## PSN-L Email List Message

Subject: Re: Crossed wire suspensions - more analysis
From: ChrisAtUpw@.......
Date: Tue, 25 Oct 2005 18:07:56 EDT

```In a message dated 25/10/05, Brett3kg@............. writes:

> http://bnordgren.org/seismo/zerohng2.pdf
>
Hi Brett,

Two quick comments on foil / wire suspensions:

In the case of the 'traditional crossed foil hinge', since the lengths
of the foils stays constant, the sum of the two triangles on any one side of
the hinge axis also stays constant. This is exactly the relationship which
gives the crossing point the form of an ellipse with the two top corners as the
foci - also the two bottom corners. This assumes that the foils are completely
flexible and in therein lies the only problem with this hinge. You are bending
the foil by very significant amounts very close to the end fixtures and this
can give a high stress level and internal frictional losses - no material is
completely, instantaneously flexible. Since both angles on the left hand side
increase more rapidly than those on the right hand side - or vice versa - there
will be SOME net hinge force opposing rotation.

In the case of the rolling foil / wire hinge, the lengths between
contact points stay constant and the lengths to the crossing point stay constant.
The physical foil / wire crossing point can therefore only move in a circle
around the top rod. The end contact points of the foil now lie on a circle the
diameter of the suspension rods, so there are much lower bending stresses and
the bend radius can be made large, minimising internal frictional losses. Since
the bend angle stays constant on both sides, there will be NO net hinge force
opposing rotation - hence it is a Zero Torque Suspension (assuming that the
wire / foil dimensions on both sides are equal).

Defining the centre of rotation can be thought of by considering two
fixed pulleys some distance apart with a figure of 8 belt around them. With
equal pulley diameters, they rotate in opposite directions by the same angle.
Taking lines projected from the centres of the two pulleys, initially going
through both axles, the lines will always cross on the line which is at right
angles to the centre of the line joining the axles, giving a cosine 1/2 deflection
angle variation. This explains why the changes you calculated were so small.

You can make rolling suspensions with strips of foil as well as with
wires. The nickel coated 8 thou piano wire was an obvious 'first choice' to try
out, partly since it is so readily available. You can buy hard drawn Nichrome
fine wire as well as rolled wire tape (as used in your electric toaster). It
has about half the ultimate strength of piano wire, but it is very corrosion
resistant. Other foils are available. See www.smallparts.com and
www.ksmetals.com You may be able to get bronze shim foil from a metal stockist. A rather
thick bronze strip is sold for draft excluder on doors. Sean Morrissey tried out
narrow strips of this as a seismometer suspension. Niobium foil is used on the
gravitational wave detection experiments and it has a very good reputation as
a hinge material, but I don't know where they get it from.

Regards,

Chris Chapman
In a message=20=
dated 25/10/05, Brett3kg@............. writes:

http://bnordgren.org/seismo=
/zerohng2.pdf

Hi Brett,

Two quick comments on foil / wire s=
uspensions:

In the case of the 'traditional cro=
ssed foil hinge', since the lengths of the foils stays constant, the sum of=20=
the two triangles on any one side of the hinge axis also stays constant. Thi=
s is exactly the relationship which gives the crossing point the form of an=20=
ellipse with the two top corners as the foci - also the two bottom corners.=20=
This assumes that the foils are completely flexible and in therein lies the=20=
only problem with this hinge. You are bending the foil by very significant a=
mounts very close to the end fixtures and this can give a high stress level=20=
and internal frictional losses - no material is completely, instantaneously=20=
flexible. Since both angles on the left hand side increase more rapidly than=
those on the right hand side - or vice versa - there will be SOME net hi=
nge force opposing rotation.=20

In the case of the rolling foil / w=
ire hinge, the lengths between contact points stay constant and the lengths=20=
to the crossing point stay constant. The physical foil / wire crossing point=
can therefore only move in a circle around the top rod. The end contact poi=
nts of the foil now lie on a circle the diameter of the suspension rods, so=20=
there are much lower bending stresses and the bend radius can be made large,=
minimising internal frictional losses. Since the bend angle stays constant=20=
on both sides, there will be NO net hinge force opposing rotation - h=
ence it is a Zero Torque Suspension (assuming that the wire / foil dimension=
s on both sides are equal).

Defining the centre of rotation can=
be thought of by considering two fixed pulleys some distance apart with a f=
igure of 8 belt around them. With equal pulley diameters, they rotate in opp=
osite directions by the same angle. Taking lines projected from the centres=20=
of the two pulleys, initially going through both axles, the lines will alway=
s cross on the line which is at right angles to the centre of the line joini=
ng the axles, giving a cosine 1/2 deflection angle variation. This explains=20=
why the changes you calculated were so small.=20

You can make rolling suspensions wi=
th strips of foil as well as with wires. The nickel coated 8 thou piano wire=
was an obvious 'first choice' to try out, partly since it is so readily ava=
ilable. You can buy hard drawn Nichrome fine wire as well as rolled wire tap=
e (as used in your electric toaster). It has about half the ultimate strengt=
h of piano wire, but it is very corrosion resistant. Other foils are availab=
le. See www.smallparts.com and www.ksmetals.com You may be able to get bronz=
e shim foil from a metal stockist. A rather thick bronze strip is sold for d=
raft excluder on doors. Sean Morrissey tried out narrow strips of this as a=20=
seismometer suspension. Niobium foil is used on the gravitational wave detec=
tion experiments and it has a very good reputation as a hinge material, but=20=
I don't know where they get it from.

Regards,

Chris Chapman
```