From: ChrisAtUpw@.......

Date: Sun, 6 Jul 2008 14:52:14 EDT

In a message dated 2008/07/06, charles.r.patton@........ writes: > 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 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. Hi Charles, OK But you will likely be in trouble if you use the ball on the end of the arm. Put the ball on the vertical upright and the plate on the end of the arm. The centre of curvature of the ball defines the swing angle and you want this to be fixed --> NOT dependant on the precision placement of the ball / any slip or creep movement of the suspension during operation. The position of the plate is not really critical. I use this suspension type and I can get a 30 seconds period quite OK. I use a 1/2" SS ball rolling on a section of 'skin graft' polished scalpel blade 16 thou thick. The cost is less than 50c !! The arm rotates around the centre of the ball. The SEP Lehman uses crossed tungsten carbide rollers for both suspensions with the bottom vertical roller on the support column and the cross roller on the arm. I have been able to set one up for 30 seconds without any problems. My comments relate to these system types. I can confirm from practical experience that BOTH these systems work well and are stable at long periods. Remember that crossed foil suspension systems do work fine in commercial seismometers! Not the crossed flexure (Bendix bearings, > or single flexure -- although I > asked the question does this apply to them, too?) In spades! 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". You can only use 1 mm balls (eg ball point pens -- BIC use Carbide balls) if you have a very light load, only an ounce or so. Otherwise either the ball or the flat will fail fairly rapidly, if not immediately, in compression. You get a ring fracture about the contact point, or the ball digs a dimple into the counterface. In practice, you set up a pendulum for the desired period, by slowly reducing the angle that the suspension makes with the vertical. If there is a small LINEAR correction to the theoretical swing angle, this should compensate for it. 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 instability. 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. I have only observed this when the tilt axis has been lifted above the neutral point. I don't understand why you consider the mass to be reducing in height as the arm rotates. When the ball is mounted on the end of the ARM, the contact point moves proportionately to the right as the mass swings to the right, which should lift the mass slightly? However, this depends on the SQUARE of the deflection angle d, from the 1 - d^2/2 approximation for the cosine term, so it could cause problems. For a 56 cm beam at 10 seconds, the axis tilt is about 1.3 degrees. This gives about the 1/2 thou rise per 1" bob deflection as you stated. With the ball on the vertical column, the length of the arm also increases by a very tiny amount as the bob swings to one side. This INCREASES the stability slightly, rather than DECREASING it. > 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. This is REALLY NOT a great idea! Reverse the ball and plate mountings! Put both balls on the vertical column, both plates on the arm. 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? Possibly. You have the load of the mass opposed by the bending of the foil. It also depends on whether the top and bottom flexures are both mounted vertically, or whether the top flexure is perpendicular to the support wire / diagonal rod. Both systems have been used. If so, the upper suspension 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. If you have vertical crossed flexures top and bottom, as the mass swings to the right the bottom suspension point moves slightly to the left, but it also moves marginally toward the support column. The top suspension point moves slightly to the right, but it also moves marginally toward the support column. If the flexures are identical, the suspension movements toward the vertical column, while square law, should increase the stability. The change in the axis angle should be ~linear and hence compensated during the tilt / period setup procedure. If you used a very short vertical separation of the flexures, the angular cross change of the suspension could be unstable. > 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. My feeling is that problems getting stable long period Lehman suspensions are more likely related to the use of softer materials, like HT bolts, for the counterface. At the loads commonly used in Lehmans, dimples can form under the ball and give erratic results. (Try inserting a strip of Al ---> the arm will ~stop responding to all but the strongest signals!) The use of a real knife blade will NOT allow you to get long stable periods. You are applying a force to the edge close to or in excess of it's load bearing capacity. The edge will either roll over or shatter depending on the metal temper, or dig a wedge into the counterface - or all three! > What immediately comes out of this is that just simple observation of > the prolate cycloid curve is that the upper pivot and lower pivot are > tracing different curves because they are effectively 180 degrees out of > phase in the equation so right away balance has to be changing. Now > which way? Remember that we are dealing with very small angles where Sin(theta) ---> theta and cos theta ~= 1. It is easy to get mislead by considering large angles. Interesting discussion! I hope that I have got the mechanical relationships correct this time! Regards, Chris Chapman In a me= ssage dated 2008/07/06, charles.r.patton@........ writes:

Chris,

Admittedly my description is brief. I left unsaid that everything is p= erfectly rigid and properly set up. The pivot types I'm really interes= ted in are ones used on 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=20= the same for the suspension wire / beam to the upper pivot point on the upri= ght.

Hi Charles,

OK

But you will likely be in trouble if yo= u use the ball on the end of the arm. Put the ball on the vertical upright a= nd the plate on the end of the arm. The centre of curvature of the ball defi= nes the swing angle and you want this to be fixed --> NOT dependant on th= e precision placement of the ball / any slip or creep movement of the suspen= sion during operation. The position of the plate is not really critical. I u= se this suspension type and I can get a 30 seconds period quite OK. I use a=20= 1/2" SS ball rolling on a section of 'skin graft' polished scalpel blade 16=20= thou thick. The cost is less than 50c !! The arm rotates around the centre o= f the ball.

The SEP Lehman uses crossed tungsten ca= rbide rollers for both suspensions with the bottom vertical roller on the su= pport column and the cross roller on the arm. I have been able to set one up= for 30 seconds without any problems.

