In a message dated 2008/02/19, Brett3mr@............. writes:

> Both those issues were of great interest to pendulum clock makers.  The=20
> latter was studed by no less of an authority than Pierre-Simon LaPlace who=
=20
> came to two conclusions.  First, a (very) small radius would be better tha=
n=20
> a knife-edge.  Second, it might even be possible to consider a roller.  He=
=20
> studied the geometry and concluded that the deviation from pendulum arc=20
> circularity was a small fraction of the edge radius.  That and very=20
> thorough analyses of flexure suspensions, including effective pivot point=20
> and nonlinear losses are covered in detail in the most excellent book  by=20
> A. L. Rawlings "The Science of Clocks & Watches  3rd edition, 1993"=20

Hi Brett,

       I dug out my copy, but it is unfortunately silent on many of the=20
suspensions that we might want to use. In particular, the rolling wire/foil=20=
types=20
have an accurate centre of rotation, extremely low hysteretic loss and ALSO=20
have ZERO TORQUE. The variation of stiffness and torque are two of the probl=
ems=20
of Cardan single foil suspensions, but crossed wires/foils are a bit better.=
=20
=20
> >So the way I perceive it, a big problem is having a system where the axis=
=20
> >of rotation remains constant, quite accurately.  Unfortunately the only=20
> >solutions I keep coming back to are bearing style things.  So then the=20
> >question becomes, =E2=80=9CCan a bearing be made that has low loss?=E2=
=80=9D =20

    Categorically yes.

       But a > concurrent question is do I really need a very low amount of=20
> loss?  I know recent discussions have experimented with crossed pivots of=20
> extremely low=20
> >loss.  Why?  The immediate next step will be to add a damper to get to=20
> >something close to critical damping.   My understanding is that the only=20
> >reason to have low loss is to be able to use lots of feedback to lengthen=
=20
> >the period.  But if the period can be achieved directly, and it includes=20
> >some damping, so what?  In my mind, the important item is=20
> >hysteresis/stiction.   As bearings and bearing surfaces can easily be=20
> >ground to a ten-thousandth or even better, 10 or 20 second period=20
> >structures should be in reach.

       Again yes. You need to measure movements down to nano metres, so you=20
need extremely low hysteresis / stiction -.whatever system you use. Feedback=
=20
will not compensate for this.

> For displacement-to-force feedback and possibly for other configurations,=20=
I=20
>=20
> believe you are exactly right.  The main reason for having low pivot loss=20
> is to make it 'easy' for the feedback to do its job, resulting in higher=20
> loop gain.  In general the pivot losses in such an instrument should have=20
> very little effect on the instrument performance.  Consider that the STS-1=
=20
> used bearings which I believe had a relatively poor hysteresis spec., yet=20
> its performance was considered to be pretty good.

       Don't know where you get this from. The STS-1 used crossed foils. The=
=20
problems of making the STS-1 eventually lead to it's replacement!=20

> >Back to possible structures.  The structure I originally presented is=20
> >probably not possible geometrically.  But one that is obviously possible=20
> >is as follows.  Imagine a hollow cylinder (like a pipe) that has been=20
> >centerless ground to be round.  Now take a high density rod like lead or=20
> >tungsten and center it down the axis of the cylinder with fine adjustment=
=20
> >screws so you can offset the center of gravity by a fraction of a=20
> >thousandth.=20

       Let's define out objectives. We don't want extreme periods, just mayb=
e=20
10 seconds instead of 1 second. Trying to get very long periods makes the=20
task increasingly difficult and the small anelastic effects become major=20
problems, as do thermal variations / expansions.

       I am fairly confident that you could extend the period by using=20
feedback to SOFTEN the suspension forces of a standard vertical pendulum. Ra=
ndall=20
can then keep his 1 mm WC low loss bearings - no problem.

    Regards,

    Chris Chapman  =20
In a me=
ssage dated 2008/02/19, Brett3mr@............. 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 <=
BR>
came to two conclusions.  First, a (very) small radius would be better=20=
than 

a knife-edge.  Second, it might even be possible to consider a roller.&=
nbsp; 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 =20=
by 

A. L. Rawlings "The Science of Clocks & Watches  3rd edition, 1993"=
 




Hi Brett,



       I dug out my copy, but it is unfortunat=
ely silent on many of the suspensions that we might want to use. In particul=
ar, the rolling wire/foil types have an accurate centre of rotation, extreme=
ly 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 c=
rossed wires/foils are a bit better. 

 

>So the way I perceive it,=20=
a big problem is having a system where the axis 

>of rotation remains constant, quite accurately.  Unfortunately the=20=
only 

>solutions I keep coming back to are bearing style things.  So then=20=
the 

>question becomes, =E2=80=9CCan a bearing be made that has low loss?=E2=
=80=9D  




    Categorically yes.



       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 t=
o get to 

>something close to critical damping.   My understanding is tha=
t the only 

>reason to have low loss is to be able to use lots of feedback to lengthe=
n 

>the period.  But if the period can be achieved directly, and it inc=
ludes 

>some damping, so what?  In my mind, the important item is 

>hysteresis/stiction.   As bearings and bearing surfaces can ea=
sily 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 movemen=
ts down to nano metres, so you need extremely low hysteresis / stiction -.wh=
atever system you use. Feedback will not compensate for this.



For displacement-to-force feedb=
ack and possibly for other configurations, I 

believe you are exactly right.  The main reason for having low pivot lo=
ss 

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 ha=
ve 

very little effect on the instrument performance.  Consider that the ST=
S-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. Th=
e STS-1 used crossed foils. The problems of making the STS-1 eventually lead=
 to it's replacement! 



>Back to possible structures=
..  The structure I originally presented is 

>probably not possible geometrically.  But one that is obviously pos=
sible 

>is as follows.  Imagine a hollow cylinder (like a pipe) that has be=
en 

>centerless ground to be round.  Now take a high density rod like le=
ad or 

>tungsten and center it down the axis of the cylinder with fine adjustmen=
t 

>screws so you can offset the center of gravity by a fraction of a 

>thousandth.
 



       Let's define out objectives. We don't=20=
want extreme periods, just maybe 10 seconds instead of 1 second. Trying to g=
et very long periods makes the task increasingly difficult and the small ane=
lastic effects become major problems, as do thermal variations / expansions.=




       I am fairly confident that you could ex=
tend the period by using feedback to SOFTEN the suspension forces of a stand=
ard vertical pendulum. Randall can then keep his 1 mm WC low loss bearings -=
 no problem.



    Regards,



    Chris Chapman