the compliant capacitor - harvard university...• huge, nonlinear strain capabilities •...
TRANSCRIPT
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David R. Clarke
School of Engineering and Applied Sciences Harvard University
The Compliant Capacitor
KAUST , February 2015
Partial support from National Science Foundation
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Materials Design for Compatibility with the Human Body
• Most materials development has been driven by human needs
• Shelter, defense, transportation, entertainment …..
• Strong, stiff, unyielding, hard …..
• Some materials have been developed for replacing structural body parts
• Artificial teeth, hip implants…..
• Only now are materials being developed that are compatible with humans
and extending their capabilities
soft, compliant, conformable, capable of a range of motion……..
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The Human Compatibility Materials Space
NB. Strictly, skin is a viscoelastic material not elastic so it has no true elastic modulus. But one can speak about instantaneous modulus
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Muscles and Actuators
We use muscles for • walking and running • dancing • swimming • getting up and sitting down • moving our eyes • swinging our arms • turning our head • gripping, holding and letting go • …….
Force
Displacement (stroke) Frequency
Actuator Capabilities
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Approximate Range of Characteristics of Existing Mechanical Actuators
Huber et al., Proc. R Soc. A453 2185 (1997)
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The Humble Capacitor
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The Humble Capacitor: The Essential Physics
A capacitor is usually used to store electrical energy so it requires a large dielectric constant and large area. Electrical energy stored is:
2
21 EP OC εε=
hA
hEA
VQC O
S εεσ===
h 2
2
2hhAVU o
electricalεε
=
Capacitance:
Attractive force between opposite charges is: induces electrostrictive strain that for most dielectrics is ppm, ie nanometers
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Coulombic attraction between the charges creates a Maxwell force that compresses the dielectric (equivalent to electrostatic actuator in MEMS) produces strain Elastomers are incompressible, ie volume change = O. So, if reduce thickness, expands laterally
22
===
hVEP ooz εεεεσ Y
s zz
σ−=
2
2
22:0
hYV
YPsssssV oyxzyx εε===++==∆
Freeing the Capacitor -- The Compliant Capacitor
Applying a voltage to a capacitor produces opposite charges in the electrodes across the dielectric.
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Stiffness (million times smaller than standard capacitors)
2
2
22 hYV
YP
oεελ ≈≈Actuation stretch
Voltage
Thickness
Coulombic attraction between the charges creates a Maxwell force that compresses the dielectric (equivalent to electrostatic actuator in MEMS) produces strain Elastomers are incompressible, ie volume change = O. So, expands laterally
22
===
hVEP ooz εεεεσ Y
s zz
σ−=
Freeing the Capacitor -- The Compliant Capacitor
Applying a voltage to a capacitor produces opposite charges in the electrodes across the dielectric.
Replacing a ceramic dielectric with an elastomer leads to a million times greater strain !
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During actuation, the voltage increased at a rate of 20 V/s until electrical breakdown.
12x speed
VHB 4905 elastomer (Acrylic-based) Prestretched to 250%
Carbon nanotube electrodes Quantify actuator deformation, stretch, λ
As elastomers are incompressible, so
hH /2 =λ
orr
=λ
How much can the compliant capacitor stretch ?
2≈=orrλ
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Stretch
• Loosely cross-linked, long chain molecules •Transparent materials • Highly insulating • Dielectric constant ~ 2.6 • On stretching – chains straighten • Huge, nonlinear strain capabilities • Incompressible – Poisson ratio 0.5
Typical elastomers: • Natural rubber (latex) • PDMS • Arcylic (3M VHB 7905) • Polyurethane
The Molecular Structure of Elastomers
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Compliant capacitor as an electrically
driven artificial muscle
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Canon EF 50mm
http://www.flickr.com/photos/doegox/2750019800/
Electric Motor
Gear Assembly
Limitations of traditional lenses: • Bulky • Slow • Complicated design, multiple gears • Noisy • Limited focusing range
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Focal length is constant Focusing by moving lens
A Conventional Electrically Focusing Camera
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The Human Eye: Focusing
Focusing is associated with change in shape of the ocular lens
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An alternative approach: Change focal length of the lens by changing its curvature Solution: Constant volume liquid droplet contained between transparent sheets whose areas can be altered with an applied voltage. Requires: Transparent, compliant electrodes
An Electrically Tunable, Adaptive Lens
Dielectric elastomer membrane
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Demonstration of a Tunable Lens
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0 V and 4.5 kV The scale is in mm.
High Speed Response
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Calculating the dynamic range of focal length: • Constant volume • Spherical curvature, h/a < 0.25 • DEA membrane, D2 → curvature decrease • Passive membrane, D1 → curvature increase
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∆𝑓𝑓𝑚𝑚𝑚𝑚𝑚𝑚 =𝑓𝑓𝑚𝑚𝑚𝑚𝑚𝑚 − 𝑓𝑓𝑜𝑜
𝑓𝑓𝑜𝑜𝑥𝑥 100%
Color indicate maximum focal change
Dynamic Focal Range
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The maximum focal length variation (∆fmax) depend on relative diameter of the membranes (D1/D2), but independent of the refractive index.
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Foca
l len
gth
chan
ge, ∆
f/fo (
%)
Color indicate maximum focal change
Dynamic Focal Range Depends on Diameter Differences
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The Compliant Capacitor
as a Machine Element
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Machine Elements of Soft Robotics
• Actuators
• Linear actuators
• Biaxial actuators
• Rotary drives
• Soft clamps
• …………..
