Finite-element analysis of a 6" woofer

[Dave Zan]

Without the dust cap, the cone bends at 1.474 kHz as shown...

Now the educational part starts!
I don't know if you have read the current thread about cone so-called "break up".
Some of the claims there are definitely incorrect, I hope your simulations will provide better information.
I am particularly interested in the radially symmetric modes, to see the extent to which the surround resonance contributes to the response of the speaker.
It will be simpler if the surround contribution is small, so we only have to consider the behaviour of the cone itself.
I have seen discussions of surround resonance but not found much data, so I look forward to more of your results.

Best wishes
David

 

[panson_hk]

Plate and shell elements are different. There are also different kinds of these types of element which work well for some situations but not for others. The degrees of freedom they discard can be required near boundaries or where more general elements are used.

If you are not experienced using these elements it may be wise after you have built a full model to run a few checks to prove that you have not suppressed important degrees of freedom and have used sufficient resolution. That is, setup a representative simulation and repeat it using several levels of grid refinement everywhere, low and high order elements, elements that suppress no degrees of freedom and those that suppress ones considered unimportant,... and compare the results looking for differences.

Thanks Andy. I will use the thin-walled element carefully.

My FEA code (midas NFX) uses plate/shell interchangeably. It has membrane element. I believe membrane of midas NFX is equivalent to plate (a more common name) of other codes.

 

[panson_hk]

Now the educational part starts!
I don't know if you have read the current thread about cone so-called "break up".
Some of the claims there are definitely incorrect, I hope your simulations will provide better information.
I am particularly interested in the radially symmetric modes, to see the extent to which the surround resonance contributes to the response of the speaker.
It will be simpler if the surround contribution is small, so we only have to consider the behaviour of the cone itself.
I have seen discussions of surround resonance but not found much data, so I look forward to more of your results.

Best wishes
David

Thank you David.

I aware of the thread, but have not read it thoughtfully. It is a main topic (break up) for my study.

Elastic modulus and damping of rubber is frequency dependent (how about foam). I wonder using constant elastic modulus/damping ratio in simulation would result in good result. On the other hand, the freq. dependent effect may be not as big as other effects.

I have been reading a paper http://lab.fs.uni-lj.si/ladisk/data...plementation in a finite-element analysis.pdf

 

[Dave Zan]

...Elastic modulus...is frequency dependent (how about foam)....

Yes, I recall Klippel has some equipment to test exactly this, so presumably it is sufficiently important to justify his considerable prices.
There should be some information on the website too.

Bohdan Raczynski did his own FEA analysis and achieved an impressive match with measured results.
http://www.bodziosoftware.com.au/Cone_Break_Up.zip
I don't know how detailed the frequency dependent materials models were.
I will email him and ask for more details.

Best wishes
David

 

[panson_hk]

Hi David,

I have seen the Klippep MPM tool. Based on the available information, it doesn't seem to provide modulus and damping across the audio band. It provides a single value for each.

Based on their AES 2018 paper, they include that in a different way. The method of MPM is not good for higher frequencies. I guess we need that of dynamical mechanical analyzer (DMA).

AES E-Library >> Optimal Material Parameter Estimation by Fitting Finite Element Simulations to Loudspeaker Measurements

Thanks for the Bohdan's analysis. The SoundEasy guy, right?

 

[Dave Zan]

Thanks for the Bohdan's analysis. The SoundEasy guy...?

Yes, maybe the SoundEasy bloke since he is in Australia
I didn't notice the Klippel MPM limitations until after I posted my comment and too late to edit.
Just to fit the FEA to measurements seems reasonable, also because the article you linked in #23 shows the parameters vary only slowly and smoothly.

Best wishes
David

 

[andy19191]

Elastic modulus and damping of rubber is frequency dependent (how about foam). I wonder using constant elastic modulus/damping ratio in simulation would result in good result. On the other hand, the freq. dependent effect may be not as big as other effects.

I have been reading a paper http://lab.fs.uni-lj.si/ladisk/data...plementation in a finite-element analysis.pdf

I have only glanced at the paper but it looks typical for the simple largely unphysical damping models in general FE codes: some experimental effort to provide information to tune the damping model for a particular geometry. If the damping is tuned to be good in one frequency range it will almost always be at the expense of others.

Alternatively one can specify damping in terms of the modes rather than space (probably depending on the FE package). The problem here is that damping in the surround, cone and spider is different and varies differently with frequency. It can however account for damping in the glued joints which isn't straightforward in space.

Damping plays a significant role in the detailed motion of a speaker driver particularly for soft cone drivers. The simple models in most general FE codes are fairly unphysical and rely on being tuned up with supporting experimental information. The resulting model may or may not be adequate depending on the questions you want it to answer.

More sophisticated damping models exist but are rarely available in general purpose FE codes. They typically require the material properties to be defined on a nomograph something like this. An example of their use with an FE code is given here. If you are looking to use FE simulations to investigate the detailed motion of high performance soft cone drivers like the Scan-Speak study mentioned earlier my guess is this is the level of damping model that is likely to be required. For other studies the simpler damping models may be sufficient.

 

[panson_hk]

Thank you Andy for your valuable information.

What do you think about elastic modulus linearity? I use linear elastic modulus in static analysis with nonlinear geometry enabled. I think this is a typical setting. I wonder actual stress-strain data of tensile test should be used to improve accuracy.

 

[andy19191]

What do you think about elastic modulus linearity? I use linear elastic modulus in static analysis with nonlinear geometry enabled. I think this is a typical setting. I wonder actual stress-strain data of tensile test should be used to improve accuracy.

The assumptions made depend on the information you want from the simulations and the resources available. A general answer isn't really possible.

If you are studying the combined large deflection nonlinearities of the surround, spider and motor in order to maximise the linear region, smooth behaviour beyond xmax or something similar then it is likely appropriate subject to the soft parts not changing their properties substantially at relevant frequencies (likely lowest in the passband), extensions or, possibly, temperatures.

It is likely to be inappropriate when studying the forced response of a speaker driver over a frequency range. Given normal computing resources and the desire to vary quite a few driver parameters in order to work towards an optimum design this usually means some form of modal analysis. This normally assumes small deflections in the geometrically linear region and material properties that are linear or efficiently linearizable within a modal analysis.

 

[andy19191]

Any more progress this week?

 

[panson_hk]

All computing power has been allocated for other stuffs since early this week. Hope to have some progress later this week/weekend.