From: ChrisAtUpw@.......

Date: Tue, 19 Feb 2008 02:05:01 EST

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 pointand 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 aconcurrent 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., yetits 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