My comments relate to these system type= s.

I can confirm from practical experience= that BOTH these systems work well and are stable at long periods.

Remember that crossed foil suspension s= ystems do work fine in commercial seismometers!

Not the crossed flexure (Bendix bearings,or single flexure -- although I asked the question does this appl= y to them, too?)

In spades!

What I'm trying to think about is not spurious effects such as compression <= BR>(Rockwell hardness), and lack o= f sufficient rigidity in the structure, but rather the effect that a rolling= geometry inherently has. If one thinks about what happens when a prop= erly adjusted Lehman gate swings, the plumb bob is taking a flatter and flat= ter trajectory as the period is increased. As I recall, a 10 second pe= riod pendulum will lift about 1/2 a thousandth inch per 1 inch swing. =20= So if the geometry

causes the bob to drop 1/2 a thousandth per inch of swing then it cancels wh= at other wise would be a stable adjustment. The problem is that a 20 s= econd 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 0.000= 1".

You can only use 1 mm balls (eg ball po= int pens -- BIC use Carbide balls) if you have a very light load, only an ou= nce or so. Otherwise either the ball or the flat will fail fairly rapidly, i= f not immediately, in compression. You get a ring fracture about the contact= point, or the ball digs a dimple into the counterface.

In practice, you set up a pendulum for=20= the desired period, by slowly reducing the angle that the suspension makes w= ith the vertical. If there is a small LINEAR correction to the theoretical s= wing angle, this should compensate for it.

So a very small swing starts to have an acceleratingchange of length leading to a total flatting of the bo= b trajectory and then "flopping" of the pendulum bob. This swing may c= ome from slight floor tilt and what might otherwise be stable is not because= the geometry leads to instability. The only saving grace I see is tha= t the

twist that also takes place is in the direction of increasing stability (lif= ting the bob) but in my mind it is secondary in effect to the primary drop d= ue to the effective pivot point change leading to an apparent pivot point /=20= beam / bob length change.

I have only observed this when the tilt= axis has been lifted above the neutral point.

I don't understand why you consider the= mass to be reducing in height as the arm rotates. When the ball is mounted=20= on the end of the ARM, the contact point moves proportionately to the right=20= as the mass swings to the right, which should lift the mass slightly? Howeve= r, this depends on the SQUARE of the deflection angle d, from the 1 - d^2/2=20= approximation for the cosine term, so it could cause problems.

For a 56 cm beam at 10 seconds, the axi= s tilt is about 1.3 degrees. This gives about the 1/2 thou rise per 1" bob d= eflection as you stated.

With the ball on the vertical column, t= he length of the arm also increases by a very tiny amount as the bob swings=20= to one side. This INCREASES the stability slightly, rather than DECREASING i= t.

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=20= both lead to dropping the bob as it swings.

This is REALLY NOT a great idea! = Reverse the ball and plate mountings! Put both balls on the vertical column= , both plates on the arm.

Now if flat foil flexures are used, the upper flexureis on the bob side and initially bends at some point,= but as the bob moves sideways, doesn't the flexure point move towards the u= pright?

Possibly. You have the load of the mas= s opposed by the bending of the foil. It also depends on whether the top and= bottom flexures are both mounted vertically, or whether the top flexure is=20= perpendicular to the support wire / diagonal rod. Both systems have been use= d.

If so, the upper suspension is effectiv= ely getting longer, lowering the bob during a

swing, again unstable. The low= er beam flexure is in tension on the back (further away from the bob) side o= f 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 up= right which also leads to an effective shortening of the bottom beam, again=20= the unstable lowering of the bob.

If you have vertical crossed flexures=20= top and bottom, as the mass swings to the right the bottom suspension point=20= moves slightly to the left, but it also moves marginally toward the support=20= column. The top suspension point moves slightly to the right, but it also mo= ves marginally toward the support column. If the flexures are identical, the= suspension movements toward the vertical column, while square law, should i= ncrease the stability. The change in the axis angle should be ~linear and he= nce compensated during the tilt / period setup procedure. If you used a very= short vertical separation of the flexures, the angular cross change of the=20= suspension could be unstable.

Much of this came about as I co= njectured why so many anecdotal stories about the difficulty of adjusting Le= hmans in the long period realm. So the thought experiment described above.

My feeling is that problems getting sta= ble long period Lehman suspensions are more likely related to the use of sof= ter materials, like HT bolts, for the counterface. At the loads commonly use= d in Lehmans, dimples can form under the ball and give erratic results. (Try= inserting a strip of Al ---> the arm will ~stop responding to all but th= e strongest signals!) The use of a real knife blade will NOT allow you to ge= t long stable periods. You are applying a force to the edge close to or in e= xcess of it's load bearing capacity. The edge will either roll over or shatt= er depending on the metal temper, or dig a wedge into the counterface - or a= ll three!

What immediately comes out of t= his is that just simple observation of

the prolate cycloid curve is that the upper pivot and lower pivot are

tracing different curves because they are effectively 180 degrees out of

phase in the equation so right away balance has to be changing. Nowwhich way?

Remember that we are dealing with very=20= small angles where Sin(theta) ---> theta and cos theta ~=3D 1. It is easy= to get mislead by considering large angles.

Interesting discussion! I hope that I h= ave got the mechanical relationships correct this time!

Regards,

Chris Chapman