PSN-L Email List Message
Subject: Re: pivots vs bearing structures
Date: Mon, 18 Feb 2008 21:27:57 -0700
Charles, Thanks, I think I understand the idea. If I have other question I
----- Original Message -----
From: "Charles R. Patton"
Sent: Monday, February 18, 2008 7:09 PM
Subject: Re: pivots vs bearing structures
> 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?
>> ----- Original Message ----- From: "Charles R. Patton"
>> Sent: Monday, February 18, 2008 10:22 AM
>> Subject: Re: pivots vs bearing structures
>>> Hi Ted,
>>> 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.
>>> 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
>>>> If I can I would like to try your idea in the shop.
>>>> ----- Original Message ----- From: "Charles Patton"
>>>> Sent: Sunday, February 17, 2008 10:08 PM
>>>> Subject: Re: pivots vs bearing structures
>>>>> 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
>>>>> 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.
>>>>> Charles R. Patton
>>>>> Randall Peters wrote:
>>>>>> 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).
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