The Effects of Manufacturing The Effects of Manufacturing Imperfections on Distributed Imperfections on Distributed

Mass GyroscopesMass Gyroscopes

Professor Andrei Shkel

Adam Schofield and Alexander Trusov

Department of Mechanical Engineering, UC Irvine

Yaniv Scherson

Mechanical Engineering/Materials Science, UC Berkeley

Gyroscopes

F = ω x v_ _ _

Drive Direction

Sen

se D

irect

ion

• Oscillating resonator displaces in sense direction

• Displacement in sense direction is used to measure rotation

Figure1: Distributed Mass Gyroscope

DriveDirection

SenseDirection

Figure 2: Mass is oscillated in drive direction and subsequently displaced in sense direction under a rotation.

Fixed Points

Drive Direction and Sense Direction

Gyro’s Drive and Sense ModesGyro’s Drive and Sense Modes

Project ObjectiveProject Objective

Develop an FEM (finite element model) of Develop an FEM (finite element model) of the Distributed Mass Gyrothe Distributed Mass Gyro

Determine the effects of imperfections on Determine the effects of imperfections on the natural frequency of the resonatorsthe natural frequency of the resonators

Beam Width

Gap Size

Natural Frequency AnalysisNatural Frequency Analysis

Critical Mesh Density

Theoretical ApproximationTheoretical Approximation

Beam Width

k2

k3k4

k1

•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 ApproximationTheoretical Approximation

 

Formula 1: Total stiffness of radial resonating mass.

4321

111

111

kkkk

k tot

Formula 2: Stiffness of a beam where E is young’s modulus, h is beam height, w is

beam width, and L is beam length.

3

3

i

ii

L

whEki

Formula 3: Natural frequency, f, related to the total stiffness, k, and mass, m, of the resonator.

m

kf tot

2

1

• Better understand effects of beam width imperfections on natural frequency of resonators

•Improve future designs that account for effects of imperfections

Future WorkFuture Work1)1) Compare actual natural frequencies of Compare actual natural frequencies of

resonators to Finite Element Modelresonators to Finite Element Model

2)2) Measure changes in natural frequency Measure changes in natural frequency due to imperfectionsdue to imperfections

3)3) Develop a model to describe how natural Develop a model to describe how natural frequency changes with imperfectionsfrequency changes with imperfections

Thanks to:Professor Andrei Shkel

Alex Trusov, Adam Schofield, and Shkel GroupIMSURE program and faculty

fellow student researchersZeiss Labs

NSF