In #006 I showed the CAD drawing for an electrodynamic loudspeaker driver. Now, we will do a Finite Element Analysis (FEA) for said driver, to see how it performs when it comes to its frequency response.
The CAD was made so diligently that no additional repairs or modifications were needed in the simulation software COMSOL Multiphysics. A fully coupled vibroacoustic simulation was setup, with the inclusion of the electromagnetics as a lumped circuit à la the one shown below (modified from ):
The lumped circuit is two-way connected to the discretized FEA domain, and so a very accurate estimate of the driver's performance should be obtained. All of the elastic domains are given their respective material parameters, based on memory, googling and the extensive material library in COMSOL Multiphysics. The component in the above circuit are given realistic values based on datasheets for similar sized drivers. The air domain needs density and sound speed, and all boundary conditions need to be set up as to best describe the associated physical setup, which would give us the measured data.
Below is shown an animation of the sound field resulting from the membrane displacement at a frequency of 5,120 Hz. The air loading is included in the simulation, but is probably not very important for the final outcome.
So how does the loudspeaker perform, when it comes to on-axis pressure, which is usually thought of as the most important characteric of the loudspeaker driver? Well, have a look below:
Well, it is okay-ish. There has been no fiddling with the numbers, just the first response that came out, from a driver drawn from scratch without any manufacturing drawings, and with realistic, but made up, physical parameters. The notch around 4 kHz needs some attention, but since everything needed to investigate the effect of different changes in the setup is in the CAD and FEA, such an investigation could be carried out, before doing any prototyping.
The above example clearly illustrates how, for certain applications at least, you can come a looooong way in just a couple of days, without having to involve any CAD designers, spend money on tool manufacturing and so on, as long as you are highly proficient in simulations, know the mathematical intricacies of the implementation, and have experience with the application.
: Klippel,W. “Nonlinear modeling of heat transfer in loudspeakers”. Audio Eng Soc, 114th Convention, 2003