel.
"X Symmetry" Press the "X Symmetry" button.
"OK" Press the "OK" button to apply these boundary conditions.
Mouse Referring to Figure 6.5, click on one of the surfaces that has Y symmetry.
<Ctrl> Mouse Holding down the <Ctrl> key, click on the other surface that has Y symmetry.
"Setup: Constraints: General Constraint"
Click on the "General Constraint" button in the
"Constraints" panel.
"Y Symmetry" Press the "Y Symmetry" button.
"OK" Press the "OK" button to apply these boundary conditions.
Mouse Referring to Figure 6.5, click on one of the surfaces that have Z symmetry.
<Ctrl> Mouse Holding down the <Ctrl> key, click on the other surface that has Z symmetry.
"Setup: Constraints: General Constraint"
Select the "Setup" tab. Click on the "General Constraint" button in the "Constraints" panel.
"Z Symmetry" Press the "Z Symmetry" button.
"OK" Press the "OK" button to apply these boundary conditions.
Figure 6.5: Symmetry Constraints
Assigning the Parameters
Once the model has been constructed and the loads and constraints have been applied, use the FEA Editor environment to specify material properties.
Mouse Right-click on the "Element Definition" heading for Part 2.
"Edit Element Definition…" Select the "Edit Element Definition…" command.
Mouse Click on the "Thermal" tab.
153.85 Type "153.85" in the "Stress free reference temperature" field.
"OK" Press the "OK" button.
Mouse Click on the "Material" heading for Part 1.
<Ctrl> Mouse Holding down the <Ctrl> key, click on the "Material"
heading for Part 2 in the tree view.
Mouse Right-click on one of the selected headings.
"Edit Material…" Select the "Edit Material…" command. The "Element Material Selection" dialog will appear.
"Edit Properties" Press the "Edit Properties" button.
30e6 Type "30e6" in the "Modulus of Elasticity" field.
0.3 Type "0.3" in the "Poisson's Ratio" field.
6.5e-6 Type "6.5e-6" in the "Thermal Coefficient of Expansion" field.
"OK" Press the "OK" button to exit the "Element Material Specification" dialog.
"OK" Press the "OK" button to accept the information entered into the "Element Material Selection" dialog for Parts 1 and 2.
"Setup: Model Setup:
Parameters"
Select the "Setup" tab. Click on the "Parameters" button in the "Model Setup" panel.
1 Type "1" in the first row of the "Thermal" column.
"OK" Press the "OK" button to accept the information entered in the "Analysis Parameters" dialog.
"Analysis: Analysis: Check Model"
Select the "Analysis" tab. Click on the "Check Model"
button in the "Analysis" panel.
"Tools: Environments: FEA Editor"
Select the "Tools" tab. Press the "FEA Editor" button in the "Environments" panel.
Analyzing the Model
"Analysis: Analysis: Run Simulation"
Select the "Analysis" tab. Click on the "Run Simulation"
button in the "Analysis" panel.
Reviewing the Results
"View: Appearance: Visual Style
Select the "View" tab. Click on the options button to the bottom of "Visual Style" button in the "Appearance"
panel. Select "Shaded with Mesh" from the pull-out menu.
If you look closely at the disk/hub interface, you can see that the nodes on each part move together due to the bonded contact. You may want to increase the displaced model "Scale Factor" to exaggerate the deformation more ("Results Options: Displaced Model Options"). The disk is trying to shrink in both diameter and thickness. However, because of the bonded contact, the thickness of the disk at its ID can only shrink as much as the hub compresses axially.
We will compare this behavior, and the resultant stresses, to a second version of the model. This time, frictional surface contact will be used between the parts. A second design scenario will be created so that the results of each version may both be retained.
* * * Case 2
"Tools: Environments: FEA Editor"
Select the "Tools" tab. Press the "FEA Editor" button in the "Environments" panel.
Mouse
"Copy"
Right-click on the "Design Scenario 1" heading at the top of the tree view and select the "Copy" command. Design Scenario 2 will be created and will be the active scenario.
Mouse Right-click on the "Contact (Default: Bonded)" heading.
"Surface Contact" Select the "Surface Contact" command.
Mouse Right-click on the "Contact (Default: Surface)" heading.
"Settings …" Select the "Settings…" command. The "Contact Options" dialog will appear.
Mouse Activate the "Include Friction" checkbox.
0.3 Type "0.3" in the "Static Friction Coefficient" field.
"OK" Press the "OK" button.
Analyzing the Model
"Analysis: Analysis: Run Simulation"
Select the "Analysis" tab. Click on the "Run Simulation"
button in the "Analysis" panel.
If you once again closely examine the disk/hub interface with the mesh displayed, this time you'll see that the nodes of the disk shifted axially along the length of the hub. The thickness was able to decrease due to thermal shrinkage despite the friction in the interface. Animating the on-screen image will make the effect more apparent.
You should also see a significant reduction in the maximum von Mises stress value (approximately 33,000 psi versus 43,300 psi). Figure 6.6 (next page) shows a comparison of the results for the bonded and frictional surface contact versions of the model.
Result Options
The total contact force can be determined for each contact pair in a model in the Results environment. Right-click on the heading in the tree view for the contact pair and select the
"Contact Force" command. A "Contact Force" dialog will appear with the total contact force for that pair. The contact distribution can be seen by using the "Results: Element Forces and Moments: 1) Axial Force" command. This will display the contact force in the individual contact elements.
An archive containing both design scenarios, with results, is available in the "Chapter 6 Example Models\Results Archive" folder in the class directory or in the copy of the solutions folders on your computer.
Figure 6.6: Comparison of Stress and Deformed Shape (Front View)