In a message dated 2006/10/05, Bobhelenmcclure@....... writes:

>   I submitting this note in order to give others the benefits of my own 
> sometimes trial-and-error efforts to build a seismic sensor. I am sure that 
> Chris Chapman will continue to contribute, as well.

Hi Bob,

       Is that meant to be an invitation?

>   Both Chris Chapman and I favor the use of Neodymium Iron Boron magnets 
> arranged in a four-pole structure for generating the magnetic field needed for 
> velocity sensing and damping in seismic sensors. The magnets are powerful, 
> relatively cheap, and easily obtained. The magnets I favor are block magnets, 6 
> mm thick, 18 mm wide, and 50 mm long. They are magnetized in the thickness 
> direction and are of the composition known as N38. They have a coercive force 
> of about 12,000 Oersteds (CGS units), corresponding to 1.2 Teslas in the SI 
> system.
>  
>   Construction of a four-pole magnet assembly is very simple, but also very 
> hazardous. These magnets are attracted to steel and to each other with a 
> force of about 57 pounds per square inch, and any skin caught between them can be 
> badly nipped. You must keep loose magnets very far away from steel or each 
> other and wear heavy leather work gloves when handling them. The magnets are 
> brittle, and will break if they crash together or with steel. The pole plates 
> are mild steel, thick enough to carry the flux of the magnetic circuit. More 
> on that later. One of the plates must have clearance holes for 3/16" bolts, 
> one hole in each corner. The plates, for the above magnet dimensions, should 
> measure two inches by at least three inches.

       So just two of these magnets could probably lift you right off the 
floor......
       You need to plan your assembly, place the magnets over a 3 ft away and 
be very careful. You will likely sometime get a pinched finger, but with care 
you can avoid broken bones or a crushed finger joint. I am not being 
alarmist. 
       You MUST avoid flying magnets!    

       Which is one reason why my designs favour rather smaller magnets and 
separate the damping and detector functions. The other reason for this is that 
the systems were designed for school use and you then want to separate out the 
two functions for educational / demonstration purposes. You already have a 
large field increase by using the NdFeB magnets in comparison with Alnico and a 
more sensitive and flexible orientation with the quad magnet arrangement, so 
you can cut down on total coil turns and still get better performance. This can 
reduce the resistance and may allow ~more signal amplification. The minimum 
noise is determined by the input noise impedance characteristics of the opamp. 
You ~match the coil resistance to this notional resistance figure to get the 
best performance. In amateur seismic work, you are usually limited in practice 
by the ambient environmental noise. 

       I prefer zinc plated 1/4" OD set screws to 3/16" OD. Mostly personal 
choice, but they are a bit more rigid and it also increases the magnetic 
coupling between the two backing plates, which can carry stray fields. You won't get 
the total flux of any two magnets matching exactly.

>   Slide two magnets onto each plate, with opposite poling on each plate. 
> When you have one magnet in position on a plate, carefully hold the second 
> magnet above the first. You will feel either an attraction or a repulsion of the 
> second magnet toward the one on the plate. Make sure the force is repulsive, 
> then slide the second magnet into place beside the first. When the magnets 
> are positioned on each plate, make a wooden or plastic shim somewhat thinner 
> than the final magnet gap you intend to use. I would use a shim about six 
> inches long and the same width as the paired magnets, which would be about 1.5 
> inches for the example. With the shim covering the magnets of one plate, hold 
> the second plate over it, getting no closer than enough to determine if the 
> force between them is attractive or repulsive. The correct alignment is 
> indicated by an attractive force. You now place the upper plate (magnets down) on the 
> shim at one end of the lower plate and slide the upper plate and magnets up 
> over the lower magnets. You now have a sandwich of upper and lower assemblies 
> tightly squeezing the shim in between.

       If you are doing it this way, I suggest that you attach the plastic 
shim or preferably a wood block firmly to the first magnet with PVC or gaffer 
tape. This can help prevent accidents. The forces can be really dangerous. 

>   Place four bolts in the plate with the holes. Note than these bolts are 
> used to hold the plates apart, not together. Use the bolts to jack the plates 
> apart to get the desired gap spacing, and then you can withdraw the shim. If 
> each of your plates have clearance holes drilled in them, you will need two 
> nuts for each screw.

       I mount the two magnets on the first block. Then I fit the four bolts 
with two nuts each. The inner one I do up finger tight, the outer one I leave 
at ~ 1.5" along the thread. Then I prepare the second plate. I grip the first 
plate with my hand to prevent the plates getting too close and slide the 
second plate onto the bolts. With Bob's more powerful magnets, I would use a wood 
safety block and adhesive tape in place of my hand. I rock this plate till it 
contacts the nuts and then back off the nuts sequentially about a turn at a 
time till I get the desired central magnet separation.

