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Simulation Overview - Loudspeakers Design via Shape and Topology Optimization

Da cynics

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Sorry for the vague question.
Is it correct to assume that there is a performance that can only be achieved by precise simulation?
 
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René - Acculution.com

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Sorry for the vague question.
Is it correct to assume that there is a performance that can only be achieved by precise simulation?
That is a good question and the answer is yes. As you can post process your variables in the entire geometry and see the effect of each change you make , you can reach insight you cannot get out of any measurement. When you apply optimisation on top of your simulation the computer can reach optimised geometries that would take millions of year to reach by pure combinatorics/trial and error.
 

hex168

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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.
This reminds me of an FAA investigation I heard about. A plane half-full of vacationing Poles had crashed in New York Harbor. The black box recording revealed that, just before the crash, the pilot announced that the Statue of Liberty was visible through the windows on the left. The FAA determined that the instability was caused when all the Poles were on the left-hand side of the plane.
 
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René - Acculution.com

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This reminds me of an FAA investigation I heard about. A plane half-full of vacationing Poles had crashed in New York Harbor. The black box recording revealed that, just before the crash, the pilot announced that the Statue of Liberty was visible through the windows on the left. The FAA determined that the instability was caused when all the Poles were on the left-hand side of the plane.
Lol. But it should be modified towards one or more poles on the right hand side ;)
 

Ilkless

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Stunning work!

Based on your experience, what are the considerations that go into basket designs? It seems to me that in the high-end (mid)woofer market, the Scanspeak Illuminator marked a big shift in basket design into extremely open baskets with very smooth shapes (SB Satori, Scanspeak Illuminator/Ellipticor, Vifa NE) and the spider exposed, and a comparatively small but powerful neo motor:

1621877139069.png


1621877131560.png

1621877254884.png


1621877390324.png


Contrast with basket designs that were developed before the Illuminator (Skaaning. Accuton, SEAS Excel):

1621877962796.png


1621877864511.png


1621877892364.png


What are the advantages of the first kind of design, its limitations, and is it always superior to the second kind of basket design/driver construction? Why are the more open baskets harder to find for cheap?

Thanks!
 
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René - Acculution.com

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Stunning work!

Based on your experience, what are the considerations that go into basket designs? It seems to me that in the high-end (mid)woofer market, the Scanspeak Illuminator marked a big shift in basket design into extremely open baskets with very smooth shapes (SB Satori, Scanspeak Illuminator/Ellipticor, Vifa NE) and the spider exposed, and a comparatively small but powerful neo motor:

View attachment 131762

View attachment 131761
View attachment 131763

View attachment 131764

Contrast with basket designs that were developed before the Illuminator (Skaaning. Accuton, SEAS Excel):

View attachment 131767

View attachment 131765

View attachment 131766

What are the advantages of the first kind of design, its limitations, and is it always superior to the second kind of basket design/driver construction? Why are the more open baskets harder to find for cheap?

Thanks!
Well, I have not actually been involved in projects where the basket was really discussed. I think they are often designed by mech engineers, somewhat independent of the acou engineers. You have both some structural considerations and some acoustical, in that the basket has to hold up the weight of the other parts, should be rigid enough that the reaction forces are transfered to the cabinet, should not block the sound too much, and such. I have been involved in one project where the basket was closed off to be water resistant (for automotive), and there it lead to some big issues, which could be solved using simulations to understand what was going on.
 

Frank Dernie

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-Introduction-

May 20 I will give a presentation on the COMSOL Acoustics Day on state-of-the-art loudspeaker simulation techniques, and I will give ASR readers a little sneak peek here. As always, feel free to ask away in the thread, and I will try and answer as best I can.

View attachment 130029

-Loudspeaker Simulations-
There are many different simulations that are relevant for exploring loudspeaker behavior. Below I have made a rough overview of what typically is being requested.

View attachment 130008

So we can deal with single-physics (acoustics, structural mechanics, electromagnetics) or multi-physics problems (any combination of the beforementioned). And the study types can vary from static, to steady-state where you basically run a frequency sweep, to a modal analysis where you find eigenfunctions and eigenvalues of your system (see e.g. my post on Room Gain), to transient analyses where you apply a time-varying input and look at the transient and the steady-state response together.

