Difference between revisions of "Electromechanical converter"

Revision as of 14:21, 8 August 2022

General

Madly high power densities

In Nanosystems the maximal power densities that are to expect to be (at least) possible with
electrostatics based electromechanical conversion at the nanoscale are conservatively estimated.
The power densities that are predicted to be at least possible already are extremely high.
Exceeding no less than 1MW/mm³!! See quantitative section below for the math.

This should not come as a surprise since electrostatic machines scale favorably for the small scales.

The relevant scaling law to "blame" for these power densities

In Nanosystems Chapter 2.4. Scaling of classical elecrtomagnetic systems
in Sub-chapter 2.4.3. Magnitudes and scaling: steady-state system
the Formula (2.27) states:
[math] electrostatic–power–density \propto \frac{electrostatic–power}{volume} \propto L^{-1} [/math]
See the page about scaling laws for a derivation.

What does this mean? This means:
When scaling an electrostatic motor/generator

• from say 100mm (10cm about 4inch) macroscale size down
• to say 100nm nanoscale size (~500carbon atom diameters)

(which is a factor of a million) then the volumetric power density of this motor/generator
will also goes up from

• one (unit of power density) to
• a million of these units.

(also a factor of a million)

In fact even more so since at the macroscale imperfections lower dielectric strength and breakdown voltage
is limiting achievable electrical field strengths to much lower levels than what is possible at the nanoscale.

Practical everyday consequences of high power densities

In everyday practice that won't mean we'll have motorcycles more powerful than Saturn Five space rockets.

• Mainly because that just won't be needed.
• Secondarily because energy density does not scale that well. A carried along energy storage would be used up in no time.

In everyday practice what rather will be the case is that the volume of motor metamaterial (say in motorcycles) will be very very small and likely directly integrated into the bearing metamaterial. In terms of this wikis terminology:
muscle motors in infinitesimal bearing make shearing drives.

There won't be a motor in the engine room of vehicles instead the most voluminous things remaining are

• energy storage
• structures for thermal waste heat cooling (bigger means the flow in convection cooling can be laminar and silent)
• the structural frame

What when really pushing the limits?

When really pushing the limits for whatever reasons (maybe not in the context of motorcycles) then one might worry about cooling. Given the high performance of diamondoid heat pipe systems and diamondoid heat pump systems combined with the waste heat being only a tiny fraction of the total power due to high efficiency of the electromechaical conversion, this looks good though. The bottleneck may be the radiators. When the waste heat needs to be pushed out of the machine phase. They'd need to be build big and out of refractory gemstone-like compounds since they might get white hot. In Earths atmosphere one would want to add an impressively strong air stream by blowing in cold air with medium movers. That would look quite impressive actually. In vacuum the radiated waste hear power scales with the fourth power of temperature (Stefan–Boltzmann law) . That's quite good but physical materials have an ultimate limit in temperature. That is there is a temperature above which no material can exist in the solid state (without pressurization to technologically impossible levels).

Quantitatively

From Nanosystems 11.1.7 Charge carriers and charge density

• Electrode length: l_electrode = 20nm
• Electrode diameter: w_electrode = 3nm (electrode width)
• Rim electrode separation: s_electrodegap = 3nm (inter electrode distance)
• => Electrode area: A_electrode = l_electrode * w_electrode = 60nm²

• Field strength: E_electrode = 0.2V/nm
  (wiki-TODO: Find origin of field strength assumption. Is it 10V and 50nm min motor radius mentioned in next section?)
• Charge per area: Q_electrode/A_electrode = ε_0 * ε_r * E_electrode = ~0.0018C/m²
  (neglecting beneficial insulator polarization i.e. ε_r=1) (neglecting stray fields ∫ E·dA = Q/ε)
• Charge per electrode Q_electrode = ~3.3*10^-19C (about two electrons worth of charge)
• Charge per rim-arclength: (Q/l) = Q_electrode/(s_electrode+s_electrodegap) = 5.5*10^-11C/m

From Nanosystems 11.7.3. Motor power and power density

• Motor rim speed: v = 1000m/s
• Current: I = 2*v*(Q/l) = 110nA (factor 2 for "including contributions from both sides of the rotor")
• Voltage: U = 10V
• Absolute power: P = U*I = ~1.1µW

• Motor radius: r = 195nm
• Motor thickness: t = 25nm
• Motor volume: V = pi*r²*h = ~2*10^^-22m³

• Motor volumetric power density: epsilon = P/V > 10¹⁵W/m³
  This is means >1MW/mm³!!