>   Now it is time to discuss what field strength you get, and what thickness 
> of steel is required. Suppose for my example using 6 mm thick magnets, I use 
> a gap of 6 mm. The resulting distance between plates is 18 mm, 12 mm filled 
> with magnet, and 6 mm with air. I call the ratio of total magnet thickness to 
> total plate separation the filling factor. To a first approximation, the gap 
> field the coercive force of the magnetic material multiplied by the filling 
> factor. In this example, the coercive force is 12 KOe and the filling factor 
> is 2/3, so the gap field is 8 KOe. The accuracy of this estimate depends on 
> the magnet width compared to the gap size. If the gap becomes appreciable 
> compared to the width, you will get more fringing field and less-than-expected 
> gap field. 

       Can you run through the maths and assumptions of this please? 

>    For my example magnet structure, I use 1/4 inch thick steel plates. I 
> find that there is a very slight saturation of the plates in the region between 
> magnet pairs. When I use 24 mm wide magnets, there is a lot of saturation 
> and a lot of external stray field around the whole assembly. I have to put 
> steel side plates on the assembly to eliminate the saturation and the stray 
> field. Steel can carry a flux density of about 20 to 24 KOe without saturation. 
> Without saturation, the magnetic circuit of a 4-pole structure consists of a 
> closed rectangular flux path, with lines traveling through magnets, gaps, and 
> steel. The steel must carry the same total number of lines of flux as the gap 
> and magnets. The number of lines is proportional to the gap flux density 
> multiplied by the magnet width. In the example of 8 KOe and 18 mm width, this 
> corresponds to 8,000 times 1.8, or 14,000 lines per lineal centimeter of magnet 
> structure. The quarter-inch-thick steel (0.625 cm) must carry a flux density 
> of 22,000 KOe. It does so, barely.

       Kaye and Laby list the flux density of mild steel at 21.5 k Oer at 
saturation. 
      If you made the backing plate to just cover the magnets, all the flux 
would have to go through the centre of the mild steel plate. If you increase 
the backing plate area, flux can go through this surrounding strip, reducing the 
overall thickness required, down to about 1/2 minimum, before you have to 
increase the thickness. I leave a 1/2" wide border around my magnets.
       The closer the two plates, the greater the field in the gap, so the 
more flux that the plates have to carry in the critical central area.  
       I put a rounded corner of the magnet just onto the backing plate, 
rotate it till one edge is on the plate, reduce the angle till maybe 1/4 of the 
magnet is flat on the plate and then slide the magnet into position.

>   The next topic is coil design. By following the above magnet assembly 
> design principles, you know the approximate gap field, so by also knowing the 
> magnet length you will be able to estimate the number of coil turns you will 
> need to achieve a given output sensitivity in volts per meter per second. If 
> the end loops of the coil extend beyond the ends of the magnet, each turn is 
> immersed in a total field length of twice the magnet length. In the example 
> design, the magnet length is 50 mm, so L per turn is 0.1 m.
>  
>   The output voltage generated by the moving coil is Volts = B * N * L * 
> Vel, where B is field strength in Teslas, N is number of turns, L is length per 
> turn in the field, and Vel is velocity in meters per second. One Tesla 
> corresponds to 10,000 Oersteds. Suppose n = 1100, B = 0.8 Tesla, and L = 0.1 meter. 
> Then Volts/Vel = 0.8 * 1100 * 0.1 = 88 v-s/m, which is a good number to 
> strive for.
>  
>   A wire size of #38 or less will allow this number of turns to fit 
> comfortably within the gap field cross-section. The coil will have a resistance low 
> enough to permit resistive shunt damping of a pendulum weighing up to a 
> kilogram, in my opinion. My sensors have a pendulum mass of about 0.1Kg, and 
> critical damping is achieved at about 30 kOhms. Since the coil resistance is only 
> 340 Ohms, the shunt damping imposes negligible loss on output sensitivity. 
> Even a kilogram mass would require only about 10% loss of output using shunt 
> damping.

       The damping force required also depends on the set period. What period 
are you using?
       What effect does this damping current have on the input noise in 
practice? Can it be significant?
       Looking at the commonly available lists of insulated wire, the Beldsol 
polyurethane coated copper wire which you can solder directly without 
stripping is stocked in sizes down to 36 AWG. You may have to hunt hard / go to 
professional suppliers for 38 AWG and smaller diameters - higher numbers. The 
properties of copper wire are listed in the www under AWG copper wire.

