The Effects of Manufacturing Imperfections on Distributed Mass GyroscopesPowerPoint PresentationSlide 3Gyro’s Drive and Sense ModesProject ObjectiveNatural Frequency AnalysisSlide 7Theoretical ApproximationSlide 9Slide 10Future WorkThanks to: Professor Andrei Shkel Alex Trusov, Adam Schofield, and Shkel Group IMSURE program and faculty fellow student researchers Zeiss Labs NSFThe Effects of Manufacturing The Effects of Manufacturing Imperfections on Distributed Imperfections on Distributed Mass GyroscopesMass GyroscopesProfessor Andrei ShkelAdam Schofield and Alexander TrusovDepartment of Mechanical Engineering, UC Irvine Yaniv SchersonMechanical Engineering/Materials Science, UC BerkeleyGyroscopesF = ω x v_ _ _Drive DirectionSense Direction• Oscillating resonator displaces in sense direction• Displacement in sense direction is used to measure rotationFigure1: Distributed Mass GyroscopeDriveDirectionSenseDirectionFigure 2: Mass is oscillated in drive direction and subsequently displaced in sense direction under a rotation.Fixed PointsDrive Direction and Sense DirectionGyro’s Drive and Sense ModesGyro’s Drive and Sense ModesProject 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 resonatorsBeam WidthGap SizeNatural Frequency AnalysisNatural Frequency AnalysisCritical Mesh DensityTheoretical ApproximationTheoretical Approximation Beam Widthk2k3k4k1•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 seriesTheoretical ApproximationTheoretical Approximation Formula 1: Total stiffness of radial resonating mass.4321111111kkkkktot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.33 iiiLwhEkiFormula 3: Natural frequency, f, related to the total stiffness, k, and mass, m, of the resonator.mkftot21• Better understand effects of beam width imperfections on natural frequency of resonators•Improve future designs that account for effects of imperfectionsFuture WorkFuture Work1)1)Compare actual natural frequencies of Compare actual natural frequencies of resonators to Finite Element Modelresonators to Finite Element Model2)2)Measure changes in natural frequency Measure changes in natural frequency due to imperfectionsdue to imperfections3)3)Develop a model to describe how natural Develop a model to describe how natural frequency changes with imperfectionsfrequency changes with imperfectionsThanks to:Professor Andrei Shkel Alex Trusov, Adam Schofield, and Shkel GroupIMSURE program and facultyfellow student researchersZeiss