Simulations of Simulations of Microgyroscope Dynamics Dynamics Microgyroscope Oscar Vargas Oscar Vargas Major: Mechanical Engineering Mentor: Laura Oropeza-Ramos Advisor: Kimberly L. Turner July 28, 2005
� Goals of the research Goals of the research � Analyze non- Analyze non -linear micro linear micro- -gyroscope dynamics gyroscope dynamics • • through numerical simulations in MATLAB through numerical simulations in MATLAB � Activities Activities � • Understand MEMS principles Understand MEMS principles • � Reading from books, papers and discussions Reading from books, papers and discussions � • Understand Linear and Nonlinear Micro Understand Linear and Nonlinear Micro- -gyroscopes gyroscopes • � Dynamics of gyroscopes Dynamics of gyroscopes - - Coriolis Coriolis effect effect � � Study principles of vibration (parametric oscillation) Study principles of vibration (parametric oscillation) � • Use MATLAB Use MATLAB • � Create numerical simulations for different parameters Create numerical simulations for different parameters � values, mostly stiffness and mass values, mostly stiffness and mass 2 Microgyroscopes UCSB Microgyroscopes UCSB UCSB Microgyroscopes
What is a gyroscope? � What is a gyroscope? What is MEMS? � � What is MEMS? � Micro Electro-Mechanical Systems • Macro Macro- -gyroscope gyroscope • • Micro Micro- -gyroscope gyroscope • http://www-bsac.eecs.berkeley.edu/archive/users/hui-elliot/mems.html Applications � Applications � Benefits of MEMS? � Benefits of MEMS? � • Ships Ships • • Cars Cars • • Low cost Low cost • • Planes Planes • • Toys Toys • • Batch fabrication • Batch fabrication • • Less material Less material • Smaller Smaller – – Less Energy Less Energy • • • Less energy Less energy http://www.bridgedeck.org • Miniaturization Miniaturization • 3 Microgyroscopes UCSB Microgyroscopes UCSB UCSB Microgyroscopes
Drawing of a micro-gyroscope Coriolis effect Ω z v z y x uu r r r = ×Ω F 2 ( m v ) c � A person looking at a ball traveling parallel to the y axis as he rotates Robust Micromachined Vibratory Gyroscopes by Cenk Acar Dynamics 2 d x dx dy + + = + Ω m c k x F 2 m x x e z 2 dt dt dt 2 d y dy dx + + = − Ω m c k y 2 m y y z 2 dt dt dt m = mass c = damping F= external force Ω = angular velocity k = linear spring coefficient 4 Robust Micromachined Vibratory Gyroscopes by Cenk Acar Microgyroscopes UCSB Microgyroscopes UCSB UCSB Microgyroscopes
Using Parametric Resonance to Increase Sensitivity � Interdigitated comb-fingers � Non-interdigitated comb-fingers Harmonic oscillation Parametric oscillation Robust Micromachined Vibratory Gyroscopes by Cenk Acar Induced frequency response in a parametric Induced frequency response in a harmonic gyroscopes gyroscopes Parametric resonance has a high amplitude for longer bandwidth � Parametric resonance has a high amplitude for longer bandwidth � � Parametric resonance is less sensitive to changes in parameters thus gyro more robust 5 Microgyroscopes UCSB Microgyroscopes UCSB UCSB Microgyroscopes
Results of numerical simulations Displacement Frequency Response 10.00 2m_1k 9.00 8.00 ) m 7.00 (u 6.00 e d 5.00 litu 4.00 p m 3.00 A 2.00 1.00 0.00 18250 18350 18450 18550 18650 18750 t (Dimensionless) Frequency(Hz) � Amplitude in the x axis, � Response in the x direction, actuated direction driving direction Displacement Frequency Responce 1.20E-04 2m_1k 1.00E-04 ) m (u 8.00E-05 e d litu 6.00E-05 p m 4.00E-05 A 2.00E-05 0.00E+00 18250 18350 18450 18550 18650 18750 Frequency(Hz) � Response in the y direction, � Amplitude in the y axis, sensing direction 6 induced direction Microgyroscopes UCSB Microgyroscopes UCSB UCSB Microgyroscopes
� Maximum amplitude vs. stiffness Amplitude vs. Stiffness for different masses 2.50E-04 4m ) plitude(um 3m 2.00E-04 2m 1.50E-04 1m 1.00E-04 Am 5.00E-05 m=0.275 ng 0.00E+00 0 5 10 15 20 Stiffness(N/m) Future Work � Structure of a micro-gyroscope 7 Microgyroscopes UCSB Microgyroscopes UCSB UCSB Microgyroscopes
Thank you Trevor Hirst Laura Oropeza-Ramos Liu-Yen Kramer Kimberly L. Turner Nick Arnold Turner group Michael Northen 8
Coriolis Ω z v z y uu r r r x = ×Ω F 2 ( m v ) c http://www.uvi.edu/SandM/Physics/dave/DavesArchives/111003 /Phys211NetPlay.html � A person looking at a ball � Foucault Pendulum swinging on traveling parallel to the y axis as the north pole he rotates 9 Microgyroscopes UCSB Microgyroscopes UCSB UCSB Microgyroscopes Robust Micromachined Vibratory Gyroscopes by Cenk Acar
Scaling Scaling •Time: 1 0 •Friction: 1 2 • van der Waals: 1 1/4 •Thermal losses: 1 2 •Diffusion: 1 1/2 •Piezo-electricity: 1 2 •Distance: 1 • Mass: 1 3 •Velocity:1 •Gravity: 1 3 • Surface tension: 1 • Magnetics: 1 3 •Electrostatic force: 1 2 •Torque: 1 3 •Muscle force: 1 2 •Power: 1 3 •Friction: 1 2 10
Two Type of Actuators Two Type of Actuators � Interdigitated comb-fingers � Non-interdigitated comb-fingers x x y g d x h ε 2 N hV = = − + 3 2 F F ( r x r x V ) e e 1 3 g 2 d x dx dy + + = + Ω m c k x F 2 m x x e z 2 dt dt dt 2 d y dy dx + + = − Ω m c k y 2 m y y z 2 dt dt dt 11
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