Nonlinearity induced bifurcations and chaos in loudspeakers

[Zink]

Howdy, recently i've been interested in the idea of building large sealed subwoofers (18" drivers, ~200L) but recently came across some papers which i haven't seen discussed anywhere online showing some complex effects of nonlinear distortions, particular in larger boxes when user with higher input power. I've had a bit of a read over the papers but the implications still are unclear to me how much of an issue this is and finding what balance of box and driver parameters are ideal to avoid it.

The papers basically show at higher power levels a rapid breakdown of speaker behavior particular in larger boxes due to nonlinearity in effective stiffness between the motors suspension and the compliance of the air in the box. I've seen a handful of old comments online mentioning nonlinearity of air being an issue but often not giving good explanations why. It seems most transducers are generally only linear within a few mm of xmax, the newest paper gives a full complex mathematical formula for showing these effects using wave digital filters but the math is a bit above my level and i'm unsure how i could substitute in my own values for transducer/box to find the limitations of my own designs and where the limits lie. Has anyone got more information on this topic or done any of their own research or have thoughts? It mentioned while the graphs look concerning in theory higher order box designs (BR, bandpass ect) should have even worse issues than sealed :O

Here are the papers and a borrowed image from one.

https://www.sciencedirect.com/science/article/abs/pii/S0003682X21000682

First and newest paper is not public so you will have to track down your own copy...
but the older three are free to read:

https://www.researchgate.net/publication/267797837_Confirmation_of_chaos_in_a_loudspeaker_system_using_time_series_analysis

https://www.researchgate.net/publication/23638269_Verification_of_chaotic_behavior_in_an_experimental_loudspeaker

https://www.researchgate.net/publication/5325548_A_route_to_chaotic_state_on_an_electrodynamic_loudspeaker

 

[kemmler3D]

Welcome to ASR! This is definitely interesting stuff, although a bit over my head personally.

As far as I understand it though, they were able to induce some pretty crazy behavior in these LF drivers at high current.

I read the 2008 paper Verification of chaotic behavior in an experimental loudspeaker.


What surprised me was how measurable hysteresis was - they got different impedances from the driver depending on which direction frequencies were swept.

They also clearly got subharmonics to appear, which some people will tell you are almost a myth.

The chaos theoretical outputs of those measurements are pretty much beyond me (don't ask me what a UPO or fractal dimensionality are) but they do seem to suggest possible ways to optimize loudspeaker behavior at high amplitudes... maybe?

how i could substitute in my own values for transducer/box to find the limitations of my own designs and where the limits lie.

Looking at this paper, they were driving the speaker pretty hard, as much as >100w continuously. This was a ~6" woofer that they were pushing hard at with a 45hz tone, give or take. This is pushing the boundaries of good sense with a 6" driver.

This is a very brutal usage compared to what you have planned.

On some levels the outcomes of this experiment are very interesting, because they're characterizing distortion in a more sophisticated way than I've seen.

On the other hand, you don't need to do that (or any math) to know whether your driver is going nonlinear. The results of this type of test will show up in a traditional distortion measurement, just not with the same specificity. A few mm of xmax for an 18" driver is probably all you need unless you're running concerts, in which case you're probably still more or less within the linear regime.

 

[Zink]

Welcome to ASR! This is definitely interesting stuff, although a bit over my head personally.

Thanks, i've been lurking the forums here for a while and the discussion content here is great, i believe there is a lot of value in a more technical scientific approach to loudspeakers. In the end they are just mechanical engineering systems and should be treated objectively as such to a large degree.

Looking at this paper, they were driving the speaker pretty hard, as much as >100w continuously. This was a ~6" woofer that they were pushing hard at with a 45hz tone, give or take. This is pushing the boundaries of good sense with a 6" driver.

This is a very brutal usage compared to what you have planned.

On some levels the outcomes of this experiment are very interesting, because they're characterizing distortion in a more sophisticated way than I've seen.

On the other hand, you don't need to do that (or any math) to know whether your driver is going nonlinear. The results of this type of test will show up in a traditional distortion measurement, just not with the same specificity. A few mm of xmax for an 18" driver is probably all you need unless you're running concerts, in which case you're probably still more or less within the linear regime.

As it happens i do plan on running concerts, the reason for the very uncommon choice of sealed subs mostly comes down to the styles of music i listen too and intend to have played back, lots of hitech/psycore/slambient/breakcore type stuff which is very modern and highly produced and often 200-300bpm type range requiring fast transients, accuracy and dynamic range that i have noticed is somewhat lacking in most larger systems i've heard. I would say 98%+ of PA systems don't have this requirement and this music is fairly niche. A lot of people seem to be making music in a studio that simply can't be played back loudly and accuratly without getting muddly and being somewhat dissapointing. The low output of sealed boxes boxes is highly inconvenient but the sonic benifits are hard to ignore in terms of settling time and group delay.

