Momentum - April 2021 - 12

Student Generation
test. The sampling parameters and point
locations for a modal test are critical to gathering
valid data. We had no familiarity with conducting
a full-scale modal test, so this entire project was
more for the experience than the end result. Still,
we had a great result despite our inexperience!
We suspended the chassis using bungees,
simulating a free-free condition, similar to the
simulation. Fifty-four points were identified as
important and marked on the structure. Six triaxial accelerometers (measures in 3 directions
simultaneously) were attached to points
throughout the chassis to accurately determine
the movement of each point and create the
geometry to allow us to visualize the mode
shapes. We moved the accelerometers nine times
and impacted in three locations for each move to
collect measurements of input force and
acceleration response at all critical points. These
measurements included drive-points, which are
measurements of where you impact and retrieve
response at the same point. These measurements
are used to confirm that the test was uniform
throughout the measurement process.
Once all of the data was collected, we
performed a curve-fit to determine the mode
shapes and natural frequencies. Curve-fitting is
the process of selecting poles (natural
frequencies) to use in the modal analysis. In
comparing the FEM natural frequencies and the
measured Frequency Response Functions (FRFs),
we found 11 modes after the rigid body modes.
Rigid body modes are defined as the movement
of the whole structure along or about a single
axis. Flexible body modes are all the other
modes that follow, where different parts of the
structure move in different ways.
The FRFs show the peaks of several
measurements lining up to confirm the values for
the natural frequencies of the structure. The
coherence values are close to 1 at the peaks of
the FRF, showing that the response is a result of
the input, and therefore a good measurement.
Good practice in depicting FRFs is to show the
y-axis in a log scale and present the plot in a
linear scale, showing that we weren't sure of all of
the proper ways to analyze dynamic data, which
is something we learned as we went through this
process.
Once all modes were identified, we compared
the FEM to the physical test. We looked at the
visualization of the mode shapes from the
simulation and compared them visually to those
produced from the physical test. Additionally, the
11 non-rigid-body mode frequencies of both the
physical test and the FEM were compared. We

12 April 2021

Comparison of Flexible Body Mode Natural Frequencies
between the FEM and Experimental Test
Mode no.

FEM frequency (Hz.)

Experimental
frequency (Hz.)

Error %

7

42.78

41.85

-2.17

8

58.21

56.73

-2.54

9

72.06

71.82

-0.33

10

75.52

73.96

-2.07

11

78.89

80.67

2.26

12

110.82

109.52

-1.18

13

112.09

110.47

-1.45

14

122.35

123.89

1.26

15

127.14

128.71

1.23

16

138.33

138.02

-0.22
FRF and
Coherence
plots for a few
measurements
gathered on
the chassis.

saw that the greatest percent error as only 2.54%, meaning the simulation
was accurate concerning our experimental test. This is great, especially for
never having done this before!
Now that the FSAE team understood what frequencies were present in a
standard chassis, we could design future vehicles with this in mind. This test
included everything from conception, to test plan and setup, parameter
estimation, and FEM construction and correlation. That was the whole goal
of this: to learn.
And, just like that, we were dynamics people! n
Cora Taylor, a Ph.D. student majoring in mechanical
engineering with a focus in structural dynamics at Michigan
Technological University, wrote this article for MOMENTUM.
She was a member of the university's Formula SAE team
during her undergraduate career from 2015-18 and was
president of the team for the 2017-18 academic year. She is
2019 recipient of the SAE Rumbaugh Outstanding Student
Leader Award. 

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Momentum - April 2021

Table of Contents for the Digital Edition of Momentum - April 2021

Momentum - April 2021 - Cov1
Momentum - April 2021 - Cov2
Momentum - April 2021 - 1
Momentum - April 2021 - 2
Momentum - April 2021 - 3
Momentum - April 2021 - 4
Momentum - April 2021 - 5
Momentum - April 2021 - 6
Momentum - April 2021 - 7
Momentum - April 2021 - 8
Momentum - April 2021 - 9
Momentum - April 2021 - 10
Momentum - April 2021 - 11
Momentum - April 2021 - 12
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