Size constraints of generators

[milkman_78]

Based on what I have gathered so far, I don't see why a micro-scale generator wouldn't work, but then again I am a geographer with modest calculus skills. My biggest problem is not knowing how much I don't know, and I am hoping some kind and wise soul on PF can cure my ignorance.

Let's say I need to generate 3.5 volts/0.5 amps to light up an LED bright enough to be visible outside in daylight, but the micro-generator must fit in a cylinder ~ 2.5mm diameter and ~4.0mm to 4.5mm in length.

I was thinking of a design that would exploit "printed" circuitry and "print" a serpentine "coil" consisting of say 20 windings each 4.0mm long (roll the printed circuit into a tube that's 2.5mm in dia.). If I took a diametric rod magnet that was 2.4mm in diameter and 4.0mm long and placed it concentrically inside the cylindrical coil, the distance between the magnet and the windings would be 0.5mm.

Unless I've missed something, the remaining parameters needed to calculate output would be the Gaussian strength of the magnet and the number of times the magnetic field cycles through the coil in a second (to determine voltage), and the cross section area of a winding (to determine amperage).

Is there a mathematical relationship between the magnet's Gauss rating and the rate of flux change that would satisy the volage requirement? If so, I would need help deriving a function to express that relationship. How do I determine the minimum area of a winding's cross section needed for 0.5 amps (I don't know how "thick" I can print)?

Thanks in advance!

 

[Simon Bridge]

Welcome to PF;
As you get smaller you need to change technology.
http://www.techtimes.com/articles/1...lest-electric-generator-at-one-atom-thick.htm

First reaction: it looks like you are thinking in terms of ideal materials in large-scale approximations.

For the device you describe - work out the biggest magnet you could use (it's a physcally small magnet - you can google for manufacturer specs) and then work out how fast you have to spin the coil to get the required Vrms and power. Then work out if the components are strong enough. This still ignores the way physics changes as you get to small scales... but should start you off.

 

[milkman_78]

Thank you Simon,

I investigated the link you recommended and aparrantly piezoelectric generation does not scale well. From the article, " layering the material has to be done in a specific way: an odd number of layers must be used, or the electrical current will cancel itself out. In addition, the more layers that are used, the weaker the electrical current." The article did not give specs on the relationship between generator size dimension and electrical output, but I will certainly delve further into it.

I am trying to determine if I can exploit angular momentum that is already being generated for a gyroscopic application (2 birds:1 stone), so I will check out manufacturer's magnet sizes and specs.

Thank's again for your input. Can you please lead me to some formulae to help with my calculations? I've employed Faraday's Law, but do not know how to gauge the strength of field reduction as the spacing between generator and magnet's surface are varied.

 

[Babadag]

Try this article:

http://elearning.vtu.ac.in/16/ENotes/Elec%20Mac%20Des/Unit7&8-VH.pdf

Nevertheless here it is about large machines the principles are the same.

 

[Simon Bridge]

.. although the principles are the same - the designs usually involve approximations that may not be valid on a small scale.
At tiny scales, small differences in consistency can have a big impact. High speeds will also run foul of hysteresis effects.
Generally, as you scale down a machine, the tolerances have to be so much more exact.

Fortunately, the described device is not quite quantum scale...

Can you please lead me to some formulae to help with my calculations? I've employed Faraday's Law, but do not know how to gauge the strength of field reduction as the spacing between generator and magnet's surface are varied.

That would be very sensitive to geometry ... so long as the magnet is much bigger than the "coil" you should be able to keep the coil in the "uniform" region.

 

[milkman_78]

For the device you describe - work out the biggest magnet you could use (it's a physcally small magnet - you can google for manufacturer specs) and then work out how fast you have to spin the coil to get the required Vrms and power. Then work out if the components are strong enough.

Thanks! This was great advice and got me to the tweaking stage!

 

[milkman_78]

Try this article:

http://elearning.vtu.ac.in/16/ENotes/Elec%20Mac%20Des/Unit7&8-VH.pdf

 

[milkman_78]

Thanks for the article. The scales of application are indeed different, but the formulae will be very useful!

 

[Simon Bridge]

Thanks! This was great advice and got me to the tweaking stage!

... well done: for your purposes, you don't want to go to very detailed calculations anyway, these can get arbitrarily complicated. See what you can achieve under proof of concept first.