Diy Piezo Spring Reverb

[Rob Strand]

Thanks Rob, a good reading while I'm still in bed. (thanks Yellow Fever vaccine )

That paper is a good start.  The numbers seem to make sense.

Parker & Bilbao say: "The magnetic bead is driven torsionally by passing a signal into
a nearby electromagnetic coil. Torsional vibration of the magnet/wire
system translates to vibration tangential to the path of the
wire at a point within the helix."

Yes, I've read that before in the National Semiconductor Audio Handbook.  It actually describes things is a bit more detail.   I'm fairly sure most information around came from Accutronics literature of the 1970's.
See part 2, section 5-7 to 5-10 from this document,
https://e2e.ti.com/support/amplifiers/audio_amplifiers/w/design_notes/3315.blast-from-the-past-1980-nsc-audioradio-handbook
https://e2e.ti.com/cfs-file/__key/communityserver-wikis-components-files/00-00-00-00-03/1980-NSC-Audio-_2600_-Radio-Handbook-_2D00_-Part-2.pdf

It also implied the torsional drive has a slow propagation which helps give the long delay.

In order to get a torque that rotates the end of the spring the magnet must magnetized across the cylinder.
What concerns me about having this type of system is the magnet also needs to be pointing in the right direction.  If the magnetic field points across the gap you don't get any torque.  The magnetic field needs to be in parallel to the faces of the gap and perpendicular the axis of the spring.  That's going to be a headache for manufacturing.  It also means you can stuff up the motor or sensor by rotating the magnets.   I used to think the magnets were polarized along the axis and the magnet applied a torque but it did so by rotating along the magnet diameter line .  That would pull the wire up and down.  That way you don't care about the magnet orientation.

Because of that I'm scared to pull one apart to the point that I can get to the magnets and measure the direction of the magnetic field!

The ratio R/r on the Fc eq. looks like the rotation of one closed turn.

I've always approached this stuff as the cut-off is near a resonant frequency where the forces for against the spring and the forces against the inertia of the mass are about equal.  More or less like the sqrt(k/m) example you gave before except more general in that freq is proportional to sqrt(stiffness / mass).   If you apply this to the spring or a wire you get the r/R^2 term.    I did that a couple of ways (not expecting the exact answer) and what I noticed is the Fc in the paper doesn't depend on N which I suspect you can only get by solving the equations for the distributed system.

Other than that, I haven't tried to analyse this thing any further than the paper.

It makes me wonder,
-the speaker gives a nice punch to the spring along the axis. The movement of the turns is visible, so the spring must be expanded enough to avoid turns hitting each other.
-and the edges of the coil are fixed at both sides, no rotational force at all.

The thing about these 2D/3D systems its when you excite one mode of oscillation it tends to oscillate the others.  So it turns out any drive system will work.  Maybe if you drive the intended mode directly it gives a more efficient drive and receive system.   There was one DIY reverb which used a speaker but instead of driving longitudinally, the speaker was mounted side-on and an arm from the face of the speaker connected to the end if the spring.  It was done in a way that the in-out motion of the speaker caused a rotation of the spring.   I also remember reading the magnetic field across the diameter can prevent mechanical noise and help with feedback immunity.  So maybe rotational sensing is also good.

[Rob Strand]

What if you fix the spring with one of those swivels, allowing it to rotate?

Friction/stiction might cause creaks.   I suspect that why an elastic end piece is better.

[Rob Strand]

The reverb tank is in a cylindrical cardboard tube.  It has a shielded wire (output?) and two unshielded red wires coming out.  I get about 60 ohms across the red wires, but the shielded wire reads open.  Maybe it was driven with a transducer, but has a piezo pickup?  Who knows!  I haven't tried to open it because I might list it on Ebay.

That's a funky set-up.  Probably not worth risking damaging the unit.

The magnetic drive and ceramic sense seems to be the way to go.   I don't know about the unit I posted from the magazine.   I seemed to recall the magazine implied it had a low impedance and they put a resistor in series with it.   Unfortunately that doesn't help identify the drive system.    The old Motorola piezo tweeters used to have a similar set-up, so maybe it was piezo drive.

