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
Introduction Introduction Motivation Background Dan White (University of Nebraska–Lincoln) ENGM 875 December 14, 2007 2 / 30
Introduction Motivation Low-power (wireless) sensor nodes Environmental sensing Temperature Light Hazardous material detection Chemical Nuclear Machine monitoring Tire pressure Bearing health Dan White (University of Nebraska–Lincoln) ENGM 875 December 14, 2007 3 / 30
Introduction Background Requirements Long service life Low costs Low/zero maintenance Dan White (University of Nebraska–Lincoln) ENGM 875 December 14, 2007 4 / 30
Introduction Background Power sources Need ≈ 10 ′ s µ W for years . Solar Chemical: battery, fuel cell Mechanical vibration Thermal: Peltier-Seebeck effect Charge storage: capacitor Dan White (University of Nebraska–Lincoln) ENGM 875 December 14, 2007 5 / 30
Introduction Background Power source comparison Dan White (University of Nebraska–Lincoln) ENGM 875 December 14, 2007 6 / 30
Problem Problem Statement General converter Electrostatic conversion Dan White (University of Nebraska–Lincoln) ENGM 875 December 14, 2007 7 / 30
Problem General converter General converter m ¨ z + ( b e + b m )˙ z + kz = − m ¨ y Dan White (University of Nebraska–Lincoln) ENGM 875 December 14, 2007 8 / 30
Problem General converter Equation of motion Refinement: m ¨ z + f m ( z , ˙ z ) + f e ( z , ˙ z ) + kz = − m ¨ y f m geometry/material dependant, minimize f e controllable Dan White (University of Nebraska–Lincoln) ENGM 875 December 14, 2007 9 / 30
Problem Electrostatic conversion Electrostatic conversion Mechanical system damping from electrical energy conversion 1 q 1 q 2 Coulomb force: F c = d 2 4 πǫ 0 → Vary charge separation Model mechanical-electrical energy transfer position/velocity - voltage/current Dan White (University of Nebraska–Lincoln) ENGM 875 December 14, 2007 10 / 30
Problem Electrostatic conversion Out-of-plane gap closing converter Current converter type: Dan White (University of Nebraska–Lincoln) ENGM 875 December 14, 2007 11 / 30
Approach Approach description Mechanical modeling Electrical modeling Dan White (University of Nebraska–Lincoln) ENGM 875 December 14, 2007 12 / 30
Approach Mechanical modeling Mechanical modeling Air squeeze-film damping: f m = 16 µ W 3 L z ˙ z 3 z - distance between plates (not from equilibrium) µ - viscosity of air, ∝ pressure W - width of plate L - length of plate Dan White (University of Nebraska–Lincoln) ENGM 875 December 14, 2007 13 / 30
Approach Electrical modeling Electrical modeling Capacitance: C variable = ǫ 0 WL z ǫ 0 - permittivity of free space ≈ air Charge: Q = C ∗ V Dan White (University of Nebraska–Lincoln) ENGM 875 December 14, 2007 14 / 30
Approach Electrical modeling Electrostatic force: f e = − Q 2 2 ǫ 0 WL Q - charge on variable capacitor W = F ∗ z = 1 2 QV V = Q / C Q 2 z F ∗ z = 1 2 Q Q C = 2 ǫ 0 WL Charge is constant during travel from z min → z max and z max → z min z > 0 : Q = Q 0 ˙ z < 0 : Q = 0 ˙ = ⇒ f e only acts when plates moving apart Dan White (University of Nebraska–Lincoln) ENGM 875 December 14, 2007 15 / 30
Results Results Equation of motion In Vacuum Dan White (University of Nebraska–Lincoln) ENGM 875 December 14, 2007 16 / 30
Results Equation of motion Equation of motion z > 0 : ˙ z + 16 µ W 3 L Q 2 m ¨ z + kz = − ˙ 2 ǫ 0 WL − m ¨ z z 3 z < 0 : ˙ z + 16 µ W 3 L m ¨ z + kz = − m ¨ ˙ z z 3 Dan White (University of Nebraska–Lincoln) ENGM 875 December 14, 2007 17 / 30
Results In Vacuum In vacuum µ → 0 Q 2 z > 0 : m ¨ ˙ z + kz = − 2 ǫ 0 WL − m ¨ z z < 0 : m ¨ ˙ z + kz = − m ¨ z Or: Q 2 m ¨ z + 4 ǫ 0 WL (1 + sgn (˙ z )) + kz = − m ¨ z Dan White (University of Nebraska–Lincoln) ENGM 875 December 14, 2007 18 / 30
Results In Vacuum Free vibration simulations f e = 0.062500 1 x dx E 0.5 0 -0.5 -1 0 2 4 6 8 10 12 14 16 t (s) Dan White (University of Nebraska–Lincoln) ENGM 875 December 14, 2007 19 / 30
Results In Vacuum Free vibration simulations f e = 0.160000 1 x dx E 0.5 0 -0.5 -1 0 2 4 6 8 10 12 14 16 t (s) Dan White (University of Nebraska–Lincoln) ENGM 875 December 14, 2007 20 / 30
Analysis Analysis Energy extraction z = 0 detection ˙ Dan White (University of Nebraska–Lincoln) ENGM 875 December 14, 2007 21 / 30
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 = E extract ¯ T event Dan White (University of Nebraska–Lincoln) ENGM 875 December 14, 2007 22 / 30
Analysis z = 0 detection ˙ z = 0 detection ˙ Control circuitry triggered at z extrema Low power detection circuit Not necessarily clocked/periodic Dan White (University of Nebraska–Lincoln) ENGM 875 December 14, 2007 23 / 30
Future Future directions Control laws Simulation accuracy Device optimization Non-resonant operation Dan White (University of Nebraska–Lincoln) ENGM 875 December 14, 2007 24 / 30
Future Control laws Control laws Better charge insertion/extraction profile Maximize energy extraction w.r.t. electronics Dan White (University of Nebraska–Lincoln) ENGM 875 December 14, 2007 25 / 30
Future Simulation accuracy Realistic simulation Match measured results Dan White (University of Nebraska–Lincoln) ENGM 875 December 14, 2007 26 / 30
Future Device optimization Optimization Exploration of parameter-performance surfaces Need a specific application for optimization Dan White (University of Nebraska–Lincoln) ENGM 875 December 14, 2007 27 / 30
Future Non-resonant operation Sub-resonant operation Spectrum of forcing < resonance Large force “sets” large E pot = 1 2 kx 2 Return to equilibrum slowed by electrical damping Dan White (University of Nebraska–Lincoln) ENGM 875 December 14, 2007 28 / 30
Conclusion Conclusion Dan White (University of Nebraska–Lincoln) ENGM 875 December 14, 2007 29 / 30
Conclusion Dan White (University of Nebraska–Lincoln) ENGM 875 December 14, 2007 30 / 30
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