I Necessary conditions for energy harvesting

[anorlunda]

I still don't get the question. Perhaps if the OP restated the question, with a diagram and with definitions of the term used, it may become clear.

 

[jbriggs444]

I still don't get the question. Perhaps if the OP restated the question, with a diagram and with definitions of the term used, it may become clear.

Guessing:

We have a rigid, transparent box. We can look inside but cannot touch. Inside is an arbitrary arrangement of gizmos and parts which may be anchored to the inside of the box, may be bouncing around or may be connected to each other. There are mechanical energy sources within the box. Maybe gasoline motors. Maybe electric motors with some wires piping in electrical energy from outside.

We are allowed to attach an arbitrary mechanism to the outside of the box and to anchor the mechanism, if desired. Our goal is to maximize the average mechanical power that we can harvest from the bouncing, twisting and shaking of the box.

We are not allowed to harvest heat energy. No Maxwell's demon.

 

[A.T.]

I still don't get the question.

See post #20.

 

[anorlunda]

See post #20.

#20 says

You have a closed box that undergoes some given cyclic motion. Inside you have a suspended mass. What is the general approach to get the upper limit for the energy per cycle that you can extract continuously from the relative motion of the box and suspended mass?

Define extract.

The motion of the box is unlimited. Why then is energy not unlimited? Alternatively, why us there any upper limit at all?

Sorry, still clear as mud.

 

[A.T.]

...just to charge your PC battery is not a worthwhile activity

Powering sensor boxes this way makes perfect sense, as it allows them to work continuously and autonomously.

 

[A.T.]

Why then is energy not unlimited? Alternatively, why us there any upper limit at all?

See post #18

 

[sophiecentaur]

Powering sensor boxes this way makes perfect sense, as it allows them to work continuously and autonomously.

Powering a sensor box AND the telemetering power. How much power? We haven't specified the numbers involved and, in Engineering and Physics, the numbers are very relevant. Without setting the scene and specifying some performance parameters there is no proper answer.
A vague idea of harvesting enough energy to supply some very low powered device would need to compete with a couple of primary cells that would work for two years or more. Batteries are pretty autonomous.

 

[Seppo Turunen]

In some cases, yes. But if you have to stop your industrial production line to change batteries, you may think differently. Also, if you have hundreds of sensor units in your production plant or in your vehicles, your maintenance team may not be able to cope with the additional workload without hiring more people.

 

[anorlunda]

@Seppo Turunen , please clarify your question. One one hand, it sounds like you're trying to solve an industrial problem. On the other hand, it sounds like some kind of theoretical gedanken (thought) exercise. It is not fair to ask us to provide answers when we are not sure of the question.

 

[sophiecentaur]

In some cases, yes. But if you have to stop your industrial production line to change batteries, you may think differently. Also, if you have hundreds of sensor units in your production plant or in your vehicles, your maintenance team may not be able to cope with the additional workload without hiring more people.

If the circumstances were different then the solution would be different.
We would all probably be in agreement if we actually knew what the target of the original question was.

 

[A.T.]

We haven't specified the numbers involved and, in Engineering and Physics, the numbers are very relevant.

Since this is the Physics sub-forum, not the Engineering/Homework one, it seems appropriate to ask about a general approach to the problem, rather then just one specific case.

If the circumstances were different then the solution would be different.

Yes, that is the point of physics: Find general approaches that are applicable to a wide range of cases.

 

[A.T.]

To compute how much energy you could potentially extract (upper limit), you would have to compute the difference between the achievable maximal and minimal potential energy of the suspended mass over a cycle, based on the varying acceleration field in the local reference frame of the device, and on the limits of the suspended mass' displacement.

@Seppo Turunen
I think my suggestion above was too simplistic. Since the acceleration field in the local reference frame is time dependent, you cannot just look at the potential extrema, but rather would have to find the cyclic local trajectory for the suspended mass that maximizes the work done on it by the acceleration field.

 

[Seppo Turunen]

Sounds logical to me. Trying to think what this would mean for one-dimensional motion in the x direction, it first seems to me that a pretty good candidate trajectory would consist of waiting until the acceleration reaches its positive maximum and then letting the mass quickly move from x min to x max, followed by waiting until the the acceleration reaches its negative peak, and then quickly returning to mass to its original position. The work done would be 2 * m * amax * (xmax-xmin) which seems difficult to surpass. Then I realize that I have not considered the possibility of there being multiple local minima and maxima during the operating cycle. Maybe it is not wise to waste all available leeway in the x direction to a small maximum if there are larger ones coming?

 

[A.T.]

Then I realize that I have not considered the possibility of there being multiple local minima and maxima during the operating cycle.

Yes, exactly. For arbitrary acceleration profiles, you have to do some numerical optimization.

You would need that anyway, if you want to include realistic electrical power generation efficiencies, because these might depend on velocity. So for some parameter combinations the optimum could require that one cycle of the suspended mass corresponds to several cycles of the machine (or vice versa).

 

[sophiecentaur]

Since this is the Physics sub-forum, not the Engineering/Homework one, it seems appropriate to ask about a general approach to the problem, rather then just one specific case.

Show me one bit of Experimental Physics (or Theory about a practical situation) which doesn't include Engineering principles. This thread starts with an Engineering situation,

The reason I am asking for some clarity about the intended application to this is that there are two distinct situations. One, in which the 'prime mover' is moving, independent of what you choose to hang on it (say the con rod of a steam loco and a 100g harvesting device) or is the aim to extract as much Power as possible from the prime mover, without affecting it 'too much'. You have to decide, very early on, which it is that you're interested in.

It's a matter of appropriately Matching (an Engineering idea) the source to the load. The motion of an oscillating magnet / armature needs to be specified if possible. Is it harmonic or is it random? Obviously there is a much better chance of an optimal system is it can be tuned to the source. Has this been considered yet? Some energy should be drawn throughout the interval of the motion.

I remember my second year Electronics lecturer (in my Physics course) being very snobby about his claim that Engineers just didn't understand the necessary Physics in their circuit theory. This thread may be risking the inverse problem.

 

[sophiecentaur]

You would need that anyway, if you want to include realistic electrical power generation efficiencies,

At least you are acknowledging the importance of Engineering in this problem. That's pleasing.

 

[A.T.]

The reason I am asking for some clarity about the intended application to this is that there are two distinct situations. One, in which the 'prime mover' is moving, independent of what you choose to hang on it (say the con rod of a steam loco and a 100g harvesting device) ...

Yes, this. And it was clarified already:

What are known are the trajectory and the speed of the movement. I then assume that both of these can be maintained ...

 

[sophiecentaur]

Yes, this. And it was clarified already:

The question was actually dismissed, rather than dealt with or clarified. If it can be 'maintained' under all circumstances then there is no limit to the value of the suspended mass, nor even, perhaps, how far it can move relative to the oscillating item. It's the equivalent of a sky hook and not a good place to start from.
It seems to be equivalent to a Constant Voltage or Constant Current source so the problem reduces to 'take as much energy as you want'. Why not include the concept of matching here?

 

[A.T.]

then there is no limit to the value of the suspended mass, nor even, perhaps, how far it can move

A sensor box obviously has such limits:

I want to attach to a push rod of an engine a sensor box that uses the movement of the rod to power its circuitry.

 

[sophiecentaur]

A sensor box obviously has such limits:

Of course. Limits imposed by Engineering considerations. Nothing can be treated as 'obvious' - you know that.