A static anaylysis could be relevant in conjunction with a structural mechanics to investigate the stiffness symmetry of spiders and surrounds as a function of displacement as shown below. The analysis takes into account the non-linear geometry, so that for small displacements the rolls 'unfold' with little strain, but at larger displacements you get more relative strain.

View attachment 130009

A typical steady-state problem would be a vibroacoustics (multi-physics) problem, where you model a complete driver and apply a harmonic voltage signal over a frequency range:

View attachment 130026

Assuming that all materical properties are correct, and the simulation in general is done correctly, you will get all information equivalent to Spinorama, plus much more. In the acoustics domain the only degree of freedom solved for is (complex valued) pressure, and that is all you need to calculate velocity, intensity, power, directivity index, and whatever else your heart pleases.

A modal analysis is relevant in several cases, for example to investigate the structural modes of a driver. Below a spider resonance is observed at a certain frequency, and so you can find all modes in the relevant frequency range and compare your findings to a steady-state frequency sweep to see if some modes lead to resonances.

View attachment 130011

Remember, modes exist independently of excitation, and not all modes are necessarily excited. So if you for example see a rocking mode in your modal analysis, you should remember how the excitation will work against such a mode.

Finally, transient responses can be relevant both to see the initial wave propagation, but also for investigating non-linear distortion coming primarily from the structural mechanics and electromagnetics. For the acoustics it can be relevant if you have high particle velocity/pressure, if you have small enclosures and drivers with large excursions, if you are looking at Doppler effects, and so on.

One technique that I have build into the software package COMSOL Multiphysics is Phase Decomposition, which allows me to dissect the cone and surround vibration to see which parts of the displacements add to, subtract from, or neither, the sound pressure in any observation point. A very underutilized technique in the loudspeaker industry.

View attachment 130013

Now, while the above analyses can be challenging enough in themselves, you can take things even further if start combining these analyses with formal, mathematical optimization. There are generally three groups of optimization, Parameter Optimization, Shape Optimization, and Topology Optimization (generally this is the ascending order of complexity).

View attachment 130015

With Parameter optimization you can control the geometry via parameters such as lengths and heights, but basic shapes are retained. With Shape optimization boundaries are described in a way that allows the basic outline/shape to be controlled, but topology remains. Finally, with Topology optimization the topology of the geometry is allowed to change so that domains and holes are controlled completely by the algorithm. The underlying mathematics of multi-physics optimization is quite involved, so I will instead show the potential via some examples.

First is an acoustics shape optimization case where a compression driver geometry is optimized. This particular combination of physics and optimization can also be used for waveguide design, but the compression driver design has some more challenging aspects to it. The blue lines on the initial geometry are allowed to change shape, and the resulting geometry has the curved phase plug channels seen on the right, with a nice resulting pressure response.

View attachment 130016

Next, a generic setup with vibroacoustics and shape optimization. This was to explore how to do this particular multiphysics problem with shape optimization and it is rare to see any work with full vibroacoustics modelling with optimization included. I ended up using the Rayleigh integral for the acoustics, which made life a lot easier. The cone was allowed to change its shape, and the result was less relevant, as this was more of a test case.

View attachment 130017

I have also done shape optimization combined with the magnetics system, where a boundary was allowed to change its shape. Again, the results are less relevant for test cases than for actual client cases that I would probably not be allowed to show anyway.

View attachment 130018

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
Brilliant!
 

alex-z

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-Introduction-

May 20 I will give a presentation on the COMSOL Acoustics Day on state-of-the-art loudspeaker simulation techniques, and I will give ASR readers a little sneak peek here.

Is there any way to watch the presentation now? Forgot to watch the live version.
 
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René - Acculution.com

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Is there any way to watch the presentation now? Forgot to watch the live version.
It was recorded but I don't know when it will be available. The US version was yesterday, with a panel discussion instead of user presentations.
 

redshift

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-Introduction-

May 20 I will give a presentation on the COMSOL Acoustics Day on state-of-the-art loudspeaker simulation techniques, and I will give ASR readers a little sneak peek here. As always, feel free to ask away in the thread, and I will try and answer as best I can.

