Chris,

At 02:05 AM 2/19/2008 -0500, you wrote:
>In a message dated 2008/02/19, Brett Nordgren writes:
>
>>Both those issues were of great interest to pendulum clock makers.  The
>>latter was studed by no less of an authority than Pierre-Simon LaPlace who
>>came to two conclusions.  First, a (very) small radius would be better than
>>a knife-edge.  Second, it might even be possible to consider a roller.  He
>>studied the geometry and concluded that the deviation from pendulum arc
>>circularity was a small fraction of the edge radius.  That and very
>>thorough analyses of flexure suspensions, including effective pivot point
>>and nonlinear losses are covered in detail in the most excellent book  by
>>A. L. Rawlings "The Science of Clocks & Watches  3rd edition, 1993"
>
>Hi Brett,
>
>        I dug out my copy, but it is unfortunately silent on many of the 
> suspensions that we might want to use. In particular, the rolling 
> wire/foil types have an accurate centre of rotation, extremely low 
> hysteretic loss and ALSO have ZERO TORQUE. The variation of stiffness and 
> torque are two of the problems of Cardan single foil suspensions, but 
> crossed wires/foils are a bit better.

The rolling foil design is the one I like the best, but I would feel better 
if there were more experimental results to prove it's as good as I think it 
will be.  see:   http://bnordgren.org/seismo/zerohng2.pdf

>        But a
>>concurrent question is do I really need a very low amount of loss?  I 
>>know recent discussions have experimented with crossed pivots of extremely low
>> >loss.  Why?  The immediate next step will be to add a damper to get to
>> >something close to critical damping.   My understanding is that the only
>> >reason to have low loss is to be able to use lots of feedback to lengthen
>> >the period.  But if the period can be achieved directly, and it includes
>> >some damping, so what?  In my mind, the important item is
>> >hysteresis/stiction.   As bearings and bearing surfaces can easily be
>> >ground to a ten-thousandth or even better, 10 or 20 second period
>> >structures should be in reach.
>
>
>        Again yes. You need to measure movements down to nano metres, so 
> you need extremely low hysteresis / stiction -.whatever system you use. 
> Feedback will not compensate for this.

Don't agree with Chris here.  Without feedback, mechanical issues are 
important, but if you have reasonably strong feedback (loop gain), which 
should be possible at all frequencies in the mid and low region, any 
*small* effects, linear or non-linear will be made insignificant by the 
feedback.  However, at the highest frequencies, the spring and pivot will 
influence the performance, because the feedback disappears there.

>>For displacement-to-force feedback and possibly for other configurations, I
>>believe you are exactly right.  The main reason for having low pivot loss
>>is to make it 'easy' for the feedback to do its job, resulting in higher
>>loop gain.  In general the pivot losses in such an instrument should have
>>very little effect on the instrument performance.  Consider that the STS-1
>>used bearings which I believe had a relatively poor hysteresis spec., yet
>>its performance was considered to be pretty good.
>
>
>        Don't know where you get this from. The STS-1 used crossed foils. 
> The problems of making the STS-1 eventually lead to it's replacement!

See http://www.c-flex.com/technicaldata.pdf  which shows that the 
crossed-foil bearings take a "set" each time they are rotated which I 
consider to be a pretty good indication of significant hysteresis.  This is 
consistent with the observation that the foils must undergo considerable 
bending stress near their points of connection with the sleeves.  I believe 
that C-Flex is the successor to a series of companies which made these 
bearings and am assuming that Streckeisen used either them, or something 
very similar in the STS-1.  Crossed foils are not necessarily low 
hysteresis.  That's why I'm partial to the rolling foil design.

>> >Back to possible structures.  The structure I originally presented is
>> >probably not possible geometrically.  But one that is obviously possible
>> >is as follows.  Imagine a hollow cylinder (like a pipe) that has been
>> >centerless ground to be round.  Now take a high density rod like lead or
>> >tungsten and center it down the axis of the cylinder with fine adjustment
>> >screws so you can offset the center of gravity by a fraction of a
>> >thousandth.
>
>        Let's define out objectives. We don't want extreme periods, just 
> maybe 10 seconds instead of 1 second. Trying to get very long periods 
> makes the task increasingly difficult and the small anelastic effects 
> become major problems, as do thermal variations / expansions.
>
>        I am fairly confident that you could extend the period by using 
> feedback to SOFTEN the suspension forces of a standard vertical pendulum. 
> Randall can then keep his 1 mm WC low loss bearings - no problem.

Chris, can you give a bit more detail about what you're thinking here. 
(block diagram or such)  Almost by definition, any significant positive 
feedback is going to oscillate.  Are you possibly thinking of using 'feed 
forward', sometimes called 'open loop compensation' here.  That's not 
feedback but is a technique for reducing error effects, usually used to 
moderately improve performance in combination with the usual negative 
feedback.

I won't say that positive feedback can *never* be of use, but it has to be 
combined with an even stronger dose of negative feedback in order not to 
oscillate, and even then you have to be careful.

Brett



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