Momentum - April 2021 - 11

Student Generation
that I hadn't explored before, but I had always
enjoyed my dynamics-based classes. So I figured
I'd give it a try to see if dynamics was for me, by
implementing it on the team. I wasn't sure where
to start, but then, as FSAE often does, a great
opportunity presented itself to me.
My senior year I became a part of a group of
diverse senior members that were commissioned
to design the next year's competition chassis. The
three of us had varying interests. One had an
interest in suspension design. The second had a
greater interest in manufacturability. And the
third, me, well I wanted to try to explore
structural dynamics. The first two were pretty
easy to satisfy with this capstone, but the third...
well, Michigan Tech FSAE had never had someone
interested in structural dynamics, so it wasn't
clear whether I was going to be able to pursue
my passion with this project.
We had to figure out how all three of us would
pursue our engineering passions in a cohesive
way to succeed in our project, and this is how it
happened.
The project started with the suspension
design, which was, to some extent, based on past
cars. So we knew we could design a chassis that
met all the template requirements around them.
As we worked to design the physical tube
structure, keeping ease of manufacturability in
mind, we developed a finite element model
(FEM) of the chassis and adjusted it with design
changes. This model is designed to simulate the
chassis structure and its constrained and loaded

Final FEM of chassis with 2D representation of 1D elements
showing joint and tube thickness.

MOMENTUM

The Michigan Tech FSAE team after competition at Formula SAE Michigan.
physical torsional stiffness tests. The values determined from the simulation
gave the team a good idea of what the actual torsional rigidity would be.
The model was also used to identify the structure's resonant frequencies
and mode shapes. These dynamic properties can be used as another
comparison metric for torsional rigidity and to understand what frequencies
of the chassis could be excited and make the driver uncomfortable as a
result of engine RPM or track input.
One of the first steps in creating a FEM is determining what type of
elements to use. Overall, 1D elements are easier to manage. If we were to
have used 3D elements, based on FEM best practices, the elements would
have had to be small enough to create three elements across each tube
thickness. This would result in the elements being too small for the software
to solve. With the 1D elements, we were able to create a solvable model and
apply thin-walled tube dimensions to each of the component groups of
tubes with common tube thicknesses.
Next, we had to determine what element size would give us the proper
runnable resolution. The model we created was in length units of mm. It was
decided that an element size of 10 would allow for appropriate resolution
while not complicating the system too much. This 10mm element size was
only applied along the axis of the tubes.
When creating the mesh, we ensured all elements were oriented in the
proper direction and that all connections between elements were present at
joints. One of the errors we identified early on was that the 2D realization of
the 1D elements showed the tubes as meshed into one another, centered
around one node. This error may be fixable but would have required
additional modeling hours that we deemed unnecessary, since we weren't
looking for a perfectly accurate model. However, this mistake led to the
simulation being stiffer and heavier than the physical chassis due to the
extra material and rigid joints, so we just noted that during any comparisons
using the simulation.
Now that the model was created, we could apply 4130 steel material
properties, boundary conditions, and loads. For the comparison to a physical
torsional rigidity test, we fixed the suspension points and applied a moment
in the center of the front hoop. For the modal test, we left the structure
floating in space, in free-free.
Using the resonant frequencies and mode shapes outputted from the
simulation, we determined our sampling parameters and necessary
measurement points throughout the structure to be used for the physical

April 2021 11
Momentum - April 2021

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