[mac]

Thanks again Rob for those TI pdfs.

It also implied the torsional drive has a slow propagation which helps give the long delay.

In order to get a torque that rotates the end of the spring the magnet must magnetized across the cylinder.
What concerns me about having this type of system is the magnet also needs to be pointing in the right direction.  If the magnetic field points across the gap you don't get any torque.  The magnetic field needs to be in parallel to the faces of the gap and perpendicular the axis of the spring.  That's going to be a headache for manufacturing.  It also means you can stuff up the motor or sensor by rotating the magnets.   I used to think the magnets were polarized along the axis and the magnet applied a torque but it did so by rotating along the magnet diameter line .  That would pull the wire up and down.  That way you don't care about the magnet orientation.

Because of that I'm scared to pull one apart to the point that I can get to the magnets and measure the direction of the magnetic field!

In a standard reverb tank the magnet moves in circles, not along the spring axis, and that movement creates torsional waves along the spring.
It's like the Earth's orbital and axial (or spin) momentum.
I had noticed this when I tried magnets inside coils, as I wrote before in this post.

http://sound.whsites.net/articles/reverb.htm

I've always approached this stuff as the cut-off is near a resonant frequency where the forces for against the spring and the forces against the inertia of the mass are about equal.  More or less like the sqrt(k/m) example you gave before except more general in that freq is proportional to sqrt(stiffness / mass).   If you apply this to the spring or a wire you get the r/R^2 term.    I did that a couple of ways (not expecting the exact answer) and what I noticed is the Fc in the paper doesn't depend on N which I suspect you can only get by solving the equations for the distributed system.

Roughly speaking, Fc is calculated from the group velocity, which is an "average" speed, ie, the envelope of many waves. L or N are likely to get lost going in circles along the spring

There was one DIY reverb which used a speaker but instead of driving longitudinally, the speaker was mounted side-on and an arm from the face of the speaker connected to the end if the spring.  It was done in a way that the in-out motion of the speaker caused a rotation of the spring.   I also remember reading the magnetic field across the diameter can prevent mechanical noise and help with feedback immunity.  So maybe rotational sensing is also good.

I'll try this. I hope the piezo can read it.

I also thought of two speakers face to face, and two thick wires glued to the cones. One wire soldered to the upper side of the spring, the other to the lower end.
When the speaker cones move they do what you do with your hands when your are turning the car's wheel.

mac

[mac]

Main difference between this speaker-piezo reverb and a standard reverb:

- In a reverb tank the spring is under torsion forces, not along the axis.
The model in the PDFs Rob posted before describes a wave travelling along the spring.

- The speaker force on the spring is mostly axial. Radial and angular displacements are negligible as the frequency goes down.
The turns move along the axis, and nodes and peaks are visible, like a gas on a pipe.

Things to have in mind if you try this,

>The separation or tension of the spring is critical to avoid turns hitting each other at lower frequencies, or larger wavelenghts.
>Spring should be hold tightly at both ends.
>Thick wires roll off highs.
>A floating piezo absorbs part of the speaker energy.
>Piezos are sensible, any speaker distortion will get in the way.

I update the circuit, I'm using two opamps as buffers and I'm getting an overall tone improvement.
Uploading soon.

mac

[Rob Strand]

In a standard reverb tank the magnet moves in circles, not along the spring axis, and that movement creates torsional waves along the spring.
It's like the Earth's orbital and axial (or spin) momentum.
I had noticed this when I tried magnets inside coils, as I wrote before in this post.

Thanks for the link.   OK I get that part.  I still don't know which way the magnets are polarized, which determines how the forces/torque are applied.  When the magnet orbits I suspect this is a *result* of the spring.   It's like a guitar string if you pluck it any way, or bang the guitar, the strings eventually follow an elliptical motion.

I applied the maximum DC current to the reverb and tried to observe/feel force.   I could not feel or see the any deflection or rotation.  I could hear a small "tick".   I might repeat the test again with the spring removed.

Roughly speaking, Fc is calculated from the group velocity, which is an "average" speed, ie, the envelope of many waves. L or N are likely to get lost going in circles along the spring

That makes sense.   The results which have N are likely to be macro effects, not wave propagation, like the transverse motion when you hit the reverb.   The frequencies are much lower.