Citations:

• "The power density is large compared to that of macroscale motors: >10¹⁵W/m³." ...
  
• "(Cooling constraints presumably preclude the steady-state operation of a cubic meter of these devices at this power density.)"
  

Following is Nanosystems 11.7.4 Energy dissipation an efficiency

All numbers or chosen model design

• e. Summary: It seems possible to make bearing losses dominant (a few nW)
  and with that get efficiencies >99% at these extreme power densities. Even more efficient at lower power densities.
  Especially with roller contacts instead of sliding tunneling contacts.

• a. Ohmic: Losses under conservative assumption of the conductivity of bulk macroscale aluminum: ~0.1pW
• b. Tunnelwiderstand: Losses <3pW
• c. Bearing losses: From ~1.3pW up to a few nW
• d. Contact drag:
  — jumping leakage electrons: minimizable by (details ...)
  — thermoelastic damping & phonon drag: still to evaluate potentially dominant! But massively reducible roller contacts rather than tunneling contacts.

(wiki-TODO: Add retracing of math here)

Porting macroscale electrostatic machines to the nanoscale

The scaling law for electrostatic performance is very favorable for such miniaturization.

• Voltages become much lower (down to ~1V like in computer chips) – this still gives massive electric fields over nanoscale distances.
• Currents become much higher due to massive device parallelity

Designs that might need not much changes:

• pelletron
• Wimshurst machine
• The Gläser machine (or Lewandowski machine) [1] – cylindric Wimshurst machine
• A small cylindric simplified Voss machine [2]
• Lord Kelvin Replenisher [3]
• Bennet's doubler

Machines needing obvious modifications for the nanoscale:

• Kelvin water dropper
  Could that be done in a nanoscale version with shooting solid-state charged pellets?
• Van de Graaff generator:
  Charge seperation would be done in rather different way.
  Well, avoiding rubber (since not a gemstone-like compound), it would essentially become a similar to a pelletron. (replicate nanoscale charge separation mechanism)

Contacting options

Geometry options:

• tunneling contacts
• roller contacts
• flexing connections for reciprocating drives
  flex must be low enough to not disturb the electric properties (conductivity) of conducting material too much.

Material options:

• graphite ribbons
• conductive nanotubes
• conventional metals like aluminum
• ...

References

• Energy conversion
• Graphene, Nanotubes, Semi gemstone-like structure
• Non mechanical technology path

In the book "Nanosystems"

Treatment of electromechanical energy conversion
and electrostatics in general in Nanosystems (taken from it's glossary):

• Electrostatic actuators, 335, 336
• Electrostatic motors, 336-341, 370
• Electrostatic generators (DC), 336-341

• Electrostatic energy, scaling of, 30
• Electrostatic force, scaling of, 29

• Elecrostatic fields, 29, 200
• Elecrostatic interactions in MM2, 48, 200

Electromagnetic power densities
do not scale well down the nanoscale.

Related

• Power density – High performance of gem-gum technology
• For comparison of power densities: Mechanical energy transmission

External links

Here is a website with an extreme detailed collection of information regarding the history of electrostatic machines:
Electrostatic Machines written by by Antonio Carlos M. de Queiroz.
Especially interresting seem

• The Lord Kelvin "Replenisher"
• The Gläser machine (or Lewandowski machine) – cylindric Wimshurst machine
• A small cylindric simplified Voss machine – this one seems very simple to build just for fun
• A 2 disks Toepler electrostatic machine – (longer sparks than the simplified Voss machine)

On wikipedia:

• Category:Electrostatic_generators
• Wikipedia: Electrostatic generator

Videos:

• Cylindric Wimshurst machine by Antonio Queiroz – This one is powerful and compact – nice
• Sparks from cylindrical Wimshurst machine by Antonio Queiroz
• Youtube channel of Antonio Queiroz featuring lots of electrostatic machines: [4]
• Mini Lord Kelvin Replenisher – made form drinking cup and aluminum foil