Difference between revisions of "Mechanical-electrical analogies"

Latest revision as of 14:47, 10 June 2023

There's 1:1 correspondence between mechanical and electrical quantities

Basic:

• voltage U in volts V ~ force F in newton N ~ moment M in Nm
• current I in ampere A ~ speed v in m/s ~ angular speed omega in rad/s
• power P=U*I ~ P=F*v ~ P=M*omega
• resistance R=U/I ~ R'=F/v ~ R=M/omega -- (conductivity just the inverse)

Electrostatic:

• charge Q in As ~ position x in m ~ angle alpha in rad
• capacity C in As/V ~ linear-stiffness k in N/m ~ angular-stiffness in kappa in Nm/rad
• electric field E in V/m ~ ...
• dielectric constant epsilon in (As)/(Vm) ~ ... ?
• D ...

Magnetostatic:

•  ? ... ~ mass m in kg ~ moment of intertia kg*m^2
•  ? ... ~ linear impulse kg*m/s ~ ...

Note that there are also 1:1 corresponcences to the inverse quanities (switching current with volatge - everything else follows automatically).

One can build mechanical circuitry (out of mechanical circuit elements) just as one does with electrical elements.

Limits of the correspondence

At a slightly closer look similarities break down

• There is no simple electrical analogy to gearboxes. One usually uses pulse width modulation for voltage.
  Linear amplification corresponds to simple mechanical advantage of a lever.
• escapements can be a extremely compact alternative to pulse with modulation for current (aka buck converters).

In general there are mechanical elements that combine more functionality in a smaller and simpler design. Conversely these smaller and simpler designs tend to mix different functionalities together. They don't do "separation of concerns" properly and thus are not as versatile or more difficult be used in automated design generation.

So it can have benefits to refrain from the usage of these classical macroscale function mangling elements incurring more space useup.

Related: Analogies and their dangers

Pulse width modulation

• Drop voltage from a higher to a lower level => reduction of driving force
• Regulate current to a constant value => constant speed drive.
  (when a constant voltage is behind there is a limit at which current cant be kept up to set value)

Misc

A fundamental law: Very accurate measurements require very big sensors (averaging out noise). That holds for both electrical, mechanical and other systems.

An extreme example is the detection of gravitational waves where distances of a fraction of a atomic nucleus can be measured. Such accuracies fundamentally cannot be reached by small sensors, not to speak of individual nanoscale sensors.

Related

• Nanomechanic circuits
• Mechanical circuit element
• Mechanical pulse width modulation

• Analogies and their dangers
• Lagrangian mechanics for nanomechanical circuits

• Mechanical computation

• Drive subsystem of a gem-gum factory
• Lagrangian mechanics for nanomechanical circuits

External links

Online simulator for the physical spintronics kit:
https://simulator.spintronics.com/

Wikipedia:

• Impedance analogy
• Mobility analogy
• Mechanical–electrical analogies
• Analogical models