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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
            Adam Schofield and Alexander Trusov
      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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