Gary,

I agree with Chris that the decay times are likely being affected by the=20
rigidity of your setup.  Precision pendulum clock makers learned long ago=20
that they needed to have an extremely rigid mounting from which to hang the=
=20
pendulum, or the energy loss could be considerable.  Air resistance is a=20
smaller effect at our long periods, but with a good enough pivot, you might=
=20
be able to see its effect.

It's my opinion that a decaying exponential is a decent approximation to=20
what you will normally observe.  There are undoubtedly second-order=20
nonlinearities due to all sorts of things, as observed by Dr.=20
Peters.  Plotting the difference between what you observe and a theoretical=
=20
exponential curve might be interesting, but I argue that the difference=20
will not be all that large.  Possibly worth some more experiments?

It would be interesting to see how a rolling foil pivot would=20
perform.  See:  http://bnordgren.org/seismo/RollingLehman.pdf  and=20
http://bnordgren.org/seismo/zerohng2.pdf    In theory that should have=20
virtually no friction.  It might not be easy to implement as the hinge=20
would need to be on the back side of the support from the boom, and you=20
would need some sort of way for the boom to wrap around the support.  That=
=20
is shown in "RollingLehman.pdf", which is a top view of two possible ways=20
of designing the pivot.  That pdf also includes a sketch of the hinge=20
design which I got from Chris Chapman.  Also, you would need to carefully=20
adjust the support wire length so that the tension on the upper and lower=20
foils will be roughly equal.  With that arrangement, most damping would=20
likely be from motions of the top of the support rod.  The foils should be=
=20
as thin as you can make them.  If the mass isn't too great, you might be=20
able to use .001" foil.

Regards,
Brett

At 04:07 PM 7/3/2008 -0700, you wrote:

>I have been taking my time to get my first Lehman up and running. First=20
>just to learn how the thing works and then to optimize the operation. In=20
>the last month we have had lots of discussion on various Tungsten rods and=
=20
>other materials for the 2 horizontal rods and ball bearing support system.=
=20
>I first tried various rod materials by trying to get as long resonant=20
>period, but came to the conclusion this was difficult to repeat. Meredith=
=20
>on his 6/25 message got me thinking to take a different approach. I reset=
=20
>the Lehman for a short period (about 10 seconds) and then connected the=20
>sensor to the amplifier and watched the display as the amplitude decayed.=
=20
>Now we have something that can be easily measured and repeated. I=20
>standardized on measurements for 5 minutes or 300 seconds. The decay=20
>equation is Y=3D A e- t/T where t is time and T is the time constant of the=
=20
>system. For materials I used hardened steel, stainless steel, tungsten=20
>carbide (as received), tungsten carbide (mirror polished) 1/8 diameter=20
>rods. The ball bearing is =BC diameter silicon carbide.
>
>Here is what I found for the time constants:
>
>Hardened steel: 154 seconds
>
>Stainless steel: 125 seconds
>
>Tungsten carbide ( as received): 155 seconds
>
>Tungsten carbide (mirror polish): 191 seconds
>
>
>
>The goal is to have a high time constant, indicating lower friction.
>
>
>
>Polishing: The tungsten carbide as received actually had a very good=20
>polish when received, but not quite a mirror finish. I obtained 3 diamond=
=20
>polishing grit sizes, starting out with 35u, then 15u, and finally 3u. The=
=20
>35 and 15u actually made the tungsten carbide rod rougher. I followed=20
>Chris Chapman s method for polishing using a bent sheet of copper with the=
=20
>diamond paste.
>
>
>
>Conclusion: Polished tungsten carbide rods have the lowest friction.
>
>
>
>
>
>Gary
>
>
>
>
>
>
>
>
>
>Gary Lindgren
>
>585 Lincoln Ave
>
>Palo Alto CA 94301
>
>
>
>650-326-0655
>
>
>
>www.blue-eagle-technologies.com
>
>cymonsplace.blogspot.com
>
>
>
>



               My e-mail address above should be working, but if not
you can always use my mail form at: http://bnordgren.org/contactB.html
                            using your Web browser.=20


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