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Subject: Re: Lehman
From: Karl Cunningham karlc@..........
Date: Fri, 15 Jun 2001 09:54:36 -0700

Dave --  Here are some of my thoughts...

I believe you are correct that there is some friction in bending the 
spring.  "Hysteresis loops" exist for bending all materials but are pretty 
low in good springs.  I don't have a feel for what good quality spring 
material might exhibit, but I would expect it might be better than 0.1% if 
conservatively loaded.

Another source of hysteresis is in anchoring the spring to the supporting 
material.  The stress in the outer fibers of the spring at the anchor must 
be less than the strength of the anchor mechanism, or sliding will occur 
(with associated losses).  And even when not stressed past their tensile 
strength, adhesives tend to have much greater hysteresis losses than 
metals.  One solution is to have a thick cross section in the spring where 
it is anchored so the stress in the outer fibers is reduced, and have a 
thinner cross section away from the anchor where bending is desired.  This 
makes the spring a lot more complicated, though.

Here's a theory I have about the hysteresis.  I have thought that the 
effect of hysteresis in the Lehman can be modeled as a stiff spring 
connected to parts with both static and dynamic friction components.  (The 
stiff spring represents the spring constant of the boom.)  Whenever outside 
forces stop acting on the system, an equilibrium is reached with stress on 
the stiff spring balanced by a component of gravity resulting from any 
offset in the pendulum from its lowest point.  This stiff spring effect 
results in much shorter natural period and lower sensitivity.  Once the 
static friction component is overcome by stressing the stiff spring enough, 
the natural period lowers and the dynamic friction component represents the 
loss of the system.  If outside forces are again removed, the system may 
come to rest with the frictional component at a different point and with a 
different stress on the stiff spring.  The more the stress in the stiff 
spring when things come to rest, the easier it is for the static friction 
to be overcome since gravity is helping.

The rolling contact also suffers from friction due to the small indentation 
resulting from pressure at the point of contact.  There is hysteresis in 
deforming the material and also some sliding that occurs between the two 
surfaces being deformed and then restored as the deformation follows the 
area of contact.

Rolling contacts are also subject to dust and contamination which adds to 
friction.  I suppose even a fingerprint might be significant.

My force-balance seismometer (which mechanically is basically a Lehman) 
uses a carbide pivot point against a hardened steel plate.  I saw a 
significant improvement in sensitivity after putting a drop of oil on the 


--On Friday, June 15, 2001 11:13 AM -0400 David Saum  

>> From:    CapAAVSO@.......
>> Date:    Thu, 14 Jun 2001 10:01:42 EDT
>> A low friction pivot is still a friction pivot!!! A friction-free pivot
> has
>> been described consisting of a ring going around the lower pivot post
>> with
> a
>> spring wire under tension in back of the post. The spring stores energy
> and
>> gives it back to provide a completely friction-free pivot.
>  It is not clear to me why a "real" spring is more "friction-free" than a
> ball
> bearing rolling on a glass plate.  Any real spring will generate heat as
> it bends
> (from internal friction).  Without test data I do not see that either
> pivot design
> has inherently lower friction.  However, the ball bearing technique seems
> to be simpler to build since it does not require a machine shop.
> Ciao,
> Dave

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Larry Cochrane <cochrane@..............>