From: Charles Patton charles.r.patton@........

Date: Sat, 05 Jul 2008 22:49:31 -0700

Brett, 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. Regards, Chas. Brett Nordgren wrote: > Charles, > > 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. > > Regards, > Brett > > At 04:07 PM 7/5/2008 -0700, you wrote: > >> Chris, >> 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. >> Regards, >> Chas. > > > __________________________________________________________ > > 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)