View attachment 130029

-Loudspeaker Simulations-
There are many different simulations that are relevant for exploring loudspeaker behavior. Below I have made a rough overview of what typically is being requested.

View attachment 130008

So we can deal with single-physics (acoustics, structural mechanics, electromagnetics) or multi-physics problems (any combination of the beforementioned). And the study types can vary from static, to steady-state where you basically run a frequency sweep, to a modal analysis where you find eigenfunctions and eigenvalues of your system (see e.g. my post on Room Gain), to transient analyses where you apply a time-varying input and look at the transient and the steady-state response together.

A static anaylysis could be relevant in conjunction with a structural mechanics to investigate the stiffness symmetry of spiders and surrounds as a function of displacement as shown below. The analysis takes into account the non-linear geometry, so that for small displacements the rolls 'unfold' with little strain, but at larger displacements you get more relative strain.

View attachment 130009

A typical steady-state problem would be a vibroacoustics (multi-physics) problem, where you model a complete driver and apply a harmonic voltage signal over a frequency range:

View attachment 130026

Assuming that all materical properties are correct, and the simulation in general is done correctly, you will get all information equivalent to Spinorama, plus much more. In the acoustics domain the only degree of freedom solved for is (complex valued) pressure, and that is all you need to calculate velocity, intensity, power, directivity index, and whatever else your heart pleases.

A modal analysis is relevant in several cases, for example to investigate the structural modes of a driver. Below a spider resonance is observed at a certain frequency, and so you can find all modes in the relevant frequency range and compare your findings to a steady-state frequency sweep to see if some modes lead to resonances.

View attachment 130011

Remember, modes exist independently of excitation, and not all modes are necessarily excited. So if you for example see a rocking mode in your modal analysis, you should remember how the excitation will work against such a mode.

Finally, transient responses can be relevant both to see the initial wave propagation, but also for investigating non-linear distortion coming primarily from the structural mechanics and electromagnetics. For the acoustics it can be relevant if you have high particle velocity/pressure, if you have small enclosures and drivers with large excursions, if you are looking at Doppler effects, and so on.

One technique that I have build into the software package COMSOL Multiphysics is Phase Decomposition, which allows me to dissect the cone and surround vibration to see which parts of the displacements add to, subtract from, or neither, the sound pressure in any observation point. A very underutilized technique in the loudspeaker industry.

View attachment 130013

Now, while the above analyses can be challenging enough in themselves, you can take things even further if start combining these analyses with formal, mathematical optimization. There are generally three groups of optimization, Parameter Optimization, Shape Optimization, and Topology Optimization (generally this is the ascending order of complexity).

View attachment 130015

With Parameter optimization you can control the geometry via parameters such as lengths and heights, but basic shapes are retained. With Shape optimization boundaries are described in a way that allows the basic outline/shape to be controlled, but topology remains. Finally, with Topology optimization the topology of the geometry is allowed to change so that domains and holes are controlled completely by the algorithm. The underlying mathematics of multi-physics optimization is quite involved, so I will instead show the potential via some examples.

First is an acoustics shape optimization case where a compression driver geometry is optimized. This particular combination of physics and optimization can also be used for waveguide design, but the compression driver design has some more challenging aspects to it. The blue lines on the initial geometry are allowed to change shape, and the resulting geometry has the curved phase plug channels seen on the right, with a nice resulting pressure response.

View attachment 130016

Next, a generic setup with vibroacoustics and shape optimization. This was to explore how to do this particular multiphysics problem with shape optimization and it is rare to see any work with full vibroacoustics modelling with optimization included. I ended up using the Rayleigh integral for the acoustics, which made life a lot easier. The cone was allowed to change its shape, and the result was less relevant, as this was more of a test case.

View attachment 130017

I have also done shape optimization combined with the magnetics system, where a boundary was allowed to change its shape. Again, the results are less relevant for test cases than for actual client cases that I would probably not be allowed to show anyway.

View attachment 130018

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

Slightly misleading title; a better one would be:

“Loudspeaker Actuator Design via Shape and Topology Optimization”.

