PSN-L Email List Message

Subject: Re: question for force balance experts
From: Brett Nordgren brett3nt@.............
Date: Wed, 17 Aug 2011 10:45:04 -0400


Randall,

At 09:05 AM 8/17/2011, you wrote:
>Maybe you can answer the following question and=20
>simply tell me if it=92s a stupid hypothetical scenario?
>      Years ago as I thought about force balance=20
> applied to seismology, I thought about the following.
>Why not take a simple =91mass measuring instrument=20
>(like a commercial Mettler laboratory balance)=92=20
>that also uses force feedback; and =91jazz up the=20
>electronics=92 to look at earthquakes with it?  I=20
>assume that the obvious limitation of so doing=20
>derives from the fact that the =91natural period=92=20
>of this package, without the feedback, is prohibitively short.

I believe that if sufficiently sensitive (lots of=20
decimal places) it would act as an accelerometer,=20
flat to DC. (F=3DMA)  It's not clear how well it=20
would respond to rapid ground motions, but at the=20
low end it should do fine.  The limitation would=20
be in achieving the required extreme resolution=20
while still supporting a sufficiently large=20
mass--likely not possible using traditional electronic balance designs.

>And we all know that period lengthening is what=20
>yields high sensitivity.  It is a simple matter=20
>to show that the sensitivity of an=20
>=91electronics-less=92 instrument is proportional to=20
>the square of the period.  In the case of a=20
>pendulum I will (for anybody interested)=20
>describe how this works in a manner that is very=20
>easy to understand.  For other instruments you=20
>have to use more challenging mathematics.

I would, instead, opt for a spring-less=20
instrument in which the entire mass was supported=20
by the feedback coil-magnet.  Relative to our=20
present designs it would require significantly=20
extending the dynamic range of the integrator=20
circuit output, (to provide ~100mA) which is why,=20
although it would work, it would also be too=20
noisy.  You might also be able to do it with the=20
present circuit by summing a very stable 100mA=20
bias current  into the coil in place of the spring.

As I now believe I understand it, the only real=20
function of the spring is to support the mass=20
near the desired rest position, while at the same=20
time being sufficiently 'soft' so as to not=20
interfere with the operation of the feedback=20
force transducer as it controls the mass.  Which=20
is to say, the spring should be compliant enough=20
to not excessively reduce the loop gain at=20
frequencies below the spring-mass resonance.  In=20
our instruments sufficient compliance corresponds=20
with a spring-mass resonance of around 3 seconds.

>        Now if you say, =93yes Peters, this cannot=20
> work for the reason you just gave; then explain=20
> to me why not.   If you claim that the=20
> over-riding constraint is the electronics, then=20
> we immediately have another challenge; i.e.=20
> what do we do to improve the electronics to=20
> make it possible?  On the other hand, if the=20
> electronics is indeed adequate to the task=ADthen=20
> I can only come to the following=20
> conclusion=ADthat it cannot work because of a=20
> spring problem!  After all, perfectly adequate=20
> electronics should compensate for any degree of=20
> hardness in a perfect Hooke=92s law spring.
>       If you agree with my conclusion, then you=20
> must also recognize that there is more to the=20
> complexity of springs than we have naively assumed.
>Randall

My current conclusion is that the spring doesn't=20
really have much to do with the fundamental=20
operation of a feedback seismometer.  I sort of=20
consider it as a necessary evil.

Brett



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