>   There is one significant complication to this type of magnet and coil 
> design, having to do with the fact that pure copper is diamagnetic, and coil and 
> its pendulum are subject to forces other than the desired restoring force of 
> a garden gate pendulum. In the example design this diamagnetic force is a 
> decentering force, making it very difficult to adjust the sensor to a state of 
> stable long period equilibrium. I reduce this effect by essentially potting 
> the coil in acrylic plastic, which is also diamagnetic, and having the 
> boundaries of the plastic extend well outside the edges of the magnetic field. Using 
> a heavier pendulum would be of great benefit, as well.

       Pure copper is diamagnetic, but some copper wire contains a tiny 
amount of iron, which is strongly paramagnetic. The properties may vary in 
practice. This is even more of a pest and can result in the coil being attracted by 
the strong field gradient at the edge of the magnets. With these high fields, 
you can get the situation where the coil has two stable positions over the edges 
of the magnets, with an unstable region in between. You may need to check 
your reel, or your wound coil, or wind a sample coil for a repulsion / attraction 
test. You may get an even stronger effect when the winding is close to / over 
the central N/S magnet join.
       You can reduce this type of problem by increasing the separation 
between the coil and the edges of the magnets a bit, but this reduces the 
sensitivity; by limiting the travel of the arm so that the coil does not get too close 
to the edges of the magnets and by increasing the magnet area and hence the 
available coil travel, but this may require a thicker backing plate and gives a 
higher coil resistance. The force on the winding is proportional to H x dH/dr, 
which falls off very rapidly with increasing r at the edges of the magnet.
       I appreciate the value of using a wider plastic plate to reduce the 
change of susceptibility with position. I suspect that it may be important to 
have a solid plastic core to the coil to reduce forces associated with the 
cental magnet join.
       Also, the less copper that is used, the lower the force.

       Regards,

       Chris Chapman
In a me=
ssage dated 2006/10/05, Bobhelenmcclure@....... writes:



  I submitting this note i=
n order to give others the benefits of my own sometimes trial-and-error effo=
rts to build a seismic sensor. I am sure that Chris Chapman will continue to=
 contribute, as well.




Hi Bob,



       Is that meant to be an invitation?



  Both Chris Chapman and I=
 favor the use of Neodymium Iron Boron magnets arranged in a four-pole struc=
ture for generating the magnetic field needed for velocity sensing and dampi=
ng in seismic sensors. The magnets are powerful, relatively cheap, and easil=
y obtained. The magnets I favor are block magnets, 6 mm thick, 18 mm wide, a=
nd 50 mm long. They are magnetized in the thickness direction and are of the=
 composition known as N38. They have a coercive force of about 12,000 Oerste=
ds (CGS units), corresponding to 1.2 Teslas in the SI system.

 

  Construction of a four-pole magnet assembly is very simple, but also=20=
very hazardous. These magnets are attracted to steel and to each other with=20=
a force of about 57 pounds per square inch, and any skin caught between them=
 can be badly nipped. You must keep loose magnets very far away from steel o=
r each other and wear heavy leather work gloves when handling them. The magn=
ets are brittle, and will break if they crash together or with steel. The po=
le plates are mild steel, thick enough to carry the flux of the magnetic cir=
cuit. More on that later. One of the plates must have clearance holes for 3/=
16" bolts, one hole in each corner. The plates, for the above magnet dimensi=
ons, should measure two inches by at least three inches.




       So just two of these magnets coul=
d probably lift you right off the floor......

       You need to plan your assembly, place t=
he magnets over a 3 ft away and be very careful. You will likely sometime ge=
t a pinched finger, but with care you can avoid broken bones or a crushed fi=
nger joint. I am not being alarmist. 

       You MUST avoid flying magnets! &nb=
sp;  



       Which is one reason why my designs favo=
ur rather smaller magnets and separate the damping and detector functions. T=
he other reason for this is that the systems were designed for school use an=
d you then want to separate out the two functions for educational / demonstr=
ation purposes. You already have a large field increase by using the NdFeB m=
agnets in comparison with Alnico and a more sensitive and flexible orientati=
on with the quad magnet arrangement, so you can cut down on total coil turns=
 and still get better performance. This can reduce the resistance and may al=
low ~more signal amplification. The minimum noise is determined by the input=
 noise impedance characteristics of the opamp. You ~match the coil resistanc=
e to this notional resistance figure to get the best performance. In amateur=
 seismic work, you are usually limited in practice by the ambient environmen=
tal noise. 



