PSN-L Email List Message

Subject: Re: pivots vs bearing structures
From: tchannel1@............
Date: Mon, 18 Feb 2008 21:27:57 -0700

Charles, Thanks,  I think I understand the idea.  If I have other question I 
will ask.
----- Original Message ----- 
From: "Charles R. Patton" 
Sent: Monday, February 18, 2008 7:09 PM
Subject: Re: pivots vs bearing structures

> Ted,
> The whole thing is an upside down pendulum.  Think about a rocking chair. 
> It has the same properties as this cylinder.  The center of mass of the 
> body sitting in the chair is below the center of the circle formed by the 
> rockers on the floor.  So the top of the rocker and the person rock 
> back-and-forth on the floor.  Now imagine that the floor is jerked by some 
> force such as an earthquake.  The mass of the body in the chair stays in 
> place but the rockers stay in contact with the floor but they assume a 
> “rocked” position.  Now the chair will rock back and forth over the new 
> position.  So by analogy, due to inertia this rolling pendulum will tend 
> to stay in position while the plate is moved, but due to the contact with 
> the plate the cylinder will be rotated. The result will be that the weight 
> will want to roll back to restore the weight to its lowest point so the 
> cylinder will rock until it dissipates the potential energy transferred to 
> it by the plate displacement.  This is exactly what happens to a normal 
> pendulum.  The bob stays in place while the support pivot moves in 
> synchronization with the floor, so if the bob position relative to the 
> floor is measured, it yields the displacement due to the seismic event. 
> In exactly the same way the rolling cylinder’s position will be displaced 
> relative to the floor/surface plate in proportion to the seismic event. 
> (It’s interesting to note that you can have a free 2X gain simply by 
> monitoring the position of the top of the cylinder rather than the axis of 
> it.)  What complicates this rolling pendulum is that it will also have 
> significant rotational inertia.  So it lowers the resonant frequency a bit 
> from what might be expected by the weight unbalance distance plugged into 
> a simple pendulum equation based on T=2*Pi*Sqrt(l/g).  (Recognize that 
> this equation only works on small angles and assumes all weight is 
> concentrated at the bob point.  Furthermore, in some ways it obscures the 
> relation of the swing angle vs. the height change of the bob weight by 
> talking about the length of the pendulum.  The length is only important in 
> that as it increases, it reduces the amount the weight is lifted vs the 
> distance the pendulum swings.  The cylinder pendulum brings to the fore 
> that the weight is lifting by very small amounts as the pendulum swings.) 
> You don’t even need sine/cosines to do the simple math for this one. 
> Imagine a 1000” pendulum.  Now swing it 1”.  What’s the lift?  Since the 
> numbers are so big, just take the square root of the sum of the squares 
> (the old Pythagorean theorem) and subtract the pendulum length. (Sqrt ( 
> 1000^2 + 1^2)) – 1000 = 0.0005”
> (The purists out there may hate me as this isn’t set up geometrically 
> correct, but it’s simple and quick and close enough that I can’t measure 
> the difference without a laser interferometer.)
> So to tweak the cylinder pendulum into a 10 second period you’ll need to 
> be able to tweak the center of mass to something like 0.007 inch off 
> center (not likely with my micrometer!)  But the rocking period comes to 
> the rescue.  Just keep tweaking until the period is about right.  Go too 
> far and the cylinder will want to topple, i.e., rotate 180 degrees and 
> come to a rest.
> In practical terms it will have some of the same problems all long period 
> pendulums do—notably the sensitivity to tilt inherent in long period 
> pendulums.  As Randall points out, friction is critical.  An important 
> consequence of the weight height changing very little for long periods is 
> that the restoring force – that force trying to return the pendulum bob or 
> cylinder back to its resting point is being reduced to very small numbers. 
> And that change in resting point is the very item being measured for 
> indication of a seismic event.  The one thing that this should have over 
> standard pendulums is it’s ability to handle big seismic displacements, 
> perhaps plus/minus two inches or so for a three inch cylinder. 
> Potentially another advantage would be better temperature stability due to 
> the geometric symmetry not present in a Lehman for instance.  The simple 
> test will be to build it, give it a gentle shove and see if it can 
> approach a 10 or 20 second period of rocking back and forth.  Another 
> point I want to mention is that I’m sure the “Rollamite” wires are 
> critical for another reason.  At a microscopic level, the surfaces of the 
> plate and cylinder, even if mirror polished, will have hills and valleys 
> that will want to “lock” the cylinder to a position due to the low 
> restoring force mentioned above.  The wires will have only point contacts 
> that I feel will help ameliorate the problem, so although Chris mentions 
> thin foils, I lean in the direction of thinking fine wire is better.
> Hope this helps,
> Charles Patton
> tchannel1@............ wrote:
>> Charles,  Yes the .jpg helps...  Please can you now explain how a 
>> pendulum is attached, or to which part it is attached?
