Simulation Overview - Loudspeakers Design via Shape and Topology Optimization

[Head_Unit]

improving the strength of the basket to minimize structural failures during handling and transportation.

I once worked at a company that shall remain nameless...they had a cool looking magnet structure, super beefy. 18" woofers. At one point the aluminum baskets were...
1.8 mm thick!?!?

Yeah, they broke a lot. So I redesigned the basket to be much stronger, and easier to manufacture. But since they had literally containersful of baskets (why so many???) they kept building with the old baskets

 

[Head_Unit]

Room modes are a good topic, and it is on the short list.

There are some online simulations which I believe simulate rectangular rooms with perfect inelastic walls. I really dislike that as I feel it's misleading (though maybe it's not a big difference?)
--> I think what would be most useful would be NOT simulations of perfect rectangular rooms, since I'm pretty sure few people have totally sealed rectangular rooms made of concrete. It would be really interesting compare such perfect rooms to real rooms:
- You have like a door into a kitchen or hallway or both.
- Angled cathedral ceilings
- Real drywall-on-stud walls, difference versus ideal perfect walls.
- And how the pressure varies vertically since usually sims are shown as a view from above, which gives the impression the pressure is the same at all heights.
As a loudspeaker engineer I gotta say I found the first post really really interesting.

 

[René - Acculution.com]

There are some online simulations which I believe simulate rectangular rooms with perfect inelastic walls. I really dislike that as I feel it's misleading (though maybe it's not a big difference?)
--> I think what would be most useful would be NOT simulations of perfect rectangular rooms, since I'm pretty sure few people have totally sealed rectangular rooms made of concrete. It would be really interesting compare such perfect rooms to real rooms:
- You have like a door into a kitchen or hallway or both.
- Angled cathedral ceilings
- Real drywall-on-stud walls, difference versus ideal perfect walls.
- And how the pressure varies vertically since usually sims are shown as a view from above, which gives the impression the pressure is the same at all heights.
As a loudspeaker engineer I gotta say I found the first post really really interesting.

Good topics to get into. It is a really good idea to understand the modes in a room where you can analytically calculate them such as rectangular room. With the simple calculators these same modes are found but to add doors and such you really need simulations.

 

[Vintagefan]

Regarding those baskets, looking at the past and in your car gives us a possible solution: oval baskets!
Instead of having a circel with 1 symmetrical and high Q, you have 2 and 4 symmetricals smearing the modes and resulting much lower Q. Regarding suspension and cone behauviour the same. Oh, yes genelec monitors perhaps Nowadays or KEF b139 a while ago.

 

[Vintagefan]

Another extreme attempt by yamaha: elephant ears

 

[Adam Bernau]

Another extreme attempt by yamaha: elephant earsView attachment 235032View attachment 235033

I actually have working specimen of the Yamaha speaker in my vintage Electone 70s organ!

 

[Alexium]

What about simulating midrange and tweeter drivers? Domes, BMRs? Do these approaches work just as well for them as for typical subwoofer and midbase drivers?

 

[NTK]

What about simulating midrange and tweeter drivers? Domes, BMRs? Do these approaches work just as well for them as for typical subwoofer and midbase drivers?

Certainly. In case of BMRs, Tectonic uses COMSOL extensively on their BMR designs.

Multiphysics Helped Design the Gold Standard for VR Audio

To develop a VR headset with immersive audio, Valve Corporation teamed up with Tectonic Audio Labs. See how they used multiphysics to achieve their goal.

www.comsol.com

 

[René - Acculution.com]

What about simulating midrange and tweeter drivers? Domes, BMRs? Do these approaches work just as well for them as for typical subwoofer and midbase drivers?

Yes, all of the above. And waveguides and phase plugs.

Certainly. In case of BMRs, Tectonic uses COMSOL extensively on their BMR designs.

Multiphysics Helped Design the Gold Standard for VR Audio

To develop a VR headset with immersive audio, Valve Corporation teamed up with Tectonic Audio Labs. See how they used multiphysics to achieve their goal.

www.comsol.com

Certainly. In case of BMRs, Tectonic uses COMSOL extensively on their BMR designs.

Multiphysics Helped Design the Gold Standard for VR Audio

To develop a VR headset with immersive audio, Valve Corporation teamed up with Tectonic Audio Labs. See how they used multiphysics to achieve their goal.

www.comsol.com

Yep, this is what I do also, plus much, much more ;-)

 

[mgrobins]

Moving into Topology optimization, here is a structural mechanics case, where I optimize the stiffness of a basket (for some given constraints). The holes that appear compared to the initial geometry completely grow out of the mathematics, which I find highly fascinating.