I also thought of two speakers face to face, and two thick wires glued to the cones. One wire soldered to the upper side of the spring, the other to the lower end.
When the speaker cones move they do what you do with your hands when your are turning the car's wheel.

On one hand I think it's the old problem that if the system isn't perfectly symmetrical all the propagation modes exist.   So it doesn't matter how you excite or detect you end up getting a bit of each.   On the other hand, when I calculated the longitudinal wave speed, I get delays about half that of what the Parker paper predicts.    That could mean the dominant propagation in your set-up is longitudinal not torsional (as assumed in Parker paper).

            mac1    mac2
mass [g] 0.74   13.61
Td [ms] 14.16   55.87

Perhaps that explains why your mac2 spring sounded about right (?).   The Parker equations predict a longer delay.

Here's a good summary of the simpler equations,
http://www.physics2000.com/PDF/Non-CalcText/Ch13WaveSpeedNonCalculus.pdf

Keep in mind that L in this paper, the length of the spring in the operating position, is actually H in the Parker  paper.

What you do think?   

[Rob Strand]

Grrrr.  Forgot to post this. 

Here's the link for the DIY unit with the ceramic cartridge,

http://www.ozvalveamps.org/reverbs.htm

Scroll down to half way until you see.
   Radio Constructor
   Reverberation Unit by Hal Moorshead

From what I can work out the article is actually from Practical Wireless (UK) July 1970, not Radio Constructor.

[thermionix]

-

[Rob Strand]

I haven't had a chance to go over this one properly.   It's referred to in the Parker paper,

http://newt.phys.unsw.edu.au/music/people/publications/Fletcheretal2001.pdf

The paper starts with a beam.  In this context the orientations of transverse/longitudinal/torsional take on different meanings.  (Later on it translates to the axis of the helix.)

[mac]

I still don't know which way the magnets are polarized, which determines how the forces/torque are applied.  When the magnet orbits I suspect this is a *result* of the spring.   It's like a guitar string if you pluck it any way, or bang the guitar, the strings eventually follow an elliptical motion.

And I still don't know IF the driving magnetic field is
- like in a standard transformer, the lines along the lamination, with the upper and lower lines running in opposite directions
- if there is some leaking field between laminations, forming a vertical field, a kind of N-S magnet.

I found this post at diyaudio,

http://www.diyaudio.com/forums/parts/289882-spring-reverb-transducers.html

It seems it's magnetized radially.
Neodymium magnets of this type can be found for a few bucks.

On the other hand, when I calculated the longitudinal wave speed, I get delays about half that of what the Parker paper predicts.    That could mean the dominant propagation in your set-up is longitudinal not torsional (as assumed in Parker paper).

            mac1    mac2
mass [g] 0.74   13.61
Td [ms] 14.16   55.87

Perhaps that explains why your mac2 spring sounded about right (?).   The Parker equations predict a longer delay.

When a spring is compressed or expanded by a force, a speaker, you have to use the shear modulus, not Young's modulus.
The Young modulus is used because a torsion force can be thought as a hammer hitting the spring in the "s" direction, as defined in the Parker Bilbao paper. You are compressing the wire a bit along that direction, ie, along the wire.
That is, a "longitudinal" wave running along the wire. From the distance, we called this wave torsional.
In my case, the speaker deforms the spring in a different way, almost perpendicular to the wire. This looks like a "transverse" wave along the wire. But again, from the distance we say it's a longitudinal wave along the spring axis.
Messy, isn't it?

IIRC, and this is stuff I haven't seen in 30 years, my delay time should be,
Tm=2*Lt/sqrt(G/d)
where
Lt: the uncurled lenght of the wire
G: shear modulus, 44,7*e(9) N/m2 [kg/m/seg2] for copper
d: density, 8960 kg/m3 for copper

I am hearing a short echo, similar to the audio latency of my old Power Mac 7300/180 of about 13ms.
The formula above gives me near 6ms for mac2 spring.

