Infinitesimal bearing

Infinitesimal bearings or infinibearings for short.

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With the availability of Advanced atomically precise technology (APM)
it no longer makes sense to build conventional roller-bearings in which macroscopic speed differences meet at nanoscale contacts.

Instead advanced APM technology allows to build a new type of macroscopic bearings
that spread macroscopic speed differences over many layers (a passive mechanical metamaterial)
such that at nanoscale contacts only nanoscale-typical speed differences remain.
Paired with the flawless gemstone surfaces of crystolecule gears
those metamaterial bearings become for all practical purposes wear free.

A small demo stack of building blocks for a relative speed distributing metamaterial.

From classic to infinitesimal bearings. More layers reduce the relative speed differences. The result has lower friction and higher damage tolerance.

Different configrations (end to end connections) of infinitesimal bearing metamaterial can produce different types of bearings

A note on the naming choice for here on this wiki

The name is chosen due to the analogy with infinitesimal calculus.
Taking a sum with increasingly smaller steps and eventually infinitely many infinitely small ones.
It is literally a sum of speed differences here.
Albeit in most cases each layer takes the same constant speed difference.
Maybe there can be benefits in doing variations but it's not immediately obvious and comes with increased design difficulty.
Infinitesimal bearings obviously can't go all the way to infinity as they are a physical thing.
But they can go beyond human perception senses.
The bearings layers are no longer visible,feelable or otherwise perceptible without microscopy tools.
And they can go to the smallest possible physical scale limited the size of atoms.

Details

To reduce the relative speed of two surfaces one can stack many layers with minimal thickness onto each other. Each of those layers is imperceptibly small - thus the "infinitesimal" in the name. The layers are just thick enough to accommodate the necessary nano-mechanics. These nanomechanics are crystolecule gears (not roller bearings) and further structure that makes sure that every layer handles the same part of the total speed difference. Note that due to superlubrication a single layer can take well-perceivable macroscopic speeds without being destroyed thus bearings replacing today's macroscopic ones will need to use only a very thin stack of infinitesimal bearing layers (often the whole layer stack might be less than 32µm thick and thus as good as imperceptible by eye). Since there's no static friction and very low speed dependent dynamic friction in diamondoid nanomechanics (see superlubrication) the bearing's efficiency can be expected to be exceptional.

It is still to investigate how a macroscopic infinitesimal bearing will perform relative to nanoscopic DMME bearing and for a more intuitive feel for the performance how long an infinitesimal bearing of certain size would turn till it e.g. reaches half its initial speed.

As in all products of advanced nanosystems the nanomechanics must (through their structure) provide some redundancy to cope with radiation damage. This makes the design of a bearing metamaterial more complicated
(TODO: Add a more detailed Model)

(TODO: Design and testprint a macroscopic model structure for demonstration.)

Cheating on the scaling law

• The Problem: Critics argue that nanomachinery has terrible scaling because surface area
  (and thus friction) grows much faster than volume as you make things smaller
• (One part of) the solution: Infinitesimal bearings "cheat" this by distributing the speed difference across many layers,
  so each layer operates at lower speeds (quadratic reduction in friction per layer) while only linearly increasing the total surface area

Cheating on "more (bearing) surface area of smaller (machinery) structures".
Cheating on "exploding friction from exploding surface area of nanomachinery" by using infinitesimal bearings.

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When the total speed difference that the bearing is supporting is kept constant
the power dissipation per volume scales with size:

• linearly with mono-layer sleeve bearings
  (note that here the whole power dissipation is concentrated on a single layer in the considered volume)
• quadratic with infinitesimal bearings

(wiki-TODO: Add the math in detail.)

Scaling only one dimension (bearing thickness)

Doubling the number of layers

• halves the speed which quarters the dynamic friction (P ~ v²) (v->v/2 => P->P/4)
• doubles the surface area which doubles friction (P ~ A) (A->2A => P-> 2P)
• thus in combination it halves friction (v->v/2 && A->2A => P->P/2)

Reducing friction further (slightly larger scales)

Retaining atomic precision but going to slightly larger scale atomically precise roller gearbearings (optimization problem)
arranged into an infinitesimal bearing metamaterial may hold the potential for extraordinary low friction bearings.

Related AP metamaterials

Integrating active drive into infinitesimal bearings one may get shearing muscle motors.

Adding chemomechanical or electromechanical motors into the layers
changes it into an interfacial drive (an active metamaterial).
There the add-up of layer movement acts as one of the methods
to accumulate nano motion to macroscopic levels (Convergent mechanical actuation).

Misc

Infinitesimal bearings enforce a fixed speed relationship between layers. Thus they can be used for mechanical advantage (a transmission).

Depending on the deformation and closing topology of the bearing layers with nanoscale thickness various kinds of bearings can be made:

• normal radial bearings
• axial thrust bearings
• conical bearings
• linear prismatic sliding bearings
• heavily deformed bearings (gemstone nano-layers are highly flexible)
• ...

Related

• Scaling laws
• Superlube tubes

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Atomically precise bearings:

• Atomically precise slide bearings
• Atomically precise roller gearbearings

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• Friction in gem-gum technology

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• Mocle … another metamaterial concept possibly in part building on this one
• Emulated elasticity … another possible basic mechanical metamaterial

Alternate names

• infinitesimal bearing
• stratified shear bearing
• stratified shearing bearing
• stratified shear-roll bearing
• multi layer speed gradient bearing

External links

• Youtube Videos:
  A model of a mechanism that demonstrates the basic principle and the fact that it can be "mis"used as a mechanical transmission
  It works with chains too

• https://en.wikipedia.org/wiki/Infinitesimal