Simulations of Simulations of Microgyroscope Dynamics Dynamics - - PowerPoint PPT Presentation

Simulations of Simulations of Microgyroscope Microgyroscope Dynamics Dynamics

Oscar Vargas Oscar Vargas

Major: Mechanical Engineering Mentor: Laura Oropeza-Ramos Advisor: Kimberly L. Turner July 28, 2005

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• 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

Microgyroscopes Microgyroscopes Microgyroscopes UCSB UCSB UCSB

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• What is MEMS?

What is MEMS? Micro Electro-Mechanical Systems

• Applications

Applications

• Ships

Ships

• Planes

Planes

• Benefits of MEMS?

Benefits of MEMS?

• Low cost

Low cost

• Batch fabrication

Batch fabrication

• Less material

Less material

• Smaller

Smaller – – Less Energy Less Energy

• Less energy

Less energy

• Miniaturization

Miniaturization

• What is a gyroscope?

What is a gyroscope?

• Macro

Macro-

• gyroscope

gyroscope

• Micro

Micro-

• gyroscope

gyroscope

Microgyroscopes Microgyroscopes Microgyroscopes UCSB UCSB UCSB

• Cars

Cars

• Toys

Toys

http://www.bridgedeck.org http://www-bsac.eecs.berkeley.edu/archive/users/hui-elliot/mems.html

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Microgyroscopes Microgyroscopes Microgyroscopes UCSB UCSB UCSB

Robust Micromachined Vibratory Gyroscopes by Cenk Acar

m = mass c = damping F= external force Ω = angular velocity k = linear spring coefficient

Robust Micromachined Vibratory Gyroscopes by Cenk Acar

v

Ωz

z

x

y

A person looking at a ball traveling parallel to the y axis as he rotates

2 2

2

x x e z

d x dx dy m c k x F m dt dt dt + + = + Ω

2 2

2

y y z

d y dy dx m c k y m dt dt dt + + = − Ω

Coriolis effect Drawing of a micro-gyroscope Dynamics

2 ( )

c

F m v = ×Ω uu r r r

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Using Parametric Resonance to Increase Sensitivity

Harmonic oscillation Parametric oscillation

Induced frequency response in a parametric gyroscopes Induced frequency response in a harmonic 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

Robust Micromachined Vibratory Gyroscopes by Cenk Acar

Microgyroscopes Microgyroscopes Microgyroscopes UCSB UCSB UCSB

Non-interdigitated comb-fingers Interdigitated comb-fingers

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Amplitude in the x axis, actuated direction Amplitude in the y axis, induced direction Response in the x direction, driving direction Response in the y direction, sensing direction

Microgyroscopes Microgyroscopes Microgyroscopes UCSB UCSB UCSB

Displacement Frequency Response

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 18250 18350 18450 18550 18650 18750

Frequency(Hz) A m p litu d e (u m )

2m_1k

Displacement Frequency Responce

0.00E+00 2.00E-05 4.00E-05 6.00E-05 8.00E-05 1.00E-04 1.20E-04 18250 18350 18450 18550 18650 18750

Frequency(Hz) A m p litu d e (u m )

2m_1k

Results of numerical simulations

t

(Dimensionless)

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Microgyroscopes Microgyroscopes Microgyroscopes UCSB UCSB UCSB

Maximum amplitude vs. stiffness for different masses

Amplitude vs. Stiffness

0.00E+00 5.00E-05 1.00E-04 1.50E-04 2.00E-04 2.50E-04 5 10 15 20

Stiffness(N/m) Am plitude(um )

1m 2m 3m 4m m=0.275 ng

Structure of a micro-gyroscope

Future Work

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Thank you

Trevor Hirst Liu-Yen Kramer Nick Arnold Michael Northen Laura Oropeza-Ramos Kimberly L. Turner Turner group

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v

Ωz

z

x

y

Coriolis

A person looking at a ball traveling parallel to the y axis as he rotates

http://www.uvi.edu/SandM/Physics/dave/DavesArchives/111003 /Phys211NetPlay.html

Microgyroscopes Microgyroscopes Microgyroscopes UCSB UCSB UCSB

Foucault Pendulum swinging on the north pole

2 ( )

c

F m v = ×Ω uu r r r

Robust Micromachined Vibratory Gyroscopes by Cenk Acar

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Scaling Scaling

• Time: 10
• van der Waals: 11/4
• Diffusion: 11/2
• Distance: 1
• Velocity:1
• Surface tension: 1
• Electrostatic force: 12
• Muscle force: 12
• Friction: 12
• Friction: 12
• Thermal losses: 12
• Piezo-electricity: 12
• Mass: 13
• Gravity: 13
• Magnetics: 13
• Torque: 13
• Power: 13

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Two Type of Actuators Two Type of Actuators

3 2 1 3

( )

e

F r x r x V = − +

2 e

N hV F g ε =

Non-interdigitated comb-fingers Interdigitated comb-fingers

x y x d

g

h

2 2

2

x x e z

d x dx dy m c k x F m dt dt dt + + = + Ω

2 2

2

y y z

d y dy dx m c k y m dt dt dt + + = − Ω

x