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MultiWay Conventional loudspeakers with crossovers 

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6th October 2018, 07:29 AM  #1 
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Join Date: Aug 2005

Finiteelement analysis of a 6" woofer
A 6" woofer will be analyzed by finiteelement software. FE results will be compared to test data of a physical data.
It is a typical woofer obtained from a factory mainland china. The main purpose of this study is to see how close the virtual driver to the physical driver. 3D drawing of the driver is not available from the factor. On the other hand 2D drawing in pdf and kit of parts are given. 3D drawing is then created based on the 2D drawing and components. The 3D geometry is shown in the graph below. Rollsurround characteristic will be investigated first. Initially, linear rubber in the material library is used for simulations. At first, stiffness vs displacement, kms(x), of the surround is of interested. Although linear rubber material (linear elastic) is assumed, geometric nonlinearity will result in nonlinear kms(x). Therefore, nonlinear static analysis is employed. Last edited by panson_hk; 6th October 2018 at 07:40 AM. 
6th October 2018, 07:34 AM  #2 
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6th October 2018, 07:44 AM  #3 
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6th October 2018, 07:53 AM  #4 
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Outer flange of the surround is glued to the chassis. Hence, its boundary condition in the software is fixed. At this stage of analysis, cone (diaphragm) is assumed a rigid body. The inner surround flange can only displace in the vertical zaxis direction. An evenly distributed force (BC) is added to the inner flange as shown in the axisymmetric model below. This model is used for nonlinear static analysis.

6th October 2018, 08:15 AM  #5 
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Nonlinear static analysis result is presented here. Rubber mechanical properties: elastic modulus 6.1 MPa, Poisson's ratio 0.49, mass density 1000 kg/m^3.
The graph below is showing the surround model moving into the motor. The maximum displacement is 11.35 mm. The curve shown below represents load scale (force) vs displacement. This is equivalent to typical kms(x) graph where force = stiffness x displacement. We can see the curve is pretty much a straight line up to ~8 mm. Last edited by panson_hk; 6th October 2018 at 08:29 AM. 
6th October 2018, 08:49 AM  #6 
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FEA data: displacement vs force load can be curve fitted (nth order polynomial) in numerical tools such as octave, scilab and matlab. Target Kms(x) is the firstorder derivative of the polynomial as depicted below. Stiffness is nearly a constant in the region of 5 mm to 5 mm.

6th October 2018, 09:39 AM  #7  
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Quote:
A few years ago ScanSpeak got a number of companies to simulate a small wideband driver (I think) in order to evaluate modelling capabilities. I have had a brief google but failed to find anything. Is anyone aware of a link to any reports? The results were reportedly not wholly positive with the difficulties of incorporating sufficiently accurate damping being the main culprit (I think). Sorry about the vagueness but I am trying to recall the contents of an email exchange from a few years ago which I no longer possess and where this was peripheral to the main topic. 

7th October 2018, 02:29 AM  #8 
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7th October 2018, 03:13 AM  #9 
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The Kms(x) shown in Finiteelement analysis of a 6" woofer is based on the rubber in the material library. It may not be a good representative of the actual rubber surround. We could measure hardness of the rubber and make conversion to elastic modulus.
An axisymmetric model with the cone is used for modal analysis for estimating the piston frequency. Using rubber in the library and given cone mass, piston frequency is 45.3 Hz as shown in the graph. 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. Last edited by panson_hk; 7th October 2018 at 03:25 AM. 
7th October 2018, 07:08 AM  #10 
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Location: Jyväskylä, Finland

Hi panson_hk, do you know Peter Larsen (Loudsoft) and these FEA programs?
Design software  FINE Speaker Software Demo of FineCone YouTube
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