Fall 2012
Lab 8: Report (30 Points)
Name:
MAE 323
User ID:
Hertzian Contact
Problem Statement:
Two different industrial rollers (below) are made of a mineral-filled elastomer. They are
controlled by a hydraulic slide mechanism which brings them together with a force of 2500 lbf
for the purpose of flattening and curing sheet stock of composite material for the electronics
industry. The elastomer material has a Young’s Modulus of 1.0e5 psi and Poisson’s Ratio of .3.
The two rollers are both 5 inches long. You are tasked with determining the maximum contact
pressure experienced by the rollers. You are to construct an appropriate finite element model
and compare your result to an analytical solution.
©2012 Alex Grishin/Prashant Mohan
Analytical Equations And Mesh Refinement
This problem can be solved analytically using the Hertz solution. This solution predicts a
maximum contact pressure, p equal to:
pmax 
2F
b
where:
p max  Max. contact pressure
F  Total load (per unit thick ness) in the direction of normal contact
b  radius of contact
The contact radius, b can be estimated by:
b
4

F
r1r2
r1  r2
Where  is given by:

1  12 1  22

E1
E2
Alternatively, students may use the formulae presented at
http://en.wikipedia.org/wiki/Contact_mechanics#Contact_between_two_cylinders_with_parallel
_axes to find the maximum contact pressure. Perform a local mesh refinement (using the sphere
of influence, for example) to get a maximum contact pressure that comes within 3 percent of the
analytical value. If you use a sphere of influence, keep in mind that both bodies will require one.
Please use a minimum of two refinement iterations. Also, please try to remember all the lessons
we learned previously about the Workbench mesh sizing controls.
Table 1 Convergence Study (8 Points)
Iteration Element Size Max.
Pressure
Analytical
(psi)
Max.
Pressure
FEA (psi)
Percent
Change
1
2
3
4
The questions below assume that you created a 2D finite element model (either plane stress or
plane strain, depending on what you thought was most appropriate). To answer the questions,
you may want to reproduce your solution in the other 2D formulation for comparison (in the
project page, right-click on the top cell (Static Structural) and select “Duplicate”). In the
Duplicated model, change the 2D formulation (for example, if the first model was plane stress,
change the copied model to plane strain), then re-run to view results.
©2012 Alex Grishin/Prashant Mohan
Questions:
If a two dimensional model is constructed to approximate the Hertz solution, which is
better-- plane stress or plane strain? Give an argument for each (6 points)
This was the first lab in which we explicitly defined a material property. Was this
necessary to assess the stress and contact pressure response (explain why or why not)?
(2 point)
For the figures below, show contour plots superimposed on the mesh. This is done by first
clicking on one of the stress results in the tree outline and then selecting “show elements” from
the “edges” drop down menu (this is just to the left of the “Min”, “Max” buttons). Also, make
sure the contour plots reflect the final, converged result.
Figures
Figure 1: Boundary conditions for the first model. (2 points).
Figure 2: Mesh for the converged model. (2 points).
Figure 3: σy stress for the first model (2 points).
Figure 4: Zoomed in (close-up) view of the contact status for the first converged model (This
comes from the contact tool. 2 points).
Figure 5: Zoomed in (close-up) view of the contact pressure for the first converged model (This
comes from the contact tool. 2 points).
Figure 6: Zoomed in (close-up) view of the contact penetration for the first converged model
(This comes from the contact tool. 2 points).
Figure 7: σy stress for the second (copied/duplicated) model (2 points). .
©2012 Alex Grishin/Prashant Mohan