View attachment 130019

Next, an acoustic topology optimization where the complete multiphysics for the driver is included, but the optimization only takes place in the acoustics domain. With an objective to flatten the frequency response, a phase plug (in grey) has appeared in a domain in from of the driver assigned to be topology optimized. Again, this is a case I have never seen done before; including optimization in a full model of a realistic driver. It should of course be investigated how the off-axis response is affected, but imagine the time savings that are possible, compared to the traditional methods with clay modelling, and general trial and error with no guidance.

View attachment 130021

A final example is actual a heat conduction topology optimization case. As heat affects the material parameters of the structural mechanics and magnetics domains (and also the acoustics to some degree), it is desireable to lead heat away from the driver. So I thought this could be an interesting challenge. While I had never done any heat conduction cases, I spend a day reading relevant papers and setting up the simulation, and set the computer to work over the night. And I got this pretty heat sink.

View attachment 130022

-Closing remarks-
The above techniques are not all being utilized in the loudspeaker industry yet, but with the interest I am experiencing from several of them it will just be a matter of time, before we see more designs that are aided by formal optimization. Also, there are more simulations that I have not touched upon in the above, but I am working on composites with anistropic layer, metamaterials, and additional optimization cases, that will benefit the loudspeaker industry, so stay tuned.

- About me -
René Christensen, Denmark, BSEE, MSc (Physics), PhD (Microacoustics), FEM and BEM simulations specialist in/for loudspeaker, hearing aid, and consultancy companies. Own company Acculution, blog at acculution.com/blog

Rene' are you familiar with any work being done on Topology Optimisation for cabinet design? With cabinets where space is of vital consideration and bracing essential, I think that the organic designs that may be produced by CNC or 3D printing are something to look at.

I'm designing 2 new subs right now and working within fixed external dimension constraints, reducing the volume of internal bracing is very helpful. EG 5L of bracing in MDF by traditional means (probably not simulated only modelled based on resonant freq's) is rigid in every direction and voluminous. It could be reduced to approx 1L using hollow aluminium tube or structures of directional stability. An organic topology simulation for furniture produces amazing outcomes and I wonder how much advantage could be gained in speakers to optimise dimensions AND coincidentally minimise resonance.

 

[René - Acculution.com]

Rene' are you familiar with any work being done on Topology Optimisation for cabinet design? With cabinets where space is of vital consideration and bracing essential, I think that the organic designs that may be produced by CNC or 3D printing are something to look at.

I'm designing 2 new subs right now and working within fixed external dimension constraints, reducing the volume of internal bracing is very helpful. EG 5L of bracing in MDF by traditional means (probably not simulated only modelled based on resonant freq's) is rigid in every direction and voluminous. It could be reduced to approx 1L using hollow aluminium tube or structures of directional stability. An organic topology simulation for furniture produces amazing outcomes and I wonder how much advantage could be gained in speakers to optimise dimensions AND coincidentally minimise resonance.

I could do that, but with any bracing you are just moving resonances up in frequency. Also, there needs to be a target, which could be a global stiffness, but perhaps it would be better to have one or more forces applied and a fixed bottom. So one would have to really think about how it should be setup. Haven't seen anyone do it. In the next issue of audioXpress I have an article on the topic of acoustic topology optimization, but you are looking at solid mechanics topopt.

 

[Ilkless]

Rene' are you familiar with any work being done on Topology Optimisation for cabinet design? With cabinets where space is of vital consideration and bracing essential, I think that the organic designs that may be produced by CNC or 3D printing are something to look at.

I'm designing 2 new subs right now and working within fixed external dimension constraints, reducing the volume of internal bracing is very helpful. EG 5L of bracing in MDF by traditional means (probably not simulated only modelled based on resonant freq's) is rigid in every direction and voluminous. It could be reduced to approx 1L using hollow aluminium tube or structures of directional stability. An organic topology simulation for furniture produces amazing outcomes and I wonder how much advantage could be gained in speakers to optimise dimensions AND coincidentally minimise resonance.

Genelec has been doing that for a decade for cabinet + port design in its current range, albeit with aluminium castings/moulded polycarbonate as medium. And it works really well with low diffraction, low enclosure resonance and port resonance, such as seen in the Stereophile measurements of the G Three, and the Klippel measurements here.