Currently looks like 8x double 18's would have enough output to do outdoor shows in the roughly 400-600(?) person size i think. Already have some early designs drawn up.
This fairly new eighteensound driver looks fairly suitable for sealed use, these boxes will be reverse loaded for cooling as they will be driven fairly hard and fast for multiple days non stop. https://www.eighteensound.it/en/products/lf-driver/18-0/4/18NLS4000


Some hornresp sims of 16x drivers in said box, some more room for eq optimisation on this for sure.

And box design pending a bunch of redesign, depth is a bit long currently and has some resonant modes in the working band so might go wider and less deep. Also needs bracing drawn up ect...



Still will be a while to go before i gather up some funds for this system so mostly just trying to do as much analysis as i can currently before placing any orders.

 

[restorer-john]

as they will be driven fairly hard and fast for multiple days non stop

Music festivals or bush doofs?

 

[Zink]

Music festivals or bush doofs?

Small-medium sized doofs mostly is the plan
But assuming the system is up to the job i wouldn't be against renting it out to more mainstream events.

 

[JSmith]

doofs

JSmith

 

[Waxx]

That kind of raves typically use (folded) horn systems based on old Turbosound rigs, and most people are so high on dope they don't care about accuracy anymore, it needs to be loud and fast. I know, because i was "sound engineer" in that scene for quiet some time. a few decades ago...

 

[Zink]

That kind of raves typically use (folded) horn systems based on old Turbosound rigs, and most people are so high on dope they don't care about accuracy anymore, it needs to be loud and fast. I know, because i was "sound engineer" in that scene for quiet some time. a few decades ago...

I've had the chance to listen to a few systems currently going around and had a few chats with the owners/builders, Meta Sound (best i've ever heard), Nexus Sound, Sub Temple, Buzz speaker hire's Void Nexus and their new MM-Acoustics rig and some various smaller systems over the years. I've been going to outdoor parties for bit over 10 years now and run a few parties with my own very small system so have a fairly good understanding of what's around and needed for various types of music.

As i mentioned in an earlier post, some of the newer music styles that literally didn't exist 10 years ago are notably more demanding on the sound system and pushing the limits a lot more than previous styles like regular psytrance and techno. Myself and many others have been able to notice some flaws in the music reproduction when scaled to larger rigs that i'm attempting to address with this build.

 

[JSmith]

newer music styles that literally didn't exist 10 years ago are notably more demanding on the sound system and pushing the limits a lot more than previous styles like regular psytrance and techno.

Nah... try some 30+ year old hardcore techno for example and see how the sound systems react to that.


JSmith

 

[kemmler3D]

some of the newer music styles that literally didn't exist 10 years ago are notably more demanding on the sound system and pushing the limits a lot more than previous styles like regular psytrance and techno.

Not that I keep up with the vagaries of breakcore subgenres, but we've had 0dBFS @ 20-40hz electronic music for many years now, sonny. And the live sound sucked ass back then too. If you lived through the dubstep craze then you know people have been abusing their subs for quite some time now. And let's not forget about speedpunk, even though I think everyone's blessedly forgotten it by now.

In all seriousness, If you're doing sound outdoors your job gets much easier, as you really only need to worry about reasonable placement relative to the crowd and the performance of the speakers themselves.

I think the real upshot from that research for the would-be sub designer is that you need to keep xmax as low as possible to avoid nonlinearities.

And at 200+ BPM your RT60 and clarity will become a big focus, as you imply. You may need to set up cardioid subs if you're playing any of that stuff indoors and you want to be able to make out the beat.

 

[Waxx]

breakcore and psycore was arround 20-25 years ago when i was in the scene, those are not new. Breacore was rather big with the infamous Breakcore gives me wood parties in Ghent (where i was sound engineer) at that time And the hardtek and acid core and raggacore was also very demanding.

And i'm not talking yet about modern UK steppers dub that even asked more bass response than those styles. What is happening now is not that new. UK steppers goes back to the late 1980's with crews like Jah Tubby's and Jah Shakka and the most infamous soundsystem stack of that time, King Earthquake (that lived up to his name).

The most famous sound crew in that harder electronic rave music today in Belgium for those styles is now Warboel from Brussels, but it's a semi-illigal scene so the crews try to stay out of the mainstream view as most parties are still illigal raves down here...

 

[Zink]

Nah... try some 30+ year old hardcore techno for example and see how the sound systems react to that.