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Devising A Uniaxial Actuator
Complaint capacitor creates a biaxial strain.
Apply through thickness electric voltage. Equi-biaxial strain
Insert aligned and parallel stiffeners Apply electric voltage
How do we use it to create uniaxial strain ?
Elongation perpendicular to stiffeners
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Uni-axial Fiber Stiffening of Dielectric Elastomer
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Cylindrical geometry chosen to minimize electrical breakdown at edges
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Uni-axial Actuator with no Stiffening
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Cylindrical Actuator Using Fiber Stiffened Elastomer
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Uniaxial Actuator
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Mimicking Finger Action
Mechanical element analog: unimorph or bimetallic strip
Fingers gripping an object
Fingers striking piano keys
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End deflection
Blocking force
The Simplest Robotics Element: The Unimorph
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4x accelerated
Dielectric Elastomer Unimorph Actuation
NB. Transparent electrodes
Curling instability due to field induced curvature in two mutually perpendicular directions
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The Dielectric Elastomer Based Unimorph
Expansion parallel and perpendicular to beam axis, causes bending in two perpendicular directions. As the strains can be large, the out-of-plane bending can be large.
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Unimorph Actuation
Observations
Finite element computations
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Aligned, Parallel Fibers Introduce Anisotropic Stiffness
Aligned fibers produces higher stiffness parallel to fibers than perpendicular to them. Enylon >> EVHB. This breaks the flexural deformation response symmetry of the beam
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Simulations Show Suppression of Curling
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Simulations Show Suppression of Curling
A single fiber can be sufficient to break deformation symmetry
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Fiber Stiffened Dielectric Elastomer Based Unimorph
Fabrication:
Optical Micrograph:
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An Inchworm Based on Fiber Stiffened Unimorph
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Effect of Elastic Anisotropy in Unimorphs
Low volume fraction of aligned fibers create elastic anisotropy and alters response
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A Simple Soft Robotics Component: The Gripper
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Mechanical Energy Harvesting
with a Compliant Capacitor
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Energy Harvesting Schemes
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Small-Scale Energy Harvesting
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P
Q+
Q−
Q+
Q−
Φ
Convert mechanical energy to elastic energy
Convert elastic energy energy to electric energy through change in capacitance
Harvesting Electrical Energy Through Mechanical Work
Recall: Electrical energy of a capacitor is:
Change in stored elastic energy:
Essentially a device for transferring charge from a low to high voltage – A voltage Step-Up Transformer
22
2
2
2 VChVE o
electrical ==εε
∫=∆ dLPEM
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λλλλ
=∝)/()/(
11C 2
1λ
λλ
=∝)/(
C 421
λλ
λλ=∝
)/(C
What is Optimum Mechanical Loading Configuration ?
Capacitance Change
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Power Source
Dielectric Elastomer
Capacitor
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0 0
MEE NetDensity /∆= :densityEnergy
NetE∆
Power Supply
Harvesting Mechanical Energy: Energy Cycle
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5.4. to1.2 from range in the changes s,experimentour In λ
Linear Servo
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Equi-biaxial Mechanical Loading Configuration
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Top down View:
Side View:
Movie
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Measured Energy Harvesting Cycles
Schematic
0.5 Hz cycles
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4λ∝C
Pre-set current limit
Leakage Current kVPS 3=Φ4λ∝C
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P
LLλ1L
λ2L
2/ λHModel indicates that capacitance scales with fourth-power of stretch under biaxial loading
Verification of Stretch Scaling
Max stretch is 4.25
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∫+
Φ=∆Φ=∆0
0 charge
TT
TLinLin dtiQE
Electrical Energy from Power Source:
Electrical Energy Harvested:
∫+
Φ=∆Φ=∆0
0 harvest
TT
THhHh dtiQE
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L (mm)
F (N)
ФDE (kV)
iharvest (μA)
icharge(μA)
Representative Generator Cycles
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Energy density with cycle number
The average energy density of the first eight cycles is 560J/kg with a power density of 280W/kg.
MEE NetDensity /∆=inhNet EEE ∆−∆=∆
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Improved Harvesting Cycle ?
Shian et al.,
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Representation in two conjugate work planes
NB. Mechanical energy storage is separated from the subsequent energy conversion so can occur non-uniformly or even intermittantly while energy conversion can occur over a shorter time.
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Improved Harvesting Cycle
Shian et al.,
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Pre-strain :( ) /L L Lχ ′ ′= −
3. Join strips side-by-side. 4. Release stretching force
2. Pre-strain
1. Two elastomer strips
Stretching force
Complex Shapes From Bi-strips: Pre-straining, Joining and Release Operation
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1 cm
44 cm 42 cm 40 cm 37 cm
34 cm
28 cm
22 cm
18 cm
Release of a narrow bi-strip to form a Hemi-helix
Perversions
After release After release and rotating one end ---- a regular helix
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Examples of Morphological Shape Transitions
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• Elastomers are soft, compliant, stretchable
• Elastically compatible with humans
• Ideal for Soft Robotics
• Shape changes can be electrically actuated
• Large scale elastic effects
• Transparent but can be colored
• Combination ideal for new optic and mechanical devices
• Elastomer sheets are mass produced
Elastomers Offer Opportunities For New Machines and Devices