       I prefer zinc plated 1/4" OD set screws=
 to 3/16" OD. Mostly personal choice, but they are a bit more rigid and it a=
lso increases the magnetic coupling between the two backing plates, which ca=
n carry stray fields. You won't get the total flux of any two magnets matchi=
ng exactly.



  Slide two magnets onto e=
ach plate, with opposite poling on each plate. When you have one magnet in p=
osition on a plate, carefully hold the second magnet above the first. You wi=
ll feel either an attraction or a repulsion of the second magnet toward the=20=
one on the plate. Make sure the force is repulsive, then slide the second ma=
gnet into place beside the first. When the magnets are positioned on each pl=
ate, make a wooden or plastic shim somewhat thinner than the final magnet ga=
p you intend to use. I would use a shim about six inches long and the same w=
idth as the paired magnets, which would be about 1.5 inches for the example.=
 With the shim covering the magnets of one plate, hold the second plate over=
 it, getting no closer than enough to determine if the force between them is=
 attractive or repulsive. The correct alignment is indicated by an attractiv=
e force. You now place the upper plate (magnets down) on the shim at one end=
 of the lower plate and slide the upper plate and magnets up over the lower=20=
magnets. You now have a sandwich of upper and lower assemblies tightly squee=
zing the shim in between.




       If you are doing it this way, I suggest=
 that you attach the plastic shim or preferably a wood block firmly to the f=
irst magnet with PVC or gaffer tape. This can help prevent accidents. The fo=
rces can be really dangerous. 



  Place four bolts in the=20=
plate with the holes. Note than these bolts are used to hold the plates apar=
t, not together. Use the bolts to jack the plates apart to get the desired g=
ap spacing, and then you can withdraw the shim. If each of your plates have=20=
clearance holes drilled in them, you will need two nuts for each screw.



       I mount the two magnets on the first bl=
ock. Then I fit the four bolts with two nuts each. The inner one I do up fin=
ger tight, the outer one I leave at ~ 1.5" along the thread. Then I prepare=20=
the second plate. I grip the first plate with my hand to prevent the plates=20=
getting too close and slide the second plate onto the bolts. With Bob's more=
 powerful magnets, I would use a wood safety block and adhesive tape in plac=
e of my hand. I rock this plate till it contacts the nuts and then back off=20=
the nuts sequentially about a turn at a time till I get the desired central=20=
magnet separation.



  Now it is time to discus=
s what field strength you get, and what thickness of steel is required. Supp=
ose for my example using 6 mm thick magnets, I use a gap of 6 mm. The result=
ing distance between plates is 18 mm, 12 mm filled with magnet, and 6 mm wit=
h air. I call the ratio of total magnet thickness to total plate separation=20=
the filling factor. To a first approximation, the gap field the coercive for=
ce of the magnetic material multiplied by the filling factor. In this exampl=
e, the coercive force is 12 KOe and the filling factor is 2/3, so the gap fi=
eld is 8 KOe. The accuracy of this estimate depends on the magnet width comp=
ared to the gap size. If the gap becomes appreciable compared to the width,=20=
you will get more fringing field and less-than-expected gap field. 



       Can you run through the maths and assum=
ptions of this please? 



   For my example mag=
net structure, I use 1/4 inch thick steel plates. I find that there is a ver=
y slight saturation of the plates in the region between magnet pairs. When I=
 use 24 mm wide magnets, there is a lot of saturation and a lot of external=20=
stray field around the whole assembly. I have to put steel side plates on th=
e assembly to eliminate the saturation and the stray field. Steel can carry=20=
a flux density of about 20 to 24 KOe without saturation. Without saturation,=
 the magnetic circuit of a 4-pole structure consists of a closed rectangular=
 flux path, with lines traveling through magnets, gaps, and steel. The steel=
 must carry the same total number of lines of flux as the gap and magnets. T=
he number of lines is proportional to the gap flux density multiplied by the=
 magnet width. In the example of 8 KOe and 18 mm width, this corresponds to=20=
8,000 times 1.8, or 14,000 lines per lineal centimeter of magnet structure.=20=
The quarter-inch-thick steel (0.625 cm) must carry a flux density of 22,000=20=
KOe. It does so, barely.




       Kaye and Laby list the flux density of=20=
mild steel at 21.5 k Oer at saturation. 