 

[René - Acculution.com]

Genelec has been doing that for a decade for cabinet + port design in its current range, albeit with aluminium castings/moulded polycarbonate as medium. And it works really well with low diffraction, low enclosure resonance and port resonance, such as seen in the Stereophile measurements of the G Three, and the Klippel measurements here.

They are not doing formal topology optimisation. But of course they have optimised their designs.

 

[Glen20]

Rene' are you familiar with any work being done on Topology Optimisation for cabinet design? With cabinets where space is of vital consideration and bracing essential, I think that the organic designs that may be produced by CNC or 3D printing are something to look at.

I'm designing 2 new subs right now and working within fixed external dimension constraints, reducing the volume of internal bracing is very helpful. EG 5L of bracing in MDF by traditional means (probably not simulated only modelled based on resonant freq's) is rigid in every direction and voluminous. It could be reduced to approx 1L using hollow aluminium tube or structures of directional stability. An organic topology simulation for furniture produces amazing outcomes and I wonder how much advantage could be gained in speakers to optimise dimensions AND coincidentally minimise resonance.

There has been a lot of work done recently in composite meta materials for making next generation acoustically stealth submarines. Combinations of progressively damped multi material, multilayered honeycombs with the aid of 3d printing. extruded plastic fibers, and carbon fibers to make all or part of the honeycomb.
Honeycombs combined with viscoelastic materials bonded to steel plates is a common investigation.
3d printed honeycombs have been combined with prepreg nonwoven natural fibers (hemp, flax) honeycombs on one side and stiffer woven carbon fiber prepreg honeycombs on the other for excellent acoustic damping. Though I can't find the reference. I found a lot of others.



Borresen’s (picture above I hope) has a 3D-printed zirconium woofer basket to make it rigid yet apparently vibration-free. Diaphram is composed of four laminated layers, two in carbon fiber, an intermediate layer with aramid in a honeycomb pattern and finally a titanium layer with special coating.
This has apparently move potential resonances away from the device’s working range, which extends up to 2500 Hz

I presume just cost off manufacture for metal 3d printing a subwoofer enclosure would be non economic even before the R n D. profit is considered

Some references regarding submarine composites , 3dprinting honeycombs etc.
https://doi.org/10.1016/j.compstruct.2021.113974
Three-dimensional printing technology has the ability to fabricate very complex, even arbitrary structures, and has already been applied to print cellular functional structures, including ultra-elastic hierarchical foams [6], ultralight metallic microlattices [7], hierarchical porous ceramics [8] and honeycombs, such as regular honeycombs [9], [10], [11], [12], [13], density-graded honeycombs [14], hierarchical honeycombs [15] and multi-material honeycombs [16].

https://doi.org/10.1016/S0263-8223(00)00175-6
DOI : 10.14429/dsj.71.15954
DOI: 10.12783/dtetr/icaenm2017/7834
DOI:10.3390/jmse11020409
https://doi.org/10.1146/annurev-matsci-070616-124032
https://doi.org/10.1121/10.0005850
https://doi.org/10.1016/j.pmatsci.2015.05.001
https://doi.org/10.1016/j.matdes.2018.01.059
https://doi.org/10.3389/fphy.2022.1068833
https://doi.org/10.1177/00219983211066386
https://doi.org/10.1016/j.compositesb.2021.109248
https://doi.org/10.1016/j.compstruct.2021.115120
https://doi.org/10.1016/j.compstruct.2022.115893
https://doi.org/10.3390/polym14245434
DOI : 10.14429/dsj.71.15954
https://doi.org/10.3390/jcs5020062

 

[René - Acculution.com]

There has been a lot of work done recently in composite meta materials for making next generation acoustically stealth submarines. Combinations of progressively damped multi material, multilayered honeycombs with the aid of 3d printing. extruded plastic fibers, and carbon fibers to make all or part of the honeycomb.
Honeycombs combined with viscoelastic materials bonded to steel plates is a common investigation.
3d printed honeycombs have been combined with prepreg nonwoven natural fibers (hemp, flax) honeycombs on one side and stiffer woven carbon fiber prepreg honeycombs on the other for excellent acoustic damping. Though I can't find the reference. I found a lot of others.


