Difference between revisions of "Increasing bearing area to decrease friction"
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get practical levels of throughput (aka product production rate). <br> | get practical levels of throughput (aka product production rate). <br> | ||
This is due to the [[scaling law]] of [[higher throughput of smaller machinery]]. | This is due to the [[scaling law]] of [[higher throughput of smaller machinery]]. | ||
| + | |||
| + | === Math === | ||
| + | |||
| + | * P … (wearless) frictive losses – in W | ||
| + | * A … bearing area – in m² | ||
| + | * n … number of [[sub layers]] – an integer | ||
| + | * v … speed of assembly … in m/s | ||
| + | * gamma … dynamic friction coefficient – W/(m²*(m/s)²) | ||
| + | |||
| + | <math> P = \gamma A n v^2 </math> <br> | ||
| + | Applying the trick: <br> | ||
| + | <math> P' = \gamma A (x n) (v/x)^2 </math> <br> | ||
| + | <math> P' = \gamma A n v^2 /x </math> | ||
| + | |||
| + | Related: [[Compenslow]] | ||
| + | |||
| + | This has limits though! | ||
== Limits to the trick == | == Limits to the trick == | ||
Revision as of 13:10, 28 August 2022
Friction in atomically precise diamondoid slide bearings ...
- is dominated by dynamic friction
which scales quadratically with speed:
1/2x speed => 1/4x friction | 1/10x speed => 1/100x friction - is proportional to the bearing area (2x area => 2x friction)
For details see: Friction
Side-note:
Low speed friction in macroscale bearings is quite different as it is
speed independent, area independent, load dependent.
The trick
This allows for a neat trick:
- Halving speed and
- doubling machinery
(this keeps the total throughput constant) leads to
- quartering friction losses due to reduced bearing speed
- doubling friction losses due to increased bearing area
Overall a halving of friction.
Q: But isn't doubling the amount of machinery a problem?
A: No! There is exceptionally little machinery needed to
get practical levels of throughput (aka product production rate).
This is due to the scaling law of higher throughput of smaller machinery.
Math
- P … (wearless) frictive losses – in W
- A … bearing area – in m²
- n … number of sub layers – an integer
- v … speed of assembly … in m/s
- gamma … dynamic friction coefficient – W/(m²*(m/s)²)
[math] P = \gamma A n v^2 [/math]
Applying the trick:
[math] P' = \gamma A (x n) (v/x)^2 [/math]
[math] P' = \gamma A n v^2 /x [/math]
Related: Compenslow
This has limits though!
Limits to the trick
See math on main page: Limits to lower friction despite higher bearing area
- assembly motions can be slowed down by adding more sub layers.
- transport motions can not be slowed by adding more sub layers.
At some point assembly motions reach become similarly slow as the assembly motions.
At this point adding further sub-layers there is no further reduction of frictive losses but rather frictive losses ride again. (eventually linearly).
Applications cases
- This can be applied in the design of gem-gum on-chip factories to
optimize thickness of assembly layers of gem-gum factories
or just to get estimates for likely system geometries - This is the theoretical basis for infinitesimal bearings.
