ENGM 875 Project Vibrations in a MEMS Electrostatic Energy Converter - - PowerPoint PPT Presentation

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ENGM 875 Project Vibrations in a MEMS Electrostatic Energy Converter Dan White University of NebraskaLincoln December 14, 2007 Dan White (University of NebraskaLincoln) ENGM 875 December 14, 2007 1 / 30 Introduction Introduction

SLIDE 1

ENGM 875 Project

Vibrations in a MEMS Electrostatic Energy Converter Dan White

University of Nebraska–Lincoln

December 14, 2007

Dan White (University of Nebraska–Lincoln) ENGM 875 December 14, 2007 1 / 30

SLIDE 2

Introduction

Motivation Background

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SLIDE 3

Introduction Motivation

Low-power (wireless) sensor nodes Environmental sensing

Temperature Light

Hazardous material detection

Chemical Nuclear

Machine monitoring

Tire pressure Bearing health

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SLIDE 4

Introduction Background

Requirements Long service life Low costs Low/zero maintenance

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SLIDE 5

Introduction Background

Power sources Need ≈ 10′sµW for years. Solar Chemical: battery, fuel cell Mechanical vibration Thermal: Peltier-Seebeck effect Charge storage: capacitor

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SLIDE 6

Introduction Background

Power source comparison

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SLIDE 7

Problem

Problem Statement

General converter Electrostatic conversion

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SLIDE 8

Problem General converter

General converter m¨ z + (be + bm)˙ z + kz = −m¨ y

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SLIDE 9

Problem General converter

Equation of motion Refinement: m¨ z + fm(z, ˙ z) + fe(z, ˙ z) + kz = −m¨ y fm geometry/material dependant, minimize fe controllable

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SLIDE 10

Problem Electrostatic conversion

Electrostatic conversion Mechanical system damping from electrical energy conversion Coulomb force: Fc = 1 4πǫ0 q1q2 d2 → Vary charge separation Model mechanical-electrical energy transfer

position/velocity - voltage/current

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SLIDE 11

Problem Electrostatic conversion

Out-of-plane gap closing converter Current converter type:

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SLIDE 12

Approach

Approach description

Mechanical modeling Electrical modeling

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SLIDE 13

Approach Mechanical modeling

Mechanical modeling Air squeeze-film damping: fm = 16µW 3L z3 ˙ z

z - distance between plates (not from equilibrium) µ - viscosity of air, ∝ pressure W - width of plate L - length of plate

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SLIDE 14

Approach Electrical modeling

Electrical modeling Capacitance: Cvariable = ǫ0WL z

ǫ0 - permittivity of free space ≈ air

Charge: Q = C ∗ V

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SLIDE 15

Approach Electrical modeling

Electrostatic force: fe = −Q2 2ǫ0WL

Q - charge on variable capacitor W = F ∗ z = 1

2QV

V = Q/C F ∗ z = 1

2Q Q C = Q2z 2ǫ0WL

Charge is constant during travel from zmin → zmax and zmax → zmin

˙ z > 0 : Q = Q0 ˙ z < 0 : Q = 0

= ⇒ fe only acts when plates moving apart

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SLIDE 16

Results

Equation of motion In Vacuum

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SLIDE 17

Results Equation of motion

Equation of motion ˙ z > 0 : m¨ z + 16µW 3L z3 ˙ z + kz = − Q2 2ǫ0WL − m¨ z ˙ z < 0 : m¨ z + 16µW 3L z3 ˙ z + kz = −m¨ z

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SLIDE 18

Results In Vacuum

In vacuum µ → 0 ˙ z > 0 : m¨ z + kz = − Q2 2ǫ0WL − m¨ z ˙ z < 0 : m¨ z + kz = −m¨ z Or: m¨ z + Q2 4ǫ0WL (1 + sgn(˙ z)) + kz = −m¨ z

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SLIDE 19

Results In Vacuum

Free vibration simulations

0.5 1 2 4 6 8 10 12 14 16 t (s) fe = 0.062500 x dx E Dan White (University of Nebraska–Lincoln) ENGM 875 December 14, 2007 19 / 30

SLIDE 20

Results In Vacuum

Free vibration simulations

0.5 1 2 4 6 8 10 12 14 16 t (s) fe = 0.160000 x dx E Dan White (University of Nebraska–Lincoln) ENGM 875 December 14, 2007 20 / 30

SLIDE 21

Analysis

Energy extraction ˙ z = 0 detection

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SLIDE 22

Analysis Energy extraction

Energy extraction With no mechanical damping, reduction in mech. E represents mech-to-electrical energy conversion Maximum extraction if return to equilibrium Application is periodic “single” events: P = Eextract

¯ Tevent

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SLIDE 23

Analysis ˙ z = 0 detection

˙ z = 0 detection Control circuitry triggered at z extrema Low power detection circuit Not necessarily clocked/periodic

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SLIDE 24

Future

Future directions

Control laws Simulation accuracy Device optimization Non-resonant operation

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SLIDE 25

Future Control laws

Control laws Better charge insertion/extraction profile Maximize energy extraction w.r.t. electronics

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SLIDE 26

Future Simulation accuracy

Realistic simulation Match measured results

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SLIDE 27

Future Device optimization

Optimization Exploration of parameter-performance surfaces Need a specific application for optimization

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SLIDE 28

Future Non-resonant operation

Sub-resonant operation Spectrum of forcing < resonance Large force “sets” large Epot = 1

2kx2

Return to equilibrum slowed by electrical damping

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SLIDE 29

Conclusion

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SLIDE 30

Conclusion Dan White (University of Nebraska–Lincoln) ENGM 875 December 14, 2007 30 / 30