PSN-L Email List Message
Subject: Re: Is a Lehman geometry rolling pivot inherently unstable?
From: Charles Patton charles.r.patton@........
Date: Sat, 05 Jul 2008 22:49:31 -0700
It would seem me, too, that the figure-8 pivot is very similar to a ball
on a plate except that the figure-8 pivot would have about twice the
effect due to the point of contact moving along a second curved surface
adding to the effective pivot point movement. One quick observation
-- you say, "...traced out a circle, accurate to +/- 0.00043" or 43
microinches per degree."
But 0.00043" is 430 microinches, not 43 microinches and in my brief
conjecture, 100 microinches is enough to lead to failure of the swing
trajectory in a 20 second period Lehman.
Brett Nordgren wrote:
> Just a quick comment relating to my studies of the geometry of the
> 'figure-8' pivot, which may also apply to the rolling geometry (or
> not). What I found was that, although the axis of rotation moved
> somewhat as the hinge rotated, a point on the beam actually described
> quite an accurate circular arc. In my extreme example, using 1" dia
> rollers and a 5" boom, the center of rotation moved about 0.009" per
> degree of rotation, however, over +/- 5 degrees, the end of the beam
> traced out a circle, accurate to +/- 0.00043" or 43 microinches per degree.
> After looking at it for awhile it became apparent that, as the center of
> rotation changed, the instantantaneous radius of curvature also changed
> to largely compensate, resulting in the nearly circular locus. When I
> get a free moment, I'll see if a similar analysis gives similar results
> for your rolling pivot.
> At 04:07 PM 7/5/2008 -0700, you wrote:
>> Admittedly my description is brief. I left unsaid that everything is
>> perfectly rigid and properly set up. The pivot types I'm really
>> interested in are ones used on a a Lehman geometry where rolling pivot
>> types are used, such as a carbide ball in the end of the beam rolling
>> on a hard plate and the same for the suspension wire/beam to the upper
>> pivot point on the upright. Not the crossed flexure (Bendix bearings,
>> or single flexure -- although I asked the question does this apply to
>> them, too?) What I'm trying to think about is not spurious effects
>> such as compression (Rockwell hardness), and lack of sufficient
>> rigidity in the structure, but rather the effect that a rolling
>> geometry inherently has. If one thinks about what happens when a
>> properly adjusted Lehman gate swings, the plumb bob is taking a
>> flatter and flatter trajectory as the period is increased. As I
>> recall, a 10 second period pendulum will lift about 1/2 a thousandth
>> inch per 1 inch swing. So if the geometry causes the bob to drop 1/2
>> a thousandth per inch of swing then it cancels what other wise would
>> be a stable adjustment. The problem is that a 20 second pendulum
>> would be more like 0.0001"/inch. Even a very small ball-point pen
>> ball is perhaps 0.04" in dia --so 1/2 diameter is 200 times 0.0001".
>> So a very small swing starts to have an accelerating change of length
>> leading to a total flatting of the bob trajectory and then "flopping"
>> of the pendulum bob. This swing may come from slight floor tilt and
>> what might otherwise be stable is not because the geometry leads to
>> unstability. The only saving grace I see is that the twist that also
>> takes place is in the direction of increasing stability (lifting the
>> bob) but in my mind it is secondary in effect to the primary drop due
>> to the effective pivot point change leading to an apparent pivot
>> point/beam/bob length change.
>> Now to discuss the flat flexure problem. When rolling points are used,
>> the lower point is in compression on a plate and the upper is in
>> compression on the opposite side such that the both lead to dropping
>> the bob as it swings. Now if flat foil flexures are used, the upper
>> flexure is on the bob side and initially bends at some point, but as
>> the bob moves sideways, doesn't the flexure point move towards the
>> upright? If so the upper supension is effectively getting longer,
>> lowering the bob during a swing, again unstable. The lower beam
>> flexure is in tension on the back (further away from the bob) side of
>> the upright. This time it's not clear to me which way the bend point
>> moves, if at all, however my suspicion is that the bend point moves
>> toward the upright which also leads to an effective shortening of the
>> bottom beam, again the unstable lowering of the bob.
>> Much of this came about as I conjectured why so many anecdotal stories
>> about the difficulty of adjusting Lehmans in the long period realm.
>> So the thought experiment described above.
> Public Seismic Network Mailing List (PSN-L)
> To leave this list email PSN-L-REQUEST@.............. with the body of
> the message (first line only): unsubscribe
> See http://www.seismicnet.com/maillist.html for more information.
Public Seismic Network Mailing List (PSN-L)
[ Top ]
[ Back ]
[ Home Page ]