PSN-L Email List Message

Subject: Lehman damping
From: S-T Morrissey sean@...........
Date: Sun, 7 Nov 1999 23:57:41 -0600 (CST)


Hydraulic and eddy-current damping were mainly used on mechanical
direct-recording seismometers of decades ago. Some hybrid moving-
coil sensors were made, though. The Sprengnether "H" series of the
late 40's had a moving-coil output for a galvanometer and a copper
bar damper. The bar is about 2" square and 3/8" thick, since thicker
provides for greater induced currents. The magnet had a shunting
mechanism to vary the field and hence the damping.  However, the 
damping was not very predictable, and varied with the position of
the copper bar in the gap of the large U channel magnet.

And a word about the word damp:
To damp is to attenuate the amplitude of a repetitive motion; ie: damping.
To dampen is to throw water on something: dampening a towel.

Here is an edited repeat of a previous mote about damping seismometers:

Re electromagnetic damping: 
Most moving coil seismometers only use resistive damping. If properly
calculated, no other damping is needed or should be used. THis uses
the motion of the main signal coil to generate a voltage that induces
a current in a resistor connected in parallel with it to dissipate
the energy of the motion and thus damp it. It is very predictable and
easy to do. The loss of signal output that results is easily made up by 
additional (about x2) gain of the amplifier.

Damping is generally expressed in relation to what is needed for "critical"
damping, which means that after a step input, the output returns to
a zero output voltage as rapidly as possible without overshooting.
This damping has a value of 1. But it has a price, namely significant
loss of the signal in the damping resistor. So generally damping is
set at 0.8 of critical, which cuts the loss by about half, but the overshoot
to an impulse input is minimal. Much less than 0.8, the natural period
of the seismometer will dominate the response. On the other hand, if
a fairly broad response is desired, and the seis and the amplifier have
enough output and/or gain, damping as high as 2 can be used.

Note that actually calculating the proper resistor depends on how much
you know about the geophone or seismometer. The manufacturers data will
sometimes even give the value for critical damping. But if the geophone
is a mystery device, a generally good approximation is to measure the
resistance of the coil and use that value for the damping resistor.

To calculate the value of the damping resistor to be used, one first
has to know or determine the open circuit damping, called Bo. It
is the mechanical air-dashpot function of the coil movement, and is
often listed in the specifications for the seismometer. For most
seismometers, it ranges from 0.2 to 0.4, where a value of 0.8 is for
critical damping. It can also be determined from the logrithmic 
decrement of the free oscillations of the undamped seismometer.
For starters, it can be assumed to be 0.3.

Then the motor constant and resistance of the main coil have to be
determined or found in the specifications. For a home=made device,
this is done by balancing an added weight with a measured current.
If 1 gram is balanced by 1 ma, the constant is 9.8*1gm/1ma Newtons/Ampere.
Conveniently enough a Newton/Ampere = a Volt/meter/second = V*sec/m.
For a horizontal, a V shaped thread with 90 degrees at the bottom will
pull each upper end sideways with half the weight hung at the bottom.

The electromagnetic damping Bem needed is determined by 
subtracting the Bo from the required total Bt.
		Bem = Bt - Bo
		(If you don't know your Bo, use a value of 0.3)

Then the damping resistor is calculated by:
		Bem = G^2 / (2*omega*M*(Rs + Rd), or

		Rd = [G^2 / (Bem*2*omega*m)] - Rs

	Where Bem is the electromagnetic damping, G is the main coil
	constant, omega is the angular frequency, equivalent to 
	2*pi/Tn, where Tn is the natural period, and M is the mass.

For an L4-C, with a 5500 ohm coil, with G = 270 V/m/sec, Bo = 0.27,
we want Bt to be 0.77, so Bem = 0.5, M = 1 kgm, omega = 2*pi (1 second)
we calculate a damping resistor Rd of 6102 ohms for critical damping.

For an S5000 Long Period Seis, with a 500 ohm coil, G = 100 V/m/sec,
Bo = 0.1, we want a flatter response with Bt = 1, so Bem = 0.9,
omega = 2*pi/15 (seconds), M = 11 kg, we calculate a resistor of
705 ohms for Bt = 1 (the LP is over damped for a broader response).

For an HS-1 4.5 hz geophone with a 1250 ohm coil, G = 41 V/m/sec, and
Bo = 0.28; we want critical damping with Bt = 0.8, so Bem = 0.52,
omega = 2*pi*4.5 (hz), M = 0.022kg, we calculate Rd = 1348 ohms.

This method of damping is the only method currently being used on
velocity sensors. The method is so exact that often the resistor
for Rd is installed inside the smaller geophones at the factory.
Metal-film resistors are used for lower noise.

When one is connecting a seismometer to an amplifier with a low
input impedance Ra, that value is in parallel with the seismometer,
so must be taken into account. So if Ra = 10k ohms, and Rd is to
be 5k ohms, the actual resistor to be used is Rs = Rd*Ra/(Ra-Rd),
or in this case Rs = 10k ohms. Generally very high input impedance
amplifiers are not used because of noise considerations, so this
detail is often overlooked.

Unfortunately I have no idea what the constants for a Lehman might
be. I note that the coil is 1/4 pound of # 34 wire which has 8310 feet
per pound and 2168 ohms per pound at 20 deg.C.

So assuming the coil is about 500 ohms, I would try a damping resistor
of about 1000 ohms, unless you can determine or know the constant G of the
main coil and can calculate the value. You will need to know the 
mass and the period of the seismometer.

With this type of damping, the response should be flat to velocity
from roughly the natural period to whatever low-pass filter you
have in your amplifier. (BTW another place to check to see if the
shorter p-wave phases are being filtered out).



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Larry Cochrane <cochrane@..............>