Anyway, the axial spring model is similar to a gas on a pipe. Have to dig deeper for better aproximations.

http://home.uni-leipzig.de/prakphys/pdf/VersucheIPSP/Mechanics/M-16E-AUF.pdf

mac

[mac]

I wonder if an unused guitar mic can be used to drive a magnet attached to a spring, or a magnetic spring made of a guitar string.

And I was thinking of a different kind of spring, a flat balance spring.
The external side of the wire perpendicular to the speaker to have torsion motion, and the center attached to the piezo.



mac

[Rob Strand]

And I still don't know IF the driving magnetic field is
http://www.diyaudio.com/forums/parts/289882-spring-reverb-transducers.html

It seems it's magnetized radially.

I can't see how a radially polarized magnet can work.    They only work when
you poke magnetic material inside the hole; that conducts the field out of the hole.
(The other use is putting things inside the hole.)

I'm pretty sure I've got a handle of how the motor system works.  There is just a vertical field
inside the gap between the core faces.   The magnet tries to align with the field and that produces
a torque on the magnet.   For case C it's already aligned so to the torque is low.  There can be a weak vertical force due to a different mechanism; basically the field is slightly stronger near the core and that causes a force due to the field gradient.

Here's the cases for the different magnets.   The arrows represent the field direction.  The circular paths in B and D represent the rotation due to the torque.



What isn't clear is if is case B or D.    Case B requires alignment of the magnet during manufacturer which borders on impractical to me.   Misalignment of the magnet could result in case C which is fairly useless.

When a spring is compressed or expanded by a force, a speaker, you have to use the shear modulus, not Young's modulus.

I understand what you are saying here.   

The longitudinal speed in the simple paper is in terms of k and M.   k is the compression/expansion spring constant.     k actually contains G.   (When you design springs for a certain k you use G plus the geometry and turns.)

If you look at equation 2.4 and figure 1 of the Fletcher 2001 paper he formulates the longitudinal speed in terms of G (inside of c_psi_0).   The interesting thing is in equation 2.4 the longitudinal speed, along the helix axis, is slower by a factor of 1/sqrt(2).  That and the fact G is less than E explains why the longitudinal speed is slower by a factor of 2.

That is, a "longitudinal" wave running along the wire. From the distance, we called this wave torsional.
In my case, the speaker deforms the spring in a different way, almost perpendicular to the wire. This looks like a "transverse" wave along the wire. But again, from the distance we say it's a longitudinal wave along the spring axis.
Messy, isn't it?

(Yes) The geometry of the beam and the geometry of the helix flip some of the co-ordinates.   I guess the significant contribution from Wittrick 1966 was to unravel the calculations.

I am hearing a short echo, similar to the audio latency of my old Power Mac 7300/180 of about 13ms.
The formula above gives me near 6ms for mac2 spring.

That seems quite short.

IIRC, and this is stuff I haven't seen in 30 years

Same here.   I've only use small amounts of this stuff over the years. 
My deeper intuition seems to have gone out the window.

[Rob Strand]

And I was thinking of a different kind of spring, a flat balance spring.
The external side of the wire perpendicular to the speaker to have torsion motion, and the center attached to the piezo.

I don't see why it won't work. I guess the issue is to get enough delay.
If you tried to connect more than one spring (by connecting the inside to the inside then the outside to the outside) it's probably easier to just use the cylindrical spring.

[Digital Larry]

I really love this thread the longer it goes on.  I think spring reverb is "just one of those things" that some clever guy invented because nothing else was possible at the time.  It didn't really do what it was supposed to do perfectly, but it took on a life of its own and is now highly sought after (at least in some musical situations).  I'm really interested to hear what anyone comes up with using no traditional springs, especially if it can do long (4 to 6 second perhaps) decay times.

Even though I have digital reverbs galore I put a real spring in when I built up my modular synth system.

As a kid we used to "zing" on the garage door springs with a screwdriver.  Hours of cheap entertainment!

[Rob Strand]

I think spring reverb is "just one of those things" that some clever guy invented because nothing else was possible at the time.  It didn't really do what it was supposed to do perfectly, but it took on a life of its own and is now highly sought after (at least in some musical situations).