Nice, nothing wrong with a bit of old gabber but sadly it doesn't get much play time at the parties i usually go too

Not that I keep up with the vagaries of breakcore subgenres, but we've had 0dBFS @ 20-40hz electronic music for many years now, sonny. And the live sound sucked ass back then too. If you lived through the dubstep craze then you know people have been abusing their subs for quite some time now. And let's not forget about speedpunk, even though I think everyone's blessedly forgotten it by now.

Breakcore is the odd one out of the genres i mentioned and not quite as fast as the others.

Haha yep i am indeed old enough to remember the dubstep era, i actually still quite enjoy it. More-so the chunkier UK style rather than the squeaky skrillex stuff but it do still hear it played out somewhat regularly here.

I'll link a few assorted tracks to clarify some of the styles that i've found issues with, its often common in these genres the bass line will be kick-bass-bass-bass but at 200bpm, the in between bass bits can really start to blur together especially at the lower frequencies where there is often high group delay on some box types.

https://soundcloud.com/wachumarecords%2F12-mirror-me-unalloyed-gold https://soundcloud.com/bilycore%2Fbilycore-kromacore https://soundcloud.com/theongoingarcanum%2Flaw-of-the-jungle https://soundcloud.com/jiazihulive%2Fjiazihu-vallak-macabre-tale-release-soon-in-va-cyberroots

breakcore and psycore was arround 20-25

Weirdly, not the same psycore as the old psycore, a whole new branch came out from the psytrance scene about 6-7 years ago as a darker faster version of darkpsy+hitech and has basically no connection to the previous genre by the same name from the hardcore electronic scene. But yeah breakcore ain't new.

I think the real upshot from that research for the would-be sub designer is that you need to keep xmax as low as possible to avoid nonlinearities.

Yep i think that's the only real conclusion to come for unless i try to rebuild the simulation formulas with my own inputs.
Luckily if the hornresp sims are anything to go by the displacement is actually fairly low in the 30-100hz region where most of the music is.

 

[Waxx]

Nice, nothing wrong with a bit of old gabber but sadly it doesn't get much play time at the parties i usually go too

Breakcore is the odd one out of the genres i mentioned and not quite as fast as the others.

Haha yep i am indeed old enough to remember the dubstep era, i actually still quite enjoy it. More-so the chunkier UK style rather than the squeaky skrillex stuff but it do still hear it played out somewhat regularly here.

I'll link a few assorted tracks to clarify some of the styles that i've found issues with, its often common in these genres the bass line will be kick-bass-bass-bass but at 200bpm, the in between bass bits can really start to blur together especially at the lower frequencies where there is often high group delay on some box types.

https://soundcloud.com/wachumarecords%2F12-mirror-me-unalloyed-gold https://soundcloud.com/bilycore%2Fbilycore-kromacore https://soundcloud.com/theongoingarcanum%2Flaw-of-the-jungle https://soundcloud.com/jiazihulive%2Fjiazihu-vallak-macabre-tale-release-soon-in-va-cyberroots

Weirdly, not the same psycore as the old psycore, a whole new branch came out from the psytrance scene about 6-7 years ago as a darker faster version of darkpsy+hitech and has basically no connection to the previous genre by the same name from the hardcore electronic scene. But yeah breakcore ain't new.


Yep i think that's the only real conclusion to come for unless i try to rebuild the simulation formulas with my own inputs.
Luckily if the hornresp sims are anything to go by the displacement is actually fairly low in the 30-100hz region where most of the music is.

When i hear that "new hardcore" played today it's just a simpler version of the old gabber house and hardtek and hardcore of our time (1990's and early 00's). It's not new at all. Idem with the modern Breakcore, those things did happen also 20 years ago, it was just more underground than now.

 

[tmuikku]

Hi,
if you make sealed subs for PA consider heat which would build build up and rob headroom rather quick I speculate. Perhaps mount drivers magnet out or something. Heat would increase voice coil resistance, which would reduce electrical damping and subject the driver to jump resonance, another bifurcation

https://www.researchgate.net/publication/267836914_Jump_Resonance_in_Audio_Transducers

Perhaps use as much and big woofers as possible, in order to keep power&excursion per woofer down to maintain overall best sound, including all non-linearities, it all is related to excursion, SPL.

 

[Zink]

Hi,
if you make sealed subs for PA consider heat which would build build up and rob headroom rather quick I speculate. Perhaps mount drivers magnet out or something. Heat would increase voice coil resistance, which would reduce electrical damping and subject the driver to jump resonance, another bifurcation

https://www.researchgate.net/publication/267836914_Jump_Resonance_in_Audio_Transducers

Perhaps use as much and big woofers as possible, in order to keep power&excursion per woofer down to maintain overall best sound, including all non-linearities, it all is related to excursion, SPL.

