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Finite-element analysis of a 6" woofer
Finite-element analysis of a 6" woofer
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Old 7th October 2018, 08:47 AM   #11
panson_hk is offline panson_hk  Hong Kong
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Hi Juhazi,

Yes, I knew his software.
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Old 7th October 2018, 10:40 AM   #12
andy19191 is offline andy19191  Europe
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We need actual rubber elastic modulus to get good result. In contrast to static analysis, we need to obtain elastic modulus of the rubber under cyclic loading. Elastic modulus of rubber is not a constant but frequency dependent.
This is where things get fun. Damping is important for drivers and speakers but, unlike mass and stiffness, it is difficult to model reasonably accurately. Not only is there damping within materials themselves but there can be significant additional damping/friction in joints.

There are a range of damping models for materials but the more realistic ones are often not implemented in general FEA codes. The adopted model will determine the number and kind of coefficients needed to represent the stress/strain/rate of strain/... relationship. It will also determine how much larger and slower the simulation will become. Which dynamic models does your FEA code support?
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Old 8th October 2018, 11:16 AM   #13
panson_hk is offline panson_hk  Hong Kong
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Originally Posted by andy19191 View Post
This is where things get fun. Damping is important for drivers and speakers but, unlike mass and stiffness, it is difficult to model reasonably accurately. Not only is there damping within materials themselves but there can be significant additional damping/friction in joints.

There are a range of damping models for materials but the more realistic ones are often not implemented in general FEA codes. The adopted model will determine the number and kind of coefficients needed to represent the stress/strain/rate of strain/... relationship. It will also determine how much larger and slower the simulation will become. Which dynamic models does your FEA code support?
Thanks for your comment.

To my knowledge, damping seems to be geometry dependent too. I measured stiffness and damping by means of bending (fixed-free cantilever) test of rectangular beam of the surround rubber. Damping obtained from the bending test and damping of the complete cone-surround are not the same.

The FEA tool supports typical proportional damping model and structural damping. It supports creep as well. Are these answers of your question?
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Old 8th October 2018, 11:27 AM   #14
panson_hk is offline panson_hk  Hong Kong
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Hi guys,

Let me update the driver type being studied. I don't have parts for the one with rubber surround, but for another 6" woofer with foam surround. Luckily, they are essentially identical except the surround material. I don't need to make changes to the already created models and just need to update the material properties.

Please see photos of the driver and its soft parts.
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File Type: jpg parts 1.jpg (113.7 KB, 199 views)
File Type: jpg parts 2.jpg (81.6 KB, 201 views)
File Type: jpg parts 3.jpg (118.8 KB, 200 views)
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Old 8th October 2018, 12:32 PM   #15
panson_hk is offline panson_hk  Hong Kong
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A rectangular beam was cut from the outer flange of the surround part. The beam was fixed a one end and free at the other end for bending test. Laser sensor measured the displacement of the free end. Vibration level was kept small in order to use Euler-Bernoullis (simple) bending theory to correlate elastic modulus to measured resonance frequency. The beam resonance frequency obtained is 55.7 Hz.

Vibration analysis package written by Tom Irvine was used to get elastic modulus. The GUI of the script is shown in the graph. Elastic modulus obtained is 5.5 MPa where mass density is 350 kg/m^3.
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File Type: png Beam Bending 3.5x20mm 0.5V.png (78.2 KB, 183 views)
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Old 8th October 2018, 04:09 PM   #16
andy19191 is offline andy19191  Europe
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The FEA tool supports typical proportional damping model and structural damping. It supports creep as well. Are these answers of your question?
Yes those are two of the simpler models. They tend to need experimental input to produce something reasonable for small deflections over a modest frequency range. It will be interesting to see how you get on.
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Old 9th October 2018, 03:41 AM   #17
panson_hk is offline panson_hk  Hong Kong
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Paper cone mass density estimated is 910 kg/m^3. A quarter solid model was created to perform modal simulation. Together with the mass of dust cap and voice coil former, the mode 1 (piston mode) frequency is 33.4 Hz as shown in the graph.

We can verify this result later with the actual driver (spider removed).

The complete driver TS parameters are

FS 40.8715 Hz
VAS 11.3314 L
RE 3.9000 Ohms
QMS 9.7463, QES 0.8307, QTS 0.7655
BL 6.3000 Tm
dBSPL 81.7136
SD 1.327E-2 m2
CMS 0.4606 mm/N, MMS 32.9206 g, RMS 0.8674

L1kHz 1.3019 mH
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File Type: png 6inch woofer 10.png (95.1 KB, 151 views)
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Old 10th October 2018, 05:03 AM   #18
panson_hk is offline panson_hk  Hong Kong
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Using shell (plate) elements for complete cone-dust cap-surround modal analysis. Simulation can run much faster even with higher mesh density (not the one shown).
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File Type: png 6inch woofer 11.png (277.6 KB, 56 views)
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Old 10th October 2018, 05:58 AM   #19
panson_hk is offline panson_hk  Hong Kong
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Without the dust cap, the cone bends at 1.474 kHz as shown. It would not bend like that in the presence of voice coil. At this frequency, elastic modulus of the surround would be higher than that measured by low-freq. test.
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File Type: png 6inch woofer 12.png (209.6 KB, 53 views)

Last edited by panson_hk; 10th October 2018 at 06:08 AM.
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Old 10th October 2018, 10:21 AM   #20
andy19191 is offline andy19191  Europe
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Using shell (plate) elements for complete cone-dust cap-surround modal analysis. Simulation can run much faster even with higher mesh density (not the one shown).
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.
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