So very true.  Like a lot of stuff from the early days.  The Fender Rhodes comes to mind.

The thing that amazes me most about guitar stuff is the sound of guitar is defined by a combination of Tube amps, totally flawed speakers from a hi-fi perspective, and the inherent limitations of pickups.   A good deal of technical improvements only seems to subtract from that winning combination.   You wonder how it came to be.

I'm really interested to hear what anyone comes up with using no traditional springs, especially if it can do long (4 to 6 second perhaps) decay times.

Even though I have digital reverbs galore I put a real spring in when I built up my modular synth system.

You might be interested in this stuff.   Stefan Bilbao, the co-author of the Parker paper, seems like he's got this stuff down at all levels,

http://www.acoustics.ed.ac.uk/group-members/dr-stefan-bilbao/
http://www.ness-music.eu/wp-content/uploads/2013/06/dafx13.pdf
https://www.researchgate.net/publication/224586163_A_Virtual_Model_of_Spring_Reverberation

[Rob Strand]

After lot of pain I've managed to work out the way the reverb springs are driven.

The reverb motor system causes the magnets to rotate about their axis.  That implies the magnets are polarized diametrically and the magnets field is orientated horizontally.

A positive current into the center pin causes the magnets to rotate in a clockwise direction when looking at the magnets from the spring side.    From what I can make out a positive on the center pin gives a B-field vertically upwards across the gap (opposite directions to my diagram posted previously).   That means the magnets are polarized diametrically and orientated horizontally from right to left.



Comments:
- The torques on the left hand magnet seem stronger than the right hand magnet.  This might be due to the fringing around the end of the core.  It would be better to extend the core further to right.


The problems & solutions:
-  I've never spent so much time deciding a motion was a rotation or a vertical vertical movement.
- The forces and torques are tiny.
- With the springs loaded you cannot see any spring motion.  The tension is too high.
- The stiffness/friction in the pivot sometimes makes a rotation look like a vertical movement.
   This was particularly a problem when the springs were removed.
- I used about 800mA DC to give the largest force/torque possible.
- I checked the movement two ways: 
   The first way was to removed the springs and attach wires with just enough mass and moment that they were the dominant load.  That got round the pivot friction issue.
   The second  was to insert the spring but to add a long wire link at one end so I could tune the spring tension just enough to see the movements.

Anyway,  the good thing is the rotary drive was mentioned in the NSC Audio Handbook, the Parker Paper, and the Rod Elliots ESP website.   So I can only conclude it is that way.    That brings up the question on how to align the magnets in production.   It also means the magnet must be mechanically attached to the end-pivots, otherwise the magnets will spin without transferring torque to the springs.

[PRR]

To maybe state an obvious:

You can find the poles of a round magnet with a very fine pin. If a pin sticks top/bottom, or left/right, it is magged across a diameter.

If it IS poled that way, then in production you lay the magnet on an iron surface. Presto, one pole goes to the iron and now you know which way to go. Logically this could be an iron jig which then slides into the pickup assembly.

[Rob Strand]

You can find the poles of a round magnet with a very fine pin. If a pin sticks top/bottom, or left/right, it is magged across a diameter.

I'm working on it  .  I've got to find something suitable.   I tried sticking stuff to the magnets but I couldn't feel anything.  The magnets are very weak and/or the things I've tried are actually stainless.

If it IS poled that way, then in production you lay the magnet on an iron surface. Presto, one pole goes to the iron and now you know which way to go.

Good idea!  I noticed the magnets are also phased correctly, so maybe take that one step further and use a magnet so it points in the right direction.   It didn't occur to me before but they might first make the little wire pivot assemblies with the magnets attached then magnetize them later.  There's little hooks for the springs which are mounted in a consistent way so that ensures the magnets would point in the right direction.

If it IS poled that way

I'm very certain of it.  I played around with it for ages until I was sure.

[PRR]

> I played around with it for ages until I was sure.

Your interpretation agrees with all I have read, but I am very glad you are doing the confirmation.

(Yes, random assembly and post-magnetizing makes sense too.)

[mac]

A better circuit for the speaker-piezo,



mac