Have a look at previous posts i already discussed this and linked a picture of the proposed box design

 

[tmuikku]

Oops, missed it Yeah resonances inside the box, big panels can resonate loud, and there's gonna be resonance on the cavity in front as well. I encourage to build a prototype before actual production run to make sure quality is as high as you want it. Big boxes are pain to build and can have quite obvious "box sound" to them in home hifi size territory and these are at least double in size. But, perhaps you have more experience than me and can handle it!

 

[tmuikku]

I suppose you know the powersoft m-force subs with linear actuators? Beasts: https://www.powersoft.com/en/applications/oem-solutions/m-force-sub
And gives hint how demanding it actually is to make sufficient SPL at very low frequency.

There is number of videos by Dave Rat in youtube with his supersubs, which I think are using these as well. Here is fun one

 

[Zink]

Oops, missed it Yeah resonances inside the box, big panels can resonate loud, and there's gonna be resonance on the cavity in front as well. I encourage to build a prototype before actual production run to make sure quality is as high as you want it. Big boxes are pain to build and can have quite obvious "box sound" to them in home hifi size territory and these are at least double in size. But, perhaps you have more experience than me and can handle it!

I've done a few helmholtz/eigenmode analysis in comsol already, having the drivers on an angle really helps reduce some of the more extreme modes but potentially some more non parallel surfaces internally along with several bracing parts with a small amount of damping material in some specific spots will hopefully do the job. But yes do agree a test box before commencing the whole build is part of the plan.

I suppose you know the powersoft m-force subs with linear actuators?

Yep done a bit of reading on them and general moving magnet linear oscillating actuator design. It generally seems like when a transducer has extremely high BL and BL^2/Re which is usually coupled with tight suspension it can get a strong peak response around resonance that really requires a vented/bandpass/horn design with low tuning to stretch and smooth out the final response. Transducers ideal for sealed boxes are not particularity common these days as the design of them doesn't follow quite the same path as whats currently available on the market. Using a Mforce in a sealed box would be a massive waste wouldn't be able to use it anywhere near its capacity really requires box loading from what i can see and i'm specifically trying to avoid higher order box designs due to the unavoidable phase/stored energy issues that they all contain.

 

[Waxx]

Horn subs are still the best for this. Most soundsystems today used by dj crews use huge folded horns, much like the Labhorn. And if it are not horns, they are paraflex (a kind of TL variation) designs, that go very loud and low, but are not clean in sound at all. These music styles don't require clean neutral subwoofers, they need to be very loud and go low (40Hz minium, mostly lower) and distortion is an inherent part of the sound, even in the music itself.

 

[tmuikku]

I've done a few helmholtz/eigenmode analysis in comsol already, having the drivers on an angle really helps reduce some of the more extreme modes but potentially some more non parallel surfaces internally along with several bracing parts with a small amount of damping material in some specific spots will hopefully do the job. But yes do agree a test box before commencing the whole build is part of the plan.

nice, you seem to be on top of the game!

Some thoughts in case you haven't already considered them as well.
You can reduce lowest mode inside by having the transducer midway of long dimension, or in case of multiple transducers put their acoustic center mid of the longest dimension. Non-parallel walls just randomize modes, and internal divider panels can make even longer paths and lower modes and so on, not really addressing any of it. They could be effective on short wavelengths, but also any damping material is. Perhaps there is something to exploit like 1/4 wave resonators, but in general the lowest mode would be loudest and hardest to tame so most problematic one. Anything that fits inside the box has quite little effect to it due to huge wavelength, hence putting transducer midway of long dimension is a good start for a good sounding closed box. If it is a problem in the first place.

If you imagine such box where woofer is middle of long dimension, for a given volume it could be relatively slim in depth and have relatively big square baffle with 1-4 woofers on it so that their acoustic center is center of the baffle. But then there is the utility, like standard truck dimensions, ply sheet sizes and so on. On the other hand, borrowing from big horn systems you might be able to get some extra output by maximizing baffle area and assemble a huge wall with the boxes. Not sure if there is enough benefit on such low frequencies though in any reasonable number of boxes and with big wall you might end up interference issues higher up in frequency requiring more processing. You'd have to make manifold kind of thing to house the driver magnet out but not sticking beyond the "baffle" robbing the volume inside, only few panels sizes and no angled panels for easy assembly though. And so on.

edit. attached rough sketch to illustrate.


I really haven't thought this kind of systems before so it's just for fun. There is lots of things to consider and I'm likely not familiar with most of them what comes in your application. Hope this helps you to gather your thoughts to get forward!