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Z88
A
URORA
®
E
XAMPLE
M
ANUAL
Example 10: Pinion
(Plane stress element No. 14 with 6 nodes)
is a registered trademark (Nr. 30 2009 064 238) of Univ. Prof. Dr.-Ing. Frank Rieg
Example Manual
10. Example: Pinion (Plane stress element No. 14 with 6 nodes)
In this example we examine a pinion, which hub is pressed on a shaft. The amount of the
gap pressure of the interference fit assembly is 100 N/mm². Because of the expansion of
the hub into the tooth system, the deflection is to be analyzed. The tooth system on the
outside is omitted.
input file:
b14_1.cos
CAD-data
At first it is necessary to create a new project with and . In this case, e.g.
Example10,
you have to confirm the dialogue with
Enter
and close the window with
OK
.
Now, you have to import the COSMOS file, which is named above.
With
the example file
b14_1.cos
can be imported. On the right hand a
context menu is opened (
Figure 1
), with which it is possible to load the Cosmos file
. The element type, which is to choose, is
plane stress elements
(
Figure 1
)
.
Figure 1: Import of a COSMOS file with disc elements
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Example Manual
With the
button you switch to the preprocessor. On the right side of the window
you can see the load cases and that already a load case containing boundary conditions
exists. If you click there, the loads and the fixings are shown
(
Figure 2
)
. To blank the dis-
play with the boundary conditions deselect the load case by clicking “--“.
Figure 2: Imported structure with constraints
The legend on the left hand indicates what kind of boundary condition is displayed: dis-
placements, pressures, surface loads, loads, etc. With
View
Size constraints
you can
minimize or maximize the single nodes.
The structure itself was designed in Pro/ENGINEER WF4. In the module Pro/MECHANICA
the material (steel: E = 206,000 N/mm² and ν = 0.3), constraints, mesh seeds (global
max. 6, global min. 3) and the pressure p = 100 N/mm² have been allocated. Afterwards
the disc values had been defined and the mesh was created as plane stress elements out
of triangles. The next step was to emit as a NASTRAN file (formerly also COSMOS files
were possible, which are used here) parabolic with coordinate system CS0 as b14_1.cos.
3
Example Manual
The choice of the constraints is important: The allocation of the gap pressure is no prob-
lem, but the right choice of the bearing to hold on the one hand the structure in the area
and not to constrain on the other hand the expected deformation. Here, the concept of
the “virtual fixed-point” had been applied
(
Figure 3
)
:
Figure 3: Description of the bearing with the “virtual fixed-point“
Thus, four points of the structure were defined. The two points at 3 and 9 o´clock are
constrained into Y direction; in X direction they can be moved. The two points at 6 and
12 o`clock are fixed into X direction; in Y direction they can be moved. Thus a “virtual
fixed point” occurs in the middle.
To compute the structure, you have to change to the solver menu using the
button. It
is supposed that an inappropriate numbering of nodes exist because of the circular
closed structure. The last nodes contact the first nodes and therefore a bad conditioned
total stiffness matrix is produced (compare Z88 Aurora Theory Manual). Because of that,
it is recommended at the solver menu to select “
node sort
” (Cuthill-McKee-algorithm) in
,
before you use the Cholesky solver
.
By clicking the
button, the calcu-
lation starts.
If the calculation was completed successfully, you can select the postprocessor with the
button.
4
Example Manual
Figure 4: Magnitude of displacements in the postprocessor
As expected the highest von Mises stresses exist in the interior edge, i.e. at the hub bo-
rehole. The three Gauss points at every finite element are distinguishable
(
Figure 5
)
.
Figure 5: Stress at Gauss points
5
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