>> Ted
>> ----- Original Message ----- From: "Charles R. Patton" 
>> To: 
>> Sent: Monday, February 18, 2008 10:22 AM
>> Subject: Re: pivots vs bearing structures
>>> Hi Ted,
>>> See:
>>> It's about 350 KB so you can download it at your leisure.
>>> The "Rollamite" like wires primarily keep the orientation of the 
>>> cylinder under control.  They are also likely to make the cylinder less 
>>> likely to hang or stick due to dust and lint ( the relatively high 
>>> pressure of the wires will cut through many of the contaminants. I 
>>> recommend non-magnetic parts, lead, brass, aluminum so that the changing 
>>> magnetic field of the earth is not a factor.  (It might not be anyway, 
>>> but I believe in trying to head off some variables from the start.)
>>> Hope this makes the idea a bit clearer.
>>> Regards,
>>> Charles Patton
>>> tchannel1@............ wrote:
>>>> Hi Charles and Others,  I have a small shop and love to build new 
>>>> things, some work, some don't, but I always learn in doing.
>>>> I can not picture your idea, could you send me a sketch?   I have made 
>>>> a couple of the Folded Pendulums sensors and found the concept very 
>>>> promising.
>>>> If I can I would like to try your idea in the shop.
>>>> Ted
>>>> ----- Original Message ----- From: "Charles Patton" 
>>>> To: 
>>>> Sent: Sunday, February 17, 2008 10:08 PM
>>>> Subject: Re: pivots vs bearing structures
>>>>> Randall,
>>>>> I understand the folded pendulums you mention, but I want to touch on 
>>>>> several related subjects.  Back of the napkin pendulum length for 10 
>>>>> secs is about 1000 inches.  A one inch swing would be a ½ milli-inch 
>>>>> rise. This gives me a bit of feel/insight on possible error 
>>>>> mechanisms. It strikes me that one general problem with flexures is 
>>>>> that they are not a pivot in the sense of having a known axis like a 
>>>>> bearing does.  I haven’t totally worked out the ramifications, but I’m 
>>>>> sure this is the reason many amateurs have problems taking Lehman 
>>>>> style instruments to long periods. Even if they’re not using flexures, 
>>>>> pivot points are a round point that also may or may not have a 
>>>>> constant point of rotation, depending whether it is rotating in a 
>>>>> pocket or rolling on the surface of its pivot support, so the length 
>>>>> may well be getting shorter as it rotates and a shorter length on the 
>>>>> beam equates to the weight dropping, not rising as is necessary for 
>>>>> stability and so the distance to un-stability is around ½ a 
>>>>> milli-inch.
>>>>> So the way I perceive it, a big problem is having a system where the 
>>>>> axis of rotation remains constant, quite accurately.  Unfortunately 
>>>>> the only solutions I keep coming back to are bearing style things.  So 
>>>>> then the question becomes, “Can a bearing be made that has low loss?” 
>>>>> 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.
>>>>> 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.  (The hollow cylinder construction is to 
>>>>> reduce the rotational moment of inertia.)  Now place this cylinder on 
>>>>> a surface plate (again a commonly available object that can be 
>>>>> obtained flat to fractions of a ten-thousandth.) that is level better 
>>>>> than a ten-thousandth per inch.  Use very fine steel (a few 
>>>>> thousandths) wire as Rollamite bands.  The cylinder should roll to 
>>>>> center the mass down. So lets assume a three inch dia. pipe.  That’s 
>>>>> roughly 10 inches circumference, or 2.5 inches to 90 degrees, and 
>>>>> raising the mass by the amount of the off-center that could be easily 
>>>>> set to 1 mill.  Easily greater than 10 seconds rotation period? Once 
>>>>> you have that structure in mind, chop off ¾ of the cylinder not in 
>>>>> contact with the surface plate. As long as the center of mass is below 
>>>>> the center of rotation this has become an upside down pendulum that is 
>>>>> stable on the surface place and the rotational inertia has been 
>>>>> reduced to a minimum.  The position sensor is placed to monitor the 
>>>>> mass at the ‘top’ of this pendulum.
>>>>> Just some more idle musings.
>>>>> Regards,
>>>>> Charles R. Patton
>>>>> Randall Peters wrote:
>>>>>> Charles,
>>>>>>     In effect, what you have described, is to take advantage of the 
>>>>>> same property that is used by the folded pendulum, which
>>>>>> comprises both a `regular' pendulum and also an 'inverted pendulum. 
>>>>>> Separated from each other and connected by a rigid
>>>>>> horizontal boom, their relative influence ('restoring' from the one, 
>>>>>> and 'destoring' from the other) is determined by how close
>>>>>> the inertial mass is placed to one or the other.
>>>>>>     Because the folded pendulum can be made to have a very long 
>>>>>> period, upper valuve being limited by mesoanelastic complexity,
>>>>>> it appears clear then, that the feedback drive of the primary 
>>>>>> pendulum by an inverted secondary one is capable (for ideal
>>>>>> meaterials) of very long period indeed, and therefore very great 
>>>>>> sensitivity.  Moreover, since the adverse effects of material
>>>>>> problems can be essentially eliminated by means of the feedback, I 
>>>>>> see this as a really attractive idea to try and demonstrate!
>>>>>> Are there any takers?  (meaning folks like Brett who know how to make 
>>>>>> control systems work right).
>>>>>>     Randall
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