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# UROP Undergraduate Research Opportunities Program

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```									The Effects of Manufacturing
Imperfections on Distributed
Mass Gyroscopes

Professor Andrei Shkel
Department of Mechanical Engineering, UC Irvine

Yaniv Scherson
Mechanical Engineering/Materials Science, UC Berkeley
Gyroscopes
_     _    _
F=ωxv
Sense Direction

Drive Direction

• Oscillating resonator displaces in sense direction

• Displacement in sense direction is used to measure rotation
Drive Direction and Sense Direction

Sense
Direction

Drive
Direction

Fixed Points

Figure1: Distributed Mass Gyroscope   Figure 2: Mass is oscillated in drive
direction and subsequently displaced in
sense direction under a rotation.
Gyro’s Drive and Sense Modes
Project Objective
 Develop an   FEM (finite element model) of
the Distributed Mass Gyro
 Determine the effects of imperfections on
the natural frequency of the resonators

Gap Size

Beam
Width
Natural Frequency Analysis
Critical Mesh Density
Theoretical Approximation

k1
k2

Beam Width

k3
k4

•Treat beams 1 and 2 in parallel and beams 3 and 4 in parallel

•Treat upper and lower suspension beams as a system of beams in series
Theoretical Approximation
E  hi  wi
3
1             1
k tot                                              ki 
1   1        1   1
                                                       Li
3
k1 k 2       k3 k 4
Formula 1: Total stiffness of                  Formula 2: Stiffness of a beam where E is
radial resonating mass.                       young’s modulus, h is beam height, w is
beam width, and L is beam length.

1    k tot
f       
2     m
Formula 3: Natural frequency, f, related to the
total stiffness, k, and mass, m, of the resonator.
• Better understand effects of beam width
imperfections on natural frequency of resonators

•Improve future designs that account
for effects of imperfections
Future Work
1)   Compare actual natural frequencies of
resonators to Finite Element Model
2)   Measure changes in natural frequency
due to imperfections
3)   Develop a model to describe how natural
frequency changes with imperfections
Thanks to:
Professor Andrei Shkel
Alex Trusov, Adam Schofield, and Shkel Group
IMSURE program and faculty
fellow student researchers
Zeiss Labs
NSF

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