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 = ω x v _ _ _ Drive Direction Sense Direction Oscillating resonator displaces in sense direction Displacement in sense direction is used to measure rotation

Figure1: Distributed Mass Gyroscope Drive Direction Sense Direction 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 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 Beam Width Gap Size

Natural Frequency Analysis

Critical Mesh Density

Theoretical Approximation Beam Width k2 k3 k4 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 Approximation Formula 1: Total stiffness of radial resonating mass. 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. 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