View attachment 267081
Borresen’s (picture above I hope) has a 3D-printed zirconium woofer basket to make it rigid yet apparently vibration-free. Diaphram is composed of four laminated layers, two in carbon fiber, an intermediate layer with aramid in a honeycomb pattern and finally a titanium layer with special coating.
This has apparently move potential resonances away from the device’s working range, which extends up to 2500 Hz

I presume just cost off manufacture for metal 3d printing a subwoofer enclosure would be non economic even before the R n D. profit is considered

Some references regarding submarine composites , 3dprinting honeycombs etc.
https://doi.org/10.1016/j.compstruct.2021.113974
Three-dimensional printing technology has the ability to fabricate very complex, even arbitrary structures, and has already been applied to print cellular functional structures, including ultra-elastic hierarchical foams [6], ultralight metallic microlattices [7], hierarchical porous ceramics [8] and honeycombs, such as regular honeycombs [9], [10], [11], [12], [13], density-graded honeycombs [14], hierarchical honeycombs [15] and multi-material honeycombs [16].

https://doi.org/10.1016/S0263-8223(00)00175-6
DOI : 10.14429/dsj.71.15954
DOI: 10.12783/dtetr/icaenm2017/7834
DOI:10.3390/jmse11020409
https://doi.org/10.1146/annurev-matsci-070616-124032
https://doi.org/10.1121/10.0005850
https://doi.org/10.1016/j.pmatsci.2015.05.001
https://doi.org/10.1016/j.matdes.2018.01.059
https://doi.org/10.3389/fphy.2022.1068833
https://doi.org/10.1177/00219983211066386
https://doi.org/10.1016/j.compositesb.2021.109248
https://doi.org/10.1016/j.compstruct.2021.115120
https://doi.org/10.1016/j.compstruct.2022.115893
https://doi.org/10.3390/polym14245434
DOI : 10.14429/dsj.71.15954
https://doi.org/10.3390/jcs5020062

The Börresen case is actually topology optimization. I showed it in a recent audioXpress article.

 

[René - Acculution.com]

Rene' are you familiar with any work being done on Topology Optimisation for cabinet design? With cabinets where space is of vital consideration and bracing essential, I think that the organic designs that may be produced by CNC or 3D printing are something to look at.

I'm designing 2 new subs right now and working within fixed external dimension constraints, reducing the volume of internal bracing is very helpful. EG 5L of bracing in MDF by traditional means (probably not simulated only modelled based on resonant freq's) is rigid in every direction and voluminous. It could be reduced to approx 1L using hollow aluminium tube or structures of directional stability. An organic topology simulation for furniture produces amazing outcomes and I wonder how much advantage could be gained in speakers to optimise dimensions AND coincidentally minimise resonance.

The final design will depend on the overall setup and the targets and constraint in question, but here is an example.

 

[frascati]

I recently saw an article on how a fully magnetic suspension was accomplished in a turntable platter. Maintaining concentricity with precision was always the hurdle. Could this ever find its way into eliminating the loudspeaker spider altogether?

 

[René - Acculution.com]

I recently saw an article on how a fully magnetic suspension was accomplished in a turntable platter. Maintaining concentricity with precision was always the hurdle. Could this ever find its way into eliminating the loudspeaker spider altogether?

I think this would be problematic for a loudspeaker, where you need to prevent rocking involving forces and torques from a complex geometry, if your aim is to keep the enclosure from moving at all.

 

[Cbdb2]

Thanks a lot, I have been working on that blog for several years now, and it was meant to be a first a step towards being more known, and down the line going self-employed based on the shown fields of interest. And last month it came to fruition

I am happy to hear that, that is the experience that makes it worth writing. I have later seen it done in other books, and perhaps it is well-known to some (in my experience engineers are often not even up to speed with complex numbers, so maybe not...), but it makes a lot of sense once you see it.

I am contemplating making a post that takes into consideration poles/zero placement, LTI systems, causality, stability, region of convergence, modes, transient/steady-state reponse,..., and shows how it all fits together. If only engineers were more inclined to really embrace these learnings, companies could save soooo much time, but if I can inspire just a few people then that is also something.

Engineers not up to speed on complex numbers? Half of my EE courses (40 years ago) used them. Has engineering changed that much?

 

[René - Acculution.com]

Yes. And the companies are not encouraging their engineers to work theoretically with the their problems. I was often asked why I had books open instead of just doing measurements.

Engineers not up to speed on complex numbers? Half of my EE courses (40 years ago) used them. Has engineering changed that much?