guided beam

Microsystems LaboratoryUC-Berkeley, ME Dept.

Parametric and Optimal Design of MEMS – Class#9MEMS Class#9

Liwei Lin

Professor, Dept. of Mechanical Engineering

Co-Director, Berkeley Sensor and Actuator Center

1Liwei Lin, University of California at Berkeley

The University of California, Berkeley, CA94720

e-mail: lwlin@me.berkeley.edu

http://www.me.berkeley.edu/~lwlin

Microsystems LaboratoryUC-Berkeley, ME Dept.

Outline

General Solving Procedures for Meandering Flexures

Nonlinear Effects of Beams to Systems

Sensor Designs

2Liwei Lin, University of California at Berkeley

Meandering Flexure

3

Examples

4

Solving Processes

Continue on x & y components

5

Free-Body Diagram

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Unified Beam Bending Theory

Continue withBeam2, 3 … 7

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Summary

8

Matrix to Solve M0 (set 7 = 0)

9

Continue: Solution Procedures

Please read Professor Pisano’s class notes for detail derivations.In principle, the 51 unknowns can be solved.The values of , x, y on each b b l l d

10

beam can be calculated.

One can derive kx & ky

Example: ky

11

Example: Boundary Conditions

12

Example: Fixed-Guided Beam

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Example: Fixed-Guided Beam

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Non-linear Behavior

15

Sources of Nonlinearity

16

Estimation of Shear Effects

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Width & Thickness Convention

18

Beam Curvature

19

MEMS Spring Hardening Effect

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MEMS Spring Hardening Effect

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Detailed Derivations in theOld lecture notes

MSMS Beams – short summary

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MSMS Beam Examples

23

6/12/00 24

Duffing Equation

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Duffing Equation

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Percentage Nonlinearity

27

Resonant Sensor Designs

28

Capacitive Gyro Sensors

• Simplified Gyro Structure

Sense

Drive

Sense electrode

Drive electrode

Gyro Design

• Drive modeF iFrequency is about 9900Hz

Gyro Design

• Sense modeF iFrequency is

about 10016Hz