I know; I’m a bit anal at times. :cool:
 

Frank Dernie

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Slightly misleading title; a better one would be:

“Loudspeaker Actuator Design via Shape and Topology Optimization”.

I know; I’m a bit anal at times. :cool:
Hi,
I assume English isn't your first language, it is the loudspeaker drivers that are being optimised and, typically the drivers are referred to as "loudspeakers" in English, even though the same word is also used to describe a complete assembly.
 

redshift

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Hi,
I assume English isn't your first language, it is the loudspeaker drivers that are being optimised and, typically the drivers are referred to as "loudspeakers" in English, even though the same word is also used to describe a complete assembly.

You’re right.

In my native language there is a difference between loudspeaker elements/drivers/actuators and the complete assembly.

:)
 

TLEDDY

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I am not even stating that I understand even ten percent of your explanation, despite having read it repeatedly… it is just outside my knowledge base. I do believe I understand enough to appreciate the vast knowledge required to present the material and the concept therein.

May you succeed more than you hope for… once more, I am overawed by the genius on this Forum!

Tillman
 
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René - Acculution.com

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I am not even stating that I understand even ten percent of your explanation, despite having read it repeatedly… it is just outside my knowledge base. I do believe I understand enough to appreciate the vast knowledge required to present the material and the concept therein.

May you succeed more than you hope for… once more, I am overawed by the genius on this Forum!

Tillman
Thanks for your kind words. If there are particular topics that you would like explored, let me know. If simulations in general are of interest to you or anyone else, I would recommend COMSOLs own blog, their cyclopedia, and you can also have a look at my blog, as some entries to getting started.

comsol.com/blog
acculution.com/blog

/René
 

Ericglo

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In case anyone missed it, Erin interviewed Rene on his channel. I just got around to watching/listening to it this week.

I would love to see Erin get two of his guests together like Rene and Laurie Fincham. They could ask each other questions and bounce ideas off of each other and the chat room.

 
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René - Acculution.com

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In case anyone missed it, Erin interviewed Rene on his channel. I just got around to watching/listening to it this week.

I would love to see Erin get two of his guests together like Rene and Laurie Fincham. They could ask each other questions and bounce ideas off of each other and the chat room.

It would good to know which topics the viewers are interested in. When doing these presentations, I constantly wonder if anyone really cares about all those pescy details that are so important for what I do. And I am not really a 'loudspeaker guy"; I work on a lot of different products and do research in meta-materials and other topics with students and alone, so I don't have a lot anecdotes about building loudspeakers, it is more physics and math for me. I have discussed topics with Erin such as Radiation and Polar Patterns, Understanding Phase, Understanding Modes, and that would be more up my alley. Finding the time is a difficult, though....
 

alex-z

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It would good to know which topics the viewers are interested in.

I think the most beneficial collaboration would be a video on how sound behaves within rooms, how it interacts with common acoustic treatment types, and perhaps even how the room structure itself behaves at low frequencies.

While I personally benefit from your articles on loudspeaker optimization and simulations, it is a rather niche topic, meanwhile anyone with a speaker system benefits from a broader understanding of room acoustics. Especially if you describe the meaning of things like "eigenmode", which initially flies over the head of many people, even though they are capable of understanding it.

Not necessarily an entire physics lesson, just "for the purposes today eigenmode means pattern in an oscillating system" so that viewers focus on the topic, rather than the wording.
 
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René - Acculution.com

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I think the most beneficial collaboration would be a video on how sound behaves within rooms, how it interacts with common acoustic treatment types, and perhaps even how the room structure itself behaves at low frequencies.

While I personally benefit from your articles on loudspeaker optimization and simulations, it is a rather niche topic, meanwhile anyone with a speaker system benefits from a broader understanding of room acoustics. Especially if you describe the meaning of things like "eigenmode", which initially flies over the head of many people, even though they are capable of understanding it.

Not necessarily an entire physics lesson, just "for the purposes today eigenmode means pattern in an oscillating system" so that viewers focus on the topic, rather than the wording.
Room modes are a good topic, and it is on the short list.
 
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