## PSN-L Email List Message

Subject: Re: Morrisey's seismometer
From: ChrisAtUpw@.......
Date: Mon, 5 Sep 2005 10:33:48 EDT

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In a message dated 05/09/2005, alexmirabal2000@........ writes:

I got from the web some drawings and explanations related to  this design,
but I would like to get a better knowledge (maybe a more detailed  explanation)
of the mechanic part: Transfer Function and its mathematical  components, how
to calculate free period experimentally, etc...

Dear Alexander,

The principles of the STM-8 are  essentially similar as those of the La
Coste vertical seismometer published  in 1935.
You have an ~horizontal arm with a seismic mass on  the end. You need to
support it in such a way that the forces are nearly, but  not quite,
compensated out as the beam angle changes. La Coste wound his spring  so that the whole
assembly had 'zero length'. This means that the load / length  graph goes
through the point zero force / zero length. Most coil springs  have a minimum
physical length, so they require a 'pre tension' type  winding. (You can also
wind flat spiral springs.)
In the STM-8 setup, you use a flat strip bent into  about 3/4 circle and
positioned at an angle under the beam, with low torque foil  suspensions. This
extreme bend gives a load /extension graph which you can match  up to the
torque / angle graph due to the seismic mass. If they matched  identically, you
would have no net torque as the angle changed and hence an  infinite period.
The problem with this is that steel spring constants are  temperature sensitive,
but don't match those of the mass + arm, so it is only  'stable' over a few C
deg range. The more precise the balance and the longer the  period, the
greater the influence of the temperature variations. However,  you can get a very
considerable improvement by using the spring material  Ni-SpanC, which has a
very low temperature coefficient. Two leaf springs are  sometimes used to
provide a greater compensation accuracy. The position of the  arm needs to be
critically damped to give stable operation - as does any  oscillatory system.
The alternative Sean uses is to provide  electronic position sensing down
to maybe 1 nano metre and force feedback,  usually electro-magnetic, to
stabilise the mechanical system and to define it's  period. The damping may be
purely feedback or magnet / plate inductive  type. (Don't ever try to use oil
damping!) The electronic constants and  feedback gain override the mechanical
properties. Electronic feedback damping  gives more noise on the signal and a more
complicated circuit, but it is widely  used.
I hope that this provides some background knowledge  for you.

Regards,

Chris Chapman

In a message dated 05/09/2005, alexmirabal2000@........ writes:
<=
FONT=20
style=3D"BACKGROUND-COLOR: transparent" face=3DArial color=3D#000000=20
size=3D2>I got from the web some drawings and explanations relat=
ed to=20
this design, but I would like to get a better knowledge (maybe a more deta=
iled=20
explanation) of the mechanic part: Transfer Function and its mathemat=
ical=20
components, how to calculate free period experimentally, etc...=20

Dear Alexander,

The principles of the STM-8 are=20
essentially similar as those of the La Coste vertical seismometer publi=
shed=20
in 1935.
You have an ~horizontal arm with a seismic mass=
on=20
the end. You need to support it in such a way that the forces are nearly, bu=
t=20
not quite, compensated out as the beam angle changes. La Coste wound his spr=
ing=20
so that the whole assembly had 'zero length'. This means that the load / len=
gth=20
graph goes through the point zero force / zero length. Most coil spring=
s=20
have a minimum physical length, so they require a 'pre tension' type=20
winding. (You can also wind flat spiral springs.)
In the STM-8 setup, you use a flat strip bent i=
nto=20
about 3/4 circle and positioned at an angle under the beam, with low torque=20=
foil=20
suspensions. This extreme bend gives a load /extension graph which you can m=
atch=20
up to the torque / angle graph due to the seismic mass. If they matched=
=20
identically, you would have no net torque as the angle changed and henc=
e an=20
infinite period. The problem with this is that steel spring constants are=20
temperature sensitive, but don't match those of the mass + arm, so it is onl=
y=20
'stable' over a few C deg range. The more precise the balance and the longer=
the=20
period, the greater the influence of the temperature variations. Howeve=
r,=20
you can get a very considerable improvement by using the spring material=20
Ni-SpanC, which has a very low temperature coefficient. Two leaf springs are=
=20
sometimes used to provide a greater compensation accuracy. The position of t=
he=20
arm needs to be critically damped to give stable operation - as does any=20
oscillatory system.
The alternative Sean uses is to provide=20
electronic position sensing down to maybe 1 nano metre and force feedba=
ck,=20
usually electro-magnetic, to stabilise the mechanical system and to define i=
t's=20
period. The damping may be purely feedback or magnet / plate inductive=20
type. (Don't ever try to use oil damping!) The electronic constants and=
=20
feedback gain override the mechanical properties. Electronic feedback dampin=
g=20
gives more noise on the signal and a more complicated circuit, but it is wid=
ely=20
used.
I hope that this provides some background knowl=
edge=20
for you.

Regards,

Chris Chapman
```