      If you made the backing plate to just cover t=
he magnets, all the flux would have to go through the centre of the mild ste=
el plate. If you increase the backing plate area, flux can go through this s=
urrounding strip, reducing the overall thickness required, down to about 1/2=
 minimum, before you have to increase the thickness. I leave a 1/2" wide bor=
der around my magnets.

       The closer the two plates, the greater=20=
the field in the gap, so the more flux that the plates have to carry in the=20=
critical central area.  

       I put a rounded corner of the magnet ju=
st onto the backing plate, rotate it till one edge is on the plate, reduce t=
he angle till maybe 1/4 of the magnet is flat on the plate and then slide th=
e magnet into position.



  The next topic is coil d=
esign. By following the above magnet assembly design principles, you know th=
e approximate gap field, so by also knowing the magnet length you will be ab=
le to estimate the number of coil turns you will need to achieve a given out=
put sensitivity in volts per meter per second. If the end loops of the coil=20=
extend beyond the ends of the magnet, each turn is immersed in a total field=
 length of twice the magnet length. In the example design, the magnet length=
 is 50 mm, so L per turn is 0.1 m.

 

  The output voltage generated by the moving coil is Volts =3D B * N *=20=
L * Vel, where B is field strength in Teslas, N is number of turns, L is len=
gth per turn in the field, and Vel is velocity in meters per second. One Tes=
la corresponds to 10,000 Oersteds. Suppose n =3D 1100, B =3D 0.8 Tesla, and=20=
L =3D 0.1 meter. Then Volts/Vel =3D 0.8 * 1100 * 0.1 =3D 88 v-s/m, which is=20=
a good number to strive for.

 

  A wire size of #38 or less will allow this number of turns to fit com=
fortably within the gap field cross-section. The coil will have a resistance=
 low enough to permit resistive shunt damping of a pendulum weighing up to a=
 kilogram, in my opinion. My sensors have a pendulum mass of about 0.1Kg, an=
d critical damping is achieved at about 30 kOhms. Since the coil resistance=20=
is only 340 Ohms, the shunt damping imposes negligible loss on output sensit=
ivity. Even a kilogram mass would require only about 10% loss of output usin=
g shunt damping.




       The damping force required also depends=
 on the set period. What period are you using?

       What effect does this damping current h=
ave on the input noise in practice? Can it be significant?

       Looking at the commonly available lists=
 of insulated wire, the Beldsol polyurethane coated copper wire which you ca=
n solder directly without stripping is stocked in sizes down to 36 AWG. You=20=
may have to hunt hard / go to professional suppliers for 38 AWG and smaller=20=
diameters - higher numbers. The properties of copper wire are listed in the=20=
www under AWG copper wire.



  There is one significant=
 complication to this type of magnet and coil design, having to do with the=20=
fact that pure copper is diamagnetic, and coil and its pendulum are subject=20=
to forces other than the desired restoring force of a garden gate pendulum.=20=
In the example design this diamagnetic force is a decentering force, making=20=
it very difficult to adjust the sensor to a state of stable long period equi=
librium. I reduce this effect by essentially potting the coil in acrylic pla=
stic, which is also diamagnetic, and having the boundaries of the plastic ex=
tend well outside the edges of the magnetic field. Using a heavier pendulum=20=
would be of great benefit, as well.




       Pure copper is diamagnetic, but some co=
pper wire contains a tiny amount of iron, which is strongly paramagnetic. Th=
e properties may vary in practice. This is even more of a pest and can resul=
t in the coil being attracted by the strong field gradient at the edge of th=
e magnets. With these high fields, you can get the situation where the coil=20=
has two stable positions over the edges of the magnets, with an unstable reg=
ion in between. You may need to check your reel, or your wound coil, or wind=
 a sample coil for a repulsion / attraction test. You may get an even strong=
er effect when the winding is close to / over the central N/S magnet join.
       You can reduce this type of problem by=20=
increasing the separation between the coil and the edges of the magnets a bi=
t, but this reduces the sensitivity; by limiting the travel of the arm so th=
at the coil does not get too close to the edges of the magnets and by increa=
sing the magnet area and hence the available coil travel, but this may requi=
re a thicker backing plate and gives a higher coil resistance. The force on=20=
the winding is proportional to H x dH/dr, which falls off very rapidly with=20=
increasing r at the edges of the magnet.

       I appreciate the value of using a wider=
 plastic plate to reduce the change of susceptibility with position. I suspe=
ct that it may be important to have a solid plastic core to the coil to redu=
ce forces associated with the cental magnet join.

       Also, the less copper that is used, the=
 lower the force.



       Regards,



       Chris Chapman